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Ch. 6 of the book: "What Next?" (Including graphs of per-capita world and US oil)
Sept 9, 2012 Draft by: John Howe, howe@megalink.net, http://www.solarcarandtractor.com

Background: There is a growing body of evidence that shows we are at the peak or broad plateau of maximum world oil extraction. This precarious, ephemeral period in the epoch of recorded human history, itself only a tiny fraction of longer archeological time, signals the end of energy-dependent growth. Oil and the myriad petroleum-based products we have become so dependent on, in just the last century, are critical and fundamental to our modem lifestyle. These undeniable facts are further exacerbated by a debt-based financial system, also dependent on continued growth and cannot function without cheap and abundant energy, specifically oil.

This opening statement is ominous enough, but it does not include the concurrent three-fold explosion of world population also in the last century, a little over one human lifetime. It is totally incomplete to focus only on the contemporary peak and imminent decline of geologically finite oil while human numbers continue to grow inexorably. The purpose of this paper (Chapter 6 in the book subtitled, "What Next?") is to integrate a quantitative view of the second half of the oil age with various scenarios of continued population growth. The specifics of peak oil are frequently under-emphasized by population activists and visa-versa. Both subjects can be lost in the activism of environmentalism, and climate change. Obviously, all are related and extremely complex. The mainstream public hears only confusion and non-quantitative panaceas.


Population Growth vs. Oil Extraction:

The first graph (fig. 6-1) picks up from and expands the right-hand side of the graph from the overview Chapter I (see bottom of this blog). Shown are eight different rates of population growth and possible decline by age and average fertility rates ranging from three children by each female (3 cpf) to no children (0 cpf). Contrasted, in heavier lines, are three curves of diminishing world oil extraction. The basic middle curve "H" is the decline expected for the second half of the oil age and typical of any finite-resource extraction. This phenomenon for oil extraction is well established as Hubbert's Curve and the area under the curve, beginning now at peak, is increased and equivalent to 1.3 trillion barrels of remaining oil. This prediction can be substantiated by the fact that we have already used over 1 trillion barrels in the first half of the oil age and the world extraction rate of conventional oil has not increased since peaking at 75 million barrels per day in 2005. Because world oil extraction escalated to the extremely high plateau of one-billion barrels every thirteen days, we have extracted and consumed one-half trillion barrels of oil in just the last twenty years, about one generation! The suggestion of an imminent end to the oil age is so ominous and alarming there is now a strong counter-movement underway to debunk the science. Confusion is increased by the inclusion of non-conventional oil and other liquid fuels. We will never use the last barrel buried somewhere in the earth, but there is no denying that remaining oil is becoming increasingly expensive to extract, both energy-wise and financially.

Fig 6-1

Oil Extraction:

Curve (NO) shows the net oil available for use, after a steadily-increasing oil (or energy equivalent) input of one percent per year, yields even less usable oil output than curve "H". This is called energy returned on energy invested (EROEI) and shows a more dire picture for the timing and availability of future oil in just the next 50 years. The third oil curve, shown by shaded squares, gives a one-half trillion additional surplus, benefit of the doubt, to the optimists (energy "experts", politicians, and economists) who argue that improved technology and new discoveries will prove Hubbert grossly wrong. None of the three curves shows any increase in the annual rate of world oil extraction, thus signaling an end to unprecedented oil-based growth as in the last century. The curves shown are for conventional crude oil and natural gas liquids. Non-conventional liquids like biofuels and tar-sands oil are not included because of their low EROEI and minimal effect on the conclusions.

(Page 1)


Population Growth (new quantitative methodology, not unrealistic extrapolations):

The eight combinations of possible future population shown in figure 6-1 are determined using the following starting point and ground rules:

1. The "snapshot" of time (shown as 2012) quantifies the beginning demographic profile by percentage of the total population in each age group. Obviously, if we start with only young people just entering their reproductive age, there will be a much greater population bulge (momentum) than if the initial closed-group is made up only of middle aged grand parents and seniors just beginning to die off. For our analysis I have assumed two different starting profiles from US and world census data. The younger concentration profile is typical of the world as a whole. The older make-up is typical for the U.S. To Summarize, the percentage of the total population by average age in each age group is as follows and shown in the lower left comer of figure 6-1:

Younger Demographic Profile (ydp)    Older Demographic Profile (odp)

Years 0 to 20                         40%                                                    32%

Years 21 to 50                      43%                                                    47%

Years 51 to 80                      17%                                                    21%

2. The average age at reproduction is 25 years old, that is if each female has only one child (1 cpf) that would be when she is 25. If she has 2 children one might be at 24 and one would be at 26. Of course, in real life, there may be females having children in their thirties, but this would be averaged by teen childbirth and the math and the conclusions would not change. Gender distribution is assumed as 50/50.

3. The average age at death is 80 years old. Some may die at 65 and others at 95. The total, average numbers remaining to be fed until 80 would be the same. The luxury of modem health care leading to unprecedented old age has been labeled "death control".

At this point the crux of the entire population problem will be emphasized one more time. You can't have traditional fertility plus old age. A quantitative law jumps out: It is numerically impossible for any closed society (no immigration or emigration) with a typical age distribution profile, like the world or US, to reproduce greater than an average of one child per female and avoid increasing population in the near term future if the members expect to live to be grandparents and great grandparents. It is true, and conventional wisdom, that a fertility rate of two children per female (2 cpf) will eventually level off at a “replacement” level. But, as shown in figure 6-1, this would take about fifty years and the final, stable, closed-society population would have increased about thirty percent and not decline thereafter.  We can't live to be old with modem health care and adequate food and concurrently have more than one child per female (I cpf). Each of the increasing numbers will be competing for a maxed-out food supply. It's been shown, historically, that it is impossible to support increasing numbers without, at the same time, inevitably degrading the agricultural base (carrying capacity). History teaches of numerous "crashes", "collapses", and "overshoots". This is already happening today in large parts of the world while, concurrently, we are beginning a reduction in the artificial, oil-based energy level that made the excess population possible in the first place. Our short oil age facilitated old age in many ways especially sharply reduced manual labor, dependable year-round nutrition, improved health care, and reduced infant mortality. We would all like this lifestyle to continue.                 

(Page 2)


4. It should be clearly understood that the above ground rules, conclusions, and methodology hold true regardless of the original, numerical size of the closed society. I conveniently selected singular digits, beginning at zero, on the 'v" ordinate

(axis) to represent the world, the largest undeniably-closed society which has presently swelled to seven billion people. All subgroups as a part of the world (where else?), must average to the world growth numbers. Some may grow more, some less, but each will have to follow the same methodology. Some like China may attempt to take control of their population destiny. Others (like sub-Saharan Africa) will just let nature take its course and, without energy and food input from somewhere else, must suffer the inevitable consequences of exceeding their regional carrying capacity.

Another reason for using single digits on the "'Y" axis is to show world oil extraction in tens of millions of barrels per day on the same graph. This shows clearly that population continues to increase while the temporary, two lifetime (eight-generation total) oil age is about to decline into its second half. All societal subgroups will experience the growing tension (gap) between increasing population and decreasing oil. An idealistic, "localized" community of seven-hundred, or an autonomous nation

with seventy-million, even if each has bountiful food resources for their present population, must ultimately respect the same numerical limitations on reproduction. Otherwise, when times are good, like any other species, they soon multiply to the limits

of their own carrying capacity and either begin encroaching on their neighbors or suffer Malthusian "misery", All it takes is climate change or poor land use to trigger disaster.

The Math:

This section is included to show the methodology. The conventional wisdom that a "replacement" fertility between 2 and 2.2 will suffice is dangerously false. (Fast forward to the next section to avoid the details.) It is simple, but tedious, to do the numbers using the above ground rules. Examples follow so anyone can verify the conclusions shown graphically or use a different demographic starting profile than the two shown. Referring to the younger demographic profile, typical of the world, we see 40% of the total population is between 0 and 20 years or 2% per each year. Likewise, there are 43% /30 (divided by 30) or 1.43% each year between the ages twenty-one to fifty, and 17%/30 or 0.57% per year between the ages of fifty-one to eighty. At the end of the first year, one-half of the age 25 population group who are the females, give birth to one child (1cpf), Because 1.43% of the population is now 25 years old, the female one-half of this age group (1.43%/2) or 0.72% of the total population will be added as new babies. For instance, if the closed-society population was 1000, 7.2 new babies would be added.

In this same first year, 0.57% of the population, male or female, would die leaving a gain of 0.72% minus 0.57 % or a net increase of 0.15%. This does not sound like much, but the significant point is that the population continues to increase even with a fertility rate of only one child per female. As this birth minus death rate continues for four more years, the net gain would be 5 times 0.15% or 0.75%. Our hypothetical population of 1000 has grown in five years to 1007.5 people. If we did similar math for a fertility rate of two children per female (2 cpf), our community of 1000 would grow to 1043 mouths to feed in five years, hardly sustainable with a fixed agricultural base. Likewise, in five years, a world of seven billion people will have grown by 301 million people to 7.3 billion people.

(Page 3)


When we enter the sixth year of our model, things get more complex because the original twenty year olds are now reaching the average reproductive age of 25, and there are more of them. At the same time the numbers reaching the average age of 80 are the same as the first five years. Using the younger demographic profile typical of the world, there are 40%/20 years or two-percent per year of the total population turning 25 years old. Of these, one-half or one-percent are females. If each female has one child (I cpf) and dieoff continues at 0.57% per year, the net gain each year is one minus 0.57 or 0.43% per year. This average pace will continue for the next twenty years until the last original female baby, less than a year old when we started twenty-five years ago, reproduces. At this rate in the next twenty years, population would increase another 20 times 0.43% or 8.6%. Our original hypothetical population of 1000 would add another 86 mouths to feed in addition to the 7.5 increase in the first five years, for a total increase of 93.5 in twenty-five years, with a fertility rate of only one child per female! With this model, the starting world population of seven billion will increase to 7.654 billion.

In the 26th year, for the first time, the female babies born in the first year become mothers, and our original mothers become grandmothers. Of the 0.72% of the population born in the year one, only one-half (0.72%/2) or 0.36% are females. If each mother continues the one child per female model, there will only be 0.36% of the population added as new babies while, at the same time, the death rate at 80 is still 0.57 % per year. This contrast leads to a negative population growth of 0.36% minus 0.57 % or a negative 0.19%. per year. For the next five years this downward pace will result in a total population reduction of 0.95%. Our original community of 1000, that had grown to 1093 will now decline by the year thirty to 1084 people. World population starting at seven billion would pass peak population and decline to 7.588 billion, but it took thirty years!


By now, the mathematical methodology presented should be clear. In the graph (fig. 6-1) the numbers are continued for 80 years, two different starting age profiles, and five different fertility rates. The conclusions are profound and disturbing. A closed

community, nation, or world, living within the limits of diminishing finite resources, specifically, energy and fuels, non-renewable minerals, arable land, and water, cannot reproduce more than one child per female (lcpf) and simultaneously live to

old age without exceeding its carrying capacity. To repeat: a society can't have it both ways! This conclusion may, in a nutshell, be a short history lesson and future prediction for the world, including all closed-loop, smaller communities. Constant ignorance and violation of the mathematics have repeatedly led to starvation, war, genocide, ecological devastation, infanticide,  depravation, misery, and even cannibalism. The world is now at this tipping point.

Per-Capita World Oil Consumption:

A simpler, summary way to show the contrast and imminent divergence between increasing population and concurrent declining energy is to divide the total world oil availability by total world population. A single barrel of oil contains 42 gallons of extremely convenient energy. This amount of energy is equivalent to 1,846,000 watt hours or 6.3 million BTU. It would take a human working continuously twenty-four thousand (!!) hours to generate an equivalent amount of work. Admittedly, there are efficiency losses in converting the oil energy to mechanical work, but the oil-powered machine does not need to eat or stop for rest.

(Page 4)


A pint or two of equivalent liquid fossil fuel energy would have been utopian to preindustrial humans. Now we take for granted thousands of gallons a year, for each of us, of convenient labor-saving energy but at wildly different rates throughout the world. The per-capita curves in figure 6-2 demonstratively show the rise and fall of the oil age in the two-lifetime span of 160 years.

Fig 6-2

The demographic methodology for population momentum explained in this chapter shows that continuation of a stable per-capita oil-energy availability with any fertility rate greater than zero (0 cpf) cannot coexist with the expected decline in oil extraction, no matter how optimistic the decline might be! The present per-capita extraction and consumption of less than four barrels per year, per human, is unarguable fact and a world average only. Currently the most energy extravagant consumers, led by Americans, each presently use (bum up) over twenty-four barrels of oil per year, six times the world rate. In fact, Americans use about twenty- five percent of the world oil production with only five percent of the population. China is gaining but still uses only twelve percent of world oil with twenty percent of the population for a per-capita consumption of two barrels per person per year, about one half the world average shown in figure 6-2.

A most important observation from the per-capita consumption graph (fig. 6-2) is: we have already passed the peak of per-capita world oil. This historic fact occurred thirty-two years ago in 1980 at 4.5 barrels per year. Although major sources such as Alaska, the North Sea, and Russia had not yet hit their peak and world oil extraction continued to increase, the total output did not keep pace with the corresponding growth in population. Per-capita availability began an inexorable decline with only a brief respite made possible because of the last major oil extraction surges between 1980 and 2010.

US Oil Extraction and Consumption:

Because there is only one world, overall extraction and consumption have to be the same. Therefore the per-capita average is simply the ratio between usage and world population. However, as stated above, there are gross disparities between different nations that constitute this average. Clearly, some parts of the world have achieved exceptional consumption rates typified by the lifestyle we Americans take for granted. The references for the numbers are US census data and the EIA (Energy Information Administration).

The next graph (fig. 6-3) shows the historic first half and the projected second half of the two-lifetime oil age for the US lower 48 states and Alaska. Also included are US population numbers also reported by the census department prior to 2010 and projected forward using the methodology explained earlier in this chapter. Also, as a subset of the world, we in the US have to deal with immigration and emigration adjustments. The fertility-rate population projections and conclusions would be the same for any autonomous nation. It makes no difference if the population is immigrant, white, black, religious, rich, poor, republican, or democrat. Everyone has to eat and aspires to a long comfortable, healthy life.

Fig 6-3

Important observations in figure 6-3 are: US extraction did, in fact, peak in 1970 at 3.5 billion barrels per year or 10 million barrels per day. This is about one-half the present US consumption rate of 19.7 million barrels per day. M. King Hubbert was publically derided for predicting the US peak back in the 1950's. But subsequent reality proved the veracity of his techniques which are now the context for prediction of world oil peaking and the second half of the oil age with the following provisos:

(page 5)


US oil extraction has not exactly followed a mirror-image decline rate as would be simply predicted by a Hubbert's curve. New technology and eight-fold higher prices have eased the decline rate somewhat, but there is no argument that domestic extraction of conventional oil is only about half what it was at peak. During the rapidly growing period from 1920 to 1970, oil extraction increased by about four percent per year. After peak in 1970, US oil extraction decreased about one and one-half percent per year. Presently, US lower 48 states plus Alaska extraction is two billion barrels per year or thirty-percent of our consumption of seven billion barrels per year. Of this prodigious rate of oil consumption, the highly-touted Bakken shale oil ("fracked" tight sand) contribution is 600,000 barrels per day or 0.22 billion barrels per year, only eleven percent of our domestic extraction. The American public does not comprehend the magnitude of these numbers and is led to believe that 600,000 Bakken barrels per day will prevent the end of the oil age. In order to give every benefit of the doubt to these optimists, the reduction of future US extraction rate is projected (flattened) to one percent per year.

US oil consumption (including US oil extraction) is continued forward in figure 6-3 as one-fourth of predicted world consumption. Steadily declining EROEI is not included although oil will continue to become more and more difficult to extract. Also, in favor the optimists, an additional 300 billion barrels (0.3 trillion) are added beyond that expected in the second half of Hubbert's curve of world extraction. Continuing forward just 58 years to 2070, US oil consumption would, as one-fourth the world extraction rate, drop below the more-optimistic US extraction decline rate of one percent per year. By that time, total US consumption would have to decrease by over eighty-five percent and by then, in less than one lifetime, we either would have taken extreme measures to decrease both population and energy consumption or total chaos will have ensued, nationally and world-wide.

Figure 6-3 also shows future US population momentum at one child per female (1cpf) and two children per female (2cpt) using the same methodology (including the eighty year life span) explained earlier in this chapter. (Present US fertility is 1.86 cpt) Note again that the conventional wisdom of two children per female "replacement rate" further exacerbates our predicament by increasing population thirty percent higher than now before stabilizing and not dropping. In 2012, in rounded numbers, US net increase is four million births plus one million immigrants (one-half illegal), minus two million deaths, for a net increase of three million per year (4+ 1-2=3). That's 250,000 per month additional jobs and food required to keep from slipping backwards to more unemployment and economic decline. (The Aug. 2012 increase was 96,000.)

Per-Capita US Consumption:

The final graph (fig. 6-4) combines the extraction, consumption, and population curves developed in figure 6-3. At the bottom for reference is the "less optimistic" average world per-capita oil consumption for 1.5 children per female. The much higher US per capita consumption of25% ofworld oil is projected forward on the same time-line at one (lcpf) and two children (2cpf) per female. Now we can see that 1 cpf gives about a ten year delay before reaching the lower per-capita consumption as would be expected with 2 cpf. The continued attempt to access 25% of world oil ensures we will continue our part in competition for dwindling oil including directly-related foreign presence, geo-politics, territorial conflicts, and deteriorating human-rights.

Fig 6-4

(Page 6)

We can also see that if the US was to depend only on domestic oil (the lower 48 states plus Alaska) for energy, we would be close to the four barrels per year current average for the world. Americans are precariously dependent on foreign oil (including Mexico and Canada) to continue any semblance ofour unique energy-intensive lifestyle for a few more years. A few extra billion barrels from ANWAR, off-shore, or tight "fracked" oil will not change the prognosis. We will soon be forced, whether we like it or not, to sharply reduce our use of oil, especially for non-essential and inefficient  transportation. In a later chapter, the argument is made for coupon gas-rationing as the best way to equitably reduce consumption and the direct effect of high fuel prices on the economy. Our food system will be especially impacted because it will no longer be possible for one farmer to feed 300 people thousands of miles away. The best we can plan for is that the US carefully nurture its remaining oil endowment, reduce fertility rates, precisely limit immigration, move to local or personal agriculture, and begin immediately to segue to a more expensive (than fossil energy) solar-electric future. Of course, none of these are likely to happen, let alone all in tandem. Although the whole subject seems hopeless does not mean it should not be clarified and quantified for reference in the immediate future.

The ultimate challenge through the ages has been to control and reduce human reproductive rates, in an acceptable way, to a level commensurate with finite, and now declining energy supplies. The only answers may be massive education, peer pressure, and honest leadership within a sovereign national or regional society. Everyone must be involved. Those who are not, only exacerbate the predicament, guaranteeing that all will be dragged down together.

The critical subject of population control has been addressed since the beginning of recorded history, and probably before, but not documented. All surviving cultures had to thread a precarious path between a fertility rate of about three (3cpt) to ensure continuity, and not more, which would have exceeded the local carrying capacity most often leading to collapse. This was before modern health care and long life spans. Now, we urgently need to reduce fertility to 1cpf in order to navigate the end of the oil age plus the ecological devastation we have caused by over populating every niche of the world. There are hundreds of books that venture into the details of fertility control. I will not go further with this except by suggesting (in Chapter 1) that male vasectomy would be a better choice rather than leaving it to the mothers to limit population to available resources. One of the best books in my collection on population is "More" by Robert Engelman (Island Press, 2008). It is easy to read and explains among other birth control methods, emmenagogues and pessaries (neither word is in my pocket Webster's Dictionary), which were used by women before modern contraceptives were invented.

"To know and not act is to not know." (Chinese proverb) or, “We are all descendants of thieves, and the world's resources are inequitably distributed. But we must begin the journey to tomorrow from the point where we are today. We cannot remake the past. We cannot safely divide the wealth equitably among all peoples as long as people reproduce at different rates. To do so would guarantee that our grandchildren and everyone else's grandchildren would have only a ruined world to inhabit." See "Lifeboat Ethics", by Garrett Hardin (1915-2003)

(Page 7)

John G. Howe is a  semi-retired mechanical engineer running his own company, Howe Engineering Co.,  since 1981. He works 175 acres of mixed farm and wood lot in New England. He is author of “The End of Fossil Energy.”  Mr. Howe
became a serious student of energy issues as a farmer and while manufacturing bicycle-powered generators and thresher/winnowers for resale. In  recent years his increasing concern about the demise of fossil energy has led to  the publication of three editions of his energy book with the following  subtitles, which read successively: First edition (2004) “A Plan for  Sustainability,” Second edition (2005), “The Last Chance for Sustainability, and  Third edition (2006), “The Last Chance for Survival.” He is currently working on  the fourth edition, “What Next?” See: http://www.solarcarandtractor.com  for updates and insights from John G. Howe.

Fig 1-2 from Chapter 1

Fig 1-2


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