An Introduction to Nuclear Fuel for David McKay

David McKay made what I would categorize as a blunder in his new book, "Sustainable Energy Without the Hot Air". McKay asks,

Could nuclear power be “sustainable”?

Then he asks a two more questions

How great are the world- wide supplies of uranium, and other fissionable fuels? Do we have only a few decades’ worth of uranium, or do we have enough for millennia?

These are excellent questions, but unfortunately McKay goes about answering them in a totally wrong headed fashion and muddies the waters rather than producing greater clarity on the subject. First McKay relies on USGS estimates of Uranium and Thorium reserve. Secondly he greatly underestimated the amount of money that could economically be spent to spent to recover uranium and thorium. McKay reports the world land reserve of uranium to be 4.7 million tons, and if the price of uranium went up to $130 a kilogram an additional 22 million tons could be recovered. Thus according to McKay the world's total recoverable Uranium reserve from land sources is 27 million tons.

In addition to the uranium

Worldwide thorium resources are estimated to total about 6 million tons, . . .

McKay tells us. This is interesting because in 1969, the United States Atomic Energy Commission estimated the recoverable thorium reserve of the United States @ $500 per pound - may be $2000 a pound at today's prices - to be 3 billion tons.  At 2008 prices coal with the equivalent energy would cost 100 times more to mine.

McKay does note that

one paper published in 1980 estimated that the low-grade uranium resource is more than 1000 times greater than the 27 million tons we just assumed.

McKay is probably correct that there is not enough uranium in sustain a once through nuclear economy over the long hall, but no one has ever thought there was. Manhattan Project nuclear scientist began to talk about breeder reactors during World War II, because they anticipated a long term uranium shortage.

I was disappointed by David McKay's treatment of nuclear energy in his new book Sustainable Energy Without the Hot Air. McKay has made the book available for free downloads, but considering the weakness of McKay's treatment of nuclear power I would have reservations about recommending it as an reliable source on energy issues. McKay failed to make clear, and I suspect did not delve deeply enough into the subject to clarify for himself the potential for energy recovery from uranium and thorium. He failed to identify nuclear technologies that could assure the recovery of the full energy potential of naturally occurring fissile and fertile isotopes. A fissile isotope will fission after absorbing a neutron. A fertile isotope, after absorbing one or more neutron undergoes a transformation into a fissile isotope. TU Delft tells us:

Not all nuclei are fissionable by introducing a neutron, in fact, the number of fissile nuclei is rather limited. However, neutrons interact with all nuclei. One type of interaction is absorption, where the incident neutron is absorbed into a nucleus and becomes part of a nucleus. Usually the resulting isotope is unstable and the newly formed nucleus shows radioactive decay. A special case of neutron absorption happens when a heavy, non-fissile nucleus,absorbs a neutron and decays to become a fissile nucleus. The most important 2 of these mechanisms are the U-238 chain and the Th-232 chain:

U-238 (non-fissile) + n -> U-239 -> Np-239 -> Pu-239 (fissile)
Th-232 (non-fissile) + n -> Th-233 -> Pa-233 -> U-233 (fissile)

In these reactions, new fissile material (nuclear fuel) is formed from material which was previously non-fissile. Most reactors in the world use uranium fuel with 95+% U-238, and in all nuclear reactors U-238 is converted to Pu-239. In a power reactor roughly 40% of all power is produced by fissions of Pu-239, so conversion is an important (and universal! ) effect in nuclear reactors.

About 0.7% of uranium atoms are fissile U-235. The other 99.3% of uranium atoms are fertile U-238. When U-238 absorbs a neutron it almost always undergoes a nuclear transformation process and becomes Pu-239. Pu-239 is fissile about 2/3rds of the time in most reactors, and that is good enough to sustain chain reactions, so Pu-239 can serve as reactor fuel, although it is not the best possible reactor fuel in Light Water Reactors.

How much of natural uranium can become fissile and be "burned" in the nuclear process? Potentially all of it, but burning it all depends heavily on what technology you chose to use, and the compromises you choose to make. in addition Thorium-232 will transform into fissionable U-233 after absorbing a neutron, and there a are some real advantages to using Thorium-232 rather than Uranium-238 as the basis for a fuel cycle. (I strongly suggest that the curious read WASH-1097, a document that explains a whole lot very well. WASH-1097 is moderately teckie, but learning to cope with teckie talk is the rout to personal empowerment in a technological age. Don't just take my word for what I write here.)

McKay, unfortunately did not read WASH-1097. It is clear from WASH-1097 that fissile U-233 can be produced by breeding Th-232, and that U-233 is very good nuclear fuel. Among other good qualities is that an efficient thorium fuel cycle reactor can transform 100% of the thorium feed into it, and burn up to 98% of the transformed thorium. The other 2% is transformed into Neptunium-237 that can be burned in fast reactors.

How much Thorium might be available for future reactor use? WASH-1097 contained an estimate from the USAEC that for 500 nineteen sixty nine dollars per pound, maybe 2000 two thousand eight dollars, the United States had a recoverable thorium resource of three billion tons. To understand the potential value of that resource we might compare it to coal. The price of coal last week on the international market was $105 per ton. That price has been depressed by 40% due to the international economic downturn (depression?). It takes about 3 million tons of coal to keep a a one billion watt power plant producing electricity for a year. The coal, at last weeks market price would cost $315 million. One billion watts of electricity could be produced with one ton of thorium. The price for the thorium? $4 million. Thus at a price for thorium that is a little more than 1% of the price of coal, enough thorium is in the ground in the United States to provide all the electricity the United States uses for over one hundred million years. But even this would not deplete the United States' thorium resources.

How much thorium would be potentially available energy use? Martin Sevior et al state:

The Rossing mine in Nambia mines Uranium at an Ore concentration of 300 ppm at an energy cost 500 times less than the energy it delivers with current thermal-spectrum reactors. If the energy cost increases in inverse proportion to the Ore concentration, shales and phosphates, with a Uranium abundance of 10 - 20 ppm, could be mined with an energy gain of 16 - 32.

Now remember that Savior and associates base this astonishing statement on the recovery of less than 1% of the potential nuclear energy in Uranium ore. Since the energy of all or almost all of the energy found in uranium or thorium is well over 100 times the amount captured by current nuclear technology, the theoretical energy gain from mining uranium at 10 to 20 PPM uranium or thorium with maximum burn nuclear technology would recover 1600 to 3200 times the energy expended in mining. Even when extracting uranium at its average crustal concentration of 1 to 3 PPM, the total energy recovery would at least 160 times the energy expended. There are 3 x 10(13) tons of uranium in the earth's crust, and three to four times as much thorium. It is probable that over time geological processes would bring enough uranium and thorium to the surface to replace the uranium and thorium used in energy generation.

So far I my argument has simply referred to a theoretical maximum energy recovery from from Uranium and Thorium. WASH-1097 offers us the basic facts about nuclear burnup:

The most significant nuclear advantage of the U-233(Th-232)U-233 cycle over the Pu-239(U-238)Pu- 239 cycle in thermal reactors is the potential of a higher conversion ratio. The importance of a high conversion ratio, CR, in assuring good utilization of resources is directly related to the burnup needs. In a converter reactor, CR units of bred fuel are produced for each unit of fuel consumed, and the net consumption of nuclear fuel is, then, proportional to (1-CR). Hence, other things being equal, a reactor with a conversion ratio of 0.6 would consume twice as much fuel per unit energy developed as a reactor having a conversion ratio of 0.8. The higher conversion ratio leads directly to a lower depletion charge in the fuel cycle cost.

In Molten Salt Reactors nuclear fuel is continuously reprocessed. Fission products are constantly removed to insure efficient operation. Thorium once it is sent into the system will typically stay in the reactor blanket or core until it captures a neutron and begins the nuclear transformation process. Once thorium enters the system it remans there until neutron capture leads to its withdrawal, either in the form of protactinium or as U-233. U-233 is then reintroduced to the core as nuc lear fuel.

We have seen that almost all reactors produce some new fuel that helps replace fuel that is used. How much new fuel is replaced is dependent on the conversion ration as TQ Delft tells us:

The ratio of (# of new fissile nuclei / # of consumed fissile nuclei) is known as the conversion ratio. This ratio can be estimated as follows:

1. For every fissile nucleus consumed, X new neutrons are released
2. For a stable chain reaction, one neutron is needed to sustain the reaction: X must be larger than 1
3. To have 1 new converted nucleus for every fissioned nucleus, one neutron is needed: X must be larger than 2
4. Neutrons will leak from the reactor, so X must be appreciably larger than 2 to make a practical reactor with a conversion ratio > 1.

If you are using a solid fuel, h uranium fueled reactor TU Delft tells us:

The value of X is highly dependent on the energy of the incident neutrons, as shown in the figure, and X grows rapidly for high-energy interactions. For thermal energies X = 2.4, which is not large enough to have a conversion ratio > 1. At high energy, X > 3 and this enables a conversion ratio > 1: at high energies more neutrons are available for conversion reactions, and it is possible to convert more nuclei than are consumed.This is known as breeding: the process of making nuclear fuel from material which was previously not fissile

Does it really take 3 neutrons to produce a conversion ratio of more than 1 to 1?

During World War II Eugene Wigner and Enrico Fermi argued about this. Fermi pointed out two problems with conversion in Uranium fueled reactors: (a) One third of Plutonium-239 do not fission when when they absorb slow neutrons. So with fast neutrons X is close to 3 with plutonium fuel, but in ordinary reactors it is under 3. (b) Neutron poisons - isotopes produced by nuclear fission - capture to many of the neutrons produced by fission thus lowering the conversion ratio. This meant that a special type of reactor, a fast neutron reactor, would be needed to produce enough neutrons from Pu-239 fission to overcome the neutron poison problem.

Eugene Wigner pointed out to Fermi that uranium was not the only fertile material that could be used in the nuclear process. Thorium 232 could be converted to U-233, and U-233 was excellent nuclear fuel. Nine out of ten U-233 atoms fission with slow neutrons, and that would produce enough neutrons to produce a conversion ratio of 1 to 1 or better provided neutron poisons could be somehow taken out of the reactor. This was impossible with the ordinary solid fuel used in reactors, but Wigner thought that if the fuel was dissolved in a liquid, it could be continuously processed and the neutron poisons removed. In 1948 a nuclear engineer Ed Bettis invented a reactor that would be fueled with liquid uranium tetrafluoride (U4F) salts as its fuel. Wigners associate, Alvin Weinberg, recognized that such a reactor could convert thorium-232 into U-233 at a ratio of 1 to 1 or even higher if carefully designed. The trick was to design the reactor to also be a miniature chemical plant. Learning how to do that would take a lot of work, but there was no theoretical reason why it could not be done.

There were several advantages of using the Th-232 + n -> Th-233 -> Pa-233 -> U-233 conversion system. Because U-233 was such a good nuclear fuel it left very little nuclear nuclear waste behind it. Out of every 100 thorium atoms introduced into the liquid fueled reactor in the form of liquid thorium-fluoride salt, 98% can be used up as nuclear fuel inside the reactor. The other 2%, converted by the nuclear process into Neptunium-237 can be used as a nuclear fuel in fast neutron reactors. Thus a reactor that uses the liquid fluoride thorium fuel cycle could potentially convert 100% of all thorium introduced into the reactor into nuclear fuel, and burn 98% of it. That meant that a Liquid Fluoride Thorium Reactor (LFTR) could produce a billion watts of electricity in a year from a ton of Thorium. Geologist estimate that there are between 120 and 160 trillion tons of thorium in the earths crust. In the 1960’s, Rice University geologists explored the Conway Granite formations of Vermont looking for thorium deposits. They reported finding it in concentrations of 56 + or - 6 ppm everywhere the looked. They even drilled down to the bottom of the huge granite massive and found reported that the Conway Granite formation is 1000 feet deep. They calculated a thorium content of 3 X 10(6) metric tons of thorium per 100 feet of depth. This calculation is based on a total outcrop area of Conway granite of 307 square miles.

Of course not every granite formation is as thorium rich as the Conway Granite formation. The Conway Granite is by no means unique, Helen E. Carter, Peter Warwick, John Cobb, and Geoff Longworth reported finding 17.544 ± 0.626 PPM uranium and 47.099 ± 4.326 PPM of Thorium in 5 samples of granite from the UK. Clearly then there is enough recoverable Uranium and Thorium in granite to keep us going for a very long time.

The EROEI from mining Conway granite for thorium and using the thorium as a basis for a nuclear fuel cycle in LFTRs would be somewhere in the neighborhood of 10000 to 1. Avin Weinberg recognized that uranium and thorium were the key to abundant and inexpensive energy, and coined the phrase "burn the rocks" which as Weinberg noted contained "an inexhaustible source of energy -- enough to keep you going for hundreds of millions of years".