As mentioned previously, the thorium cycle can reach positive breeding rates in a thermal spectrum. However, in order to solve the problem of the poison­ing by neutron captures on fission products and 233Pa, liquid fuels have to be used since they allow online extraction of selected nuclei. This is made pos­sible by the use of molten salt reactors (MSRs).

The concept of molten salt reactors has been extensively studied in the 1950s, 1960s and 1970s, in particular in the USA, where a demonstrator was operated for a few years at the Oak Ridge National Laboratory. The design of the molten salt breeder reactor (MSBR) was a cylindrical assembly of high-density graphite hexagons, each hollowed out to accommodate a

channel for molten salt circulation. Above and under the core salt tanks and graphite axial reflectors are located (see figure 11.8). The fuel circulates from the bottom to the top at a velocity of around 2 m/s. The fraction of the fuel which is outside the core (heat exchanger, reprocessing unit) is about 30%. Of course, a significant part of the delayed neutrons will be emitted outside the core, which reduces the proportion of delayed neutrons that can be used to control the reactor.

The use of a liquid fuel allows continuous feeding of the core with fertile or fissile nuclei, in order to maintain the reactivity and to keep the chemical composition of the salt constant. It saves having large reactivity reserves at the beginning of the irradiation, and improves the neutron balance. Different extraction methods can be considered. One of them is based on a liquid — liquid extraction process, which consists of exchanging thorium and lithium dissolved in molten bismuth for the constituents to be removed from the salt. Chemically, the fission products are more or less similar to thorium, and their extraction efficiencies can vary: they are around 20% for halogens and rare earths, around 5% for Zr and semi-noble metals and 1% for alkaline elements. These values have to be confirmed at an industrial scale, but seem accessible within a few tens of years. Figure 11.9 shows a simplified schematic of the materials reprocessing principle.

The reprocessing time is a free parameter which can be adapted to the performances one tries to reach. A fast reprocessing rate will correspond to an optimal breeding rate. The carrier salt can be LiF-BeF2-(HN)F4, where HN denotes heavy nuclei. The proportions are around 70:17.5: 12.5mol% respectively.

The main advantage of the thermal spectrum is the fissile inventory, which is greatly reduced compared with the fast-spectrum case. A 1 GWe reactor needs around 67 tons of Th and only 1.1 tons of U. Table

For clay porosity equal to 20%, measurements of the diffusion constant for water give the value D0 = 1.6 x 10~3m2/year. The diffusion constants for dissolved elements depend on the type of element and reflect its greater or smaller affinity for clay. The sorption phenomena on the mineral surfaces is taken into account through a reduction of the diffusion constant D by the delay coefficient. Table I.1 shows examples of delay coefficients and solubility limits giving the maximum possible concentration in water for each element, according to its chemical properties. Note, in the table, that radium, which is always one of the descendants of actinides, is delayed 100 times less than thorium, uranium, or the minor actinides. Radium could then well play an important role in the transfer of radioactivity due to the actinides. In fact, only Ra, descending from U, has a half-life that is large enough (1600 years).

The delay coefficients are measured in the laboratory, by studying the sorption of an aqueous solution of the element by a clay sample with the

same properties as the layer. These evaluations are done also as a function of the temperature.

If one wants to assess the future of nuclear energy, it is, of course, useful to compare its cost with that of other means of electricity production. We report in table 2.19 some cost estimates, given in US0 per kWh.

The table shows that, among the renewable energies, only wind energy has reached competitiveness with fossil fuels and nuclear power. However,

Table 2.19. Cost estimates in US0 per kWh for different energy production technologies.

1 This figure includes investment cost for a new plant with 5% actualization rate. At present the cost of nuclear electricity is much lower (down to 2^ per kWh) since the initial investment has been paid off [39].

this close competitiveness is only attained if the electricity produced by the windmills is used as input to the general network. Biomass may also be com­petitive in specific sites if no long-distance transportation of the bio-fuel is required. In the future, thermal solar energy might reach competitiveness in well-insolated sites, and if long-term energy storage is not needed. To be complete one should stress that wind energy, small biomass facilities, and solar devices might be very suitable in remote sites where no electricity network exists. Also, energy saving efforts should have a high priority: it is largely preferable to invest a given amount of money to save, say, 7 TWh annually, than to build an additional 1 GWe facility.

The table shows that the only competitive and massive energy producing method which could be an alternative to fossil fuel facilities is nuclear power. However, the market trends favour combined gas fuelled facilities which reach very high efficiencies and involve investment costs only one-third of those required for a nuclear facility, even in a favourable institutional context like France. A ‘rebirth’ of nuclear power is only probable, in the not-too-distant future, if a strong policy to reduce greenhouse gas emissions is put into effect worldwide. This ‘rebirth’ will probably be possible only if, in public opinion, the nuclear waste problem is solved satisfactorily, and if a Chernobyl-type accident is demonstrated to be impossible.

The maximum operating temperature of the water in PWR (resp. BWR) is 325 °C (resp. 288 °C) and the pressure 155 bar (resp. 72 bar). Because of the high pressure a pipe or vessel rupture may occur and lead to partial or total loss of coolant. In such a case, emergency core-cooling systems would have to come into play. If these fail, the core will melt partially or completely. This is called a core melt accident. The probability of a core melt accident has been calculated to be around 5 x 10~5 per reactor-year for PWRs,[21] and 4 x 10~6 per reactor-year for BWRs [59]. Continuous safety improvements have been made, taking advantage of experience, and recent safety evaluations yield a core melt probability of 10~5 per reactor — year for PWRs [60]. Although core melting induces a large release of radioactivity, the reactor containment structure should prevent significant release to the external atmosphere, as was indeed demonstrated in the Three Mile Island accident. The probability that, despite the containment,^ significant radioactivity would be released to the exterior is one to two orders of magnitude lower than that of core melting. The risk for an individual living in the vicinity of the reactor to die from a cancer induced by accidental radioactivity release is estimated to be around 10~8 for today’s PWRs.

Although the above numbers appear to be small or very small, some prominent experts such as Weinberg [61] have argued that, should the use of nuclear power expand again, a core melt probability of 10~4 (which would lead to one core melt every other year for a 5000 nuclear reactor fleet) would be socially unacceptable. It was, therefore, important to

design deterministically safe reactors. Such is the PIUS [62] design. The PWR reactor is immersed in a huge pool of borated water, and special passive locks ensure that the cooling water and the borated water do not normally mix. If the pressure of the cooling water becomes too high the locks open automatically and the reactor is flooded by the borated water. This would, first, make the chain reaction impossible, and second, ensure residual heat evacuation via natural convection. However PIUS would have a small thermodynamical efficiency and make inspection and maintenance difficult.

Truncation. MCNP can operate energy or time cut-offs; the particle is killed below an energy threshold. This is good because it saves time, but it is dangerous because low-energy particles can produce highly energetic ones (fissions) and thus lead to erroneous results. Similar time cut-offs exist when the particle time exceeds a given cut-off.

Population control methods use particle splitting and Russian roulette to control the number of particles in various regions. Each MCNP cell is given an importance I. For example, if a neutron of weight W passes from a cell of importance 2 to one of importance 8, it is split into 8=2 = 4 identical neutrons each with a weight W=4. Conversely, if the neutron passes from a cell of importance 8 to one of importance 2, a Russian roulette is played and the neutron is killed with the probability 1 — | = 75% or, worded differently, followed with a 25% probability and a weight W x 4. This type of popula­tion control can be applied to the energy range.

The most important experimental observable with respect to hybrid reactors is the number of neutrons produced per proton-nucleus reaction. Recent measurements of neutron multiplicities have been made by Hilscher et al. [110] for thin and thick targets of Pb and U between 1 and 5GeV. Thin target measurements can be compared with those obtained by different INC calculations done in the frame of the OECD workshop [106]. The measurement for thin targets was carried out at 1.22 GeV, while the bench­mark calculations were carried out at 0.8 and 1.6 GeV. In table 6.1 we give a sample of the results of the benchmark and a linear interpolation to 1.22 GeV together with the experimental result. Also present in the last column of the table is a systematics established by Pearlstein [105]. Table

6.1 shows a scatter of close to 30% both on the calculated and measured values.

In the preceding we have discussed the extraction of a single component from the aqueous feed. The selection is possible because of the large differences between the values of D for this component and other species like fission products. In general, with TBP, uranium and plutonium have high distribution

coefficient values and are co-extracted. Further separation between plutonium and uranium is thus required. In general this is done first by redissolving uranium and plutonium from the organic phase into an aqueous phase with low nitric acid concentration. Then plutonium is reduced from the tetravalent to the trivalent state with a mild reductant such as U4+ which does not reduce the hexavalent uranium. The trivalent plutonium cannot be dissolved back into an organic solvent, so that a new dissolution leaves the plutonium in the aqueous phase while uranium dissolves in the organic phase. In general, in order to increase the purity of the recovered uranium and plutonium, addi­tional scrubbing is necessary. These different steps, as typically implemented in the Purex process, are shown in figure 9.6.

The chosen reference value of the multiplication factor is 0.98. However, fuel evolution leads to deviations from the reference. As already mentioned, it is possible to limit these deviations by balancing the reactivity losses due to neutron absorption by fission products by an increase of the fissile nuclei concentration. Figure 12.3 shows the evolution of kef computed with and

without neutron capture by fission products. The initial decrease of k is due to the building up of the 233Pa inventory.

The reference total thermal power is 1500 MW, corresponding to an electric power of 635 MW. The specific power is around 500 kW/l. The fuel initial mass amounts to 30 tons with 10% of 233U. The foreseen burn-up for an in-pile lifetime of 5 years is 100 GWd/ton, which is equivalent to 10% of the initial load.

The main channel through which the radionuclides stored can re-ascend from a deep geologic site implies dissolution and water transport. The quality of a site thus depends on the following.

• Poor water mobility within the site.

• The thickness and quality of the confinement layer.

• The solubility limits of the radioelements in the water present in the medium. In general, this solubility depends on the pH and on the mechan­isms that regulate the water chemistry in the medium.

• The sorption properties of the radioelements by the medium; these too depend on the pH and how the water chemistry is regulated by the medium.

Various geologic formations seem to have satisfactory properties as disposal sites. The most popular are clay, as discussed here, granite and salt. Values representative of water mobility in these three media are given in table I.4.

As the table shows, water mobility in granite is particularly low. However, granite is seldom free of faults through which water can infiltrate. It is thus important to find structures whose characteristic dimensions are sufficient to ensure satisfactory performance. As is shown in table I.4, these characteristic dimensions are as 16 to 1 compared with clay, leaving many possibilities open. Civil engineering works, thermal constraints due to the heat released by the wastes, and possible seismic events can have con­sequences that have to be evaluated.

In spite of its large diffusion coefficient, salt is often considered a particularly promising medium. Indeed, a salt bed can be durable only in the absence of water, making the value of the diffusion constant purely academic. The diffusion of radioelements in anhydrous salt is thus extremely slow. Moreover, as salt creeps easily, it should fill up the constructions on the site rather quickly. However, salt is and probably will continue to be of economic value. A decision to work the site after the memory of its use is lost is thus possible. In this case, water injected in the vein to retrieve the salt more quickly would be laden with radioelements since the diffusion constant is large. Finally, in the long term, invasion of the disposal site by water cannot be excluded.

Finally, clay seems to offer excellent capabilities, combining the qualities of salt and of granite: small diffusion constant in spite of water saturation, creep properties sufficient to ‘eradicate’ defects, and good sorption of a large number of elements.

In the case of normal operation of a representative geologic disposal site, the risks to the most exposed population remain extremely marginal at all times in the future. The main confining agent is the geologic formation. Its mobility, its solubility, and its several million years half-life make 129I the main potential agent causing irradiation to the critical populations. Almost all of this iodine should end up in the biosphere within several hundred thousand years. In contrast, the transuranic elements are very unlikely to contaminate the biosphere.

The reflections presented here rest on rather limited measurements of clay diffusion properties. A great deal of validation work remains to be done. The influence of temperature and mechanical constraints has to be ascertained. A thorough exploration of the site to obtain precise descriptions of the clay layer is needed. However, it seems that nuclear waste disposal can be considered a realistic and feasible option that should not bring on major risks to future generations.

Acknowledgments. The authors thank G Pepin and E Tevissen from ANDRA for providing the documents that served as the basis for this presentation and for the helpful information they supplied concerning the phenomena considered.

A discussion of the possible future of nuclear energy requires some informa­tion on the general question of world energy perspectives.

2.1 World energy perspectives

2.1.1 Energy consumptions

The relative contribution of the main energy sources to world needs is shown in table 2.1 [19]. The table shows that nuclear energy provides only a modest part of the total amount produced. This is partly related to the fact that nuclear energy is only used for electricity production, which only represents about 30% of global energy needs. However, table 2.2 [20] shows that this is not the whole story. Clearly, a number of countries with nuclear capabilities like Germany, the US and the UK resort to nuclear energy on a modest scale, especially when compared with a country like France.