Because the reactivity follows closely a linear relation with burnup, it is possible to predict the burnup B„ obtainable in «-zone fuehng with 3.2 w/o 23SU by the approximate equation (3.6), which for this case becomes

B„ = 20,833 —— (3.83)

(1 T 1 ‘

Burnups for «-zone fueling predicted by this equation are compared below with those obtainable by Watt [W2] using computer codes CELL [B2] and CORE [К1].

The agreement is remarkably good, considering that the computer codes take into account the changes in cross sections and reactor parameters that occur as fuel composition changes, and also follow spatial nonuniformities in flux and fuel composition. All these factors have been neglected in this section.

Figure 3.30 Change of reactivity in PWR with burnup. (o) Equation (3.35) and Table 3.15; (—) Eq. (3.82).

1.1 Uranium Fuel

The fuel processing operations to be used in conjunction with a nuclear power reactor and the amount of nuclear fuel that must be provided depend on the type of reactor and on the extent to which fissile and fertile constituents in spent fuel discharged from the reactor are to be recovered for reuse. Figures 1.10 and 1.11 outline representative fuel processing flow sheets for uranium — fueled thermal reactors generating 1000 MW of electricity, at a capacity factor of 80 percent.

The simplest flow sheet, Fig. 1.10, is applicable to heavy-water reactors fueled with natural uranium containing 0.711 w/o 235 UX Feed preparation for this type of reactor consists of purifying natural uranium concentrates, converting the uranium to U02, and fabricating the U02 into fuel elements. In this type of heavy-water reactor, fission of 235 U initially present in the feed and fission of plutonium formed from 238 U will produce about 6800 MWd of heat per metric ton (1 MT = 1000 kg) of fuel before the fuel is so depleted in fissile material and so loaded with neutron-absorbing fission products that the reactor is no longer critical. Since the heat of fission is 0.95 MWd/g, complete utilization of 1 MT of fuel would generate 950,000 MWd of heat. In this type of thermal reactor, thus, 6800/950,000 = 0.0072 fraction of the natural uranium, about 0.7 percent, is converted to heat.

As the efficiency of conversion of heat to electricity in a heavy-water nuclear power plant is about 30 percent, the rate at which a 1000-MW plant would have to be supplied with natural uranium is

(0.8X1000 MWX1000 kg/MT) = ,,,

(6800 MWd/MTX0.3) 8/ y

or 143 MT of uranium per year.

In commercial transactions uranium concentrates are measured in short tons (2000 lb) of U308. In this unit, the annual uranium consumption of this reactor would be

(143 MT UX1-1023 short tons/MTX842 MT U3Os/714 MT U,) = л tons y Q (1 ^ 0.995 3

assuming 99.5 percent uranium recovery in conversion.

Spent fuel discharged from this reactor contains about 0.2 w/o plutonium and about 0.3 w/o 235 U. This content of fissile material is so low that its recovery is hardly economical, so that no recovery step has been shown.

Figure 1.11 shows three possible fuel processing flow sheets for reactors cooled and moderated by light water. The specific example shown is for a pressurized-water reactor. Fuel for this type of reactor consists of U02 enriched to around 3.3 w/o in 235 U. The expected performance of this type of reactor is described in some detail in Chap. 3, Sec. 7. After

^w/o = weight percent.

m. SPENT FUEL REPROCESSED, URANIUM AND PLUTONIUM RECYCLED

Figure 1.11 Fuel processing flow sheets for 1000-MWe pressurized-water reactor. Basis: 1 year, 80 percent capacity factor.

producing 33,000 MWd of heat per metric ton, the fuel ceases to support the fission chain reaction and must be discharged from the reactor. This spent fuel still contains around 0.83 w/o 23SU and about 0.6 w/o fissile plutonium. In part I of Fig. 1.11 this spent fuel is stored without reprocessing, as in the heavy-water reactor example of Fig. 1.10. The annual consumption of U308 for the light-water reactor, without reprocessing, is 262 short tons U308, substantially greater than for the heavy-water reactor.

Under some conditions it is economically attractive or environmentally preferable to reprocess spent fuel in order to (1) recover uranium to be recycled to provide part of the enriched uranium used in subsequent lots of fuel, (2) recover plutonium, and (3) reduce radioactive wastes to more compact form. In part II of Fig. 1.11 the recovered 0.83 percent enriched uranium is recycled and the 244 kg of plutonium recovered per year is stored for later use in either a light-water reactor or a fast-breeder reactor. This recycle of uranium to the isotope separation plant reduces the annual U308 feed rate to 220 short tons, still appreciably greater than for the heavy-water reactor.

In part III of Fig. 1.11, the recovered uranium is recycled and reenriched and the recovered plutonium is recycled to provide part of the fissile material in the reactor fuel assemblies. Two kinds of fuel assemblies are used. One kind is the same as used in cases I and II, which consist of U02 enriched to 3.3 w/o 235 U. The annual feed rate of these assemblies is 18.3 MT of enriched uranium. The other kind consists of mixed uranium and plutonium dioxides, in which the uranium is in the form of natural U02. Their annual feed rate is 8.9 MT of heavy metal (uranium plus plutonium), including 445 kg of recycle plutonium. The total annual U308 feed rate is 160 short tons, which is less than for the heavy-water reactor of Fig. 1.10.

In part III of Fig. 1.11, the 160 short tons of U308 consumed per year corresponds to a daily feed rate of 341 kg natural uranium. As this pressurized-water nuclear power plant has a thermal efficiency of 32.5 percent, the fraction of the natural uranium feed converted to energy is

(0,8X1000 MW/0.325) _

(341 kg/day)(950 MWd/kg) ‘

Even with plutonium recycle, thus, this thermal reactor converts less than 1 percent of natural uranium to energy. This low uranium utilization results from the fact that the conversion ratio of 238 U to plutonium in a thermal reactor is less than unity.

In a fast reactor, on the other hand, the conversion ratio can be greater than unity, and almost all of the uranium can be converted to energy, in principle. Figure 1.12 shows the fuel processing operations associated with a fast-reactor power plant breeding plutonium from 238 U. Because of the low absorption cross section of plutonium for fast neutrons, it is necessary to use a mixture of about 20 percent plutonium and 80 percent 238 U in the core of such a reactor and to surround the core with a blanket of natural or depleted uranium to absorb neutrons leaking from the core and convert them to plutonium. Two types of fuel elements must be prepared for a fast-breeder reactor, then, blanket elements fabricated from natural or depleted uranium, and core elements containing around 20 w/o plutonium. Most fast reactors under development propose use of mixed Pu02-U02 for core elements; mixed PuC-UC is also being considered. The core elements of a fast reactor are expected to generate from about 65,000 to 100,000 MWd of heat per metric ton before discharge; as they still contain nearly their original plutonium content, reprocessing is required. The blanket elements also must be reprocessed for plutonium recovery. Some savings can be effected by reprocessing both types of elements together, as shown in Fig. 1.12. Uranium recovered in the reprocessing plant can be recycled to provide most of the uranium used to prepare core and blanket elements. Plutonium recovered in the reprocessing plant provides all the enrichment needed for core elements, plus the net production of plutonium from the plant. With good conservation of neutrons in the reactor and efficient recovery of plutonium in reprocessing and core fabrication, a 1000-MWe fast-reactor

power plant is expected to breed about 265 kg/year of net plutonium product. A fast-reactor power plant cooled with sodium or helium is expected to have a thermal efficiency of 40 percent. If it could convert 100 percent of its uranium feed to heat, a 1000-MWe plant would consume only

of uranium. Because of reprocessing losses and conversion of some uranium to nonfissile isotopes, the uranium consumption of a practical fast-breeder system is expected to be somewhat greater, perhaps 4 kg/day, or 1.5 MT/uranium/year. This is much less than for a thermal reactor, and could be in the form of the depleted uranium tailings from the isotope separation plant of Fig. 1.11.

Section 1 of this chapter lists the principal fuels used in nuclear reactors, and Sec. 2 describes the effects of reactor irradiation on them, with emphasis on changes in fuel composition and reactivity. Section 3 describes methods of managing fuel and neutron-absorbing poisons aimed at increasing energy production, while reducing costs and controlling deterioration of fuel. Section 4 goes into some detail regarding fuel management in a pressurized-water reactor (PWR) and gives the results of computer calculations of fuel-cycle performance. Section 5 develops a procedure for calculating fuel-cycle costs and applies it to this PWR example, using cost bases anticipated for the year 1980. Section 6 develops an approximate method for calculating the fuel-cycle performance of a PWR suitable for hand calculation and compares the results with more precise ones obtained from a computer code. Section 7 presents fuel-cycle flow sheets for a PWR whose fuel is enriched with 235 U or plutonium, a high-temperature gas-cooled reactor (HTGR), and a liquid-metal fast-breeder reactor (LMFBR).

The principal objective of this chapter is to develop an appreciation of the demands made by the reactor on the steps in the nuclear fuel cycle that provide fuel for the reactor and reclaim fuel from it.

Gamma rays are photons—electromagnetic radiation-given off when a nucleus undergoes transition from a state of higher energy to one of lower energy. The wavelength X of the radiation is related to the energy change AE of the nucleus emitting this quantum of radiation (or photon) by the equation

(2.8)

Figure 2.3 Range of beta particles in aluminum. For other materials, a useful approximation is that the range is inversely proportional to the density of electrons.

2.997925 X 10s m/s. Because energy changes of 0.1 MeV or more are common, gamma rays have wavelengths less than 1.2 X 1СГ9 cm. This is much shorter than the wavelength of visible light, around 10"5 cm. Gamma rays are in fact hard, or high-frequency, x-rays. They penetrate relatively great thicknesses of matter before being absorbed. Instead of having a well-defined range, like alpha or beta particles, a beam of gamma rays loses a certain fraction of its intensity per unit distance traveled through matter. The thickness of air, water, concrete, and lead required to dissipate one-half the intensity of a beam of gamma rays is plotted against energy per photon in Fig. 2.4.

Figure 2.4 Thickness required to reduce the intensity of a beam of gamma radiation by a factor of 2.

Because of the penetrating nature of gamma radiation, overexposure of the body to it results in deep-seated organic damage. Of the three types of radiation from radioactive substances, gamma radiation is by far the most serious external hazard and is the one that requires heavy shielding and remotely controlled operations.

Because a photon has neither charge nor mass, the parent and daughter nuclides in a gamma-radioactive transformation are nuclear isomers. A few gamma-active nuclides have half-lives long enough to be isolated and studied. Some of these are listed in Table 2.3. Many gamma-emitting nuclides resulting as products of alpha — or beta-radioactive decay have such short lives that the gamma ray appears to occur simultaneously with the alpha or beta emission that produced the gamma-active isomer. Data on gamma rays are customarily given with data on the parent alpha or beta emitter even though the gamma ray comes from the daughter nuclide. Frequently a number of gamma rays are emitted in cascade, as the unstable nuclide rapidly moves through several intermediate energy states before reaching its ground state. An example of this in the decay of ‘^Ba is shown in Fig 2.5.

If this refueling pattern with 3.2 w/o fresh fuel is repeated through additional cycles, the fuel-cycle performance in cycles 7 and 8 will be as shown in Figs. 3.23 and 3.24. The relative power and burnup per cycle found in each location in cycle 7 and cycle 8 are almost identical, and the average burnup per cycle is exactly the same, 10,081 MWd/MT. This is evidence that a steady-state condition has been reached.

Table 3.3 summarizes the fuel-cycle performance of this reactor through the first eight cycles. The maximum value of the relative power, in the next-to-last column, levels off at a

value of 1.37. The average burnup of fuel levels off at a value of 30,400 MWd/MT. Table 3.3 shows that when a reactor is refueled for a sufficient number of cycles in identical fashion, its performance in each cycle reaches a repetitive, steady-state behavior. When this occurs, the sum of the bumups of all assemblies discharged [(64X30,400)= 1,945,600] approaches the bumup increment of all assemblies in the reactor [(193X10,081)= 1,945,633].

Table 3.4 gives the relative power at the beginning of steady-state cycle 8 and the bumup of each assembly at the end of this cycle. The maximum relative power is 1.70 (acceptable), the maximum local burnup is 38,052 MWd/MT, and the maximum assembly burnup is 35,991 MWd/MT. Fuel can probably tolerate this much burnup without excessive mechanical deteriora­tion.

Center­

line

Fuel Lot 1 Initially 2.25 w/о U-235

Fuel Lot 2 Initially 2.80 w/o U-235 Fuel Lot 3 Initially 3.30 w/o U-235 Fuel Lot 4 Initially 3.20 w/o U-235

Cycle Average Burnup « 9,652 MWd/MT Cycle Thermal Energy * 835.2 GWd

Center­

line

Fuel Lot 2 Initially 2.80 w/o U-235

Fuel Lot 3 Initially 3.30 w/o U-235

Fuel Lots 4, 5 Initially 3.20 w/o U-235

Cycle Average Burnup « 9894 MWd/MT Cycle Thermal Energy = 866.5 GWd

Figure 3.22 PWR, assembly power and burnup distribution, cycle 3.

The change in number of atoms of neutron-absorbing nuclide N with time due to neutron reactions alone, and in the absence of a source of this nuclide, is

dN

^ = — oe01V (2.80)

where the product оаф represents the sum of the effective аф products defined in Sec. 4.7.

For time-independent effective cross sections and neutron flux, Eq. (2.80) integrates to

ЛГ = №е-0«*’ (2.81)

where № is the number of atoms at t = 0. оаф is sometimes referred to as the “burnout constant,” and In 2/оаф is the half-life for burnout. For example, in a flux of 1014 n/(cm2,s), the half-life for burnout of a nuclide with an absorption cross section of 100 b is

If neutron absorption in species 1 results in a single nuclear reaction with a nonradioactive product, the number of product atoms N2 formed is

N2 =№(l -е-°°фт) (2.83)

If two or more competing reactions take place, the number of stable product atoms formed is

N2 =№ ^( 1 — е-°“фг) (2.84)

°a

where ac is the capture cross section for the reaction producing the product nuclide in question. Modification of these equations for simultaneous neutron reaction and radioactive decay will be treated in Sec. 6.

This section presents flow sheets giving the amount of nuclear materials consumed and fuel-cycle services required per year for four reactor systems: light-water reactor (LWR) fueled with slightly enriched uranium (Sec. 7.1); light-water reactor fueled with plutonium and natural uranium (Sec. 7.2); high-temperature gas-cooled reactor (HTGR) fueled with thorium, fully enriched 235 U, and recycle 233 U (Sec. 7.3); and liquid-metal fast-breeder reactor (LMFBR) (Sec. 7.4). These flow sheets have been adapted from studies by Pigford [PI, P2], which used consistent assumptions regarding cross sections and nuclide quantities transferred between different reactor types. As the bases for these studies were slightly different from those used for light-water reactors earlier in this chapter, the material quantities in Sec. 7.1 differ slightly from those in Secs. 5 and 6.

Figure 1.13 shows fuel processing arrangements needed for the two types of thorium-fueled reactors mentioned in Sec. 4. As the conversion ratio of the high-temperature gas-cooled reactor (HTGR) is slightly less than unity, feed for this reactor consists of thorium plus some highly enriched 235 U from a uranium isotope separation plant. In the fuel preparation operation thorium, enriched UF6, and uranium recovered from spent fuel and recycled are formed into fuel elements consisting of the carbides ThC2 and UC2 or the oxides Th02 and U02 clad with graphite. Fuel processing after irradiation consists of burning the carbon out of the fuel, followed by separation of the mixed oxides by solvent extraction into uranium to be recycled and radioactive fission products and thorium to be stored. The recycled uranium is a mixture of isotopes, mostly »>U formed by absorption of neutrons in thorium. More detail is given in Chap. 3.

Fuel processing operations for the molten-salt breeder reactor are simpler in principle than for the HTGR. As the conversion ratio is expected to be above unity, no fissile feed is needed

after the reactor and its fuel cycle are in steady state. As the reactor uses fluid fuel, no fuel fabrication is required. Net feed for the reactor consists merely of ThF4, to replace thorium converted to 233 U, and BeF2 and 7LiF, to replace solvent salt withdrawn from the reactor to purge certain fission products. Fuel reprocessing for this reactor is conducted by high — temperature, nonaqueous methods. These methods remove fission products and net bred uranium and return the fissile uranium to solution in the molten salt, so that no reenrichment or fabrication of the recycle uranium is required.

As the fuel in a nuclear reactor is irradiated, it undergoes nuclear transmutations that cause its composition to change in the following ways:

1. Fissionable material is consumed.

2. Neutron-absorbing fission products are formed.

3. Heavy nuclides, mainly isotopes of uranium and plutonium, are formed.

These changes in composition bring about changes in reactivity of the fuel, which eventually decreases to such an extent that the reactor will no longer be critical unless the spent fuel is replaced with fresh fuel.

The changes in fuel composition to be discussed in this chapter take place over a much longer period of time than the buildup of 13SXe and 199Sm to steady-state concentrations, because the cross sections of the nuclides involved are much smaller, being less than 2200 b for the most part. These changes continue to take place during the entire lifetime of the fuel charge, which may be as great as a year or more. The changes in reactivity caused by changes in composition of all nuclides except 13SXe and 149 Sm are called long-term reactivity changes.

One of the principal objectives of fuel-cycle analysis is to follow quantitatively the changes in concentration of fissile and fertile nuclides and fission products during neutron irradiation.

Another important objective is to follow the changes in reactivity that take place as fissile nuclides are depleted or formed from fertile nuclides, and as neutron poisons are formed through buildup of fission products or burned out through reaction with neutrons.

A third important objective is to follow the shifts in flux and power density distribution that take place in a reactor as a result of spatially nonuniform changes in fuel composition and reactivity. Calculation of these shifts in flux and power density, however, requires very detailed attention to local changes in composition. These calculations cannot be readily carried out by simple analytic or graphic procedures and must be done with a high-speed computer. Consequently, this chapter is concerned primarily with changes in fuel composition and reactivity and discusses only briefly changes in flux and power density distribution. Primary emphasis is placed on determining the fraction of fuel that can be made to undergo fission before the reactor ceases to be critical, as this determines the amount of heat that can be produced from the fuel, and the composition of spent fuel discharged from the reactor, as this is related to its value if processed for reuse.

Figure 3.3 is an example of the change in composition of fuel in a PWR during irradiation, calculated by the computer code CELL [B2]. In this example fuel charged to the reactor contained 3.2 w/o 235 U in total uranium. The extent of irradiation, plotted along the x axis, is
expressed in terms of the “burnup,” in megawatt-days per metric ton (MWd/MT), which is the same as kilowatt-days per kilogram. This is the amount of heat liberated by the fuel through fission and other nuclear reactions. Because complete fission of 1 g of 235 U produces 0.948 MWd of heat, burnup of 10,000 MWd/MT (1 Mg) corresponds to fission of around

(10,000) (100)

(1,000,000) (0.948)

This figure shows that 235 U concentration decreases almost exponentially with bumup. 236 U, a neutron-absorbing isotope of uranium, builds up to a concentration of around 0.4 percent of total fuel. »Pu, a fissionable isotope, builds up to a concentration of around 0.6 percent. *<>Pu builds up more slowly to around 0.3 percent. When 240Pu absorbs a neutron, 241 Pu, another fissionable isotope, is formed. When this absorbs still another neutron, 242 Pu, a neutron
absorber, results. The net effect is that 239 Pu and 241 Pu are desirable isotopes, which increase the reactivity of fuel, and 240Pu is not detrimental because it makes a fissionable isotope. 242 Pu, however, like 236 U, is a deleterious, neutron-absorbing end product.

The changes in fuel composition just described cause the reactivity of the fuel to decrease with increasing bumup. The reactivity is defined as the difference between the rate of neutron production by fuel and the rate of neutron consumption, divided by the rate of neutron production. If the reactivity is zero, the reactor will be just critical without insertion of control poisons; if the reactivity is negative, the reactor power will die out; if the reactivity is positive, the reactor can be brought to a steady power level by insertion of sufficient neutron-absorbing control poison to reduce its reactivity to zero. Figure 3.4 shows how the reactivity of a PWR whose fuel composition is spatially uniform decreases with bumup. Lines are plotted for four different initial fuel compositions: 2.8, 3.2, 3.6, and 4.0 w/o 235 U. To a rough approximation, reactivity decreases linearly with bumup and increases linearly with w/o 235 U in fuel at the start of irradiation.

The reactivity of fuel in an actual reactor differs from Fig. 3.4 in two respects. First, Fig. 3.4 refers to a very large reactor, so large that neutron leakage to the outside has negligible effect on reactivity. A finite-sized reactor would have somewhat less reactivity than plotted here; the reactivity of a 1060-MWe PWR would be about 0.05 units less. Second, the composition of fuel in an actual reactor is nonuniform spatially, both because fuel of different composition may be placed in different positions in the reactor and because the composition of

Figure 3.4 Change of reactivity with bumup for uniformly fueled infinite PWR.

fuel in different locations changes at different rates since the neutron flux is nonuniform. For these two reasons, Fig. 3.4 can give only general trends; determination of the change of reactivity with bumup in a practical reactor and the amount of energy that a given change of fuel can produce before the reactor ceases to be critical requires very detailed analysis of changes in composition and reactivity taking place at many different locations throughout the reactor.

Reactivity decreases with increasing bumup because the increase in 239 Pu and 241 Pu content is not sufficient to compensate for the decrease in 235 U content, and because 236 U, *°Pu, 242 Pu, and fission products, whose content increases, are neutron-absorbing poisons.

Another very important effect of irradiation on fuel, which is noted here but not discussed further, is the change in physical properties that takes place. Fuels often change dimensions and swell, blister, or crack. Fission-product gases may be released and build up appreciable pressure inside cladding. Physical properties important in limiting fuel performance, such as thermal conductivity, may be changed. In many cases impairment of physical properties or intolerable dimensional changes limit the amount of heat that can be obtained from fuel rather than loss of reactivity. In a well-designed reactor, however, physical properties should remain satisfactory until fuel ceases to be critical. Currently, U02 fuel for LWRs is being designed to remain intact until about 3.5 percent fissions, corresponding to generation of around 35,000 MWd of heat per metric ton of fuel (35,000 MWd/MT). For fast reactors whose fuel is more expensive to fabricate, bumups of 100,000 MWd/MT are thought to be desirable for maximum economy.

The transition involving the emission of a positron, i. e., a positively charged electron, is, in fact, another form of beta decay. Within the nucleus a proton is converted to a neutron. The positron is continuously distributed in energy up to some characteristic maximum energy, similar to the distributions of Fig. 2.2, accompanied by a corresponding distribution of neutrino energy. The emitted positively charged electron, as it passes through the field of atomic electrons in the surrounding matter, undergoes strong electrostatic attraction to these atomic electrons. The positron and negative electron then annihilate each other in a single reaction, and the resulting energy appears as two photons moving in opposite directions, each with an energy of 0.511 MeV. Further examples of positron-emitting nuclides are listed in Table 2.4.