It is interesting to calculate how many plants would be required and what it would cost if all energy were generated by nuclear plants. Other consequences of this possibility are worth considering.

I will consider various cases, ranging from American electric energy to all energy in the world of 15 billion people, assuming the energy were used at American levels.

For now I will make rough estimates - perhaps to be refined later, although the uncertainties may not justify attempts at precision.

American Electric Energy
At present 109 nuclear reactors generate 1/5 of American electricity. The obvious calculation says that 500 reactors would generate all of it. This requires some qualifications.

First, 500 separate power plants wouldn't be wanted, because already some plants have several reactors. There might not be a need for many new plants, just more reactors at present plants, except in areas not presently served by nuclear power. If we imagine that a power plant could serve a square 300 miles on a side and consider the continental U.S. as 3,000 miles by 1,500, then 50 plants would do it. I would guess that there are more than 50 plants now, but they are certainly not located in the centers of squares. Anyway a few hundred plants would do it.

Second, present reactors come in a range of sizes; I don't have the average yet. Many are 1,000 megawatts electrical, and that was somewhat of a standard. However, it has been proposed that if the reactors were somewhat smaller (600 megawatts was mentioned), more of the plant could be built in factories rather than assembled on site. On the other hand, the two reactors recently completed in Japan by General Electric were each 1354 megawatts, which is certainly bigger than the American average, and it may indeed be bigger than the largest operating in America. Apparently some companies are betting that reactors will get bigger and others that they will get smaller. Probably some of each will be built.

I welcome help in making these estimates more precise.

All American energy
About 1/4 of American energy goes to produce electricity. This suggests that 2,000 reactors would generate all our energy. However, a power plant generates about 1/3 of the energy it consumes as electricity. If energy can be used directly as heat, then a power plant can generate more energy to be used as heat than it can as electricity. This requires a means of moving heat from the power plant to where it is used. Sometimes it would be convenient to locate a chemical plant that uses heat near the power plant, but this might require a relaxation of rules requiring that nuclear plants be isolated.

District heating plants are used in some European cities and in the former Soviet Union. The heat is moved in hot water or steam.

However, electricity is a convenient and flexible way of moving energy, so it isn't obvious how much advantage there would be in using nuclear heat directly.

All world energy at American standards at present population.
The U.S. has about 1/20 of the world population, so it would seem that 40,000 reactors would be required to meet the world's energy requirement at American usage levels. American energy usage levels will only be required at an American standard of living.

All world energy at American standards at 15 billion population.
The arithmetic suggests 120,000 reactors - in say 6,000 power plants.

All world energy at present energy usage levels.
I'll put this in when I get around to looking up the facts.

All world energy less energy conveniently generated in other ways.
Presumably there is no need to replace well-functioning hydroelectric plants, plants powered by wood scrap and other wastes. Moreover, it may be convenient for a very long time to use petroleum to power aircraft.

Q. What about costs?

A. If we take $2 billion as a nominal cost for a 1,000 megawatt plant, then we are talking about $1 trillion for the capacity to generate all American electricity, $4 trillion to generate all American energy, and $240 trillion for all world energy for 15 billion people at American levels of energy usage. At present the U.S. spends 8 percent of a GDP of about $6 trillion on energy. Thus the capital cost for the U.S. would be slightly less than one year's GDP. I suppose that if we imagine 25 years for the transition, it wouldn't be much more than current capital spending on energy.

The $2 billion estimate came from a recent Canadian proposal to build a reactor in Indonesia. American reactors that were delayed a long time for regulatory reasons have cost much more, but we can assume that the regulations will become stable worldwide. We can also expect that if reactors are built on the scale postulated, costs will come down a lot from experience. Indeed they may approach the low levels anticipated when nuclear power was first proposed. Perhaps we should consider $1 billion per 1,000 megawatt reactor as a likely cost.

World costs would be correspondingly larger. Incidentally, there is an estimate that the world will spend $13 trillion to $20 trillion on capital costs of electricity generation between now and 2020. Of course, this would not bring the world up to American standards of electricity use, much less replace other sources of energy.

Q. What about uranium supply?

A. Going to nuclear energy on this scale almost certainly requires breeder reactors within 100 years or so. It was long ago estimated that they would cost about 1.5 times as much as conventional reactors, but there is no industry yet. Uranium supply will be adequate for a few billion years.

Q. What about the 40 year life of reactors?

A. That will require replacing or rebuilding them. The main reason for replacing power plants has been obsolescence, i.e. more economical ways of generating energy are discovered. Nuclear reactors may also have to be replaced, because of nuclear damage to the reactor structure. Replacing or rebuilding reactors will not be as expensive as rebuilding whole plants. Buildings and other facilities may not have to be replaced so often. Indeed experience in building reactors will probably give them lives considerably longer than 40 years.

Q. What about the waste from so many reactors?

A. If the fuel rods are reprocessed, and I think they will be, then each reactor produces about one cubic meter of waste per year. We are talking about 60,000 cubic meters per year. Imagine it as a parallelopiped, 10 meters by 20 meters by 300 meters. One repository could handle it, although I suppose political considerations will require that many nations have their own.

The purpose of this page is not to advocate that all energy be generated by nuclear reactors, although that might eventually be a good idea. The purpose is to show that humanity can get all the energy it needs or wants. Nuclear energy is used in what mathematicians call an existence proof.

Q. Wouldn't so many reactors make nuclear war very likely?

Every country that has tried to manufacture plutonium nuclear weapons has done so using plutonium production reactors rather than using fuel from power reactors. It seems likely that a desperate war between countries of even moderate technology would get nuclear and be very bad whether or not nuclear power was in wide use.

Up to: Sustainability FAQ

I welcome comments, and you can send them by clicking on jmc@cs.stanford.edu

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