The FuTure oF nuclear Fuel cycle - MIT Energy Initiative

Figure 3a.2 elasticity of uranium resources with respect to ore Grade
0
-0.5
s = 0.39 In x - 0.55
minus s, Semi-empirical elasticity (% per %)
-1
-1.5
-2
-2.5
-3
-1.25 Analytical Approximation
-1.61
-1.88
-2.03
-2.15
-2.50
-2.78
-2.93 -3.05
-3.40
Numerical Solution
-3.5
-4
100 1000 10000 10000c
uranium ore Grade (ppm)
C G i
` =
Cr Gr
`j j
[2]
in which
i= n
` -a
s
j
where
n = economy of scale exponent (typically 0.7)
α = learning exponent: ln(f/100) / ln2
(hence 0.23 for f = 85%)
In Eq. [2] Cr and Gr are reference (start of interval) values: for example, $/kg U NAT and cumulative
gigawatt years of electric energy generation, respectively. Note that G can also be
expressed as cumulative uranium consumption, since we assume a constant proportionality
of 200 MT/GWe-yr at full power.
It should be evident that extrapolation into an ill-defined future is not properly a deterministic
undertaking. Hence, following the lead in a similar effort in 1980 by Starr and Braun of
EPRI, a probabilistic approach was adopted [4].
appendix to chapter 3: Formulation of cost/cumulative resource elasticity Model 145