This thesis is intended to contribute to policy analysis on nuclear energy planning, and also as a contribution to applied mathematics. From point of view of nuclear policy analysis, this thesis is not designed to offer realistic detail on nuclear engineering itself, which is of second order relative to our chosen problem. The goal is to address some large scale problems in the management of the world stocks of two important nuclear fuels, Uranium (an economically finite natural resource) and Plutonium (the result at first of policies for Uranium burning, and later of policies on fast reactor breeding).This thesis assumes, as a ‘political’ working hypothesis, that at some future timeworld governments will agree urgently to decarbonise the world economy. Up tothat point, assuming no previous large progress towards decarbonisation, basic world electricity consumption will have continued to grow at its historic average of 1.9% compound. This rate is hypothetically a combination of slower growth in the developed world and faster growth in the developing world. On this hypothesis, a necessary but not sufficient condition for decarbonising the economy would be the complete decarbonisation of future basic electricity demand, plus the provision of sufficient extra decarbonised electricity supply to take over powering all land transport. The demand for electricity for land transport at any time is assumed to equal (in line with historical experience) an increment of approximately 20% above the contemporary basic world demand for electricity. The hypothetical scenario for achieving this model of decarbonisation, without major stress to the worlds economic and social system, is to expand nuclear power to meet the whole of basic electricity demand. This would leave intermittent renewable sources to power the intermittent electricity demands of road transport.This thesis explores the above hypothetical future in various ways. We first listpublished forecasts of future Uranium use and future Uranium supply. These suggest that presently known Uranium reserves can meet demand for many decades. However on extrapolating the cumulative demand for Uranium that results from the above working hypothesis, we find that if a dash to decarbonise world electricity supply begins immediately, this would consume a very large multiple of presently known Uranium reserves. Sustaining that decarbonisation for only a few more decades of demand growth would consume further large multiples of the known Uranium supply. A delay in the start of the dash for decarbonisation by only a few decades greatly increases the cumulative Uranium demand needed to reach decarbonisation even briefly.Therefore the sustained achievement of decarbonisation, in a world economy ofthe historical type, requires such large Uranium resources that a successor fuel cycle is required. This thesis models only the case of a Uranium-based fast reactor fuel cycle, since this cycle can in principle consume all the cumulative past and future Plutonium stockpile, and can then meet its own Plutonium needs for a long period (hundreds or thousands of years), allowing ample time for economic adjustment. However a commercially effective fast reactor technology is some decades away.Up to this point, the thesis has only added two physical factors to the existingdebate on Uranium needs: namely cumulative growth of electricity demand at itshistoric rate, and a political choice for 100% physical decarbonisation of the electricity supply.The mathematical and economic contribution of the thesis then begins. We askthe following questions:1. Under what circumstances would profit-maximising investors (or an economicallyrational centralized economy) actually choose to build enough reactors to decarbonise the world electricity supply?2. Would the need for investors to make a profit increase or decrease the life ofthe economically accessible Uranium reserves?3. What is the effect of accelerating or delaying the technical availability of fastreactors?4. When if at all would there be shortages of Uranium or Plutonium?5. Under what circumstances would rational investors chose a smooth and physically feasible handover from Uranium burning to fast reactors, thus avoiding the need for a large but temporary return to fossil fuel?The above questions set a mathematically demanding problem: four interactingphysical stocks and two physical flow variables ( control variables) must simultaneously be optimized, along with their economic effects. The two control variables are the rate of building or decommissioning Uranium burners, and the rate of building or decommissioning fast reactors. The first control variable drives the cumulative stock of Uranium burning reactors, and hence the resulting maximum physical supply of electricity (with sales income bounded by demand), less the costs of operating, and of new investment. This variable also drives the cumulative depletion of the finite economically extractable reserve of Uranium, and it simultaneously drives an increase in the free Plutonium stock (from Uranium burning). The second control variable, the rate of building or decommissioning fast reactors, drives a decrease in the Plutonium stock (from charging new fast reactors) and it drives a cumulative increase in the stock of fast reactors. This affects the resulting rate of supply of electricity and of income less operating costs and new investment costs. The combined sales of electricity from the two reactor systems is bounded by the total world demand for electricity.The thesis explores this problem in several stages. A fully stochastic form of theproblem (stochastic in the price of electricity) is posed using the tools of contingentclaims analysis, but this proves intractable to solve, even numerically. Fortunatelythe price increases needed to impose decarbonisation are very large, and they result from discrete and long lasting government actions. Hence for policy analysis it is adequate to assume a large one off change in electricity price, and observe the progress towards the resulting evolving equilibrium. This problem is also addressed in stages, firstly we optimise the Uranium burning and the fast reactor cycles in isolation from each other, then we allow some purely heuristic and manually controlled interaction between them. Finally we solve, and economically optimize, the total dynamic system of two physical control variables and the resulting four interacting dependent stock variables. As far as we know this is the highest dimension system yet optimised by these particular state space methods .Results show that the electricity price can be set high enough to motivate profitmaximising investors to invest enough in Uranium burning achieve rapid decarbonisation, followed by a smooth disinvestment and simultaneous reinvestment in fast reactors, which smoothly transfers the total (growing) electricity demand a successor fast reactor system.Sensitivity analysis shows that setting the electricity price too low achieves nothing, or Uranium burning only, while setting it high achieves decarbonisation (and consumes the economically available Uranium supply) too fast, leaving a supply gap to be filled by fossil fuel use, before fast reactors can take over. Delayed arrival of the fast reactor technology greatly increases the need for Uranium.Conversely, an unrealistically early arrival of fast reactor technology means thatthe fast reactors start to be built immediately, but only slowly, because too littleUranium has yet been burnt to provide enough Plutonium starting charges. Yet inthis scenario the time taken to exhaust all Uranium is longer than when fast reactors become available later. Also individual Uranium burners have much longer economic lives, while the time evolution of the Plutonium stock has two large peaks, separated by a dip close to zero. Our mathematical optimization method is a general one, so although this last scenario is practically unrealistic for the real world Uranium- Plutonium problem, it illustrates the possibility of quite subtle solutions in other problem contexts.
|Publication status||Published - Jan 2013|
- PDE Real Options Finite-Difference Uranium Plutonium Nuclear Power Systems