Nuclear Technology / Volume 176 / Number 2 / November 2011 / Pages 227-237
Technical Paper / Fuel Cycle and Management / dx.doi.org/10.13182/NT11-A13298
Formulas are given for extrapolating uranium prices that could result from future trajectories for the cumulative use of native uranium. The logarithm of the extrapolated price is given by a monotonically increasing trend curve plus a sinusoidal oscillation calibrated to historical data. The trend curve as a function of cumulative extraction of native uranium accounts both for accessing lower ore grades and for exploiting more-difficult-to-access richer ores as the more easily accessed richer ores are depleted. Accounting for both of these effects, the logarithm of the monotonic price trend is linear in the logarithm of cumulative extraction of native uranium, with least variance between observations and data of a power-law slope of 1/4.5 up to the point where a limit on the accessibility of the remaining highest-grade ores is reached. (However, a slope of 1/5.6 gives an almost equally good fit.) As an example, a ratio 4 of maximum depth of other mines to maximum depth of current uranium mines is used as a measure of the accessibility limit. This limit is first reached when the background trend curve uranium price reaches $143/kg of elemental uranium, in U.S. dollars inflation adjusted to year 2007 prices ($US2007). Thereafter, the accessibility limit gradually reduces the cumulative amount of native uranium extracted at a given cost below that computed from the power law, multiplying it by a factor of 0.59 when the trend price reaches 300 $US2007/kg. Increases of nuclear energy produced per kilogram of uranium mined with increasing uranium costs are also accounted for. A fraction of global nuclear energy users can develop a higher nuclear energy production rate per kilogram of mined uranium, e.g., by reusing the fissile material in spent fuel. Resulting cumulative cost changes as a function of cumulative nuclear energy use are presented in graphical and tabular form for a variety of input parameters.