The Meaning of Sustainability

• Albert Bartlett
• April 1, 2012
• Forum Papers
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Nuclear Fission And Fusion

In what follows I am assuming that there will be no major scientific or technological breakthroughs in the energy sector in the next century or so. I am uncertain about the role conventional nuclear fission power will play during the next hundred years. In the U.S. we have failed to provide the promised long-term storage for spent nuclear fuel and there seems to be little support in Washington, DC, to find an answer to the problems of what to do with the existing and predictable future quantities of high- level nuclear waste. Nevada has said that it does not want the Yucca Flats nuclear waste depository located in its borders. It could be expected that, if asked, the people in the other 49 states would say that they do not want the nuclear waste to be stored in their states, either. Unless some way can be found around this impasse, the future of nuclear power in the U.S. does not seem to be very bright. Yet if the lights don’t come on when one turns on the switch, people will quickly develop strong support for electrical power from nuclear fission.

Conventional nuclear plants are extremely expensive to construct and to operate and they are very complex. They are subject to occasional accidents, which frequently turn out to be very serious. The finite nature of the supply of uranium suggests that nuclear power is not sustainable. So I don’t include nuclear fission as a big player in my view of the distant future.

I have even less hope that there will be the successful development and widespread application of nuclear fusion within the next century or two. Fusion research has been continuing since the end of World War II with the hope that fusion will produce large quantities of low-cost electricity. Judging from the size of today’s experimental fusion facilities, any plant using fusion to generate electricity will be very large, very complex and very expensive. Fusion still has a long way to go before it can be expected to meet the demands of the electricity market, which requires reliable electric power 24 hours a day and 365 days a year. The uncertainties are so large that I feel that it would be unwise to count on the widespread availability of fusion-generated electricity on any proposed timetable. Therefore, I leave fission and fusion out of the following discussion of sustainability.

Sustainability of the Solar Society

In the long run, a century or more from now, if our society survives the catastrophic collapse predicted by Limits to Growth, the surviving society will be powered solely by solar energy, which includes wind, waterpower, and tidal energy. All of the easily available fossil fuels will have been used to the point where more extraction is uneconomic. Geothermal energy may provide a small fraction of the energy needed by the surviving society. This sounds pretty austere, but the solar society was anticipated with optimism by the famous American inventor Thomas A. Edison many years ago¹⁶:

[box type=”note”]I’d put my money on the sun and solar energy. What a source of power! I hope we don’t have to wait until oil and coal run out before we tackle that.[/box]

Sustained Availability

But it is not all doom and gloom. The concept of “Sustained Availability” gives us some freedom to make limited use of fuel and mineral resources during the transition period between the present and the distant future.
Do you remember from calculus that the integral from zero to infinity of exp(-kt) is finite and has the value 1/k. This mathematical fact has a useful consequence. Suppose that P is the annual production of a resource in tons per year and that P varies with time according to the equation

[typography font=”News Cycle” size=”24″ size_format=”px”]P = P(0) exp (-kt)[/typography]

where t is the time in years, P(0) is the present rate of production and k is the fractional change in P per year.

[typography font=”News Cycle” size=”24″ size_format=”px”]k = – (dP/P)/dt[/typography]

For a declining curve, dP is negative. The graph of production in tons per year vs. time will be a declining exponential, of the same form as the decay curve for a sample of a radioactive material. The area under the complete curve of tons per year vs. years from zero (the present time) to infinity is the total amount of the resource (tons) that is consumed in all of the future. This can be set equal to the estimated size R of the total remaining resource in tons to give a special value of k for which the total resource consumption between now and infinity on the declining exponential curve is equal to the present size R of the resource. In other words, a special value of k can be found for the reserves of a resource so that the production of the resource declines steadily but R lasts forever!

What is the particular value of the constant k which will allow the resource to last forever? This can be answered by example. It has been stated that world petroleum will last 40 years at present rates of consumption. In this case the particular value of k to make world petroleum last forever is (k =1/40 = 0.025). So if the global use of petroleum is made to decline 2.5% per year the petroleum will last forever! This decay curve has a “half life” of
28 years.

It’s important to note that:

[box type=”note”]at every point on the decaying production curve, the life expectancy of the then remaining resource will be 40 years at the then current rate of production.[/box]
This has been called “Sustained Availability” (SA). The concept and the options available to a producing country that is following SA to divide production between domestic consumption and export were all examined in mathematical detail in 1986.¹⁷

More recently, and completely independent of this earlier work, the concept of SA, without the mathematics, has been reinvented and applied to world petroleum production. In the petroleum business, the present rate of production divided by the size of the estimated remaining resource P(0)/R at a given time is called the “Depletion Rate.” This is the fraction of the remaining resource that is produced this year; it is the reciprocal of the life expectancy of the resource “at present rates of consumption.” World petroleum today (2012) is estimated to last about “40 years at present rates of consumption.” The depletion rate is then 2.5% per year.
In 2004 the geologist Colin Campbell of Ireland and the physicist Kjell Aleklett of Uppsala University in Sweden proposed “The Uppsala Protocol” which called for oil producing countries to agree voluntarily to an accord18:

[box type=”note”]No country shall produce oil at above its current depletion rate, such being defined as annual production as a percentage of the estimated amount left to produce.[/box]

Thus, qualitatively Campbell and Aleklett independently re-invented the concept of Sustained Availability that had been published eighteen years earlier.

The concept of Sustained Availability (the Uppsala Protocol) can be applied to the finite reserves of any non-renewable fuel or mineral resource. The rate of decline, k, can be adjusted at any time based on new evaluations of the life expectancy of the resource “at present rates of consumption.”

This is pretty good. We can use finite resources, such as petroleum, on declining curves in a way that allows future generations to access the resources just as the present generation does but in declining amounts each year. This path for resource production has the unique feature, noted above, that at every point on the declining exponential curve, the life expectancy of the then remaining petroleum at the then present rate of consumption will be 40 years!

We now have a “bridge” between our present society with its lavish use of non-renewable energy and the society of the future which will have to live pretty much exclusively on solar energy.