10.100. Operation and maintenance charges include the payroll for the plant, clerical, engineering, and administrative staffs, and the costs of main­tenance materials and supplies, including chemicals for the treatment of reactor and condenser water and radioactive wastes produced in the reactor installation. In the same category are the costs of such miscellaneous items as liability insurance, public relations, training of new workers, travel, etc. In general, however, operation and maintenance costs contribute a rela­tively small proportion to the overall energy costs.

11.93. The basic objective of the reactor radwaste system is to reduce the radioactivity in liquid and gaseous wastes to such levels that they can be safely discharged to the environment. The general procedures used for this purpose are natural decay and decontamination, either by evaporation or by demineralization. Natural decay is commonly used to decrease the activity of short-lived gaseous radionuclides, such as nitrogen-16 and sev­eral isotopes of krypton and xenon. Gaseous wastes are thus held up for a period of time, from 30 minutes to several days, before discharge.

11.94. Liquid wastes contain such a wide range of fission (and other) products that natural decay is of minor consequence. These wastes are therefore treated by a decontamination process. The aqueous waste so­lution may be evaporated and the vapor condensed. The condensate is essentially pure water which can be reused in the plant or discharged. In the alternative demineralization process, dissolved radioactive substances are extracted by passage through an ion-exchange resin. The evaporator residues and spent resins contain the removed radioactive material and are disposed of in a safe manner.

11.95. The choice between evaporation and demineralization depends on circumstances and may vary from one plant to another. The decontam­ination factor, i. e., the ratio of the activity concentration before to that after treatment, is 103 to 104 for evaporation but is only 10 to 102 for demineralization. On the other hand, installation and operation is less expensive for a demineralizer. If the liquid waste contains significant amounts of dissolved material (other than fission products), decontamination by evaporation is preferred to avoid rapid saturation of the ion-exchange resin.

11.96. Radwaste treatment systems differ to some extent for pressur — ized-water and boiling-water reactors. There also are some variations among reactor systems of the same type fabricated by different vendors. The descriptions that follow are thus intended to indicate the general principles of operation of radwaste systems.

Introduction

12.104. The designations source term or fission product source terms refer to the amount and type of radioactive materials which would be available for escape to the environment from a reactor plant that has undergone a severe accident. Source term studies consider various accident sequences as described above and the chemical and physical processes that affect the transport of radionuclides from the point of origin, such as a damaged fuel element, to the environment. Probability considerations and the behavior of the radionuclides once they reach the environment are normally considered beyond the scope of source term studies.

12.105. Consideration of the fission product nuclides and their behavior during an accident release is a logical starting point in our study of accident consequences. However, space limitations prevent a detailed step-by-step discussion of the various processes that contribute to fission product trans­port during typical severe accident scenarios.

8.40. In addition to archival journals, some other literature sources are of particular interest to nuclear engineers.

Reports

8.41. It has been customary over the years to publish the results of work sponsored by the U. S. government in the form of both progress reports and final reports. Although some of this work eventually makes its way into the archival journals, the report literature provides a picture of ongoing activities. Various types of reports are also required as part of the reactor licensing process (§12.237). For example, Safety Analysis Reports are an excellent source of information regarding power reactor systems. The Elec­tric Power Research Institute in Palo Alto, California also maintains a Research Report Center for its sponsored work. The EPRI Journal, a periodical that describes EPRI activities, lists newly issued reports.

9.105. As for normal nonboiling heat transfer, it is possible to describe the heat-transfer rate for a flow-boiling system in terms of a heat-transfer coefficient and a temperature-difference driving force. However, from the reactor core design viewpoint, the boiling heat-transfer coefficient is not of great significance. With boiling present, heat is transferred from the heated (fuel rod) surface to the liquid coolant by several evaporative mech­anisms resulting in vapor-bubble growth but not requiring much of a tem­perature-difference driving force between the surface and the bulk of the fluid. Since the temperature driving force is small compared with that in nonboiling systems, the designer is primarily concerned with fixing speci­fications to allow a sufficient margin based on the critical heat flux limi­tation. Therefore, the following paragraphs devoted to a discussion of the boiling heat-transfer coefficient are intended for background only.

9.106. It is apparent from Fig. 9.13 that log(q/A) is a linear function of log(ts — tSSLi) over a considerable portion of the nucleate boiling range, so that the general expression

J = C{f, — U", (9.37)

where C and n are constants, is applicable to a particular set of conditions. If the difference between the temperature of the heated surface and the saturation temperature of the coolant is represented by Дtb9 equation (9.37) may be written as

2 = C(Atby.

If hb represents the boiling heat-transfer coefficient, it may be defined by

so that

9.107.

For subcooled or local boiling, the relationship

has been found to be applicable, where q/A is in W/m2, p is the pressure in MPa, and Дtb is in kelvin [13]. In the region of a PWR channel prior to the inception of local boiling, the heat-transfer coefficient is predicted using equation (9.35). Since equation (9.38) applies to the local-boiling region, designers often define the initiation of local boiling as the point where the surface temperatures predicted by the two equations become equal.

9.108. Although the heat-transfer coefficient is of little importance in the design of a BWR, it is often desirable to evaluate the surface temper­ature of the fuel elements corresponding to a desired average heat flux. This temperature may be important from the standpoint of corrosion resist­ance, and it may also serve as a reference for estimating the maximum internal temperature within the fuel element. According to equation (9.38), the temperature difference Atb at the surface is proportional to the 0.25 power of the heat flux. The surface temperature itself would thus appear to be relatively insensitive to changes in the flux.

Example 9.7. Determine the surface temperature of the fuel in a re­actor core under subcooled-boiling conditions at a system pressure of 7.2 MPa when the average heat flux is (a) 0.5 MW/m2 and (b) 5 MW/m2. The saturation temperature of water at this pressure is 288°C.

(a) From equation (9.38),

Щ-г (5 X 10T25 = 6.6 К (6.6°C)

The fuel surface temperature is consequently 288 + 6.6 ~ 295°C. (b) For an average heat flux of 5.0 MW/m2,

Ath = (6.6)(10)025 = 12 К (12°C),

so the fuel surface temperature is 288 + 12 = 300°C. (As stated, the surface temperature is not very sensitive to changes in the heat flux; the temperature increases from 295°C to only 300°C for a tenfold increase in heat flux. However, the higher flux may be above the critical heat flux limit.)

10.32. Design flexibility has been the most significant trend as operating experience has accumulated during the post decade and assemblies have been available from several vendors. As the use of lumped burnable poisons has increased, more flexible designs have been developed that do not require separate rods in control cluster positions. For example, absorber material can be fabricated with the fuel, either as a coating or integral with the fuel pellet [6].

10.33. Gadolinia bearing rods, which have been used in BWR assem­blies for some time, are now being used in PWR assemblies. Such use of gadolinia as a solid solution with the U02 pellets permits a variation of absorber concentration as well as a selection of the number and location of absorber rods within the assembly. The capability to shape the power distribution is thereby enhanced. Similar advantages may be obtained by using a thin coating of ZrB2 as a burnable poison on the surface of selected fuel pellets. Boron is somewhat easier than gadolinium to model neutron — ically, although it has the disadvantage of not being combinable with ura­nium oxide. On the other hand, for gadolinium rods, the buildup during exposure of the high neutron capture isotope, gadolinium-157, results in a slightly higher residual poison penalty than for boron-coated rods.

10.34. Increasing the water/fuel ratio in PWR lattice design improves uranium utilization and reduces fuel costs. This could be done by reducing the rod diameter. The resulting slight decrease in the negative moderator temperature coefficient can be compensated for by decreasing the soluble boron and, in turn, increasing the solid absorber in the assembly. Uranium utilization is also improved by using some natural uranium oxide pellets at each end of the fuel rod to serve as an axial blanket. However, some increase in axial power peaking results. Thus, the use of partially enriched axial blankets is another option.

10.35. Hardware improvements are also receiving continued attention. For example, the use of zircaloy-4 instead of Inconel in spacer grids im­proves neutron economy. Assembly components, such as the upper tie plate, have been redesigned to ease the replacement of damaged rods between burnup cycles, and if desirable, to reconstitute (rebuild with some different rods) the assembly. Another significant PWR improvement is the use of debris filters in the assembly bottom nozzles to prevent foreign particles from entering the core. In the past, such foreign material would be trapped in the rod spacer grids and cause vibration-induced wear (fret­ting) of the rods.

Introduction

11.13. In Chapter 6 we considered the biological effects of radiation and exposure limits. However, the environmental impact of a nuclear power plant depends on how the sources of radiation exposure, i. e., the decaying isotopes, are transported to people. Similarly, in considering the long-term storage of radioactive wastes, we must evaluate the probability of some of the stored isotopes migrating from the storage site and leading to harmful exposure.

11.14. By radiation exposure pathways is meant the various ways in which sources of radiation are transported to cause exposure. As indicated in Fig. 11.1, the transport pathways from radioactive effluents can be fairly

complex when the food chain is considered. Should leaking waste con­tainers be the pathway source, the usual concern is transport through groundwater and then to sources of potable water or through the food chain to people. However, the pathway term is usually applied to radio­nuclides from reactor effluents rather than those from waste containers.

12.27. Some of the signals that would cause actuation of the protection system were mentioned in Chapter 5. A more complete listing is given here for water-cooled reactors; unless otherwise indicated, the trip signals apply to both PWRs and BWRs.

1. Rapid increase in the neutron flux during startup, resulting in a too rapid rise in the thermal power

2. High neutron flux during power operation, indicating an overpower above the permissible level

3. Abnormal reactor system temperature or pressure

4. Loss (or decrease) of coolant flow, e. g., from a pump failure

5. High steam flow, e. g., from a break in a steam line

6. Closure of a main steam isolation valve, especially in a BWR (see item

12)

7. Turbine-generator trip, e. g., from a loss of load

8. Loss of power supply for instruments (dc) or for pumps, valves, etc. (ac)

9. High water level in the pressurizer (in a PWR)

10. Low water level in the reactor vessel (in a BWR)

11. Low feedwater flow or low water level in a PWR steam generator

12. High radioactivity in the steam from a BWR

Shutdown Cooling

12.28. Although the reactor shutdown cooling system is not generally regarded as a component of the protection system, shutdown cooling is nevertheless an essential aspect of reactor protection. When a reactor is shut down, either deliberately or in response to a severe transient, the self­sustaining fission chain reaction is terminated but a considerable amount of sensible (or stored) heat is still present in the fuel rods. Furthermore, heat continues to be generated by decay of the fission products and (for a short time) by fissions caused by delayed neutrons. Hence, cooling of the reactor core must be maintained for many days after shutdown. The sensible heat and the delayed fission heat are removed within about half a minute and then only the decay heat determines the cooling requirements. The thermal power from this source is initially about 7 percent of the operating power of the reactor at shutdown, assuming the reactor has been operating for a substantial time. The decay power decreases to about 1.3 percent after an hour, 0.4 percent after a day, and 0.2 percent at the end of a week (see Fig. 2.33).

12.29.If the normal heat removal system is still operative when the reactor is tripped, cooling will, of course, be adequate. Steam, produced in the steam generator of a PWR or in the reactor vessel of a BWR, bypasses the turbine and goes directly to the condenser. The condensate then returns to the steam generator (in a PWR) or to the reactor vessel (in a BWR) in the usual way. When the system temperature and pressure have decreased to a sufficient extent, the cooling function is transferred to the residual — heat removal (or shutdown cooling) system which circulates primary system coolant through the reactor vessel and independent heat exchangers cooled by a separate service water supply system. This service water is obtained from the so-called ultimate heat sink which usually also provides the con­denser cooling water. Since the heat sink is required for safe emergency shutdown of the reactor and subsequent dissipation of the residual heat, the system must be capable of operating for at least 30 days even if the most severe natural phenomenon expected at the plant site should occur.[20]

12.30. In some situations, the reactor would be tripped and isolation valves in the steam supply would close automatically to prevent the escape of possibly radioactive steam to the environment. The normal heat removal and condenser system would then not be available for cooling the fuel. In a PWR, a large condensate tank can provide an auxiliary supply of feed water to the steam generators to permit reactor cooldown for about 8 hours. By this time, the conditions would be suitable for the residual-heat removal system to function. In a BWR, a pressure-relief valve permits controlled release of steam to the pressure-suppression pool where it would be condensed (§12.51). The level of the water in the reactor vessel is then maintained by the reactor core isolation system which is supplied by water from a condensate storage tank. Finally, the residual-heat removal system can be actuated.

12.31. If electric power is lost when the reactor is tripped, so that the pumps cannot operate, overheating of the fuel can be prevented by re­leasing steam from the safety valves. This can be continued as long as feed water is available (from the auxiliary system) to the steam generators in a PWR or to the primary system in a BWR. In the meantime, startup of the emergency (diesel) generators will permit operation of the essential pumps, pending the restoration of offsite power.

12.126. In an explosion, gases are formed so rapidly that the propa­gation front moves with supersonic velocity so that a shock wave is pro­duced. The resulting kinetic energy can be destructive. In severe accidents, two types of explosions are possible. One is a vapor explosion, or so-called steam explosion. The other is a result of a chemical reaction, or combustion, normally of hydrogen produced from zirconium oxidation. If the speed of the combustion wave is subsonic, we have deflagration or burning rather than the supersonic detonation.

12.127. The postulated vapor explosion during a severe accident is a result of the interaction of molten fuel with liquid water coolant. Several steps in this interaction take place, the details of which are important is assessing the load on the containment structure. Since both experimental and theoretical research on mechanisms is ongoing, we can only present some of the principles involved.

12.128. When the molten fuel contacts the water, steam is formed very quickly at the interface that separates the two liquids during a short met­astable period. This period may last from a few milliseconds to a few seconds, after which the film becomes unstable, resulting in very rapid fragmentation of the hot liquid fuel. The greatly increased interface surface area which quickly propagates throughout the molten fuel-water mixture then results in the formation of much more steam at a rate that can produce a detonation-like shock wave. Thus, adequate modeling requires a de­scription of the fuel-coolant mixing, so-called “triggering” when the met­astable condition is disturbed, and the subsequent explosion propagation step [35].

12.129. The role of hydrogen formed from the zirconium-steam re­action during a severe accident is reasonably well understood and is de­scribed by suitable modeling codes. Also, several countermeasures nor­mally prevent explosions in the containment. For example, thermal or catalytic recombiner devices combine the hydrogen and oxygen present so that the hydrogen concentration remains below flammable limits. Another approach is to “inert” the containment by substituting nitrogen for air during normal operation. A number of glow or spark plug ignitors distrib­uted throughout the containment deliberately burn the hydrogen in a con­trolled manner close to the point of formation, thus avoiding an explosion involving a large mass of reactant [36].

9.24. The term conduction refers to the transfer of heat by molecular (and sometimes electronic) interaction without any accompanying mac­roscopic displacement of matter. The flow of heat by conduction is gov­erned by the relationship known as the Fourier equation, i. e.,

«’-4 (9-6)

where q is the rate (per unit time) at which heat is conducted in the x direction through a plane of area A normal to this direction, at a point where the temperature gradient is dtidx.[3] The quantity к, defined by equa­
tion (9.6), is the thermal conductivity. In SI units, q is expressed in J/s (or W), A in m2, and dt/dx in °C/m (or K/m); hence, the units of к are (W/m2)(m/K), usually written in the form W/m • K. In English units, к will be in Btu/(hr)(ft2)(°F/ft).

9.25. The thermal conductivity A: is a physical property of the medium through which the heat conduction occurs. For anisotropic substances, the value of A: is a function of direction; although methods are available for making allowance for such variations, they are ignored in most analytical solutions of conduction problems. The thermal conductivity is also tem­perature dependent and can generally be expressed in a power series; thus,

к = c0 + cxt + c2t2 + • • • ,

which, in many cases, may be approximated to the simple linear form

к = A0(l + at).

Where considerable accuracy is desirable (and possible), allowance must be made for the variation of thermal conductivity with temperature. But very frequently, especially when the temperature range is not great, к is taken to be constant. However, when uranium oxide is used as fuel, as it is in most power reactors, the temperature gradients are quite large, and allowance must be made for the variation of the thermal conductivity with temperature (§9.46). Some values of к of interest in reactor design are given in the Appendix.

9.26. Upon integration of equation (9.6) over the x direction, it is found, for unidirectional heat flow by conduction in a slab of constant cross section, with к independent of temperature, that

q = — kA h ~ *2, (9.7)

Xi — X2

where tx and t2 are the temperatures at two points whose coordinates are

and x2. The result means that the temperature gradient at a point, i. e., dt/dx, in the Fourier equation (9.6) may be replaced by the average gradient over any distance, i. e., by (tx — t2)/(x1 — x2).

9.27. If tx — t2 is replaced by Дt, the temperature difference, and x2 — Xi by L, the length of the heat-flow path, equation (9.7) upon rearrange­ment takes the form

_ At 4 ~ L/kA’

This expression is analogous to Ohm’s law, I = E/R; hence the quantity L/kA is often called the thermal resistance for a slab conductor. The analogy between conduction of heat and electricity is the basis of the thermal circuit concept which is very useful in solving heat-transfer problems. In general, the rate of heat flow q is equivalent to the current /; the temperature difference At is the analogue of the potential difference (or EMF) E; and the thermal resistance replaces the electrical resistance.