The most important considerations determining the form of the steam generator are the nature of the joints at the ends of the tubes, and the accommodation of differential expansion between the tubes and the shell. If the tubes are welded to tubeplates that form part of the boundary of the secondary sodium circuit the welds are exposed to sodium or sodium vapour, and the frequency of even very small leaks from the steam side must be very low. In some older reactors the tubes were in the form of a U so that the welds at the ends of each tube were positioned above the level of the sodium in the shell and protected from it by a layer of argon. This helped to reduce the thermal stresses at the joints and accommodated relative thermal expansion of the tubes and the shell.

Thermal expansion stresses can be minimised if the tubes are not straight. One such configuration features helical tubes wound in suc­cessive layers in an annular cylindrical bundle. This has the advantage that it can accommodate very long individual tubes in reasonably com­pact units, but the flow pattern on the sodium side is very complex so that it is difficult to ensure uniform heat transfer conditions, and steam generators of this form are expensive to manufacture. An alternative “hockey-stick” design, utilising tubes that are straight over most of their length but with a single bend near one end, has been proposed.

I

4

Figure 4.11 Tube-to-tubeplate welds for a straight-tube steam generator.

If straight tubes are used there has to be an expansion bellows in the shell, and care has to be taken in design to ensure that the flow patterns on both sodium and water sides are uniform to minimise temperature differences between the tubes.

In a straight-tube steam generator the tubes can be welded at both ends to spigots machined on the tubeplates. At one end the holes in the tubeplate and the spigots have to be large enough so that, during manufacture, the tubes can be passed through them and welded with an offset weld at one end and a butt weld at the other. The arrangement is shown in Figure 4.11. These welds can be inspected from inside the tubes.

An alternative design that avoids exposing welds to sodium alto­gether makes use of “thermal sleeves”. The tubes pass through indi­vidual nozzles in the shell that contains the sodium and are welded to a header positioned outside. The nozzles are in the form of sleeves

welded to the shell and brazed to the tubes. The brazes and the tube-to — header welds can all be inspected from the outside. The thermal sleeve design has the advantage that the joints between the sleeves and the tubes, and those between sleeves and the shell, are not stressed by the steam pressure, and a leak in neither allows water or steam to come into contact with sodium. The disadvantage is that in a large heat exchanger the manifold, which has to connect many hundreds of tubes, is very complicated and expensive. The arrangement is shown in Figure 4.12.

The problems of steam leaks can be avoided almost completely by the use of double-walled heat exchangers with some means of detecting leakage of either steam or sodium into the space between the walls. The disadvantage is that the heat transfer coefficient is bound to be much worse than in a single-walled heat exchanger, and the cost is higher.

If a single-walled design is chosen the risk of leaks has to be accep­ted. A leak puts the heat exchanger in which it occurs out of action

until it is repaired. The effect on the availability of the plant can be reduced by having a large number of separate small heat exchangers or heat exchanger modules, any one of which can be shut down for maintenance or repair without reducing the power output of the whole plant by much. On the other hand it is cheaper to build a small number of large heat exchangers. In the end a choice has to be made between better plant availability and lower capital cost. The design provisions that have to be made to ensure the safety of the plant in the event of a leak in a steam generator are described in section 5.3.3.

Useful discussions of steam generator design are given by Hayden (1976) and Lillie (1978) and of the performance of tube-to-tubeplate welds by Broomfield and Smedley (1979).

The neutron density n in a reactor is in general a function of position r, the energy E of the neutrons, the direction Й in which they are trav­elling, and time t. The neutron density n obeys a linear version of the Boltzmann equation called the neutron transport equation, the deriv­ation of which is given in many standard works on neutron transport (e. g. Davison and Sykes, 1957; Duderstadt and Hamilton, 1976). It can be written in a simplified form as

д П

= — v& • grad n — v^n + T + F + S. дt (1.1)

1 2 3 4 5

If each term in equation 1.1 is multiplied by a small element dV dE dfi the terms on the right-hand side can be thought of as the contributions to neutrons appearing in the volume dV and the energy interval dE and travelling in a small solid angle dfi surrounding the direction Й as follows.

1. This is the rate at which neutrons already in dEd ^ move into dV across its boundary, v being the neutron speed corresponding to E, so that v2 = 2E/m where m is the mass of a neutron. (Relativistic effects are not important: even a 4 MeV neutron is travelling at only a tenth of the speed of light.)

2. This is the rate at which the neutrons in dV dEd ^ interact with the nuclei in dV. It is assumed that any interaction removes the neutron from dEd ^. £r is the total macroscopic cross-section in dVdE and is independent of Й.

3. This is the rate at which neutrons already in dV are scattered (elast­ically or inelastically) from other energies and directions dE7 d&7 into dE d&.

4. This is the rate at which new neutrons from fission appear in dV dEd ^. Delayed neutrons are ignored in equation 1.1 for simplicity.

5. This is an additional source of neutrons in dV dEd ^ (from spon­taneous fission, for example, or from a spallation source driven by an accelerator).

T is given by

T = d&’ dE’v’£s (E’ ^ E, Й ^ to)n(i, E’, ft7, t). (1.2)

4n 0

£s is the macroscopic scattering cross-section in dV (including both elastic and inelastic components). It is a function of E’, E and ft — ft7. Up-scattering in energy is not important in a fast reactor so £s is zero for E’ < E.

F is given by

TO

F = dE’n(E’ )v’£ f (E’ )v(E’ )x(E )/4n. (1.3)

0

£ f is the macroscopic fission cross-section in dV and v is the average number of neutrons generated in each fission event. x is the fission spectrum that is assumed to be independent of the energy of the neut­ron causing the fission. It is also assumed that fission neutrons are generated isotropically.

S is usually assumed to be zero in a critical reactor because in an operating power reactor spontaneous fission is negligible as a source of neutrons.

If S = 0 all the terms in equation 1.1 are linear in vn and it is usual to work in terms of the neutron flux ф defined by

ф(г, E, Й, t) = v(E)n(r, E, Й, t). (1.4)

v is about 14000 m/s at 1 eV and 14000 km/s at 1 MeV.

In a cylindrically symmetrical fuel element, the temperature Tfs of the surface of the fuel is related to the temperature of the surrounding coolant Tc by

(2.1)

where q is the linear heat rating in the fuel element, h is the heat transfer coefficient between cladding and coolant, Ks is the thermal conductivity of the cladding, and hf is the heat transfer coefficient between the fuel and the inside surface of the cladding. Rs is the outer radius of the cladding and Rf is its inner radius, which we can also take to be the outer radius of the fuel because, as we shall see, at times the fuel is in close contact with the cladding, and even when it is not the gap between them is small.

In a fast reactor there is usually no significant flux depression in the fuel element and the fission rate can be taken to be approximately uniform over its cross-section. The temperature distribution within the fuel itself however is complicated by the fact that over the wide temperature range in question the variation of the fuel conductivity Kf has to be taken into account. If the fuel temperature at a distance r from the axis is Tf (r), and if the fuel is solid and heat is generated uniformly throughout it, then

CKf(T)dT=4П 1 — R2 ■

and the maximum fuel temperature Tfm is given by

Under some circumstances, however, there is a cylindrical hole in the centre of the fuel. If this has a radius Rh and heat is generated uniformly throughout the annular fuel region the temperature at r is given by

where a = R2h/R2f. The maximum temperature is given by

Comparison of equations 2.3 and 2.5 shows that for constant q the presence of a central hole reduces the maximum temperature.

The cloud of vacancies and interstitial atoms produced by a neutron scattering event diffuses through the crystal lattice under the influence of thermal agitation. If the motion were entirely at random the density of vacancies and interstitials would rise until production was balanced by recombination at sinks such as grain boundaries and dislocations, where they would meet and annihilate each other. The motion is not entirely random, however. The stress field around a dislocation inter­acts with the stress fields around both interstitials and vacancies, and tends to attract them, but the interaction with an interstitial is stronger. As a result the interstitials tend to cluster together at dislocations and other defects in the crystals, leaving an excess of vacancies that also tend to form clusters rather than recombining. The normal form of

a cluster of vacancies is a flat mono-atomic layer that eventually col­lapses leaving an edge-dislocation ring, but if there is a nucleus, which may consist of a few atoms of an inert gas (helium), vacancies migrate to it and form a three-dimensional void.

Figure 3.11 is a series of electron micrographs of irradiated AISI type 316 stainless steel showing typical polyhedral voids about 0.1 ц-m in diameter. As these voids are formed and grow the mean density of the material falls and it swells. Most metals swell in this way when irradiated but the rate and extent of swelling vary widely from one to another.

Temperature has an important effect on swelling as may be seen in Figure 3.11. Figure 3.12 shows the ranges of values of void

density and mean diameter that are typically observed. The greater size of the voids at higher temperature is probably due to the increased mobility of vacancies at higher temperatures, but the corresponding reduction in the number of voids is not entirely understood because the mechanism of nucleation is uncertain. It may be that at high tem­perature the helium atoms migrate to existing voids and are not avail­able as nuclei of new ones. Alternatively nucleation may be connec­ted with the “spikes” of displaced atoms due to a neutron scattering event, the damage caused by which anneals out more readily at high temperature.

The result for many materials is that the swelling rate is high in a certain temperature range and low in others as shown in Figure 3.12. For 316 stainless steel there is little swelling below 350 °C. At high temperatures impurities may be very important, and above 600 °C the swelling is inhibited by the formation of very large voids on large grains

of carbide. This is strongly dependent on the carbon concentration, and one way to reduce swelling is to reduce the amount of carbon in the material.

Swelling is also reduced if there are many dislocations because they tend to attract the vacancies, although weakly, and if there are enough of them the number of vacancies left to form voids is small. This is shown by the much reduced swelling in 20% cold-worked 316 stainless steel as compared with annealed material, especially below 500 °C, as shown in Figure 3.13.

Finely dispersed precipitates within the grains also tend to reduce swelling because they attract both interstitials and vacancies and allow recombination. The nickel-rich alloy Nimonic PE16, in which the y’ phase is finely dispersed, is resistant to swelling for this reason. In a similar way the martensite crystals in ferritic-martensitic steels and the dispersions of nanometre-sized particles of oxide in oxide-disperse- strengthened or “ODS” steels have similar effects. For this reason these materials may be particularly attractive for the cladding and the structure of the core.

In most materials the amount of swelling increases with time and because it depends on the interaction between vacancies and nuclei the increase is nonlinear. Initially swelling accelerates as irradiation proceeds, but at very high doses there is some evidence that it may saturate.

318 Stainless Steel

Cold-Worked 316

Annea ed 316

Nimonic

Displacements per Atom

Figure 3.14 Irradiation creep in various materials.

So far we have discussed protective systems aimed at detecting an accident in its early stages and preventing it from developing. Another type of protective system mitigates or controls the consequences of an accident. One such is the post-accident heat removal system.

The rate at which “decay heat” is generated by the decay of radio­active fission products in the fuel after a long period of steady operation is shown in Table 5.1 and Figure 5.2. The heat production is slightly less after shorter periods of operation because fewer of the long-lived fission products have accumulated. It will be seen that even a year after shutdown a 3000 MW (heat) reactor generates more than 1 MW.

Because it is essential to remove this heat and keep the fuel cool for a long period after even the most severe of accidents it is necessary to provide several independent and diverse cooling systems.

The first means of removing the decay heat is to use the normal route to the main condenser via the steam generators. However this requires most of the plant to be intact and operable, and in particular the primary and secondary sodium pumps and the boiler feed and condensate extract pumps have to have electrical supplies.

If the steam plant is not available it may be possible to reject heat directly from the secondary sodium circuits, for example by cooling the external surfaces of the steam generator vessels by circulating air. Almost certainly, however, natural convection cannot be relied on and electrical supplies are needed to power the cooling fans, as well as the sodium pumps.

To cater for the possibility that the secondary sodium circuits are not available it is usual to provide separate dedicated decay-heat rejec­tion circuits with heat exchangers in the reactor vessel. The coolant in these circuits rejects heat to the atmosphere in air-cooled heat exchangers. Because sodium freezes at 98 °C for a sodium-cooled reactor the auxiliary coolant can be a mixture of sodium and potassium which freezes below normal atmospheric temperature. Such decay — heat rejection circuits can be designed to operate entirely by natural convection on both the liquid metal and air sides. With such a heat — rejection system the fuel can be cooled safely even if the secondary circuits do not work and there is no electrical power, because natural convection within the reactor vessel can be relied upon to transfer the heat to the decay-heat rejection heat exchangers.

An additional defence against overheating can be provided by cooling the surface of the reactor vessel itself. This can be done for example by surrounding the leak jacket with a water-cooling circuit that rejects heat to the atmosphere and, as in the case of the liquid metal decay-heat rejection circuits, can be made to work by natural convection. A system of this type is sometimes known as an “RVACS” (reactor vessel auxiliary cooling system). Figure 5.3 shows a typical decay-heat rejection system in diagrammatic form.

All these ways of rejecting decay heat depend on the fuel and the structure of the core remaining intact after the accident and on the primary sodium being able to circulate through it. Provisions for cooling the fuel debris after a very severe accident that has destroyed the core structure are discussed in section 5.4.7.

To illustrate the effects of various design options on the flux and importance spectra, in the following paragraphs comparisons are made with the “reference core” described in Table 1.1, which is a simplified representation of a 2500 MW (heat) breeder reactor. The “absorber” component represents the effect of the control rods when the fuel is

new or of the accumulated fission products at the end of its irradiation life. The stainless steel structure is assumed to be 74% Fe, 18% Cr and 8% Ni. The overall density of the fuel material is 80% of the theoretical density of the oxide, allowing for porosity incorporated to accommodate fission products (as explained in Chapter 2). The spectra are derived from a fundamental mode calculation based on the ANL 16-group cross-section data (Tamplin, 1963). The enrichment E, defined as Pu/(U+Pu), is adjusted to make the reactor critical.

Figure 1.7 shows the spectrum of the flux in the reference core com­pared with the spectrum of neutrons as they are born in fission of 239Pu. (The fission spectrum for other isotopes is very similar.) The energy of the fission neutrons is reduced by scattering so that the peak is at around 0.3 MeV, and below this energy the flux falls off steeply until there are hardly any neutrons with energies less than about 1 keV. The spectrum in a fast reactor is very different from that in a thermal reactor.

At high energies, above about 0.5 MeV, inelastic scattering in 238U and to a lesser extent in 56Fe and 23Na is very important. Excitation of the lowest energy level of the 238U nucleus reduces the energy of a neutron by 45 keV and the corresponding values for 56Fe and 23Na are 845 and 439 keV respectively, so the effect of inelastic scattering is

very marked. At lower energies it is elastic scattering that reduces the energy of the neutrons and the lightest nuclei such as 23Na, 16O and 12C are the most important moderators. Many collisions are needed, however, to reduce the energy, and the chance that the neutron will diffuse out of the core or be absorbed is large, so the flux declines steadily with decreasing energy. A few of the neutrons are captured in 23Na or 56Fe but most are absorbed in 238U.

The neutron importance, also shown in Figure 1.7, increases with energy. Above 1 MeV it is high because of the possibility of fission in 238U. At low energies, below 3 keV, (not shown in Figure 1.7) it

rises with decreasing energy because the fission cross-section in 239Pu rises more rapidly than the capture cross-section in 238U, so the lower its energy the more likely a neutron is to cause fission and therefore contribute to the reactivity. It should be remembered that a neutron captured in 238U is lost as far as maintaining the chain reaction is concerned even though it causes the generation of a new fissile nucleus.

Fuel Material. The effect of replacing oxide fuel in the reference core by carbide or metal is shown by comparing the spectra in Fig­ure 1.8. (The overall densities are 10900 and 14300 kg m-3 respectively,

both 80% of theoretical.) Fewer moderating atoms are present in (U, Pu)C than in (U, Pu)O2 and even though a carbon nucleus is lighter than oxygen there is less moderation so the mean neutron energy is higher, as indicated by the fact that the peak in the spectrum is at a higher energy. This is usually called a “harder” spectrum. At the peak of the spectrum neutron importance increases with energy so the harder spectrum resulting from a change from oxide to carbide fuel allows fissile material to be replaced by fertile. As a result of this, and the higher fuel density, the enrichment is lower and there are more captures in the fertile material in the core. The importance is higher above 1 MeV because the enrichment is lower and more 238U is present, and it is lower at lower energies because the ratio of fissile material to absorbers is lower.

Similar, but greater, changes result if oxide is replaced by metal as the fuel material.

Coolant. The choice of coolant has a great effect on the neutron flux and the performance of the reactor mainly because it occupies such a large fraction of the core volume. The effect is mainly due to differences in the inelastic scattering at energies above about 1 MeV. Figure 1.9 shows the spectra for reference cores cooled by sodium, lead-bismuth eutectic (54.5%Pb, 45.5%Bi) and carbon dioxide. Lead- bismuth eutectic and carbon dioxide are much poorer moderators than sodium (lead-bismuth because the atoms are heavier, carbon dioxide because it is much less dense), so in both cases the flux spectrum is harder. The fission-neutron spectrum peaks at around 2 MeV (see Figure 1.7). Strong inelastic scattering in 238U and iron scatters many of these neutrons down to around 0.7 Mev, causing the sharp peaks in the lead-bismuth and carbon dioxide spectra. However elastic scattering in sodium is particularly strong at this energy so this peak is “smoothed out” in the sodium spectrum.

Although lead-bismuth is a poor moderator it has a high macro­scopic scattering cross-section, whereas that of a gas coolant is very low. As a result the former leads to a lower critical enrichment than

sodium and the latter to higher. Largely as a result of this the neutron importance curve is steeper for lead-bismuth and shallower for carbon dioxide.

Core Size. Figure 1.10 shows what happens if the core of the reactor is made smaller. It compares the spectrum for reference cores with — B2 = 18 m-2 (a cylinder 1 m high and 2 m in diameter) and — B2 = 28 m-2 (0.9 m high and 1.2 m in diameter). The difference is that 47% of the fission neutrons leak from the smaller core whereas only 32% leak from the larger. As a result the spectrum is harder and, as in the

case of a gas-cooled core, the importance curve is shallower because the critical enrichment is higher.

Plutonium Composition. These comparisons have been made assuming the fissile material in the core is pure 239Pu, but this is in prac­tice very unrealistic. The plutonium is most likely to originate from the reprocessing of irradiated thermal reactor fuel. In the thermal reactor higher plutonium isotopes are formed by successive neutron capture reactions, and the longer it is irradiated — i. e. the higher the burnup — the more of them there are. For example plutonium from AGR fuel irradiated to 20000 MWd per tonne consists of Pu-239, 240, 241 and

233U and 232Th. The flux spectrum is harder in the thorium case because there is less inelastic scattering at high energy. The enrichment is higher (27% compared with 23%) because the fission cross-section of 233U is lower than that of 239Pu in the 0.1-1.0 MeV range where the flux peaks. However there is a very significant difference in the importance spectra, which for the thorium reactor is almost completely flat. This is because the fission cross-section of 233U is significantly higher than that of 239Pu at lower energies.

Neutron Balance. Table 1.2 shows the sources and fates of the neut­rons in these cores and illustrates the effects of the different spectra. As compared with a thermal reactor, fast fission in 238U, and in the cases where they are present, 232Th, 240Pu and [1]Pu, is a more significant source of neutrons, and loss of neutrons by capture in the coolant or the structure is quite insignificant. In contrast many neutrons leak from

the core, but these are not necessarily lost because they can be made use of if the core is surrounded either by a breeder containing fertile material or by waste materials to be eliminated by transmutation.

An oxide-fuelled thorium-cycle reactor with this specification would not breed because the capture cross-section of 232Th is lower than that of 238U in the keV energy range, but a higher breeding ratio can be attained with carbide fuel.

Thermal creep in the fuel is usually described by an empirical relation­ship of the form

sth = Aone B/T,

where a is the stress, є is the strain, T is temperature and A, B and n are constants. Usually n = 1, B is about 4 x 104 K, and typical results for stoichiometric UO2 (x = 0) give A — 2 x 10-4 s-1 Pa-1. If the fuel is not stoichiometric it is harder, whereas mixed oxide is usually found to be softer.

The resulting relaxation time for thermal stress is shown in Figure 2.11. It is very short in the centre of the fuel, and over times of the order of seconds or more this part of the fuel can support only hydrostatic pressure. The outer part of the fuel on the other hand is quite rigid.

A second source of creep strain is due to the irradiation itself. The effect of a fission event is to melt the small volume of the fuel through which the fission fragments travel. Any shear stress in the melted region is transferred to the surrounding material causing it to strain a little. Then another fission event melts another region causing another additional strain, and so on. The result is a steady strain — rate proportional to stress and fission-rate density but only weakly dependent on temperature. Various experimental correlations have been proposed, typically of the form

Є f = A1 fa (2.7)

with A1 ~ 1.8 x 10-36 m3 Pa-1 ■ f is the fission-rate density in m-3 s-1, so with a in Pa equation 2.7 gives є in s-1.

The effect of irradiation creep is also shown in Figure 2.11. The relaxation time in the outer part of the fuel is substantially reduced but it is still hard on a timescale of days or weeks.

It is of course impossible to observe what happens to the fuel during irradiation but it is probably more or less as follows. After the fuel has swollen to touch the cladding the cladding exerts a compressive normal stress on its surface. The resulting stress distribution is shown in Figure 2.12. The fuel is incapable of exerting hoop stress in the central region, which is soft and stress-free because it is in contact with the central void. It is also incapable of exerting hoop stress at the outer edge where there are radial cracks. Thus the compressive surface stress is borne by a compressive hoop stress in a narrow ring of fuel just at the root of the cracks.

In steady operation the load-bearing ring moves slowly outwards as more of the fuel has time to relax the imposed stress and allow the cracks to close. But if there are changes in reactor power and therefore in the fuel temperature distribution the development is interrupted.

If the power rises, for example, the cracks reopen to some extent and the load-bearing ring is moved inwards.

The primary coolant receives heat in the reactor core, flows to a region where the neutron flux is low to transfer its heat to the secondary coolant in the intermediate heat exchangers, and then returns to the core. In fixing the layout of this primary coolant circuit two main choices have to be made: whether the heat exchangers and circulating pumps should be in separate vessels from the core or in the same one, and whether the pumps should be located before or after the heat exchangers.

A “pool” reactor is one in which the entire primary circuit is con­tained within a single vessel, as shown in Figure 4.1 A. The core is surrounded by a neutron shield and around this are placed the pumps and heat exchangers. In a “loop” reactor, in the other hand, as shown in Figure 4.1 B, the core is contained in a small vessel with the main neutron shield outside. Hot coolant from the core passes through pipes to the heat exchangers and then back to the core vessel.

The choice between the two schemes is affected by such consid­erations as the design and manufacture of the vessels, the design of the refuelling system, the operating conditions of the pumps, and ease of inspection and maintenance. That the choice is finely balanced is shown by the fact that reactors of both types have been built, but most proposed future reactors are of the pool type.

The main advantages of the pool layout are that the coolant pressure-drop is low and the reactor vessel is very simple in shape without irregularities that might act as locations of high stress. The primary circuit can be arranged so that hot coolant never comes into

contact with the vessel. In a loop reactor parts of the pipework and of the vessel are in contact with hot coolant at temperatures at which thermal creep may be important, while other parts are in contact with cold coolant so that thermal stresses have to be allowed for. In addi­tion there may be the possibility of stress concentrations caused by the pipe branches on the sides of the vessel.

On the other hand a pool reactor vessel is so large that it has to be assembled on site whereas a loop reactor vessel can be made in a factory where the quality of manufacture can be controlled more easily. The roof of a pool reactor vessel is much larger than that of a loop vessel and if advantage is to be taken of the potential simplicity of the vessel itself the pumps and heat exchangers, and possibly the entire core and neutron shield, have to be suspended from it. Moreover part of the underside of the roof is exposed to the temperature of the hot coolant. As a result it is a complex and expensive structure.

A pool reactor has the advantage that there is room within the vessel for a temporary store for irradiated fuel, usually surrounding the neutron shield. Fuel can be transferred from the core to the store without lifting it above the coolant so that no special provision has to be made for cooling it while in transit. It can be left in the store, immersed in coolant, until the fission-product decay power has decayed suffi­ciently to make handling easier when it is removed for reprocessing. A loop reactor vessel is unlikely to have enough room for an irradi­ated fuel store. Irradiated fuel has to be removed from the vessel to a separate store by a machine that is capable of cooling it while it is in transit.

Both pool and loop reactors have pipework or structure operating at the temperature of the hot coolant. The difference is that in a loop reactor the hot pipework is part of the primary coolant containment, and if it should fail radioactive primary coolant could be released. To offset this disadvantage, however, the loop system has the advantage that it may be possible to inspect the high-temperature pipework more easily because it is accessible from outside. It may even be possible to do maintenance work on one coolant loop by closing it off with valves without shutting down the whole reactor. Inspection and mainten­ance of the pipework and structure within a pool reactor vessel are difficult.

Figures 4.2 and 4.3 show a typical arrangement of the components of a pool reactor. In the arrangement shown the core and neutron shield are supported by a strongback attached to the bottom of the vessel while the other main components — the primary pumps and the intermediate heat exchangers — are supported by the roof of the vessel. An alternative arrangement is to hang the core and shield from the roof as well. This has the advantages that the vessel carries only the weight of the sodium it contains and being simply shaped is relatively lightly stressed, and that stresses due to thermal expansion are minimised. Another alternative is to support the vessel and the core from below, but in this case thermal expansion stresses are greater.

9

Above-Core 17 Reactor Roof

Structure 18 Outer

10 Hot Sodium Pool Rotating Shield

11 Cold Sodium Pool 19 Inner

12 Primary Sodium Pump Rotating Shield

13 Pump Motor 20 Fuel-Handling

14 Auxiliary Motor Mechanisms

15 Intermediate Control Rod

Heat Exchanger Mechanisms

16 Secondary Sodium Pipes

Figure 4.2 Arrangement of the primary circuit of a pool reactor.

A typical pool reactor vessel may be about 17 m in diameter and 16 m deep, containing about 2000 tonnes of primary sodium and made of stainless steel about 20 mm thick. It is surrounded by a second “leak jacket” or “guard vessel”, so that even if the main vessel should break the sodium level cannot fall below the top of the core and emergency

Figure 4.3 Plan of the roof of a pool reactor with three secondary circuits.

cooling can be maintained. The space between the vessels provides access for inspection of the main vessel, for example by means of a remotely-controlled vehicle carrying an ultrasonic probe that can examine the welds, particularly those where the stongback is attached.

The inner vessel separates the hot and cold parts of the primary coolant circuit so that all the sodium in contact with the main vessel is at the cooler core inlet temperature. In some cases the inner vessel has a double wall to minimise the transfer of heat between the hot and cold sodium, but an alternative is to shape the lower part of the inner pool so that the sodium in it remains stagnant and acts as an insulating layer.

The reactor roof is a complex structure. Part of its underside faces the surface of the hot pool and has to be protected by thermal insula­tion, usually in the form of thin steel plates, and by a cooling system.

Access through the roof to the core is provided by two rotating plugs mounted eccentrically one within the other. When the reactor is oper­ating they are situated so that the control-rod drive mechanisms moun­ted on the inner plug, and the above-core structure that hangs beneath it, are located centrally over the core. When the reactor is shut down for refuelling the control-rod drives are disconnected, leaving the con­trol absorbers themselves in the core to hold it subcritical. The plugs can then be rotated so that fuel-handling mechanisms mounted on them are positioned above the core and breeder locations as required. The perimeters of the plugs have metal dip seals to prevent leakage of the cover gas. The seals are made of a metal alloy that is solid while the reactor is operating but can be melted when it is shut down to allow the plugs to rotate without breaking the seal.

The above-core structure serves to locate the control-rod drives accurately. It also carries the core outlet instrumentation, consisting of thermocouples to measure the coolant outlet temperature from each subassembly, and in many cases also coolant sampling take-offs that can be used to locate failed fuel (see section 5.2.3).

The vessel for a loop reactor may have inlet and outlet primary coolant connections in the side walls. Some loop reactor designs, how­ever, use a larger vessel so that there is room for the inlet and outlet pipes to pass through the roof and the vessel itself can be simple in form and lightly stressed like a pool reactor vessel. This gives the addi­tional advantage that more space for fuel handling or storage within the vessel may be made available.

The advantages and disadvantages of loop and pool schemes are discussed in detail by Campbell (1973).

Even if fast reactors are used to consume radioactive waste in due course their main function is likely to be to breed fissile material because in this way they can have a transforming effect on the world’s energy resources.

Consider a uranium-fuelled reactor in which N atoms of 235U are fissioned. While this is happening CN new fissile atoms of 239Pu can be produced. If these in turn are fissioned in the same reactor and the conversion or breeding ratio C is unchanged (this is unlikely to be quite true because the fissile material has been changed, but the effect on the argument is not important), a further C2N fissile atoms are produced. If these are fissioned, C3N are produced, and so on indefinitely. The total number of atoms fissioned is therefore N(1 + C + C2 + …). If C < 1, the series converges and its sum is N/(l — C).

Conversion ratios for 235U-fuelled thermal reactors are in the range 0.6 (for light-water reactors) to 0.8 (for heavy-water reactors and gas — cooled reactors). L is particularly large in light-water reactors because neutrons are readily absorbed by hydrogen.

If the fuel is natural uranium N cannot exceed 0.7% of the total number of uranium atoms supplied. If the reactor is a thermal reactor with a conversion ratio of 0.7 and the plutonium bred is recycled indefinitely the total number of atoms fissioned cannot exceed 0.7/(1 — 0.7) и 2.3% of the number of uranium atoms supplied.

In a real system not even this number can be fissioned. When the fuel is reprocessed to remove the fission products and the excess 238U some 235U is inevitably lost. In addition some 239Pu is lost by conversion to higher isotopes of plutonium. As a result thermal converter reactors can make use of at most about 2% of natural uranium.

For a breeder reactor, however, with C > 1, the series diverges and in principle all the fertile atoms supplied can be fissioned. In practice, however, some are lost for the reasons mentioned earlier and the limit is around 60% of the fertile feed. Thus from a given quantity of natural uranium fast breeder reactors can fission about 30 times as many atoms as thermal converters and as a result can extract about 30 times as much energy.

To determine the importance of this difference we have to know how much uranium and thorium are available. The amount depends on the price, and a 2010 estimate by the World Energy Council suggests that, worldwide, about 230000 tonnes of uranium are recoverable at a price up to $40/kg, but that if the price were to rise to $260/kg ten times as much would be accessible. The extent of reserves of thorium is much less certain but seems to be comparable with those of uranium. Thorium can be made available as an energy resource only by means of breeder reactors.

Complete fission of a tonne of uranium, were that possible, would generate about 1 TWd, or 0.09 EJ, of energy in the form of heat. (An exajoule, EJ, is 1018 joules.) Thus if all the $40/kg uranium in the world were used as fuel for thermal reactors that, with recycling, fissioned 2% of the feed, some 400 EJ thermal would be produced. If the same uranium were to be recycled to exhaustion in fast breeder reactors it would produce about 12000 EJ. But if the higher utilisation would allow the higher price of $260/kg to be paid so that the greater resource became available the production would rise to 1.2 x 105 EJ. These quantities can be compared with about 9.0 x 1011 tonnes of “proved recoverable” coal reserves that could yield some 3000 EJ, or 1.6 x 1011 tonnes of “proved recoverable” oil that could yield about 800 EJ. In 2007 some 71 EJ of electricity was generated throughout the world.

There is considerable uncertainty about the true extent of mineral reserves in the earth’s crust because new discoveries continue to be made. However, in spite of this the overall conclusion is that uranium used in thermal reactors has the potential to make a contribution to the world’s energy consumption that is comparable with, but smal­ler than, that of oil, whereas uranium used in fast breeder reactors could contribute considerably more than, possibly 40 times as much as, all the world’s fossil fuel. Thorium used in breeder reactors could probably make a similar contribution. Together they could provide the world with all the energy it needs for centuries to come. And they would do this without adding to the amount of carbon dioxide in the atmosphere.

Equation 1.25 shows three effects of a change in density of a non­fissile isotope: a “moderating” effect due to the change in £sg^g<, a “capture” effect due to the change in Esg, and a “scattering” effect due to the change in Dg. There is a fourth “self-shielding” effect, which is shown in equation 1.40: if is changed all the group cross-sections for the resonant isotopes, such as £cg in equation 1.38, are altered. For lead-bismuth or gas coolant all these effects are small but not so for sodium. The various components of the sodium temperature coefficient of reactivity are as follows.

An increase in temperature reduces the density of the sodium and this reduces £cg giving an increase in reactivity and a positive capture contribution to the temperature coefficient, but it is a small contribution because the sodium does not capture many neutrons in the first place.

The reduction in has the effect of hardening the spectrum — that is of shifting the peak in ф shown in Figure 1.7 to a slightly higher energy. Figure 1.7 also shows that in a plutonium-fuelled reactor the peak occurs in the range where ф* increases with energy, so there is a gain in reactivity. Because sodium is an effective moderator this posit­ive moderating contribution to the sodium temperature coefficient is large.

As Ss decreases Scg decreases because ф* in equation 1.38 increases more than J. There is a similar effect on S f but, as in the case of a change in the fuel temperature explained later, in a breeder reactor the capture effect from 238U is greater than the fission effect from 239Pu and 241Pu so the reactivity increases, giving another small positive contribution to the sodium temperature coefficient.

These three components, due to the capture, moderating and self­shielding effects, are contributions to the фф term in equation 1.25, so they all depend on position in roughly the same way. They are greatest at the centre of the core and smaller at the edges. The effect of scattering is quite different, however. A decrease in the scattering cross-section increases the diffusion coefficient Dg and this results in a decrease in reactivity, depending this time on V фg — Уф*. It is therefore zero at the centre and reaches a maximum in the outer parts of the core.

Table 1.4 shows the effect of increasing the coolant temperature uniformly throughout the core of a small sodium-cooled breeder. In this case the resulting reactivity change is the small difference between two large quantities and is just positive, giving a small overall positive sodium temperature coefficient.

The effect of a local change in sodium temperature or of a local loss of sodium may, on the other hand, be positive or negative depending on where in the core it happens. Figure 1.26 shows the effect of loss of coolant from various points on the axis of the core of a larger breeder

Table 1.4 Components of the sodium
temperature coefficient of reactivity of
a small fast reactor

Component dk/д T (K 1)

reactor. Near the centre moderating, capture and self-shielding domin­ate and the reactivity change is positive, but towards the edges leakage becomes more important and it is negative.

Chapter 5 describes extreme hypothetical accidents in which the sodium is lost completely from all or part of the core. The reactivity

increase due to complete loss of coolant from the whole core of the small reactor of Table 1.4 would be 4 x 10-5, but if coolant was lost only from the part of the core where the sodium coefficient is positive it would be as high as 7 x 10-3. For a large 2500 MW (heat) reactor the effects are more positive, and the gain in reactivity might be 0.017 for complete loss of sodium and 0.020 if it was lost only from the central region.