Fuelling the future?

Energy Policy 74 (2014) S5–S15

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Energy Policy journal homepage: www.elsevier.com/locate/enpol

Fuelling the future? Paul Warren n, Giuseppe De Simone International Atomic Energy Agency, Austria

H I G H L I G H T S







We develop a model of uranium cost dynamics with productivity growth and learning. Productivity growth/learning will tend to reduce uranium extraction costs. Under some productivity growth/learning assumptions uranium costs may decline. Extraction cost declines have been observed in other commodities over the long-run.

art ic l e i nf o

a b s t r a c t

Article history: Received 20 January 2014 Received in revised form 22 July 2014 Accepted 12 August 2014 Available online 24 September 2014

Questions regarding exhaustible resource supply are best posed in terms of how extraction costs and prices will evolve as lower quality resources are exploited. To address such questions in the context of uranium the authors develop a model of long-run cost dynamics which (1) builds on a classic model of declining uranium ore grades, (2) includes both new and existing parameterizations of extraction cost structures, (3) incorporates the extraction cost impacts of learning and productivity growth, and (4) is driven by the IAEA's most recent uranium demand projection. The authors emphasize the importance of allowing interaction between temporal versus cumulative cost mitigating processes (productivity growth and learning respectively) and such processes' interaction with demand growth profiles. It is demonstrated that – under rather conservative assumptions on the dynamics of these processes – the rate of increase of uranium extraction costs is significantly attenuated relative to that which might otherwise occur. Indeed in some cases – again, for rather conservative assumptions on productivity growth and learning – it may not be unreasonable to anticipate that such costs may decline (as have those of several commodities over the past century). The policy implications of such attenuated – or even declining – uranium costs are significant. & 2014 International Atomic Energy Agency. Published by Elsevier Ltd. All rights reserved.

Keywords: Uranium supply Ore grade Cost dynamics

1. Introduction Questions regarding exhaustible resource supply are best posed in terms of how extraction costs and prices will evolve as lower quality resources are exploited, rather than in terms of attempting to identify a date when society will “run out” of a particular resource. In that context, the central objective of this paper is to address concerns around the way in which the need to mine lower grades of uranium as higher grade deposits are exhausted will influence the cost of uranium. In particular this paper seeks to explore the potential roles of both productivity growth and learning as forces which may counteract the tendency of a movement towards the exploitation of lower uranium grades to result

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in significant increases in extraction costs. In addition to seeking to quantify the potential dynamics of such costs under some (rather conservative) assumptions regarding productivity growth and learning, the paper also highlights the significance of evolving technology on the uranium demand side – in particular the consequences for demand of recent shifts in uranium enrichment technology. A number of significant policy-relevant issues arise in the context of this paper's central preoccupation with the ore-grade/ extraction cost relationship, including the desirability (and feasibility) of relying – to any significant degree – on nuclear energy as an alternative to GHG-emitting fossil fuels, the desirability of reducing reliance on the currently predominant ‘once-through’ nuclear fuel cycle in favour of cycles based on reprocessing, the need to explore the potential of other types of fissile material (e.g., thorium) to fuel nuclear energy generation, and the desirability of improving and deploying ‘breeder’ reactor technologies.

http://dx.doi.org/10.1016/j.enpol.2014.08.011 0301-4215/& 2014 International Atomic Energy Agency. Published by Elsevier Ltd. All rights reserved.

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1.1. Background There have been several attempts to address the question of the uranium ore versus cost relationship – and still more to address the (more general) question of the quality versus cost relationship for the broader class of exhaustible resources. Perhaps surprisingly the seminal theoretical paper in the area of exhaustible resource extraction and price evolution says nothing about this relationship. Hotelling (1931) assumes that the exhaustible resource is homogeneous, thereby abstracting from issues of declining quality.1 However a number of subsequent theoretical papers have gone some way towards recognizing the importance of declining resource quality within Hotelling's asset pricing/forward looking framework. For example Pindyck (1978) and Heal (1976) develop a theoretical framework recognizing the relationship between declining ore grades and rising extraction costs. Gaudet (2007) extends the basic Hotelling theoretical model in another direction, by including progress in extraction technology. Whilst a more in-depth discussion of such progress will be postponed until Section 3.1 it may be noted that – as with Pindyck and Heal – this more general model predicts that in the long run the price of an exhaustible resource will increase at a rate which is less than the discount rate, in contrast to the Hotelling's model. Broadly, Gaudet's model is somewhat akin to the model presented below in its recognition of the impact of technological change on extraction cost, and therefore on market prices. Turning to empirical evidence, there is considerable support for a key assumption of this paper – that resource extraction will exhibit a tendency to deplete successively lower grade resources. In hard rock mining2 this physical depletion effect is observed in the exhaustion of high ore grades – see for example, Norgate and Jahanshahi (2010) and Mudd and Diesendorf (2008). A priori, such a movement down a trajectory of declining ore grades might be expected to lead to increased (per unit) extraction costs and prices; perhaps surprisingly however historical data on commodity prices does not – in general – demonstrate increasing price trends. Shropshire et al. (2008) presents evidence on the historic price behaviour of a variety of minerals. Based on data from the United States Geological Survey data, this evidence suggests a declining price pattern for several commodities, while increases in long term cost are found only in a few cases. Schneider and Sailor (2008) conduct a similar exercise and observe a general trend of “flatness combined with dispersion”.3 This pattern seems contrary to the idea that extraction costs and uranium prices will increase as higher ore grades are exhausted. In this paper we will consider the dynamic factors which may oppose the price-increasing effect of resource depletion. Dale (2012) reviews the estimates of ‘ultimately recoverable resources’ (URR) of non-renewable energy sources: coal, conventional and unconventional oil, conventional and unconventional gas, uranium for nuclear fission. There is a large range in the estimates of many of the energy sources, even those that have

1 It should be noted that the extractive behaviour assumed to underlie the model presented in this paper differs qualitatively from that implicit in the models of Hotelling in another key aspect. Hotelling's model treats stocks of exhaustible resource as assets, whose value is dependent on forward-looking behaviour, and (changes in) whose price is determined with reference to relative rates of return on financial assets by arbitrage arguments. In contrast, the model developed in this paper assumes behaviour which is essentially myopic. It also assumes implicitly (as does Hotelling) that price determination takes place within competitive markets. Taken together these two assumptions imply that observed prices will equal extraction costs. 2 Uranium mining is one example of hard rock mining. 3 Here we attempt to model extraction costs. We would expect that – in the long run, and in competitive markets – prices would tend to track such extraction costs, albeit ‘noisily’.

been utilized for a long time. If it is assumed that the estimates for each resource are normally distributed, then the total value of ultimately recoverable fossil and fissile energy resources is 70,592 EJ. If, on the other hand, the best fitting distribution from each of the resource estimate populations is used, the total value is 50,702 EJ, a factor of around 30% smaller. Focusing on uranium resources, projections of global nuclear power demand and its relative fuel supply requirements are abundant and commonly produced by academic and governmental institutions (see e.g., IAEA, 2013; Matthews and Driscoll, 2010; Pevec et al., 2011; Dittmar, 2011). Concerns over the increasing scarcity of uranium resources for electricity generation have driven the debate over the future of nuclear power (see Gabriel et al. (2012) for a recent example). A useful survey of existing uranium supply estimates is provided by Schneider and Sailor (2008). The paper reviews the most significant estimates of the abundance of uranium extracted from the earth's crust as related to the cost of extracting it. As in this paper, Schneider and Sailor's starting point from which to analyse and produce uranium supply curves is Deffeyes and MacGregor's crustal abundance model which relates ore grades and estimated amount of uranium. Supply curves are then reviewed by estimating their α and β coefficients, which identify the relationship between ore grade and quantity extracted, and ore grade and extraction cost, respectively. The paper maps the resulting supply curves and concludes that important differences exist across estimates, but that all of the estimates suggest that the uranium availability will be higher than the Red Book projections,4 in some cases by an order of magnitude. Schneider and Sailor note that the models existing in the literature ignore the effects of innovation in exploration and extraction. The authors hypothesize that innovation might maintain low uranium prices even in the long run. As mentioned above, the study then considers the long-term price evolution of other minerals (both with time and with accumulated resources extracted) and observes a flat to negative trend. The authors' conclusion is that no study to date had considered longterm unit-based technological learning (in mining) that underlies this behaviour. The paper which is closest to the current one in both its preoccupations and broad approach is that of Matthews and Driscoll (2010). Whilst there are a number of key differences, between this paper and theirs,5 Matthews and Driscoll do rely on Deffeyes and MacGregor's (1978, 1980) crustal abundance model at the core of their work. They investigate, different industry growth scenarios, the impact of policies on industry growth, various recycling options, energy balances and environmental impacts of once-through as opposed to recycling and reprocessing. Their paper also discusses the economic viability of fast reactors, and the use of alternative fuels (thorium and seawater uranium). The findings are that Light Water Reactor technology can sustain a big expansion of nuclear power and be cost competitive well beyond 2050, and that concerns over

4 The ‘Red Book’ (whose most recent release is more properly known as Uranium 2011: Resources, Production and Demand) is an authoritative assessment of uranium supply and demand published jointly by the OECD/NEA and the IAEA every two years. 5 Matthews and Driscoll do not explore the role of productivity growth, or discuss the importance of considering the relative force of cost reducing processes such as learning in a general equilibrium framework (although they do consider learning in their model – see chapter 2.2). They do not draw on explicit uranium demand projections, and rely on (sophisticated) approximations in several instances (such as in considering the implications of improved enrichment technologies). The issue of adjusting productivity growth for diminishing ore grade does not arise in their model. Perhaps most interestingly Matthews and Driscoll assume a joint distribution for parameters characterising economies of scale, ore grade elasticity and learning. This allows them to identify what are effectively confidence intervals bounding the evolution of uranium cost as a function of cumulative nuclear electricity generated.

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resource depletion should not motivate a rushed large scale deployment of alternatives to the ‘once-through’ fuel cycle, since sufficient resources exist to allow for further R&D and a gradual introduction of alternatives. Similar results are achieved by Pevec et al. (2011) who address the issue of sustainability of uranium and thorium resources by modelling various scenarios – based on different expansion rates of nuclear power – out to 2100. Their conclusion is that current nuclear fuel resources are sufficient to support a long term growth of nuclear power up to one third of total energy production, and compatibly with reduction in CO2 emissions. The authors use “conservative assumptions” and delay the introduction of fuel reprocessing and innovative reactors until 2065, or even 2100. They also consider that extraction technology improvements will further extend resource availability. Broadly then, nuclear fuel resources are not seen as a constraint for long term nuclear power expansion – a perspective which is supported by the analysis in the remainder of this paper.

1.2. Plan of paper Section 2 sets out the methodology for this paper, describing the underpinnings and development of a static model whose generalisation (together with the discussion of a number of scenarios which are developed using the generalised model) is a key result of Section 3. In Section 2.1 we address the question of how much uranium is available at different concentrations in the earth's crust – what geologists term ‘grade–tonnage’ relationships. We describe work by Deffeyes and MacGregor's (1978,1980) – building on earlier work by Ahrens (1953) – which characterizes the distribution of different grades of uranium resource via a lognormal distribution. This lognormal distribution will form the basis of the ore grade trajectory which is at the core of the remainder of this paper. In Sections 2.2 and 2.3 we integrate this ore grade trajectory with – respectively – two alternative uranium demand scenarios and three alternative cost structures. The resulting model is described in Section 2.4. This model is static in the sense that it does not give rise to any form of path dependency. In contrast, in Section 3 we develop a truly dynamic model: one which incorporates both the temporal cost reducing process of (multifactor) productivity growth, and the accumulative cost reducing process of learning, and illustrate the way in which this path dependence will fundamentally alter the relationship between extraction cost and ore grade.6 Section 3.1 discusses the importance of factoring potential (temporal) productivity growth processes into uranium extraction cost projections, and presents the results of doing so. Section 3.2 discusses the importance of factoring potential (cumulative) learning processes into such projections, and Section 3.3 integrates both of these types of process into a truly dynamic model. In Section 3.4 we use this dynamic model to explore the implications of the shift in enrichment technology from gaseous diffusion based to centrifuge based technology. The latter is considerably more efficient with regard to energy use, and can be expected to lead to a reduction in the percentage of natural uranium which is left in the tails by the enrichment process. This shift is modelled within an optimizing framework, and the implications for the evolution of uranium costs are explored. Finally, Section 4 contains the main conclusions and policy implications of the paper. 6 It is worth noting that 6% of the global uranium produced in 2009 was a “co-product” from the mining of copper and/or gold (OECD/NEA & IAEA, 2012). Insofar as the cost (of uranium recovery) versus concentration (of uranium) relationship is likely to be more complex in such a context our model is applicable primarily to the 94% of uranium production which is not co-production.

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2. Method and material In this section we develop the first – static – version of our model. The core of this model is an ore grade ‘trajectory’ discussed in Section 2.1 – a relationship between the cumulative quantity of uranium extracted and its grade. This (declining) ‘trajectory’ is integrated with a profile describing the evolution of uranium demand over time (see Section 2.2 below). Effectively this sequence of annual uranium demands will drive the ore grade down the ore grade trajectory, since annual demands represent increments to the accumulated total of uranium which has been extracted. The second aspect of the static model discussed below is the extraction cost structure. In Section 2.3 we explore three alternative parameterizations of a simple mapping from ore grade to cost per unit of uranium extracted. Two of these parameterizations are taken from existing literature, a third is based on estimation from a hitherto unreleased IAEA database. In Section 2.4 we present a number of scenarios, designed both to locate our static model relative to existing models of the uranium cost/accumulated output relationship and to explore the implications of alternative cost structures on the evolution of uranium costs over time. 2.1. A lognormal model of uranium ore grades There is considerable uncertainty over the amount of uranium in the earth's crust – and even more uncertainty over how that amount is distributed between different concentrations.7 Given that the resources required to extract uranium from a given deposit are likely to increase as the concentration of uranium in that deposit decreases, this distribution – as characterised for example by the prevalence of parts of the crust with higher than average concentrations, relative to those with lower than average concentrations – will be key to determining the economic viability of exploiting more or less of the uranium resource. This paper adopts an approach to modelling this distribution which originated in work by Ahrens (1953), who noted that the abundance of trace elements in granites could be well represented by a lognormal distribution. Authors such as Harris (1988) and Deffeyes and MacGregor's (1978, 1980) built on this work, noting in the case of Deffeyes and MacGregor that “Our approach has been to ask whether the distribution of uranium in the earth's crust can be well approximated by a bell-shaped [lognormal] curve.” Deffeyes and MacGregor acknowledge that unimodal distribution such as the lognormal may not always be appropriate. In this context it is important to note that Skinner (1976) and others have argued that a bimodal distribution may be more appropriate for uranium – and for minor metals (those that make up less than 0.1% of the crust by weight) more generally. In contrast to the unimodal (single lognormal) distribution the bimodal distributions features distinct lognormal distributions – the leftmost one for common rocks, the rightmost one for high concentration (and thus economically recoverable) ores.8 Deffeyes and MacGregor hypothesize, however, that in contrast to – for example – chromium, the “enormously 7 Concentration or crustal abundance is typically measured in parts per million or ppm. 8 The two distributions may be regarded as falling on either side of a so-called mineralogical barrier, a limiting percentage by weight such that at concentrations in excess of the mineralogical barrier ores will form (i.e., uranium will be available in relatively ‘easily’ exploitable forms) while at concentrations below the mineralogical barrier uranium atoms will substitute for atoms which resemble them in size and electrical charge, requiring that the common rock within which the uranium is contained be “pulled apart” chemically at high cost (not least in terms of energy requirements) if the uranium is to be recovered. See the discussion in Skinner (1976) for further details.

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complex range of geochemical behaviour and widely different kinds of economic deposit” exhibited by uranium make it more likely that its distribution might be adequately described by a (unimodal) lognormal. In order to test this hypothesis they estimate the masses of all the various geologic ‘units’ which contain uranium, and draw on existing literature on average uranium concentrations in those units in order to rank them in the order of concentration – resulting in the histogram shown in Fig. 1 (taken from Lehmann (2008)). They go on to suggest that this histogram can be well fitted by a lognormal distribution, from which key parameters can be estimated. In particular, approximation of the histogram in Fig. 1 by a continuous density function allows the derivation of a supply elasticity at each ore grade – i.e., the percentage increase in available ore that will result from a given percentage decrease in ore grade. This supply elasticity has played a significant role in work by a number of authors of papers including the majority of the long-term uranium supply models reviewed by Schneider and Sailor (2008), and more recently the work of Matthews and Driscoll (2010). Clearly it will decline as the ore grade declines, and so the exact value will depend on the grade which is being considered. As noted by Deffeyes and MacGregor, the ore grade elasticity over the range of concentrations currently being mined is of particular interest, as being indicative of the increase in recoverable uranium likely to result from reductions in grade which are in immediate prospect; the value of the elasticity over the relevant range suggests that a 10-fold decrease in ore grade will result in a 300-fold increase in recoverable uranium. Schneider and Sailor note that values for the ore grade elasticity ranging from 2.48 to 3.5 can be found in the literature on uranium supply. Rather than take a single elasticity value in this paper, we acknowledge explicitly that this value will vary by using Matthews and Driscoll's explicit parameterization of the

Deffeyes and MacGregor lognormal distribution (see parameter values in Table A3.2 of Matthews and Driscoll) to model the oregrade/ore-availability cumulative distribution function at a high level of resolution in our model. 2.2. Uranium demand We use IAEA's Reference Data Series no. 1 (IAEA, 2013) to estimate projected uranium demand requirements over coming decades. IAEA (2013) is an annual publication projecting nuclear power, energy and electricity estimates up to 2050. The data sources for the RDS-1 estimates vary according to the type and include the IAEA, the United Nations Department of Economic and Social Affairs (particularly data on population), OECD/NEA, the World Bank among others. The data are presented in two scenarios, where low and high estimates reflect different but not extreme sets of assumptions regarding factors affecting nuclear power deployment at country, regional and global levels. The resulting estimates are not intended to be predictive, but aim to provide plausible range of nuclear power capacity and generation levels worldwide. The low estimate represents a “conservative but plausible” case, whereby current trends in market structure, technology, resources and regulation continue in virtually unchanged fashion, and country capacity expansion plans are not necessarily met. The high case projections relax these assumptions, but they still represent a plausible and technically feasible scenario. In particular, in the high estimate nuclear expansion in the Middle East is assumed to be fully pursued and climate change policy measures generally adopted. Nuclear power forecasts reflect both the current macroeconomic difficulties many major economies have experienced in the past few years, and unfavourable market conditions vis-à-vis competing

Fig. 1. Uranium distribution in the earth’s crust.

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technologies: subsidized renewable energy capacity expansion and the low natural gas price. Projections are made difficult by the uncertainty over nuclear safety generated by the Fukushima Daiichi accident, This accident contributed to delay or closure of some of the planned nuclear power expansion or extension projects. However, long run projections still see nuclear power as a prominent electricity generating technology, driven by economic and population growth, and climate change and energy security concerns. In this context IAEA (2013) revised downwards its 2012 capacity estimates to 2030, by about 20 Gw(e) in both low and high scenarios. Nuclear electricity generation is estimated at 2346 TWh in 2013, and is expected to grow to 3548 TWh in 2050 in the low estimate scenario. The high estimate scenario projects nuclear power generation to 5689 TWh in 2030 to reach 8971 TWh in 2050.

2.3. Modelling the extraction cost structure We draw on three alternative cost functions in the scenarios developed below. The starting point for all three is a fairly general relationship between ore grade and cost (a cost function), which can be written as follows9:

β K P0 ð1Þ ¼ K0 P where K is the ore grade of uranium (ppm U), K 0 is the reference ore grade for model calibration, P is the long term marginal production cost of uranium, P 0 is the reference long term marginal production cost for model calibration, and β is the fit parameter. Schneider and Sailor (2008) identify various estimates for the β coefficient above. In the simplest model, there is an implicit assumption that the cost of extracting uranium is inversely proportional to its grade concentration (thus β ¼ 1). The resulting hyperbolic cost function can be considered the starting point of our uranium demand model. Modifying this assumption, other models obtain results that place more or less weight on the importance of declining ore grades to determine extraction costs. Kim and Edmonds (2005) estimate the β coefficient by fitting the available data which relate ore grade to uranium extraction costs. In their study, they use the average grade extractable at the upper bound of the Red Book cost brackets ($40, $80, and $130) to obtain a β coefficient of 0.78. In other words, as ore grades decline, extraction costs increase more than proportionately. Using more recent data, based on a survey carried out in the framework of the IAEA's UDEPO database,10 we estimated a new cost function to underlie our uranium extraction cost model. The database contains detailed information about deposit physical characteristics, including ore grades, and each deposit is associated with a cost category. Specific extraction costs associated with each deposit are not available, but an ordered categorization of cost profiles still contains valuable information for analysis. Earlier work (e.g., Kim and Edmonds, 2005) used point observations, such as the average value within the category, or the upper or lower bound of each bracket, to estimate a linear regression and obtain the desired coefficient. The limitation of 9 It is important to note that in general ore grade will not be the only determinant of extraction cost (although it will likely be the most significant). In particular, a deposit's size (‘reserve tonnage’) will influence costs insofar as it will determine the volume of uranium over which fixed costs (capital costs) can be spread. Given that the central issue addressed by this paper is the that of upward pressure on costs as higher ore grades are exhausted, we follow other authors in focusing on the role of ore grade in determining costs. 10 The World Distribution of Uranium Deposits (UDEPO) is a database – collated and maintained by the IAEA – on technical, geographical and geological characteristics of worldwide uranium deposits.

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this technique is in the loss of relevant information as the fitting line is forced to pass through the imposed value. To preserve as much information as possible, we estimated a new β coefficient by applying the interval regression technique, which associates the point observations regarding uranium ore grades with the corresponding cost ranges within a probability of 95%, without imposing stricter constraints. The obtained coefficient is significantly higher, with β ¼2.25. Halving the ore grade or extracted uranium results in a less-than-double increase in extraction costs. This result allows significant more optimism as to whether or not the remaining natural uranium resources will be sufficiently available at a viable cost to sustain nuclear power generation. In our model, we use the hyperbolic cost function (β ¼1) as the starting point for further analysis. Kim and Edmonds (β ¼0.78) estimate is used as a pessimistic relationship between ore grade and cost of extraction, while our estimated β¼2.25 will be used as an optimistic cost function.

2.4. A static model: ore grades, cost structures and demand growth Fig. 2 illustrates the relationship (in cost/cumulative extraction space) between our model – with three alternative cost structure parameterizations – and the ‘optimistic’ and ‘conservative’ cases presented by Schneider and Sailor (the starting value is normalized to 1 at 2.59 Mtu of cumulative uranium extracted, to allow comparability of curve slopes). Schneider and Sailor's simplest ‘optimistic’ and ‘conservative’ curves assume that the change in uranium extraction cost is the inverse of the decrease in ore grade. In other terms, both assume a β coefficient equal to 1. Crucially, what differs between the two curves is the underlying assumed elasticity capturing the relationship between ore grade and the quantity of uranium extractable (denoted in their model by α). Their “optimistic” and “conservative” curves assume roughly the highest (3.32) and lowest (2.48) values for the α coefficients identified in their literature survey (Schneider and Sailor, 2008). As noted above, in contrast to using a fixed elasticity estimate our model implements the Deffeyes and MacGregor ore grade/ cumulative extraction relationship via explicit derivation of a continuous high resolution ore grade trajectory – essentially a parameterization of the Cumulative Distribution Function (CDF) of the lognormal. The fact that a curve derived from using this approach with a value of β ¼1 (what we will refer to as our ‘static base case’) lies so close to Schneider and Sailor's ‘optimistic’ curve suggests that a value of α¼3.32 is a better approximation to the underlying shape of that CDF than the ‘conservative’ value of 2.48. In Fig. 2 we also chart static curves corresponding to values for β ¼0.78 and β ¼ 2.25, corresponding – as discussed in Section 2.3 – to a pessimistic and an optimistic relationship between ore grade and cost of extraction respectively. Fig. 3 integrates the ‘low [demand] estimate scenario’ described in Section 2.2 with our static model. In other words, we allow the annual increments of cumulative uranium extraction to drive the ore grade down the Deffeyes and MacGregor trajectory, while assuming that – for example in the β ¼1 case – a halving of ore grade will cause a doubling of unit cost. This allows us to translate the curves shown in cost/cumulative extraction space in Fig. 2 into cost/time projections out to 2100. Notwithstanding the fact that in Fig. 3 curves are projected over time, they remain static in that they assume neither temporal (MFP growth) nor accumulative (learning) processes. Effectively, MFP growth is restricted to 0% p.a. and learning is set at 100%. Having shown that this ‘special’ case of our more general model yields similar results to those from at least one of the models set out in Schneider and Sailor, we relax these restrictions in the next

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Fig. 2. Extraction cost scenarios by cumulative extraction; compared with Schneider & Sailor (2008).

Section, and explore the dynamic (and path dependent) consequences for uranium costs.

3. Results and discussion This section will emphasize important contribution of allowing interaction between temporal (MFP growth based) cost mitigating processes, accumulative (learning based) cost mitigating processes, and the evolution of demand. Higher demand will lead to faster learning – which will tend to reduce unit extraction costs – but will also result in ore of a given quality being extracted sooner rather than later – limiting the extent to which MFP growth can reduce costs. In this sense “history matters” – specifically the unit extraction cost for ore of a certain ppm will depend not only on its location on the ore grade trajectory, but also on the rate at which past uranium demand has driven the mining sector's extractive activities down that trajectory In Section 3.1 we discuss productivity growth in mining. We highlight two important issues which arise when attempting to incorporate MFP growth into uranium cost projections: (1) the need to identify a reasonable estimate of mining productivity growth which is adjusted for ore quality (in order to avoid ‘double counting’ the ore grade effect in our model); and (2) the need to focus on productivity growth in the mining sector relative to that in other sectors. We go on to present scenarios which build on those in Section 2.4 but incorporate the effects of reasonably parameterized MFP growth processes. In Section 3.2 we discuss learning, noting once again that it is relative learning that matters. We then present scenarios which,

again, build on those in Section 2.4 but incorporate the effects of optimistic and pessimistic relative learning assumptions. Finally in Section 3.3 we combine both MFP growth and learning into a dynamic base case. In addition to illustrating possible implications for the evolution of uranium costs over time, we illustrate the nature of the path dependency introduced by the combination of MFP growth and learning. 3.1. Productivity growth Ceteris paribus the exploitation of poorer grades of uranium ore will tend to lead to increased extraction cost. However, a key feature of the model developed for this paper is the recognition that even as movement down a trajectory of declining ore grades tends to lead to increased extraction costs (as emphasized by – for example – van Leeuwen and Smith (2008)), so improvements in relative mining productivity have the potential to mitigate such cost escalation over time. This section examines the three-way relationship between declining ore grades, extraction cost and relative productivity growth. For our productivity measure we rely on the concept of Multi-Factor Productivity (MFP) growth, an indicator which accounts for the change in output from one year to the other (value added) that is not explained by changes in inputs such as labour and/capital11 (see e.g., Topp et al., 2008). Our focus will be on relative productivity growth because we expect relative sector specific costs to be homogeneous of degree 11 MFP growth can be decomposed into three components: technological change, technical efficiency and scale effects – see BREE (2013).

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Fig. 3. Extraction cost scenarios to 2100; compared with Schneider & Sailor (2008).

0 in relative sector specific MFP – e.g., a doubling of MFP in sector A will, if matched by a doubling of MFP in sector B, leave relative costs unchanged between these two sectors. Several studies seek to assess the impact of productivity growth on mining costs. Measures of change in mining productivity include labour productivity (Shropshire et al., 2008; Parry, 1997), energy use per ton of mined ore (Norgate and Jahanshahi, 2010; van Leeuwen and Smith, 2008) and Multiple Factor Productivity (MFP) growth, as in BREE (2013) and Topp et al. (2008). Pool (1994) analyzes long term trends in prices and production for various metals to assess the impact of technological change. Observing near-zero average price changes over time, the study equates the rate of increase in production with technological change rate. On the one hand technological change allows for exploitation of ever-decreasing ore grades at observed relatively constant prices; on the other hand, due to the Deffeyes and MacGregor crustal relationship, lower ore grade deposits are increasingly more abundant than higher quality resources. As a consequence, Pool (1994) concludes that, at constant prices, the effect of technological change is to provide an “ever-increasing resource base” for future metal extraction. Parameterization of the productivity growth assumed by our model in this Section will draw on recent work (BREE, 2013; Topp et al., 2008) which has sought to arrive at an estimate of productivity growth adjusted for the impact of declining ore grade on output. BREE and Topp et al. calculate MFP in the mining industry in Australia to examine the effects of technological change and natural

resource input bias on mineral price change. The studies, based on Australian Bureau of Statistics (ABS) data, find that unadjusted MFP in the mining sector declined by 30% between 2000–2001 and 2009–2010. However, when adjusted for deposit quality depletion and production lags, MFP growth becomes positive, with rates between 2.3% and 2.5% from 1985–1986 to 2009–2010 (BREE, 2013; Topp et al., 2008). These figures represent absolute MFP growth in the mining sector, whereas – as discussed above – it is relative MFP growth which will drive changes in mining sector costs. While estimates of global MFP growth have identifies figures as low as 0.3% p.a. (UNIDO, 2007) in this paper we develop scenarios which are based on relative annual MFP growth rates of 0.1% and 0.3% – figures which can be argued to be very conservative. 3.2. Learning We introduce the relative learning effect to account for those changes in uranium output that are not explained by increases in factor input levels, nor by changes in MFP. Learning can be thought of as changes over time in resource production which depend on improved practices within existing technology constraints. Once again, as is the case with MFP, it is relative learning that matters. Given the range of estimates of the cost reducing effect of learning commonly found in the literature (typically from 70% to 90%, implying that a doubling of accumulated production implies 30% and 10% cost reductions respectively) we adopt a conservative value of 95% – beyond the high end of this range. Our

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assumption implies that a doubling of accumulated uranium output will result in a very modest 5% reduction in uranium extraction costs relative to the reduction in production costs elsewhere in the economy. We use the cost coefficient corresponding to 95% learning to parameterize our cost function and thereby complete a crustal abundance, MFP and learning effect long-term uranium cost model.12

3.3. A dynamic base case: temporal and accumulative processes and path dependency Fig. 4 provides perhaps the best illustration of the path dependency which arises from combining temporal and accumulative cost reducing processes in our most general model. Fig. 4 can be understood as follows: for any value of β, if there is no MFP growth and 100% learning suppose we get curve A. Then if we assume o100% learning (95%) and 4 0% p.a. MFP growth (0.3% per annum) and a demand profile that drives ore grade slowly down the Deffeyes MacGregor (1978, 1980) curve then by the time we reach an ore grade as low as p ppm we have gained some additional cost reduction from learning, and some additional cost reduction from the MFP growth that has taken place (curve B). If we move faster down the curve, (driven by a higher demand profile) then by the time we reach p ppm we have achieved the same cost saving from learning (which just depends on accumulated output) but less cost saving from MFP growth (because we've had fewer periods of such growth) – yielding curve C. The final scenario outlined in this Section is illustrated in Fig. 5. What is notable in this figure is that under rather conservative assumptions on (relative) MFP growth and learning, and with a reasonably plausible cost structure (the upper trajectory corresponds to a β value of 1, the lower to a value of 2.25), we arrive at a situation of declining uranium extraction costs over time. It should be noted that such declines in metal (and other commodity) prices have been common over the past 100 years, as discussed in Section 1.1. 3.4. Improved energy efficiency in enrichment: implications for supply adequacy In this Section we deploy the dynamic model developed above to explore the implications of a shift from gaseous diffusion uranium enrichment technology to the more energy efficient centrifuge enrichment technology. Insofar as this shift results in a fall in the cost of separative work (i.e., lower $/SWU) we anticipate that it will result in a “more economical” use of uranium, which will manifest itself in the form of a lower tails assay.13 The enrichment of natural uranium is an important stage of the light water reactor fuel cycle. U235 (the fissile material commonly used as fuel in such light water nuclear reactors) must be at concentrations of 3–5% for use in fuel but occurs at much lower concentration in natural uranium (0.71%). So, after mining, milling, 12 We assume throughout a single (relative) learning rate associated with the main extraction technologies (open-pit, in situ leaching and underground mining). In reality it is possible – even likely – that different technologies may have somewhat different learning rates. However, it is important to note that all of the scenarios presented in the paper assume learning rates which are deliberately conservative. The main messages of the paper (the existence of forces liable to counter the influence of decreasing ore grades on extraction cost, and the importance of ‘path dependence in determining the time profile of those costs) would remain valid if the technology- and/or deposit-specific learning rates were to be even more moderate – provided those rates were (strictly) less than 100%. 13 The analysis below, which leads to the conclusion that the shift away from gaseous diffusion will result in a lower tails assay, is in line with the findings of other authors – see Schneider, et al. (2013).

Fig. 4. Path dependency in extraction cost by cumulative extraction relationship.

and conversion into UF6 gas, natural uranium must be ‘enriched’ into so-called Low-Enriched Uranium (LEU). Enrichment tailings are a by-product of this process. Fig. 6 illustrates the main stages of the front-end of the ‘once-through’ uranium fuel cycle. The uranium enrichment process can be carried out mainly by use of two alternative technologies: gaseous diffusion and centrifuge. The former was the only technology in use until the 1980s, when centrifuge facilities began to capture increasing market share (see Rothwell, 2009). Centrifuge technologies have a considerable advantage in terms of cost savings, particularly in electricity consumption. Rothwell calculates the levelized costs of both technologies: electricity consumption of diffusion facilities represent over 80% of total costs, or 2500 kWh/SWU, compared to 62 kWh/SWU in the case of centrifuge technologies, or less than 10%. Diffusion technologies are therefore highly sensitive to electricity costs. In levelized terms, centrifuge technologies show costs between 3 and 4 times lower than gaseous diffusion enrichment processes. Observing current trends in the enrichment market, Rothwell predicts that diffusion technology will be retired in the next decade. This reduction in cost and the use of more efficient technologies, coupled with relatively high uranium market prices, have allowed utilities to reduce uranium requirements and specify lower tails assays at enrichment facilities (OECD/NEA & IAEA, 2012). ESA (2013) estimates that the average tails assay in the EU was 0.24% (down from 0.25% in 2011), in line with the trend of increasing separative work requirements for the coming decades for EU facilities pursuing higher enrichment assay and lower tails assay. In line with these trends, we incorporate in our uranium demand model changes in enrichment tails assays requirements over time, as obsolete technology is replaced by more efficient methods. In this scenario, we investigate the implications of a shift from gaseous diffusion uranium enrichment technology to the more energy efficient centrifuge enrichment technology. Insofar as this shift results in a fall in the cost of separative work (i.e. lower $/SWU) we anticipate that it will result in a “more economical” use of uranium, which will manifest itself in the form of a lower tails assay. Exactly how much more “economical” that use can be expected to be can be quantified by setting the derivative of an expression for the cost of low-enriched uranium fuel with respect to the parameter measuring tails assay equal to 0 (see Bunn et al., 2003, pp. 93–95). Focusing solely on the enrichment stage of the fuel fabrication process, ignoring fractional losses during that stage, and assuming for simplicity that enrichment takes place “overnight” (i.e., ignoring time value of money considerations) we can write "      # V xf  V x^ t 2V x^ t 1 1  2x^ t þ ¼γ þ  xf  x^ t xf  x^ t 1  2x^ t x^ 1  x^ t

ð2Þ

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Fig. 5. Extraction cost dynamics with 0.3% relative MFP growth per annum and 10% relative learning.

Fig. 6. Front-end of the ‘once-through’ uranium fuel cycle.

where x^ t is the optimal tails assay, xf is the assay of the feedstock uranium, V ðxÞ ¼ ð2x  1Þlnðx=ð1  xÞÞ; C S is the cost of separative work ($/SWU), C U is the cost of uranium ($/kgU) and γ ¼ C S =C U . Although Eq. (2) does not have an analytical solution it can be approximated via an exponential expression (see A.16 in Bunn et al.) or else solved manually. Noting that the expression in A.16 fixes the feed assay at 0.711% (see note 6 in Rothwell), we adopt the latter approach here,

allowing movements in the cost of separative work and uranium to drive movements in x^ t over time. Specifically, we first project the operating cost per SWU (i.e., the numerator of γ) for gaseous diffusion and centrifuge plants using the cost breakdowns presented in Rothwell together with projections of labour, electricity and materials costs out to 2100. In doing so, we assume that gaseous diffusion enrichment capacity is phased out by 2020 and that replacement and additional enrichment capacity is brought into service to meet demand. In other words, the gaseous diffusion (GD) will be aiming for a higher tails assay than the centrifuge will be aiming for. At the same time, the cost of uranium (i.e. the denominator of γ) will be driven by the movement to lower grade ores and the (mitigating) growth in relative productivity and accumulated learning. For each time period in the projection then, we solve for x^ t using γ ¼ C S =C U and Eq. (2).14 Since the ratio of uranium feed to enriched product R is given by R ¼ ðxp  xt Þ=ðxf xt Þ (where xp is the assay of the product) we can then calculate the feed requirement (i.e., the amount of uranium required) by simple multiplication. Note that for the (limited) period during which gaseous diffusion and centrifuge technologies are anticipated to ‘coexist’ we recognize that plants using these different technologies would aim for different tail assays (reflecting their different SWU costs and therefore values of R), but following Rothwell we assume the higher cost profile (the GD technology) as the marginal price the market will take, as expected in a non-competitive oligopolistic market such as the enrichment one. Reducing tails assays in the enrichment phase of uranium fuel cycle implies a relative decrease in uranium requirements for electricity generation. The Red Book estimates that a 0.05% reduction from the currently used 0.3% average enrichment tails assay would, ceteris paribus, reduce uranium demand by 9.5%. Pool (1994) calculates a similar impact of tails assays reduction on total uranium demand. We illustrate the reduction in accumulated global uranium demand following technological change in uranium enrichment in Fig. 7. Fig. 7 shows profiles for uranium demand based on the electricity

14 Solution is via a Generalized Reduced Gradient (GRG) nonlinear optimization algorithm, as appropriate for a problem such as Eq. (2) which is nonlinear but smooth.

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Fig. 7. Accumulated uranium requirements to 2100 (with vs without tails optimization).

generation low estimate projection in IAEA, (2013); RDS, extrapolated to the year 2100, assuming a generation of 30,000 kWh per kg of natural uranium, following WNA (2012). The upper curve illustrates the demand for uranium based on historic tails concentration values (typically around 0.3%) while the lower profile assumes a shift to a new optimal tails concentration, and is based on the (evolving) R coefficient estimated using the calculations on optimal tails described above. The effect of technological shift in enrichment processes is reflected as an offset between the two curves, representing a reduction in long term uranium demand. By 2100, as shown, the accumulated reduction in natural uranium demand is approximately 1.25 Mtu. Within the framework outlined above, with 0.3% per annum relative MFP growth, and a 95% learning rate this results in a cost of uranium around 2.3% lower than would have been the case in the absence of the shift in enrichment technology and consequent tails re-optimization.

4. Conclusion and policy implications This paper has sought to demonstrate the importance of productivity growth and learning as processes which can be expected to counteract the tendency of the exploitation of lower uranium grades to result in significant increases in uranium costs. It has shown that – under rather conservative assumptions on the dynamics of these processes – the rate of increase of such costs is significantly attenuated. Indeed in some cases – again, for rather conservative assumptions on productivity growth and learning – it may not be unreasonable to anticipate decreasing costs (as shown in Fig. 5 above). From a policy perspective it is important to recognize and account for productivity growth and learning processes in modelling the cost dynamics of uranium supply. Although it has long been recognized that nuclear energy has the potential to make a significant contribution towards GHG-emission reduction globally (for example the IPCC (2007) estimates that nuclear energy has the largest and lowest cost GHG reduction potential in electricity generation) the desirability and feasibility of relying – to any significant degree – on nuclear energy as an alternative to GHGemitting fossil fuels are clearly dependent on the degree to which the costs of nuclear energy can be expected to escalate as poorer quality resources are exploited. In terms of determining priorities for government funding of R&D, the need to reduce reliance on the currently predominant ‘once-through’ nuclear fuel cycle in favour of cycles based on reprocessing is more (or less) urgent as cost escalations anticipated to arise in the event of continued reliance upon the former are more (or less) significant. Similarly, the need to provide incentives to encourage exploration for, and

development of, resources of fissile material other than uranium may be perceived as less pressing if the scenarios presented above are viewed as plausible, as would the necessity of achieving rapid improvement and deployment of ‘breeder’ reactor technologies.

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