11.79. Separation of uranium from the fission products can be accom­plished by volatilization since nearly all of the fluorides of the latter ele­ments vaporize at higher temperatures than uranium hexafluoride. Ura­nium may therefore be recovered from a mixture of fluorides by distillation at a relatively low temperature. If plutonium is present, difficulties arise because of the chemical reactivity of plutonium hexafluroide, but sepa­ration of plutonium from uranium can be accomplished by a more com­plicated volatilization process.

11.80. In reprocessing fast-reactor fuels, the complete removal of fission products may not be necessary since their effect on the neutron economy is much less in a fast-neutron spectrum than it is in a thermal spectrum. In these circumstances pyrochemical (or pyrometallurgical) processes are of interest. Among the procedures which has been proposed are high — temperature chemical methods involving molten salts and molten-metal refining by oxidation and volatilization. None of these processes have yet achieved commercial status and so will not be considered further. However, pyrochemical processes offer advantages over the Purex process from the weapons proliferation viewpoint since there is only partial removal of the fission products.

12.95. As described in previous sections, design basis accidents are used to establish design requirements for plant safety systems. In the event of such an accident, the proper operation of such safety systems would prevent melting of the reactor core. However, as a result of the Three-Mile Island accident in 1979 (§12.179), in which partial core melting occurred, it be­came clear that studies were needed of accident scenarios that would lead to core degradation and the resulting possible transport of released fission products to the environment. The term severe accident has come to des­ignate such an accident for analysis purposes. Such studies are helpful in establishing confidence levels and identifying possible failure modes. An accompanying research program has provided supporting data.

12.96. Severe accident scenarios commonly used evolved from those developed in the Reactor Safety Study (RSS), which is often referred to as WASH-1400 [6]. Since the engineered safety features are provided to prevent fuel degradation, to have a severe accident we must not only have an initial “fault” such as a loss-of-coolant break but an additional failure of one or more of these engineered safety features. We will deal with the three representative sequences for PWRs that are often studied as well as two important BWR sequences. We are including accident sequence sym­bols that originated with the Reactor Safety Study (§12.208) only as a convenience to readers who may be familiar with them.

12.196. Numerous changes have been made to the remaining RBMKs in the former Soviet Union to improve their safety. These include reducing the void reactivity coefficient by adding fixed absorbers to the core, in­creasing the fuel enrichment from 2.0 percent to 2.4 percent, adding 24 fast-acting shutdown rods, and modifying the control rod design. The new core physics characteristics are claimed to make the potential for prompt criticality extraordinarily low for all design-basis accidents [39]. The need for improved management controls, operator training, and discipline was also recognized. Since some of the radiation released in the accident af­fected the food chain in other countries, it became clear that there was a need for better international cooperation in exchanging information, de­veloping standards, and other safety-related matters. The Chernobyl ac­cident provided few technical lessons applicable to U. S. LWRs since their design is so different. Also, many institutional improvements had already been made as a result of the Three Mile Island experience. Emergency response to the Chernobyl accident provides useful data applicable to all reactor operations. In very many ways, the Chernobyl accident provided lessons and experiences that improve nuclear power safety. Unfortunately, it also served to reinforce the fears of nuclear reactors held by many members of the public.

8.23. In engineering design, there is often the desire not only to use the systems concept to develop a feasible solution to a given problem, but

to use various formal methods to find an optimum or best solution. To accomplish this, the various parameters controlling the system are adjusted to yield “behavior” that is best in relation to a prescribed so-called “figure of merit” or design goal.

8.24. Application of various formal optimization approaches to nuclear engineering problems, particularly to those in fuel management, has at­tracted the attention of researchers for many years [3]. However, since most methods require extensive iteration by computer, approximations in modeling the core in fuel reloading problems (§10.40) have been necessary to maintain a practical level of calculation effort. Therefore, the resulting uncertainty in the results has limited commercial interest in applying ex­isting methods. This picture could change as improved core modeling meth­ods are developed utilizing newer computers, particularly those based on parallel processing. Separate from the fuel reloading problem, the optimum design of the total plant to provide energy at minimum cost has been standard practice for many years. In the case of the plant, the number of significant parameters is modest compared with the reload core. Thus, computer modeling of the plant design problem is easily managed.

9.89. Boiling is of importance in nuclear reactor systems both as a means of achieving high heat-transfer rates from fuel to coolant and for generating steam in a heat exchanger. The mechanisms involved are complex and depend upon many factors, including surface conditions. For the prelim­inary treatment of boiling heat transfer from a solid fuel rod, it is convenient to consider a heated surface at temperature ts, immersed in a pool of liquid. Suppose the temperature difference between the heated surface and the liquid saturation temperature, i. e., ts — tSSLt, is steadily increased;[6] the corresponding variation in the heat flux, i. e., q/A, across the surface is then as shown in Fig. 9.13, in which both scales are logarithmic. Although the data in this figure are representative of natural convection boiling from a heated surface in a pool of water at atmospheric pressure and a liquid temperature of 100°C, some of the same general characteristics apply to forced convection boiling and to other pressure and temperature conditions.

9.90. The curve for pool boiling can be divided into a number of regions, in each of which the mechanism of heat transfer is somewhat different from that in the others. Until the heated surface exceeds the saturation temperature by a small amount, heat is transferred by single-phase con­vection; this occurs in region I. The system is heated by slightly superheated liquid rising to the liquid pool surface where evaporation occurs. In region II, vapor bubbles form in crevices on the heated surface; this is the nucleate boiling range in which formation of bubbles occurs upon nuclei, such as solid particles or gas adsorbed on the surface, or gas dissolved in the liquid. Nucleate boiling is a common phenomenon, since it is encountered in standard power-plant steam generators.

9.91. The steep slope of the heat flux curve in region II is a result of the mixing of the liquid caused by the motion of the vapor bubbles. A maximum flux is attained when the bubbles become so dense that they coalesce and form a vapor film over the heated surface. The heat must then pass through the vapor film by a combined mechanism of conduction and radiation, neither of which is particularly effective in this temperature range. Consequently, beyond the maximum, the heat flux decreases ap­preciably despite an increase in temperature. The maximum flux, which is a design limitation, is referred to as the DNB (departure from nucleate boiling) value (§9.98). In region III, the film is unstable, it spreads over a part of the heated surface and then break down. Under these conditions, some areas of the surface exhibit violent nucleate boiling, while film boiling, due to heat transfer, occurs in other areas.

9.92. For sufficiently high values of ts — £sat, as in region IV, the film becomes stable, and the entire heated surface is covered by a thin layer of vapor; boiling is then exclusively of the film type. If attempts are made to attain large heat fluxes with film boiling, as high as those possible with nucleate boiling, for example, the temperature of the heated surface may become so high as to result in damage to the material being heated. This is called a burnout and is, of course, to be avoided. It may also be noted from Fig. 9.13 that if a system undergoing nucleate boiling is operating at conditions near the maximum of the curve, a slight increase in the heat flux will cause a sudden change to film boiling, which could result in burnout.

9.93. Subcooled {or local) boiling occurs when the bulk temperature of the liquid is below saturation but that of the heated surface is above sat-

(Л (Л

uration. Vapor bubbles form at this surface but condense in the cold liquid, so that no net generation of vapor is realized. Very high heat fluxes can be obtained under these conditions; values as large as 4 x 107 W/m2 have been reported in forced-convection heating of water, but 6 x 106 W/m2 appears more realistic if the surface temperatures are to be kept low enough to avoid burnout. When the bulk temperature of the liquid reaches the saturation point, the vapor bubbles no longer collapse and then bulk boiling occurs.

10.18. Should the reactor be initially loaded with a complete core of a single enrichment, the power distribution will be similar to the flux distri­bution shown in the reflected reactor case of Fig. 3.18. This means that the fuel located in the region of high power will “burn” faster than the fuel in regions of lower power. Although the power distribution will tend to “flatten” with time as the fuel in the higher power regions becomes depleted of fissile atoms, the fuel in the lower flux regions will be under­utilized when the core reactivity is reduced to the level requiring shutdown for refueling.

10.19. Furthermore, safety limitations are based on the highest power fuel rod, which normally will be operating at the highest temperature. Thus, if the maximum power of the core is close to the average power, the reactor could be operated at a higher level than would be permissible if the peak-to-average power ratio would be higher. As we will see, the fuel can be better utilized and the reactor operated at a higher power level if reloading is done on a staggered basis. Also, if there is good neutron coupling between fresh fuel and fuel about to be discharged, additional burnup can be obtained, since the older fuel can be used to control reac­tivity. Otherwise, parasitic absorbers would be required.

10.20. Further explanation of staggered refueling may be helpful here. As an example, let us consider a typical PWR core containing 193 fuel assemblies. For our present orientation purposes, assume that the planned fuel burnup is about 2.6 TJ/kg U (or 30,000 MW • d/t), which corresponds to about three calendar years of operation. During annual shutdowns for refueling and plant maintenance, a batch of about 64 assemblies averaging the planned burnup of 2.6 TJ/kg U would be removed from the core and replaced with fresh fuel. We would have remaining in the core two batches, one exposed to 1 year of irradiation, the other to 2 years. The assemblies in these three batches would then be rearranged or “shuffled” in a carefully designed pattern that includes the fresh fuel to provide good neutron cou­pling. After one year of operation, the process is repeated, but the loading pattern may be slightly different to accommodate possible differences in individual assembly burnup histories. We can see that from material bal­ance considerations, the number of batches resident in the core must be equal to the number of burnup periods experienced by a given discharged batch. It should be noted that most present PWRs now operate on 18- or 24-month cycles, with burnup in the range 40,000 to 60,000 MW • d/t.

However, the staggered refueling principles are the same as for the example given here.

10.21. This fuel batch reactivity sharing behavior, which is inherent in staggered reloading, is shown in Fig. 10.2. The batch reactivity, p, is plotted versus burnup. Note that the ordinate is reactivity, defined as the excess of neutron production per neutron produced, not the multiplication factor, к, i. e.,

к — 1

It has been shown that p is a linear function of burnup for LWR fuel for a practical burnup range [4]. When the reference assembly batch is inserted in the core at zero burnup, two previous batches are shown in the figure to be also in the core, with reactivities corresponding to burnups of 10 and 20 GW • d/t, respectively. We see that as a result of reactivity sharing, the oldest batch burnup is extended well into the negative reactivity range. The figure shows an idealized equilibrium loading scheme in which each identical one-third core batch is replaced after a three-operating-cycle burn­up of 30 GW • d/t on a staggered basis.

11.1. During recent years, an assessment of environmental effects has been a necessary part of every major construction activity in the United States. In many cases, the achievement of a balance between the benefits of the activity and the impact on the environment has resulted in contro­versy. Therefore, before considering nuclear power effects, it is helpful to examine what is meant by environmental “contamination” and the effects of fossil-fueled energy sources.

11.2. Although the terms contamination and pollution are synonymous in many dictionaries, there is a distinction from the environmental view­point. By contamination, we merely mean the introduction of a foreign or “unnatural” substance, while pollution is a stronger term describing a level of contamination that is harmful, such as smog from automobile exhaust systems. However, the picture becomes complicated when we consider the introduction of natural substances, which can be harmful. For example, volcanic eruptions have released large quantities of particulate matter and

radioactivity into the atmosphere. Natural springs sometimes contain un­pleasant and harmful sulfur compounds. Natural background radiation levels vary from place to place as a result of the influence of cosmic radiation at higher altitudes and the proximity to minerals such as granite containing radioisotopes. Therefore, one must view the introduction of foreign sub­stances into the environment as undesirable only if harmful effects result compared with the impact of “everyday” natural events.

11.3. Environmental considerations apply to many sectors of our in­dustrialized society, particularly where materials are processed. Effluents from metal smelters, chemical plants, and petroleum refineries must be controlled, for example. The reduction of pollutants from motor vehicles is a continuing challenge. Similarly, energy production is a vital component of this society. Nuclear and fossil fuels are our primary energy resources. Therefore, it is only fair to view the environmental impact of nuclear power plants in comparison with the impact of the other option, fossil-fueled plants.

12.11. In a broad sense, the term quality assurance includes all actions necessary to provide adequate confidence that a component, structure, or system will perform satisfactorily in service. Engineering codes and stand­ards are an important aspect of quality assurance, since they represent the recognized practice for assuring acceptable levels of quality and perform­ance in materials and components. A number of preexisting codes, such as the ASME Boiler and Pressure Vessel Code (§7.26), have been im­proved, supplemented, or completely revised to satisfy requirements of the nuclear industry.

12.12. Standards have played a vital role in the practice of all branches of engineering for many years. These are generally developed by profes­sional society committees and represent a consensus for acceptable pro­cedures, quality requirements, or performance criteria. Often, uniform testing and evaluation methods are prescribed. Such development is co­ordinated by the American National Standards Institute (ANSI) (§8.42).

12.13. Hundreds of standards are relevant to the practice of nuclear engineering. These cover all aspects of nuclear power plant design, con­struction, equipment performance, and instrumentation, as well as the manufacturing of nuclear fuels. Many standards also deal with computer codes and information transfer. Since standards document accepted prac­tice, it is important for a nuclear reactor engineer to become familiar with those standards that are relevant to a given professional assignment. These are generally available in technical libraries or through ANSI.

12.14. Special code requirements are established for nuclear safety grade components, which are considered vital to plant safety. When such com­ponents such as valves are manufactured to meet these stringent require­ments, they may be labeled with an “N” stamp. Categorization into classes, depending upon safety significance, with differing requirements for quality assurance and in-service inspections is as follows:

Safety Class 1. This, the most vital category applies to components of the primary coolant system, whose failure would cause a major coolant loss.

Safety Class 2. In this category, we have structures and components that are required to fulfill a safety function such as shutting down the reactor, cooling other safety systems, and controlling the release of radioactivity.

Safety Class 3. This applies to systems whose failure would allow release to the environment of gaseous radioactivity that would normally be held for decay within the plant.

Nonsafety grade components must meet “high-quality industrial stand­ards.” Since a significant additional expense is associated with safety grade components, there has been in the past a design incentive to specify such components only for essential safety functions.

12.15. Many standards have been incorporated into Federal Regulations and Regulatory Guides issued by the U. S. Nuclear Regulatory Commission (NRC). General quality assurance criteria are specified in Title 10 of the Code of Federal Regulations, Part 50, Appendix В (10 CFR 50). Specific quality assurance requirements appear in the Regulatory Guide dealing with the particular topic considered.

12.16. There are five major aspects of a quality assurance program:

1. The actual formulation of the program itself includes specific detailed pol­icies and procedures.

2. Should design be required, quality control of the necessary practices is needed.

3. Component and material procurement activities require the enforcement of quality assurance requirements.

4. Inspection and test procedures are prescribed to assure that all specifications are met.

5. Auditing and record-keeping procedures are provided to assure adherence to requirements.

12.116. The alkali metals, such as cesium and rubidium, are both re­active and volatile in their elemental form. In the fuel, gaseous cesium tends to exist in thermodynamic equilibrium with several cesium com­pounds. Upon failure of the fuel, a fraction of the cesium present will combine with most of the iodine, but the remainder is likely to react with steam present to form cesium hydroxide. Other reactions could occur with the various substances present but it is likely that the compounds formed will have low volatility.

Tellurium

12.117. Tellurium is the most significant fission product of the chalcogen class, which also includes selenium. This importance is a result of both the concentration of its several isotopes (about 1 percent of the fission prod­ucts) and their radiotoxicity, primarily because they are iodine precursors. Under accident conditions, it is expected to be released from the fuel in elemental form and then react with various structural materials. Tellurium behavior appears to be dependent on the particular accident scenario and is the subject of ongoing studies.

9.17.

In reactor cooling problems, it is often of interest to estimate the maximum heat-generation rate (or power density) at a point in a given fuel channel, rather than for the whole reactor core. In equation (9.1), the first (Bessel function) term gives the radial flux distribution, whereas the second (cosine) term represents the axial distribution in a cylindrical re­actor. In any specified axial fuel channel, at a fixed radial distance r from the reactor center, the neutron flux distribution is

where (фщах)ахіаь the maximum flux at the center of the given channel, is equal to ;фтах/о(2.405г/Я’).

9.19.

The result expressed by equation (9.5), or the simplification for the core without end reflectors, is also applicable to fuel channels in a rectangular parallelepiped reactor. For this geometry, the flux distribution in any direction parallel to one of three principal axes is represented by an expression analogous to equation (9.4). The only change necessary is to replace H by the actual length of the reactor core in the given direction, and Я’ by the effective length including allowance for the reflector.