MIT approach

The MIT analysis [11] notes that a lower ore concentration (yield Y) means more ore (rock) is extracted per tonne of U: so extraction work is proportional to 1/Y. It then assumes that economies of scale (instantaneous) and learning (cumulative) both exist for extraction. Random parameter values are assumed for scale economy, and a fixed parameter value for learning. From its modelling MIT concludes:

  • The benefits of large future instantaneous output rates (scale), and large future cumulative outputs (learning) will drive U cost/te growth only slowly.
  • U cost/te will not increase markedly, and may even decline over next 50 Mte of U

University of Manchester approach

The University of Manchester approach [12] considers that in open-cast mining, the work (and hence cost) of extraction (excavation, transport to mill), and the work (and hence cost) of separation (milling etc.) both depend on yield Y. This implies that:

  • The work of extraction (te of ore per te of U) is proportional to 1/Y
  • The work of separation (per te of ore) is also proportional to 1/Y

Hence, the work of separation (per te of U) is proportional to (1/Y)².

The modelling also considered how economies of scale (instantaneous) and learning (cumulative) should be included, and concluded that they are actually alternative ways of parameterising the same long-term cost fall; in other words, that it is double counting to include both.

Learning curves invariably have asymptotes, and a sustained fall of an industry learning curve (often called an experience curve) needs successive jumps of the asymptote. This may be caused by technical progress (where quite large jumps have a surprisingly mild appearance in a long-term experience curve), or jumps in design scale (which are empirically smoothed by post-investment learning). Overall, in the long term, learning effects would be expected to diminish, and scale economies would be expected to dominate. Economies of (large) scale exist in activities whose surface area grows slower than volume, and whose surface area drives cost, but whose volume drives sales value. In the case of open-cast mines, however, the total cost and total value are both driven by the mine’s volume, so scale economies are slight.

As detailed in the University of Manchester work [12], this leads to a model where separation cost rises more rapidly than modelled by MIT, and eventually grows explosively as indicated in the figure.

Indicative cost multipliers with increasing cumulative uranium consumption

Credit: Source data interpolated from [10]. Assumes scale benefits of consuming U at 20 times today’s rate.

Indicative cost multipliers with increasing cumulative uranium consumption

Applying this to nuclear power station economics reveals that rising cost of uranium can have surprisingly a strong effect on overall project economics, as it affects the ‘current account’ operational cash surplus, most of which will be already committed to paying back the original investment.

A form of the (1/Y)² cost dependence in open-cast mining will be shared by in-situ leaching (ISL), which accounts for a growing percentage of uranium extraction. ISL was not specifically modelled in this study but it is hoped to explicitly include this in future work.

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This article was published in the September 2012 issue of Nuclear Engineering International.