The above discussion implies that the radioelements are fully soluble in water. In truth, many elements are poorly soluble and that is liable to moderate their transfer. If the flow through the clay layer, or the man­made barrier, is insufficient to evacuate the radioelements as they are released by the fuel or the package, their concentration in the water that is in contact with them will increase until, possibly, a saturation limit Cmax is reached, beyond which they will precipitate in the vicinity of the source. To such a concentration limit corresponds a value of the flow entering the clay layer or the man-made barrier. This can be obtained from the stationary density equation:

Experience with fast breeders shows that a typical [48] 1.2 GWe reactor requires an initial inventory of 5 tons of plutonium. A 1200 MWe reactor

produces around 0.25 tons of plutonium annually, corresponding to a doubling time of 20 years. However this value of the doubling time does not take into account the reprocessing stage. The longer the cooling time of the used fuel before reprocessing, the longer the effective doubling time. As an example, if the residence time of the plutonium in the reactor is 4 years, and the cooling time also 4 years, the plutonium inventory is doubled, and so is the doubling time. The transition from a PWR — (BWR-) based system to a fast reactor system was studied. It was assumed that a strong PWR programme starts in 2010, first breeders starting progressively in 2020. By 2030 no new PWRs are connected to the grid, leaving the field to fast reactors. Figure 2.7 shows the evolution of the reactor park cor­responding to a plutonium production of 250kg/GWe by the PWRs and 200kg/GWe by the fast breeders.

A cooling time of 1 year was assumed. The target of 9000 GWe by 2050 can be reached. For longer cooling times it is found that the target cannot be reached. Cooling times as short as 1 year are probably not possible with standard aqueous reprocessing and would require pyro-chemical reprocessing. After 2050 the PWRs would be phased out progressively and the doubling time of the FR could be adjusted to the desirable evolution of the reactor park. In figure 2.7 a 1.5% annual increase of the nuclear park was assumed.

Figure 2.8 shows the plutonium stockpile outside the reactors. It displays three regimes. First the Pu inventory increases slowly until 2030 as

a result of the production by the increasing PWR (BWR) park. The decrease between 2030 and 2050 reflects the sharp increase in the number of fast reactors. The increase after 2050 is due to the slower increase of the number of fast reactors. Instead of keeping the total plutonium stockpile at such a high value, it could be possible to use the excess neutrons for the transmutation of fission products, for example. Alternatively, reactor sizes could be reduced, giving more flexibility to the power system.

In our scenario the last PWR reactors will be phased out in 2070. At that time the total amount of natural uranium used would reach 12 million tons, close to the presently estimated reserves. This means that the number and lifetime of the PWR park cannot be considered as an easily adjustable variable to achieve the strong increase of nuclear power between 2030 and 2050. This increase will be difficult to achieve and requires the early development of breeders, as well as the availability of as much reprocessed plutonium as possible. The generalization of MOx incineration has to be weighed against this requirement. Similarly, incinerating plutonium in HTR reactors may be counterproductive if spent fuel reprocessing is not possible. Until the development of breeder reactors the best use of reproces­sing facilities might be the fabrication of Pu-Th fuels for PWRs, producing 233U, which could be used as described in section 4.2.2.

Of course, accepting a lower value for the target in 2050 would make things easier. For example, a target of 7000 GWe could be reached with a doubling time of 32.5 years. Another possibility would be to increase the share of more efficient plutonium-producing reactors such as the CANDUs.

Consider, now, that a large, sudden reactivity is inserted into the reactor while it is running at nominal power. In this case the time to be considered between neutron generations is the prompt time, i. e. for a PWR, rnf = 0.1ms. The power increase is too rapid for the cooling system to be efficient. The cooling system is no longer efficient and melt-down of the fuel elements may occur. Boiling of the water coolant leads to a strong decrease of the reactivity and to a limitation of the power surge. In other types of reactor like RBMK and fast reactors the decrease of the reactivity only occurs with fuel dissemination.

In conclusion, we see that the safety of critical neutron reactors depends strongly on the delayed neutron fraction of the fuel as well as on the tempera­ture coefficients, especially on the Doppler temperature coefficient. These strong dependences severely constrain the type of fuel which can be used in critical reactors in safe conditions. We shall see that hybrid reactors might be very helpful in alleviating these constraints.

There is a very big difference between precision (statistical error or uncertainty) and accuracy (systematic error). Accuracy will depend on the code (bugs, nuclear data, specific treatment, etc.) and on the user (wrong hypothesis, bad use of particular method, etc.). The precision will depend on the number of events in the region concerned and on the statistical method used.

What is a good uncertainty?

If the result of a run is ф with N histories contributing to this quantity, the uncertainty is Аф / 1/vN; thus, to divide this error by 2, N has to be multiplied by 4. But the computer time is proportional to N, so the duration of the run is also multiplied by 4. In general, an MCNP result with an uncertainty less than 10% is sufficient, but only if the entire volume has been visited by particles. In order to check the confidence in a result, MCNP gives the evolution of a number, the figure of merit (FOM) which is defined by FOM = 1/(Аф2 x T) where T is the computer time. This number must be approximately constant (T / N and Аф / 1/VN) for the result to be credible.

The OECD has recently organized benchmarks [105, 106] comparing available INC calculations. These benchmarks have shown that small — angle neutron spectra were particularly sensitive tests of the code.

Small-angle neutron spectra

The SATURNE group studied these observables before the close-down of the Saclay (France) synchrotron SATURNE. Figure 6.1 shows the small — angle neutron spectra for a number of targets and 1 GeV incident protons. The data are compared with a calculation using the Bertini INC and with one using the Cugnon INC. Although still not perfect, it is clear that the Cugnon INC is a significant improvement over the Bertini INC. The figure shows the importance of the delta charge exchange peak, 300 MeV lower than the high-energy quasi-elastic peak. Both peaks correspond to a process by which the proton is changed into a neutron. Figure 6.2 shows similar results and comparisons made by the Los Alamos group [90]. Here again, the improvement obtained with the more modern ISABEL [86] INC calculation is clear. The delta peak involves real charged pion exchange, the quasi-elastic peak the excitation of the target into an isobar analogue state. The delta peak is a preferential doorway for the energy deposition of

the high-energy proton (or neutron) into the target nucleus. Indeed, for heavy nuclei the average energy deposition is close to 300 MeV.

The basic step for organic uranium and/or plutonium extraction involves first a thorough mixing of the aqueous and organic phases in order to max­imize the interphase area, and second a reseparation of the phases. Figure 9.3 shows a schematic view of this process.

Flux conservation implies that

IF(x0 — X1)=4(У0 — У1). (9.20)

Further, at equilibrium the concentrations are related by

У0 = DX1. (9.21)

In a single-step extraction У1 = 0. In this case, substituting equation (9.21) into equation (9.20) yields

— if

X1 = (IeD + If) X0 which gives the fractional recovery

= 4.У0 = x0 — X1 = 1

P IFX0 x0 (1 + (If/DIe ))

In its first version, this proposal aimed primarily at massive energy production. Later on, applications to incineration and transmutation were carefully con­sidered. The accelerating system involves three cyclotrons working in series and bringing protons to an energy of 1 GeV, with an intensity of about 10 mA. Such a system represents a significant technological jump in compari­son with the cyclotrons of SIN (Villigen-CH). The fast subcritical arrange­ment’s multiplication coefficient is about 0.98. The anticipated gain of 120 would yield a total thermal power of 1500 MW and electric power of 600 MW.

In order not to slow down the neutrons, and to extract a specific power on the order of 0.5 MW/l, cooling is ensured by liquid metal. For safety and neutronic reasons, lead is preferred. While molten lead does not present fire and explosion hazards like sodium, it has some drawbacks: chemical toxicity, corrosion and radionuclide production from neutron irradiation or as a result of the spallation process. Cooling by lead or a lead-bismuth alloy has already been used, in particular in the reactors of Russian nuclear submarines. Corrosion of the steel (of martensitic type) components was

Spent fuel

(every 5 years)

Figure 12.1. View of the system proposed by the CERN group. The molten lead pool is 30 m high and 6 m in diameter. It contains 10 000 tons of molten lead.

tempered by controlled oxidation by oxygen dissolved in the molten coolant. Molten lead would allow us, as in the sodium case, to keep a low pressure in the reactor, and to obtain high thermodynamical efficiency, due to the high operating temperature.

Figure 12.1 shows a schematic view of the proposed system, while figure 12.2 shows a more detailed view of the subcritical assembly. The proposed system is characterized by a high level of safety. No major accident, even intentional, is possible.

The computations done so far rely on the data available concerning the site in the east of France. Those pertaining to the geological medium rest first on existing documentation, and second, between 1994 and 1996, on non — (or only slightly) invasive methods.

• Through drillings, the characteristics of the geological formation have been measured at the local scale; the samples taken were used to measure and establish geological, geomechanical and geochemical properties.

• The non-intrusive methods are those of geophysics, particularly 3D geo­physics, effected on the whole of the projected underground laboratory. No tectonic events were detected, thus confirming the seismotectonic stability of the site, one of the selection criteria.

Evolutions due to external causes are also considered, especially the geomorphologic and hydrogeologic consequences of climate change. The surveys have not detected any significant influence of such changes on radio­nuclide transfer times, even under extreme conditions. A succession of climate change events is also examined.

The Boltzmann equation expresses the variation with time of the number of neutrons present in an elementary volume V of surface S. We can write this as:

We define each of the terms of the right-hand side of equations (3.16) and (3.17):

entering — exiting

div(J(r, v, t)) d3r

V

expresses the total current entering the volume if the normal is directed outwards;

S(r, v, t) is the external neutron source. In the second term of the right-hand side, the fission source r/f(v), is the velocity spectrum of the fission neutrons, ni is the number of neutrons per fission of species i, and the macroscopic cross-sections are assumed to be time independent; i indexes fissioning nuclei

inscattered =

where j indexes all species of scattering nuclei.

outscattered+absorbed

‘(r, v, t) E.(T](r, v) d3r

where XT = Xs + Xa.

In the above expressions we have, for the sake of simplicity, neglected the fi dependence of the cross-sections and integrated over fi. The Boltz­mann equation is obtained as

div(J(r, v, t)) + S(r, v, t)

‘(r, v, t)J2 чФ№)(Ц1)(г, v’) + sij)(r, v! v)) dv

hJ

— ‘(r, v, oX) v)

j

where we made use of ‘(r, v, t) = vn(r, v, t).

The ingestion radiotoxicity of an element is a measure of the biological con­sequences of its ingestion. The radiotoxicity is defined as

R(Sv) = Fd(Sv/Bq)A(Bq) (3.138)

where R(Sv) is the radiotoxicity in Sievert per mass unit, Fd(Sv/Bq) is the dose factor in Sievert per Becquerel activity and A(Bq) is the activity. For 1 kg mass

1 32 1019

A(Bq/kg=w^) -г (3Л39)

where A is the atomic mass of the element. The International Commission on Radiation Protection (ICRP) has evaluated the dose factors [65], some of which are given in table 3.7 [66].

Fission products decay by fl radiation, while transuranic elements decay essentially through a radiation. For the same disintegration rate, a emitters are much more radiotoxic than fl emitters, as can be seen from table 3.7, with the exception of 129I which has very peculiar biological properties, with a very high affinity for the thyroid gland.

The use of ingestion radiotoxicity as a measure of noxiousness is subject to question. For example, in the case of underground storage, the probability for the radioactive species to enter the biosphere is of paramount importance. Plutonium and, generally, other actinides, have very low mobility, especially in clay, so that they contribute little to the radiotoxicity released to the bio­sphere. In contrast, elements like niobium, technetium and iodine are very mobile and are, potentially, the chief contributors to radiotoxological release from deep underground storage. Calculations such as those given

in the Appendix show that, indeed, the dominant contribution to the future possible exposition of populations comes from 129I.