Helium is one of a family of gases (which also includes argon, neon, and xenon) commonly referred to as the inert gases or noblegases. Apart from some exceptions of purely academic interest, atoms of these gases do not form com­pounds with other elements (hence their description as inert). Helium, which has a molecular weight of 4, is present in small quantities in the atmosphere but is more commonly derived from oil and natural gas wells.

The inert gas argon (atomic mass 40) is much more available; air contains

0. 94% by volume of this gas. Unfortunately, argon is not suitable as a reactor coolant, since irradiation by neutrons causes it to form a radioactive isotope (argon-41) that decays with a half-life of 1.8 h, emitting both p and y rays. This neutron absorption and the resultant activation of the coolant circuit are unac­ceptable. Helium, though more expensive than argon, is not activated in a neu­tron flux and is, therefore, much more suitable.

Helium has been employed in the so-called high-temperature gas-cooled re­actor (HTR). Here, the fuel is in the form of uranium carbide clad in graphite, which acts as both the cladding material and the moderator. With helium it is possible, in principle, to operate such reactors at very high temperatures (typi­cally in excess of 800°C) without any chemical attack on the moderator-dad. However, it is usually impossible to maintain the helium coolant in a pure state, because in an actual circuit there will be a small leakage of water vapor from the boilers, ingress of air and other materials through leaks of the circulators, and release of gases originally adsorbed on the graphite. Although the helium itself does not react with the graphite or the steel structures even at high oper­ating temperatures, the impurities do, and this limits the temperatures that can

3.1.1 Steam

Steam has better thermodynamic properties as a coolant than carbon dioxide. Its high specific heat allows good heat transport with lower mass flow rates and smaller, more compact piping systems than in other gas-cooled units. This has led to a number of studies of the possibility of using steam as a reactor coolant. However, at high temperatures and pressures, steam is a highly corrosive oxi­dizing fluid, and stainless steels may be the only suitable construction materials for use with steam at temperatures above about 600°C.

In a conventional oil-fired or coal-fired boiler, it is normal to superheat the steam (i. e., increase its temperatures above the saturation temperature) before feeding it to the turbine. This increases the overall thermodynamic efficiency of the power generation of the cycle. In the normal nuclear boiler (e. g., the B^WR the steam is not superheated. However, there have been a number of attempts to introduce superheating in nuclear boilers and to make the nuclear reactor closer to a conventional system. In this case, the steam can be regarded as a supplementary coolant to the boiling water in the other parts of the reactor. In general, it is not economically attractive to introduce superheating in this way, mainly because it requires the use of stainless steel cans and hence an increase in the enrichment of the fuel. However, a number of plants in the former Soviet Union do employ superheating on a regular basis.

One of the design basis fault conditions for a PWR listed in Chapter 4 is rupture of a steam generator tube. Such an event occurred at the R. E. Ginna PWR sta­tion in New York State on January 25, 1982. The Ginna station is based on a two-loop Westinghouse PWR. At 9:25 a. m. the plant was operating at 100% power [490 MW(e)]. Shortly thereafter the primary reactor coolant system pres­sure dropped significantly, followed by nearly simultaneous activation of the HPIS, reactor trip-turbine trip, and containment isolation. The pressurizer went almost empty. This is the behavior expected when a steam generator tube bursts (ruptures), allowing primary circuit water to pass into the (lower-pres­sure) secondary side of the steam generators. Following standard procedures for responding when it is suspected that a steam generator tube has ruptured, the operators tripped the main coolant pumps and closed the main steam isola­tion valves on the suspect steam generator.

The operators opened the PORV connected to the pressurizer in order to equalize the primary and secondary circuit pressures quickly and stem the leak.

This action allowed reactor coolant to drain into the pressurizer relief tank. However, when this operation was completed and an operator tried to close the PORV again, it failed to close (as at TMI-2), requiring the operator to shut the block valve and thus isolate the flow, which he did promptly. The depres­surization resulting from the opening of the PORV caused flashing in the pri­mary circuit, pushing water into the pressurizer and causing a void to form in the top part (upper head) of the reactor vessel. This situation was recognized and rectified by starting a main circulating pump some 2 h after the start of the incident. No excessive fuel temperatures were noted.

The operation of the PORV caused the pressurizer relief rupture disk to blow and some 5,000-10,000 gallons of water drained into the sump of the contain­ment building, which had been isolated by this stage. During this time, the damaged steam generator was isolated on the secondary side and the pressure in this steam generator went up to the point where the secondary relief valve lifted. This resulted in a minor radioactive release to atmosphere, mainly of krypton and xenon.

The plant was subsequently cooled down, first by using the undamaged steam generator to remove the residual heat and then, after about 24 h, by the low-pressure residual heat removal system.

Subsequent inspection of the damaged steam generator showed that a loose pie-shaped metal object, weighing about 2 lb, was present in the steam gener­ator. This object had vibrated and severely damaged a number of steam gener­ator tubes, causing one of them to rupture and leading to the events described above. The object appears to have been present in the steam generator for a number of years, having been introduced inadvertently during earlier mainte­nance work. Flow through the damaged tubes was blocked by plugging them, and the unit has been returned to power.

Unlike the accident at Three Mile Island, the operator response at Ginna was good, although somewhat delayed compared with the operating guidelines for this type of incident. Although the Ginna incident has received the most pub­licity, it is noteworthy that steam generator tube ruptures had occurred previ­ously, one example being an incident in P’^T. Unit No. 2 at Prairie Island, Oregon, on October 2, 1979.

If it has been decided to reprocess spent fuel with the objective of recovering valuable uranium and plutonium, the fuel must first be transported to a repro­cessing plant using the flasks described in the previous section. The stages that the fuel then goes through in the separation process are illustrated schemati­cally in Figure 7.10. First, the flask is taken off the vehicle, the spent fuel is re­moved under water, and the flask is decontaminated and returned to the power station for further use. The fuel is loaded into a storage rack under water until it is ready to be fed into the reprocessing plant.

In a modern reprocessing plant like THORP (Thermal Oxide Reprocessing Rant) operated by British Nuclear Fuels at Sellafield, the actual separation process is undertaken after at least 5 years’ storage of the spent fuel in the ponds. The fuel element is first stripped of as much of its extraneous metal structure (grids, support plates, etc.) as possible. These remnants are stored separately and treated as intermediate-level waste (see Chapter 8). The fuel pins themselves are sheared into small lengths between 1 and 4 in.; these sheared fuel pieces fall down a chute into a perforated basket (see Figure 7.10). This basket is then transferred to the dissolver. The shear needs to be of modular construction to allow replacement of the blade and for maintenance.

In the dissolver the fuel is dissolved in hot (90°C) 7 M nitric acid. Dissolution of the fuel takes place quickly and can be controlled by the rate of shearing. The cladding pieces, or “hulls,” are withdrawn in the basket and again sent for disposal as intermediate-level radioactive waste. Various types of dissolver, both batch and continuous, have been developed. As the fuel dissolves, fission gases are released: the inert gases krypton and xenon and other volatiles such as io­dine and carbon dioxide as well as oxides of nitrogen and steam. The dissolver off-gas systems must be able to cope with this mixture. The system recovers as much of the nitrogen oxides as possible as nitric acid.

The fuel solution itself still contains some undissolved particulates, both from the cladding and from fission products. The solution is therefore clarified using a centrifuge. The clarified nitric acid solution containing the fission products, the uranium, and the plutonium is next passed through the chemical separation plant. This involves a solvent extraction system.

Solvent extraction is a process that allows separation of dissolved materials. Suppose we have two liquids that do not mix, such as oil and water. If we have a solution of two substances, A and B, in one of the liquids, and component B is soluble in the other liquid but component A is not, then we may solvent-ex­tract component B from the original mixed solution of A and B by essentially shaking up (“contacting”) the solution with an immiscible liquid in which only B is soluble. By then removing component B from the-‘ resultant solution. w,.-

have achieved a separation of A and B. Various types of equipment are used in chemical engineering for this process, and it is beyond the scope of this book to go into them in detail. Probably the most commonly used devices in repro­cessing plants use mechanical stirrers to mix the two liquids, followed by set­tling tanks that allow their separation, with each of the liquids containing the respective components. These are called mixer settlers. Alternatively, vertical pipes containing perforated metal plates may be used, with one fluid flowing up the pipe and the other flowing down it. To promote mixing of the fluids, such columns are subjected to pulses, and they are often referred to as pulsed columns. A typical pulsed column is shown in Figure 7.11. The first objective of solvent extraction in the reprocessing plant is the separation of the valuable uranium-plutonium mixture from the nitric acid solution, which also contains the fission products. This is done by contacting the nitric acid fuel solution with an organic solvent, typically tributyl phosphate (TBP) diluted with odorless kerosene (OK). In a typical extraction plant, all but about 0.1% of the uranium and plutonium in the fuel solution is removed into the TBP phase.

Separation of the uranium from the plutonium is also achieved by solvent extraction. The first step is to redissolve the mixture in a clean acid stream and then add a substance to the stream to change the condition of the plutonium and render it insoluble in TBP. Thus, when the new acid stream is contacted again with the TBP, the plutonium remains in the acid stream while the uranium passes into the TBP. The success of the extraction process is largely dependent on the efficiency of the transfer from the aqueous phase and vice versa. In gen­eral, the uranium-plutonium will dissolve preferentially in the TBP when the aqueous phase has a high nitric acid content and will dissolve preferentially in the aqueous phase when it has a low nitric acid content. Thus, the final stage of the extraction is to take the uranium from the TBP stream by contacting the stream again with an aqueous phase having a low concentration of nitric acid.

The output of the separation stages in the reprocessing plant consists of streams of uranium, plutonium, and fission products dissolved in nitric acid. Each of these streams may be concentrated by evaporation and subsequently purified, if necessaiy, by additional solvent extraction stages. The uranium and plutonium are precipitated as uranium and plutonium nitrates, which are then heated to convert them into oxides, which may then be reused in the prepara­tion of nuclear fuel. The fission product stream is usually concentrated by evap­oration and passed to storage tanks for long-term storage and ultimate conversion into a solid form; we shall discuss this process in Chapter 8.

Once the uranium and plutonium have been extracted, the decay heat gen­eration is almost totally associated with the fission product stream in the repro­cessing plant. Any heat transferred to the solvent phase, together with the intense radiation, tends to degrade the solvent and cause difficulties in the op­eration of the plant.

The thermal and radiation problems in reprocessing plants are obviously fewer the longer the fuel has been stored in the cooling ponds prior to repro­cessing. It is for this reason that for thermal reactor systems the storage period is 5 years or more. However, this is not possible for fast reactors, where the eco­nomics of the fuel cycle dictates a fast turnaround in reprocessing. Much more fissile material is contained in fast reactor fuel than in thermal reactor fuel, and failure to utilize this valuable capital resource results in a considerable eco­nomic penalty. Furthermore, the rate at which fast reactors can be built is lim­ited because of the very much larger total inventory of valuable fissile material associated with each reactor.

Therefore, fast reactors present greater difficulties for reprocessing than do thermal reactors. They already have a higher specific heat generation rate, as seen in Figure 7.7, and their spent fuel must be reprocessed on a much shorter time scale, typically 6-9 months after removal from the reactor. The very high concentration of fissile materials in the streams presents a further difficulty. In the design of a reprocessing plant for both thermal and fast reactor fuel, one must take into account the possibility of developing a nuclear reaction (critical­ity) within the plant. This can be prevented in many cases by designing the plant so that the geometry of the pipes containing the solutions of fissile mate­rial is so unfavorable to the nuclear reaction that the plant can be regarded as “ever-safe.” This is particularly important in the reprocessing of fast reactor fuels where the concentrations of fissile material are high and the throughputs are small. Such plants are successful when proper attention is given to the design details; an example is the U. K. Atomic Energy Authority’s fast reactor fuel re­processing plant at Dounreay in Scotland, which is illustrated schematically in Figure 7.12.

REFERENCES

Jenkins, G. E.C., Lee, M. D., and N. Wall 0995). “Improved Refueling of Advanced Gas- Cooled Reactors.” Nuclear Europe Worldscan 15 (March-April): 44.

Nuclear Fuel Reprocessing Technology 0985), published by British Nuclear Fuels pic, Information Services, Risley, Warrington, U. K.

Fi^we 7.12: Reprocessing plant for the U. K. prototype fast reactor :it Doirnreav. Scot!.;’

Fuel Reprocessing Services 0986), published by British Nuclear Fuels pic, Information Services, Risley, Warrington, U. K.

Fuel Handling and Site Ion Exchange Effluent Plant (1985), published by British Nu­clear Fuels pic, Information Services, Risley, Warrington, U. K.

The extent to which one form of energy can be converted into another is limited by practical considerations. The fraction converted in a given process is often re­ferred to as the efficiency of the process. Thus, in converting x units of energy in form A to y units in form B, the percentage efficiency is defined as 100y/x. The energy not converted to form B (i. e., x — y units) may remain in form A or may find its way into other forms (C, D, etc.) as a result of the process.

An example of energy conversion leading to power generation is hydroelec­tric power generation. The potential energy of the water in a mountain reservoir or lake is first converted into kinetic energy of a turbine, which in turn is converted into electrical energy by means of a generator. All of these energy conversion processes are quite efficient; with good design they might even approach 100% efficiency. The energy not converted to electrical energy in this process is mainly dissipated by increasing the thermal energy of the water leaving the power station.

Another common example of energy conversion is that of converting the chemical of fossil fuels (e. g., coal or oil) into electrical ^energy through the

medium of a conventional power station. "Tils case is ilustrated in Figure 1.2. Suppose that we start with 1W GJ* of chemical energy in the form of coal. ^uls energy is released at a high temperature (typically 2000°C). Some of the energy (typically 10 GJ) leaves the power station as thermal energy in the flue gases going up the stack. However, most is transferred by thermal radiation and con-

•One gigajoule of energy would be sufcient to power a 1 00-watt light bulb for 116 days (nearly 4 months).

Fi^are 1.2: Energy conversion in a power station.

vection to the water in the boiler tubes, converting this water into high-pressure steam at perhaps 500°C. This steam is passed into a turbine, where some of the thermal energy is converted into electrical energy (typically 35 GJ), and the rest of the original energy (55 GJ) is rejected as thermal energy into lukewarm cool­ing water at 25-40°C.

Thus, only about one-third of the original chemical energy in the coal has ac­tually been converted into a useful alternative form, namely, electrical energy. The efficiency achievable in the conversion of thermal energy (the intermediate form of energy in the process described here) into electrical energy is deter­mined by the temperature range over which the process operates. If we were able to reject the heat at a temperature close to absolute zero, the residual ther­mal energy would be negligible. However, we are forced to reject the energy at a temperature slightly above that of our normal surroundings, at which temper­ature a very large amount of the thermal energy still remains. Thus, if we lived on a planet where the ambient conditions were close to absolute zero, our en­ergy conversion efficiencies could be made much higher, though there would be some other difficulties. This basic limitation on the conversion of thermal en­ergy into other useful forms is fundamental to thermodynamics.

We may make better use of the chemical energy used in power generation if we can use the thermal energy leaving the station directly, for example, for domestic or industrial heating. However, this heat is not very useful at the luke­warm temperatures of the cooling water. A combined heat and power (CHP) station rejects heat at a higher and more useful temperature (100°C, say), but, for the reasons explained above, this leads to some reduction in the electrical output of the station. This trade-off between heat and power generation can sometimes be economic, particularly where there is a large demand for heat. Thus, CHP stations have found extensive application for power generation and district heating in the Scandinavian countries and Russia.

A device for converting thermal energy into another form of energy (kinetic, potential, electrical, etc.) is referred to as a heat engine. A typical heat engine would be the turbine of a power station. Other examples are the jet engine of an airplane and the internal combustion engine of an automobile. All these de­vices take thermal energy generated at a temperature 7j, carry out some form of energy conversion, and reject the residual thermal energy at a lower tempera­ture, TY Here, Tv and ‘Fz designate temperatures on the absolute (kelvin) scale of temperature. The maximum efficiency 11 obtainable from any heat engine is given by an equation first derived by Carnot in 1824:

This equation shows that if r; is zero on the absolute scale, the efficiency can theoretically approach unity (i. e., 100%). However, in practice it is necessary to reject the heat at a temperature somewhat above normal ambient temperature (e. g., 300 K or 27°C). Thus, the maximum efficiency is likely to be around 50—60% in a common heat engine, with practical efficiencies being lower than this because of departures from ideal behavior.

Perhaps a majority of nuclear reactors used for research are of the pool type, often referred to as “swimming pool” reactors. The core is immersed in a pool of

light or heavy water, and heat exchangers are placed outside the reactor vessel to extract the heat. This principle of reactor design can generally be applied only when the primary coolant is an unpressurized liquid, which is the case only for the liquid metal-cooled fast reactor (see Figure 2.15 for an illustration of the cir­cuit). Examples of reactors with this type of coolant circuit are the British proto­type fast reactor (PFR) and the French Phenix reactor. However, it is also possible to design sodium-cooled fast reactors with loop-type circuits. Examples of such reactors are the Japanese sodium-cooled fast reactors JOYO and MONJU.

In the latter designs, the primary circuit pump and the intermediate heat ex­changers are external to the vessel containing the reactor core, as illustrated in Figure 3.8. Thus, in these designs the sodium is pumped from the reactor ves­sel through pipes connecting it to the heat exchanger.

The advantages of the pool-type design are that there are no external pipes, which reduces the risk of pipe ruptures, and there are no connections to the tank containing the coolant pool below the liquid level, as illustrated in Figure 3.9. Moreover, in pool-type reactors, the large quantity of sodium in contact with the core can act as a heat sink in case of circulation failure. In fact, with a well-designed sodium-cooled fast reactor of this type, it is possible to ensure decay heat removal by natural circulation alone, and we shall return to this point in Chapter 4. The pool design, however, has the disadvantage that the main core structures are submerged under many thousands of tons of active sodium and are difficult to get at (to monitor their structural integrity) and to

maintain. Access and maintenance are much easier in the loop-type reactor, but the existence of external pipework introduces the possible hazards of a loss-of- coolant accident.

1 Decay heat removal using PORVs

Example: Following the TMI accident, a utility was considering the possibility of in­creasing the number of PORVs in its 4000-MW(t) PWR system to allow release (in the form of steam) of the full decay energy at 100 s from shutdown. Assuming a flow area for each valve of 0.002 m2, how many valves would be required?

Solution: After 100 s, the decay heat rate may he estimated from Table 2.2 and is

3.2 X 4000 I 100 = 128 MW

The flow area required can be estimated assuming a release rate of 17,000 MW/rn2 (see Section 4.3.2).

128

Thus Flow area =——— = 0.0075 m2

17,000

and four PORVs would be required.

Problems: A 3000-MW(t) PWR has two PORVs, each with a flow area of 0.0015 m2.

Would these valves be sufficient to allow release of decay energy from the reactor ves­
sel in the form of steam, and consequent maintenance of fuel cooling by “feed-and — bleed" operation, at 1 h from shutdown?

2 Evaporation ojcoolant

Example: Following a small-break loss-of-coolant accident, the fuel of a 3800-MW(t)

P’^TC has become uncovered and the top half of the fuel is dry. What is the rate at which the core is becoming uncovered at 1 h after shutdown, assuming a mean void fraction in the wetted region of 0.5? Also assume that the fuel occupies 40% of the core volume, that the core diameter is 3.6 m, and the core length 4 m, and that the heat flux is uniform in the core. The system pressure during the uncovery period was 85 bars. Solution: The volume of water per meter length of the core in the wetted region is given by

Cross-sectional area of corex ( 1 — void fraction)
x(l — fractional area occupied by fuel)
= | 2Lx 3.6x 3.6 X (1-0.5) x (1-0.4) = 3.054m3/m

The heat release rate to water from the submerged half of the fuel at 1 h from shut­down is given (using Table 2.2) by

1 4

x—= 2.66 X107 W 1QQ

Evaporation rate of water

heat release rate

latent heat of evaporation of water at 85 bars 266 x!07 W

1.40 x 106 J/kg

It is now necessary to iterate to ensure consistency with only half of the core being un­covered in 1 h.

Problem: For the reactor core described in the example, the heat flux would not in
practice be uniformly distributed. Rather the flux profile along the core length follows a law that would typically be of the following form:

1t(z + a)
L + 2a

where q is the local heat flux, if. av the average heat flux, z is the distance from the bot­tom of the core, L is the core length, and a is a constant. F is a form factor (ratio of peak to average heat flux). Assuming F = 1.4 and a = 0.3, calculate the total time re­quired to totally uncover the core described in the example. Assume a constant heat input equivalent to that occurring 1 h after shutdown, that the core is initially just filled with a steam mixture water with 50% void fraction, and that the void fraction remains constant during the uncovery. Also, plot the movement with time of the mixture level.

3 Fuel blockage in a fast reactor

Example: Calculate the location and magnitude of the peak dad temperature in the peak rated channel of a fast reactor under normal flow conditions. Would a blockage leading to a 50% reduction in flow lead to the fuel elements exceeding the creep limit of 670°C, above which ballooning of the cans would occur? In the calculations, assume a 3300-MW(t) reactor having hexagonal fuel assemblies, which each have 325 fuel pins 5.84 ^m in diameter with the distance across the faces of the hexagon being 135 ^m. The normal mass rate of flow through each subassembly Щ) is 39kg/s, and the core length is I m. Liquid sodium enters the core region at 370°C. In the core region the peak fuel rating in the highest-rated fuel assembly is 44 kW/m’ and (for the purposes of this present calculation*"’), assume that the local rating r is given by

..

r = rmax sin — = 44 sin — max L L

where z is the distance from the beginning of the core and L is the core length. Assume a heat transfer coefficient x between the fuel and the sodium of 55,000 W/m2 K at the full flow conditions and 32,000 W/m2 K at 50% flow. Assume that the sodium has a specific heat capacity (c) of 1275 J/kg K.

Solution: The total heat generation rate (QJ in this assembly is:

• The difference between this value and the value of 27 k W/m given in Table 2.3 is that the figure in the table was an average rating including those parts of the fuel in the blanket and outer core regions.

••Note: The equation for flux profile implies that the flux goes to zero at the bottom and top of the core. This simplifies the calculation, but the actual profile would go to a finite rating at the extremities of the

ГПГР ЯПГІ indpprl rhprp i<.: finitP opnprsrinn nf hp-:.it in thp hlon’L-pr rpoinn -.1 ant] hplnu. r thp rnrp

The temperature rise Д across the element under full flow conditions is thus

and for this condition

325. 1

—— sin — =—— cos —

Mcp L Da L

= tan"1 (-0.4763)

= 0.8585 m

At z = 0.8585 m, the maximum pin surface temperature for normal flow conditions is given by

= 370 + 1-cos

Mep1t ^ L J

rxL

+ max sin —

7tDa L

= 370 + 325 x 44,°0° X 1 a + 0.9028)

39 x 1275x

______ 44, 000 X 1_____

X 5.84 X 10-3 x 5.5 x 10^

= 370 + 174.2 + 18.7 = 562.9

Thus, the peak clad temperature is normally well below the creep limit of 670°C. For a f1ow reduction of 50%, the peak clad temperature occurs at a distance z from the inlet given by

The clad temperature at this position is given by

325rZ

rL

+ —^ sin 1tDa L

325 x 44,000 X 1
39x 1275x

= 370 + 352.6 + 28.4 = 751.0°C

Thus, a flow blockage leading to a 50% reduction in flow would lead to the peak clad temperature in excess of the creep limit of 670°C and would be unacceptable. Problem: If, for the fast reactor described in the example above, the flow reduction due to blockage was even greater than 50%, boiling of the sodium would ultimately begin at the fin surfaces. The boiling point of sodium would be required to initiate boiling; calculate the flow reduction that would be required to cause boiling to start on the peak-rated fuel assembly. Also calculate the position on the fuel assembly at which such boiling would be initiated.

6

Faster fusion reactions are possible with a range of mixtures involving the iso­topes of hydrogen, helium, and lithium. These include:

2D + 2D ^2He + n + 0.96×10-B J 2D + 2D ^2T + ’H + l.19xi0-15 J 2D + 5D ^ ‘He +n + 5.2x 10_11 J

Most research effort is being directed at the last of the reactions because it is the least difficult reaction to achieve (Figure 9.1 ).

Most (80%) of the energy released is in the form ofkinetic energy of the neu­tron. Note that though the energy released per fusion reaction is typically 10 times less than for a single fission reaction, the neutrons are released with per­haps 5 times as much energy.

Deuterium, as we saw in Chapter 3, occurs in ordinary water at a concentra­tion of 0.016%) and can be readily separated by chemical processes. Tritium

does not occur naturally but can be produced from lithium by bombardment with a neutron. Thus:

6 Li +n ^ *He + ‘T + 7.7 x lO’13 J
’Li + n ^ ‘He + T + n — 4.0 x 10~u J

As we shall see later, it is possible to arrange the system so that the neutrons from the fusion reaction are used to breed more tritium from these reactions. This is done in a blanket in a manner similar to that used in a fast fission reactor. The power generated in such a fuel cycle for each gram of lithium is 36 million joules (10,000 kWh).

It is interesting to compare the energy available from these isotopes with, say, the figures given in Table 1.2. There, we saw that the world’s readily avail­able uranium resources, utilized in fast reactors, could release around 1023 J and using the uranium in the ocean could increase this figure to around 1026 J. These figures compare with the current world electrical consumption of 1.8 x 1 0iy J/year. In fusion reactions the deuterium in the oceans could release around 3 x 1031 J, while the land-based lithium reserves could yield around 1028 J, and including the lithium in the oceans would raise the figure to 2 x 102H J. Thus, the fuel resource with fusion reactions can be considered limitless, cer­tainly beyond a million years.

Let us therefore turn our attention to how we might tap into this immense source of energy. The fusion reaction is difficult to achieve because the deuterium and tritium nuclei are each positively charged electrically. Like charges repel each other and this force can be overcome only if the nuclei approach each other with sufficient velocity—millions of kilometers an hour—to overcome the mutual re­pulsion. That means heating up the gaseous deuterium-tritium mixture to a tem­perature around 100 million degrees or more. At a temperature of a few thousand degrees the gas becomes ionized; that is, the electrons separate from the atoms and the separate electrons and nuclei move randomly (Figure 9.2). Such a mater-

ial is known as a plasma Plasmas exist in the sun and stars and also in such everyday items as neon signs and electric arcs.

It is not enough to heat the plasma to the required temperature. It is also nec­essary to hold the plasma at that temperature for sufficient time for the reaction to take place. Clearly, the length of time will depend on the number of nuclei in a given volume of plasma. The required conditions have been identified in the Lawson criterion, which states that the product of the time for which the plasma is confined ‘tr and the density of the plasma (n) must be greater than 102° s/m3

n x X > 1020 s/m2

Thus, if the density of the plasma is 102° nuclei per cubic meter, the plasma must be held at 100-200 million degrees for 1 s.

9.2 CONFINEMENT

How are we to “confine” the plasma long enough so that it does not touch (and melt) the walls of the vessel in which the reaction is to take place? In the Sun and stars the fusion plasma is held together by large gravitational forces. On Earth we obviously cannot use such forces to contain a plasma in any convenient-sized ap­paratus. Two ways have been tried to provide this confinement of the plasma.

1. Magnetic confinement. Since plasmas are excellent conductors of electricity, they can be acted on by magnetic fields (Figure 9.3). Thus, magnetic fields can be used to shape and confine the plasma in such a manner that it does not touch the walls of the vessel in which the gaseous mixture is held. If the plasma did come into contact with the vessel walls, it would quench, losing its energy and high temperature very rapidly.

2.

Inertial confinement. The alternative to magnetic confinement is to contain the isotopic mixture frozen solid at about 15 K as a small spherical pellet or

bead (Figure 9.4). This spherical pellet is then bombarded from eveiy direc­tion by beams of high-powered lasers, which compress and heat the mixture to fusion temperatures. Inertia holds it together long enough—perhaps a nanosecond (10-9s) for the fusion reaction to take place. This time can be so short because of the very high densities achieved.

Considerable research is being done on the inertial confinement process at the Lawrence Livermore Laboratoiy at the University of Rochester, New York and at the Los Alamos Laboratory, New Mexico. There are, however, funda­mental difficulties with this route to a practical system. These are the low effi­ciency of the laser (1-2%), the low fraction of fusion energy released to date (-0.01%), and the difficulties of engineering a device to produce a continuous power output involving ignition of a stream of frozen pellets at a high rate.

Most effort is therefore being devoted to trying to achieve a fusion reaction using magnetic confinement. The sticture of magnetic fields is often indicated by lines of force or field lines’, the stronger the field, the greater the density of the lines. Within a magnetic field, charged nuclei take a spiral path in the direction of the field lines as illustrated in Figure 9.5a. A magnetic field line causes a charged nucleus to spiral around it (Figure 9.5a). If the field is ananged so as to close on itself in a circle within a circular chamber (Figure 9.5b), the particles will spiral around the field and remain trapped within the circular chamber, or toms. Unfortunately, this does not always happen in practice due to instabilities that occur in the plasma. Nevertheless,

Г^І The sudden inwards movement compoeases and heats the D & T mixture up to conditions for fusion to take place

Figure 9.5: (a) Particle spiraling around a magnetic field line. ( {J) A closed toroidal system. ( cl A magnetic mirror or bottle.

most ofthe experiments that have tried to achieve controlled ft sion reactions make use of this closed doughnut-shape configuration. Another possibility is to constrict the magnetic field lines at each end of a tube. Particles trying to escape by spiraling along the field lines are reflected back into the central region. This arrangement is called a magnetic mirror or bottle (Figure 9.5c).

The boiling-water reactor (BWR) differs from the PWR in that it generates steam directly within the core and does not have a separate steam generator. The sys­tem is illustrated in Figure 2.10a Water at a pressure of about 70 bars (1000 psia) is passed through the core, and about 10% of it is converted to steam. The steam is then separated in the region above the core, the water being returned to the bottom of the core via the circulation pump and the steam passing from the top of the vessel to the steam turbine. The steam from the turbine is passed through a condenser, and the condensate is returned to the reactor vessel as
shown in Figure 2.1 Oa. The core power densities in a B’^TC. are about half those in a P"^R (though still much higher than those in gas reactors). The fuel ele­ments consist of 12-ft-long bundles of Zircaloy-canned U02 pellet fuel with an enrichment similar to that in P"^R. Each bundle of fuel is contained within a square channel constructed of Zircaloy, as illustrated in Figure 2.10 b.

The advantage of the B’^TC. is the elimination of the steam generator, which has been one of the most troublesome features of the P"^R. However, in the P"^R the coolant passing through the reactor is contained within the reactor/steam generator/circulator circuit. In the B’^TC. the coolant also passes

through the steam turbine and the condenser. Corrosion products and in-leak­age from the turbine and condenser are passed to the reactor, where they may be activated by the reactor neutrons to produce radioactive isotopes, which cir­culate around the system. Also entering the coolant stream are small amounts of radioactive substances leaking from damaged fuel elements, including the rare gases xenon and krypton. These find their way into the inert gas removal sys­tem in the condenser. Thus, the reactor must be operated with many of the ex­ternal components maintained under radioactive conditions, which is not the case with the P^WR Consequently, B^WRs give somewhat higher (though care­fully limited) radiation doses to their operators. Another problem with existing B^WRs has been cracking of the stainless steel pipework due to corrosion under the highly stressed conditions. This is similar to the steam generator problems in P^WRs in that it can be cured by using a different design approach (i. e., using stress corrosion-resistant material), but many existing plants will continue to be susceptible to it.

The analysis of B’^WR must also consider the full range of break sizes. Peak clad temperatures tend to be highest in the design base accident (i. e., full pipe rup­ture) described above. Peak clad temperature increases with break size in the

Figue 4.31: Steam binding in a B’^TC during a hypothetical LOCA event.

range (}-100 cm2 and then falls with break size before rising again, reaching the value for 100 cm2 again at around 1000 cm2 and subsequently rising again con­tinuously with break size up to the maximum possible size, i. e., full pipe rupture.

The sequence of events outlined in Section 6.2 applies to a PWR; the situation with regard to other reactor types can he summarized as follows:

Boiling-Water Reactor (B^R). The situation is veiy similar to that in the P^^ regarding sequences of core meltdown, fuel-water interaction, and ulti­mate disposition of the molten fuel pool.

CANDU. The melting sequence is not considered to be very likely because of the large pool of moderator heavy water through which the individual fuel channels pass. Analysis of the heat transfer events following a loss-of-coolant accident and failure of the emergency core cooling system has indicated that significant fuel melting would not occur and provided the means of extracting heat from the moderator were still intact, the accident would be controlled. However, should a single-pressure tube fail and the moderator become pres­surized as a result of the release of high-pressure steam into it, the moderator could be expelled and its cooling effectiveness for the other channels removed. That this is at least a remote possibility is indicated by the accident at Lucens, described in Chapter 5. If the moderator was expelled, fuel melting would pro­ceed in the same way as for the other water reactors; again, this event could be contained provided there were no steam explosions or other events that dis­rupted the containment.

Magnox Reactor. The inherent basic safety features of the Magnox reactor (the fact that the graphite itself may absorb a great deal of heat and that decay heat removal can be maintained even if the reactor is depressurized) have led to the view that a full core meltdown is not credible. However, some studies have been done on the effects of meltdown of single channels, specifically those with the highest rating. That such single-channel events are credible is borne out by the accidents in this type of reactor discussed in Chapter 5. In the Magnox reactor systems, such events can lead to small releases of activity since the reactors do not have the hermetic containment that is provided for water re­actors.

Advanced Gas-Cooled Reactors (AGRs). Full meltdown accidents are not considered credible for this type of reactor for much the same reasons as men­tioned above for the Magnox reactors. Furthermore, with AGRs, much higher fuel temperatures can be sustained before fuel damage since the fuel is in the oxide form and clad in stainless steel (in a Magnox reactor the fuel is in the form of uranium metal clad in magnesium alloy). Tests in the Windscale proto­type AGR showed that the fuel temperature can approach to within 50°C of the melting point of steel without clad meltdown and significant fuel damage. How­ever, single-channel fuel melting due to local blockage effects, or due to the dropping of a fuel stringer during the refueling operation, is still considered possible and is taken account of in the design. As explained in Chapter 4, the rise of temperature following a loss-of-coolant accident in an AGR is very slow indeed compared with that in a P’^TC or a B’^TC. This means that there is time to take alternative actions, even if off-site power is lost and the local power sup­plies feeding the emergency circulators fail to operate immediately. It is inter­esting to compare the situations in an AGR and P’^TC; in the AGR the consequences of a fuel meltdown would be more serious since it does not have hermetic containment; on the other hand, the probability of a meltdown is even smaller than in the case of the P’^TC.

Liquid Metal-Cooled Fast Reactors. The very high fuel ratings in fast reac­tors have led to much interest in the possibility of core meltdown and its con­sequences. One accident scenario is that of failure of all the primary sodium coolant pumps and complete failure of the reactor shutdown system. As the sodium reaches its boiling point in the channels of maximum rating, sodium boiling and voiding occur, and this has a net positive reactivity effect on the re­actor, which accelerates the heating. Melting of the fuel and cladding occurs in about one second after sodium voids are formed in a particular fuel assembly. In the area of that assembly there is a complex mixture of liquid fuel, sodium vapor, liquid steel, fuel fragments, fission gas, and steel vapor. If the fuel chan­nel walls melt, adjacent channels may also be damaged and melted.

Calculations of the consequences of these events are highly complex be­cause of the coupling between the nuclear reactions, the heat transfer processes, and the fluid flow processes. Two different outcomes are possible, depending on such things as the reactor design and reactor state at the begin­ning of the accident:

1. If, during the meltdown, a large fraction of the original fuel has managed to remain within the active core region, an extremely large increase in reactiv­ity occurs and the fuel is actually blown apart and dispersed by the fission product gases in the interstices of the fuel pellets. The dispersal of the fuel terminates the nuclear reaction, though the resultant shock wave may dam­age the reactor structure and breach the containment.

2. If the fuel inventory has been reduced to about half the original amount by gradual leakage, or if large quantities of blanket materials have diluted the fuel, a severe power excursion will not occur. The molten fuel will fall ro the bottom of the reactor and the sequence of events will be similar to that de­scribed above for the P’^TC, including the possibility of a vapor explosion due to interaction between the molten fuel and the liquid sodium still in the vessel. The possibility of this form of accident has drawn great attention to the reliability of shutdown systems in fast reactors; one possible design ap­proach is to arrange the core structures so that an excessive increase in core temperature causing its thermal expansion will trigger an automatic shut­down of the reactor. Combined with the fact that the decay heat can be re­moved by natural circulation to air-cooled heat exchangers and the enormous heat capacity of the sodium coolant, this inherent shutdown sys­tem would give the fast reactor system a “walkaway" safety capability that is not available in other reactors, which depend on the operation of active sys­tems demanding operator actions and/or totally reliable power supplies.

Clearly the attention given to core meltdown accidents varies from reactor to re­actor and depends on the assigned credibility for such accidents. In general, the objective is to bring down the likelihood of an accident and in particular its public consequences to a minimal level.