The present disclosure is in the field of transuranic material processing. It is particularly, but not exclusively, concerned with reduction in the prevalence of Plutonium and other actinides.

Background

The estimated world stockpile of transuranic (TRU) waste is over 3 kilotonnes, which represents a major economic and environmental liability. This waste is composed of a number of isotopes of transuranic elements, some of which have very long half lives, some so long that it is very difficult to demonstrate the secure storage of waste over the practical lifespan of any storage solution. Thus, there is a desire to find methods of processing the waste, so that natural radioactive decay need not be relied upon.

Approaches to this processing of waste generally involve the imposition of nuclear reactions on such materials, by active intervention. This process of actively imposing nuclear reactions on such materials, is known as incineration. The reader will appreciate that the use of this term in this context does not imply a chemical process, but of course chemical processes may also ensue, depending on the chemical reactivities of the products of such nuclear reactions. It has been proposed to incinerate waste, on a large scale, in a critical or subcritical fast reactor. It is envisaged that this approach could achieve the virtual elimination of TRU waste. However, the need for a low moderation coolant presents multiple challenges and is not commercially proven. Subcritical fast reactors require reliable and economic accelerator technology. Given the large number of reactors which would be required to incinerate waste, this represents a substantial barrier to effective implementation. The nuclear industry is by its nature, and by regulation, risk-averse, and the adoption of new, unfamiliar and unproven technology is not desirable.

In contrast, Light Water Reactor (LWR) technology is commercially proven and well understood, with materials technology now at a stage in development that it is possible to design for at least 60 years of life. The Thorium (Th) fuel cycle appears to exhibit desirable features in fulfilling the aim of reducing long-term nuclear waste liability, as only a small quantity of TRU material is bred from Th-232. Th-based fuel does not require enrichment and is relatively abundant. In contrast, incineration of waste in an LWR, partially or completely fuelled with Uranium (U), reduces TRU destruction as additional TRU material will be bred from U-238. However, adoption of the Thorium cycle in reactor technology has been slow. This is partly because of a legacy of reactors designed with the development of nuclear weapons in mind. Also, significantly, Th-232 is not fissile, unlike U-235. Instead, fissile U-233 is bred from Th-232 when it absorbs a neutron. The chain reaction in a Th reactor cannot be self sustaining until sufficient U-233 has been bred. Thus, in a Thorium reactor, it is necessary to initiate nuclear reactions using a fissile isotope or neutron source. Extensive studies have been conducted by the JAEA to develop a Reduced- Moderation Water Reactor (RMWR) (Uchikawa S, Okubo T, Kugo T, Akie H, Takeda R, Nakano Y, Ohnuki A, Iwamura T: Conceptual Design of Innovative Water Reactor for Flexible Fuel Cycle (FLWR) and its Recycle Characteristics. Journal of Nuclear Science and Technology, Vol. 44, No. 3, p. 277-284 (2007)).

By reducing the gap between nuclear fuel pins and possibly by increasing the void fraction (VF) of the coolant, the degree of moderation can be reduced, resulting in a faster neutron spectrum. Downar et al. (Downar T J, Xu Y: The Utilisation of Thorium Fuel in a Generation IV Light Water Reactor. Advanced Reactors with Innovative Fuels. Workshop Proceedings, Chester, UK 22-24 October 2001 . OECD NEA, BNFL) modified this concept to investigate a fuel mixture of Th and weapons-grade Plutonium (Pu). However, making variations of this type can result in mechanisms being created which exhibit positive feedback properties. There may also be significant material and thermal-hydraulic (TH) challenges related to this design.

Clearly, the above research was carried out on the possibility of destruction of weapons-grade Plutonium. This specific research does not appear to lend itself to the destruction of "dirty" Plutonium - the mixture of TRU elements (of which Plutonium isotopes may admittedly form a large proportion) which arise from the normal operation of a Uranium fuelled LWR.

It is worth noting that the nature of waste varies with perception. In a "regular" LWR, waste is anything which hinders breeding and fission of fissile material, and causes inefficiency in the nuclear chain reaction fundamental to the operation of the reactor. Thus, for a reactor fuelled with Uranium isotopes, particularly enriched Uranium (i.e. U- 238 with an artificially raised concentration of U-235), waste will consist of material based on elements of higher proton number than Uranium, such as Plutonium (Pu) and the minor actinides (MA). While some isotopes of Pu are fissile, the reactivity of the waste will decrease over time in the reactor. These actinides are not easily rendered useful, and can be a hindrance to effective operation of a reactor.

By increasing the concentration of the fissile isotopes through enrichment, the Pu can be used to make weapons, which is undesirable. In general, such radioactive waste is hazardous if released, through accident or a 'dirty bomb'. It can also present substantial difficulties regarding its safe disposal and/or storage. For instance, the long half lives of many of the actinide isotopes mean that it is very difficult to design a suitable storage facility with performance predicted for a suitable lifetime relative to the natural decay of the waste. In particular, the half life of Np-237 is about 2 million years, so the expectation that a storage facility will exist at a time in the future when such material has decayed to a negligible amount, is difficult to justify.

For a Thorium reactor, it will be appreciated that a wider definition of "waste" may be appropriate, but bearing in mind that products of neutron capture of Thorium isotopes may include potentially useful isotopes of Uranium. The present disclosure studies examples which focus on dirty Plutonium, i.e. Pu and MA based waste, but the reader will appreciate that the invention is not limited to the processing of waste of such composition.

It is desirable, when designing a nuclear reactor, to consider one or more of the following technical features. Embodiments described below may deliver one or more of the advantages set out. In particular, a reactor may be designed by reference to a desire to improve fuel sustainability. This might be brought about by breeding fuel. This could be encouraged by choice of starting material, and the nuclear reaction implemented in the reactor. Bombardment of nuclear fuel by neutrons can be used to induce neutron capture, which itself may cause the nuclear fuel to transmutate into elements which may decay naturally, or by other induced reactions, in a manner conducive either to energy generation, to safe and stable end products, or both. If a starting material can be selected which transmutates into further instances of usable nuclear fuel, such as fertile or fissile materials, then this can be advantageous.

Further, it is highly desirable that nuclear waste stockpiles do not increase in size, or not significantly so. Nuclear waste can be broadly characterised by its lack of usefulness for other industrial applications, or by its generally deleterious impact on the environment, or both. Certain materials are inherently politically undesirable as well, due to their suitability for production of nuclear weapons and the fear (whether rational or not) of radiation being released to the environment. Production of such materials is discouraged, or carefully managed by regulation.

It is also desirable to look to produce a reactor design which enhances efficiency in terms of useful energy generation. Any modification of a reactor, to increase its usefulness in processing waste, needs to be offset against any increase in energy costs which may result. The full life cycle of the reactor and fuel should be considered. This will, in turn, reduce or limit the increase in the financial risk to investors.

Finally, it is desirable that a new reactor design should either improve or maintain existing safety levels.

A large majority of the world's commercial nuclear reactors are light-water-cooled. In these reactors, light water (i.e. regular H ₂ 0) also acts as the moderator. There are two types of LWR: Pressurised Water Reactors (PWRs) and Boiling Water Reactors (BWRs). In a PWR, the water is kept at a high pressure and remains in the liquid phase. In a BWR, the pressure can be much lower, such that the water boils in the core. In a BWR, therefore, the VF, and therefore the water density in the core, varies.

These reactors are fuelled by enriched Uranium (U), consisting of U-238 and fissile U- 235. Pu is produced as a by-product and some LWRs are partly fuelled with recycled Pu in MOX. TRU isotopes decay exponentially at various rates, causing transmutation into different isotopes.

When a neutron in a nuclear reactor interacts with a nucleus, one or more of a number of different events may take place.

• The neutron may be scattered.

• The neutron may be captured, causing the nucleus to increase in mass.

• Nuclear fission may result.

The likelihoods of these reactions occurring are related to effective target areas, known as the 'scattering,' 'capture' and 'fission' cross-sections.

These cross-sections vary with incident neutron energy. This behaviour is further complicated by the presence of resonances in the cross-section (a quantum mechanical effect resulting from the discrete energy levels of the nucleus). The presence of an isotope causes the neutron energy distribution to change by absorbing neutrons of different energies at different rates. There will be dips in the neutron flux at resonance energies, which reduces the number of neutrons available for further absorption at resonance energies. This effect is called 'self-shielding'. Similarly, resonances of different isotopes will interfere.

Therefore the neutron flux at different energies, and the nuclear reaction cross- sections, are implicit (i.e. iteration is required) and the cross-sections vary with time due to evolution in isotope populations.

Neutrons are emitted during fission as 'fast' neutrons. During scattering collisions with nuclei, these neutrons slow down, eventually to 'thermal' energies. This process is called moderation. By deliberate interposition of a suitable moderating material, into a reactor, moderation can be used to bring neutrons down to speeds more suitable for neutron capture. Light nuclei (such as hydrogen in water) are effective moderators. Moderation is generally encouraged in commercial nuclear reactors as U-235 has a very large fission cross-section at thermal energies. Neutron capture reactions can be used to 'breed' fissile fuel from other, 'fertile' isotopes. Pu-239 and U-233 are produced by neutron absorption and subsequent beta decay of U-238 and Th-232 respectively. This is an attractive proposition for fuel sustainability but the isotopes must somehow be bred if criticality is to be maintained.

Fuel temperature is one factor which affects reactor performance, because it affects the distribution of nuclear velocities. A change in fuel temperature thus changes the distribution of collision energies with neutrons of a particular energy. The effect of this is that, at higher energies, resonances become broader. This effect is called Doppler Broadening. To ensure stable and safe operation of a nuclear reactor, negative feedback is important. This is formalised by requiring that several coefficients of reactivity are negative.

If a LWR heats up, the coolant temperature will increase and the VF (volumetric fraction of water vapour) may increase. This decreases the coolant density, and therefore the neutrons become faster on average. If this increase in neutron speed were to cause increased reactivity, then the reaction rate would increase, which could result in an increase in coolant temperature. Thus, a positive feedback loop could arise, which would have the potential to cause a serious accident.

Similarly, if the fuel temperature increases, the effect of Doppler Broadening changes. If this results in increased reactivity, then a similar positive feedback mechanism occurs. The Void Coefficient (VC), Moderator Temperature Coefficient (MTC) and Doppler Coefficient (DC) must therefore be kept negative.

The VC, (increase in reactivity ( k _eff ) with VF at constant coolant temperature) is therefore evaluated as: where VFO is the VF at the operating condition.

The MTC (increase in k _eff with moderator temperature and corresponding density decrease, at constant VF) is thus evaluated as: (2) where Tc is the coolant temperature at the operating condition. This coefficient is not relevant for a BWR where the coolant is in the 2 phase region.

The DC (increase in ^e S with fuel temperature) is evaluated as:

2Qk _e jf _T f ₊₂₀ k _e jf _T f where Tf is the fuel temperature at the operating condition.

The build-up of Minor Actinides (MAs) has a tendency to make the core more reactive with 100% VF near the operating VF. The constraint that the core must be less reactive at 100% VF than at its operating condition was applied to the Japanese RMWR, which is a BWR. Therefore it is also applied to the model of a BWR considered here. This constraint is not applied to the PWR considered here, as the condition of a PWR core entirely filled with steam without having been shut down is considered to be extremely unlikely.

The 100% VC is evaluated as:

100% VC = ⁱ oo ^% Kff _F o ₍₄₎

100(1 - VFO)k _{eff VF=wm} k _{eff VFO}

The reactivity of the reactor without control rods, soluble boron or burnable poisons naturally varies throughout the fuel cycle as the actinide populations change and fission products accumulate. It is important that the reactivity variation is low enough so that control rods can be used to prevent the reactor being supercritical at all times. A parameter called the integral control rod worth describes their effectiveness.

The integral control rod worth (ICRW) is evaluated as: ICRW - k _e g _{rods out} k _e g _{rods in} (5)

The present disclosure is particularly, but not exclusively, directed to the use of Th- based fuels in a LWR. Th-based fuels have multiple advantages over U-235 or Pu fuels bred from U-238. Land-based U-235 reserves are limited (natural U is only 0.7% U-235), U extraction from seawater may not prove economic, and fuel enrichment is usually required. Th is approximately 3 times as abundant as U, and occurs in nature as the fertile isotope Th-232. When a Th-232 nucleus absorbs a neutron, it decays into the fissile isotope U-233 which can be used for power generation. Neutron absorption in U-238 leads to the production of Pu isotopes and other TRUs (referred to as 'Minor Actinides'). As noted above, collectively, TRU waste is referred to as 'dirty Pu'. This represents a considerable waste problem and proliferation risk, and is a principal source of negative public opinion towards nuclear power. Background example - the Energy Amplifier

Rubbia et al. (Rubbia C, Buono S, Kadi Y, Rubio J A: Fast Neutron Incineration in the Energy Amplifier as Alternative to Geological Storage: The Case of Spain. CERN/LHC/97-01 (EET) (1997)) proposed the Energy Amplifier (EA) concept as a method of incinerating large quantities of TRU waste. This consists of an Accelerator Driven Subcritical Reactor (ADSR) fuelled with a Th and dirty Pu MOX (the composition is given in Table 1 ).

The EA is a suitable basis for comparison with the present disclosure on waste incineration because of the high performance demonstrated by the design, and because the waste incineration methodology is in many ways comparable. The composition is by atomic proportion. Table 1 sets out dirty Pu composition in the example disclosed in Rubbia et al.:

Table 1

Np-237 0.07507 Am-241 4.86E-03

Np-239 7.54E-09 Am-242 4.38E-05

Pu-236 9.24E-07 Am-243 9.13E-03

Pu-238 0.02204 Cm-242 4.89E-04

Pu-239 0.52988 Cm-243 7.21 E-06 Pu-240 0.21747 Cm-244 3.35E-03

Pu-241 0.10193 Cm-245 2.04E-04

Pu-242 0.0355 Cm-246 2.29E-05

The EA presents a challenging design condition for materials and structures. It requires a liquid metal coolant and a high neutron flux of 10 ¹⁶ cm ^"2 s ^"1 . A reliable and economically viable particle accelerator is required.

The present description provides the reader with sufficient information to enable development of large scale incineration of dirty Pu in an LWR. The reader will understand that the nature of the technology requires that the disclosure is based on simulated models, rather than real examples, and that the commissioning of a reactor will involve certain other design phases before reaching realisation. However, the completeness of the present disclosure is not put in doubt by the fact that no working reactor according to the presented design has yet been implemented. This is normal practice for work in this field. An embodiment in accordance with the disclosure may exhibit one or more advantages. Some of these will now be discussed. The reader will appreciate that delivery of each of these advantages will depend on the exact implementation chosen by the designer, and no commitment is made by the present disclosure as to delivery of any or all of these advantages in any particular implementation of the present invention.

As a coolant, water is safe and well understood. Activation of the coolant is not an issue, as long as a high level of coolant purity is maintained. Decades of experience of designing reactors to handle and contain the coolant can be drawn on, including extensive experience of the design and behaviour of structural components. This favours use of an LWR to implement an embodiment of the invention, to use fuel economically and to recycle actinides a commercial proposition in the medium term. Given the large sunk costs of designing a reactor, the long product life and the lengthy time from design to operation, it would be challenging to introduce a radical reactor concept on a commercial scale within the next 20 years. It is also debatable whether there would be sufficient knowledge available to expect to run a liquid-metal-cooled reactor for approximately 60 years. The highly corrosive environment in a liquid metal reactor may necessitate the use of new materials and limit product life. Gas-cooled fast reactors may have problems safely enduring Loss Of Coolant Accidents, and high temperatures may cause material life problems. Critical fast reactors are more susceptible to reactivity excursions than thermal reactors due to a lower prompt neutron lifetime which makes it more difficult to ensure that they are safe.

MA recycling in a thermal neutron spectrum is difficult due to the low fission cross- sections and high capture cross-sections of MAs for neutrons of thermal energies. This reduces the reactivity and therefore the rate at which MAs can be incinerated. As dirty Pu contains a significant fraction of MAs, and this fraction increases over time, there has been significant research on dirty Pu incineration in fast reactors.

If most of the power from a reactor can be produced from TRU waste, then the waste incineration rate is proportional to the reactor power. In Rubbia et al.„ the same composition of TRU material produced in a conventional LWR was added to the reactor, so a large proportion of the power was produced by incinerating the fissile isotopes in the waste. An alternative strategy is to deal with the MAs separately (e.g. Fukaya Y, Nakano Y, Okubo T: Study on High Conversion Type Core of Innovative Water Reactor for Flexible Fuel Cycle (FLWR) for Minor Actinide (MA) Recycling. Annals of Nuclear Energy, Vol. 36, Issue 9, p. 1374-1381 (2009)), although this may require additional reprocessing capability. 63% of the composition of dirty Pu is fissile Pu-239 and Pu-241 . The MA population will initially rise in such a reactor, but the refuelling strategy can be adjusted to ensure MA populations remain at tolerable levels. Despite a significant decrease in waste reactivity with time in the reactor, criticality and high levels of waste incineration can be maintained due to U-233 breeding.

Certain limitations of the concepts set forth in this disclosure are recognised, to enable the reader to take account thereof in the design of an effective LWR in accordance with an embodiment. For instance, it is proposed herein that Th-Pu MOX be used in a LWR. While some experiments have been conducted into the use of this fuel, it has never been used commercially. Over time, the MA proportion of the fuel will increase, which may also affect fuel pellet fabrication. The concept is furthermore predicated on nuclear fuel reprocessing. Moreover, depending on the eventual batch strategy and refuelling interval, it is possible that significantly more reprocessing may be needed than for current schemes. This will increase costs. This must be offset against not needing to enrich the fuel and the tariff the operator could levy for recycling the waste. Reprocessing increases the amount of medium and low level waste that must be disposed of. The economic benefits of reprocessing spent fuel from a U-fuelled reactor are questionable given the low current cost of U. On the other hand, this cost may rise in the future. Of course, the reader will appreciate that, depending on a variety of factors, it is entirely possible that an embodiment of the present disclosure could require no more reprocessing than existing schemes, and the present disclosure does not make any assertions as to this point.

Additional high level waste is produced in the form of fission products (although these generally have shorter half-lives, with some exceptions). In addition, as in the U fuel cycle, radioactive actinides are produced through neutron capture and decay in the Th fuel cycle.

Separating the Uranium to remove U-233 from the reactor during reprocessing produces a high quality, fissile fuel which could potentially be used to make a bomb. This material is difficult to handle due to gamma emission from U-232. Previous studies have considered adding U-238 to the reactor to reduce the fissibility of the U at the end of the fuel cycle. This approach is not discussed in detail here.

The above drawbacks are generally true of any Th-fuelled transmutation concept. More reprocessing may, however, be required if the reactor is large and the power density is considerably lower in a more thermal reactor than in a fast reactor and therefore the burn-up before reprocessing may be lower. However, U-233 retention may offset this somewhat.

Another possible drawback of the adoption of the present disclosure is that older waste tends to contain more Am-241 than "fresh" waste, due to decay of Pu-241 . Due to stability and reactivity constraints, older waste may need to be diluted with newer waste or high quality Pu. Similarly, waste which has been undergoing transmutation for a long period of time may need to be diluted for further transmutation as it becomes less fissile, reducing transmutation rates.

Stability considerations and the decreased reactivity of MAs in this reactor relative to a fast reactor, mean that this performance limitation is more significant for a LWR. Some work has already been done on the possibility of encouraging transmutation in LWRs. This work is acknowledged in the following discussion of certain prior art references.

Waris et al. (Waris A, Su'ud Z, Permana S, Sekimoto H: Influence of Void Fraction Change on Plutonium and Minor Actinides Recycling in BWR with Equilibrium Burnup. Progress in Nuclear Energy, Vol. 50, Issues 2-6, p. 295-298 (2008)) found that recycling of MAs in conventional BWRs required increased enrichment of U-235 but that this requirement was reduced as the VF was increased and the moderation decreased.

Extensive studies have been conducted by the JAEA to develop a Flexible Light Water Reactor (FLWR) concept. They propose reactors designed to recycle Plutonium, and potentially MAs, and to breed fissile Plutonium from U-238. These are designated the High Conversion (HC) FLWR and the RMWR. The gap between fuel pins was reduced and the VF was increased, resulting in a faster neutron spectrum. For MA loading in the HC-FLWR, around zero net MA production was found to be possible when MAs were loaded in the core. However, MA loading tended to increase the VC, and reducing the core height was necessary to increase neutron leakage, which mitigated this. The neutron leakage is described by the geometric buckling of the reactor, which depends on the reactor geometry and is higher when the leakage is greater. Limiting the fuel rod diameter also improves the VC. The 100% VC was defined. A design criterion was that this (and the VC) had to be negative. This criterion was found to limit performance.

FLWRs have a core height of about 1 .5m. The RMWR is the second stage of the FLWR research program and, in this design, the gap between fuel pins may be as low as 1 mm. The core average void fraction may be -70%, compared to -40% in a conventional BWR. The core pressure drop in the RMWR is low due to the low core height.

Heavy- and light-water-cooled PWR-type RMWRs have also been proposed, as have taller cores. While the results of any TH analysis for these concepts are not known, as they are under active investigation, the tight pitch in these modified designs is thought to be possible from a TH standpoint. Work by Downar et al. modified this concept to investigate Th fuel. The advantages of this have been discussed. This design had a negative VC, suggesting it would be possible to increase the height of the core or make MA loading feasible. This was because Th-232 has a smaller fission cross-section in the fast spectrum, and a smaller resonance integral than U-238. The neutron spectrum achieved in this core design was far closer to the spectrum in a fast reactor (e.g. JOYO) than in a conventional PWR or BWR. Weapons-grade Pu was used to maintain criticality and produce neutrons to breed U-233.

Use of thorium fuel to reduce stockpiles of high quality Pu in a conventional PWR was investigated by Porsch and Sommer (Porsch D, Sommer D. Thorium Fuel in LWRs: An Option for Effective Reduction of Plutonium Stockpiles. Advanced Reactors with Innovative Fuels. Workshop Proceedings, Chester, UK 22-24 October 2001 . OECD NEA, BNFL) and found to be an "effective option".

Nunez-Carrera et al. (Nunez-Carrera A, Lacouture J L F, del Campo C M, Espinosa- Paredes G: Feasibility Study of Boiling Water Reactor Core Based on Thorium- Uranium Fuel Concept. Energy Conversion and Management, Vol. 49, Issue 1 , p. 47- 53 (2008)) demonstrated a potentially economic Th- and U-fuelled BWR core. A stated goal was to minimise MA production, but MA incineration was not considered. Stability of the reactor was also demonstrated. A small gap between fuel pins was found to improve reactivity and fuel breeding and reduce waste production. Masumi et al. (Masumi R, Aoyama M, Yamashita J: Minor Actinide Transmutation in BWR Cores for Multi-recycle Operation with less Minor Actinide to Fissile Plutonium Amount Ratio. Journal of Nuclear Science and Technology, Vol. 32, No. 10, p. 965- 970 (1995)) found that MA incineration in BWRs decreased reactivity less if the moderator fraction was decreased. It was stated that the addition of fissile Pu reduced transmutation rates due to the formation of MAs from Pu. Therefore the MA-to-Pu ratio generally increased during operation. However, by loading MAs in a LWR core, it was found that this ratio could be decreased. The proportion of the isotopes incinerated was around 50% after the 3 ^rd recycle. Wallenius and Westlen (Wallenius J, Westlen D: Hafnium Clad Fuels for Fast Spectrum BWRs. Annals of Nuclear Energy, Vol. 35, Issue 1 , p. 60-67 (2008)) demonstrated that MA incineration could be performed at the top of an uprated BWR where the VF is higher. This work assumed U and MOX fuel and a conventional BWR layout (so the coolant volume ratio was not decreased) but Hafnium clad fuel was used to reduce moderation.

Th0 ₂ fuel has generally been considered for Th-fuelled reactors. Handling MA fuels may be problematic. This provides motivation to limit the MA population in the reactor, although some increase in MA proportion is thought to be unavoidable without separating MAs from dirty Pu. Thus, in each of the above references, the absence of discussion of MA handling, and the assumption that Pu is "weapons grade" and thus of a high level of purity, is significant.

An extensive study of TRU waste incineration in PWRs was conducted by Shwageraus et al. (Shwageraus E: Rethinking the Light Water Fuel Cycle. PhD Thesis MIT (2003)). A standard Westinghouse PWR design with a cladding outer diameter of 9.5 mm, and a square pin pitch of 12.6 mm was assumed. The power density was 104.5 W/cm ³ . The fuel temperature was 900 K and the coolant temperature was 583 K.

Shwageraus concluded that there was insufficient moderation in a conventional LWR to utilise Th. Conventional or reduced moderation was concluded to result in short cycle lengths and therefore uneconomical amounts of reprocessing as the Pu burns out quickly. Shwageraus also observed that increasing the coolant volume fraction increased the TRU destruction rate. The coolant volume fraction was varied by varying the water density.

Summary

In general terms, an aspect of the invention comprises the processing of transuranic, TRU, material in a Reduced Moderation Water Reactor, by mixing the TRU material with Th-232.

An aspect of the invention involves operating a Thorium based fuel cycle in a Light Water Reactor, with a fuel comprising a mixture of fertile Thorium and transuranic material, through a first fuel cycle, then replenishing the fuel with further Thorium and said transuranic material, including some or all Uranium-233 bred in said first fuel cycle. Another aspect of the invention comprises operating a Light Water Reactor, LWR, including the steps of loading the LWR with a mixture of Th-232 and dirty Plutonium, Pu, and moderating the reactor at a moderation rate lower than that which would be required to maintain a chain reaction if the reactor were loaded with enriched Uranium.

The mixture may be a mixed oxide fuel, MOX.

As will become apparent from the following description of specific embodiments, the generalised concept above provides the opportunity to implement a RMWR which can achieve rapid and near-complete destruction of TRU waste.

Brief description of drawings Figure 1 is a schematic diagram of a Light Water Reactor in accordance with an embodiment of the invention;

Figure 2 is a schematic diagram of a cross section through fuel rod assemblies and control rods of the LWR illustrated in figure 1 ;

Figure 3 illustrates a graph showing typical variation in reactivity with VF for a Th- fuelled RMWR with moderate MA loading;

Figure 4 illustrates a graph of performance of a lumped model of the LWR over 5 years;

Figure 5 illustrates a schematic illustration of a model used for fuel assembly geometry in a modelling tool, MCNPX; Figure 6 illustrates a graph of burn up behaviour for a first case modelled in a first approach illustrating an embodiment in the present disclosure;

Figure 7 illustrates a graph of burn up behaviour for a second case modelled in the first approach illustrating an embodiment in the present disclosure; Figure 8 illustrates a graph of burn up behaviour for a third case modelled in the first approach illustrating an embodiment in the present disclosure;

Figure 9 illustrates a graph of burn up behaviour for a fourth case modelled in the first approach illustrating an embodiment in the present disclosure;

Figure 10 illustrates evolution of reactivity coefficients over reactors' lives across the four cases; Figure 1 1 illustrates evolution of k _eff over reactors' lives across the four cases of the first approach;

Figure 12 illustrates refuelling strategies for two cases described in a second approach modelled to demonstrate an embodiment in the present disclosure;

Figure 13 illustrates a graph of cumulative average TRU incineration for the two cases of the second approach;

Figure 14 illustrates a graph showing evolution of Pu and U-233 populations for a first of the two cases of the second approach;

Figure 15 illustrates a graph showing evolution of significant MA populations for a first of the two cases of the second approach; Figure 16 illustrates a graph showing evolution of Pu and U-233 populations for a second of the two cases of the second approach;

Figure 17 illustrates a graph showing evolution of significant MA populations for a second of the two cases of the second approach;

Figure 18 illustrates a graph of one batch end of cycle calculations for each of the two cases of the second approach;

Figure 19 illustrates relative soluble Boron requirements for the two cases of the second approach; Figure 20 illustrates moderator reactivity coefficients for the first of the two cases of the second approach;

Figure 21 illustrates moderator reactivity coefficients for the second of the two cases of the second approach; and

Figure 22 illustrates maximum soluble Boron for negative VC, for the two cases of the second approach. Figure 23 illustrates fuel assembly design (red (solid circle) = fuel, green (circular ring) = control material).

Figure 24 illustrates refuelling strategies.

Figure 25 illustrates SOC Th proportion.

Figure 26 illustrates cumulative average incineration rates. Figure 27 illustrates EOC one-batch burn-ups.

Figure 28 illustrates evolution of Pu and U isotope populations for the dirty Pu reference case.

Figure 29 illustrates evolution of significant MA populations for the dirty Pu reference case. Figure 30 illustrates evolution of Pu and U isotope populations for the dirty Pu/MA case.

Figure 31 illustrates evolution of significant MA populations for the dirty Pu/MA case.

Figure 32 illustrates evolution of isotope populations for different dirty Pu cases.

Figure 33 illustrates moderator reactivity coefficients for the dirty Pu reference case. Fig 34 illustrates moderator reactivity coefficients for the dirty Pu/MA case.

Figure 35 illustrates moderator reactivity coefficients for the dirty Pu low enrichment case. Figure 36 illustrates pin power distribution with rods out (refer to Fig. 1 ).

Figure 37 illustrates pin power distribution with Ag-ln-Cd rods in.

Figure 38 illustrates pin power distribution with enriched B ₄ C rods in.

Figure 39 shows schematic illustration of fuel assemblies with a demonstrative heterogeneous distribution of Th and TMU.

Figure 40 illustrates a pin assembly model used to demonstrate an embodiment of the invention;

Figure 41 -53 illustrate graphs of results used in support of the description of the embodiment.

Description of Specific Embodiments

In this description, the concept of the RMWR, as explored above in the context of weapons-grade Pu, is further developed to enable its application to the problem of waste incineration.

In short, one significant variation on previous explorations is the reduction in the gap between fuel pins. Of course, the weapons-grade Pu used in previous research is replaced by dirty Pu.

The present disclosure makes no assumptions as to advances in materials technology in order to target medium-term commercial viability. That is, the present disclosure does not rely on development of new materials in order to bring into effect a reactor in line with a disclosed embodiment.

In order to set forth suitable examples of a reactor in accordance with embodiments of the invention, it is inevitable that computerised modelling tools are required. That is, it is impractical to research in the field of the invention using physical examples, for reasons of safety, cost and time. Modelling tools have now reached a level of sophistication that the results thereof can be relied upon, and are widely adopted, including in prior art examples set out above.

Several tools are used in this disclosure to analyse this reactor concept. The software tools available are described in Table 1 . Nuclear data from the JEF-2.2 Nuclear Data Library (JEFF Report 17, NEA Data Bank, April 2000) was used in WIMS and MCNPX.

To present examples to the reader, two approaches are disclosed. A first approach employs a PWR in which a moderation ratio is altered with respect to previous examples of PRW type reactors. A second approach uses a PWR without making modifications to existing moderation designs. In describing the first approach, a variety of well-established numerical methods are demonstrated to show the reader how the behaviour of a reactor configured as specified is expected to behave. With the knowledge of the first approach, the second approach is described using fewer numerical methods.

Approach 1

In the present embodiment, the reader is directed to a diagrammatic illustration of a pressurised water reactor in figure 1 . The reader will appreciate that the reactor 10 is shown in extremely schematic form. It comprises an encapsulation 12, fuel assemblies 20 and control rods 22. A coolant inlet 30 and a coolant outlet 32 are illustrated. The reader will understand that the coolant inlet 30 and outlet 32 are connected, in use, to a coolant circuit, for instance with a steam generator, compressor and turbine, for electricity generation. Detailed description of the latter elements is not required for an understanding of the embodiments of the present invention. A more detailed illustration of the configuration of the fuel assemblies 20 and control rods 22 is set out in figure 2. The assemblies are hexagonal in cross section, with 469 fuel pins. This arrangement will be familiar to the reader from previous designs of fuel assembly. Fuel loading is homogeneous, and in-core fuel management is not considered in the present description. The modelling assumes a fuel density of 10.05 g/cm ³ . The assemblies are arranged in an approximately circular configuration.

Each fuel assembly 20 is clad in a Zircaloy (Zircaloy-2 in a BWR, and Zircaloy-4 in a PWR) channel box. Gaps are specified between channel boxes for the Y shaped control rods 22, as in the RMWR. The clad thickness is 0.86 mm, as in that example. It will be noted by the reader that the gap between fuel pins is generally lower than in a standard LWR, but higher than the minimum previously considered for RMWR designs. In the models considered herein, the fuel temperature is taken to be 900 K for the PWR examples and 1 100 K in the BWR example. Accordingly, the coolant temperature is 583 K in the PWR examples and 550 K in the BWR example.

As there are a large number of possible configurations for this reactor it is important to determine the constraints on the design and establish a configuration within which these constraints are not violated. The requirements of the design are: a) Negative VC and MTC (for a PWR) throughout reactor life.

b) Negative 100% VC throughout reactor life (see Figure 3) for a BWR. c) Sufficient reactivity throughout reactor life.

d) Thermal hydraulic considerations:

a. Manageable pressure drop (ideally low enough to allow passive heat removal).

b. The power specified as 4 GWth. This should be uniform throughout life, with comparable power density to existing reactor designs. c. Maximum fuel temperature comparable with existing commercial reactors.

e) Negative DC throughout reactor life.

Figure 3 illustrates typical variation in reactivity with VF for a Th-fuelled RMWR with moderate MA loading. This data is generated for an example comprising a PWR (0% VF) which has a negative VC without buckling, and in this case also has a negative 100% VC. A BWR with a 50% VF also has a negative VC without buckling, but neutron leakage is required for a negative 100% VC. So a BWR not only has to satisfy the often limiting 100% VC condition, but has a generally more challenging stability condition due to the increased VF.

As the neutron spectrum becomes faster, the ratio of fission cross-section to capture cross-section increases for many MAs, which has the tendency to cause a positive VC and MTC. However, the total absorption cross-section tends to decrease. Therefore, for a finite reactor, the neutron leakage probability increases. Hence, increasing geometric buckling is an effective strategy for improving the VC and MTC.

The parameters which can be varied to achieve waste incineration within these constraints are summarised in Table 2.

Table 2

Parameter Effect on Constraints on Performance

PWR or BWR; The 100% VC condition may be relaxed for PWR. The MTC average VF for condition can be relaxed for a BWR. The average coolant BWR density is higher for a PWR, so a lower gap between fuel pins may be required. A PWR is simpler to analyse. A higher VF may allow a higher gap between fuel pins.

Fuel pin pitch A higher pitch improves the TH performance. Pin diameter A lower pin diameter may decrease reactivity but improve VC.

Core diameter Affects reactor power and buckling. Higher buckling improves

VC but decreases k _eff .

Core height As above, but a flatter core reduces pressure drop and maximum fuel temperature. This may be important when the gap between fuel pins is low.

Assembly diameter Larger assemblies reduce moderation but may decrease ICRW.

Refuelling strategy Frequently removing U-233 and replacing with dirty Pu improves waste incineration but reactivity and VC constraints will limit this. A shorter cycle length allows frequent removal of fission products, improving reactivity and VC, but increases reprocessing costs. As an alternative to topping up with dirty Pu the following options can be considered:

1 . Replace entire fuel load every few decades and start on fresh waste. This results in a good incineration rate but the poor waste conversion means this was not considered.

2. Allow U-233 to build up in the reactor and add less dirty k

Pu. This improves the VC and ^e ff , with a relatively small reduction in incineration rate. This strategy reduces the need for reprocessing, and also reduces proliferation potential.

3. Removing Am from the reactor by reprocessing as Am- k

241 in the reactor makes the VC and ^e B worse. This requires new techniques and results in Am stockpiles which would require a long-term repository.

4. Improve the quality of Pu used for refuelling later on in the reactor's life (e.g. use decommissioned warheads). This is an effective strategy for recycling warheads but it is undesirable to make the design dependent on having warheads available in 20-30 years.

Flux Sets reactor power. A lower flux reduces radiation damage to clad and reactor pressure vessel, power density and burn-up rate, but makes decay more significant, notably from Pu-241 to

While the reader will appreciate that a full parametric study might be desirable, an intention of this disclosure is to present an initial, feasible design, while gaining an understanding of how the design affects the performance. From this, no doubt the reader will understand that more detailed design can be generated.

The present disclosure considers two extreme cases (a PWR with moderation similar to a Generation III+ PWR and an RM-BWR with high VF), and an intermediate case (an RM-PWR with two different refuelling strategies). The following procedure is applied in this analysis:

1 . Set the distance between fuel pins to 13.2 mm and fix the assembly size and gap between channel boxes to the design shown in figure 2.

2. Select a fuel pin diameter (which also sets the pitch).

3. Assume a starting fuel load (Th with dirty Pu enrichment).

4. Estimate the flux and find the reaction cross-sections (averaged over the fuel assembly) after 200 days of burn-up (to get approximately average cross- sections for the operating cycle) using WIMS.

5. Use these cross-sections as an input to the lumped model. Determine a flux and refuelling strategy using Refuelling Strategy 2 in Table 2.

6. Check the power density, and find the reactor size required for 4 GWth.

Calculate the waste incinerated per year assuming a 4 GWth reactor. Check that the burn-up rate is fairly constant.

7. If the lumped model is computed using starting cross-sections, or the flux and isotope population evolution has significantly changed from a previous iteration, go to step 3, using the flux and isotope populations after 30 years to derive the cross-sections. This helps account for the variation in cross-sections over time by using average values. Both sets of results are retained for future comparison.

8. Use WIMS to evaluate the VC and DC, and also the MTC for PWRs and the 100% VC for BWRs, at the start and end of the fuel cycle at the end of each decade, assuming the reactor is infinite. In practice, these coefficients must be checked over every cycle. However, over several decades the approximations in the calculation methods and the uncertainty of the operating condition of the final design mean that checking the coefficients every year of the reactor's life is not worthwhile. In reality, the fuel loads, flux and fuel management strategy can be varied in detail over the lifetime of the reactor. 9. Evaluate the minimum buckling required for k _eff of at least 1 (without control rods), and the maximum buckling required for negative VC and 100% VC using WIMS and EVENT. To do this, evaluate the reactivity at each condition at one value of buckling using EVENT, and solve for a constant c where: k _eff = k _mi (l + cB ² T ^l (6) k _in{ is the reactivity found using WIMS and k _eff is the reactivity in EVENT calculated for a finite reactor. To evaluate the maximum buckling, calculate B ² for k _e g = \. This calculation is valid for a homogeneous medium, and as the reactor is effectively being treated as a homogeneous medium in EVENT, the calculation will be reasonably accurate. To evaluate the minimum buckling, solve for B ² using Equation 6 where k _eff for the operating condition and the perturbed condition are equal.

10. If a feasible buckling exists, check that this gives a sensible reactor size. If not, return to step 3. If this doesn't work after a few attempts, go to step 2.

1 1 . Determine the height and radius of the reactor within the feasible buckling range, while being sympathetic to TH considerations. Y shaped control rods 7.5 mm in thickness were assumed to be present between the fuel assemblies as in the RMWR. This increased the actinide density within the fuel assembly. It was assumed that control rods could be placed in every gap between fuel assemblies as this simplified the analysis and allowed greater reactivity control. 1. Lumped Model

A modified version of the lumped model described in Coates et al. (Coates D J, Lindley B A, Parks G T: Actinide Breeding in a Thermal Spectrum ADSR. Part 1 : The Development of a Lumped Thermal Reactor Model. Submitted to Annals of Nuclear Energy (201 1 )) can be used to rapidly evaluate the burn-up behaviour for a given design and refuelling strategy. The model is used to give a long-term prediction of the validity of a specific design condition and therefore allow enough such conditions to be evaluated to gain an understanding of the constraints on the design. A 60-year calculation can take less than a minute to perform (the ode45 solver in Matlab (Matlab R2009a., The Mathworks) can be used to greatly reduce the run-time), and it is possible to define and implement different refuelling algorithms quickly and easily.

One-batch refuelling is considered in this example, i.e. the entire fuel load is reprocessed at the end of the fuel cycle. In some cases the refuelling interval is 1 year. In some cases it is possible to increase this to 2.5 years. The accumulation of fission products tends to decrease reactivity over the cycle and make the VC and MTC more positive, so it is likely to be easier to produce an initial feasible design with a short cycle length. The optimum fuel cycle length will be found by a more detailed analysis.

In particular, the fuel cycle length of any practical design can be adjusted over time until a limiting condition is met. In current reactors, this is generally the reactivity dropping below 1 . In the designs presented here, the fuel cycle length is constant, whereas in reality the transient nature of the fuel loading makes a varying fuel cycle length more appropriate. The Th-dirty Pu mixture loaded at the beginning of each fuel cycle can be optimised based upon the current isotope composition of the fuel, in contrast to the very simple refuelling algorithms used here to demonstrate the concept.

In this example, refuelling is assumed to take 20-30 days, and a simplified model of this period is used. This is thought to be a pessimistic assumption as discussed in Verhagen et al. (Verhagen F C M, Wakker P H, van Bloois J T: Minimizing PWR Reloading Time by Optimising Core Design and Reshuffling Sequence. TopFuel 2003 Conference, Wuerzburg, Germany, March 16-19 2003). Increased reactor availability will obviously increase the waste burn. In reality, the reactor would be reloaded with reprocessed fuel available from a previous cycle of another reactor, which will affect the impact of decay processes (notably beta decay of Pa-233 and Pu-241 ). During reloading, the flux is set to zero. Decay is allowed to proceed for 15 days, which results in a large decrease in Pa-233 as it decays into U- 233. Some of the U is then removed for reprocessing. This is consistent with the refuelling strategy of the EA described in Rubbia et al., where all the U was removed. Removal of U from nuclear fuel is a proven process, and allows the core to be loaded with additional waste. In this model, the U is replaced with a Th-232/dirty Pu mixture, again consistent with the EA. Unlike in the EA, not all of the U is removed at the end of the cycle. This is due to the decreased reactivity of the waste in the reactor, and the need to maintain a negative VC and MTC. Over time, the build-up of MAs tends to make the VC and MTC worse, so it becomes necessary to reduce the dirty Pu proportion after a point. The reactivity of the dirty Pu also reduces over time due to the build-up of non-fissile isotopes. Therefore, it is necessary to supplement the reactivity by retaining U-233. This is a viable strategy, but not necessarily the best one. Despite this, the average kg TRU burn per GWd over the cycle remains better than the EA in some cases. The refuelling strategy is therefore dependent on two parameters: the proportion of U retained, and the enrichment of dirty Pu in the Pu/Th mixture used to top up the reactor. These parameters are step changed at a few points in the reactor's life to demonstrate the reactor concept. The reader should note that the idealised model described above has a practical analogue. For example, if half of the U-233 in the core is replaced at the end of the year, this could be implemented in practice by removal of the U-233 from half of the fuel pins. When refuelling with a mixture of 50% dirty Pu, 50% Th (for example), the additional Pu would be spread over several fuel elements to give a more homogeneous increase in enrichment.

2. Cross-Section Derivation and Lumped Model Verification Using WIMS

In this approach, the cross-sections for fission and capture reactions are derived using WIMS for the starting compositions of the fuel. The cross-sections are calculated after around 200 days of operation, so the effects of fission products and oscillating U-233 population are treated in an average sense. The lumped model is then used to derive an estimate for the evolution of isotope populations. In reality, the cross-sections depend on isotope populations. This is partly compensated for by re-deriving the cross-sections using WIMS after 30 years operation and using these cross-sections to generate a new set of results. The second set of results is used as a best estimate, but if the two results are markedly different, additional iterations can be completed. The estimates of transmutation rates for both iterations are generally similar.

The capture cross-section generally reduce with isotope population due to resonance self-shielding. Therefore, the capture cross-sections for U, Am and Cm isotopes reduce over time. Despite this, a model generated from cross-sections after 200 days provides good agreement with WIMS over five years of operation (without reloading). The error is virtually zero for the Th-232 population, about 2% for U, Np, Pu and Am, and about 5% for Cm. This is shown in Figure 4, which shows performance of the lumped model over 5 years, with lines plotted from the lumped model, and points plotted from WIMS. It will be seen from that graph that the lumped model is an acceptable approximation.

The flux and reloading strategies are varied in the model to achieve:

• An approximately constant burn-up rate chosen to set the power density;

· Relatively flat reactivity variation over the reactor's life, although in practice this can be micromanaged (for example, by varying cycle length);

• Limited dirty Pu enrichments.

Stability and reactivity are checked at 10-year intervals using WIMS. The minimum buckling needed to ensure stability and the maximum buckling to ensure criticality are calculated at all evaluated points. For the strategy to be feasible, the maximum buckling must be greater than the minimum buckling. In reality, the entire reactor lifetime needs to be checked to ensure stability, but the critical points can often be predicted with some confidence. The checked fuel compositions are only an approximation, and fine tuning of the final concept and operating strategy can be performed later. The approach here is sufficient to demonstrate general feasibility. Calculations over 60-year timeframes are often not performed in conceptual reactor analysis due to the computational requirements. Full burn-up and reload calculations are performed in WIMS over a 10-year period to check that the calculated burn-up, waste incineration and isotope composition of the fuel agreed reasonably well with the lumped model. The calculation is performed for a first case (described below) where the neutron spectrum is relatively thermal and therefore cross-section variation with time is greater due to the greater influence of resonances in cross-sections. The decay processes during refuelling (which will affect the evolution in actinide populations) are not modelled in WIMS.

The lumped model overestimates the waste loaded over this period by 3%, and is generally only accurate to within about 10% after 10 years. However, these errors are not considered significant in demonstrating general concept feasibility in most cases, but in designs of marginal general feasibility (notably thermal designs: see Case 2 below) a full burn-up calculation exclusively in WIMS will be performed. When a general concept has been determined, a full burn-up calculation exclusively in WIMS will ultimately be performed. 3. WIMS

WIMS9 provides a rapid and accurate way of evaluating reactivity excluding neutron leakage ( k _M ) and the reaction cross-sections for a fuel assembly. WIMS is a modular code. Due to the implicit nature of the neutron transport equations an iterative procedure using several WIMS modules is required. For a full description of the functionality of each WIMS module, see WIMS9 Issue 1 Manual (Serco Assurance; The ANSWERS Software Service).

First, the module HEAD is used to define the materials and the problem geometry. The geometry of the fuel assemblies is similar to that of a VVER reactor (a Russian PWR), i.e. the fuel pins had a triangular pitch and the fuel assemblies are hexagonal. VVER geometry is a standard option in WIMS, which makes geometry specification straightforward. The neutron energy distribution varied throughout the assembly due to the channel box and the gap between assemblies. Therefore the pins in the centre of the fuel assembly where treated as a different material to those further out and the outer layer of fuel pins was treated as a third distinct material. This distinction is also made for the coolant and cladding.

PRES, CACTUS and RES are used to perform a subgroup calculation for Th-232, U- 233, Pu-239 and Pu-240 at the estimated fuel pin temperature to represent resonance events using a subgroup treatment.

PERSEUS is then used to calculate approximate collision probabilities, which are then used by PIP to generate an approximate solution for the flux. This solution is used by COND to generate cross-sections for 1 1 groups to calculate the final solution for the flux in CACTUS.

The buckling option in CRITIC is used to estimate the effect of reactor size on reactivity, VC and MTC. To evaluate the 100% VC, VC and MTC, the coolant density is changed appropriately. The reactivity and reactivity coefficients are evaluated at the end of the cycle using the BURNUP module. This also allows the burn-up behaviour calculated by the lumped model to be verified. 4. Verification with MCNPX

MCNPX (Pelowitz D B. MCNPX Users Manual Version 2.6.0. LA-CP-07-1473.) solves the neutron transport equation by a Monte Carlo method, and is therefore conceptually different from EVENT and WIMS. It is capable of performing the same calculations as WIMS. It is much easier to specify complicated 3D geometries in MCNPX, but model run-time is significantly longer (an assembly k _M calculation in WIMS took a few seconds, while for statistical convergence in MCNPX, more than half an hour was required). However, it provides a means of verifying the results from WIMS.

Figure 5 illustrates a model used for fuel assembly geometry in MCNPX. This is used to calculate k _M for different fuel loads. Buckling is then accounted for by considering an equivalent reactor of infinite radius (specified using reflection boundary conditions) and finite height. Nuclear fuel data at 900 K is used for both models and the light water, clad and channel box are assumed to be at 600 K. The coolant density and pin diameter are chosen appropriately for each case. Table 3 sets out the result of verification of & _inf and k _eff in WIMS and MCNPX.

Table 3

As can be seen, the MCNPX calculations of k _eff agree with the WIMS calculations to within the standard deviation (approximately 0.00038) of the MCNPX calculation for initial loading and after 10 years of burn-up at 2x10 ¹⁴ cm ^"2 s ^"1 flux. However, after 30 years, when the MA concentration is higher, the calculations disagree slightly. This may be due to the lack of nuclear data at temperatures above 293 K for isotopes other than Th-232, U-233, Pu-239 and Pu-240 in WIMS. Data at 900 K is available for all actinides in MCNPX, and the use of this data instead of data at room temperature is found to affect the reactivity by a similar amount to the difference between the results. However, any potential errors in WIMS when calculating the reactivity, VC and cross- sections at higher MA concentrations should have a small effect and are certainly not expected to affect the operation of any working apparatus built in accordance with this disclosure. The rate of change of reactivity with buckling is similar in MCNPX at 0%, 5% and 100% void fraction.

Reaction cross-sections after 61 days of burn-up are calculated using WIMS and MCNPX using an initial fuel load of 14.3 at% dirty Pu. Table 4 sets out cross sections (in barns) arrived at using WIMS and MCNPX, and a calculated difference in outcome using the two approaches. It will be observed that there is close agreement between the cross-sections for fission and capture (about 2% error for isotopes present in more than trace quantities).

Table 4

Slight errors in these cross-sections are also not thought to affect the final results, given that the performance of the reactor is relatively insensitive to the exact values of the cross-sections used in the lumped model.

5. EVENT

EVENT ("A Users Guide to the FETCH Model" Imperial College London) is a program written by Imperial College, which solves the neutron transport equation by the finite element method. It is possible to output results from WIMS which 'smear' the entire fuel assembly into a single equivalent material. This information can be converted into a form suitable for input into EVENT, which can be used to solve for k _eff and the flux distribution for the entire reactor.

In this analysis technique, the reactor is assumed to be axi-symmetric, so a model is produced in RZ geometry. This is a slight approximation to the actual case where the hexagonal fuel assemblies result in a slight variation in radius with angle. In the simplest case, a cylinder of homogenised material is considered, with a reflection boundary condition at the centre line. Around 50 cm of water, of the same density as the water within the reactor, is assumed to be surrounding the reactor, except during verification against WIMS and MCNPX. The water acts as a reflector. A bare boundary condition is specified on the outer surfaces. This configuration allows the variation in reactivity with buckling to be evaluated. k

Table 5 sets out results for ^e ff after 30 years operation in a PWR with 1 .4 mm gap between fuel pins at 2.5x1014 cm-2s-1 flux with no water surrounding the core.

Table 5

As expected, WIMS and EVENT predict the same k _in{ . The standard deviation of the MCNPX results is about 0.0008. EVENT tends to predict a lower reduction in k _eff with buckling than CRITIC. EVENT is used to evaluate the effect of buckling as it allows the whole core to be considered. The coefficient c in Equation 6 is virtually constant for a given coolant density and assembly geometry, and this can be used to speed up the evaluation procedure.

A homogeneous model is considered satisfactory for the conceptual design presented here (indeed many of the referenced studies are limited to assembly level calculations).

More specific examples of application of the above numerical methods will now be described, in the following four numbered cases. Case 1 Modified Pressurised Water Reactor

In this case, a 3.9 mm gap between fuel pins is specified, giving a moderator/fuel volume ratio similar to the EPR (a Generation III+ reactor). The ratio of moderator volume to coolant volume around a single fuel pin is 1 .8, as in an EPR. An EPR has a fuel pin diameter of 9.5 mm and a square pitch of 12.6 mm, although only 92% of the rods are fuel rods (the rest are for control and instrumentation) (Ardron K (AREVA NP). Physics and Engineering of the EPR. Presentation to IOP Nuclear Industry Group. Birchwood Park, Warrington, UK, 10 November 2010).

The performance of designs in this region of moderator/fuel ratio can be found to be sensitive to the exact geometry, fuel load and neutron flux.

It is necessary, in this case, to retain all of the U-233 as the fuel is less fissile than in Reduced-Moderation designs. However, the ratio of fission to capture cross-section of U-233 is lower when the moderation was higher, so the fraction of power from U-233 is relatively low.

The initial dirty Pu enrichment is 12%. The fission products are removed every 30 months and replaced with a mixture of dirty Pu and Th. The dirty Pu fraction is 100% except between years 40 and 50, when it is 50 at%. The flux is chosen to give a power density about 50% higher than the EPR, as this is found to limit the Am population and increase the waste burn (by about 200 kg per year). The thermal-hydraulic performance of this operating point is likely to be more challenging as a result. Reducing the volume of fuel in the reactor also reduces the amount of reprocessing required. The neutron flux is 2.5x10 ¹⁴ cm ^"2 s ^"1 for the first 20 years, and this is then reduced to 2.2x10 ¹⁴ cm ^"2 s ^"1 . Due to the sensitivity of the performance to the exact geometry, the cross-sections are updated every 10 years in this case using WIMS. The burn-up behaviour is shown in Figure 6.

The reactor is able to maintain criticality and negative reactivity coefficients (without the need for buckling) throughout its 60 year life, and simulations beyond this period indicate that this condition can be maintained over multiple reactor lifetimes. The waste transmutation potential of this concept is compelling: 1336 kg per year of TRU are incinerated on average using this approach. The Am population is limited by the high capture cross-sections of Am-241 and Am-243 in the thermal spectrum. This also leads to a build-up of Cm isotopes. Cm-244 and Cm-245 are most common. Cm-245 is fissile, with a fission/capture ratio of more than 6. However, higher isotopes of Cm and trans-Curium isotopes are generally not fissile in the thermal spectrum. While the population of these isotopes remains low, this build- up may eventually affect reactivity. Nuclear data for isotopes of Cm higher than Cm- 245 is not available in WIMS and therefore augmentation of the data libraries is desirable. Using MCNPX, it is predicted that adding 0.5% Cm-246 (predicted in Case 1 after 60 years of operation) to the fuel will reduce reactivity by approximately 0.002 (negligible in the context of this analysis) and may have a small impact on void coefficient, which should not affect the feasibility of Case 1 .

The fissile Pu content of the reactor needs to be kept high due to the low equilibrium population of U-233 and neutron absorptions in the coolant. Therefore the waste content in the reactor cannot be reduced towards the equilibrium position of an exclusively Th-fuelled reactor. However, increasing the dirty Pu enrichment further may cause problems due to MA accumulation later in the reactor's life.

The large gap between fuel pins and the stability of the reactor means that a core height approaching that of a conventional PWR is appropriate.

From Figure 6 it can be seen that, as the U-233 population tends to its equilibrium value, the actinide populations are generally fairly stable, and the reactivity is sufficient to sustain the reaction. The required fissile content of the fuel mix is greater than at the start due to the build-up of MAs which poison the reactor. This is a general effect. However, if the neutron spectrum is made more thermal, the poisoning effect of the MAs becomes unsustainably severe. To retain reactivity, the dirty-Pu enrichment has to be increased during refuelling, which in turn increases the MA population of the reactor in future years. Over several decades, the required Pu enrichment exceeds 50%, and eventually the reaction cannot be maintained. The remaining TRU material in the reactor would then need to be diluted, transferred to a different design of reactor or placed in geological disposal. Nevertheless, the results of this analysis indicate that the potential for waste incineration in thermal reactors may be greater than has been previously recognised. For example, it may be possible to burn waste exclusively in a Generation III+ reactor, or perhaps transfer it to an RM-PWR after several decades.

Cases 2 and 3: Reduced-Moderation Pressurised Water Reactor

When the gap between fuel pins is reduced to 1 .4 mm, the dirty Pu remains sufficiently fissile to maintain criticality when a proportion of U-233 is removed from the reactor (Case 2). Removing U during reprocessing is a proven process. The removed U-233 is chemically identical to the U used in conventional PWRs and can be added to PWR fuel, reducing enrichment costs. The power density is reduced to limit the fuel temperature, resulting in a corresponding increase in fuel volume. The height of the core is reduced to 145 cm to ensure the stability of Case 2.

In this case, 25% of the U is removed at the end of each of the first 29 years, followed by annual removal of 5% for the next 31 years. In contrast, in case 3, U is not removed, and the fuel cycle length is increased to 2.5 years. All other actinides remain in the reactor. Fission products are removed at the end of each fuel cycle for both concepts. For Case 2, the starting enrichment of dirty Pu is 16 at%. For the first 14 years, the reactor is refuelled with 100 at% dirty Pu. For the next 15 years, this is reduced to 80%. For the next 31 years, this is reduced to 50%. The higher enrichment of the added dirty Pu is assumed to be diluted over the entire reactor. More waste is added to the reactor in the first 30 years. Beyond this, stability constraints require a reduction in waste loading and therefore an increase in U-233 retention. This results in a decrease in Pu population over the second 30 years, and the stabilisation of the Am-241 population. Removing 25% of the U-233 at the end of each year over the first 29 years keeps the U-233 population significantly below equilibrium (Figure 7). This 'frontloading' of waste may be attractive to reactor vendors as they can profit from assuming liability for the waste at an early stage. The initial waste loading of the reactor is 37.4 tonnes.

Over the reactor life, the average fissile content of the TRU material is reduced. The Am and Cm populations both increase. This is an inevitable consequence of burning Pu. The Am proportion reduces relative to an equivalent quantity of waste left to decay.

As shown in figure 7,for Case 2, after 60 years, 73% of a packet of TRU waste is incinerated. After 120 years, or two reactor lifetimes, 89% is incinerated. For a given isotopic composition, the rate of waste incineration is proportional to the volume of waste. Quicker incineration can be achieved by increasing the flux and consequentially the power density. When U-233 is retained (Case 3), the MA populations in the reactor are reduced relative to Case 2 (Figure 8, which shows burn up behaviour of case 3). Eventually, the build-up of heavier isotopes of U in the reactor bred from Th-232 causes a minimum in the Np population. The dirty Pu enrichment at the start and during refuelling is 15 at%.

U-233 retention reduces the amount of reprocessing required. As cycle length is limited by reactivity and U-233 is bred during the cycle, higher waste enrichment reduces buckling, use of burnable poisons, increasing the fuel cycle length at some points and batch fuel management strategies should allow burn-ups before reprocessing comparable to Generation III+ reactors. In particular, increasing the dirty Pu loading and decreasing the buckling may provide the potential to reduce reprocessing requirements relative to Case 1 . As in Case 1 , the reactor does not require neutron leakage to be stable. The 100% VC is sometimes positive for Case 2, but is always negative for Case 3 for 0 buckling.

The equilibrium amounts of TRU material and U-233 in the reactor can be calculated for a given set of cross-sections using the lumped model, assuming a constant Th-232 population. This equilibrium solution is used to generate new cross-sections in WIMS, and a few iterations can be performed. The starting U-233 population can then be adjusted in WIMS until the population is constant over a burn-up step. The equilibrium concentration of TRU material in a reactor refuelled with pure Th-232 is approximately 0.23 at%. This population cannot be decreased further without ceasing to operate this type of reactor. Further reduction requires re-concentration of the remaining TRU inventories but, if other reactors are fuelled with pure Th0 ₂ , they will produce TRU material until this equilibrium population is achieved. Nevertheless, this represents a very large theoretical reduction in TRU population, and this level of TRU material can be tolerated indefinitely in the reactor. The concept therefore provides the theoretical capability to end the need for long-term storage of TRU waste, although such a result may not be completely realisable in practice.

The density of the fuel in the reactor's equilibrium position is assumed to be 9.9 g/cm ³ . The reactor can maintain reactivity for 365 days if the flux is limited to 2x10 ¹⁴ cm ^"2 s ^"1 . This corresponds to a power density of about 60% of that in Case 3. The maximum buckling for feasibility was 9.64x10 ^"5 cm ^"2 . For example, this would correspond to a radius of 389 cm and a height of 412 cm. The reactor power would be 7.4 GWth. It is likely that the large height combined with the small pitch would result in an unacceptably high pressure drop and/or maximum fuel and clad temperature. The MTC, VC, 100% VC and DC are, in this case, all negative. The reprocessing requirements would probably be prohibitively high, even if burn-up was increased by implementing a batch reloading strategy.

It is generally difficult to operate a Th-232 reactor in its equilibrium position. U-233 releases approximately 2.5 neutrons per fission, of which one is required to breed fuel and another to sustain the chain reaction. Feasibility may be improved by further reducing coolant mass fraction, cycle length or flux.

However, existing conventional reactors and the large stockpiles of nuclear waste eliminate the need for a Th reactor independent of the U cycle in the medium term. Case 4: Reduced-Moderation Boiling Water Reactor

This case considers a 70% VF RM-BWR with 1 .4 mm fuel pin pitch, as this is thought to represent almost as fast a neutron spectrum as can reasonably be achieved in a water-cooled reactor. In this case, the VC and 100% VC presents a more severe limitation on waste incineration than in the RM-PWR. This results in a need to increase the geometric buckling and reduce the proportion of U-233 which is removed from the reactor. A one-year fuel cycle is considered. 10% of the U is removed for the first 20 years, after which all the U is retained. For the first 20 years the reactor is topped up with Th- 70 at% dirty Pu, after which the dirty Pu enrichment of the added fuel will be reduced to 20%. The waste burn is significantly lower than in Cases 1 and 3. However, improved neutron economy improves the proportion of power which can be produced from U- 233. The burn-up behaviour is shown in Figure 9.

Comparison of cases

1. Reactor Stability and Control

For stability limited designs, the MTC and VC are observed to be worse at the end of cycle due to the build-up of fission products. The DC changes little over the cycle and is always negative, with values typically between -2x10 ^"5 and -4.5x10 ^"5 .

The chosen core configuration and fuel management strategies ensure negative VC, 100% VC (BWRs) and MTC (PWRs). Cases 1 and 3 were stable without the need for buckling. Cases 2 and 4 require neutron leakage to ensure stability. Cycle length is limited by the MTC for Case 2 and the VC for Case 4. A further increase in reactor buckling may therefore be desirable to allow longer fuel cycles. This may result in an undesirably large radius, or a need to increase power density.

The evolution of reactivity coefficients over the reactors' lives is shown in Figure 10. Crucially, all values are negative. The performance of Case 4 is limited by the VC after 20 years but at other times the VC is more negative. This implies that the performance over the second half of the reactor's life can be improved by increasing fuel cycle length of dirty Pu enrichment. The control rods are least effective at the point when the MTC and VC are most positive, as they displace some of the moderator. Assuming the control rods are homogeneous B ₄ C manufactured with natural Boron (enrichment with Boron-10, which is about 20% of natural Boron, improves control rod performance), the minimum ICRW for Case 2 is 0.132, which is enough to cause sub-criticality of the reactor at all times. The inclusion of a graphite follower on the control rods may increase moderation and therefore the ICRW, while making the neutron spectrum more thermal. This design has been considered for the FLWR.

2. End of Cycle Reactivity

The variation in k _eff over the life of each reactor is shown in Figure 1 1 . The cycle lengths of Cases 1 and 3 are reactivity limited. The minimum reactivity of these cases occurs after -10 years when the MA populations has increased but the U-233 population is still substantially below equilibrium. k _M typically decreases by 0.04 per year for Case 1 , 0.02 to 0.03 per year for Cases 2 and 3, and 0.01 per year for Case 4. The difference in these decreases is partly due to the increased power density of Case 1 .

3. Reactor Performance Data

Table 6 sets out design and performance data for the four cases set out and discussed above.

Table 6

Case 1 Case 2 Case 3 Case 4

Neutronics Design

Flux (x10 ⁴ crrf ² s- ¹ ) 2.5 for 2.5 3 4.4

20 yrs

then 2.2

Minimum buckling (cm ^-2 ) 0 0.000446 0 0.000539

Maximum buckling (cm ^-2 ) 0.000596 0.00150 0.000552 0.00109

Fuel power/fuel volume (W/cm ³ ) 349 151 155 150

Fuel pin outer diameter (mm) 9.3 1 1 .8 1 1 .8 1 1 .8

TH Design

Number of assemblies 151 487 487 571

Effective radius (cm) 192 347 347 378

Active height (cm) 359 145 145 125

Reactor power (GWth) 4003 3997 4103 4002

Power per unit area (kW/cm ² ) 34.6 10.5 10.8 8.9

Reactor power per unit volume (W/cm ³ ) 96.3 72.7 74.7 71 .1

Design buckling (cm ^-2 ) 0.000233 0.000517 0.000517 0.000672 Performance

Maximum dirty Pu enrichment (at %) 25.9 22.2 15.0 16.6

Minimum Th-232 composition of fuel (at %) 70.5 76.7 85.0 80.8

Average TRU waste incineration (kg/yr of 1336 1 153 642 744 metal)

Average TRU waste incineration (kg/GWyr 343 313 161 203 of metal)

TRU out/TRU in ^* 0.20 0.39 0.22 0.32

Average fissile U produced (kg/yr) 0 406 0 166

One-batch fuel cycle length (yr) 2.5 1 2.5 1

Fuel volume (x10 ⁷ cm ³ ) 1 .15 2.65 2.65 2.67

^* Further transmutation is possible: this is not the maximum incineration that can be achieved.

Table 7 sets out TRU proportions in a reactor after 60 years of operation, accordance with each of the four cases set out above.

Table 7

Table 8 sets out data describing TRU incineration results for different refuelling strategies with respect to loading strategies, and compared to the case where the waste is instead left to decay from time of loading until 60 years after reactor start up.

Table 8

Case Np Pu Am Cm Trans-Cm Total Per Yr

1 vs start 6706 76426 -169 -2825 -6.1 80132 1336 1 vs left to decay 7012 68526 6821 -3085 -6.1 79269 1321

2 vs start 7166 66219 -2544 -1657 -1 .6 69182 1 153

2 vs left to decay 7679 56206 6441 -2006 -1 .6 68318 1 139

3 vs start 3255 36539 -266 -1020 -3.4 38504 642

3 vs left to decay 3524 31771 3847 -1 159 -3.4 37980 633

4 vs start 4438 42167 -1371 -568 -1 .2 44664 744

4 vs left to decay 4808 35655 4227 -784 -1 .2 43904 732

Looking at these results, the proportion of trans-Curium isotopes produced is negligible from a point of view of long-term storage liability, which justifies the consideration of a limited number of isotopes in burn-up calculations.

For comparison with other concepts, the incineration compared to input, rather than relative to decay, is considered as this is the form in which data is presented. In a 1500 MWth Energy Amplifier, 420 kg of dirty Pu are incinerated per year (280 kg/GWthyr). A 2-year fuel cycle has been proposed. The high moderation Th-fuelled PWR approach proposed by Shwageraus et al. gives theoretical destruction rates of up to -1000 kg/GWe yr (i.e. about 330 kg/GWthyr) not including the effect of TRU material bred from Th. Fuel cycles of up to 36 months were considered. However, only 75% Pu destruction can be demonstrated in Pu-Th fuel, and this figure drops to 50% for Th- Pu-MA fuel. The Th-Pu-MA fuel contains 86.3% Pu compared to 90.7% Pu in this study, and therefore is more difficult to incinerate. Further reprocessing was not considered. In particular, the Am-241 content is higher. Cases 1 and 3 are capable of achieving comparable rates of TRU destruction to these concepts, while the incineration rate of Cases 2 and 4 is substantially lower. The Cases are compared against each other in Table 9.

The reactors maintain a neutron flux consistent with thermal reactors, and therefore will experience reduced irradiation damage compared to fast reactors.

Table 9

Advantages Disadvantages

Modified High incineration with U-233 100% waste burn has not been PWR retention. 2.5-year cycle conclusively demonstrated. The length. Potentially favourable waste concentration in reactor cannot TH, suggesting lower fuel be reduced over time. The volume at the same power is performance is sensitive to the reactor possible, which reduces geometry so further validation is reprocessing needs. required. High dirty Pu enrichment is required later in the reactor life.

RM-PWR Can operate to produce U-233 Short cycle length for Case 2, leading or retain U-233 as desired. A to high reprocessing needs. Lower reduction in the TRU incineration rate if U-233 is retained. population in the reactor The higher volume of fuel in reactor towards end of its life has will probably increase reprocessing been demonstrated. More requirements.

power produced from Th.

RM-BWR Similar to RM-PWR. The stability condition is highly limiting, reducing cycle length and incineration rate.

The ability of multiple configurations of a Th/Pu-fuelled LWRs to sustain stable operation for 60 years is demonstrated above. Moreover, there is strong evidence that operation can be continued far beyond this point without the need to discharge TRU material. The desirability of removing U-233 is a political and economic decision beyond the scope of this disclosure. The Case 1 reactor is dependent on continued loading of fissile Pu, whereas in the other cases it is possible to achieve significantly above 50% of the power from U-233 if desired.

The reader will appreciate that further analysis of the TH performance of the reactor is required, in order to determine appropriate power densities and core heights. For example, the cycle length of Case 3 could be increased by increasing the reactor height, but this may result in an unacceptably high fuel temperature or core pressure drop. Heat transfer and pressure drop are both made worse by a two phase coolant, which weakens the case for a BWR. However, a larger gap between pins is possible for the same moderation in a BWR. Standard modelling tools, used in the field, will allow the skilled person to take account of these factors. It would be important to consider, in determining a working design in accordance with a described embodiment, that the need for extensive fuel reprocessing needs to be taken into account. One way of limiting this is by maximising fuel burn-up. Therefore smaller fuel volumes and/or longer fuel cycles are desirable, within the constraints of reactivity, stability and TH considerations. Of the four basic cases presented here, the reprocessing requirements of Case 1 are the lowest.

In the EPR, the approximate fuel volume is 1 .47x10 ⁷ cm ³ . It can be operated on a four- batch strategy with an 18 month fuel cycle length (Ardron K (AREVA NP) Physics and Engineering of the EPR; Presentation to IOP Nuclear Industry Group. Birchwood Park, Warrington, UK, 10 November 2010). The enrichment of the fuel is fairly high (5%). There are no enrichment costs for the Th-fuelled RMWR. Burn-ups of 55-65 GWd/t are possible in the EPR. The reprocessing requirements of the 1 -batch strategies for each Case are given in Table 10, normalised against the estimated EPR reprocessing requirements when operating with a closed fuel cycle.

Table 10: Reprocessing requirements normalised against 4-batch EPR

An EPR operating a one-batch strategy would have a relative estimated reprocessing requirement of 1 .6. Therefore allowing for further optimisation and consideration of batch strategies the economics of Case 1 appear attractive. The reprocessing required for Case 3 is high, and for Cases 2 and 4 it may be prohibitively high, making improved burn-up an essential requirement of a final design. Easy and significant improvements are possible by increasing cycle length at points of high reactivity and stability in the reactor's life. Therefore the numbers in Table 10 may turn out to be pessimistic.

In Case 1 , the reader will no doubt appreciate that the impact of build-up of isotopes heavier than Cm-245 needs to be studied in more detail. These isotopes may be important as the average numbers of neutrons required to cause fission of these isotopes are relatively high in thermal reactors but decrease rapidly with an increase in neutron energy. However, the results presented here are strongly indicative that these heavier isotopes should not affect the feasibility of the concept. The accuracy of the burn-up calculation (in WIMS and the lumped model) is limited as the flux will vary through the reactor in practice. Where specified, the flux in this study is the average flux in the reactor. Changing the flux affects burn-up. Moving fuel assemblies during refuelling will naturally affect this, and thus fuel assembly shuffling can be used to average out variations in the core.

In particular, the reader will understand that caution should be exercised in relying on the models presented herein, particularly of the RM-BWR. This model needs to be examined in more detail due to the assumption that all assemblies experience the same uniform operating condition. In reality the VF will vary axially. This will affect burn-up, flux distribution, stability and reactivity. However, preliminary calculations indicate the homogeneous approximation is sufficient for an initial presentation of the present embodiment. Calculations have been performed in WIMS with different VFs, and the smeared models stacked in the full core model in EVENT, resulting in a simple model of a heterogeneous core. Table 1 1 sets out data describing the validity of the uniform VF approximation for Case 4, and shows that k _M and k _eff are fairly similar to cases where the reactor is assumed to be homogeneous. Table 11

When the reactor is stable, the reactivity is higher at lower VF. Therefore the flux tends to be higher at the bottom of the reactor. This generally results in higher power and therefore higher burn-up at the bottom, which may affect long-term burn-up behaviour.

Use of older waste will degrade performance due to the build-up of Am-241 . However, letting the U-233 build up in the reactor is an effective strategy to allow low quality wastes to be incinerated. As decay is an exponential process, it is sensible to burn newer waste first. Weapons-grade Pu can evidently be burned in the reactor as it is more fissile, and mixing with lower quality wastes may be advisable.

Approach 2

In a second approach, the following will show that an unmodified PWR can be loaded with fuel comprising a mixture of Thorium-232 and transuranic material, to derive a result comprising processing of the transuranic material into desirable end products. In this approach, no alteration, relative to previous arrangements, is made to the moderation ratio applied to the reactor.

A reactor such as that illustrated in figure 1 is again assumed to be used. Modelling of this reactor is carried out using the familiar commonplace modelling tools.

In this case, an assembly level calculation is carried out on a standard 17 x 17 fuel assembly with 12.6 mm square pitch, 0.418 mm inner fuel pin radius and 0.475 mm outer fuel pin radius. There are 265 fuel rods per assembly and control rods were assumed to be out. The core equivalent diameter is 3767 mm and the active fuel height is 4200 mm (Pairot et al., 2009: Pairot F, Petit A, Wooldridge C. UK EPR Pre- Construction Safety Report. Chapter 4: Reactor and Core Design. Sub-chapter 4.1 - Summary description. UKEPR-0002-041 Issue 02. (June 2009)). The fuel temperature is 900K and the coolant temperature is 586 K. The clad is Zircaloy. The reactor power is 30.4 MW/te.

Two TRU compositions are considered in this approach. The first case is dirty Pu as considered by Rubbia et al., in their Energy Amplifier concept, set out in table 1 above. It should be noted that Cm246 is not modelled in this approach.

The second case contains more MAs and is taken from (Shwageraus et al., 2004). The composition (wt %) of dirty Pu/MA fuel in this case is set out in table 12.

Table 12

U234 0.0001 Pu242 5.0330

U235 0.0023 Am241 4.6540

U236 0.0019 Am242m 0.0190

U238 0.3247 Am243 1 .4720 Np237 6.641 Cm242 0.0000

Pu238 2.7490 Cm243 0.0050

Pu239 48.6520 Cm244 0.4960

Pu240 22.9800 Cm245 0.0380

Pu241 6.9260 Cm246 (not 0.0060

modelled)

The fuel is Th/TRU MOX, assumed to have a uniform density of 9.8 g/cm3, slightly less than the theoretical density as is common practice. The fuel is assumed to be MCY ₉₈ to limit oxygen release on fission, again common practice.

At the end of each fuel cycle (defined as the point when the reactivity drops to 1 , to the nearest 60 years, rounded down), the fission products are removed and replaced with Th/TRU MOX. The reloading enrichment is typically 60-70 at%. The fuel is assumed to be homogenous. In reality, in-core fuel management would be used to ensure adequate form-factors and reactivity. The start-of-cycle (SOC) Th content of the fuel never drops below 70 wt%. The starting enrichment is 13 at% for dirty Pu and 22% for dirty Pu/MA. The reload enrichments were selected on a cycle by cycle basis and are plotted in Figure 12. The refuelling is assumed to be instantaneous. In reality, decay processes will occur, notably beta decay of Pu-241 and Pa-233. This is not thought to greatly affect reactor performance, especially given the ability of the reactor to handle dirty Pu/MA fuel with high Am-241 content. The Void Coefficient, (increase in k _eff with Void Fraction (VF) at constant coolant temperature) is evaluated as:

VC = (k _eff — k _e ff o%y _F )/(5k _e ff ₅ %y _F k _e ff _t o%y _F ) (7) The Moderator Temperature Coefficient (increase in k _eff with moderator temperature and corresponding density decrease, at constant VF) is evaluated as:

MTC = (k _e ff _: 603K— k _e ff _: 583K)/(20k _e ff _: 603l<keff,583K) (8)

The Doppler Coefficient (increase in k _eff with fuel temperature) is evaluated as:

The 100% VC is evaluated as:

1 ^ eff ,VF=VM% keff ,VFO

Thus, these equations are more specific versions of equations (1 ) to (4) set out above.

The calculation is carried out using the commercial reactor physics code WIMS9 as above. An approximate flux solution is determined using 172 neutron energy groups, and then the final solution can be evaluated using 1 1 groups. A burn-up (BU) calculation is then performed. The effect of buckling is evaluated using the module CRITIC. One limitation of this analysis is the accuracy of the data available for some MAs.

Results can be benchmarked against a 3D MCNPX model with infinite radius and finite height to give equivalent geometric buckling, using data at 900K from JEF-2.2. The standard deviation of the MCNPX calculations was -0.0004. The fuel compositions are taken from SOC conditions in the Results (see below). Table 13 shows benchmark calculations for the WIMS/MCNPX model.

Table 13

nf.WIMS nf.MCNPX Relative keff.WIMS keff, MCNPX Relative

Error Error

12% dirty Pu, 0%

VF 1 .126876 1 .12718 -0.00027 1 .1 1308 1 .1 1354 -0.00041

12% dirty Pu, 5%

VF 1 .1 19099 1 .1 1886 0.00021 1 .10468 1 .10583 -0.00104

12% dirty Pu,

100% VF 0.953994 0.95391 0.00009 0.901834 0.90199 -0.00017

49 yr dirty Pu, 0%

VF 1 .1444 1 .14846 -0.00355 1 .131 12 1 .13714 -0.00532 49 yr dirty Pu, 5%

VF 1 .141758 1 .14654 -0.00419 1 .12784 1 .13283 -0.00442

49 yr dirty Pu,

100% VF 1 .187841 1 .18507 0.00233 1 .12367 1 .12757 -0.00347

86 yr dirty Pu/MA,

0% VF 1 .104439 1 .1 1207 -0.00691 1 .09182 1 .10033 -0.00779

86 yr dirty Pu/MA,

5% VF 1 .102943 1 .1 1084 -0.00716 1 .0897 1 .09794 -0.00756

86 yr dirty Pu/MA,

100% VF 1 .202651 1 .20198 0.000558 1 .13982 1 .14593 -0.00536

The error is noted to be initially negligible, but rises as the MA population rises in the reactor. For high MA loading, WIMS predicts the reactivity to be lower by about 0.7%. The VC does not appear to be significantly different. Therefore the WIMS calculation is considered satisfactory for the purposes of this analysis.

Data for Cm-246 is available from a beta version of WIMS 10, so the effect of Cm-246 can be estimated. From the capture cross section of Cm-245, the Cm-246 population is expected to rise to around 0.5% after 60 years of operation and 0.8% after 120 years of operation. 0.5% Cm-246 reduces the reactivity of the 49 yr dirty Pu by -0.2%, and 1 % Cm-246 reduced the reactivity of 86 yr dirty Pu/MA by -0.3%. The VC becomes relatively more negative by -2% / wt% Cm-246. It appears unlikely that Cm-246 or heavier isotopes will affect the feasibility of any of the models presented here, but it may be of interest to the skilled reader to explore this further in developing a physical implementation.

The Soluble Boron Worth (SBW) is evaluated as

SBW = (k _iniX - k _inW )/(Xk _inW k _iniX ) (1 1 ) where X is the concentration of soluble boron in ppm, which is taken as 1000 ppm at SOC and 500 ppm at middle-of-cycle (MOC).

From equation (1 1 ), the concentration of soluble Boron required to control the reaction at SOC can be calculated. This is then normalised against the concentration of soluble Boron required to control a one batch U-238 / 4.5 at% U-235 fuel. For each fuel cycle of Th/Pu fuel, the cycle length is normalised against the cycle length of the same Ur reference case. The relative soluble Boron required is hence the ratio of the normalised boron concentration to the normalised fuel cycle length.

1. Incineration Performance

The cumulative average incineration in kg metal/ GWth yr is plotted in Figure 13. The slight difference for the different fuels is probably a reflection of the higher TRU loading and hence higher fissile enrichment of the dirty Pu/ MA case. The decrease over time is due to the increase in U-233 fissions as it accumulates in the reactor.

For comparison, in a 1500 MWth Energy Amplifier, 420 kg of dirty Pu are incinerated per year (280 kg/ GWthyr) (Rubbia et al., 1995). A 2 year fuel cycle has been proposed (Rubbia et al., 1997). The high moderation PWR approach proposed by (Shwageraus et al., 2004) gives theoretical destruction rates of up to approximately 1000 kg/GWeyr (i.e. about 330 kg/GWthyr) not including the effect of TRU material bred from Th. Fuel cycles of up to 36 months are considered here. However, only 75% Pu destruction was demonstrated in Pu-Th fuel, and this figure drops to 50% for Th-Pu-MA fuel. Further reprocessing is not considered in this example.

Eliminating 3000 tonnes of TRU waste requires approximately 10,000 GWth yr of reactor operation (equivalent to 40 EPRs operating for 60 years each). A large number of reactors are therefore needed, so power generation should be economically competitive. Therefore, the approach here appears very competitive relative to using an Energy Amplifier as the waste incineration rate is only slightly less and the concept does not require new technology, beyond the ability to manufacture Th/ dirty Pu MOX. It also appears to be beneficial to accept about 25% decrease in ultimate waste incineration rate in order to achieve complete destruction, instead of between 50-75% in a PWR with increased moderation, although this appears to be a policy decision.

The evolution of isotopes within the reactor at SOC is shown for both cases in Figures 14 to 17. For the dirty Pu case, the TRU population is 'ramped down' after 60 years of operation to demonstrate the feasibility of a lower stable operating point. For the dirty Pu/ MA case, a higher equilibrium concentration is selected by increasing TRU loading. These two cases therefore indicate that an eventual pseudo-equilibrium point can effectively be chosen by the operator without the required fissile Pu loading becoming unmanageably high.

125 years of operation are needed to observe the MA populations tending to equilibrium. It takes a long time for these populations to accumulate through breeding of lighter isotopes. Notably, Cm-244 is bred via Am-243 and Pu-242 and takes a long time to accumulate. This then transmutes into Cm-245, which is fissile and therefore the equilibrium population of Cm-245 is lower. Higher isotopes of Cm will be produced in the reactor. The effect of Cm-246 has been considered. Even in the thermal spectrum, higher isotopes ultimately decay or fission and hence will eventually be expected to reach their own equilibrium populations. One possible source of concern is spontaneous fission of some heavier isotopes such as Cm-248 when the reactor is shut down. The equilibrium behaviour suggests that the long term evolution of reactivity and isotope population is stable relative to earlier fuel management decisions. This is important because dirty Pu becomes less reactive over time in the reactor, so it appears plausible that overloading with dirty Pu at the start of operation could require higher fissile loading later on to compensate, and subsequent escalation until the Pu enrichment becomes unmanageably high or criticality is unobtainable.

From the equilibrium position, continued loading of TRU material is possible indefinitely: in the reactor and in identical successors. TRU material would only need to be stored in the event fission power is phased out (hence near-complete incineration is claimed). The TRU proportion in the reactor can be ramped-down further in this eventuality, although this decreases BU. While the final TRU load of an EA would be lower, it would not be zero (Coates and Parks, 2010).

2. Reactivity and Control

The one-batch end-of-cycle (EOC) BU is calculated for each fuel cycle (Figure 18). This is dependent on the TRU enrichment of the fresh fuel. In practice, this may be constrained by reactivity control considerations (see below). However, neglecting control requirements, the one batch BUs are generally between 40 and 55 GWd/te. Given that modern reactors achieve 55-65 GWd/te and often operate a 4 batch strategy (Ardron, 2010), these figures are encouraging. If reactivity varies linearly with BU (without neutron poisons), operating a 4 batch strategy improves BU by 60%. Therefore, from a reactivity point of view, BU can be competitive with existing reactors. For a given TRU enrichment, the BU is generally lower for the dirty Pu/MA loading. The variation shown here is necessarily a reflection on the different reloading strategies used in each case. Notably, the dirty Pu case is driven to a different equilibrium position after 60 years of operation.

The SBW is reduced relative to a U fuelled reactor, as shown in table 14. The value is generally similar at SOC and MOC. However, the reactivity decreases much less rapidly over the fuel cycle. This is consistent with (Shwageraus et al., 2004). This is because a greater proportion of power is produced from bred isotopes (most significantly U-233). In addition, when pseudo-equilibrium is established, the population of isotopes such as Pu-240, which has a high capture cross section, decreases over the fuel cycle. These effects result in the relative soluble Boron requirement to control the reactor being initially lower, and then similar to a U fuelled reactor after 10-20 years (Figure 8). The soluble boron requirement is lower with MA loading. This is thought to be in part due to the increased loading of Pu-240 (Figure 19). The reader will note that the SOC Soluble Boron will be high due to one-batch operation.

Table 14

3. Reactivity Coefficients

The VC, 100% VC and MTC for both fuel loads at EOC are plotted in Figures 20 and 21 . The VC and MTC remain significantly negative throughout, so stable operation can be maintained. The SOC VC for the reference case is - 98 pcm/% Void, and the SOC MTC is -50 pcm/K. Adding dirty Pu results in a less negative VC and MTC.

Adding MAs is found to make these coefficients worse, which is consistent with Fukaya et al. (2009). In particular, the 100% VC becomes positive for the dirty Pu/MA loading case after -20 years and is nearly zero at one point for dirty Pu. This may be the result of the high Am-241 content of the dirty Pu/MA fuel. This is not thought to represent a safety risk, but may require attention from a regulatory perspective. Th fuel is known to improve stability relative to U fuel (Downar and Xu., 2001 ). U-233 is fissile in the thermal spectrum and hence improves stability. The VC, 100% VC and MTC are all generally more positive at SOC than at EOC. The leakage effect (Fukaya et al., 2009) was necessary for the 100% VC to be negative in the dirty Pu case, but VC and MTC are always negative in both cases for 0 buckling. These coefficients are calculated assuming zero soluble Boron. A reduction of coolant density also reduces the quantity of dissolved Boron and the SBW and hence makes the VC and MTC worse. This makes the 100% VC coefficient positive at some points for the dirty Pu case. The maximum SOC soluble Boron is calculated by solving

-5% x VC X k _e ff,5%VFX k _e ff o%VF ⁼ -ASBWx max soluble Boron (12) where p is the coolant density and A denotes the relevant change for each quantity. An equivalent calculation is performed for the MTC.

The amount of Boron that can safely be added is significantly more than the amount required to control the reaction for both fuels (Figure 1 1 ). This assumes that a four batch strategy would reduce soluble Boron requirements by 75% relative to a one batch strategy.

Use of burnable poisons and control rods can also be used to control reactivity. This is standard practice in PWRs and can be expected to have less effect on the VC and MTC.

The DC is between -2.2 pcm/K and -2.9 pcm/K for both fuel loads.

Certain advantages of embodiments of the invention will thus become apparent to the reader. A LWR with a reduced gap between fuel pins is a feasible, and potentially commercially viable, option for rapid and virtually complete incineration of TRU waste. A water- cooled reactor has the capability of incinerating as much waste per GWyr as a fast reactor without the need for accelerator technology or an exotic coolant.

A LWR can provide the capability to introduce a sustainable Thorium fuel cycle using dirty Plutonium to start the reactor. However, achieving stable operation is more challenging for a BWR than a PWR. If U-233 retention is desired, a large decrease in moderation is not required. In a thermal reactor, the U-233 produces a lower proportion of the power, allowing more waste to be incinerated per GWyr. Some reduction in moderation may be necessary to ensure that criticality can be maintained without removing TRU material from the reactor. Rapid and near-complete TRU incineration is possible in a PWR such as an EPR or AP1000. The present disclosure demonstrates that incinerating low quality waste may be feasible, whereas controlling the reaction using soluble Boron without causing a positive VC is unlikely to limit the attainable BU. Thorium can be introduced into the nuclear fuel cycle to improve fuel sustainability. Incineration rates are comparable to fast or subcritical reactors, and new coolant technology is not required, significantly reducing the commercial risk and the timeframe for implementation. In addition to potentially ending the need for storing this waste, this fuel cycle may potentially allow BU to be increased.

Further aspects/embodiments of the invention

As previously described, the production of long-lived transuranic (TRU) waste is a major disadvantage of fission-based nuclear power. TRU waste can be virtually eliminated in a pressurised water reactor (PWR) fuelled with a mixture of thorium and TRU waste, when all actinides are returned to the reactor after reprocessing. Here we consider the optimal configuration for a fuel assembly operating this fuel cycle. More particularly, the differences in performance obtained in a reduced-moderation PWR operating this fuel cycle were investigated using WIMS. The chosen configuration allowed an increase of at least 20% in attainable burn-up for a given TRU enrichment. This will be especially important if the practical limit on TRU enrichment is low. The moderator reactivity coefficients limit the enrichment possible in the reactor, and this limit is particularly severe if a negative void coefficient is required for a fully voided core. Several strategies have been identified to mitigate this. Specifically, the control system should be designed to avoid a detrimental effect on moderator reactivity coefficients. The economic viability of this concept is likely to be dependent on the achievable thermal-hydraulic operating conditions.

The fuel assembly design in this study has 469 pins arranged with triangular pitch in a hexagonal fuel assembly. The pitch was 13.2 mm and the fuel pin diameter was 1 1 .8 mm. The reduction in moderation was therefore less than has been considered in RMWRs, in which the average VF can be 40% to 60%.

It was anticipated that the moderator temperature coefficient (MTC) could limit performance. A positive 100% VC is anticipated to arise. This is permitted as the scenario of a fully voided PWR which has not been scrammed is considered implausible. In a high VF BWR this may not be the case. However, if a further reduction in moderation is to be considered, or a positive 100% VC was not allowed, a BWR may be a desirable configuration as reducing the VF reduces the moderation.

The fuel assembly design is shown in Figure 23. Control rod positions were specified to prevent excessive power peaking within the assembly with uniform enrichment across it. In practice, heterogeneous enrichment may be desirable. In particular, the higher thermal neutron fraction at the edge of the fuel assemblies results in higher power. There were 54 control rods per fuel assembly, corresponding to 1 1 .5% of the total rods compared to 8.3% in an EPR. The higher number of control rods was selected in anticipation of a decrease in integral control rod worth (ICRW) in a faster neutron spectrum. The fuel assembly was designed to produce a feasible operating point and investigate the behaviour of the system. It is therefore unlikely that the design is optimal.

The geometric buckling, 5 _g ² , of the reactor was chosen to be equal to that of a bare

EPR core. The optimal core aspect ratio may be different. Specifically, the core height could be reduced and the radius increased to improve the thermal-hydraulic performance. A core height of 300 cm and radius of 230 cm would give the same 5 _g ² and a similar core volume to a Generation III+ reactor. The clad was zircaloy with thickness 0.86 mm. The fuel temperature was 900 K and the coolant temperature 586 K. The reference power ratio was 19.9 MWt ^" .

Using simple pressure drop theory, the selected core height would have a similar pressure drop to an EPR if the flow velocity was reduced by around 15%. The drop in core mass flux approximately doubles the coolant temperature rise, necessitating a drop in coolant inlet temperature to prevent boiling and maintain a similar maximum clad temperature in steady-state operation. The departure-from-nucleate-boiling ratio (DNBR) was estimated using the round-tube correlations of (Biasi, L, Clerici, G.C., Garriba, S., Sala, R., Tozzi, A., 1967. Studies on burnout. Part 3. Energy Nucl. 14, 530-536.) and (Bowring, R.W., 1972. Simple but Accurate Round Tube, Uniform Heat Flux Dryout Correlation over the Pressure Range 0.7 to 17 MPa. AEEW-R-789, U.K. Atomic Energy Authority). This is approximate, but gives an indication of the effect of the different assembly geometry. The DNBR during normal operation is about twice as high as that in an EPR due to the decreased heat flux per unit area and lower hydraulic diameter. This assumes the same maximum form factor. The minimum DNBR may be different during a transient and so this is only a preliminary indication.

3. Analysis method

An assembly-level analysis was carried out. Two TRU compositions were considered; the first case (Table 15) was 'dirty' Pu.

Table 15 Assumed dirty Pu composition (at%).

Nuclide Proportion (at%) Nuclide Proportion (at%)

²³⁷ Np 7.507 ²⁴¹ Am 0.486

²³⁹ Np 7.54x10 ^{"7 242} Am(M) 4.38x10 ^"3

²³⁶ Pu 9.24x10 ^{"5 243} Am 0.913

²³⁸ Pu 2.204 ²⁴² Cm 0.0489

²³⁹ Pu 52.988 ²⁴³ Cm 7.21 x10 ^"4

²⁴⁰ Pu 21 .747 ²⁴⁴ Cm 0.335

²⁴¹ Pu 10.193 ²⁴⁵ Cm 0.0204

3.55 ²⁴⁶ Cm 2.29x10 ^"3 The second case (Table 16) contained more MAs.

Table 16 Composition (wt%) of dirty Pu/MA fuel.

Nuclide Proportion (wt%) Nuclide Proportion (wt%)

²³⁴ u 0.0001 242p _u 5.0330

²³⁵ u 0.0023 ²⁴¹ Am 4.6540

²³⁶ u 0.0019 ²⁴² Am(M) 0.0190

²³⁸ u 0.3247 ²⁴³ Am 1.4720

²³⁷ Np 6.641 ²⁴² Cm 0.0000

²³⁸ Pu 2.7490 ²⁴³ Cm 0.0050

²³⁹ Pu 48.6520 ²⁴⁴ Cm 0.4960

²⁴⁰ Pu 22.9800 ²⁴⁵ Cm 0.0380

²⁴¹ Pu 6.9260 ²⁴⁶ Cm 0.0060

The fuel was Th/TRU MOX assumed to have a uniform density of 9.8 g cm ^"3 , slightly less than the theoretical density, as is common practice. The fuel was assumed to be MOi.98 to limit oxygen release on fission, again common practice.

At the end of each fuel cycle (defined as the point when the effective multiplication factor k _e{{ dropped to 1 , to the nearest 100 days, rounded down), the fission products were removed and replaced with Th/TRU MOX. The reloading enrichment was typically 40-60 at%. This is the enrichment of dirty Pu in the dirty Pu/Th MOX added to the reactor to replaced burned isotopes during subsequent cycles. The fuel was assumed to be homogeneous. In reality, in-core fuel management would be used to ensure adequate form factors and reactivity. The start-of-cycle (SOC) Th content of the fuel never dropped below 70 wt%.

In addition to the reference case, two variants were considered for dirty Pu fuel: the rating was increased to 30.4 MW t ^" ; and the reloading enrichment was lower to limit the dirty Pu enrichment. The starting enrichment was 20 at%, except for the lower enrichment dirty Pu case where it was 16%. A higher initial enrichment in the dirty Pu/MA case could result in a positive MTC. The reload enrichments were selected on a cycle-by-cycle basis and are plotted in Figure 24. The resulting SOC proportions of Th in the core are plotted in Figure 25. The dirty Pu reference case was simulated over 125 years to demonstrate the achievement of equilibrium behaviour. The variants were simulated for shorter periods (until the reactor was tending towards pseudo- equilibrium).

The refuelling was assumed to be instantaneous. In reality, decay processes will occur, notably beta decay of ²⁴ Pu and ²³³ Pa. This is not thought to greatly affect reactor performance, especially given the ability of the reactor to handle dirty Pu/MA fuel with high ²⁴ Am content. In practice, already reprocessed fuel from other, identical reactors would probably be used to refuel the reactor.

The VC, i.e. the increase in k _eii with void fraction (VF) at constant coolant temperature, was evaluated as:

The MTC, i.e. the increase in k _cii with moderator temperature and corresponding density decrease, at constant VF, was evaluated as:

The Doppler coefficient (DC), i.e. the increase in k _eii with fuel temperature, was evaluated as:

^eff,920K ^eff,900K

DC =

20 & _{e i9} 20 K ^eff,900 K

The build-up of MAs has a tendency to make the core more reactive with 100% VF than at 0% VF. The constraint that the core is less reactive at 100% VF than at its operating condition was applied to the Japanese RMWR, which is a BWR. This constraint was not applied to the PWR considered here, as the condition of a PWR core entirely filled with steam without having been shut down was thought to be implausible. It was, however, illustrative to evaluate it. The 100% VC was evaluated as:

^eff,100%VF ^eff,0%VF

VC 100%

100fc _eff j00%VF^eff,0%VF

This is an illustrative calculation to demonstrate the issues associated with high transuranic enrichment in PWRs. It is relevant for a very serious loss of coolant accident without scram, which is extremely unlikely but may be important from a regulatory standpoint.

In addition, it would be worth considering the VC of a fully voided assembly surrounded by unvoided assemblies. This results in a more thermal neutron spectrum than a fully voided core but removes the increased radial neutron leakage from the voided assembly. The radial leakage is -50% of the total for the proposed geometry in this paper, compared to -25% in an unmodified PWR.

Therefore this condition may be more or less limiting than the 100% VC. While this scenario is not considered possible in PWRs, it is desirable to avoid any possibility of local positive reactivity feedback as a general mechanism that leads to accidents. Ultimately, the stability of the reactor must be calculated using a full core coupled neutronic-thermal-hydraulic model.

The assembly form factor (AFF) was evaluated as:

Maximum fuel pin power

AFF

Average fuel pin power

The analysis was carried out using a beta version of the commercial reactor physics code WIMS10A

(Newton, T., Hosking, G., Hutton, L, Powney, D., Turland, B., Shuttleworth, E., 2008. Developments within WIMS10. In: Proc. PHYSOR 2008, Interlaken, Switzerland), with nuclear data from ENDF/B-VII (Chadwick et al., 2006). The nuclear data was benchmarked against single cell and 17x17 lattice calculations found in (International Atomic Energy Agency, 2003), giving results consistent with other calculations for Th- Pu fuels, including a calculation with WIMS release version 9A (Newton and Hutton, 2002) using the JEF-2.2 library (OECD Nuclear Energy Agency, 2000. The JEF-2.2 Nuclear Data Library. JEFF Report 17, NEA Data Bank). WIMS10A was used to perform the analysis as it provided the capability to model heavier isotopes of curium

(Cm), and ENDF/B-VII is a more modern nuclear data library.

An approximate flux solution was determined using 172 neutron energy groups, and then the final solution was evaluated using 11 groups. A burn-up calculation was performed. The effect of buckling was evaluated using the module CRITIC. One limitation of this analysis is the accuracy of the data available for some MAs, leading to some variation among international benchmark calculations.

Results for the chosen design were benchmarked against a 3D MCNPX model (Los Alamos National Laboratory, 201 1 ) with infinite radius and finite height to give equivalent geometric buckling, using data at 900 K from JEF-2.2 (OECD Nuclear Energy Agency, 2000. The JEF-2.2 Nuclear Data Library. JEFF Report 17, NEA Data Bank ). The standard deviation of the MCNPX calculations was -0.0004. The fuel compositions were taken from SOC conditions after the specified number of years of operation. The isotope populations are given in Section 4. The WIMS and MCNPX benchmark calculations are shown in Table 17.

Table 17

WIMS and MCNPX benchmark calculations.

MCNPX MCNPX ^inf. WIMS MCNPX ^inf. WIMS MCNF

Case ^inf. WIMS relative ^eff. WIMS relative Ag-ln-Cd relative ¹⁰ B ₄ C relativ error error rods in error rods In error

16% dirty Pu,

1 .1 1375 1 .09975 0.00073 0.95017 0.00040 0.64894 0.001 - 0% VF 0.00034

16% dirty Pu,

1 .1 1 082 1 .09634 0.00006 0.94959 0.00042 0.64530 0.001 1 5% VF 0.00044

16% dirty Pu,

1 .08269 1 .04378 0.9701 1 0.63734 0.01 6C 100% VF 0.00444 0.00460 0.00773

54 yr dirty

1 .17062 0.00172 1 .15653 0.00237 1 .05034 0.00282 0.75094 0.007C Pu, 0% VF

54 yr dirty

1 .17102 0.00184 1 .15641 0.00235 1 .05207 0.00282 0.74920 0.006. Pu, 5% VF

54 yr dirty 1 .231 18

0.00421 1 .18980 0.00412 1 .13017 0.78691 0.01 86 Pu, 100% VF (1.245 with 0.00010 JEF-2.2)

There is good agreement between WIMS and MCNPX for k _in{ and k _s{{ at 0% and 5% VF. The VC differs by ±2 pern per % VF. This may be significant relative to the design VC (see below) but appears to be due to the statistical variation in the Monte Carlo calculations. However, there is a significant error in the 100% VF VC. This is because a thermal neutron flux is used in WIMS to calculate the multi-group cross-sections and this is, of course, less accurate in the highly voided case. This results in an error in VC of around ±5 pem per % VF in the 100% VF case. The error has a different sign in the two cases considered here, but this is due to ENDF/B-VII being used in WIMS and JEF-2.2 in MCNPX. When JEF-2.2 is used in WIMS, WIMS again overestimates the 100% VF VC relative to MCNPX. Therefore, the 100% VF VC calculation in WIMS appears generally conservative, and the WIMS approximation error is of the same order as the data library uncertainty. The 100% VF case is not used as a design criterion, but it may be advisable to use ECCO to prepare cross-sections (Rimpault, G., 1997. Physics documentation of ERANOS: the ECCO cell code. Technical Report RT- SPRC-LEPh-97-001 , CEA. in further analysis of a highly voided core.)

The error was larger after 53 years of operation. The reactivity was slightly lower in WIMS, so this error appears to result in a slight conservatism when calculating achievable burn-up.

The ICRW was evaluated as: ICRW ^"eff.rods-out ^eff,rods-in where x is the number of rods. ICRW calculations were performed for subsets of the control rods and x varied appropriately.

The ICRW was slightly overestimated in WIMS relative to MCNPX, with a significant error when the VF was 100%.

Burn-up calculations were performed with control rods out. The vacant water tubes will affect the neutron energies and therefore the evolution of the fuel compositions. This effect was not thought to compromise the overall validity of the analysis. 4. Performance

4. 1. TRU incineration

The burn-up analysis was performed for 125 years for the dirty Pu case to demonstrate the achievement of equilibrium behaviour. With dirty Pu/MA, the reactor was tending towards pseudo-equilibrium and the calculation was terminated after 49 years. Similarly, the variants on the dirty Pu reference case were terminated when their effects had been demonstrated.

The incineration rate (Figure 26) was generally 10-15% less than in a standard PWR. This was because a higher fraction of the power was generated from ²³³ U. As expected, the incineration rate was further reduced by lowering the dirty Pu enrichment. The incineration rate drops more rapidly in the uprated case as the power is higher, but the rate after a certain cumulative burn-up is comparable to the reference case.

4.2. Burn-up The one-batch end-of-cycle (EOC) burn-ups are shown in Figure 27.

The drop in burn-up after 60 years for the dirty Pu reference case is due to a reduction in the enrichment to prevent the MTC going positive. This is discussed in more detail in the next section.

The feasibility of attaining competitive one-batch burn-ups with sensible enrichments is demonstrated. Starting enrichments of 16 wt% are typical of Energy Amplifiers. The fuel will become progressively more difficult to handle as the MA content and radioactivity increase over time.

Higher TRU enrichment results in higher one-batch burn-ups. TRU enrichment will be practically limited by fuel fabrication feasibility. Hence, a measure of neutronic performance is the one-batch burn-up per wt% TRU enrichment. This is given in table 18 for the RMWR and the unmodified PWR. Table 18

Burn-up as a function of TRU enrichment.

Average one- Average TRU Performance Case batch burn-up enrichment (GWdt ^"

(GWdP) (wt%) per wt%)

RMWR, dirty Pu, 1 ^st 60 years 65.7 18.5 3.56

RMWR, dirty Pu, 2 ^nd 60 years 62.6 17.5 3.58

RMWR, dirty Pu, uprated 75.9 18.5 4.09

RMWR, dirty Pu, low enrichment 37.6 12.7 2.96

RMWR, dirty Pu/MA 44.6 17.0 2.63

PWR, dirty Pu, 1 ^st 60 years 50.6 16.9 2.99

PWR, dirty Pu, 2 ^nd 60 years 47.9 18.3 2.61

PWR, dirty Pu/MA overall 47.8 22.0 2.17

PWR, dirty Pu/MA 1 ^st 60 years 47.2 21 .0 2.24

PWR, dirty Pu/MA 2 ^nd 60 years 48.4 23.0 2.10

Reducing the moderation allows a greater burn-up to be achieved for the same enrichment. The relative increase is around 19% over the first 60 years of the dirty Pu reference case, rising to 37% over the second 60 years. The increase is around 17% over the first 60 years of the dirty Pu/MA case.

There is a decrease in performance over the second 60 years for a normal PWR as the quality of waste in the reactor decreases. Unsurprisingly, this reduction is less significant if the initial fuel load is dirty Pu/MA as the fuel is of lower quality. This is not the case in the RMWR. Reducing the reload enrichment of the RMWR results in a performance similar to that of a normal PWR. However, if a relatively low enrichment is desired, it demonstrates the feasibility of the concept with acceptable burn-up.

Increasing the rating of the RMWR increases the performance by an additional -15%. This is due to an improvement in the ratio of ²⁴ Pu absorptions to decays from -2:1 to -3:1 . Fissile ²⁴ Pu is therefore used more efficiently and the equilibrium ²⁴ Am population is reduced. ²⁴ Am is a neutron poison and makes the VC and MTC worse. Therefore, a slight improvement in VC of around -0.5 pern per % VF after the same number of cycles also resulted. As the EOC burn-up was higher, this meant that the uprated RMWR could be operated to a higher overall burn-up before the enrichment had to be reduced. The thermal-hydraulic feasibility of this operating point needs to be investigated. The RMWR provides the capability of achieving very high burn-ups. The average burn- up for the dirty Pu reference case, operating a 4-batch strategy, would be over 100 GWdt ^" [assuming a 60% improvement from a linear variation of reactivity with burn-up (Driscoll et al., 1990)]. If uprating is feasible, the burn-up approaches 120 GWd t ^"1 , which is competitive with the Energy Amplifier (Rubbia et al., 1995). This operating condition may be a challenging environment for components such as the fuel clad. However, the possibility of achieving high burn-up without requiring uranium (U) enrichment or weapons-grade Pu in the relatively benign conditions of an LWR would be a compelling argument for this technology.

4.3. Evolution of isotope populations The evolution of important isotopes for the dirty Pu reference case and the dirty Pu/MA case are shown in Figures 28 to 31 .

The principal differences with the unmodified PWR operating the same fuel cycle are an increase in equilibrium ²³³ U (due to its decreased absorption cross-section), an increase in the equilibrium ²⁴ Am population (due to a greater proportion of ²⁴ Pu nuclides decaying) and a decrease in equilibrium ²⁴³ Am and Cm isotope populations (due to the increased likelihood of isotopes undergoing fission instead of absorbing sufficient neutrons to breed these heavier isotopes).

Figure 32 shows the evolution of Pu isotope populations for the low enrichment case. Also plotted are the ²⁴ Am populations for all three dirty Pu cases. Lowering enrichment and increasing the power rating both decrease the ²⁴ Am population.

5. Reactivity and control

5. 1. Reactivity coefficients

The reloading parameters were specified to ensure that the MTC and VC remained negative throughout the life of the reactor (Figure 33 and 34). This limited the achievable enrichment and hence the achievable burn-up. The magnitude of the MTC was up to an order of magnitude less than in a conventional PWR. The control rods were assumed to be out for this calculation. The 100% VF VC was often positive but it was possible to design so that this was negative by reducing the enrichment (Figure 35). The low enrichment case does not outperform an unmodified PWR (Table 18). However, the 100% VC in the low enrichment case is relatively negative which suggests a compromise between the reference and low enrichment cases may be most appropriate if designing for a negative 100% VC. The 100% VC was negative in the PWR with dirty Pu fuel. By inspection from Table 18, if designing for a negative 100% VC a reduction in moderation may not prove advantageous.

The DC was generally between -3.5 and -4 pern K ^" . This was greater than for the unmodified PWR and may improve the performance during transients.

5.2. Control rods

5.2. 1. Control materials The control material had to be chosen to avoid a positive VC and MTC with rods in. Borosilicate control rods had a relatively low ICRW and had a detrimental effect on the VC and MTC. B ₄ C is more effective as the boron content is much higher.

An alternative is to use isotopes with high resonance integrals. An annulus of Ag / 15 wt% In / 5 wt% Cd was considered. This outperformed an enriched borosilicate rod but was not as effective as a natural B ₄ C rod. Partial or total enrichment of the B ₄ C to increase the concentration of ⁰ B was necessary to avoid a positive VC and MTC (Table 19).

Use of dysprosium has been considered to improve void reactivity in the Indian AHWR. Some isotopes of dysprosium may be suitable for control materials. Another option is enriched erbium. In a more complete analysis, the cost of each potential control material may also be considered. Table 19

Comparison of the performance of different control rod materials.

Enriched

Case Parameter Rods out ¹⁰ B ₄ C B ₄ C Ag-ln-Cd

borosilicate

16% dirty Pu 0% VF 1 .100 0.649 0.829 0.938 1 .034

16% dirty Pu 5% VF 1 .096 0.641 0.827 0.937 1 .032

-5.66x10 ^" -3.64x10 ^" ^1.68x10 ^" -2.23x10 ^"

16% dirty Pu VC 4 3 4 4 -2.36x10^

-8.35x10 ^" -5.02x10 ^" -3.00x10 ^"

16% dirty Pu ICRW 3 3 3 -1 .22x10 ^"3

16% dirty Pu AVC/ICRW 0.368 -0.020 -0.1 14 -0.269

54 yr dirty Pu 0% VF 1 .157 0.742 0.935 1 .037 1 .1 17

54 yr dirty Pu 5% VF 1 .156 0.741 0.936 1 .039 1 .1 18

-1 .79x10 ^" -7.13x10 ^"

54 yr dirty Pu VC 5 4 1 .44x10 ^"4 2.38x10 ^"4 1 .97x10^

-7.67x10 ^" ^1.10x10 ^" -2.21 x10 ^"

54 yr dirty Pu ICRW 3 3 3 -7.31 x10^

54 yr dirty Pu AVC/ICRW 0.091 -0.039 -0.1 16 -0.294

Fully enriched B ₄ C improved the VC by absorbing a large proportion of the incident neutrons, but all other materials made it significantly worse, which would result in a positive VC for the dirty Pu reference case at some points in the cycle. Therefore, B ₄ C was the preferred control material, and it should be at least partially enriched.

In the dirty Pu/MA case, if two or more batches are operated, the reactivity swing is sufficiently low that few enough Ag-ln-Cd or natural B ₄ C control rods need to be deployed to maintain criticality with a negative VC. In the dirty Pu reference case, the VC is only just negative and control of the reaction in this manner is not possible. In the low enrichment dirty Pu case, all the natural B ₄ C or Ag-ln-Cd rods can be deployed without the VC going positive. Soluble boron was not considered due to the reduced coolant fraction in the core and the additional MTC penalty of reduced boron density with coolant density. However, burnable poisons would probably be used in practice, but are not considered here.

5.2.2. Assembly design The AFF was calculated assuming a fuel load of 16 wt% dirty Pu. With the rods out, the hot rods were near the corners of the fuel assembly where the neutrons were more thermal. The AFF was 1 .34 (Figure 36). A maximum permissible AFF value was taken as 1 .5. As the MTC magnitude reduces over time, the rods-out AFF will be reduced. A better AFF is achievable by varying enrichment across the assembly, but at this stage in the investigation of this concept it was sufficient to investigate a feasible design to simplify the calculations.

With all the rods in, the AFF was reduced to -1 .2 (Figures 37 and 38). The hot rods were again located at the edge of the fuel assembly, where the neutrons were more thermal.

The ICRW decreased slightly with time as the dirty Pu enrichment increased. The maximum reactivity swing over a one-batch cycle is 0.16. This would be reduced by -60% if a 4-batch cycle was operated. Therefore, natural and enriched B ₄ C and Ag-ln- Cd provided sufficient ICRW to control and shut down the reactor. If enriched B ₄ C rods are used, it may be possible to reduce the number of control rods.

Different control rods have a different effect on the VC and have different ICRWs. In general, the outer rods have a better ICRW but a worse effect on the VC (Table 20). This suggests that, if using natural B ₄ C or Ag-ln-Cd rods, it is beneficial to control the reactor using the inner rods. Table 20

Analysis of the effect of different Ag-ln-Cd control rods.

Parameter Rods in Year O Year 54 Year 1 15

ICRW 6 innermost -3.09x10 ^"3 -2.09x10 ^"3 -2.16x10 ^"3

18 innermost -2.83x10 ^"3 -2.02x10 ^"3 -2.04x10 ^"3

12 outermost -3.93x1 (Γ ³ -3.93x10 ^"3 -2.86x10 ^"3

AVC (per % VF) 6 innermost -4.06x10 ^"6 1 .18x10 ^"5 1 .45x10 ^"5

18 innermost 3.33x10 ^"5 4.50x10 ^"5 5.08x10 ^"5

12 outermost 6.63x10 ^"5 7.50x10 ^"5 8.23x10 ^"5

AVC/ICRW 6 innermost 2.19x10 ^"4 -9.45x10 ^"4 -1 .12x10 ^"3

18 innermost -6.53x10 ^"4 -1 .24x10 ^"3 -1 .38x10 ^"3

12 outermost -1 .41 x10 ^"3 -2.22x10 ^"3 -2.40x10 ^"3

AFF 18 innermost 1 .47 1 .39 1 .38

Using the inner 18 rods, the change in VC per rod can be reduced by nearly half and the AFF remains under 1 .5 for Ag-ln-Cd. The higher ICRW of rods towards the edge of the fuel assembly may be useful for emergency shutdown.

The enriched B ₄ C rods have a much higher ICRW and therefore for certain combinations of rods the AFF can exceed 1 .5. The control rods all improved the VC (Table 21 ). As before, the rods at the edge of the fuel assembly had a higher ICRW.

Table 21

Analysis of the effect of different enriched B ₄ C control rods.

Parameter Rods in Year O Year 54 Year 1 15

ICRW 6 innermost -8.51 x10 ^"3 -7.56x10 ^"3 -7.47x10 ^"3

18 innermost -8.76x10 ^"3 -7.82x10 ^"3 -7.72x10 ^"3

12 outermost -1 .05x10 ^"2 -1 .05x10 ^"2 -9.06x10 ^"3

AVC (per % VF) 6 innermost -1 .74x10 ^"4 -1 .08x10 ^"4 -1 .13x10 ^"4

18 innermost -5.47x10 ^"4 -3.33x10 ^"4 -3.48x10 ^"4

12 outermost -3.38x1 (Γ ⁴ -8.83x10 ^"4 -2.07x10 ^"4

AVC/ICRW 6 innermost 3.40x10 ^"3 2.39x10 ^"3 2.53x10 ^"3

18 innermost 3.47x10 ^"3 2.37x10 ^"3 2.50x10 ^"3

12 outermost 2.69x10 ^"3 4.85x10 ^"3 1 .90x10 ^"3

AFF 18 innermost 1 .61 1 .51 1 .51

The control requirements can be reduced by increasing the number of batches. In the dirty Pu reference case, the rating was lower than in a normal PWR and the one-batch burn-up was significantly better. As a result, the one-batch fuel cycle length was approximately 9 years. Assuming a linear variation in reactivity with burn-up, the n- batch fuel cycle length is 2/(n + l) χ 9 years. 18 month fuel cycles are typical for PWRs. A fuel cycle of this length would result in 1 1 -batch operation for the RMWR. This would generally be considered very high due to the diminishing returns in improved burn-up (15% better than a 4-batch strategy) with a large reduction in fuel cycle length (58% relative to a 4-batch strategy) and the corresponding increase in down-time. It does, however, reduce the required control rod enrichment and may allow Ag-ln-Cd or natural B ₄ C control rods to be used instead, if combined with other VC and MTC mitigation strategies. 5.3. improvement of moderator reactivity coefficients

It has been shown that the MTC and VC limit the TRU enrichment and therefore the attainable burn-up. Various mitigation strategies are possible. 5.3. 1. In-core fuel management

Qualitatively, the VC can be improved by loading fuel with more positive VC (calculated using the change in k _ini ) on the periphery of the core, and fuel with more negative VC in the middle. When the VF increases, this causes the outside of the reactor to become 5 relatively more reactive and the flux profile to become flatter. This therefore increases the neutron leakage. This strategy is especially attractive because it does not necessarily involve compromising the form factor or reactivity.

This is similar to the strategy of using an (axial) internal blanket.. This is an effective strategy for improving the VC and is worth considering. However, it can result in

10 decoupling of the fluxes in the top and bottom of the reactor increasing the likelihood of high power peaking. Here, the transient nature of the fuel load allows this scenario to be avoided. The simplest strategy is to enrich the centre with fresh dirty Pu and the outside with dirty Pu which has been in a reactor for longer. If the Th is separated from the Pu at the end of the fuel cycle (which will incur additional cost), then the fresh Th-

15 -60 wt% dirty Pu can be diluted with additional Th from the reactor, reducing the enrichment of the old fuel. If not, some of the fresh dirty Pu can be diluted in the old fuel, but this results in a smaller fresh fuel region and is therefore less effective.

A simple calculation was performed after 54 years for the reference case dirty Pu loading using an infinite radius, finite height model in MCNPX. This represents the most 20 severe condition for the VC and MTC. The reactor was assumed to be infinitely wide with a finite height to give the correct buckling. The fresh dirty Pu was diluted to 20.2% and occupied the central 21 % of the reactor. The rest of the fuel was loaded above and below. For the specified 5 _g ² , of 0.000213 cm ^"2 , the effective diffusion length L, is found from

For homogeneous fuel, L ² is greater at 5% VF than at 0% VF by about 5%. This leakage effect improves the VC by -10 pern per % VF, without which the VC would be positive. The heterogeneous fuel load specified here increased the difference in effective L ² by a further 3%, corresponding to an additional ~7 pem per % VF improvement in VC. This is a significant improvement which would keep the VC negative with rods in if realized throughout the reactor's life.

Results also indicated that a slight improvement in k _M may be realizable using heterogeneous fuel. Further investigation is required here. Detailed consideration of in-core fuel management is necessary to determine if this improvement is realizable and practical. An additional mechanism for improving stability is to move the bred ²³³ U to the centre of the core. This requires removing U on reprocessing, which is a proven process but increases costs. Heterogeneous fuel may also result in variation in dirty Pu enrichments across the core which reduces the performance measure of burn-up per wt% TRU enrichment.

5.3.2. Geometric buckling

The Japanese RMWR has a reduced core height and therefore a higher 5 _g ² in order to improve the VC. This method could also be applied to the RMWR presented here. However, increasing 5 _g ² also increases the enrichment required to achieve a specified burn-up. Increasing the TRU enrichment in turn increases the VC.

Assuming a linear variation in reactivity with burn-up, the effect of 5 _g ² on VC was calculated by changing the 5 _g ² for the dirty Pu reference case after 0, 54 and 1 15 years. In each case, the change in VC and burn-up was calculated for different values of 5 _g ² . The change in VC with burn-up was approximately 1 .2 pern per % VF per GWd r ¹ .

The effect of a change in fuel enrichment on VC and burn-up was also calculated. The change in VC with burn-up for varying fuel enrichment was -0.55 pem per % VF per GWd Γ ¹ . Therefore increasing the TRU enrichment and the buckling resulted in a net decrease in VC. For example, if 5 _g ² was increased to 0.0005 cm ^"2 , the fuel enrichment would be increased by 0.93 wt% to maintain constant burn-up. This would cause a total change in the VC of -5.9 pem per % VF. This is of the same order as the reference case VC. This change decreases burn-up per wt% TRU enrichment. With 5 _g ² = 0.0005 cm ² , the

RMWR is -5% better than the unmodified PWR, and with 5 _g ² = 0.0006 cm ^"2 , the two have approximately equal performance. However, reducing the core height is also likely to increase the attainable power rating which may mitigate or negate the decrease in burn-up.

When the core is fully voided, L ² is much greater. Higher 5 _g ² is likely to be advantageous when designing for a negative 100% VF VC.

This calculation does not take into account the detrimental effect on VC of the increased TRU enrichment in one cycle over subsequent cycles. This effect may be significant. While fuel management strategy can be changed over a reactor's life, the core dimensions are fixed and cannot be temporarily adjusted to improve VC.

5.3.3. Void tubes

Void tubes are assemblies with many of the fuel pins removed. These improve the VC through a leakage effect, but are not considered here as they are beyond the scope of an assembly-level analysis.

6. Comparison with other reduced-moderation fuel cycles

The fuel cycles presented here achieve significantly higher burn-ups, than other arrangements but this is a consequence of higher enrichment. However, the low enrichment case would achieve 60 GWd Γ ¹ 4-batch burn-up with TRU enrichment comparable to fast reactors. An RMWR appears a competitive option if relatively low dirty Pu enrichment is required, and use of Th/dirty Pu in RMWRs can provide competitive burn-ups relative to other RMWR fuel cycle concepts.

The fuel cycle presented may be used in a reduced-moderation BWR with reduced core height for potential further gains in performance. This may also be a good option to keep the dirty Pu enrichment low, or if a smaller reactor is required due to grid restrictions.

Specific characteristics of RBWR type reactors, in the context of the present disclosure, will now be described. Stability of the reactor can be improved by heterogeneous axial design to enhance neutron leakage (Fig 39). In the illustration of Figure 39, the columns are representations of fuel assemblies in which Th is indicated in white, Th-Pu mixture is indicated in solid black, and the hatched area represents Th-U-Pu where the U is bred from Th.

Over multiple cycles, bred U-233 can be located in the central region to reduce power peaking and improve burn-up (Fig 1 b). The axial blankets improve the conversion ratio, allowing more U-233 to be bred. This may reduce the incineration rate, but has the potential to improve burn-up and stability by allowing more U-233 to be located in the internal blanket, ere U is bred from Th.

High enrichment of seed regions hardens the local neutron spectrum resulting in significant reduction in MA populations, especially Cf-252. With very high seed enrichments (e.g. 70 at%), the Cf-252 population can be reduced to negligible levels in an RBWR. In general, an RBWR may be advantageous over the PWR concepts due to the decrease in MA (e.g. Cf-252) populations.

Hexagonal Reduced-Moderation Assemblies

As part of the preliminary study of the triangular pitch RMPWR design presented previously, a steady state thermal-hydraulic analysis was performed. In particular, as there are direct cost and indirect fuel cycle advantages to operating the core at higher power density, it is desirable to determine if uprated operating points are feasible. This disclosure also provides guidance on the assembly design in order to minimise power peaking.

A 1/12th assembly model was constructed in COBRA with a triangular pitch of 1 .32 cm, fuel pins of diameter 1 1 .8 cm, an overall assembly span of 29 cm across the flats and a 3 m height. As before, a steady state calculation was performed to find the pressure drop and inlet temperature (for an outlet temperature of 597.5 K in this case). Then the MDNBR calculation was carried out at 1 12% overpower with a radial power peaking factor of 1 .587, 2K increased inlet temperature and 5% reduced mass flow rate. Figure 40 illustrates this, with pin numbers in black and subchannel numbers in red. To achieve the same power density as the Westinghouse 4 loop PWR, a rating of 26.6 MW/te is required for the RMPWR. The rating of 19.9 MW/te selected for the initial neutronic study is therefore quite low at the same mass flux, and the MDNBR is correspondingly high (Table 22).

At a rating of 26.6 MW/te, the MDNBR is reduced, as the effects of higher power peaking and higher coolant exit quality outweigh the reductions in heat flux and core height. However, it is still acceptable.

The hot rod and channel for MDNBR do not correspond to the high power peaking at the assembly edge due to the relatively high coolant area to fuel area ratio at the edge of the assembly. Instead, the critical point is very close to the centre of the assembly. Therefore, assembly design should focus on reducing the power peaking in the relatively hot rods at the centre of the assembly, not at the assembly edge as might be expected. Variable enrichment may prove a useful tool in accomplishing this, although the position of the near-centre control rods has a significant effect. At a mass flux of 3728 kg/m2/s, the pressure drop is increased slightly, despite the number of spacers being reduced from 8 to 5, but this is thought to be acceptable. At a rating of 30.4 MW/te, the mass flux must be increased to achieve an acceptable MDNBR. This results in a further increase in pressure drop. In order to operate at a higher rating, the core height may need to be reduced further which may not be desirable. Alternatively, the core outlet temperature could be reduced. Note that the quality at the critical point for this last calculation is 0.16, slightly beyond the range of validity for the W-3L correlation. This is, however, satisfactory for this initial study.

7 Reprocessing and Fabrication Issues

7.1 Introduction

Assuming that an acceptable core can be designed, the practicality and economics of the back end of the fuel cycle are crucial; especially as closed fuel cycles are generally more expensive. The objective of this section is to analyse the relative technical and practical implications of the proposed fuel cycle relative to other closed fuel cycles. The models in Sections 3 and 4 have assumed instantaneous refuelling. As has been discussed, quick refuelling is generally considered for FRs in order to breed fissile fuel at acceptable rates. This requires appropriate infrastructure and the ability to handle short cooling times. Co-location of the reprocessing plant and reactor is likely to be necessary (OECD, 2002) which may favour small scale facilities and therefore pyrochemcial reprocessing methods. However, one or two large dedicated MOX plants operating as incinerators could be located next to centralised reprocessing infrastructure. This scenario appears likely in the UK.

Long cooling times may be advisable to reduce heat from SF, mostly due to Cf-252 (Shwageraus, 2003). However, longer cooling times increase the decay of Pu-241 into Am-241 , reducing fuel cycle length (Ferrer et al., 2008).

7.2 Method

The inventory code FISPIN 10 was used to determine isotope populations, activities and reaction rates over multiple reprocessing stages during the fuel cycle and cooling. Cross section libraries were generated using the WIMS 9 models presented in previous sections.

Studies for the PWR and RMPWR were performed for 1 1 recycle stages assuming a 7 year cooling time between fuel cycles, but inventories and activities were output at 0, 5, 7 and 21 years after discharge for comparison and analysis. This is suitable for a general analysis of the fuel cycle characteristics with the potential for more specific studies later. In particular the impact of shorter or longer cooling times will be investigated, and the possibility of separating out MAs and cooling it for longer will be investigated. This may help promote the decay of Cm-244 and Cf isotopes therefore restrict build-up of heavier isotopes which are SF sources, and may also aid neutronic performance.

This may have implications for proliferation resistance (Royal Society, 201 1 ), but these may be limited (Kang and von Hippel, 2005).

7.3 Fuel cycle length For the PWR, a 7 year cooling time was found to result in a large penalty on the fuel cycle length, limiting the attainable burn-up to around 30 GWd/te with reload enrichments of around 90%. The severity of this reactivity penalty is a result of the large Pu fraction in the core. The TRU enrichment is around 22wt% at the 10th recycle stage. With these long cooling times, the 1 1 th recycle stage is around 120 years after start of operation, so while it does not appear that the fuel cycle could be maintained indefinitely, it is arguable whether an analysis of current reactor technology is relevant by this point. The MTC remains negative throughout but the 100% VC for dirty Pu loading goes positive by the 8th recycle stage. By the 9th or 10th recycle stage, the DC is not sufficient to prevent a positive total reactivity coefficient in the event of a LBLOCAWS (large break loss of coolant accident without scram).

With reload enrichments of around 50%, the RMPWR can maintain a burn-up of 48 GWd/te, a negative MTC and a negative 100% VC over 1 1 recycle stages, with the results implying this position is maintainable indefinitely.

7.4 Decay power and activity

The short term decay heat of the actinides and fission products will have an effect on the response of the reactor to a LBLOCA. The decay heat PWR fuel after 10 stages and a burn-up of 41 .2 GWd/te was compared to 5.0 wt% enriched U-235 uranium fuel at the same burn-up. It was confirmed that the very short term decay heat is still dominated by the fission products, even though the actinide decay heat is significantly higher. The fission product decay heat for Th-Pu fuel is initially slightly lower, leading to a similar total initial decay heat.

At 0.1 days, the effect of higher activity actinides results in significantly higher decay heat in the Th-Pu fuel. At 1 day, the decay heat of the Th-Pu fuel is 1 .75 times higher, and over several years the relative decay heat becomes substantially higher compared to enriched U fuel.

The actinide activity is initially very similar for both fuels but on the order of days to years, the activity of the Th-Pu fuel becomes 1 -2 orders of magnitude higher. These differences may affect the cost of reprocessing the fuel. However, the response of LBLOCA where the vessel is reflooded within 30s should be acceptable.

Table 23: Decay heat and activity of 10th stage Th-Pu PWR fuel at 41 .2 GWd/te time

Table 24: Decay heat of 5 wt% enriched U fuel at 41 .2 GWd/te

0.01 1.23E+18 2.95E+18 9.02E+04 6.15E+05 7.06E+05

0.03 9.63E+17 2.41E+18 7.06E+04 4.48E+05 5.18E+05

0.1 7.58E+17 1.94E+18 5.57E+04 3.01E+05 3.56E+05

0.3 7.03E+17 1.60E+1S 5.19E+04 2.16E+05 2.67E+05

1 5.73E+17 1.23E+18 4.27E+04 1.52E+05 1.95 E+05

10 5.78E+16 6.82E+17 5.55E+03 78978 8.45E+04

100 7.7SE+15 2.45E+17 1.57E+03 26567 2.81E+04

365.25 6.67E+15 9.32E+16 683.3 10343 1.10E+04

730.5 6.06E+15 5.21E+16 350.31 5529.4 5.88E+03

1095.75 5.72E+15 3.48E+16 282.93 3491.9 3.77E+03 The decay power is initially dominated by Cm-242 decay, with Cm-244 and Pu-238 becoming more significant on the order of a few years. The main contributions to the total activity are beta decay of Th-233, Pa-233, Pu-241 (tables 25, 26).

Table 25: Highest contributions to decay powers (W/te fuel)

Table 26: Highest contributions to activity (Bq/ te fuel)

Figure 41 provides an illustrative graph of the above results.

7.5 Thorium cycle issues Thorium reprocessing has never been performed on a commercial scale and there remain challenges in developing commercial reprocessing routes (IAEA, 2005). While it is important to be aware of these issues, the scope of this section is limited to a comparative analysis of the proposed fuel cycle with alternative thorium fuel cycles. One specific problem with the Thorium cycle is the decay time of Pa-233. It is important to recover a very high proportion of this to retrieve fissile material and reduce waste toxicity (IAEA, 2005). This requires either recovering Pa-233 with the actinides, or a cooling time of at least 12 months. This may be difficult to reconcile with the need for a fast reprocessing time to limit the impact of Pu-241 decay. Two stage reprocessing where decayed Pa-233 is extracted later may be theoretically feasible but practically undesirable.

A second problem is the production of TI-208, which emits very high energy photons (2.6 MeV). This is produced by the decay of U-232:

U-2320Th-2280Ra-2240Rn-2200Po-2160Pb-2120Bi-2120TI-208OPb -208 (stable).

The decay of Bi-212 to Tl=208 has a branching factor of 35.94%. The half lives of these decays are: 68.9 years; 1 .91 years; 87.2 days; 55 s; 0.15 s; 10.64 hr; 60.55 min; 3 min respectively. From these figures it is apparent that this is a short-lived decay chain and therefore is relevant to fuel reprocessing and fabrication rather than geological storage. In the reactor, the Th-228 approaches equilibrium after around 8 stages (Figure 42). The reprocessing time has little effect on subsequent stages because the U-232 population remains approximately constant in the short term and so the production and decay rates of Th-228 are comparable. There is a slight rise in Th-228 population after discharge, peaking after 6.5 years. This is due to the lack of neutron captures as a removal route.

The short subsequent decay times result in the TI-208 population tracking the Th-228 population closely. The maximum occurs after 6.5 years decay time at 21 % of discharge population, and at 20 years the population is still 8% above discharge population. The equilibrium quantity of TI-208 is about 6 times higher than the quantity after stage 1 .

The Th-228/U-232 ratio in the reactor is around 2.1 % for both the PWR and RMPWR. The U-232 population (and therefore TI-208) population is -14% higher in the RMPWR.

For comparison, an estimate of the equilibrium TI-208 population in a closed cycle Th FR was estimated using the cross sections from (Rubbia et al., 1995). The enrichment of Th-232 was assumed to be held constant at 85 at%. There are two U-232 production routes:

Th-232 (n, gamma) O Th-233 O Pa-233 O U-233 (n,2n) O U-232 The U-233 population can be calculated by assuming equilibrium:

^Σ Γ ,Ζ¾ 23 -½ι 232 ^{= C} V!7233 233

Th-232 (n,2n) O Th-231 O Pa-231 (n,gamma) O Pa-232 O U-232

Th-231 and Pa-232 have half lives of the order of hours, while the half life of Pa-231 is thousands of years. Therefore this can be simplified to a single path:

Th-232 (n,2n) O Pa-231 O U-232

Therefore:

H 2H,77I 232

Where x is the isotope population; φ is the flux and σ denotes the microscopic cross section of the relevant isotope; λ is the decay constant; with the subscripts having their usual meaning. The U-233 and Th-232 decays are considered insignificant. In a similar manner, the Th-228 equilibrium population can be calculated, with an estimate for the cross sections being the fast spectrum values from (JAEA, 2010).

The FR flux was estimated as 4.2 x 1015 n/cm2/s using a specific power of 53 MW/te. The FR TI-208 population is therefore estimated to be twice as high as the PWR. It is worth noting that the (n,2n) cross sections produced using WIMS or MONK were generally significantly higher for thermal reactors, and the key factor in the higher FR TI-208 population was the significantly higher flux. This higher cross section was a result of a higher neutron flux at energies above 6 MeV in the PWR and RMPWR than the FR. While the relative number of neutrons at these higher energies is indeed lower than a fast reactor, their contribution to the normalised flux is higher. Figures 43 and 44 show Normalised neutron fluxes and energies for typical well-thermal andfast systems (generated using a homogeneous 172 group monte carlo calculation in MONK) The absolute flux > 6 MeV for the fast reactor for a given rating is indeed higher than the thermal reactor.

Table 27: Equilibrium TI-208 proportions in fuel PWR RMPWR FR

5.34E- 12 6.16E-12 1.07E-1 1

The gamma activities for the 10th stage in the PWR burned to 41 .2 GWd/te are given in Tables 28 to 30. Initially, the fission product gamma source is far more significant than the TI-208 source, but after 100 days the TI-208 source is before the most significant high energy gamma emitter.

Table 28: Gamma energies at discharge

Table 29: Gamma energies after 100 days cooling lower upper Actinide fission product highest % actinide

MeV MeV photons photons contribution

0 0.01 4.99E+15 1 .95E+15 Pa233 50.82

0.01 0.02 2.39E+16 1 .25E+14 Pa233 54.49

0.02 0.05 1 .46E+14 6.90E+15 Pa233 38.52

0.05 0.1 8.60E+15 6.72E+14 Pa233 92.6

0.1 0.2 2.35E+15 7.32E+15 Pa233 95.42

0.2 0.3 2.43E+14 2.19E+14 Pa233 47.5

0.3 0.4 1 .4 E+16 1 .37E+14 Pa233 99.95

0.4 0.6 5.37E+14 1 .68E+16 Pa233 89.53

0.6 0.8 1 .24E+13 6.71 E+16 ΒΪ212 90.08

0.8 1 7.58E+12 1 .02E+15 TI208 87.43

1 1.22 1 .18E+12 9.52E+14 ΒΪ212 67.86

1.22 1.44 3.04E+10 3.15E+14 TI208 99.04

1.44 1.66 2.56E+12 4.76E+14 ΒΪ212 99.9

1.66 2 2.77E+1 1 4.06E+13 ΒΪ212 99.61

2 2.5 1 .16E+07 2.72E+14 ΒΪ214 99.93

2.5 3 5.10E+13 1 .52E+13 TI208 100

3 4 39164 5.07E+1 1 ΒΪ214 100

Table 30: Gamma energies after 1 year cooling

lower upper Actinide fission product highest % actinide MeV MeV photons photons contribution

0 0.01 1 .41 E+15 5.59E+14 Cm242 35.6

0.01 0.02 6.37E+15 7.50E+12 Cm242 33.92

0.02 0.05 7.51 E+13 2.87E+15 Am 241 63.65

0.05 0.1 6.77E+14 3.46E+14 Am 241 77.45

0.1 0.2 1 .07E+14 2.16E+15 Cm243 40.26

0.2 0.3 1 .32E+14 3.48E+13 Pb212 50.19

0.3 0.4 2.40E+13 1 .78E+13 Pa233 66.54

0.4 0.6 6.07E+13 4.75E+15 TI208 97.16

0.6 0.8 1 .32E+13 1 .64E+16 ΒΪ212 90.56

0.8 1 8.10E+12 5.39E+14 TI208 87.82

1 1.22 1 .26 E+12 5.1 1 E+14 ΒΪ212 68.63

1.22 1.44 3.24E+10 2.43E+14 TI208 99.57

1.44 1.66 2.75E+12 9.88E+13 ΒΪ212 99.92

1.66 2 2.97E+1 1 1 .81 E+13 ΒΪ212 99.61

2 2.5 1 .17E+07 1 .40E+14 ΒΪ214 99.93

2.5 3 5.47E+13 2.46E+12 TI208 100

3 4 39715 2.54E+1 1 ΒΪ214 100 Figure 45 illustrates the TI-208 population relative to U-232 population during cooling

7.6 SF neutron sources

Over 10 recycle stages, the rate of SF neutron emission rises significantly (Figure 46) due to a build-up of even isotopes of Cf and Cm. Over early stages the source is dominated by Cm-244, with Cf-252 becoming more significant after 5 stages. Cf-252 has a relatively short half life of 2.54 years, compared to 18.1 years for Cm-244. Therefore over the cooling time, the contribution of Cm-244 becomes more important.

(OECD, 2002) reported neutron sources of around 1010 and 101 1 n/s/te HM for a fast breeder reactor and a fast TRU incinerator respectively, compared to approaching 1012 n/s/te HM for this fuel cycle after 10 stages. A 5 year decay before fabrication still results in a significantly higher neutron source than the fast TRU incinerator, but of the same order of magnitude. The spontaneous neutron source therefore represents a significant problem. Adapted handling technology will be required. The neutron source at discharge would be even higher without the 7 year decay times between previous stages. In future work, the neutron source with shorter and longer reprocessing times will be investigated.

(OECD, 2002) also considers an MA burning ADS with a neutron source of order 1013 n/s/te HM, but this reactor would be a highly specialist incinerator. A faster neutron spectrum generally suppressed MA build-up as the isotopes become more fissile. However, the RMPWR only has a slightly smaller SF source than the PWR initially, and by the 10th recycle stage, the Cf-252 population and hence the SF source at discharge is higher.

(Downar et al., 2012) analysed a U-fuelled RBWR with a Cf-252 atomic fraction in the fuel of 5.56 x 10-6, compared with 3.32x10-7 and 4.32x10-7 at discharge after 1 1 stages for the PWR and RMPWR respectively. To investigate why this effect occurs, it is illustrative to consider the principle MA capture chain (neglecting isotopes with short half lives):

Pu-2420 Am-2430 Cm-2440Cm-2450 Cm-2460 Cm-2470 Cm-2480 Cf-2490 Cf- 2500 Cf-2510 Cf 252 The RMPWR is indeed effective at suppressing the build-up of the earlier isotopes in this chain. However, at later recycle stages, the population of heavy isotopes exceeds that of the PWR.

This can be explained by considering this chain as a set of simple coupled differential equations of the form (see for example (Coates et al., 201 1 )):

dx

at

Although σ is generally less for the RMPWR, φ is greater to compensate for the lower fission cross section and the rates of isotope build-up are comparable. The greater fission to capture cross section ratios for the RMPWR result in MA isotope populations saturating at lower values, but for 10 recycle stages, most of the heavy isotopes are still within their initial transients (e.g. Figure 47). Solving this system of equations (performed in Matlab for expediency), using cross sections and fluxes from WIMS and FISPIN, confirms this effect. A constant population of Pu-241 was considered. This is a representative first order approximation to the refuelling scheme. This was slightly lower in the RMPWR than the PWR. The Cm-244 population is predicted to be close to saturation after 40 years of continuous operation. This is fairly consistent with the WIMS and FISPIN simulations but these predict slight accumulation up to around 120 years. However, this simple model would not be expected to predict anything more than a general trend as it doesn't account for changing cross sections. The final saturation populations of Cf-252 are expected to be significantly higher than after 10 recycle stages (-40 years of operation) for the PWR and RMPWR, but saturation occurs earlier in the RMPWR.

A generic FR was then considered in a similar manner using one group cross sections from (Coates and Parks, 2010). This confirmed that if a FR is used, a large benefit in both the initial transient and the final saturation value results.

Figure 48 shows Accumulation of Cm-244 over time, while Figure 49 shows Accumulation of Cf-252 over time. The SF neutron problem is therefore significantly more severe in closed cycle thermal reactors than FRs, especially if short reprocessing times are required. Moving to an epithermal neutron spectrum does not mitigate this problem in the medium term. 7.7 Improvement using RBWR or increased enrichment

The following figures show that a significant decrease in Cm-244 population is possible using an RBWR. Higher Pu enrichment is also very effective. The Cf-252 population can be significantly suppressed. Figure 50 shows Cm-244 population versus time (yrs), while figure 51 shows Cf-252 population for RMPWR at 14 at% (blue) and 28 at% (green) Pu enrichment.

Figure 52 shows Cf-252 population in RBWR where:

14 at% 0.7g/cc water density = blue

28 at% 0.7 g/cc water density = green

28at% 0.4 g/cc water density = red

Figure 53 shows Cf-252 population in RBWR and Fast Reactor

28 at% 0.1 g/cc water density = blue

70 at% 0.1 g/cc water density = green

14 at% fast reactor = red

NB the RBWR is not better than the fast reactor- this is a rate effect due to not compensating for high seed region flux. The equilibrium levels will probably be similar.

8. Conclusions

Reducing the moderation in a PWR increases the burn-up for a given TRU enrichment by around 20%. This may have practical advantages for fuel reprocessing and pellet fabrication. The VC limits the possible enrichment, and this limit is quite severe if a negative 100% VC is enforced. In this case, although a reasonable burn-up can still be achieved the reduced-moderation configuration may not be advantageous. Strategies have been identified to mitigate this. The control system should be designed to minimize the effect on moderator reactivity coefficients. The economic viability is likely to be dependent on the achievable thermal-hydraulic operating point. In particular, it is necessary to perform a coupled neutronic-thermal-hydraulic analysis of the core to determine the feasibility of the design, although the steady-state thermal-hydraulic operating point appears acceptable.

Decay heat should not affect the reactor performance during LOCAs. A major issue with multiple thermal recycle of TRU waste is the very high SF neutron source. The usual issues with a closed Thorium cycle apply, although the TI-208 problem is less severe. Remote handling of spent fuel will be required. It may be difficult to compromise between the advantages of a long cooling time (Pa-233 and Cf-252 decay) and a short one (Pu-241 decay). For short cooling times, the ability to separate Pa-233 and handle high activities and decay heats will be required. An RMPWR is significantly more forgiving if a long decay time is desired.

While certain embodiments have been described, these embodiments have been presented by way of example only, and are not intended to limit the scope of the inventions. Indeed, the novel methods, products and apparatus described herein may be embodied in a variety of other forms; furthermore, various omissions, substitutions and changes in the form of the methods, products and apparatus described herein may be made without departing from the spirit of the inventions. The accompanying claims and their equivalents are intended to cover such forms or modifications as would fall within the scope and spirit of the inventions.