To point to the importance of using improved methods of fuel and poison management, we shall discuss qualitatively the multiple drawbacks of the simplest method, which is batch irradiation of fuel initially uniform in composition, with spatially uniform distribution of boron control poison and with complete replacement of fuel at the end of its operating life. An example of this would be a PWR charged with fuel of uniform enrichment containing 4 percent 235 U and 96 percent 238 U and controlled by adjusting the concentration of boric acid dissolved in the water coolant to keep the reactor just critical at the desired power level. When this reactor starts operation, the compositions of fuel and poison are uniform throughout the core, and the flux and power density distribution are very nonuniform.

Figure 3.5 illustrates the spatial variation of power density in one-quarter of the core of a 1060-MWe PWR when the enrichment of 235 U and the concentration of boron control poison are uniform throughout the core. The lines plotted are lines of constant power density expressed as kilowatts of heat per liter of reactor volume, and also as kilowatts of heat per foot of fuel rod. The maximum permissible value of the latter is around 16 kW/ft, to ensure against overheating the fuel or cladding.

This figure illustrates immediately one of the disadvantages of batch fuel management. The power density, which is proportional to the product of the neutron flux and the fissile material concentration, is just as nonuniform as the neutron flux. If the local power density must be kept below some safe upper limit, to keep from overheating the fuel or cladding, only the fuel at the center of the reactor can be allowed to reach this power density, and fuel at all other points will be operating at much lower output. In a typical uniformly fueled and poisoned water-moderated reactor, the ratio of peak to average power density is over 3, so that the reactor puts out only one-third as much heat as it could if the power density were uniform.

The nonuniform flux is responsible for a second drawback of this method of fuel and poison management, the nonuniform change that takes place in fuel composition. In the center of the reactor, where the flux is highest, fuel composition changes more rapidly than at points nearer the outside of the reactor, where the flux is lower. As times goes on, therefore, the 233 U content at the center of the reactor becomes much lower and the burnup of the fuel much higher than toward the outside of the reactor. When the end of fuel life is reached, either because fuel at the center has reached the maximum bumup permitted because of radiation damage, or because the reactor has ceased to be critical with all boron removed, the outer fuel will have produced much less heat than the central fuel. If all fuel is discharged at end of life, the unit cost of heat from the outer fuel will be much higher than the central fuel. Figure 3.6 shows the final bumup distribution in a quarter of the core of a 1060-MWe PWR if charged initially with fuel of uniform composition.

A third drawback of this method of fueling is the large change in reactivity that takes place

between the beginning and end of fuel life. The reactivity of enriched uranium decreases steadily during irradiation. To compensate for this in simple batch irradiation, it is necessary to have a relatively large amount of control poison present at the beginning of fuel life and to withdraw this as irradiation progresses until at the end of life, ideally, all poison has been removed. When soluble poison such as boric acid is used, this means a high concentration at the beginning of life, with possible adverse effects on coolant corrosion and other chemical properties, and a large system for processing coolant to remove boron. When movable control rods are used, this means a large number of rods, which adds to cost; in some reactors the bumup obtainable is limited by the amount of room available for control rod insertion.

A fourth drawback of this simple batch irradiation is the waste of neutrons through absorption by boron at the beginning of the cycle. To give a rough example, to obtain an average bumup of 20,000 MWd/MT in a PWR with simple batch irradiation, it is necessary to absorb around 16 percent as many neutrons in boron at the beginning of life as are absorbed by 235 U at that time. In some of the more sophisticated methods of fuel management, these neutrons would be absorbed in 233 U to make plutonium. As the heat of fission is around 1 MWd/g and as about 0.8 g 23SU is fissioned per gram of 23SU consumed, (0.16X1/0.8) = 0.2 g plutonium/MWd of heat could have been made with 238 U that are not made with boron. As plutonium has a value of around $20/g, production of plutonium with these excess neutrons would be worth $4/MWd of heat, or 0.5 mills/kWh of electricity in a nuclear power plant that is 30 percent efficient. At the end of fuel life this loss drops to zero, so that over fuel life the average loss due to absorbing neutrons in boron is about 0.25 mills/kWh. In a 1000-MW plant operating 7000 h/year, this is a loss of almost $2 million/year, enough to make more sophisticated methods of fuel management well worth using.

Many of the nuclides in the actinide family—U, Np, Pu, etc.—fission spontaneously as one of the modes of radioactive decay. Usually, for a nuclide with multiple modes of radioactive decay, the half-life of the nuclide is determined from the total decay rate, representing all the decay processes for that nuclide. However, in the case of spontaneous fission, a separate half-life for that process alone is used. Examples of nuclides that undergo spontaneous fission are given in Table 2.5.

The neutrons from spontaneous fission are emitted with average energies of a few million electron volts. Because the neutron carries no electrical charge, these fission neutrons penetrate quite readily through solids and liquids. They are stopped or slowed down only when they

collide with nuclei of the material through which they are traveling. A neutron loses the greatest amount of energy per collision when it collides with a hydrogen nucleus, whose mass is almost identical with the neutron mass. Consequently, hydrogenous materials are used to degrade, or “moderate,” energies of fission neutrons to energies in the few electron volt or kiloelectron volt range, where they are more easily absorbed by nuclear reactions. When energetic neutrons pass through animal tissue, the protons (hydrogen nuclei) recoiling from neutron collisions cause ionization within the tissue and can result in biological damage. Radionuclides with appreciable spontaneous fission, e. g., 252Cf, must be shielded with mixtures of hydrogenous materials and neutron absorbers (e. g., boron) to protect against external hazards.

The neutron energy cycle of the one-group reactor-physics model to be used is shown in Fig. 3.28.

Consider a unit volume containing Nm atoms of fissile material (M3U, 233 U, 239 Pu, or 241 Pu) of thermal absorption cross section am, and Ng atoms of fertile material U or 232 Th) of thermal absorption cross section ag. For this model we shall develop expressions for the number of neutrons produced or absorbed at any point in the neutron cycle per unit volume per unit time. Assume that the fissionable material absorbs only thermal neutrons. The rate of

absorption of neutrons by fissionable material is Мтотф, where ф is the thermal-neutron flux. The resulting fissions produce fast neutrons at a rate гітМтотф.

Those fast neutrons that have energies greater than about 1 MeV may cause a limited amount of fission of fertile material. To account for this, the reactor designer usually specifies a quantity e, called the fast-fission factor, which is defined as the ratio of the net rate of production of fast neutrons to the rate of production of fast neutrons by thermal fission. The fraction e — 1 of the fast neutrons comes from fission of fertile material with fast neutrons; e — 1 may be of the order of a few hundredths in a thermal power reactor. The net production rate of fast neutrons from fission is erітМтотф.

As the fast neutrons undergo scattering collisions, they are degraded in energy and also tend to diffuse toward the outer surface of the reactor where they may escape. When those remaining in the reactor are degraded to energies of a few kilovolts, they have a good chance of being absorbed in the fertile material, which has large resonances in its absorption cross section in the kilovolt range. This resonance absorption is important in producing new fissionable material, i. e., 239Pu from 238U and 233U from 232Th.

The fraction of the fast neutrons that do not escape from the reactor as they degrade from fission to resonance energy depends on the size and moderating properties of the reactor. This fraction is denoted as Pu the fission-to-resonance nonleakage probability. Hence, the rate at which fast neutrons degrade into the resonance region is eijm. Wm<7m0f,1.

These resonance neutrons may be captured in fertile material or may escape resonance absorption by undergoing elastic collisions with the moderator, which degrades them to energies below resonance. A quantity p is defined as the fraction of the resonance neutrons that are not captured but are degraded to lower energies and is called the resonance escape probability. The fraction p is a function of the relative proportions and physical arrangement of the moderator and fertile material. Hence, erimNmom4>Px{ — p) neutrons undergo resonance absorption per unit volume per unit time, and et]mNmam<l>Pxp are degraded to lower energies.

Of the latter, some diffuse to outer surfaces and escape, but the fraction P2 remains in the reactor as thermal neutrons; P2 is called the resonance-to-therma! nonleakage probability. Finally, the neutrons complete an energy cycle as ецтМтотфР1рР2 neutrons reach thermal energy per unit volume per unit time. The product PP2 is the fission-to-thermal nonleakage probability, which we shall denote as Ль-

Thermal neutrons are consumed by (1) absorption in fissionable material at a rate Мтотф (2) absorption in nonfissionable material at a rate Nto$ (і Ф m) and (3) leakage at a rate ИВгф. The absorption in fissionable material leads to regeneration of fission neutrons, as shown in Fig. 3.28.

In the steady state, when atoms undergoing fission are in equilibrium with their radioactive fission products, the energy released per fission is distributed approximately as in Table 2.10.

In a short burst of nuclear energy, such as in a fission bomb or in a rapid rise in reactor power, the total energy released is the sum of the first four terms, 182 to 191 MeV. When a reactor is shut down after reaching steady state, or when fuel from such a reactor is discharged, the energy of beta and gamma decay of the fission products, 13 MeV in all, is released gradually over a long period of time. The neutrino energy is not available. An average of 200 MeV of recoverable energy per fission is used in this text.

The rate of heat release and the intensity of radiation from the fuel are important factors in the design of emergency cooling systems for reactors, casks for shipping discharge fuel, fuel reprocessing plants, and facilities for storing fission-product wastes. These depend on the rate of fission of the fuel when it was in the reactor, the length of time the fuel was in the reactor, and the length of time the fuel was allowed to “cool” before shipping and processing. The exact calculation of these relationships is very tedious because of the large number of nuclides contributing to heat and radiation release, and large digital computers are required [B2]. An approximate statistical correlation by Way and Wigner [W2] provides simple equations suitable for quick approximations.

At a time t in days after fission, the products of a single fission undergo beta decay at a rate 0(f) given by

(See footnotes on page 56.)

tData from [B3. Dl, Gl, Kl, W1J.

ї235и and 23,Pu yields are for a fasl-reactor neutron speclrum; 233 Th and 25*U yields are for fission-spectrum neutrons.

and release energy in the form of beta particles, gamma rays, and neutrinos at a rate E(t) given by

E(t) = 3.9Г1’2 + 11.7Г1-4 eV/s (2.86)

The above equations apply after about 1 min after fission has taken place. Approximately one-fourth of this energy is due to gamma radiation and one-fourth to beta.

In a case of practical interest, a fuel sample will have been in a reactor liberating heat at some constant rate for T days, and will then have been cooled for t days. The rate of disintegration of fission products in the fuel sample in curies per watt of reactor power will be

rT+t

[№ disintegrations/^-fission)] (86,400 s/day) (dt days)

_______ Jt_________________________________________________________

(200 MeV/fission) [1.60 X 10"13 (W-s)/MeV] [3.7 X 1010 disintegrations/(s-Ci)]

О. = L9[f-o.2 -(7-+ f)-o.2]

w

Half-life Short 1.9s 32.3s 153s 28.8yr 64.1 h

for radioactive

decoy

Figure 2.14 Fission-product decay chain for mass 90.

Similarly, the ratio of the rate of beta — and gamma-energy release P<j(T, r) to the rate of heat release in fission Pf is

Pd(T’ f) = 0.0042 [f 0,2 — (T + Г)’0’2] + 0.0063[r°-4 — (T + O’0,4] (2.88)

pf

Equation (2.88) can also be written as

Pg(T, Q _ Pd(~, Q _ Pd(~ T + Q

pf Pf Pf

where the two quantities on the right-hand side are calculated from Eq. (2.88) for infinite irradiation time and for cooling times of t and T +1, respectively.

A more accurate estimate of the decay energy from fission products can be obtained from the ANS Standard [A2]. The data are presented here as the decay-heat rate F(°°, t) at cooling time t from fission products produced at a constant fission rate of unity, over an infinitely long operating period and without neutron absorption in the fission products. Values of F(°°, t) for the fission of 235 U by thermal neutrons are presented in Table 2.11. Data for the fission — product decay-heat rate from thermal fission of 239Pu and from the fast fission of 238U are also given in the ANS Standard [A2]. These data are applicable to light-water reactors containing 235U as a major fissile material and 238 U as the fertile material. The time domain of the official ANS Standard extends from cooling times of 1 to 104 s.

The fission-product decay-heat rate F(T, t) per unit fission rate for finite irradiation time T can be synthesized from

where уj and X,- are empirical constants. Values of 7,- and X,- for 235 U thermal fission are listed in Table 2.12. The data in Table 2.11 for infinite irradiation time can be constructed from Eq. (2.90) by choosing T = 10’3 s.

Alternatively, F(T, t) can be obtained from the data in Table 2.11 by

F(T, t) = F(°°, t) — F(«, T+t) (2.91)

Data in Table 2.11 for cooling times greater than 104 s can be used in Eq. (2.91) to synthesize values of F(T, t) within the time domain (1 to 104 s) of the ANS Standard.

(See footnotes on page 61.)

Table 2.11 Decay-heat power from fission products from thermal fission of Ms U and for near-infinite reactor operating time (Continued)

Decay-heat power Time after F(°°, t),

reactor shutdown, (MeV/s)/ Percent

s (fissions/s) uncertainty

^For irradiation time of 1013 s. Calculated for no neutron absorption in fission products.

Source: American Nuclear Society Standards Committee Working Group ANS-5.1, “American National Standard for Decay Heat Power in Light Water Reactors,” Standard ANSI/ANS-5.1, American Nuclear Society, La Grange Park, 111., 1979. With permission of the publisher, the American Nuclear Society.

The total decay-heat power Pd(T, t) for fission products from a reactor operating at constant total thermal power Pf, and neglecting neutron absorption in fission products, is given by the following simplified method, from the ANS Standard:

P’d(T, t) = 1.02 МШЛ (2.92)

where F(T, t) is evaluated from 235U data, using Eq. (2.90) or (2.91), and Q is the thermal energy per fission. The factor 1.02 corrects for the greater heat generation per fission from 238 U fission products during the period of about 100 s after reactor shutdown. The ratio PdIPfQ of fission-product decay heat rate at cooling time t to reactor power prior to shutdown is plotted as a function of T and t in Fig. 2.15.

Neutron absorption in fission products has a small effect on decay-heat power for t < 104 s and is treated by a correction factor G. The corrected total decay-heat power is given by the ANS Standard, in terms of thermal-neutron flux (in neutrons/cm2-s), reactor operating time T (in s), and cooling time t (in s) as

P(T, t) = P'(T, t)G

The parameter ф is the total number of fissions after irradiation time T per initial fissile atom, calculated by techniques described in Chap. 3. Equation (2.94) applies for operating times T< 1.2614 X 10® s (4 years), shutdown times? < 104 s, and ф < 3.0. A more detailed technique for calculating fission-product decay-heat power from an arbitrary time-dependent fission power, including contributions from the fission of 235 U, 238 U, and 239 Pu, is given in the ANS Standard [A2].

To predict the decay-heat rate from fission products after cooling times of several years, additional corrections must be made for absorption of neutrons in long-lived fission products, particularly the absorption of neutrons in stable 133 Cs to form 2.05-year 134 Cs. Computer codes such as ORIGEN [B2] and CINDER [El] are particularly useful for this purpose.

Estimated maximum values of the ratio G of fission-product decay-heat rate, with neutron absorption in fission products considered, to the decay-heat rate in the absence of neutron absorption in fission products are given in Table 2.13 [А2]. The data are calculated for 235 U — 238 U fuel irradiated for 4 years in a light-water reactor. For cooling times of < 104 s, the

Source: American Nuclear Society Standards Committee Working Group ANS-5.1, “American National Standard for Decay Heat Power in Light Water Reactors,” Standard ANSI/ANS-5.1, American Nuclear Society, La Grange Park, III, 1979. With permission of the publisher, the American Nuclear Society.

correction is less than a 6 percent increase. For cooling times of about 3 years, neutron absorption causes the fission-product decay-heat rate to increase by about 60 percent.

Decay of the actinides formed by neutron capture is another source of decay heat, although during cooling times of less than a few hundred years it contributes much less decay heat than do the fission products. The actinide nuclides that contribute appreciably during the first few days after reactor shutdown are 23.5-min 239U and 2.35-day ^’Np. The quantities of these actinides at the time of reactor shutdown can be calculated using the techniques described in Chap. 3, and their rate of decay after shutdown can be predicted from Eqs. (2.13) and 2.14). The decay-heat rate due to these two species can then be estimated as a function of T and t by multiplying the decay rates by the average thermal energy released per decay [A2]:

U = 0.474 MeV/decay

Np = 0.419 MeV/decay

For longer cooling times additional decay heat will be liberated by longer-lived actinides formed by neutron capture in the fuel material, e. g., 237U, 238Pu, 239Pu, 240Pu, 241 Pu, 241 Am, 242 Cm, ^Cm, etc., and by radionuclides formed by neutron reactions with fuel structural material, such as metal cladding. Methods and illustrative data that can be used in estimating the concentra­tions of such radionuclides and their contributions to decay heat are discussed in Chaps. 3 and 8.

Although the HTGR is not being widely used commercially, its high thermal efficiency, its ability to produce process heat at high temperatures, and its relatively efficient use of natural uranium resources when fed with thorium as fertile material give it potential future importance.

The core of the HTGR consists of hexagonal blocks of graphite pierced with two sets of longitudinal holes. One set of holes permits flow of helium coolant, whose outlet temperature may reach 1500°F, thus making possible high thermal efficiency. The other set of holes is filled with rods in which microspheres of nuclear fuel are imbedded in a graphite matrix. When the reactor first goes into operation, before a supply of 233 U has been accumulated, two kinds of microspheres are used.

In one kind, microspheres of fully enriched (93.5 w/o 233U) uranium carbide (UC2), about 200 цт in diameter, are coated with three concentric layers, called a TR1SO coating. The inner coating consists of porous graphite, to accommodate fuel swelling and fission-product gases. The intermediate coating, about 500 цт in outside diameter, consists of silicon carbide, to provide mechanical integrity for the spheres when the fuel is processed after discharge. The outer coating consists of impervious pyrolytic graphite, to retain fission products.

In the second kind, microspheres of thorium dioxide (Th02), about 500 цт in diameter, are coated with two concentric layers, called a BISO coating: an inner layer of porous graphite, to accommodate swelling and fission-product gases, and an outer layer of impervious pyrolytic graphite, to retain fission products.

During irradiation, about three-fourths of the TRISO-coated 235 U is consumed, leaving a residue of fission products and uranium whose isotopic content is around 20 percent 233 U, 25 percent 238 U, and 55 percent 236 U, formed by nonfission neutron capture in 233 U. At the same time, about 8 percent of BISO-coated thorium is converted to 233 U, some of which then undergoes fission.

When the first charge of fuel ceases to support a chain reaction, one-fourth of the fuel assemblies that have reacted most fully are replaced with fresh fuel. The spent assemblies are stored (“cooled”) for 150 days to permit some fission products to decay, 6.75-day 237 U to change to 237 Np, and 233 Th and 27-day 233 Pa formed by neutron capture in 233 Th to change to 233 U.

In processing the fuel, the first steps are to crush the graphite blocks and then bum them. The BISO-coated particles lose their graphite coating and become spheres of mixed uranium oxide consisting mostly of the 233 U isotope, and fission-product oxides. The TRISO-coated spheres lose their outer graphite coating, but the silicon carbide and inner graphite coating remain intact. The product then is a mixture of dense oxide spheres from BISO particles and less dense silicon carbide-coated graphite and U02 spheres from TRISO particles, both about 500 цт in diameter. The two kinds of particles are separated by elutriation with C02 gas, so that they can be processed separately with minimal mixing.

The residue of BISO particles is dissolved in mixed HN03 and HF and then separated by the Thorex solvent extraction process (Chap. 10) into a decontaminated M3U-rich uranium fraction, a thorium fraction containing 1.9-year radioactive 228 Th, and fission-product wastes.

The residue of TRISO particles is crushed to expose the remaining uranium and fission products. These are then dissolved in nitric acid and separated by a simplified version of the Purex process (Chap. 10) into a decontaminated uranium fraction containing around 20 percent 233 U and fission-product wastes.

Cooled Fuel, Totals 6734 kg Th 0.5 kg Po 462 kg U

26.1 kg Np

16.2 kg Pu 0.4 kg Am 0.2 kg Cm 792 kg FR

High Level Waste

0.1 kg Rj

26.1 kg Np

16.1 kgPu 0.4 kg Am 0.2 kg Cm

792 kg. FP

Figure 3.33 Fuel-cycle flow sheet for 1000-MWe HTGR fueled with thorium, enriched 23SU, once-recycled 23SU, and fully recycled 233U. Basis 1 year, 80 percent capacity factor.

In one possible fuel-cycle flow sheet for the HTGR, shown in Fig. 3.33, ^U-rich uranium from the BISO particles and the 20 percent 235 U from the TRISO particles are recycled as part of the fissile fuel for a later HTGR fuel cycle. When this is done, some of the graphite fuel blocks are charged with TRISO-coated fully enriched 235 U and BISO-coated thorium (point 1, Fig. 3.33), others are charged with TRISO-coated 20 percent 235U recycle uranium and BISO-coated thorium (point 2), and the rest are charged with BISO-coated 233 U-rich uranium and BISO-coated thorium (point 3). At the end of the cycle the spent fuel from the TRISO-coated fully enriched 23SU (point 4) is processed to recover uranium containing 20 percent 235 U to be recycled (point 2). The spent fuel from the TRISO-coated second-cycle 23S U (point 5) contains only 2 percent 235 U and is so highly contaminated by 236 U and fission products as to be discarded without reprocessing. The spent fuel from the BISO-coated recycle 235 U (point 6) and the BISO-coated thorium is processed to recover 233 U, to be recycled (point 3), and radioactive thorium, which is stored until 1.9-year 228 Th has decayed.

The quantities of uranium and thorium shown in the flow sheet Fig. 3.33 have been adapted from a study by Pigford [P2] of the fuel-cycle performance of the HTGR after a sufficient number of cycles have been operated to permit buildup of steady-state amounts of recycle 233 U and diluent 236 U. In earlier cycles the amounts of these two isotopes are lower.

The specific consumption of U308 and separative work in this HTGR cycle with 233 U recycle is compared in Table 3.16 with corresponding quantities for the LWR without or with plutonium recycle.

The HTGR with 233U recycle thus consumes about the same amount of separative work as the LWR with plutonium recycle, but uses only 65 percent as much natural uranium.

Although the isotopes of an element have very similar chemical properties, they behave as completely different substances in nuclear reactions. Consequently, the separation of isotopes of certain elements, notably 233 U from 238 U and deuterium from hydrogen, is of great importance in nuclear technology. Table 1.5 lists isotopes important in nuclear power applications, together with their natural abundance and processes that have been used or proposed for their separation. In addition to applications mentioned earlier in this chapter, Table 1.5 includes the use of 2D and 6 Li as fuel for fusion power, a topic treated briefly in Sec. 9, following.

The fact that isotopes of an element have very similar chemical and gross physical properties makes their separation particularly difficult and has necessitated the development of concepts and processes especially adapted for this purpose. In almost all isotope separation processes the degree of separation obtainable in a single stage is very small, so that many identical stages must be used for practical, useful separation. An example of this is the use of more than 4000 stages in the Oak Ridge gaseous diffusion plant. Chapter 12 describes principles that have been developed for dealing with separation processes that consist of a large number of similar stages, and hence are applicable to all methods of isotope separation.

Table 1.5 indicates that for isotopes of the light elements hydrogen, lithium, and boron, separation methods used or proposed include distillation, electrolysis, and chemical exchange. These methods for separating isotopes of light elements are described at length in Chap. 13, with principal application to deuterium. Mention is also made of methods for concentrating 13C, ISN, 170, and 180. These are isotopes of elements important in living systems that are used extensively as stable tracers in biological and medical research.

None of the conventional separation processes, such as distillation, ion exchange, or solvent

extraction, has been used for large-scale separation for isotopes of uranium or other heavy elements. To separate isotopes of uranium or other heavy elements that exist in gaseous form at convenient temperatures, it has been necessary to use gaseous diffusion, gas centrifugation, or one of the other novel processes described in Chap. 14. Gases to which these processes are applicable include xenon, MoF6, WF6, and UF6.

Another process that can be used to separate isotopes of all elements on a small scale, but that is too costly for large-scale production, is the electromagnetic method, which is based on the principle of the mass spectrometer. The electromagnetic method separated the microgram amounts of 235 U used to show [Nl] that this was the fissile isotope of uranium and was later employed by the Manhattan District to produce the first kilogram quantities of 235 U. The cost was so high, however, that the electromagnetic method was replaced by gaseous diffusion. The electromagnetic method is now used [Kl] to produce research quantities of separated isotopes of nearly all naturally occurring mixed elements. As the electromagnetic method is a physical rather than a chemical engineering process, it is not described further in this text.

Zoned loading. By charging fuel of different enrichments to different zones in the reactor, or by using a different concentration of poison in different parts of the reactor, it is possible to change the power density distribution from the undesirably nonuniform cos J0 distribution to a distribution in which more of the reactor operates at the maximum permissible power density. One general type of zoned loading, which is close to optimum for a reactor in which the fuel linear power limits thermal output, is a reactor designed to have uniform power density throughout a substantial fraction of its core. This may be done by providing fuel in a central region, in which the flux is made uniform, of lower enrichment than in the peripheral regions of the reactor, the so-called buckled zones. A similar result may be obtained by poisoning fuel more heavily in the flattened central region than in the peripheral buckled zones. In addition to its advantage of providing more uniform power density, zoned loading also has the advantage of providing uniform bumup for at least the fuel in the part of the reactor where the flux is uniform. A disadvantage of zoned loading is the need to use in the buckled, unflattened zone fuel of higher enrichment, and hence greater cost, than would be necessary with uniform loading. The bumup of fuel in the buckled zone is also very nonuniform.

Partial batch replacement. Another method of fuel management, designed to deal with the nonuniform bumup of fuel, which is a second disadvantage of simple batch irradiation, is

partial replacement of the fuel at the end of life instead of complete replacement. In this method, at the end of life only the most highly burned fuel is replaced by fresh fuel, and the rest of the charge is left in the reactor until the next time fuel has to be replaced. An example of how this might be done is shown in Fig. 3.7, which represents a cross section of a reactor core containing 320 square fuel assemblies, such as might be used in a large boiling — or pressurized-water reactor. Fuel assemblies are divided into groups containing equal numbers, each in a roughly annular zone. In the example of Fig. 3.7, five zones, each containing 64 assemblies, are shown, with zone 1 farthest from the center and zone 5 at the center. In the method of partial batch replacement, all zones initially are charged with fuel of the same composition. As irradiation proceeds, fuel in the central zone 5 is burned at a higher rate than fuel in the outer zones, because the flux is highest at the center of a uniformly fueled reactor. When it becomes necessary to replace fuel, either because fuel in zone 5 has reached the maximum permissible burnup, or because the reactor is no longer critical, only the most highly burned fuel, in zone 5, is replaced by fresh fuel, and irradiation is continued. When it again becomes necessary to refuel, the fuel then most highly burned, which will now probably be in zone 4, is replaced by fresh fuel, and so on. The advantage of this method of fuel management, of course, is that the fuel discharged each time has fairly uniform composition, because it comes from parts of the reactor where the flux has been fairly uniform. Disadvantages are (1) the need to open the reactor more frequently for refueling than when all the fuel is replaced at the same time, and (2) the peaking in flux and power density that occurs whenever fresh fuel is charged to the center of the reactor with partially depleted fuel elsewhere in the reactor, as in the first refueling of the foregoing example.

Scatter refueling. Flux peaking can be reduced by a different method of partial batch replacement, called scatter refueling, which is illustrated by Fig. 3.8. In this method, fuel is

divided locally into groups containing the same number of assemblies, in this case into 80 groups each containing four assemblies. At the first refueling, an assembly in position 1 from each group is replaced by fresh fuel. At the second refueling, the assembly in position 2 from each group is replaced, at the third refueling the assembly from position 3 is replaced, and at the fourth refueling the assembly from position 4 is replaced. At the fifth refueling, each assembly from position 1 is replaced for the second time, and so on. After this stage is reached, at the beginning of every fueling cycle, each group of four assemblies will contain one fresh assembly, a second assembly that has been irradiated for one fueling cycle, a third that has been irradiated for two cycles, and a fourth that has been irradiated for three cycles. At the end of the fueling cycle, each group of four assemblies will contain one assembly that has been irradiated for one cycle, a second that has been irradiated for two, a third that has been irradiated for three, and a fourth that has been irradiated for four cycles and is then discharged and replaced by fresh fuel. The life of each assembly extends over four fueling cycles. When the individual assemblies are small, the neutron flux in each of the four assemblies of a group is nearly the same and flux peaking in the freshest, most reactive fuel is largely prevented. The overall flux distribution is flatter than in a uniformly fueled reactor, because the fuel in the center is more highly burned and less reactive than the fuel at the outside. Some power density peaking still occurs, however, because even though the flux is nearly uniform in a group of four assemblies, the freshest assembly has a higher fissile content than ones that have been in the reactor longer.

Scatter refueling also has two important advantages over simple batch irradiation: (1) Fuel of a given composition can be irradiated to a higher bumup before reactivity is lost in scatter refueling than in batch irradiation, and (2) less control poison is needed in scatter refueling than in simple batch irradiation. Both of these advantages of scatter refueling are a consequence of the fact that each part of the reactor contains some relatively fresh fuel and some fuel

nearing the end of life. The fresh fuel maintains reactivity, while the older fuel is giving up more heat than it could in simple batch irradiation without ceasing to be critical. Furthermore, in scatter refueling, the more depleted fuel that is present at all times acts as a control poison to absorb excess neutrons from the more reactive fresh fuel. Moreover, many of the neutrons absorbed by depleted fuel are used productively to make plutonium. These advantages of scatter refueling are a feature of all methods of partial fuel replacement.

These advantages of scatter refueling may be expressed somewhat more quantitatively by considering how the reactivity p of fuel changes with bumup B. To a fair approximation, reactivity decreases linearly with bumup:

p = p0-aB (3.1)

where p0 is the reactivity of fresh fuel. In simple batch irradiation, the bumup of fuel at the end of life, 51 when p = 0, is

5i = (3.2)

a

The amount of reactivity to be held down by control poison at the beginning of life, pi when В = 0, is

Pi — Po (3-3)

To find the reactivity-limited burnup of fuel in и-zone scatter refueling, B„, note that at the end of life, the freshest nth fraction of fuel will have had burnup of approximately B„/n, the next older nth fraction 2Bn/n, etc., and the oldest nth fraction, ready for discharge, will have reached B„ bumup. The reactivity of this mixture of fuel is

But p = 0 at the end of life, so that

= 2np0 a(n + 1)

The ratio of the burnup obtainable in и-zone scatter refueling to that obtainable in simple batch irradiation is found by dividing Eq. (3.5) by (3.2):

in _ 2n Bl n + 1

The reactivity of fuel in и-zone scatter refueling at the beginning of a cycle is

By using (3.5),

The ratio of the reactivity change per cycle in n-zone scatter refueling to the amount in simple batch irradiation is

Pn _ ____ 2__

Pi n + 1

Values of these ratios for several values of n, the number of zones of assemblies, are tabulated below.

Thus, four-zone refueling permits attainment of 60 percent more bumup than simple batch refueling, with only 40 percent as much poison needed to control reactivity changes. The time between successive fuel replacements is only 40 percent as long in four-zone refueling as in batch, however.

Graded refueling. These equations and table show that increasing the number of zones continues to improve bumup and reduce reactivity changes, until the bumup approaches twice that obtainable from batch irradiation, and the reactivity change approaches zero. It is not feasible to approach these limits in water-moderated reactors, because fuel assemblies are relatively large, and even the biggest reactors contain only a few hundred assemblies at most, so for the reactor to contain a reasonable number of groups, six assemblies per group is practically an upper limit. Moreover, these reactors have to be shut down and opened to replace fuel, and fueling interruptions would occur too frequently with much more than six assemblies per group.

Graphite-moderated, gas-cooled reactors, on the other hand, make use of thousands of fuel assemblies and are equipped with fueling machines that permit replacement of individual assemblies without interrupting reactor operation. In these reactors it is possible, therefore, to have a large number of assemblies per group and to refuel continuously during operation. Under these conditions, fuel within the reactor is graded almost continuously in composition from fresh unbumed fuel to fully burned fuel ready for replacement. The limiting continuous case of scatter refueling with n very large is sometimes called graded refueling. In graded fueling, when it is not necessary to shut down the reactor to refuel, it is possible to keep each assembly in the reactor until it has received the same bumup; whereas in scatter refueling, with a fixed fraction of fuel replaced at the same time, fuel removed from the center of the reactor is more heavily burned than fuel removed from the outside. Because the average composition and reactivity are constant in time, and all fuel discharged has the same composition, graded fueling is easier to treat analytically than scatter refueling with a finite number of assemblies per group, because of the changes in average composition and reactivity that then take place in each cycle.

Out-in refueling. Graded and scatter refueling have the disadvantage that the flux is higher in the center of the reactor than at the outside, although the nonuniformity is not so great as in simple batch irradiation because some highly burned fuel is always present at the center in graded and scatter refueling. An alternative method of fueling designed to depress the flux and power density further at the center of a reactor is out-in fueling. In this method, fuel is divided into annular zones of equal volume, such as those shown in Fig. 3.7. At the end of the first fueling cycle, fuel from central zone 5, the most heavily burned, is removed from the reactor; fuel from zone 4 is moved into zone 5; fuel from zone 3, to zone 4; fuel from zone 2, to zone 3; fuel from zone 1, to zone 2; and fresh fuel is charged to zone 1. At the end of each subsequent fueling cycle, this sequence of fuel movements is repeated. All cycles after the first few are similar, with the same cycle time, the same average burnup of discharged fuel, and the same change in reactivity. As fuel in the center of the reactor is most heavily depleted and least

reactive, the flux and power density are depressed there relative to a uniformly fueled reactor. The upper half of Fig. 3.9 shows the power density distribution calculated by Westinghouse [Dl] for three-zone out-in fueling of a 260-MWe PWR, with a core 1.25 m in radius operated at a burnup of 15,000 MWd/MT. The ratio of radial peak to average power density is 1.3, compared with about 1.5 for simple batch irradiation in this same reactor. The ratio of bumup with three-zone out-in fueling to bumup in batch fueling is about 1.5, as predicted by Eq. (3.6), which is approximately valid for this case also. Thus, out-in fueling has many advantages for a reactor of this size. ‘

For larger reactors with high burnup, however, out-in fueling leads to too great a depression in the flux and power density at the center of the reactor. This may be seen from the lower half of Fig. 3.9, which shows the power density calculated by Westinghouse [Dl ] for three-zone out-in fueling of a 1000-MWe PWR, with a core 6.5 ft in radius, operated at a burnup of 24,000 MWd/MT. At the beginning of a cycle, the flux peaks heavily in the outside zone, and the peak-to-average radial power density ratio is 2.0. The reason for this poor

distribution is that the extra neutrons produced in the reactive outside zone 1, which are needed in the relatively unreactive central zone 3, must diffuse through a larger distance and hence require a greater flux difference than in a smaller core, with less reactivity difference.

Modified scatter refueling. For the largest reactors a combination of out-in and scatter refueling gives better results than either alone. Figure 3.10 shows how five-zone modified scatter refueling works. In this example for reactors with square fuel assemblies, fuel positions are divided into an outer zone 1 containing one-fifth of the fuel assemblies, and an inner zone containing the other four-fifths. Fuel in the inner zone is divided into groups of four for scatter refueling. At each refueling, the most heavily burned assembly in each group of four is removed from the inner zone and replaced by an assembly from the outer zone, which is moved in its entirety into the inner zone. Fresh fuel is then charged to the outer zone.

In this way the more depleted, less reactive inner zone is made to act rather like the flattened zone of zoned loading and the fresh fuel at the outside acts like the buckled zone. The peaking of power density at the center of a reactor using simple scatter refueling is reduced, without the overcompensation occurring with out-in fueling in a large reactor. The small reactivity change and high bumup obtainable with five-zone out-in or scatter refueling are realized.