Evidence for David Mackay of the one ton of Thorium per GWe year in LFTRs

David MacKay has asked me to produce evidence for my statement that the fission of one ton of Uranium or that matter Thorium-232, produces about 1 GW years of electricity. The National Physics Laboratory of the United Kingdom maintains a web page on nuclear fission, That page includes calculations of the total energy release from the fission of U-233, U-235 and Pu-239. They are:

U-233 = 197.9 MeV

U-235 = 202.5 MeV

Pu-239 = 207.1 MeV

The Mass Physical Equivalence ratio is one gram of mass is equivalent to 24.9 million kilowatt-hours (≈25 GW·h),
197.9 MeV per fission event of thorium is calculated to yield

((197.9 MeV) * Avogadro's number) / (232 grams) = 20.7401717 terawatt hours per ton

Kirk Sorensen illustrates the relative electrical yield of thorium breedingMolten Salt Reactors and Light Water Reactors in this slide:
There has been a discussion on this slide on Energy from Thorium. The working rule for calculating the thorium fuel to electricity ratio. The consensus seems to be that the ratio of 1 ton of thorium to 1 GW year seems to holds. In A Road Map for the Realization of Global-scale Thorium Breeding Fuel Cycle by Single Molten-Fluoride Flow, Kazuo Furukawa et al, calculated on the basis of research by ORNL Scientists, including my father, that in a Molten Salt Thorium Breeder Reactor,

Conversion efficiency for thermal to electrical power is 44 % as compared with 33 % for the current LWRs.

This is consistent with the ton per 1 GWe year ratio.

The full beauty of the Thorium Breeding Molten Salt Reactor system is illustrated by the following statement:

If the fuel salt leaks, the nuclear reaction will automatically stop, preventing re-criticality. There is no possibility of an extremely dangerous explosive accident in which radioactive substances are released into the atmosphere like that which occurred in Chernobyl. . . .
there is practically no TRU production in a 233U fueled MSR. On average the production of Pu and Am+Cm in FUJI-233U are respectively 0.5 kg and 0.3 g for each GWe␣y of energy production. The corresponding figures for an LWR are 230 kg and 25 kg. . . . With the elimination of TRU elements radio-waste management issue will become a “Hundred Years” problem from a “Million Years” problem allowing the incineration in the fuel-cycle after temporary storage of radio-wastes for several decades.

Kirk Sorensen illustrates the advantage of the thorium breeding Molten Salt Reactor (the LFTR) in nuclear waste management with the following slide.

Update: I could not find an online discussion of the fuel efficiency of fast reactors, so I did what any sensible person would do, i asked one of the world's leading experts on Fast Reactors, Yoon Il Chang, for help. Dr. Chang graciously responded to my request:

Dear Charles,

I am not sure if there is an on-line document, but it is a simple, straightforward calculation.

Fissioning of 1 gram produces 1 MWD energy. (This is derived from 1 gm equals Avogadro number 6x10**23 divided by 235 atoms, 1 atom fissioning produces 210 MeV energy. 1 MeV is equivalent to 1.6x10**-13 watt-sec. If you convert in proper units, you reach 1 gm = 1 MWD.)

1,000 MWe plant is equivalent to 2700 MWth if you assume 37% net thermal efficiency.
2700 MWth x 365 days/yr x 1 gm/MWD = 0.9855 tonnes ~ 1T.
Since the reactor does not operate 100%, the net fissioning will be somewhat less than 1 T/GWe-yr.
LWRs have a lower thermal efficiency (~33%), so their consumption will be somewhat grearter.

But as a rounded number, I tend to use 1 T/GWe-yr, regardless of reactor types, actual capacity factors, etc.

In the LWR, the uranium resource utilization is far less than 1%. (About 85-90% discarded in enrichment tails, of the 10-15% loaded in the reactor only 3-5% is fissioned, and therefore >99% is discarded as waste.)

In fast reactors, all uranium, including depleted uranium and used uranium and actinides in spent fuel can be fissioned through continuous recycling. In theory, more than a factor of 100 improvement in uranium resource utilization. In practice, some will be lost as processing wastes and a factor of 60 or 70 is assigned taking this into consideration. The LWR figure is more like 0.6-0.8% (higher number with recycle). Therefore, a factor of 100 is more representative ratio even if very conservative loss factors are assumed.

I hope this helps.

Yoon

I hope that Dr. Chang's Statement will provide a satisfactory response to Dr MacKay's request for more information.

Update 2: Barry Brook has contributed his calculations of IFR breeding efficiency

Barry Brook said...
Charles, I'd already done the calculation for IFRs, here:

IFR FaD 2 – fuel use
http://bravenewclimate.com/2009/12/13/ifr-fad-2/

To quote:
1 fission of a 239-Pu nucleus (bred from fertile 238-U) yields about 190 MeV of useable (non-neutrino) energy.

A mole yields 6.023E23 (Avagadro’s constant) x 190 x 1.602E-13 (joules/MeV) = 18.3 TJ of energy.
Thus completely fissioning 1 kg of 239-Pu gives (1000/239)*18.3 = 77 TJ = 7.7E13 joules.

Now, 1 GWh of energy is 3.6E12 joules.

1 GWyr (the output of a 1 GWe power station, run continuously over a course of a year) = 8760 x 3.6E12 = 3.154E16 joules.

So we require 3.154E16/7.7E13 = 411 kg of 238-U ‘feedstock’ (bred to 239-Pu and other TRU fissile isotopes) to deliver 1 GWyr.

Assume the IFR plant runs on a Rankine cycle at 35% efficiency operates at 90% capacity factor (in reality the efficiency and CF might both be higher), we would need 411*0.9/.35 = 1057 kg, or roughly 1 tonne of uranium.