The FuTure oF nuclear Fuel cycle - MIT Energy Initiative

eStimatinG Future CoStS oF uranium
We developed a price elasticity model to estimate the future costs of uranium as a function
of the cumulative mined uranium. The details of this model are in the appendix.
The primary input is the model of uranium reserves as a function of ore grade [14] developed
in the late 1970s by Deffeyes. The results of this model are shown in Figure 3.2. For uranium
ores of practical interest, the supply increases about 2% for every 1% decrease in average
grade mined down to an ore grade of ~1000 ppm. His work extended models previously applied
to individual mined deposits (e.g., by Krige for gold) [15] to the worldwide ensemble of
deposits of uranium. The region of interest in the figure is on the left-hand side, above about
100 ppm uranium, below which grade the energy expended to extract the uranium will approach
a significant fraction of that recoverable by irradiation of fuel in LWRs. The resources
of uranium increase significantly if one is willing to mine lower-grade resources.
An important factor not accounted for here in prediction of uranium resources is the recovery
of uranium as a co-product or by-product of other mining operations. The most important
category here is phosphate deposits. A recent CEA assessment [8] projects 22 million
MT from this source: by itself enough for 1000 one-GWe reactors for 100 years, subject to
the caveat that co-production is fully pursued.
Finally, several authors have noted that Deffeyes’ assessment was completed before the rich
ore deposits in Canada, at grades in excess of 3% (30,000 ppm) were discovered. This could
imply that the projected cost escalation based on his results would, in effect, be postponed
for a period.
Our model included three other features in addition to uranium supply versus ore grade
elasticity:
p Learning curve. In all industries there is a learning curve where production costs go
down with cumulative experience by the industry.
p Economics of scale. There are classical economics of scale associated with mining operations.
p Probabilistic assessment. Extrapolation into an ill-defined future is not properly a deterministic
undertaking—we can not know the exact answer. Hence, following the lead in a
similar effort in 1980 by Starr and Braun of EPRI, a probabilistic approach was adopted
[16] in our models.
The results of our model are shown in Figure 3.3 where the relative cost of uranium is
shown versus the cumulative electricity produced by LWRs of the current type. The unit
of electricity is gigawatt-years of electricity generation assuming that 200 metric tons of
uranium are required to produce a gigawatt-year of electricity—the amount of uranium
used by a typical light water reactor. The horizontal axis shows three values of cumulative
electricity production:
p G1 = 100 years at today’s rate of uranium consumption and nuclear electric generation rate
p G5 = 100 years at 5 times today’s uranium consumption and nuclear electricity generation
rate
p G10 = 100 years at 10 times today’s uranium consumption and nuclear electricity generation
rate.
34 MIT STudy on The FuTure oF nuclear Fuel cycle