2.3 Procedure for Calculating Fuel-Cycle Costs

To calculate fuel-cycle costs, it is necessary to focus attention on individual fuel sublots and determine:

1. The amount and composition of each sublot when charged to the reactor

2. The amount of electricity generated by each sublot in each period in which electricity is paid for

3. The amount and composition of each sublot when discharged from the reactor

4. The cost incurred in each step for preparing fuel before it is charged to the reactor

5. The cost or credit incurred in each step for recovering fuel after it is discharged from the reactor

6. The time at which each cost is paid or each credit is received, and the time at which revenue is received for each increment of electricity generated by each lot of fuel

A somewhat simplified, approximate procedure for calculating fuel-cycle costs will be illustrated by the example of sublot 2A of the PWR whose fuel management was described in

Assembly Number BOC Burnup, MWd/MT EOC Burnup, MWd/MT BOC Relative Power (Assent)!у /Average)

Center­

line

Fuel Lots 7, 8. 9. 10 Initially 3.20 w/o U-235

Assembly Number BOC Burnup, MWd/MT EOC Burnup, MWd/MT BOC Relative Power (Assembly/Average)

Figure 3.24 PWR, assembly power and burnup distribution, cycle 8.

Sec. 4. Information on material quantities and energy production from sublots 1A through 4B in cycles 1, 2, and 3, applicable to this example calculation, is given in Table 3.5.

The 63 assemblies of sublot 2A contain 28,171.8 kg of uranium enriched to 2.8 w/o aU. The average bumup experienced by this sublet is 16,448 MWd/MT in cycle 1 and 8700 MWd/MT in cycle 2, for a total bumup B2a of 25,148 MWd/MT. The total thermal energy produced by this sublot is

(25,148 MWd/MTX28.1718MTX24,000 kWh/MWd)= 17,003 X 106 kWh Calculations by computer code LEOPARD made by Rieck [Rl] predict that this fuel wnen

exposed to burnup of 25,148 MWd/MT will contain 27,991 kg of uranium enriched to 0.920 w/o 235 U and 161.330 kg of the fissile isotopes of plutonium 239Pu and 241 Pu.

To obtain the durations of cycles 1 and 2, and from them the times at which payments are made, credits received, and revenue obtained from the sale of electricity, the total thermal energy per cycle Ht is required and is calculated from burnup increments in the next to the last row of the table. The duration of irradiation during the ith cycle, r,-‘ — /’■, in years is obtained from Hi in the last row of the table, using a rated thermal output of 3.250 GW.

Figure 3.25 is a schematic flow sheet for lot 2A fuel cycle. This shows the fuel-cycle steps to be considered and defines notation for the material and service quantities involved in each step, the total cost or credit associated with each step, and the timing of all transactions (dashed arrows).

Table 3.6 gives numerical values for material quantities, unit costs or credits, and total direct costs or credits involved in each fuel-cycle step and calculates the overall net direct cost for lot 2A as $26.4 million. A total of $27.8 million is paid out for UF6 and fabrication in transactions 1 and 2 before any revenue is received from the sale of electricity. Because of this delay in receiving revenue, the total fuel-cycle cost includes also charges for carrying the $27.8 million advanced several years before it is recovered through revenue from the sale of electricity. Similarly, there is a financing charge on the net credit of $1.4 million in steps 3 through 6, delayed until after revenue is received from the sale of electricity.

The assumptions going into the calculation of direct costs in Table 3.6 will be described first. Then the procedure for calculating financing charges will be described, and finally a value will be given for the complete fuel-cycle cost.

Direct costs. The unit costs used in the examples of this chapter are those anticipated in 1975 for the year 1980. Because of changes since 1975, readers are cautioned to regard these costs more as examples than as firm numbers.

The unit cost of enriched uranium in the form of UF6 depends on the 235 U content of the uranium, the price paid for the natural uranium from which the uranium was enriched, the cost of the separative work expended in enriching the uranium, and the composition of the tails stream containing depleted uranium leaving the uranium enrichment plant. The procedure for calculating the cost of enriched uranium is described in Chap. 12. The unit costs

Сц[6] = $848.66/kg U for uranium enriched to 2.8 w/o 235 U fed to fabrication and cV" = $152.83/kg U for uranium containing 0.920 w/o 235 U recovered from reprocessing are based on the following assumptions:

Price of natural uranium ore concentrates, $31.55ДЬ U308

Price of natural UF6, $89.11/kg U

Cost of separative work, $100/separative work unit

235 U content of enrichment plant tails, 0.3 w/o

Thermal energy per cycle, GWh

Я/ = 24 X 10~6 Ujf ABjic 32,188 20,044 §

Duration of irrad.,yr 8766XJ250X a9 1-2553 0.7817 8 1

It is assumed that /’ = 0.99 fraction of uranium charged in the form of UF6 will be recovered as fabricated fuel. Hence, to provide U’= 28,171.8 kg of fabricated uranium, 28,171.8/0.99 = 28,456.364 kg uranium in the form of UF6 must be purchased. The direct cost of this UF6 is 28,456.364 X 848.66 = $24,149,778.

A similar procedure is used to calculate the other components of the direct cost shown in Table 3.6. Other assumptions are as follows:

Fraction of uranium and plutonium recovered in reprocessing, f" = 0.99.

Fraction of recovered uranium converted to UF6,/’" = 0.995.

The fabrication unit cost of $130/kg includes cost of converting UF6 to U02 and packaging U02 in fuel assemblies.

The shipping cost of $30/kg includes storage charges at the reactor for around 150 days to permit fuel radioactivity to decrease.

The reprocessing and conversion cost of $180/kg includes charges by the government for perpetual storage of radioactive wastes.

Financing charges. A company generating electricity that pays out Z dollars for fuel-cycle costs t years before it receives revenue from generation of electricity from that fuel must pay to the bondholders and stockholders who advanced the funds for the fuel the return they require on their investment, and must also pay income taxes to the government on the profits from which the stockholders’ return is obtained. It is possible to represent all of these financing charges as the product yZt, where у is known as the annual cost of money before income taxes. For a privately owned U. S. electric company, a value of у = 0.151 per year is representative.

To find the total fuel financing charge, it is necessary to find the amount of money advanced for fuel as a function of time. Figure 3.26 is a schematic plot of the amount of

Figure 3.26 Plot of dollars invested in fuel versus time.
money invested in fuel cycle as a function of time for an example like sublot 2A, in which revenue is assumed received from the sale of electricity at two times during irradiation, from sale of Ex kWh at time r, in cycle 1 and from sale of E2 kWh at time t2 in cycle 2. The generalization to a more realistic case, in which revenue is received at more times, should be clear.

At time fu’, Zxj’ dollars are invested in enriched uranium. This amount of money is invested for tFa — tV’ years, until tFm when ZFa more dollars are paid out to fabricate fuel. The financing cost of carrying the initial investment of Zy> dollars for tFa — ty’ years is the product of the cost of money before income taxes, y, and the area of region A, Zy(tFa — fu’)-

Between tFtt, when fabrication is paid for, and f1; when revenue is received from production of Ex kWh of electricity, the dollars invested in fuel is Zy’ + ZFm and financing costs are the product of у and area B, (Zu’ + ZFa)(tx ~ tFa).

If the total electricity production of the lot of fuel is I, mEm (Ex + E2 for sublot 2A) and the net direct fuel-cycle cost is Z/Z/=Z (where Zj is the direct cost of the /’th fuel-cycle step and ZjZj = $26,439,162 for sublot 2A), the amount of money invested in fuel after tx should be reduced by ZExl(Ex + E2 ). Between fj and t2, when the second (and in this case, the last) revenue is received from production of E2 kWh of electricity, the dollars invested in fuel is Zy + ZFa — ZExl(Ex + E2), and financing costs are the product of у and area C, [Zy< + ZFa-ZEi/(Ex +E2)} (t2-tx).

The amount of electricity generated by sublot 2A in cycle 1, Et, is obtained from the thermal efficiency of the power plant

77 = ilr = 032615 (ЗЛ4)

the average burnup increment of sublot 2A in cycle 1, AB12a = 16,448 MWd/MT from Table 3.5, and the mass of uranium, U2a =28,171.8 kg. Hence

Ex = 24n ABxzaU’ia = (24)(0.32615)(16,448)(28,171.8) = 3.6271 X 109 kWhe (3.15) Similarly, the amount of electricity generated by sublot 2A in cycle 2 is

E2 = (24)(0.32615) (8700)(28,171.8) = 1.9185 X 109 kWhe (3.16)

The total electric generation is

E = Ex +E2 = (3.6271 + 1.9185) X 109 = 5.5456 X 109 kWhe (3.17)

Between t2 and t$h when payment is made for shipping fuel, the dollars invested in fuel is the difference between the initial outlay Zy’ + ZFa and the direct fuel-cycle cost Z, which is equivalent to

Zy’+ ZFa — Z = Zy" + Z? — Zsh — ZR (3.18)

The financing cost for this time interval is the product of у and area D, (Zy" + ZP — Zr —ZSh)(tsh ~h)-

Between tgh and tR, when payment is made for reprocessing fuel and converting uranium to UF6, the dollars invested in fuel is Zy" + Zp — ZR. The financing cost for this time interval is the product of у and area E, (Zy" + ZP — ZR)(tR — tsh).

If credit for plutonium and uranium is received at a time ty“ later than tR, an additional financing charge is incurred on the value of this uranium and plutonium, Zy" + ZP, for the time interval ty" — tR, equal to the product of у and the area F, (Zy" + ZPX? u" — tR).

The sum of areas А, В, C, D, E, and F is

+ (Zu" + Zp — ZR —Zsh)(fsh + Zp ~ZR)(tR — tsf,)

+ (Zu — + Zp)(tV" — tR) = Zu — — tl)j

_l *7 (Eiti+E2t2 . ±T {Eiti +E2t2 „

Zf‘ VT^T* Fa) ^{еГ+е, tsh)

* — ‘*) — (z“-+z-> fihrir — —

Thus, the area under the curve is the sum of the product of each expenditure or credit times the difference between the mean time for receipt of revenue t

i= Eiti + E2t2

Ei +E2

and the time when the expenditure or credit is paid. This result generalizes to an expression for the area of

(3.21)

where Zj is the outlay for fuel-cycle step / (negative if a credit) at f;- and tm is the time at which revenue is received, for production of Em kWh of electricity. The fuel-cycle cost e in mills per kilowatt-hour then is

The assumptions of Table 3.7 are made to obtain the times needed to calculate the carrying-charge term for sublot 2A:

{EttT ~'<) й E’- <3-22>

A time basis of zero is taken for the start of cycle 1 (t = 0).

The mean time for receipt of revenue from sale of electricity, t, is

r= EiU +E2t2 _ (3.6271)(0.7920)+ (1.9185)(1.9355) _ , ,0„._

1- ~ЁГПГ~~————————— ШпТШБ 1 1876 yr (3-23)

From the foregoing transaction times and the direct fuel-cycle costs or credits of Table 3.6, the carrying charges and total fuel-cycle costs may be calculated, as shown in Table 3.8 for sublot 2A. Division of the total fuel-cycle cost of $33,173,168 by the electricity generated by sublot 2A, 5.5456 X 109 kWhe, and conversion to mills per kilowatt-hour of electricity by Eq.

(3.21) gives 5.9819 mills/kWhe for the unit fuel-cycle cost of lot 2A.

Table 3.8 shows that more than 20 percent of the fuel-cycle cost arises from carrying charges.

5.1 Fissile Materials

Table 2.8 lists capture and fission cross sections for the four nuclides fissile with thermal neutrons and gives the average number of neutrons produced per nuclide fissioned (n) and per

neutron absorbed (»?). These properties are needed to calculate reactor neutron balances, evaluate fuel reactivity, and work out fuel cycles.

Figure 3.31 shows the quantities of materials to be supplied or processed per year for a 1000-MWe LWR operated with recycle of uranium in spent fuel, after steady-state fuel-cycle conditions have been established. To generate electricity at this rate with a power-cycle thermal efficiency of 32.5 percent at a capacity factor of 80 percent requires that the reactor be supplied with 27,271 kg/уеаг of uranium enriched to 3.3 w/o 235U. This fuel is expected to support a bumup of 33,000 MWd/MT with three-zone fueling. Of the other material quantities shown in the flow sheet, the most significant are the following: 25,674 kg uranium containing 0.83 w/o 235 U is recovered in the form of UF6 and recycled to isotope separation. Uranium isotope separation is assumed to reject tails containing 0.3 w/o 23SU. Under these conditions the uranium isotope separation facility needs 168,090 kg/year of natural uranium feed in the form of UF6 and produces 106,974 separative work units per year (defined in Chap. 13). To provide UF6 at this rate requires an annual supply of 439,199 lb U308 in uranium ore concentrates. The fuel reprocessing plant produces 243.5 kg/уеаг of plutonium of the isotopic composition given at the right of Fig. 3.31.

Individual operations making up the nuclear fuel cycle for light-water power reactors of the type developed in the United States are shown in the pictorial flow sheet, Fig. 1.14. This follows case II of Fig. 1.11.

The first step is mining of uranium ore, which typically contains only a few pounds of uranium per ton. Uranium values in the ore are concentrated in a uranium mill, which is located near the mine, in order to reduce subsequent shipping charges. Concentration processes frequently used include leaching, precipitation, solvent extraction, and ion exchange. The principles of solvent extraction are described in Chap. 4; applications of solvent extraction and ion exchange to uranium ore processing are taken up in Chap. 5. Uranium concentrates are

(b) MOLTEN-SALT BREEDER REACTOR

Figure 1.13 Fuel processing flow sheets for reactors using thorium as fertile material. Basis: 1 year, 80 percent capacity factor.

Figure 1.14 Fuel-cycle operations for light-water reactor.

known commercially as “yellow cake,” because the sodium diuranate or ammonium diuranate commonly produced by uranium mills is a bright yellow solid. Figure 1.15 is a photograph of the uranium mill of Union Carbide Corporation.

Concentrates are shipped from the uranium mill to a uranium refinery or conversion plant. Here chemical impurities are removed and the purified uranium is converted into the chemical form needed for the next step in the fuel cycle. Figure 1.14 shows concentrates being converted into uranium hexafluoride (UF6), the form used as process gas in the gaseous diffusion process for enriching 235 U. Other possible products of a uranium refinery used in other fuel cycles are uranium metal, uranium dioxide, or uranium carbide. Uranium purification and conversion processes are also described in Chap. 5.

Light-water reactors must be supplied with uranium having a higher content of fissile material than the 0.711 w/o 235U present in natural uranium. This can be done by enriching 235 U in an isotope separation plant as depicted in Fig. 1.14, by adding plutonium to natural uranium, or by some combination. The gaseous diffusion process is the principal process that has been used thus far for enrichment of uranium on a commercial scale. As working fluid it uses UF6, the only stable compound of uranium that is volatile at room temperature. UFe melts at 64° C, at which its vapor pressure is 1.5 atm. Natural UF6 is shipped in large steel cylinders. As UF6 reacts readily with water and organic materials, it must be handled in clean equipment, out of contact with moist air.

A gaseous diffusion plant consists of many gaseous diffusion stages connected in series. Each stage contains many porous tubes made of membranes with very fine holes, termed diffusion barriers. UF6 gas at a relatively high pressure flows along the inner wall of these tubes, whose outer wall is maintained at a relatively low pressure. The UF6 gas flowing through the tube wall is slightly enriched in 233 U relative to the gas remaining on the high-pressure side. Since one gaseous diffusion stage can increase the ratio of 235 U to 238 U by no more than a factor of 1.0043, it is necessary to repeat the process in hundreds of stages to obtain a useful

degree of separation, recompressing the UF6 between stages. Large quantities of UF6 must be recycled, and the power consumption is enormous. To produce 1 kg of uranium enriched to 3 percent 23SU while stripping natural uranium to 0.2 percent requires about 13,000 kWh of electric energy. The U. S. Atomic Energy Commission built three large gaseous diffusion plants at a cost of $2.3 billion. When operated at capacity they consume 6000 MW of electric power. Figure 1.16 is a photograph of the plant at Oak Ridge, Tennessee. The large number of stages is suggested by the repetition of the basic building structure. These plants and the gaseous diffusion process are described in more detail in Chap. 14.

Enriched UF6 is shipped to the plant for fabricating reactor fuel elements in monel cylinders whose size is determined from the 235 U content, so as to prevent accumulation of a critical mass. At the fuel fabrication plant UF6 is converted to U02 or other chemical form used in reactor fuel. For light-water reactors the U02 is pressed into pellets, which are sintered, ground to size, and loaded into zircaloy tubing, which is Filled with helium and closed with welded zircaloy end plugs. These individual fuel rods are assembled into bundles, constituting the fuel elements shipped to the reactor. Conversion of UF6 to U02 is described in Chap. 5. Extraction of zirconium from its ores and separation of zirconium from its companion element hafnium is described in Chap. 7.

The length of time that fuel can be used in a reactor before it must be discharged depends on the characteristics of the reactor, the initial composition of the fuel, the neutron flux to which it is exposed, and the way in which fuel is managed in the reactor, as described in more detail in Chap. 3. Factors that eventually require fuel to be discharged include deterioration of cladding as a result of fuel swelling, thermal stresses or corrosion, and loss of nuclear reactivity

as a result of depletion of fissile material and buildup of neutron-absorbing fission products. A typical fuel lifetime is 3 years.

When spent fuel is discharged from the reactor, it contains substantial amounts of fissile and fertile material, which, in the case of light-water reactors, are valuable enough to offset part or all of the cost of reclamation. Because of the fission products, spent fuel is intensely radioactive, with activities of 10 Ci/g+ being common. Spent fuel is usually held in cooled storage basins at the reactor site for 150 days or more to allow some of the radioactivity to decay. If to be reprocessed, spent fuel would be shipped in cooled, heavily shielded casks, strong enough to remain intact in a shipping accident.

In the fuel reprocessing plant, fuel cladding is removed chemically or mechanically, the fuel material is dissolved in acid, and fissile and fertile materials are separated from fission products and from each other. The Purex process, commonly used in reprocessing plants, is described at somewhat greater length in Sec. 7, below, and in more detail in Chap. 10. Figure 1.17 is a photograph of the Purex plant of the U. S. Department of Energy at Hanford, Washington. The massive, windowless, concrete building is characteristic of these radiochemical fuel reprocessing plants. In the case of light-water reactor fuel, the most valuable products of the fuel reprocessing plant are plutonium, usually in the form of a concentrated aqueous solution of plutonium nitrate, and uranium, most conveniently in the form of UF6. Some individual fission products such as 137 Cs, a valuable gamma-emitting radioisotope, may be separated for industrial or medical use. The remaining radioactive fission products are held at the reprocessing site for additional decay, then converted to solid form, packaged, and shipped to storage vaults where they

t Curies per gram.

must be kept out of human contact for thousands of years. Procedures for handling radioactive wastes are described in Chap. 11.

Plutonium nitrate from the reprocessing plant is converted to metal, oxide, or carbide and used in fuel for fast reactors or recycled to thermal reactors. UF6 from the reprocessing plant is recycled to the gaseous diffusion plant to be reenriched in 235 U.

When the time comes to replace fuel in a reactor, either because of loss of reactivity or because of changes in its physical properties, the reactor operator is faced with a number of alternative choices. The operator must decide whether to remove all or part of the fuel in the reactor, and whether to move some of the fuel remaining in the reactor from one location to another, and he or she must choose the composition of new fuel to replace the fuel removed.

The reactor operator may also elect to add neutron-absorbing poisons to the fuel when charged, and may change control-poison concentration or move poison from place to place in the reactor during fuel life. Procedures used in charging, discharging, or moving fuel and control poison are known collectively as fuel and poison management.

2.1 Objectives

The principal objectives of fuel and poison management are as follows:

1. To keep the reactor critical during long-term changes in fuel composition and reactivity

2. To shape power density distribution to maximize power output

3. To maximize heat production from fuel

4. To obtain uniform irradiation of fuel

5. To maximize productive use of neutrons

Not all these objectives can be achieved simultaneously in a given reactor, and some compromises among them are usually necessary. Each objective will be described briefly in turn.

Maintenance of criticality. As each fuel element in a reactor is irradiated, its composition changes, as does its contribution to overall reactivity. To maintain criticality in the face of these composition changes, it is necessary either to move control poison or change its concentration or to move fuel or change its concentration. Because reactivity changes caused by changes in fuel composition occur at low rates, seldom greater than a tenth of a percent per week, movement of fuel or poison to compensate for fuel composition changes may be very slow, in contrast to the rapid movement that may be required to compensate for load changes, operating disturbances, or emergencies.

Shaping power density distribution. A nuclear power reactor and its fuel are so costly that it is very desirable, economically, to obtain the maximum amount of power from a given charge of fuel and a given size of reactor, or conversely, to design a reactor in which a desired power output can be obtained from the minimum size of reactor and the minimum investment in fuel. The optimum use is made of fuel when each element is operating at the maximum allowable condition, i. e., at the maximum allowable cladding temperature, maximum allowable thermal stress, maximum allowable heat flux, and/or maximum allowable linear power density. A uniformly fueled and poisoned reactor is far from this ideal condition because of the wide variation of neutron flux and power density from point to point. In a cylindrical reactor whose fuel and poison distribution is spatially uniform, the neutron flux and power density vary with radius r and axial distance from midplane z as /0(2.405г/Л) cos (nz/H), where R is the effective radius and H the effective height of the fuel-bearing core of the reactor. The power density at the center is more than three times the average and the power density at the outer radius, top and bottom, is nearly zero. In all power reactors designed with economical performance in mind, fuel and/or poison is so managed that the power density distribution is more uniform than this cos J0 distribution. The optimum power density distribution will depend on what factors limit power output, whether it be temperature, thermal stress, heat flux, or linear power, and usually is quite specific to a particular reactor.

Maximum heat production. Before fuel can be charged to a reactor, it is usually necessary to bring it into a closely specified chemical and physical condition and to seal it in pressure-tight cladding fabricated to narrowly specified dimensions. After fuel is discharged from a reactor, it usually still contains enough fissile material to justify its recovery through chemical reprocessing. These operations of fuel preparation and reprocessing often cost $200,000/ton of fuel or more. It is therefore economically desirable to obtain the maximum possible amount of heat from each fuel element before it is discharged from the reactor. Even at the burnup of 30,000 MWd/MT, now obtainable from oxide fuel before physical damage necessitates fuel replacement, fabrication and reprocessing contribute $6.7/MWd or more to the cost of heat, or 0.9 mills/kWh to the cost of electricity in a power plant that is 30 percent efficient. It is thus of considerable economic importance to strive for maximum burnup until limited either by physical damage or by offsetting economic factors such as the higher cost of the richer fuel needed for higher burnup. The economic optimum burnup will be discussed later in this chapter.

Uniform burnup. Because of the high cost of fuel fabrication and reprocessing, it is also important to manage fuel so that every element at discharge has been irradiated to nearly the same burnup. If this is not done, some of the fuel would have generated much less heat than elements that had received the maximum permissible irradiation, and the unit cost of heat from these underirradiated elements would be undesirably high.

Productive use of neutrons. In thermal reactors, the number of neutrons produced per neutron absorbed in fissile material (t)) is of the order of 2.0. One of these neutrons is needed to keep the fission reaction going, but the second neutron, in theory, is available to produce valuable by-products of nuclear power. In practice, of course, some of these extra neutrons are necessarily lost through leakage and absorption in reactor materials, but around 0.6 neutron is available in water-moderated reactors for productive use. Examples of productive uses of neutrons are making plutonium from 238 U, 233 U from thorium, or 60Co from natural cobalt. To maximize production of such by-products, it is desirable to use methods of fuel and poison management that minimize leakage of neutrons and their nonproductive absorption in control materials that upon neutron absorption produce relatively valueless materials. For example, it would be better to use 238 U or thorium to absorb extra neutrons than boron control poison, because plutonium from 238U or 233U from thorium may be worth as much as $20/g as nuclear fuels, whereas boron produces only valueless helium and lithium. We shall see that some methods of fuel management conveniently permit the 238 U remaining in uranium fuel after 233 U is depleted to absorb the extra neutrons produced from fresh fuel of higher 235 U content. Such a method of fuel management is clearly more desirable economically than one that uses boron control poison to absorb extra neutrons produced in fresh fuel.

Some nuclei undergo radioactive decay by capturing an electron from the К or L shell of the atomic electron orbits. This results in the transformation of a proton to a neutron, the ejection of an unobservable neutrino of definite energy, and the emission of an x-ray where the electron vacancy of the К or L shell is filled by an atomic electron from an outer orbit. Because the net change in the radionuclide species is from atomic number Z to Z— 1, similar to the nuclide change from positron emission, electron capture generally competes with all cases of positron beta decay.

The preceding example shows that accurate representation of fuel-cycle performance requires such detailed examination of the time-varying changes in power distribution and fuel composi­tion at many points in a nuclear reactor as to necessitate use of a digital computer. The purpose of this section is to develop an approximate procedure for calculating fuel-cycle performance that, although complicated, can be carried out by hand calculation. The PWR described in Sec. 4.1 will be used as example, except that its rated electric output is taken as 1054 MWe instead of 1060 MWe.

More than 300 different nuclides have been observed as the primary products of fission. The term fission products usually refers to the primary fission products, i. e., the fission fragments and their daughters resulting from radioactive decay and neutron absorption. Only a few of the primary fission products are stable, the rest being beta-emitting radionuclides. As a fission — product radionuclide undergoes beta decay, its atomic number increases whereas its mass number remains constant. The direct yield of a fission-product nuclide is the fraction of the total fissions that yield this nuclide, essentially as a direct-fission fragment. The cumulative yield of a given nuclide is the fraction of fissions that directly yield that nuclide and its radioactive decay precursors in the constant-mass fission-product chain; i. e., it is the sum of the direct yields of that nuclide and its decay precursors. Many of the fission products have such short half-lives that no accurate measure of their direct yields as primary fission products is available. However, reasonably reliable data have been secured on the cumulative yields of many of the long-lived radionuclides and on the cumulative yields of all the nuclides in a fission-product chain of given mass number [B3, Wl], The cumulative yields by mass number in the fission of M3U, 235U, and 239Pu by slow neutrons and in the fission of 235U, 239Pu, 232 Th, and 238 U by fast neutrons are listed in Table 2.9 and are shown as the familiar double-hump mass-yield curves in Figs. 2.12 and 2.13.

This situation with regard to yield and radioactive decay at each mass number is illustrated for mass number 90 in Fig. 2.14. For accurate estimation of the amount of any nuclide produced at a given time, the differential equations appropriate to such a system of yields and decays must be set up and solved. This is illustrated in Secs. 6.3 through 6.5 for selected fission-product nuclides of mass 135 and masses 147, 149, 151, and 152, which are important neutron-absorbing poisons in thermal reactors.

Figure 3.32 is a material flow sheet on the same basis as Fig 3.31 for a LWR fueled with

natural uranium, recycle plutonium, and enough plutonium from the uranium-fueled LWR of

Fig. 3.31 to provide the same burnup, 33,000 MWd/MT with three-zone fueling. The salient points to notice are the following: The 980 kg of plutonium recycled per year contains a much higher proportion of the higher isotopes 241 and 242 than the plutonium makeup from the uranium-fueled reactor. The depleted uranium recovered in reprocessing contains only 0.327

w/o 233 U, and has too little value to justify conversion to UF6 and recycle to isotope

separation. The amount of U308 to be supplied is 73,322 lb, only one-sixth that needed for Fig. 3.31.

It must be noted, however, that operation of the flow sheet of Fig. 3.32 requires 504.96 kg of plutonium from the flow sheet of Fig. 3.31, which would have to be provided by (1000 MWeX504.96/243.5) = 2074 MWe of uranium-fueled LWR capacity, a total of 3074 MWe. Considering this self-contained reactor system, the specific annual consumption of U3 08 would be

Because Fig. 3.31 without plutonium recycle shows a specific uranium consumption of 439.2 lb U308/(MWe* year), plutonium recycle reduces U3Og demand by 27 percent.

Because plutonium recycle makes possible the generation of 3074 MWe of electricity with only 2074 MWe requiring enriched uranium, the reduction in separative work demand made possible by plutonium recycle is (100X3074 — 2074)/3074 = 32.5 percent, and the specific separative work demand is (106,974X2.074)/3074 = 72.1 SWU/(MWe*year). This is to be compared with 106.974 SWU/(MWe• year) without plutonium recycle.

Because of the importance of reactor fuel reprocessing in nuclear power technology, some further discussion of this topic is warranted in this introductory chapter.

In addition to fissionable isotopes (235U, 233 U, or plutonium) and fertile isotopes (238U or thorium), spent fuel from a reactor contains a large number of fission product isotopes, in which all elements of the periodic table from zinc to gadolinium are represented. Some of these fission product isotopes are short-lived and decay rapidly, but a dozen or more need to be considered when designing processes for separation of reactor products. The most important neutron-absorbing and long-lived fission products in irradiated uranium are listed in Table 1.4.

Processing of spent reactor fuels is made especially difficult by their intense radioactivity. The process equipment must be surrounded by massive shielding, provision must be made to remove the substantial amounts of heat that are associated with this radioactivity, and in some instances damage to solvents and construction materials from the radiations emitted by the materials being processed is a problem. Another difficulty is the critical-mass hazard, which is present whenever fissionable material is handled at substantial concentrations. This often requires a limitation in the size of batches being processed or in the dimensions of individual pieces of equipment. A third difficulty is the high degree of recovery that is usually required because of the great value of the fissionable materials being processed. A fourth is the high degree of separation specified for the removal of radioactive fission products; in present

Table 1.4 Important isotopes in irradiated uranium

Long-lived radioactive fission products

processes it is necessary to reduce the concentration of some of these elements by a factor of 10 million. Another difficulty is the large number of components present, with elements of such diverse properties as the alkali cesium and the manufactured elements technetium (resembling manganese) and promethium (one of the rare earths). A final difficulty, and one that was not originally anticipated, is the chemical similarity between uranium and plutonium.

The principle of the Purex process, now commonly used for processing irradiated uranium by solvent extraction, is illustrated in Fig. 1.18. The solvent used in this process is a solution of tributyl phosphate (TBP) in a high-boiling hydrocarbon, frequently и-dodecane or a mixture of similar hydrocarbons. TBP forms complexes with uranyl nitrate [U02(N03)2] and tetravalent plutonium nitrate [Pu(N03)4] whose concentration in the hydrocarbon phase is higher than in an aqueous solution of nitric acid in equilibrium with the hydrocarbon phase. On the other hand, TBP complexes of most fission products and trivalent plutonium nitrate have lower concentrations in the hydrocarbon phase than in the aqueous phase in equilibrium.

In the Purex process, irradiated U02 is dissolved in nitric acid under such conditions that uranium is oxidized to uranyl nitrate and plutonium to Pu(N03)4. The resulting aqueous solution of uranyl, plutonium, and fission-product nitrates is fed to the center of counter­current solvent extraction contactor I, which may be either a pulse column or a battery of mixer-settlers. This contactor is refluxed at one end by clean solvent and at the other by a dilute nitric acid scrub solution. The solvent extracts all the uranium and plutonium from the aqueous phase and some of the fission products. The fission products are removed from the solvent by the nitric acid scrub solution. Fission products leave contactor I in solution in aqueous nitric acid.

Solvent from contactor I containing uranyl nitrate and Pu(N03)4 is fed to the center of contactor II. This is refluxed at one end by clean solvent and at the other by a dilute nitric acid solution of a reducing agent strong enough to reduce plutonium to the trivalent form, but not so strong as to reduce uranium from the hexavalent form. Ferrous sulfamate is frequently used. In contactor II plutonium is transferred to the aqueous phase, while uranium remains in the solvent. Solvent from contactor II is fed to one end of contactor III, which is stripped at

the other end by water, which transfers the uranium to the aqueous phase leaving the contactor.

After chemical treatment to remove degradation products, the solvent leaving contactor Ш is reused in contactors I and II.

This brief discussion of the Purex process is expanded in Chap. 10, which discusses other processes for treating irradiated fuel and which deals with novel aspects of processing highly radioactive and fissile materials.