Reply #96: Agreeing that nuclear is best, then let's calculate it the energy value

[NNadir]

of reserves in the ocean.

I'm sure that I've done this calculation before, although my figure for Uranium reserves, which I spout off the top of my head and may have read somewhere, is that the accepted value is around 3000 to 4000 years of uranium reserves. However, if Bernard L. Cohen, who has had a powerful influence on my thinking about nuclear matters, says that there is an unlimited supply, I need to carefully think about his claims, because he is a highly respected and cited scientist and is generally right.

Let us say that there are 4 billion tons of dissolved uranium in the ocean, which is certainly a reasonable figure based on what we understand about the volume of the ocean and the concentration of uranium. The means that there are 4.0 X 10^15 grams of uranium. The atomic weight of uranium is roughly 238, so this translates to 1.7 X 10^13 moles of uranium. Multiplying this by Avogadro's number, 6.0 X 10^23 atoms/mole we see that we have 1.0 X 10^37 atoms of Uranium in the ocean. The generally given yield per fission is 200 MeV (million electron volts), meaning that there are 2.0 X 10^45 eV of energy available in uranium dissolved in the sea. The conversion factor from eV to Joules is simply the unit charge, the charge on an electron, 1.6 X 10^(-19) Coulombs. Thus there are 3.2 X 10^26 Joules of energy in the form of Uranium dissolved in the ocean.

It is variously reported that world energy usage, barring a sudden (and possible) extinction or population collapse of or by humanity, will be 1000 exajoules/year (1 zettajoule) by 2050 or 1.0 X 10^21 Joules. This means that the energy reserves for Uranium (not counting Thorium) is about 320,000 years if Uranium from the ocean provided all of the world's energy needs.

(Note: I have carried some insignificant figures - that I have not shown - in this calculation.)

Now for some caveats:

First, it is certainly not the case that all of the Uranium in the oceans is recoverable. As the concentration of the element falls, the cost of obtaining it rises because the ease at which it can be recovered falls. It is notable that when the Japanese did the actual work to examine the feasibility of this technology, which they found workable at around $200-300/kg, they were placing their recovery systems directly in ocean currents. This is because a land based plant would suffer from diffusion effects resulting in local depletion in seawater, which would raise costs. Although the cost of fuel is now trivial (it is the equivalent of gasoline at less than one cent a gallon,) it is not necessarily true that 100,000 years into an ocean recovery scheme that this would be true.

Secondly, not all of the energy of a fission is recoverable. For instance, about 5% of the energy released (about 10 MeV) in a fission is in the form of neutrinos, the energy of which cannot be captured by any known means, since neutrinos interact very weakly with matter. They leak right out of the reactor and indeed, often right through the planet. Thus we immediately need to reduce our figure by 5% A similar situation applies (to a much smaller extent) to neutrons. Some neutrons leak out of the reactor and into the shielding. However this effect is small, especially in thermal reactors where most, but not all, of the neutron energy (about 1 MeV per neutron, with 2.5 neutrons per typical fission) is captured by the moderating process. Also about 3% of the energy produced in nuclear fission reaction is the decay energy of the fission products, most of which decay in the reactor, but many of which do not. Many fission products, Sr-90 for instance, are removed from the reactor long before they decay, where they account for the heat generated by spent fuel. This heat is lost. I think a reasonable value of the energy lost in this manner would be somewhere around 1%.
Transmutation strategies, and the use of portable energy devices using Sr-90 as a power source would tend to minimize these losses, but they will not wholly eliminate them and it will be a few decades before such devices are as widely as accepted and used as they were in the 1950's and 1960's.

Neither is it necessarily possible to convert 100% of natural uranium into a fissionable form such as plutonium-239. During the breeding process, many parasitic nuclei are formed. These include U-236 (from neutron capture in U-235), Pu-240, Pu-242, Am-241, Np-237, Cm-246, etc. It is widely expected that much of the energy of these nuclei can be captured either through the widespread adoption of fast neutron spectrum reactors or subcritical transmutation reactors, but invariably there will be significant losses, nonetheless. The use of some of these isotopes, particularly curium isotopes, can complicate critical reactor physics significantly however and their use will involve some serious care and attention to detail to prevent reactor excursions and thus improve reliability and economics. It is worth noting that fast spectrum reactors of the type that have been built this far, have been rather testy beasts. (I have a much better design that I'm working on, but I more or less regard it as personally proprietary.) Moreover, even the best recycling schemes can only give 99.9% recovery of actinides. Some will undoubtedly be lost to the environment where they may result in some undue hysteria.

The non-proliferation concern (and objection to nuclear energy) is serious. Any successful nuclear program will need to be internationally audited under a rigorous system of checks and balances, and there will have to be careful attention paid to the isotopic distribution of all actinide elements to minimize this risk. Although the real threat of diversion can be made almost vanishingly small for terrorist types, irrespective of what George Bush and his fellow class clowns tell you, the same does not hold true for governments. Many governments, our own included, have behaved in a grossly irresponsible fashion with respect to the use of nuclear materials.

After about 1000 years of operations, commercial nuclear power will begin to seriously decrease the overall radioactivity of the earth. Most people today imagine that this would be a good thing, since they are rather (foolishly I think) focused on the idea that radioactivity is unacceptably dangerous. This is nonsense, since life evolved in the presence of radioactivity and for most of its history, the planet has been far more radioactive than it is now. (In ancient times, when there was more U-235 proportionally than there is now, natural nuclear reactors formed and went critical for hundreds of thousands of years.) However, it may be that life depends on radioactivity in ways of which we are not aware. For instance, it may be that the well known capacity of the biosphere to restore diversity after mass extinctions - like the one we are now experiencing - may depend subtly on the presence of radioactivity to maintain a sufficient mutation rate. I have never heard this discussed anywhere before, but I still think it is not a trivial consideration. The danger of this effect is somewhat ameliorated by the presence of non-actinide radioactive elements like potassium and rubidium, but I'm not confident that such a depletion of radioactivity will necessarily prove desirable.

It is not immediately clear to me that nuclear resources are inexhaustible as Cohen claims. His expectation is based on the fact that the concentrations of uranium in the oceans as uranium is removed for industrial processes, will be restored or stabilized by the weathering of crustal rocks and injection into the sea of mantle rocks from volcanoes. This may well be, but I don't think the rates of such processes are known well enough with such absolute certainty as to encourage us to be cavalier. I am not much of a geochemist, and so I cannot say with much certainty what the actual crustal concentration of uranium is. I'm not sure that anyone, even with extensive training in geochemistry, can make more than a crude estimate. I know the uranium concentration is high here in New Jersey, where we have a rather pronounced radon problem, but I don't know what it's like world wide. Still I do not necessarily understand the rates of geochemical extraction and distribution and I expect that Cohen doesn't really either. Such processes are slow, I know, and may be slower than Cohen allows. Thus it does not necessarily follow that uranium (or thorium) resources are inexhaustible.

Overall, as I've made clear in many posts, I believe it is an important task for humanity to begin to expand it's nuclear power generating capacity as quickly as is possible. We are in a very serious emergency situation due our unrestricted population growth. If we have time left at all, we don't have much of it. I am not sure however that any of this stuff about the comforting availability of nuclear energy absolves us from our basic responsibilities as stewards of the future, to carefully examine in explicit detail all the risks and benefits of our consumption decisions, to insist to the maximal possible extent that resources be renewable. Above all it our responsibility to teach and practice the values of conservation.