The FuTure oF nuclear Fuel cycle - MIT Energy Initiative

Chapter 3 Appendix — Uranium Resource
Elasticity Model
Our conclusions on uranium costs versus cumulative production are based on a series of
models where the results depend upon the input assumptions and the model. This appendix
describes the mathematical models used in our analysis. The models can be used with different
sets of assumptions.
methodoloGy
The approach adopted involved development of a price elasticity of cumulative uranium
consumption based on Deffeyes’ model of reserves as a function of ore grade [1]. His work
extended the log-normal model previously applied to individual mined deposits (e.g., by
Krige for gold) [2] to the worldwide ensemble of deposits of uranium: See Figure A1. 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. Numerical integration of his log-normal
frequency distribution gives cumulative reserves as a function of ore grade in ppm. This result
can then be manipulated to yield the sought-for elasticity. Numerical analysis validated
the following semi-analytic approximation in the range of interest (10 2 – 10 4 ppm).
s =
% increase in cumulative reserves
% decrease in ore grade
.
r
, nx v
v
2 v
2 ; - + E
2
[1]
where
x = ore grade, ppm U
appendix to chapter 3: Formulation of cost/cumulative resource elasticity Model 143