It is, perhaps, useful to discuss some of the hidden biases in the calculation of LCOE even if it is not always possible to accurately quantify them.

One fixed discount rate

The calculations presented here assume that one discount rate applies for all time and to all forms of generation. But Eq. 5.1 indicates that the discount rate depends upon p, the coefficient of relative risk aversion, which expresses the commercial risk of a venture compared to a safe investment. It seems likely that, to a potential investor, a mature, widely deployed developed technology such as CCGT will be preferred to one that is only part developed such as coal+CC. Also, a proposal that requires heavy funding might not be as favoured as one that does not — simply because of the added difficulty of accumulating a large fund. Finally, our investor may be swayed by ‘policy risk’: the possibility that, though one form of generation may now be encouraged by government, this preference may not endure. For these and other reasons it has been suggested15 that investment in nuclear power may incur a 3-5% premium in financing costs over other technologies. A recent report for the UK Committee on Climate Change goes further, arguing that discount rates may also be skewed against high-risk projects and supports this with data gathered,16 which from investment firms in the City of London (columns 2 and 3 of Table 5.4). The report focuses on low-carbon technologies and therefore provides no values for coal-fired generation without carbon capture. For this technology, therefore, we adopt the values for CCGT but raise the numbers by 2% to account for additional policy risk. We then calculate the corresponding LCOE values and compare them with the values presented previously in Table 5.3.

Such an approach clearly has the potential to completely upset any rankings derived for a constant discount factor. With the exception of CCGT, all the average discount rates are higher than the 7.5% adopted in this study. This is consistent with the idea that private investors will generally apply higher discount rates to investments seen as large and commercially ‘risky’. As a result we see that, at the most disadvantageous rates, the LCOE values for nuclear and coal+CC are increased by 75% and 88% respectively.

Conversion is the process of manufacturing pure UF6 from the yellowcake generated by the mining and refining process. It requires the use of a combination of fluorine and HF in aqueous or gaseous form to fluorinate the oxide feed. There is one established process where this is carried out using fluorine gas alone. Purification is carried out along the way so that the conversion process will incorporate a number of stages.

There are five major providers of commercial conversion services, these being:

1 Rosatom/JSC TVEL (Russia)

2 Honey well/Converdyn (USA)

3 AREVA NC/Comurhex (France)

4 Cameco (Canada)

5 Westinghouse/Springfields Fuels Limited (SFL, UK)

All of these organisations have been operating successfully for many years, each using a different process. Figure 7.2 shows a schematic based upon the processes used by Cameco, AREVA and SFL, as while there are some differences amongst the three, they may easily be considered together.

In this process, the yellowcake is first dissolved in concentrated nitric acid to form uranyl nitrate in solution:

U3O8 + 8HNO3 ^ 3UO2(NO3)2 + 2NO2 + 4H2O [7.2]

Tributylphosphate (TBP) dissolved in a hydrocarbon diluent, such as kerosene, at a concentration of 20-25% is then mixed and agitated with the uranyl nitrate solution so that the uranium is extracted into the solvent phase. The uranium is separated from the aqueous phase with very high efficiency under the right chemical conditions, leaving the impurities behind in the aqueous phase. The uranium is then washed out of the solvent with fresh, dilute nitric acid or water to give a solution of purified uranyl nitrate. The kerosene does not have a chemical role in the extraction process, but serves to lower the density of the solvent making it easier to separate the aqueous and solvent phases. The solvent is not consumed within the process and may be recycled repeatedly, with some cleaning (typically an alkaline wash) to remove low concentrations of solvent degradation products and impurities that may be held up in the solvent. This solvent extraction process is employed with minor variations by Cameco and AREVA. SFL currently receives purified oxide from Cameco, although it has carried out purification in the past.

UFr

7.2 Example uranium hexafluoride conversion process.

Following on from solvent extraction the uranyl nitrate is boiled down to give a high concentration solution of around 1100-1300 kg/m3 uranium. This concentrated solution is then fed into a high temperature denitration unit where the water is driven off and the nitrate decomposed to give a purified uranium trioxide (UO3) product according to the reaction:

UO2(NO3)2.6H2O ^ UO3 + NO2 + NO + O2 + 6H2O [7.3]

Cameco use pot denitrators for this operation, whereas SFL used a fluidised bed reactor at 300 °C before they started to take purified oxide from Cameco. The
process used by AREVA is a little different as it injects ammonia gas into the purified uranyl nitrate solution to generate an ammonium diuranate ((NH4)2U2O7) precipitate, with the precipitate calcined at high temperature to give a purified UO3 product. AREVA has announced, however, that a planned new facility (Comurhex II) will use the denitration scheme in preference to ammonia injection.

The next stage is to convert UO3 to the intermediary product, uranium tetrafluoride (UF4), which, at atmospheric pressure, is a solid up to 1036 °C. An initial reaction is carried out by adding hydrogen and reducing to uranium dioxide (UO2) at high temperature. Cameco use a fluidised bed reactor for this, SFL use a rotary kiln and AREVA a furnace but the process is essentially the same in each case. AREVA and SFL then react the UO2 with HF gas at high temperature in a rotary kiln to give UF4. Cameco uses a wet process for this operation, where the UO2 is reacted with aqueous hydrofluoric acid at 100 °C to generate the solid UF4, which is then dried and calcined to remove water of crystallisation prior to further fluorination. The reduction and fluorination reactions are given by

UO3 + H2 ^ UO2 + H2O [7.4]

UO2 + 4HF ^ UF4 + 2H2O [7.5]

In the final stage of the conversion process, UF4 is reacted with fluorine gas at high temperature to give the UF6 product.

UF4 + F2 ^UF6 [7.6]

The highly reactive fluorine gas is generated using electrochemical cells with graphite anodes. The cells contain molten potassium bifluoride (KHF2) salt as the electrolyte, which is continuously fed with anhydrous hydrogen fluoride gas. The hydrogen fluoride is split into its hydrogen and fluorine component elements with the fluorine fed to the UF6 production reactor.

Cameco and AREVA carry out the fluorination reaction in a flame reactor at a temperature of around 800-900 °C. SFL use a fluidised bed reactor at a much lower temperature of around 450 °C. The UF6 is produced as a gas and is collected and condensed as a solid. Its temperature is then raised to liquefy it. This drives off light gas impurities, allows sampling and provides a form that may be easily dispensed. The liquid UF6 is dispensed into transport containers in batches of 12.5 tonnes and allowed to cool and solidify, a process taking around 5 days. The UF6 is then shipped to the enrichment facility, where it is referred to as ‘feed’.

Converdyn use essentially the same fluorination method described above to generate UF6 from UO2; however, the method of converting yellowcake to UO2 is somewhat different. A dry process is used where the yellowcake is dried at temperature and crushed to a uniform size. This is then reacted with hydrogen gas directly to give the UO2 feed for fluorination, rather than going through an initial dissolution and purification procedure. From there the UO2 is reacted with HF gas in a fluidised bed reactor to produce UF4 and then fluorinated with fluorine gas in
a flame reactor to give the UF6 product. In the absence of an early purification process, an extra UF6 distillation stage is added prior to dispensing into transport containers.

There are two conversion technologies in use in Russia which differ significantly from those used by Western companies. One is a wet process and the other is dry. In the wet process the yellowcake feed is first dissolved in nitric acid and the uranium extracted into a TBP/hydrocarbon mix. Instead of recovering the purified uranium in nitric acid the solvent is mixed with an ammonium hydrogen carbonate solution so that the uranium crystallises out as solid ammonium uranyl tricarbonate (AUTC, chemical formula (NH4)4UO2(CO3)3). The mix is cooled to reduce the solubility of AUTC then the solid crystals are filtered off. The filtered AUTC is then thermally decomposed. Various uranium oxides are formed at different temperatures with UO2 formed in the absence of oxygen and at temperatures of greater than 620 °C according to the reaction:

The UO2 is then dissolved in a mixture of hydrochloric and hydrofluoric acids. Chemical conditions are adjusted so that impurities can be separated as solids and uranium metal added to reduce any trace uranium (VI) to uranium (IV). Excess hydrofluoric acid is added after impurity separation, causing the uranium to precipitate out as hydrated UF4. This is separated, dried at 200-250 °C and then calcined at 450-500 °C in a hydrogen and HF atmosphere to provide the UF4 feed for fluorination, which is carried out with fluorine gas in a flame reactor. The temperature of the reactor at 1100 °C is higher than used by Western converters. The U3O8 feed from Russian mining operations has traditionally been produced to a higher purity than the standard specification used at Western facilities and if the feed is of sufficiently high purity then the U3O8 may be converted to UO2 directly by calcination without the need for solvent extraction and AUTC formation. The dissolution and fluoride precipitation process provides some purification of the uranium and is sometimes referred to as fluoride refining.

The other conversion process used in Russia is direct fluorination of U3O8 with fluorine gas in a flame reactor. The reaction for this is:

U3O8 + 9F2 ^ 3UF6 + 4O2 [7.8]

The same flame reactors that are used for fluorination of UF4 may be used with only minor modification although the reaction is more exothermic than for fluorination of UF4 so that the temperature in the reaction zone rises as high as 2000 °C. Extensive cooling is applied to the walls of the flame reaction vessel, maintaining it at a much lower temperature than found in the reaction zone and thereby preventing excessive corrosion. The U3O8 feed for this process must be of very high quality if the UF6 specification for enrichment is to be met and so the initial feed material must first be purified, This is carried out by dissolving the feed in nitric acid, purification using TBP solvent extraction, recovery as
uranyl nitrate, concentration of the solution and finally thermal denitration in a fluidised bed reactor. Reaction conditions are adjusted to form U3O8 rather than the UO3 produced by Western denitration processes according to the reaction:

3UO2(NO3)2.6H2O ^ U3O8 + 6NO2 + 2O2 +18H2O [7.9]

The U3O8 is then recovered and ground to a fine powder for feeding into the direct fluorination reactor.

The interaction of neutrons with non-fissile materials in an assembly is of importance for a number of phenomena and must be calculated by neutron physics codes as well. The interactions fall into two categories, namely absorption and scattering, each with their associated effects.

Neutron absorption in non-fissile materials is mostly undesirable since it removes neutrons from the multiplication chain and has to be compensated by more fissile material. The exception is the case of burnable absorbers, for example
gadolinium in the fuel or zirconium diboride as a coating on the pellet surface. The latter was developed by Westinghouse and also called IFBA for Integral Fuel Burnable Absorber (Secker and Brown, 2010). The purpose of the burnable neutron absorbers is to remove excess core reactivity at the beginning of an operation cycle when the core contains some fresh fuel, and to optimise assembly power distribution. While serving this purpose, these absorbers also introduce disadvantages, for example lower thermal conductivity of gadolinium bearing fuel and an increase in the gas pressure in the rod from helium produced in the IFBA coating.

The evolution of the radial power distribution in fuels with burnable poison is a complicated function of neutron fluence and spectrum. This is illustrated in Fig. 9.7, which shows the radial power distribution for various burn-ups of fuel with gadolinium. After some time, the absorbing isotopes are converted to less absorbing ones which, however, remain in the fuel matrix chemically as gadolinium with an influence on fuel properties.

When fast neutrons collide with and are scattered by atoms in assembly material, the atoms can be knocked out of their position leaving a vacancy defect in the matrix, and they can end up in a new, interstitial position deforming the matrix. During the lifetime of an assembly, every atom is displaced 20 times or more (a fast neutron (E > 1 MeV) fluence of 6 x 1020/cm2 will typically cause 1 displacement per atom or 1 dpa). The implications of this interaction are changing material properties as well as enhanced material creep and growth (Adamson, 2000).

Significant safety and performance issues arising from these effects are:

BWR channel bow. This can occur in a neutron fluence gradient causing uneven growth of the channel box. The deformation may lead to control blade insertion problems, which can be exacerbated by channel box bulging in a pressure gradient, differential hydriding and so-called shadow corrosion. A geometry change of the channel box will also influence the local power because of changes in the fuel-to- moderator ratio. A countermeasure is beta-quenching at the final production stage of the strip from which the channel is to be formed. This treatment reduces irradiation growth (at least to moderate fluences) and consequently channel bow.

PWR guide tube bow. S- or C-shaped bowing has been observed, which can be caused by creep in response to axial hold-down forces from the top nozzle springs and lateral forces from cross flow as well as by uneven irradiation-induced growth in a neutron flux gradient. The resulting geometry will impede control rod insertion and can lead to differential power in the quadrants of a core (Andersson et al. , 2004). The problem can be alleviated by using zirconium alloys, which exhibit less growth, for example Zirlo and M5, and by optimising the hold-down spring and guide tube strength.

Spacer spring relaxation. The springs, which are a part of the intermediate grids, will relax and thus lose their ability to keep the long fuel rods firmly in place. The resulting slack can lead to vibration, grid-to-rod fretting and fuel failure, in particular in PWRs. Karoutas et al. (2004) reported an interesting countermeasure, which exploits the fact that cold-worked Zircaloy has higher irradiation growth than recrystallised-annealed Zircaloy. While the grid strips are fully annealed, the springs retain the cold-work of the final forming operation. As they try to grow longitudinally more than the strip material surrounding them, they bend towards the fuel rod instead and counteract the spring relaxation.

Fast neutrons also enhance the creep-down and creep-out of the fuel rod cladding.

Westinghouse developed a pressure suppression containment, which uses ice to reduce the pressure. The loop pipework is in the lower part of the containment but the operating floor effectively separates the lower levels of the containment from the open main dome area. The two volumes are linked by a structure surrounding the NSSS, which contains refrigerated baskets of ice. The steam/ water mixture, released from the breach, flows through these and loses energy.

The use of pressure suppression containments is much more common in BWRs. In the US GE designed the containments and the NSSS and developed a series of containments as illustrated in Fig. 10.18. Each consists of a suppression pool and a main containment volume. The geometry is such that discharges from the RCS pass through the suppression pool to absorb energy. The suppression pool also provides the heat sink to quench discharges from the vessel safety relief valves and the ADS.

Systems for severe accident mitigation

LWR containments cover a wide range of strengths and volumes, which is illustrated in Fig. 10.19. Not surprisingly the pressure suppression containments have either smaller volumes or lower design pressures. Following the accident at Three Mile Island Unit 2, the need to look at the mitigation of potential beyond design basis accidents was highlighted. In particular the need to manage hydrogen production during severe accidents was identified as an issue to be addressed.

The existing plants have systems to manage the production of hydrogen post LOCA by radiolysis; however, this cannot deal with the rate of production, which

10.18 Schematic of GE BWR containments.

10.19 Typical containment volumes and design pressures of US plants (Hessheimer and Dameron, 2006).

occurs from steam zirconium reactions if the fuel clad secondary temperature limits (~1200 °C) are exceeded. This leads to the possibility that hydrogen concentrations may build up in the containment to the level where if ignited the resultant hydrogen explosion may exceed the containment ultimate failure pressure. The ultimate failure pressure typically exceeds the design pressure by a factor of 2 or more (Hessheimer and Dameron, 2006) and so large dry containments can withstand a large hydrogen burn, but the pressure suppression containments do not have a large enough margin.

The issue is the rate of release of energy since the pressure suppression systems can cope with the integrated energy release but not the instantaneous pressure increase. The solution was therefore to add passive autocatalytic recombiners to combine the hydrogen with oxygen at below the lower flammability limits or to install hydrogen igniters which would ensure combustion occurs at close to the lower flammability limit. Igniters were fitted to ice condenser and BWR Mk III containments but it was decided to inert the atmosphere of the smaller BWR Mk I and II containments. Subsequently passive autocatalytic recombiners have been installed on a number of large dry containments in Europe to provide additional defence in depth.

Severe accident management guidelines were developed for existing plants and this led to the introduction of additional systems. The prevention of containment failure following a severe accident was seen as the main focus for these additional accident management procedures. One means of achieving this was to provide
additional (usually mobile) pumps to inject water to cool the containments. In the case of BWRs water could also be injected directly into the primary circuit because dissolved boron is not used as a primary means of reactivity control so dilution by the injection of unborated water is not an issue. In other plants (e. g. Sizewell B) alternative means of providing or reinforcing existing containment cooling systems were provided.

Addition of water to the containment increases the heat sink available but does not provide a heat removal route. One means of removing energy from the containments is by periodically venting the steam generated. A number of plants back fitted filtered venting systems, which allowed the containment to be vented whilst reducing the activity discharged. The most common filters used were sand/gravel beds and water scrubbers. In some BWRs pressure-retaining vent lines were added, which allowed the venting of the smaller containments at an early stage, before significant activity is present in the atmosphere, to prevent failure.

The use of venting as a means of controlling containment failure is particularly important for steel containments. The research carried out at Sandia Laboratories (Hessheimer and Dameron, 2006) showed that there was a large margin between the design pressure and the ultimate failure pressure for both steel and concrete containments, but the failure modes tended to be different. The failure of the steel containment tended to be associated with a rapidly propagating ductile fracture rapidly releasing the stored energy. On the other hand the concrete containments failed by liner tearing and gross leakage rather than by the failure of the reinforced/ pre-stressed concrete structure. Thus the provision of venting systems on steel containments ensures a more benign failure mode in addition to reducing the release.

Generation IV systems are intended to improve significantly on current Generation III systems, which comprise advanced light water reactors (ALWRs) (Fig. 13.2) in terms of cost, safety, environmental performance and proliferation resistance (Abram and Ion, 2008). The Generation IV International Forum (GIF) is an international body established to carry out the research needed to establish the feasibility and potential performance of this next generation of nuclear power plants. The GIF Charter was signed in July 2001 by thirteen countries: Argentina, Brazil, Canada, France, Japan, the Republic of South Korea, South Africa, the United Kingdom and the United States. The Charter was later signed by Switzerland in 2002, Euratom in 2003 and, in 2006, the People’s Republic of China and the Russian Federation. In early 2006 the US also proposed a global nuclear energy partnership (GNEP) with a similar goal of delivering a sustainable and proliferation-resistant fuel cycle. GIF expects the first Generation IV systems to come on stream by 2030. Interim systems may be developed by the nuclear industry in the next 15 years, but these are not considered to be true Generation IV systems (Abram and Ion, 2008).

13.2 Historical evolution of nuclear reactors.

In 2009 GIF set the following criteria for any Generation IV system (Generation IV International Forum, 2009):

• Safety and reliability: Generation IV nuclear energy system operations will excel in safety and reliability. They will have a very low likelihood and degree of reactor core damage and will eliminate the need for offsite emergency response.

• Economics: Generation IV nuclear energy systems will have a clear life-cycle cost advantage over other energy sources. They will have a level of financial risk comparable to other energy projects.

• Sustainability: Generation IV nuclear energy systems will provide sustainable energy generation that meets clean air objectives and provides long-term availability of systems and effective fuel utilization for worldwide energy production. They will minimize and manage their nuclear waste and notably reduce the long-term management burden, thereby improving protection for the public health and the environment.

• Proliferation resistance and physical protection: Generation IV nuclear energy systems will increase the assurance that they are very unattractive and the least desirable route for diversion or theft of weapons-usable materials, and provide increased physical protection against acts of terrorism.

GIF has identified six nuclear energy systems for further development that have the potential to meet these criteria. These use a range of reactor sizes and types, energy conversion technologies, and open and closed fuel cycles. The six reactor types are:

• VHTR: very high-temperature reactor

• SCWR: supercritical water reactor

• MSR: molten salt reactor

• SFR: sodium-cooled fast reactor

• LFR: lead-cooled fast reactor

• GFR: gas-cooled fast reactor

All of these systems have been studied and, in many cases, experimental or prototype systems established. Each system has its strengths and weaknesses. The capacity of each system to meet the criteria set out by GIP is summarized in Table 13.3. GIF expects that, depending on initial results, it will eventually narrow the selection down to two or three systems for further commercial development. It is important to note that Generation IV systems will need to address all the aspects of nuclear power generation, from the mine to the final disposal of waste. They will need to address the whole fuel cycle as well as the building and disposal of plant. This life-cycle approach makes Generation IV systems (and connected initiatives such as GNEP) different from previous generations. An overview of the whole fuel cycle R&D requirements is given in Table 13.4. The following section discusses these common requirements for any Generation IV system.

Notes:

P: Primary option S: Secondary option

1 The GFR proposes (U, Pu)C in ceramic-ceramic (cercer), coated particles or ceramic-metallic (cermet).

2 The MSR employs a molten fluoride salt fuel and coolant, and fluoride-based processes for recycling.

3 The SFR has two options: oxide fuel with advanced aqueous, and metal fuel with pyroprocess.

4 The VHTR uses a once-through fuel cycle with coated (UCO) fuel kernels, with no need for fuel treatment, as the primary option.

The modelling of fuel behaviour under irradiation is described in this section. The requirements are first addressed in Section 14.3.1. The modelling approaches, and the commonly used computer programs which implement these approaches, are then discussed in Sections 14.3.2 and 14.3.3. Finally, the advantages and limitations of fuel behaviour modelling, and the future trends in such modelling, are described in Sections 14.3.4 and 14.3.5, respectively.

14.3.1 Requirements

The design and licensing of nuclear fuel require the fuel behaviour under irradiation to be predicted. This includes the behaviour of individual fuel pins and the behaviour of the fuel assembly as a whole (excluding Magnox fuel, where the concept of a fuel assembly is not applicable). The aim is to ensure that the fuel will operate safely and within design constraints, even under accident conditions.

The behaviour of a given fuel pin is governed by the evolution with time of: (a) the pin power distribution; (b) the pin boundary conditions (primarily the axial distribution of coolant temperature and pressure); and (c) the thermo-mechanical response of the fuel pin to the imposed powers and boundary conditions. (b) is in turn dependent upon (d): the evolution with time of the thermal-hydraulic behaviour of the coolant in the primary circuit, commonly termed the ‘system thermal-hydraulics’. With respect to the fuel assembly as a whole, it is generally only (e), the mechanical behaviour, that is of interest, including the stresses imposed by the loads applied to the various assembly components (during normal operation, anticipated operational occurrences and accidents).

Since the fuel behaviour in its entirety is inherently complex, and due to historical restrictions in computing power, (a) to (e) are generally evaluated separately (notable exceptions are analysis of PWR steamline break and BWR power-flow oscillation events, where (a), (b) and (d) are strongly coupled). This is achieved using a suite of computer programs, or codes, with: (i) neutronics codes; (ii) core thermal-hydraulics codes; (iii) fuel performance codes; (iv) system thermal-hydraulics codes; and (v) mechanical design codes used to evaluate (a) to (e), respectively. The codes and their interactions are summarised in Fig. 14.4 . Other types of code are used for ad hoc or specialised analysis, including computational fluid dynamics (CFD) codes for detailed thermal — hydraulic assessments, and coolant chemistry codes to evaluate the complex coolant chemistry in the primary circuit (including the dissolution of metals in the heat exchanger piping, the reactions of the resulting chemical species with the coolant and its additives, and the deposition of the reaction products on the fuel pins in the form of crud).

In general terms, the design and licensing assessment involves comparing calculated parameters with design limits according to a number of design criteria. The design criteria ensure that the functional requirements of the fuel pins and assembly structural components are met. The effects of manufacturing tolerances, model uncertainties, etc., are incorporated into either the calculations of the relevant parameters or the design limits, or both. In the case of each design criterion, the limiting pin is that for which there is the minimum margin between the parameter of interest and the corresponding design limit. Different functional requirements and design criteria generally apply in normal operation, anticipated operational occurrences (AOOs) and accidents. Further information on the

generalities of design and licensing assessments can be found elsewhere (IAEA, 2003a).

Design criteria and functional requirements vary from country to country due to the differences in regulatory regimes. There are also variations due to differences in reactor types and, to some extent, fuel types. However, as an example: a typical functional requirement would be that the fuel cladding integrity is maintained during normal operation and high probability faults; a typical design criterion which would, together with other design criteria, ensure that this functional requirement is met would be that the maximum effective (or generalised) stress in the cladding shall not exceed the yield stress of the clad material. The parameter of interest here is the maximum effective stress in the cladding, and the design limit is the cladding yield stress.

All process wastes (produced in the course of reprocessing operations) and technological wastes (wastes resulting from maintenance or dismantling) must be safely conditioned into a form that is suitable for storage and, ideally, for final disposal also. Amongst other requirements there is an expectation that the conditioned wastes will be passively safe.

466 Nuclear fuel cycle science and engineering

A ‘dedicated’ transmuter reactor13 should be able to burn any amount of TRUs or MAs, according to the chosen strategy. ‘Transmutation’ in this case means essentially ‘fission’. In order to compare the ‘transmutation’ effectiveness of different systems one has to compare the system performance at the same power (i. e. at the same number of fissions). Then, what really matters is the composition of the fuel loaded in the ‘dedicated’ transmuter reactor, since that determines which isotopes will be fissioned. Because for each actinide ~1 g is burnt (by fission) for 1 MW-day, the total mass MFi (in Kilograms) of isotope i burnt by fission in a year is given by:

M_ =—xW x365xl0"3

F’’ f,

where y is the load factor and f is the ratio of the total number of fissions in the system (all isotopes, all regions) to the fissions in the core due to isotope і and W (MW) is the power. If MTot. is the total mass of isotope і, consumed both by fission and by capture, then:

M0t. = MF. x (1 + a)

Tot, i F, i v v

where a. is the average capture-to-fission ratio of isotope і.

This shows that the ‘burning’ potential of a core is related to its power, i. e. to its fission rate. Because of this, any core with the same power will show a comparable transmutation potential. Power apart, the real difference between one core and another is determined by the ‘quality’ of the fuel that each core allows. One way of maximizing transmutation performance is to use fertile-free fuel; in essence, this means uranium-free. Unfortunately, such fuel cannot be used in a critical fast reactor because it would make it difficult to operate the reactor safely. This is a consequence of the absence of uranium, the most important result of which is a very low fraction of delayed neutrons — see e. g. Ref. 14. As an alternative, sub-critical systems (or accelerator driven systems, ADS, see e. g. Refs 15-17), have been proposed, since they could, in principle, provide a way around these potential difficulties. More recently, fission-fusion hybrid systems have also been considered.

The use of fertile-free fuel would enable an ADS to reach high transmutation levels so that a relatively small number of them would be needed to handle the TRUs arising from the electricity-producing reactor fleet. They may be thought of as a separate stratum of the fuel cycle, leaving the fuel cycle stratum devoted to electricity production ‘uncontaminated’ by the presence of MAs (see Section 17.4).

As of today, no uranium-free fuels have been definitively identified, even if some promising candidates have been pointed out.1 8-20 This suggests that, if TRU ‘burning’ is a priority objective, it may be worth exploring alternatives to ‘dedicated’ transmuter reactors loaded with uranium-free fuel. Examples are ADSs with some uranium in the fuel or fast reactors with a low conversion ratio (the conversion ratio, CR, is defined as the ratio of the fissile produced to the fissile destroyed). It has been shown,2 1 for example, that the TRU consumption rate reaches -80% of the maximum theoretical value for uranium-free fuel when the CR is of the order of -0.4-0.5 both for metal or oxide fuels and for MA/Pu ratios varying in the range -1 to 0.1, see below. Results reported in Ref. 22 indicate that, in terms of reactor control, cores with conversion ratios as low as -0.25-0.40 are in principle feasible. Since these cores allow TRU consumption, whatever the

Pu/MA ratio and fuel type, at close to 80% of the maximum theoretical consumption, it seems that U-free fuels could possibly be avoided, regardless of the scenario and specific P&T strategy.

18.1.4 General principles

Two basic options exist for the safe, long-term management of unwanted material:

1 dilute and disperse for liquid and gaseous wastes of low hazard

2 concentrate and contain for solid wastes

In everyday life we see the former deployed through chimney stacks and sewer pipes and the latter through landfills. Guidance that is specific to radioactive waste is provided through the Safety Standards of the International Atomic Energy Agency (IAEA). Its Requirements for disposal24 cover a wide range of issues including duties laid upon the government, regulator and WMO. They emphasise the importance of safety and safety assessment in planning and implementing disposal solutions. In general terms they promote an approach that may be described as concentrate and contain until the radioactivity in the waste has decayed to safe levels.

Included in the IAEA Requirements are four that are probably best seen as design objectives. These are the provision of containment, isolation, passive safety and multiple safety functions. Whilst all four are ordinary English words and phrases, in the context of radioactive waste disposal they have specific meanings. Containment relates to the radionuclides in the waste: it may be provided by physical and/or chemical means. There is an expectation that containment will persist until the hazard has been significantly reduced by radioactive decay. In addition, for heat-producing wastes, containment should be maintained whilst heat production is at a level that could adversely affect safety performance. Isolation concerns the waste as a whole and the need to keep it separate from the human environment. This means that the prime considerations are (a) erosion, i. e. exposure of the waste by removal of the covering of rock or soil and (b) inadvertent human intrusion — the possibility, for instance, that humans might drill or dig into the waste whilst, say, exploring for water or minerals. Passive safety is the idea that safety should not be dependent upon human intervention. If at some future date, knowledge of the facility were to be lost, for example, humans and the environment must still be fully protected; this is a fundamental assumption in post-closure safety assessment. Multiple safety functions refers to the need to provide diverse physical and chemical means of achieving containment and isolation. This is a recent development of the older concept of a multiple barrier system. In both cases the longevity of the safety functions or barriers must be commensurate with that of the hazard.

The notion of multiple barriers and safety functions may be illustrated through the design of a hypothetical package for metallic reactor components where atoms lying within the body of the metal have become radioactive through neutron capture. Let us imagine that this waste is cut into pieces, placed into a metal container and cemented into position (‘encapsulated’) using a free-flowing cement grout. The container is then closed with a lid, lifted into position alongside other containers in the repository and backfilled with more grout. This system provides four barriers to radionuclide migration: the waste itself, the encapsulation grout, the container and the backfill grout. The waste and the container constitute physical barriers that work by diverse means. The former must dissolve and the latter must be penetrated by corrosion before radionuclides can be released. The two grout layers provide both physical and chemical containment. Physical containment results from the low permeability of the grout, which reduces the flow of water to and from the waste. Chemical containment acts to retard radionuclide migration through two effects:

1 The high pH conditions (caused by dissolution of cement solids) reduce the solubility of the actinides.

2 The porous structure of the cement provides surfaces on which many radionuclides can sorb thereby retarding their migration.

Commercial competition should ensure a continued drive for cost reductions and it is clear that, for nuclear power, the area to focus on is capital costs and the reduction of commercial risk (and therefore discount rates) through replication. But competition cannot exist without a market so let us assume that, in the next 20 years:

• governments of European and North American countries continue to exert pressure to cut back on carbon dioxide emissions

• renewables, for whatever reason, amount to no more than 20% of nominal generating capacity

• oil becomes scarcer and more expensive

• no new intensive energy source for carbon-free electricity generation (e. g. laser fusion) becomes available.

With these assumptions it seems inevitable that nuclear power will provide an increasingly large slice of electricity generation, not only for heating, cooling, lighting, machines and the many other uses with which we are familiar but also as a substitute for fossil fuels by, for example, supplying the energy for battery — or hydrogen-powered vehicles. This would be supported by CCGT and, depending on the success of development efforts, coal-fired generation combined with carbon capture and sequestration. At the present time, however, the latter looks too expensive and will therefore need some form of government support. Obvious candidate countries for the introduction of coal+CC are those with access to low — price supplies of coal not least because successful implementation of the technology could help to support continued coal exports.

Such an expansion of nuclear power will reduce capital costs through the force of competition and the economies of scale; it will also considerably reduce uncertainties in cost estimates, many of which arise because of the long layoff from reactor construction. Other costs that are likely to be reduced through improved design are operation, maintenance, decommissioning and waste management. Fuel costs will probably rise as demand for uranium increases but, as we have seen, nuclear fuel costs constitute only around 12% of the LCOE and the cost of uranium itself constitutes about one third of this. Interestingly, a recent report19 has suggested a $210 per lb maximum price for uranium based on the cost of extraction from seawater. If this became reality, fuel costs would then constitute about 25% of the LCOE for nuclear. Even before this happened, however, wider use of MOX fuel would probably be an important factor in limiting fuel prices. More widespread use of nuclear will also increase the need for plant that has an improved ability to load follow.

Partly driven by the dearth of orders for large-scale plant, much thought has been given in recent years to the production of small modular reactors that would be capable of being constructed off-site, a practice that is normal for nuclear submarine reactors. Economies of scale would not come from the size of the plant but from the numbers produced. Many such reactor designs have been proposed: the World Nuclear Association website20 lists 16, most with an output in the range 100-300 MW(e). It is claimed that savings can be made on capital cost because these designs would allow simpler safety systems. If overnight cost could be reduced that would, indeed, be an advantage. From the sensitivity study in Section 5.2.6, however, we can see that equally powerful economic arguments might be made based on a shortening of the construction time and a reduction in discount rate because of the scaling down of the overall size and cost of the project.