11.23. The radioactivity concentrations in the 10 CFR Part 20 regula­tions are intended to provide guidance as to the maximum permissible discharges of radioactive effluents to the environment. Licensees of nuclear power plants are required, however, to control the effluents in such a manner that radioactivity levels be kept “as low as is reasonably achiev­able.” This requirement is interpreted as meaning that the levels should be kept “as low as is reasonably achievable taking into account the state of technology and the economics of improvements in relation to the benefits to the public health and safety. …”

11.24. In principle it should be possible, by increasing the complexity and hence the cost of constructing and operating the equipment of the “radwaste” system for the treatment of radioactive waste liquids and gases (§11.93 et seq.), to decrease the level of the radioactivity in effluents almost without limit. However, any such decrease means an increase in the ra­dioactive material that must be stored, at least temporarily, in the plant, thereby increasing the potential risk to people working there. Furthermore, the greater the complexity of the radwaste system, the greater the chances of failures which might interfere with plant operation. The extent of the treatment of radioactive wastes in a given plant is thus based on an analysis of the benefits that would be expected to accrue, balanced against all the costs (including risks).

11.25. In expressing the numerical guides, the effluents from a plant are considered in three categories: liquid effluents, gaseous effluents, and radioiodines and radioactive material in particulate form. The liquid ef­fluent generally contains some tritium (as tritiated water) and dissolved and suspended fission products and corrosion and erosion products that have become radioactive (§11.91). The gaseous activity consists mainly of radioisotopes of the noble gases krypton and xenon, most of which emit both gamma rays and beta particles. Because the gaseous effluent from PWRs is held up for a longer time before discharge than from BWRs, the shorter-lived isotopes have largely decayed leaving mainly krypton-85, which is almost exclusively a beta emitter, and xenon-133. The radioiodines and particulate matter are present, together with the noble gases, in the air­borne effluents from the LWR installation. Some of the solid particles are formed by radioactive decay of the noble gases.

11.26. It should be understood that the purpose of the guidelines is to assess the adequacy of a proposed nuclear plant design, especially the design of the radwaste treatment system, before construction. When the plant is operating, the radioactivity concentrations in the effluent at the plant boundary must satisfy the requirements of 10 CFR Part 20. Fur­thermore the actual radiation doses to the public must comply with the EPA standards for the fuel cycle (40 CFR 190) [5].

12.43. A containment structure enclosing the reactor primary system acts as the final backup barrier to fission product release to the environment in the defense-in-depth design of the reactor safety systems. Although containment design in LWRs is traditionally based on holding the pressure resulting from the release of the primary coolant in a loss-of coolant ac­cident (LOCA) (§12.37) and to withstand the impact of internally gener­ated missiles, margins are such that substantially higher pressures can be accommodated before failure. As we shall see later (§12.95), additional challenges are provided by so-called severe accidents in which the core is degraded. Fission product transport into the containment can be modeled analytically with various uncertainties involved. Therefore, it is useful to view the containment as the essential physical envelope which will indeed prevent the fission products from entering the environment despite the modeling uncertainties that may be present.[22]

12.44. Containments for PWRs are large cylindrical or spherical pres­sure vessels designed for pressures on the order of 345 kPa(g) (50 psig). Since the PWR containment must be large enough anyway to enclose all of the components of the entire primary system, which may include four steam generators and a pressurizer in addition to the reactor pressure vessel itself, it is practical to achieve the necessary pressure reduction merely by allowing steam formed by coolant flashing to vent into the large volume. On the other hand, the BWR primary system is contained essentially within the pressure vessel with much less building volume needed for housing it. Therefore, BWRs use means to condense the released steam in pressure suppression pools so that the containment building need not be much larger than that required to hold the system.

12.137. The only practical way to model transient behavior such as that described above in a system consisting of connected components is to use subprograms for the individual component volumes and then join them together at the component interfaces. Improved accuracy is obtained by subdividing the component and piping volumes shown in Fig. 12.10 to a level balanced by the resulting increased computational cost. Thus, we have the primary coolant circuit divided into a number of control or nodal volumes connected by junctions at which the properties change, and fluid mass, momentum, and energy are transferred as a function of time. Within each volume, so-called field equations describe in a numerical finite-difference manner the conservation of mass, momentum, and energy. A typical system code is likely to have hundreds of nodal volumes, with time steps taken to model a LOCA of the order of milliseconds. Should longer transients be modeled, the number of volumes must be reduced to keep the computing time from becoming excessive.

12.138. In Fig. 12.11 is shown a practical level of volume subdivision for the analysis of the blowdown phase in a large cold leg break LOCA for a two-loop PWR. The model for this blowdown analysis consists of 45 volumes, 56 junctions, and 28 heat slabs. Three volumes are used to model the core. Also, within the reactor vessel, the downcomer, upper and lower plenums, and core bypass are represented by other volumes. Discharge into the containment (volume 40) flows through two imaginary “valves” used to model various break sizes [36].

12.139. In modeling the various stages of a LOCA, the picture is com­plicated by the need for a two-phase description which must also account for the transfer of the conserved quantities between phases in a given volume. The reflood stage is a particular challenge. Since the physics of two-phase flow is very complex, it is necessary to apply simplifying as­sumptions for practical modeling. In the most drastic simplification, the so-called one-dimensional homogeneous, no-slip, equilibrium model, the steam-water mixture is treated as one fluid at the saturated temperature moving in one dimension. In attempting to develop greater modeling so­phistication to account for nonequilibrium and nonhomogeneity, various

SIMULATED (FLUID VOLUME) PLANT

Fig. 12.10. Schematic representation of actual and fluid-volume models of a PWR coolant loop for LOCA calculations. (The intact loops are not shown but are included in the computations.)

averaging procedures have been developed to convert the local instanta­neous governing equations written for each phase to suitable averaged governing equations for the mixture. This lumped-parameter approach is generally used for licensing-type calculations.

12.140. Higher levels of sophistication are used in the best estimate codes. Here, one also starts with a two-fluid or two-phase model but retains the individual phase relations in the calculation with expressions for in­terfacial mass and energy exchange included. However, some simplification is still needed. This varies depending on the needs of the problem. In fact, the features of most codes in common use are being updated continually. The level of representation can vary among different subprograms describ­ing behavior in individual coolant system components. Details may be found in other sources [10] and in the current literature.

12.141. A feature of the various system codes is the need to incorporate within the various subprograms available engineering correlations to pre­dict such values as heat-transfer coefficients and vaporization rates as in­troduced in Chapter 9. Selection of the proper correlation for each region of application must be provided by the code system. Associated with the use of correlations is uncertainty analysis to determine the confidence level of the results. This may be done by estimating error bands for each cor­relation and determining the cumulative error through the computational process. Of course, modeling simplifications would contribute additional uncertainties. Therefore, experimental programs that simulate various types of LOCA behavior in individual components play an important role in system code development.

9.35. Tubular heat-transfer surfaces are used in many heat exchangers, and the performance of these can be analyzed on the basis of heat con­duction through hollow circular cylinders with convection at both interior and exterior surfaces. The physical system in cross section and the thermal — circuit diagram are shown in Fig. 9.2; it is assumed that all the heat flow is in a radial direction. The inner and outer radii of the cylinder are a and b, respectively; ha and hb are the heat-transfer coefficients for the inner and outer fluids, and ta and tb are the mixed-mean temperatures of the inner and outer fluids, respectively.

9.36. The convection thermal resistances are equal to l/haAa and l/hbAb, where Aa and Ab are the areas of the inner and outer surfaces. The thermal conduction resistance of the cylinder wall remains to be de­termined. If lis the length of the cylinder, then the heat-flow rate, expressed at an arbitrary radius r, due to conduction within the wall is given by equation (9.6) as

q = — k(2irrl) —,

where к is the thermal conductivity and 2wl is equivalent to A, the area through which heat flow occurs. This expression may be rearranged and integrated over the wall thickness, i. e., from r = a to r = b; the result

Fig. 9.2. Heat conduction in a hollow cylinder with convection boundaries.

THERMAL CIRCUIT

is

q ln(b/a)/2irJt/’ (911′)

where M is the difference in temperature across the cylinder wall.

9.37. It is evident from equation (9.11) that the thermal resistance Rw of the wall is given by

= In (b/a) w 2irkl ‘

The total thermal resistance of the system under consideration is conse­quently

___ 1_ In (b/a) _1______ 1__

~ h. A„ + 2тткі + hbAb ~ UbAb’

where Ub is the overall heat-transfer coefficient based on the outer surface of the cylinder. According to the thermal-circuit concept

Я ~ ^ ~ UbAb(ta tb)

or

where

_______ 1_______

b b In (b/a) 1 [4]

Kp + * + к

9.143 As background for describing the temperature variations along the path of the reactor coolant, it is useful first to consider a classical idealized channel with uniform fuel enrichment and no axial reflector. A generalized representation of such a coolant channel, with its associated effective heat-removal area, is shown in Fig. 9.19, where the different variables are identified. The x coordinate represents the direction of cool­ant flow in a vertical channel. The rate dq(x) at which heat is added to the stream in a differential length dx of any coolant passage is then given by

dq(x) = wcp dt, (9.43)

where w is the mass-flow rate of the coolant in the channel associated with one fuel rod, cp is the specific heat, and dt is the differential temperature increase in the coolant across the length dx. For simplicity it will be pos­tulated that all heat flow within the solid fuel is normal to the coolant stream, i. e., there is no heat conduction along the fuel rod parallel to the coolant channel.[14] Then dq(x) is the rate of heat generation in a volume Ac dx, where Ac is the cross-sectional area of the fuel rod (in the y, z plane). Since the volumetric heat source is, in general, a point function Q(x, y, z), it is possible to write

j Q(x, y, z) dy dz j dx,

the integration being carried over the fuel rod cross section.

9.144. If a local average heat source per unit volume Q(x) is defined

by

it follows that

dq(x) = ACQ(x) dx.

Fig. 9.19. Generalized representation of fuel rod and coolant flow channel. (Note that the rod and channel are actually vertical.)

Hence, from equations (9.43) and (9.44), the temperature distribution in the direction of coolant flow must satisfy the relation

dt_ = ACQ dx wcp

it being understood that Q is really Q{x). If the quantity AJwcp is inde­pendent of jc, the distribution of the coolant mixed-mean (or bulk) tem­perature tm along the channel will be given by

(9.45)

where the fluid entrance temperature, te at x = 0, is chosen as the datum. This expression gives the increase in the coolant temperature due to the heat added as it flows through the channel.

9.145. By equation (9.9), the local (solid) surface temperature ts is re­lated to the coolant bulk temperature tm by

(9.46)

where h is the heat-transfer coefficient for the given conditions and dAh is a small element of heat-transfer surface, i. e., the fuel-rod surface (not its cross section). Although h will vary to some extent along the length of the channel, it will be assumed to be constant and independent of x, in order to simplify the treatment without affecting the general conclusions. If p is the circumference of the rod, which may be clad or unclad, then

dAh = p dx, and equation (9.46) may be written as

dq = hp(ts — tm) dx.

From equations (9.44) and (9.47), it is seen that

QAc

hP ‘

For a clad fuel rod, the heat-generating volume is based on the pellet radius, a, and the heat-transfer area is based on the outer clad surface. It is then best to write

QV hAh’

where Ah and V are the heat-transfer area and heat-generating volume, respectively, associated with the coolant channel.

10.82. Although spent LWR fuel is not reprocessed in the United States to recover the plutonium contained therein, extensive reprocessing is car­ried out in Europe. Also, the possibility exists that there may be a desire to make use of the energy available from plutonium recovered from dis­mantled nuclear weapons. Therefore, we will briefly examine a few of the design considerations in using some plutonium dioxide in LWRs.

10.83. Plutonium formed in present LWRs from slightly enriched ura­nium is fissioned in place during the latter part of the operating cycle. Therefore, one should anticipate no major problems in adding some plu­tonium to a fresh fuel batch. However, since fabrication costs would be high if the addition would be made uniformly to all rods, most plans call for using mixed uranium—plutonium oxide in selected rods. The large fission cross section of the fissile plutonium isotopes could result in power peaking in such rods. The neutron absorption in plutonium could also affect the reactivity worth of control rods as well as reactivity temperature coef­ficients. Therefore, we see that the use of plutonium to replace some of the uranium-235 in fresh fuel can affect the core safety characteristics and must be accounted for in the design. The use of recycled plutonium was extensively studied during the 1970s and significant literature developed [17]. Currently, recycled plutonium is being used routinely in French PWR fuels [24].

Introduction

11.60. Prior to 1976, it was generally assumed that spent fuel would be reprocessed for the recovery of uranium and plutonium for reuse as reactor fuel. It was felt that economic supplies of uranium were limited relative to future needs for the then-projected growth of the nuclear power industry. Also, planned fast reactors would require recovered plutonium for fuel.

11.61. In 1976, public concerns that the availability of chemically pure plutonium would encourage the proliferation of nuclear weapons led to a ban on reprocessing. Although the ban was lifted in 1980, reprocessing was no longer commercially attractive, for several reasons. First, processing plant operating costs had increased significantly. Next, many new nuclear power plants were canceled, depressing the price of uranium. Since new uranium reserves were also identified, the future salvage value of recycled fuel seemed uncertain, thus reducing the economic incentive for repro­cessing. In addition, there was no need for significant fast reactor fuel since a U. S. demonstration plant at Clinch River, Tennessee was canceled and there were no plans for other plants. However, without the need for a significant level of commercial justification, fuel reprocessing continues to be carried out routinely in other countries. One incentive for such oper­ations is the reduction in the volume of high-level radioactive waste that requires management (§11.63).

11.62. It appears likely that around the beginning of the next century, the combination of increased worldwide energy requirements, diminishing oil and gas supplies, and environmental concerns will lead to pressure to increase nuclear capacity substantially in the United States. With the con­servation of nuclear fuels then becoming of interest again, fast reactors are likely to play a role in this new capacity.

11.63. The disposal of reprocessed high-level waste solidified as glass in canisters requires less volume than the disposal of spent fuel and utilizes a more straightforward leakproof package system. Thus, easier disposal provides some incentive for reprocessing. As a result of all these factors, it is probable that reprocessing of stored spent fuel will be resumed in the United States at some time in the future. Therefore, the highlights of the subject will be discussed here.

12.78. Loss-of-coolant accidents fall into several categories depending on the size of the postulated break in the primary coolant circuit. Smaller breaks, which could lead to minor fuel cladding damage at worst, were considered earlier. For the design basis accident, however, a “guillotine” (or double-ended) break is postulated in one of the cold legs of a PWR or in one of the recirculation pump intake lines of a BWR (§12.73). As a result of such a break, the primary system pressure would drop and almost all the reactor water would be expelled into the containment. The drop in pressure resulting from such a loss-of-coolant accident (LOCA) would actuate the protection system and the reactor would be tripped. The fission chain reaction in the core would thus be terminated, as it would in any case because of the loss of coolant (moderator). Nevertheless, heat would continue to be released at a high rate from the sources mentioned in §12.28. The various ECCS subsystems must then provide sufficient cooling in time to minimize overheating and fuel cladding damage. The steam flow limiters and isolation valves, inside and outside the containment vessel, would close automatically to prevent the spread of possibly contaminated steam.

12.79. The thermal-hydraulic (and other) phenomena are very complex, and studies are being made to provide a better understanding for computer modeling (§12.126 et seq.). These phenomena are somewhat different for PWRs and BWRs and will be outlined separately.

12.179. The accident, which occurred in March 1979 near Harrisburg, Pennsylvania, to a PWR of Babcock and Wilcox design, was the result of an unusual combination of operator errors and equipment deficiencies. A lengthy chain of events began with an inability to pump feedwater into the secondary system, which resulted in a turbine trip shortly thereafter. The pressurizer relief valve (§13.16) then opened in response to the rise in primary system pressure but was stuck in the open position, which was unrecognized by the operators. Thus, we had what was comparable to a small-break loss-of-coolant accident.

12.180. As a result of operator confusion, the coolant inventory was further reduced by their throttling the high-pressure injection flow and draining water through the letdown line in the system used to regulate the coolant boron concentration. Boiling in the core as a result of the reduced pressure caused the operators to shut down the primary circulating pumps, leading to further steam buildup, core uncovering, and severe core damage. Earlier, overpressure on a tank receiving discharge from the pressurizer led to a minor radioactive release to an auxiliary building and then to the environment through a vent stack.

12.181. The loss of coolant was finally halted after several hours and the core was subsequently reflooded. However, it was still difficult to cool the core with the primary pumps because of the large quantities of steam and some hydrogen in the system as well as the degraded core geometry. A number of “feed and bleed” maneuvers in which water would first be injected and then the pressure reduced proved helpful. The operators were then able to activate a primary pump and achieve a relatively stable con­dition after about 16 hours.

12.182. Feed-and-bleed cooling as an operator option has since been modeled extensively with the aid of such system codes as MAAP [16]. These analyses provide a picture of the response of a given system should feedwater be unavailable and depressurization be attempted by alterna­tively injecting emergency coolant and bleeding off inventory through the pressurizer. Such a picture provides guidance for the emergency meas­ures required, particularly the time “window” that may be available for countermeasures.

8.17. The systems concept is a useful design tool for the analysis of how component and subsystem failures can propagate and affect performance.

For example, in a PWR, a reactor coolant pump could fail as a result of an electrical fault. The resulting reduction in flow would, in turn, raise the core water temperature, possibly cause boiling, then raise the fuel tem­perature, all of which would affect the reactivity as determined by the appropriate coefficients. This, and similar chains of events, can be treated analytically. Thus, a systematic study of intersystem dependencies provides the designer with a thorough examination of various modes of system response which would not otherwise be apparent.

8.18. Fault tree and event tree analyses (§12.213) are related analytical procedures for assessing the reliability of safety-related systems. As will be discussed in Chapter 12, these approaches are valuable decision tools for identifying “weak links” in intersystem functional dependencies.