11.39. After removal from the reactor and insertion in the storage pool, all of the radionuclides contained in the fuel continue the decay process. Short and moderately short half-life fission products become insignificant after a few months. Therefore, a cooling period of 150 days is a useful point of reference, which just happens to be the intended cooling period when reprocessing was planned.

11.40. The major contributions to the radioactivity of spent reactor fuel after 150 days of cooling are given in Table 11.1. The values, in curies and becquerels per metric ton (1000 kg) of uranium (initially free from plu­tonium) charged to the reactor, were calculated for a hypothetical LWR having a thermal power of 3300 MW and a fuel burnup (§10.15) of 2.85 x 1012 J (thermal)(2.85 TJ) per kilogram of uranium in the original fuel.[18] Somewhat different activities would be applicable to other operating con­ditions, but those in the table are fairly typical. An indication of the re­spective activities at times after 150 days can be obtained from the half­lives (see also Fig. 11.6). It is seen that for a cooling period of 150 days (or more) a relatively few fission products, namely, strontium, zirconium, niobium, ruthenium, cesium, and some rare-earth elements, are respon­sible for nearly all of the radioactivity. These are the most important elements from which the uranium and plutonium would be separated in spent fuel reprocessing.

11.41. The manner in which buildup of isotopes of the heavy elements occurs during reactor operation in a fuel consisting of uranium-235 and uranium-238 is illustrated in Fig. 11.2. Horizontal arrows pointing to the right represent (n, y) reactions and those pointing to the left are for (n, 2n) reactions with fast neutrons. Vertical arrows indicate beta decay. Where vertical arrows are absent, the nuclides are alpha-particle emitters. The

TABLE 11.1. Major Contributions to Radioactivity of Spent LWR Fuel After 150 Days Cooling

Main Activity

Half-Life Decay

Nuclide (years) Mode Ci/1000 kg U Bq/1000 kg U

Fig. 11.2. Heavy-isotope buildup in uranium. (Unless otherwise indicated, the nuclides are alpha-particle emitters.)

Urn’ll’

243Am ‘li! 244Am~

4 4

238Pu^ 242pu !U> 243Pu_

d 4 d

*>2Np,^238NP<.^ 239Np(^rl 240Np.._

4, , 4 4

235uln-|Tl 236y ln,|)’1 237у ZZ 238и |П’,’1’1 239y <П’?1 240g_.<_

(n.2n)

decay product is then a nuclide with an atomic number two units less and a mass number of four units less than the parent. Alpha-particle decays are of minor importance in the cooling period, but they affect the buildup of heavy isotopes at a later stage (§11.87).

11.42. Of immediate interest is uranium-237 (half-life 6.75 days) which is formed by two (n, y) stages starting with uranium-235 or by the (и, 2n) reaction with uranium-238. Any uranium-237 remaining in the spent fuel will be associated with the recovered uranium. Since uranium-237 is a gamma-ray emitter with a fairly short half-life, its presence makes the product difficult to handle. After a 150-day cooling period, however, the uranium-237 will have decayed to such an extent that the gamma activity is small enough to be tolerable. Moreover, the beta decay product, nep­tunium-237, will be separated from the uranium during the reprocessing operation.

11.43. A chart similar to Fig. 11.2 showing the buildup of heavy isotopes when thorium-232 is included in the fuel is shown in Fig. 11.3. With thor­ium-232 as fertile material, a long cooling time would be required to permit decay of the intermediate protactinium-233 (half-life 27 days) to the fissile uranium-233. During this period, the activity of thorium-234 (half-life 24 days) would also decrease to a permissible level. However, at the same time, thorium-238 (half-life 1.9 years) would accumulate as a result of the alpha decay of uranium-232 (Fig. 11.3). Since thorium-228 has strong gamma — ray emitters among its daughter products, remote handling of spent fuel would appear to be necessary regardless of the cooling time.

12.67. As a result of quality assurance programs for reactor components and inspection during operation, the probability of mechanical failures is low. Nevertheless, the consequences of possible failures must be considered in the safety analysis. Among the more important events of low probability in the nuclear steam supply system, which could conceivably cause some fuel cladding damage, are the following: (1) a small-scale break in the reactor coolant circuit, steam-generator feedwater lines, or steam lines, and (2) complete loss of ac power leading to a loss of the normal flow of reactor coolant.

12.154. Among the factors considered in evaluating a proposed site for a nuclear power plant are certain radiological criteria which serve as guide­lines. These guidelines, as stated in 10 CFR Part 100, are calculated ra­diation doses to various population groups resulting from a hypothetical accident associated with a substantial release of fission products from the reactor core, followed by leakage from the containment vessel. The con­ditions postulated for these site acceptability calculations are such that they could be realized only in the highly improbable circumstances of a major LOCA accompanied by failure of essentially all the components of the ECCS.

12.155. In considering possible radiation exposures to population, it has been traditional for siting purposes to designate certain areas or zones surrounding the reactor plant following the philosophy that only a low population density would be acceptable close to the reactor where the radiation exposure from an accident might be significant. Immediately surrounding the plant is an exclusion area, a region in which the plant management has control of all activities.

12.156. The low-population zone is the region just outside the exclusion area; the total number and density of residents (if any) in this zone should be such that appropriate protective action, e. g., taking shelter or evacu­ation, would be possible in the event of a major accident. Radiation ex­posure limits have been prescribed for the outer boundaries of each zone. For example, at the outer boundary of the exclusion area, a limiting whole — body dose to a person of 25 rem from all sources for a 2-hour period has been designated. A whole-body dose limit of 25 rem at the outer edge of the low population zone was based on the person remaining in place during the entire period of passage of the radioactive cloud resulting from the accident. The philosophy of the low population zone is incorporated in the requirement for an Emergency Planning Zone (§12.171).

12.157. Another siting consideration is the distance of the plant site from population centers. Recognizing that in the event of a serious acci­dent, the societal risk from delayed cancers may be significant up to a distance of 80 km (50 miles) from the plant site, a remote location is favored by the NRC. Candidate locations are evaluated on a case-by-case basis with the Emergency Response Planning requirement (§12.171) applicable.

12.158. To test the radiological acceptability of a given site, a procedure described in NRC Regulatory Guides 1.3, 1.4, and 1.23 is followed. An accident in which substantial core meltdown occurs is assumed, such as a LOCA with complete failure of all emergency core cooling systems. Fol­lowing the accident, highly conservative (worst-case) assumptions are pre­scribed for the fractions of the core radionuclide equilibrium inventory that would be immediately available for leakage from the containment using maximum leak rate design specifications. Allowance may be made for radioactive decay during holdup in the containment vessel and material removed by containment vessel sprays and filters. However, source term studies (§12.104) show that these site evaluation radionuclide release as­sumptions are unrealistically conservative. Therefore, it is important not to confuse these site evaluation procedures, which are prescribed to assure a consistent treatment, with risk assessment studies to be described later (§12.231).

12.159. In our procedure, the containment leak rate acts as a source of a plume that is dispersed by atmospheric conditions, leading to a radioactive concentration downwind which is ingested by a person, say at the exclusion area boundary. With the aid of further assumptions in our model, a thyroid dose commitment at this point can be derived. For this purpose a simple Gaussian plume dispersion model is assumed [18]. More sophisticated (and realistic) models are used in risk assessment studies.

9.54. The combination of nonuniform heat-source distribution and ir­regular geometries, which occur in many reactor components, complicates the calculation of thermal-conduction rates and temperature distributions. The problem is an important one because high thermal stresses frequently result from large temperature gradients. A study of the temperature stresses in reactor components, which frequently have irregular shapes, depends upon a knowledge of the temperature pattern within the materials. A number of relatively simple codes suitable for microcomputers are available to solve multidimensional conduction problems under both steady-state and transient conditions. A stepwise, finite-difference approach, as de­scribed in the following sections for transient heat conduction, is effective. An example of such a situation is found in graphite-moderated, gas-cooled reactors. These generally consist of massive graphite blocks pierced by long holes with cylindrical fuel elements and passages for coolant. Pressure vessels containing the reactor and thermal and biological shields frequently present similar difficulties in the determination of temperature distribution and thermal-stress analysis. For such cases, a rigorous solution of the basic heat-conduction equation (9.16) is usually impossible. However, approx­imate methods have been developed in some instances; thus, a circular harmonics series solution has been proposed for the case of a massive graphite block treated as equivalent to a number of adjacent cylinders [3].

9.55. Temperature patterns for nonregular boundary conditions may be determined using numerical “relaxation” methods. The procedure is first to divide the irregular volume, so far as is possible, into a number of regular subvolumes. The heat-conduction equation may now be applied to
these subvolumes in a systematic manner based on an assumed temperature distribution compatible with the boundary conditions. By carrying out a heat-balance calculation for each of the sub volumes, the inaccuracy of the assumed temperature pattern is determined and expressed as a so-called residual for each subvolume. On the basis of these residuals, the assumed temperatures are changed in a systematic manner to reduce (or “relax”) the residuals from point to point. The heat-balance procedure and tem­perature adjustment are repeated until the residuals have been reduced to zero; the corresponding temperature distribution is then taken to be the correct one.

9.172. With the increasing availability of digital computers for engi­neering calculations, methods have been developed for the treatment of core design limits in PWRs that are more realistic than the basic hot-channel concept described in previous sections. Rather than identify a single hot channel as representing the “worst case,” it is possible to analyze each channel individually and to determine the corresponding minimum DNBR and other limiting parameters. Statistical methods are then used to evaluate the number of fuel rods that may have a given small probability of failure, as a function of design and operating conditions.

9.173. In one example of the statistical core design technique [23], a radial power factor (ratio of actual to average), analogous to F%H, is com­puted for each rod in the core, and so also is an axial factor, equivalent to F; for each rod. Engineering factors, which are sometimes called “hot — channel” factors although they do not refer to a specific hot channel, are used to describe deviations from nominal (or design) values in physical characteristics of the fuel material, fuel pellet and cladding dimensions, and flow area. These factors are derived from several subfactors based on measurements made on the actual core under construction, on similar cores previously constructed, or on specified manufacturing tolerances. The subfactors are then combined statistically to yield a heat-input factor Fe, a local hot-channel heat flux factor F0», and a flow-area reduction factor Fa. Typical values of these engineering factors in a large PWR are as follows:

Heat input (or power peaking) factor FQ 1.011

Local heat flux factor FQ„ 1.014

Flow-area reduction factor FA 0.98 (interior)

0.97 (periphery)

9.174. The computations are made for several different operating con­ditions but two are of special interest, namely, maximum and average (or most probable) design conditions. For the maximum design condition, the maximum values of the radial and axial power factors are assumed to be applicable to each fuel rod in the core; the computed heat input (or heat flux) for each rod is then multiplied by the factors FQ and FQ>, both of which are greater than unity. The coolant-flow rate is determined using the Factor Fa, which is less than unity. In a particular case, the maximum radial factor was 1.78 and the maximum axial factor was 1.70; hence, with the engineering factors given above, the maximum-to-average heat flux ratio for each coolant channel is

Heat flux factor = 1.78 x 1.70 x 1.011 x 1.014 = 3.10.

In evaluating the coolant enthalpy rise, the factor includes an allowance for the reduction in the flow area which applies to all the channels; thus,

Enthalpy factor = 1.78 x 1.011 x 1.014 x 0.98 = 1.79.

By means of these data, it is possible to compute the DNB flux (and DNBR) along each fuel rod (or channel) instead of a single hot channel in the earlier treatment.

9.175. For the average (or most probable) design condition, the heat input (or power) distribution for each fuel rod is derived from neutronic calculations, and the coolant-flow rate is compatible with the location of each channel in the reactor core. The DNB data are then evaluated for each fuel rod (or coolant channel) in the usual manner.

9.176. The results obtained from the foregoing computations are treated statistically to derive the number of possible burnouts at a specified con­fidence level for various operating conditions. Table 9.4 gives the values obtained at a 99 percent confidence level for both maximum and most probable design conditions of a PWR with 36,816 rods operating at 100 percent of design power and at 112 percent overpower. It is seen that, under the worst conditions that might arise in normal operation, i. e., at maximum design conditions and 112 percent overpower, there is a 99 percent confidence that almost 99.9 percent of the fuel rods will be pro­tected from burnout. The minimum DNBR under these conditions is 1.39 at the same confidence level.

10.92. In the evaluation of alternate engineering projects involving the expenditure of funds, incurring of costs, and receipt of revenue, all at different times, a systematic treatment of the effect of the time variable of money is useful. The value of money can be considered to change as it is moved through time. In the present, for example, money has a greater value than it would have at some time in the future because it can be put to a useful purpose in the interim. Some of the terms discussed in the previous section are useful in design comparisons involving expenditures.

10.93. The present-worth concept, for example, provides for the shifting of money from one time level to another with a corresponding shift in value. If r is the effective earning rate or interest rate, then the present worth of 1 dollar due 1 year in the future is 1/(1 + r). This corresponds to shifting backward in time. Similarly, the present worth of 1 dollar in­vested a year previously would be (1 + r), corresponding to a shift forward. In electric utility economics, it is useful to know the present worth of revenue requirements for future years of plant operation. This corresponds to the case of the backward shift. In the case of simple interest (single payment), the present value, P, can be expressed as

(1 + г)"’

where n is the number of years involved.

11.86. The radioactivity of the solid reprocessing wastes, as a function of time after removal from the reactor, can be inferred from Fig. 11.6, the data for which were calculated for LWR spent fuel, assuming 99.5 percent removal of plutonium (and uranium) [12]. Solid wastes would differ in the respect that the volatile (or gaseous) species, namely, iodine, krypton, tritium, and xenon, would not be present, since they are either removed or released at the reprocessing plant or during calcination of liquid wastes. The data in Fig. 11.6 refer specifically to 1000 MW(el)-year of LWR op­eration with a burnup of 2.85 TJ/kg of fuel, initially uranium free from plutonium; 0.5 percent of the plutonium (and all the americium and curium) formed as well as 0.5 percent of the uranium are assumed to remain.

11.87. It is seen that at 1 year after discharge from the reactor, the total activity would be about 108 curies or more than 1018 Bq; it decreases by a factor of roughly ten after 10 years and another factor of about ten after 100 years. Subsequently, the activity decreases more rapidly until some 600 years have elapsed, when the decrease becomes very slow. The radio­activity then arises mainly from the long-lived, alpha-emitting transuranium nuclides, especially isotopes of plutonium and americium. There is also a small contribution from the beta-emitting fission product, technetium-99 (half-life 2.1 x 105 years). Since iodine-129 is volatile, it is not present in the solid wastes.

11.88. Because the curves in Fig. 11.6 are for the total activity of all the isotopes of a given element, they do not show some interesting vari­ations in heavy-element buildup. For example, the amount of plutonium — 238, produced in the wastes by the alpha decay of the short-lived curium — 242, increases to a maximum after some 10 years, and plutonium-240, from the decay of curium-244, attains a maximum after about 100 years. Plu­tonium-239, which is formed by alpha decay of americium-243 to neptun­ium-239 followed by beta decay of the latter, reaches a maximum activity after approximately 20,000 years. The sharp decrease in the total activity

For brevity, this will be referred to as 1000 MW(el)-year of operation.

of plutonium between about 10 and 100 years, as seen in Fig. 11.6, results from the decay of plutonium-238 (half-life 88 years) and plutonium-241 (half-life 14 years) which have made the major contribution in the early stages.

11.89. The rate of heat generation (or thermal power) in the wastes, due to radioactive decay, varies in the same general manner as the total

activity. For the 1000 MW(el)-year operation of an LWR referred to, the thermal power of the solid high-level wastes would be about 350 kW after 1 year and roughly 35 kW after 10 years; at the latter time, almost 90 percent of the heat would arise from strontium-90 (and its short-lived decay product yttrium-90) and cesium-137. After 100 years, the thermal power is approximately 4 kW, and after 600 years (or more) it is less than 0.05 kW.

12.100. This accident is caused by any event that requires reactor trip combined with a station blackout, i. e., the loss of all power, as well as the loss of capability of the secondary system to remove heat from the primary circuit. Under such circumstances, with no means for normal heat removal, the primary system pressure would rise until the relief value system would initiate blowdown. Subsequent events for a TMLB’ accident could follow those given above for the AB accident. However, in a more realistic vari­ation, designated as a TMLB accident, electrical power is assumed to be recovered in 1 to 3 hours. Should this be the case, meltdown and the subsequent scenario might be avoided.

Containment bypass accidents (V)

12.101. This is an accident category in which the containment would be compromised by such possibilities as the failure of a series of valves con­necting the high-pressure reactor coolant system with the low-pressure portions of the emergency core cooling system leading outside the con­tainment. In this category, the event scenario and consequences depend greatly on the design details of the specific reactor system. It should be noted that in the Three Mile Island accident, there was some containment compromise through the level control and purification system (§12.179).

12.199. Continuing research and studies contribute to a large body of severe accident information for various reactor types. The work has been carried out under the auspices of the Nuclear Regulatory Commission, the Nuclear Management and Resources Council (NUMARC), which serves as liaison between industry and the NRC, and the Electric Power Research Institute. NUMARC has a group that coordinates severe accident activities.

12.200. Basic research has been directed toward understanding the physical mechanisms occurring during severe accident scenarios, such as those described earlier (§12.95 et seq.) and to model the various steps analytically. Many projects are thermal-hydraulics oriented. For example, the thermal behavior of a pool of molten core debris at the bottom of a reactor pressure vessel can affect the practicality of preserving the vessel integrity by external cooling.

12.201. The assessment of severe accident risks carried out under the NUREG-1150 Program (§12.234) can identify areas of vulnerability specific to individual plants. Such work can then serve as the focus of further studies which can then lead to the subsequent development of appropriate remedial actions.

Supporting Instrumentation

12.202. During a severe accident, plant instrumentation must provide the operating staff with an indication of the plant condition. The program must therefore address the need for additional instruments, the surviva­bility of vital instruments during an accident, and the interpretation of readings.

8.31. The computer is an essential tool for modern nuclear engineering practice. Although hand calculations are valuable for instruction, concep­tual visualization, scoping, and preliminary design, the complexity of nu­clear systems demands computer calculations for final design. Hence, there is a need for computer programs to meet a wide variety of requirements. Although writing a custom program may be necessary for some applica­tions, it is first desirable to explore the availability of developed codes that will meet the need. Therefore, familiarity with the sources of available computer codes is a useful engineering tool.

8.32. An essential first step in code use is to become thoroughly familiar with the problem to be solved and to determine what codes are best for the given task. In addition to developing background from the literature, consultation with experts experienced in solving similar problems may be necessary. In the process, it is likely that code availability will be deter­mined. Our purpose here is merely to point out some common code sources should it be necessary to use them.

8.33. The National Energy Software Center at Argonne, Illinois serves as a central computer program library in the areas of reactor physics, reactor engineering, and design. Periodically, it publishes a compilation of code abstracts. The center has available for distribution to qualified users well over 1000 programs.

8.34. A second major resource is the Radiation Shielding Information Center at Oak Ridge, Tennessee (§6.159). Although the emphasis in the computer code collection is on radiation transport and shielding, much information is also provided on data analysis. User code packages are provided by the Center, which has a collection of several hundred programs.

8.35. The Electric Power Research Institute (EPRI), the research arm of the electric utility industry, is responsible for significant code develop­ment. Software packages for EPRI-sponsored work are available to mem­ber utilities and others under a licensing arrangement from the Electric Power Software Center, operated by the Power Computing Co., a com­mercial information service in Dallas, Texas.

8.36. For software not available from central collections, it is often possible to obtain packages directly from the code developer by making appropriate arrangements. However, proprietary considerations may limit availability.