Category Archives: NUCLEAR CHEMICAL ENGINEERING

Deactivation of Sodium

Goldberg [G7] has listed a number of procedures that have been used for removing or deactivating sodium adhering to LMFBR assemblies. Use of a relatively nonvolatile alcohol, such as the я-butyl ether of ethylene glycol, is reported [C8] to remove sodium metal and oxide completely in 24 h. A difficulty is subsequent complete removal of solvent. Reaction with water vapor carried by an inert gas such as argon has been used extensively to deactivate sodium adhering to fuel assemblies. The principal disadvantage is the residue of sodium hydroxide, which reacts with acid in subsequent dissolution. Amalgamation with mercury has been used in the United Kingdom and the United States. In one application, mercury removed sodium from a 40-fuel-pin batch in 0.5 h [В15]. In the Soviet Union [S12], molten lead at 400 to 500°C has been used to wash sodium from fuel assemblies and as a substitute for water in storage of fast-reactor fuel for extended periods. A disadvantage in reprocessing is the layer of lead that coats the fuel. Sodium was washed from fuel assemblies from the Enrico Fermi LMFBR [K2] by ultrasonic cleaning with a high-boiling hydrocarbon oil at a temperature above the melting point of sodium. A disadvantage is the need to remove the flammable oil before voloxidation.

Thus, all methods have disadvantages. Deactivation with moist argon seems the simplest.

Design of Repositories in Salt Formations

Figure 11.26 illustrates the three basic options for repository design:

1. Rooms, mined, accessible to store waste containers

2. Caverns, mined or leached, not accessible, to be charged through a shaft either from the surface or from a lower level

3. Galleries with storage boreholes in the floor, mined, accessible to charge the boreholes

The choice among these options depends on the type of waste and the filling technique appropriate for the type.

Accessible storage rooms are simple but useful only for waste with a low surface dose rate. Otherwise the waste would have to be stored with lost shielding, which is usually uneconomic.

Caverns may be used for wastes with higher surface dose rates because the waste container can be dropped from a shielded cask into the cavern. The heat generation, however, must be very moderate, because dropping the containers into the cavern leads to a random array not optimized in terms of heat dissipation. In West Germany an In situ solidification process for non-high-level waste is being investigated where granulated waste mixed with a binder is to be pumped into a cavern.

Single boreholes in the floors of galleries are provided to hold high-level glass cylinders. The cylinders are carried in heavily shielded casks and are then lowered into the boreholes. Single boreholes can be arranged in a way that the heat is sufficiently dissipated to maintain maximum permissible peak temperatures in the salt.

Rode mechanical stability. The main potential hazard to the integrity of an underground repository has its roots in rock mechanical failures. The stability of the repository depends on many factors, such as the volume of the rooms relative to the pillars. Convergence of rooms due to the plasticity of the salt and enhanced by the elevated temperature may cause stresses within the rock salt. It is therefore important that a repository at least for HLW should be built in a salt formation not mined before. Moreover, only the space required for a minimum number of years should be mined at the same time, and every room used up should be backfilled with crushed salt. On the other hand, convergence will help to eliminate open space in the rock salt quickly after rooms have been backfilled and will thereby be beneficial.

Another factor affecting rock mechanics is the temperature. The rock has attained a quasi-equilibrium state corresponding to the geothermal temperature gradient over millions of years. Only formations having this tectonic stability are eligible as waste repositories. Inserting high-level waste will inevitably disturb this equilibrium by raising the temperature in the salt and by creating new gradients. The natural temperature at depths of 1000 m is in the neighborhood of 40 to 45°C with gradient of a little more than 2°C per 100 m.

According to suggestions made in an Oak Ridge study [Cl], the following temperature criteria are to be met:

Waste temperature should not exceed the temperature of the solidification process.

No more than 1 percent of the salt shall be at a temperature above 250°C.

No more than 25 percent of the salt shall be at a temperature above 200°C.

If camallite interspersion is expected, the maximum temperature shall be limited to 100°C.

In West Germany 200°C is presently envisaged as an upper limit of the waste canister surface temperature.

In general, the temperature increase caused by the waste should be kept low to ensure that the quasi-equilibrium is disturbed as little as possible. It may turn out as a result of further thermomechanical analyses that it is desirable to age the solidified HLW for quite a while in engineered storage before it is put into a geologic repository.

Thermal analysis. The temperature distribution in space and time is given by the following differential equation:

cp = div (к grad T) + q’ at

where c = specific heat p = density к = heat conductivity

q’ = heat-production rate of the source per unit volume c, p, and к are functions of space and temperature. Equation (11.7) has been solved numerically [С1].

A parametric analysis has been conducted with room width, waste package array (pitch), waste characteristics, and diameter of HLW container as parameters.

Optimization leads to a set of parameters indicated in the schematic cross sections of the repository presented in Fig. 11.27. The diameter of the glass cylinders is 6 in (15.24 cm). These parameters will permit storage of the 20-year HLW production of a 1400-MT/year reprocessing plant for 20 years in an area of about 0.5 km2.

Figure 11.28 illustrates the temperature distribution throughout the repository. The maximum temperature rise at the hottest spot of the salt, according to this calculation, will be about 175°C and will be reached after about 50 years.

Extracting-scrubbing Cascade: Numerical Procedure for Use with Variable Distribution Coefficients

The algebraic procedure described in Sec. 6.5 is convenient for obtaining a rough estimate of the number of stages needed in fractional extraction, but is seldom accurate enough for design purposes, because distribution coefficients usually change as concentrations change from stage to stage. This section describes a numerical procedure that is generally applicable whenever distribution coefficients are known and the phases leaving an extraction stage are in equilibrium.

The procedure will be illustrated by the zirconium-hafnium separation example treated in Sec. 6.5. The material-balance quantities used for the present illustration are listed in Table 4.8. The relative flow rates of solvent, scrub, and feed streams are those recommended by Нигё and Saint James [H4], as are the concentrations of HN03 and NaN03 in solvent, scrub, and feed streams. Changes in volume of the aqueous and organic streams within the scrubbing section and within the extracting section are to be neglected. The concentrations of total TBP in the organic stream is specified as 2.25 mol/liter, and the slight solubility of TBP in water is to be neglected. The concentration of zirconium and hafnium in the aqueous feed, the required zirconium recovery, and the required hafnium decontamination factor are the same as in the example of Sec. 6.5; the concentrations of Zr(N03)4 and Hf(N03 )4 in the raffinate and extract streams are thereby specified.

After the above variables have been set, the cascade is fully specified and only one set of values for the number of stages in extracting and scrubbing sections will perform the specified separation. All other extractable components will be distributed in a determinate manner between aqueous-residue and organic-extract streams.

In the present example, nitric acid is an extractable component, whose split between extract and raffinate streams cannot be specified in advance. However, in the calculational procedure to be described, it is necessary to start with specified concentrations of all

Table 4.8 Material balance for zirconium-hafnium separation by fractional extraction with TBP+

In

Out

Stream:

Phase:

Feed

Aqueous

Scrub

Aqueous

Solvent

Organic

Total

Residue

Aqueous

Extract

Organic

Total

Gram-moles/

liter:

TBP

NaN03

3.5

3.5

2.25

3.5

2.25

HN03

3.0

3.0

1.6

3.03*

1.576*

Zr(N03)4

0.123

0.000

0.000

0.00123

0.0578

Hf(N03)4

0.00246

0.000

0.000

_

0.00122

5.78 X 10’6

Liters

48

48

100

96

100

Gram-moles:

TBP

225

225

225

225

NaN03

168

168

336

336

336

HN03

144

144

160

448

291

158

449

Zr(N03)4

5.90

0.000

0.000

5.90

0.118

5.78

5.90

Hf(N03)4)

0.118

0.000

0.000

0.118

0.117

0.006

0.118

*Basis: 100 liters of solvent.

* These concentrations cannot be specified in advance and must be confirmed by calculation or experiment.

components in terminal streams from the cascade, so that provisional values must be assumed for nitric acid concentration in the extract streams, and the corresponding concentration of nitric acid in the raffinate is obtained from a material balance. If subsequent calculation fails to confirm the correctness of these provisional values, new values must be assumed for acid concentration in the extract stream and the calculation repeated. The particular values of exit acid concentrations listed in Table 4.8 were arrived at by several iterative calculations and give a consistent analytical solution to the separation problem.

To obtain distribution coefficients as a function of concentration, it will be assumed that equilibria are established in the three following reactions:

H><?) + N03 ~(aq) + TBP(o) — HN03 — TBP(o) KH = 0.145

Zr4+(aq) + 4N03′(aq) + 2TBP(o) — Zr(N03)„-2TBP(o) KZr = 0.0032

Hf*+(aq) + 4N03 ‘(aq) + 2TBP(o) — Hf(N03)„ -2TBP(o) KH{ = 0.00032

The value of 0.145 for the equilibrium constant of the nitric acid complex is an average value derived from the equilibrium data of Moore [М2], Alcock et al. [Al], and Gruverman [G7], The value of 0.0032 for the zirconium equilibrium is the average value derived from the equilibrium data in Table 4.4. The value of 0.00032 for the hafnium equilibrium is derived from the separation factor of 10 measured for zirconium-hafnium mixtures by Hure and Saint James [Н4]. Distribution coefficients are then given by the following equations.

HN03:

DH — — — 0.145yTBPxNO —

*H

(4.85)

Zr(N03)4:

£>zr = ^ = 0.0032Otbp)2(*ncv)4

xZt

(4.86)

Hf(N03)4: D^f — — 0.00032(>’xbp)*C5Cno,")4 (4-87)

*Hf

where Утвр is the concentration of uncombined TBP in the organic phase and xNOj — is the total nitrate concentration in the aqueous phase. For the concentrations assumed for Table 4.8, Утвр is obtained from

Утвр = 2.25 — уп + 20 Zr + yHf)] mol/liter (4.88)

where 2.25 is the concentration of TBP in all forms in the organic phase. The aqueous nitrate concentration is obtained from

xNOj — = 3.5 + xH + 4(x& + *Hf) mol/liter (4.89)

where 3.5 is the constant concentration of sodium nitrate in the aqueous phase.

To find the required number of stages, a calculation is made of the concentrations of zirconium nitrate, hafnium nitrate, and nitric acid in the organic phase as a function of stage number in the scrubbing and extracting sections. A plot similar to Fig. 4.19 is then made of the concentration of zirconium versus the concentration of hafnium in each section. The point of intersection of the curves gives the concentrations of these components in the organic phase flowing between the two sections at the feed point, at which

Zr: УІг^г+1 = y*zt, N (4.90)

Hf: yfi tM+l =ygf„ (4.91)

The number of stages in each section (M and N) at which these concentrations are equal is the result of the first trial calculation.

A check is then made to determine if the nitric acid concentration in the organic phase leaving the extracting section equals that in the organic phase entering the scrubbing section. If

yn, N = Ун, м+і (4-92)

the provisional values assumed for nitric acid concentrations in residue and extract streams are correct. If these concentrations are not equal, new values must be assumed for nitric acid concen­trations in the residue and extract streams and the entire calculational procedure repeated.

Steps in the calculation of the concentrations of zirconium nitrate, hafnium nitrate, nitric acid, and uncombined TBP as a function of stage number n in the extracting section are given in Table 4.9.

In order to calculate equilibrium concentrations уf in the organic stream leaving stage 1, jtnOj -,i is calculated from Eq. (4.89), a trial value of Утвр. і is assumed, and Df andyf are obtained from Eqs. (4.85) through (4.87). The trial value of yfBPjl is checked by using the yf in Eq. (4.88), and when a trial value of yfBP, i that satisfies this condition is found, a consistent set of concentrations in the streams leaving the first extracting stage has been obtained.

The next step is to apply the material-balance equation (4.51) to calculate the concen­trations in the aqueous phase leaving stage 2. The calculation then proceeds up through the extracting section by a repetition of these steps.

Steps in the calculation of concentrations as a function of stage number m in the scrubbing section are given in Table 4.10. Die calculation is started with the specified concentrations y? in the organic extract stream leaving stage 1, obtained from Table 4.8. Because the concentrations yf have been chosen, the value of у? вр, і can be calculated from Eq. (4.88), and a value of x$0j-,i must be assumed to calculate values of Df and xf from Eqs. (4.85) through (4.87). Mien the assumed value of д$о,-,і agrees with that obtained by substituting the corresponding values of xf in Eq. (4.89), a consistent set of concentrations in the streams leaving the first scrubbing stage has been obtained.

Stage no. n

Aqueo

4 =

us concentratiot rf + E {yE

1, mol/liter — і ~Уо)

Total

N03’a

E

Assumed free TBP in organic phase E

ТТВР. п

Distribution coefficients

Organic concentration, mol/liter yE ~ D4

-‘ft n

5 + F^

HN03

>H, n

Zr(N03)4

.КІг. п

Hf(N03)4

Ут, п

Free

TBP*

E

УТВ?,п

hno3

rE

xH, n

Zr<N03)4

xZr, n

Hf(N03)4

„£

xHf, n

HN03

Dnb

Zr(N03)4

DzrC

Hf(NOs)4

DHfd

і

3.03^

0.001230^

0.001224/

6.53

0.570

0.540

1.897

0.1897

1.635

0.00233

0.000232

0.610

0.580

0.550

1.967

0.1967

1.664

0.00242

0.000241

0.580

2

3.09

0.00375

0.001475

6.61

0.565

0.542

1.954

0.1954

1.678

0.00732

0.000288

0.577

0.563

0.540

1.944

0.1944

1.671

0.00729

0.000287

0.563

3

3.10

0.00882

0.001523

6.64

0.555

0.534

1.918

0.1918

1.657

0.01692

0.000292

0.558

0.556

0.535

1.924

0.1924

1.660

0.01696

0.000293

0.556

4

3.09

0.01900

0.001529

6.70

0.550

0.532

1.916

0.1916

1.643

0.0362

0.000293

0.534

0.546

0.528

1.890

0.1890

1.632

0.0357

0.000289

0.546

5

3.06

0.0384

0.001525

6.72

0.537

0.523

1.880

0.1880

1.600

0.0723

0.000287

0.504

0.530

0.516

1.830

0.1830

1.579

0.0703

0.000279

0.530

6

3.00

0.0745

0.001515

6.81

0.504

0.497

1.745

0.1745

1.494

0.1299

0.000264

0.496

0.502

0.496

1.733

0.1733

1.489

0.1291

0.000263

0.502

~ 1-041 ТН,0 — 160 У2.І.0 — 0 THf. O — 0

“Calculated from Eq. (4.89).

6 Calculated from Eq. (4.85).

“Calculated from Eq. (4.86).

4 Calculated from Eq. (4.87).

“Calculated from Eq. (4.88).

^Specified concentrations.

Stage no. m

Organic concentration, mol/liter Ут = Уі + ~xo)

Assumed total N03 ~ in aqueous

phase

s

*N03~,m

Distribution coefficients

Aqueous concentration, mol/liter

S _ Ут m D

Total N03 " concentration in aqueous

phase"

VS

*N03-,m

HN03

T’H. m

Zr(N03)4

yZr, m

Free

Hf(N03)4 TBP" s s

T’Hf. m ^TBP. m

HNOa

oHb

Zr(N03 )4 Dzrc

Hf(N03)4

DHfd

HN03

VS

xH, m

Zr(N03)4

x Zr, m

Hf(N03)4

^Hf. m

і

1.576r

0.0578Z

0.00000578-^ 0.558

6.57

0.532

1.859

0.1859

2.96

0.0311

31.1 X 10"*

6.58

6.58

0.533

1.872

0.1872

2.96

0.0309

30.9 X 10"*

6.58

2

1.553

0.0727

0.0000206 0.549

6.60

0.526

1.837

0.1837

2.95

0.0396

0.0001122

6.61

6.61

0.526

1.845

0.1845

2.95

0.0394

0.0001118

6.61

3

1.553

0.0768

0.0000594 0.543

6.64

0.523

1.834

0.1834

2.97

0.0418

0.000324

6.64

4

1.562

0.0780

0.0001613 0.532

6.68

0.516

1.809

0.1809

3.03

0.0431

0.000891

6.70

6.70

0.517

1.822

0.1822

3.02

0.0428

0.000885

6.70

5

1.586

0.0784

0.000431 0.506

= 3.0

"Calculated from Eq. (4.88). * Calculated from Eq. (4.85). "Calculated from Eq. (4.86). d Calculated from Eq. (4.87). "Calculated from Eq. (4.89). ■^Specified concentrations.

The next step is to apply the material-balance equation (4.52) to calculate the concentrations in the organic stream leaving stage 2. The calculation then proceeds down through the scrubbing section by a repetition of these steps.

The large variation in distribution coefficients is noteworthy. This is caused principally by changes in the concentration of uncombined TBP. This large variation makes necessary the use of a numerical calculation method.

Figure 4.19 is a plot of zirconium concentration versus hafnium concentration in the organic phase, with points for the extracting section from Table 4.9 and points for the scrubbing section from Table 4.10. The point of intersection occurs at

Extracting: 5 < N < 6

Scrubbing; 4 < (M + 1) < 5

By interpolation, the point of intersection of the curves of Fig. 4.18 occurs at Extracting: N = 5.2

Scrubbing: M + 1 = 4.6

Thus, six theoretical stages in the extracting section and four in the scrubbing section would result in higher values of zirconium recovery and hafnium decontamination than those specified.

Finally, a check must be made to determine if organic concentrations of nitric acid in the extracting and scrubbing sections match at the feed point. That this condition is satisfied can be seen from Fig. 4.20, a plot of organic concentrations leaving a stage versus stage number. If nitric acid does not match at the feed point, a new value of nitric acid concentration in the organic extract must be assumed and the entire calculational procedure repeated.

Figure 4.20 and the McCabe-Thiele diagrams of Fig. 4.21 illustrate the principle of separation of two metals by solvent extraction with complexing agents. The largest change in organic concentration of the more extractable component, zirconium, occurs in the extracting section. After the first extracting stage the hafnium soon reaches a concentration in the organic that is almost in equilibrium with the hafnium in the aqueous feed entering the succeeding stages. The hafnium concentration in organic is actually reduced somewhat as the feed stage is

Figure 4.19 Zirconium and haf­nium concentrations in organic phase, to determine feed point in zirconium-hafnium separation example.

0. 5

Figure 4.20 Concentrations in organic phase leaving a stage as a function of stage number for zirconium-hafnium separation.

approached, because the decreasing concentration of uncombined TBP reduces the hafnium distribution coefficient. In the scrubbing section the lower flow ratio of aqueous to organic allows a relatively large decrease in the concentration of hafnium in the organic. Because some zirconium is removed from the organic in the scrubbing section, the maximum zirconium concentration occurs near the feed point, resulting in the lowest concentration of uncombined TBP at this point. The equilibrium lines in the extracting and scrubbing sections are essentially identical for zirconium, but not for hafnium.

The feed conditions have been chosen so that nitric acid in the organic feed is nearly in equilibrium with the nitric acid in the aqueous feed and scrub solution, so that little change in nitric acid concentration occurs through the cascade. The small changes in nitric acid concentration are due principally to variations in amount of TBP complexed by zirconium.

The SEPHIS [G6, H2, Wl] and SOLVEX [SI] computer codes are applications of the above techniques for calculating the number of equilibrium stages for the TBP extraction of uranium and plutonium in nitric acid solution. These codes include correlations of the

Figure 4.21 Stage concentration diagram for zirconium-hafnium extracting-scrubbing example.

extraction equilibrium constants and activity coefficients as affected by total ionic strength. Corrections for incomplete ionization of aqueous plutonium may also be important.

U. S. Uranium Mills

Table 5.19 lists the uranium mills operating in the United States in January 1977 and their capacity, as reported by the Grand Junction Office of the U. S. Energy Research and Development Administration [Ш]. Table 5.19 summarizes the processes used in the mills, when such information is available from a May 1975 report from the Oak Ridge National Laboratory [S2] and other industry sources. As uranium milling is a dynamic industry, with frequent changes in process technology and mill capacity, Table 5.19 serves more to illustrate the diversity of milling processes than to provide an invariant listing.

Part 1 of Table 5.19 lists mills using carbonate leaching. There is no standard process for recovery of uranium from carbonate leach liquors. The trend is away from precipitation with NaOH as crude Na2U207 toward further purification as by UO4 precipitation at Rio Algom or by ion exchange followed by precipitation as (NH4)2U207 at George West.

Part 2 of Table 5.19 lists mills using acid leaching and solvent extraction. All mills for which process information is available use a long-chain tertiary amine, Alamine-336 or Adogen-364, as extractant, with general features illustrated in Sec. 8.6.

Part 3 of Table 5.19 lists mills using acid leaching and anion exchange. The three types of contactors and the different eluting and final treating processes are described in Sec. 8.7.

CONCENTRATION AND EXTRACTION OF THORIUM

The principal steps in producing refined thorium compounds from thorium-bearing ores are concentration of thorium minerals, extraction of thorium from concentrates, purification or refining of thorium, and conversion to metal or the thorium compound finally wanted. This section describes the concentration of monazite, the principal source of thorium in the past; the extraction of thorium from monazite; and the recovery of thorium from leach liquors by solvent extraction. Purification of thorium is described in Sec. 9 and conversion in Sec. 10.

1.12Concentration of Monazite

Monazite is usually a minor constituent of deposits of other minerals, all of which must be separated and processed for a profitable venture. As an example, the mineral constituents of beach sands in Travancore, India, which are dredged for their zirconium, titanium, thorium, and rare-earth content, are as follows:

Monazite, (RE, Th, U)P04,0.5 to 1.0% Rutile, Ti02,3 to 6%

Dmenite, FeTi03, 65 to 80% Zircon, ZrSi04,4 to 6%

Garnet, (Fe, Mg, Ca)3 Al2Si04,1 to 5% Sillimanite, Al2SiOs, 2 to 5%

Beach sands are usually first treated by crude specific gravity methods to separate the denser minerals from silica and produce concentrate that, at Travancore, has approximately the above composition. Then the heavier minerals are separated in a series of strong electromagnets of progressively increasing intensity. The low-intensity magnet removes the most magnetic constituent, magnetite. The first pole of the high-intensity magnet separates ilmenite; the second pole, garnet; the third pole, coarse grains of monazite; and the strongest pole, fine grains of monazite. The rare earth elements in monazite make it paramagnetic. The nonmagnetic residue is treated by flotation and other means to recover rutile, zircon, and some gold. A further specific gravity treatment of the monazite fraction produces a monazite concentrate 98% percent pure.

FISSION-PRODUCT RADIOACTIVITY

1.1 Activity in Irradiated Fuel

For irradiation in a constant neutron flux, the activity of any fission-product nuclide can be evaluated from the equations in Chap. 2. When fissions occur at a constant rate and when neutron-absorption reactions in the fission product and its precursors can be neglected, the activity of a nuclide with relatively short-lived precursors can be evaluated by applying Eq.

(2.37) :

N = Fy(-e-KTR)e-^Tc (8.1)

where F = fission rate, flssions/s

N = atoms of long-lived fission product present after cooling for a time Tc TR = irradiation time, s Tc = cooling time, s

у = cumulative fission yield, atoms/atom fissioned X = decay constant for the nuclide, s’1

When the half-lives of a fission product and of its decay precursors are short compared to the irradiation time (Г1/2 < TR), the fission-product nuclide reaches saturation prior to the end of the irradiation. Its saturation activity per unit of reactor power is a constant, so that

?y=ye-KTc (when TV2<TR) (8.2)

The saturation activity is conveniently expressed in curies per watt of thermal power, or

Curies _ _XTc /disintegration^ / fission

Watt fission/s /200MeV/

w ( MeV

( Сі

» Vl.6X КГ13 W-s )

ЗЛ X 1010 disintegrations/s)

or

Curies_ 0 845 — лгс Watt

(when T1/2<TR)

(8.3)

Practical irradiation periods for fuel in power reactors are in the range of about 1 to 4 years. Most of the fission-product nuclides reach saturation in this period. An example is 8.05-day 1311, which is formed in 2.93 percent of 23SU fissions. Its saturation activity is 0.023 Ci/W.

Curies _ 0.586у7де *Tc Watt Ty г

Many radioactive fission-product nuclides have half-lives that are long compared to reactor irradiation periods, i. e., 3H, 8SKr, ’“Sr, 129I, and I37Cs. In these cases, Eq. (8.1) simplifies to

Because these long-lived nuclides do not reach saturation in the reactor fuel, their yearly production rate is important. This is obtained by dividing Eq. (8.5) by TR and setting Tc equal to zero:

Curies _ 0-586y

Watt X time “ Ty2 ( J

The short-lived daughter of a long-lived parent nuclide contributes significantly to the activity even after long cooling periods because it is constantly being formed from the parent (e. g., 90Y from 90Sr). If the half-life of the daughter is very small relative to that of its parent, the two are in secular equilibrium and the daughter activity is equal to that of the parent.

Only a few fission-product nuclides have half-lives too long for saturation but too short for the assumption of linear buildup that led to Eq. (8.4). Examples are 106 Ru, 144Ce, and 147Pm. A few radionuclides, such as ^Nb, 140La, and 147Pm, have precursors that must be considered in the calculation of activity after a few months of postirradiation cooling.

In Table 8.1 are listed those fission-product nuclides that contribute appreciably to the activity of fission products formed after long irradiation and cooled for periods of a few months or more. Fission-product activities have been calculated for uranium fuel irradiated for 3 years in the 1000-MWe pressurized-water reactor (PWR) operating as shown in Fig. 3.31. Activities are listed for fuel at the time it is discharged from the reactor and after

Table 8.1 Long-lived radioactive fission products’*’

In discharge fuel 106 Ci/yr

Elemental

boiling

temperature,

°c§

Radionuclide

Half-life

At

discharge*

150-day

decay

10-yr

decay

3H

12.4 yr

1.93 X 10*2

1.88 X 10*2

1.09 X 10’2

100

(as tritiated water)

19 Se

<6.5 X 104 yr

1.08 X 10_s

1.08 X 10’5

1.08 X 10‘s

Total^

10.0

1.08 X 10“s

1.08 X 10_s

657

MKr

10.76 yr

0.308

0.300

0.162

Total

85.0

0.300

0.162

-153.4

86 Rb

18.66 days

1.34 X 10’2

5.18 X 10’3

0

Total

1.34 X 10‘2

5.18 X 10’3

0

705

89 Sr

52.7 days

19.6

2.65

0

90 Sr

27.7 yr

2.11

2.09

1.65

Total

1.38 X 102

4.74

1.65

1357

90 Y

64.0 h

2.20

2.09

1.65

91Y

58.8 days

25.5

4.39

0

Total

2.08 X 102

6.48

1.65

3337

93 Zr

1.5 X 106 yr

5.15 X 10’s

5.15 X 10~5

5.15 X 10-5

93 Zr

65.5 days

37.3

7.54

0

Total

96.2

7.54

5.15 X 10"s

4325

93mNb

13.6 yr

3.95 X 10’6

4.98 X 10’6

2.3 X 10’s

9SmNb

90 h

0.762

0.160

0

95 Nb

35.0 days

37.6

14.2

0

Total

2.30 X 102

14.4

2.3 X 10~s

4842

99 Tc

2.12 X 10s yr

3.90 X 10’4

3.90 X 10‘4

3.90 X 10’4

Total

29.7

3.90 X 10~4

3.90 X 10‘4

3927

103 Ru

39.5 days

33.2

2.41

0

106 Ru

368 days

14.8

11.2

1.50 X 10‘2

Total

75.7

13.6

1.50 X 10’2

4227

103 mRh

57.5 min

33.2

2.41

0

106 Rh

30 s

20.2

11.2

1.50 X 10’2

Total

1.17 X 102

13.6

1.50 X 10’2

3667

toipd

7 X 106 yr

3.00 X 10‘6

3.00 X 10~6

3.00 X 10’6

Total

9.10

3.00 X 10’6

3.00 X 10_e

3112

110m Ag

255 days

0.100

6.64 X 10’2

4.52 X 10’6

110 Ag

24.4 s

4.33

8.65 X 10’3

5.88 X 10’7

111 Ag

7.5 days

1.08

1.03 X 10’6

0

Total

10.4

7.51 X 10’2

5.11 X 10‘6

2163

u3mCd

13.6 yr

2.86 X 10‘4

2.81 X 10~4

1.74 X 10’4

nSmCd

43 days

0.0150

1.34 X 10"3

0

Total

0.981

1.62 X 10’3

1.74 X 10’4

770

111mSn

14.0 days

1.62 X 10’3

9.65 X 10’7

0

1I9mSn

250 days

4.47 X 10’4

2.95 X 10’4

1.79 X 10‘8

Table 8.1 Long-lived radioactive fission products’*’ (Continued)

Radionuclide

Half-life

In discharge fuel 10* Ci/yr

Elemental

boiling

temperature,

°C§

At

discharge*

150-day

decay

10-yr

decay

123 Sn

125 days

0.242

1.05

3.87 X

io-10

125 Sn

9.4 days

0.368

5.81 X

10’6

0

126 Sn

10s yr

1.49 X 10‘5

1.49 X

10’5

1.49 X

10’s

Total

72.2

1.05

1.49 X

10’5

2722

124 Sb

60.4 days

1.11 X 10~2

1.95 X

10’3

0

125 Sb

2.71 yr

0.237

0.215

1.85 X

10‘2

126m Sb

19.0 min

6.13 X 10’4

1.49 X

10~s

1.49 X

10’s

126 Sb

12.5 days

1.55 X 10‘3

1.50 X

10‘s

1.47 X

10’5

Total

1.31 X 102

0.217

1.85 X

10’2

1625

mm те

117 days

1.66 X 10’s

6.82 X

10~6

0

125Шгре

58 days

8.47 X 10’2

8.69 X

10‘2

7.66 X

10‘3

127mTe

109 days

0.420

0.167

0

127 Те

9.4 h

1.96

0.62

0

129m Te

34.1 days

1.56

7.38 X

10"2

0

129 Те

68.7 min

9.18

3.87 X

10~2

0

Total

1.63 X 102

0.986

7.66 X

10~3

1012

129 j

1.7 X 107 yr

1.01 X 10‘6

1.02 X

10‘6

1.02 X

10~6

131 j

8.05 days

23.5

5.94 X

10’5

0

Total

2.66 X 102

6.04 X

10’5

1.02 X

10~6

183

131mXe

11.8 days

0.174

8.50 X

10~5

0

133 Xe

5.270 days

43.9

1.46 X

10‘7

0

Total

1.78 X 102

8.51 X

10‘5

0

-108.2

134 Cs

2.046 yr

6.70

5.83

0.228

135 Cs

3.0 X 106 yr

7.79 X 10’6

7.79 X

10‘6

7.79 X

10‘6

136 Cs

13.7 days

1.66

5.42 X

10-4

0

137 Cs

30.0 yr

2.94

2.92

2.33

Total

1.56 X 102

8.75

2.56

686

mmBa

2.554 min

2.75

2.72

2.18

140 Ba

12.80 days

39.5

1.18 X

10’2

0

Total

1.51 X 102

2.73

2.18

1634

140 La

40.22 h

40.9

1.34 X

10‘2

0

Total

1.49 X 102

1.34 X

10’2

0

3370

141 Ce

32.5 days

37.9

1.53

0

144 Ce

284 days

30.2

21.0

4.11 X

10’3

Total

1.48 X 102

22.5

4.11 X

10’3

3470

143 Pr

13.59 days

32.7

1.85 X

10’2

0

144 Pr

17.27 min

30.5

21.0

4.11 X

10"3

Total

1.23 X 102

21.0

4.11 X

IO’3

3017

147 Nd

11.06 days

16.0

2.58 X

10’3

0

Total

24.9

2.58 X

10’3

0

3111

147 Pm

4.4 yr

2.78

2.65

0.211

mm Pm

41.8 days

1.06

8.91 X

10’2

0

Table 8.1 Long-lived radioactive fission products* (Continued)

In discharge fuel 10* Ci/yr

Elemental

boiling

temperature,

°C§

Radionuclide

Half-life

At

discharge*

150-day decay

10-yr

decay

148 Pm Total

5.4 days

5.42

31.6

7.08 X 10*3 2.74

0

0.211

3200

151 Sm Total

«87 yr

3.41 X 1СГ2 11.5

3.41 X 10’2

3.41 X 10-2

3.16 X 10-2

3.16 X 10’2

1670

152 Eu 134 Eu

155 Eu

156Eu Total

12.7 yr 16 yr 1.811 yr 15.4 days

3.41 X 10’4

0.191

0.204

6.16

6.56

3.32 X 10~4

0.187

0.174

5.94 X 10’3 0.367

1.92 X 10~4 0.123

4.44 X 10*3 0

0.127

1430

160 ^ Total

72.1 days

3.49 X 10’2 4.01 X 10~2

8.24 X 10’3

0

2470

Total, all fission products

3.76 X 103

1.14 X 102

8.66

*Uranium-fueled 1000-MWe PWR, З-year fuel life.

*Total elemental activities for fuel at discharge include short-lived radionuclides not listed here. §G. V. Samsonov [SI],

^ Total activity of the element whose principal radionuclide(s) is (are) listed above.

postirradiation cooling periods of 150 days and 10 years. The variation of beta activity of the long-lived fission products with cooling time is shown in Fig. 8.1.

Gaseous fission products are important when possible releases of radioactive species to the air are to be considered. At the reactor site such releases can result when gaseous fission products diffuse from the fuel material and escape through defects in the fuel cladding. These radioactive nuclides are still confined within the coolant circuit of the reactor. However, coolant leaks and the need for occasional venting of insoluble and noncondensable gases from a liquid coolant system result in some handling of radioactive fission gases at the reactor site. Gaseous radioiodine is removed by adsorption in activated carbon. Radioactive noble gases are held for radioactive decay for periods of time varying from over a week to a month, after which the 8SKr and possibly some remaining 133Xe are discharged to the atmosphere. Atmospheric dilution brings the concentration of these radionuclides to levels well below tolerance. Alternatively, these vented gases may be treated by various means, such as absorption, adsorption, condensation, and/or compression into storage cylinders, for removal and long-term storage.

Most of the long-lived radioactive fission gases are still present in the fuel when it is processed to recover the uranium and plutonium. In many separation processes the first step involves mechanical chopping of the fuel rods, followed by acid dissolution of the fuel material. Gaseous and volatile fission products liberated in these steps must be disposed of safely. Of the noble fission gases, 85 Kr is the only radionuclide that is present in significant quantities after reprocessing cooling periods of a few months. At many reprocessing plants 85 Kr is discharged directly to the atmosphere through a tall release stack provided to ensure sufficient mixing with the air. Alternatively, krypton can be recovered from the off-gases by condensation, adsorption, or absorption, as discussed in Chaps. 10 and 11.

In addition to the fission-product tritium listed in Table 8.1, additional tritium is produced in the reactor by neutron reactions with boron control absorbers, with lithium contaminants, and with deuterium in the water coolant-moderator. A portion of the tritium that is produced in the coolant of light-water reactors (LWRs) is released to the environment as diluted tritiated water at the reactor site. Solid boron control absorbers containing tritium are ultimately stored as solid radioactive wastes. During fuel reprocessing a portion of the fission-product tritium is evolved as gaseous hydrogen and the remainder appears as tritiated water (НТО) or as zirconium tritide in the chopped fuel cladding. If not collected prior to fuel dissolution, the tritiated water follows the water carrier in fuel reprocessing and at present is released to the environment as tritiated water vapor or liquid.

Although most of the fission-product radioiodine will have decayed away during the preprocessing cooling period, the extremely low tolerance concentration of radioiodine requires that 1311 and 129I be removed from reprocessing effluents. Also, radioactive iodine remaining in the dissolved-fuel solution extracts readily and reacts with the organic extracting solvents. Only about 1 Сі/year of 129I is formed in a 1000-MWe reactor, but its long half-life and relatively high biological toxicity make 1291 an important long-term environmental hazard. Special processes for recovering and sequestering radioactive iodine from the off-gas in fuel reprocessing are discussed in Chaps. 10 and 11.

I31Cs and 90Sr, elements of groups I and II of the periodic table, are important in determining the radioactivity of fission products after long decay periods. They are both easy

Figure 8.1 Radioactivity of fission pro­ducts and actinides in high-level wastes produced in 1 year of operation of a uranium-fueled 1000-MWe PWR.

to remove from uranium in aqueous processing because of their very low solubility in organic solvents.

Yttrium and the lanthanides, which are grouped together under group IIIB, likewise are easily separable from uranium in aqueous processing, with the possible exception of cerium. The troublesome activity from cerium contamination is due to the beta and gamma decay of 144Pr, the short-lived daughter of 144Ce. 140La emits penetrating gamma radiation and is one of the most important rare-earth fission products to be considered if the decay period is of the order of 30 days or less. 147Nd is relatively short-lived, and its long-lived daughter 147Pm emits no gammas; both are easily removed in aqueous processing.

Zirconium and niobium, of groups IVB and VB, are both amphoteric1" in character, and their complex hydrolytic behavior makes zirconium and niobium two of the most difficult fission products to separate by aqueous processing. Group VI fission products have either very short or very long half-lives, and the most troublesome fission product in this group, "Mo, will be present in appreciable activity only for very short cooling periods. Its group VII decay daughter, 2.12 X 10s year "Tc, contributes to the long-term radioactivity of stored fission-product wastes. "Tc may be important to the long-term transport of fission products stored in geologic media.

106Ru, of group VIII, is one of the most important fission-product contaminants in fuel reprocessing because of its multiple valence states and complex chemistry in aqueous solutions. In the presence of strong oxidizing agents ruthenium may appear in gaseous form as Ru04.

PROPERTIES OF PLUTONIUM

1.1 Plutonium Isotopes

Table 9.13 lists the isotopes of plutonium important in nuclear technology and some of their important nuclear properties. Plutonium isotopes are produced in reactors by the nuclide chains shown in Fig. 8.5. Typical quantities and isotopic compositions of plutonium in various reactor fuel cycles are listed in Tables 8.4, 8.5, 8.6, and 8.7. In reactors fueled with uranium and pluto­nium, 239Pu is the principal isotopic constituent, but 238Pu contributes the greatest amount of alpha activity. With 235U-thorium fueling, 238Pu is the principal isotopic constituent.

Reaction with 2200 m/s
neutrons

Mass,

amu

Half-life

Type+

Effective

MeV

Fraction of decays

(n, 7)

Fission

per

fission

236.04607

2.85 yr

a

SF

5.868

8 X 10‘10

165

2.22

238.049511

86 yr

a

SF

5.592

1.7 X 10*9

547

16.5

2.90

2.33

239.052146

24,400 yr

a

SF

5.243

4.4 X 10‘12

268.8

742.5

2.871

240.053882

6,580 yr

a

SF

5.255

4.7 X 10’8

289.5

2.143

241.056737

13.2 yr

a

/3

a

SF

0.007

2.3 X 10-5

368

1009

2.927

242.058725

3.79 X 10s yr

4.98

5 X 10‘*

18.5

<0.2

2.15

243.061972

4.98 h

/3

0.239

60

196

244.0641

8 X 107 yr

a

SF

4.66

3 X 10‘3

1.7

2.30

Radioactive decay

Cross section, b Neutrons

^SF, spontaneous fission.

radiological toxicity, laboratory work on reactor plutonium must be carried out in airtight glove boxes.

^Pu. The isotope 240 Puis produced by neutron capture in 239 Pu. It is not fissionable by thermal neutrons, but, like all other plutonium isotopes, it fissions with fast neutrons.240 Pu is converted to a fissionable nuclide by neutron capture. Therefore, like 232Th and 238U, it is a fertile material. It undergoes alpha decay, with a half-life of 6580 years, to form 236U, which then decays to 232Th, the parent of the 4n decay series discussed in Chaps. 6 and 8. Like the other even-mass plutonium isotopes, 240 Pu produces neutrons by spontaneous fission. It is present in greater concentration in reactor plutonium than any of the other even-mass plutonium isotopes.

M1Pu. The isotope 241 Pu results from neutron capture in ^Pu. It is fissionable with thermal neutrons and contributes significantly to the energy production in uranium irradiated to high exposure and in recycled plutonium. It undergoes beta decay, with a half-life of 13.2 years, to form 241 Am, which then decays to 237 Np in the 4n + 1 decay series. The decay of 241 Pu results in only low-energy electrons and weak x-rays. Alpha particles are formed in only 2.3 X 10’3 percent of the decays. However, the beta-decay daughter 241 Am emits gamma radiation when decaying, thereby adding to shielding requirements when working with separated reactor-grade plutonium.

^Pu. The isotope 242Pu is formed by neutron capture in 241 Pu. With a half-life of 3.79 X 10s years, it is the longest-lived of all the plutonium isotopes present in any appreciable amount in reactor-produced plutonium. It alpha decays to 238U in the 4n + 2 decay series. Because 242Pu has a small neutron-absorption cross section relative to “’Pu, 240Pu, and 241 Pu, and because its neutron-capture daughter 243 Pu is relatively short lived, 242 Pu of high isotopic purity can be produced by the long irradiation of separated reactor plutonium. After a neutron-exposure fluence of 1.6 X 1022 thermal neutrons/cm2, about 60 g of242 Pu of approximately 99 percent isotopic purity is produced per kilogram of original reactor plutonium [K2]. Because of its long half-life and correspondingly lower radiotoxicity, 242Pu is useful for laboratory chemical research.

243Pu. The isotope 243 Pu, formed by neutron capture in 242 Pu, undergoes beta decay to 243 Am with a half-life of 4.98 h. Because of its short half-life, 243Pu is present only in very small concen­tration during reactor irradiation, and it disappears after irradiated fuel has been stored for a few weeks. The low concentration of 243 Pu results in negligible production of the long-lived 244 Pu in reactors.

244Pu. The isotope 244 Pu is the longest-lived of the plutonium isotopes, with a half-life of 8 X 107 years. It can be produced by neutron absorption in 243 Pu, but because of the short half-life and low concentration of 243 Pu only minute quantities of 244 Pu, of the order of 10’10 percent, are present in reactor-produced plutonium [K2]. Small quantities of244 Pu, as well as 24s Pu and 246 Pu, are present in the residues from nuclear explosions, resulting from the decay of the neutron-rich uranium isotopes 244 U, 245 U, and 246 U formed by multiple neutron capture in the high neutron flux at the initiation of the explosion.

1.2 Plutonium Radioactivity

The radioactive decay properties of the plutonium isotopes that appear in irradiated reactor fuel are listed in Table 9.14. All but 241 Pu and 243Pu are alpha emitters. Because it penetrates matter only weakly, alpha radiation is stopped by the outer layer of dead skin and is not a hazard outside the body. However, plutonium is very effective biologically when deposited in or on living tissue, particularly if by inhalation or by contaminated injuries.241 Pu is a relatively short-lived (13.2-year

Data for 236Pu through 242Pu from Valentine [VI]; data for 243Pu from Keller [К2]. The energy listed for beta decay is the maximum beta energy.

half-life) beta emitter and is of radiological significance because it is the parent of 241 Am, an alpha emitter that accumulates in tissues and constitutes a hazard comparable to that of plutonium [B2].

Personnel working with plutonium must be protected by light shielding. The external radia­tion to be shielded includes gammas from alpha and beta decay, internal conversion x-rays, gammas, and neutrons from spontaneous fission, and neutrons from (a, n) reactions in materials of low atomic number. Neutron yields for various types and forms of plutonium are listed in Table 9.15.

Kilogram quantities of plutonium are fabricated in shielded glove-box facilities [VI]. A

Table 9.15 Neutron yields for plutonium

Neutron yield,

n/(g Pu*s)

Type of plutonium

Metal^

Oxide *

Low-exposure plutonium §

51

60

High-exposure reactor plutonium

340

538

238 Pu heat source

2,150

13,500

^From spontaneous fission.

* From spontaneous fission and from (a, n) reactions.

§ Plutonium with a relatively low content of 240 Pu, resulting from irradiation of 238 U at low bumup.

Source: A. Valentine, “Capabilities for Control of Plutonium in Processing,” Plutonium Information Meeting, Jan. 1974.

typical box consists of a g in of lead sandwiched between fg in of stainless steel on the interior and •jg in on the exterior. Windows consist of 5 in of lead glass. For neutron shielding 4 in of water, paraffin, or Plexiglas is added. Exhaust ventilation from the glove boxes passes through several layers of high-efficiency particulate filters to remove plutonium aerosols and to provide essentially complete containment of the plutonium being processed.

1.3 Plutonium Electronic Structure

The electronic structures of the ions are simpler than those of the metals. In the case of plutonium, removal of the first two (7s) electrons increases the stability of the 5/level relative to the 6d level, and the electrons become firmly placed in the 5f shell. After depletion of the 7s electrons, the next four electrons are removed from the 5/ shell. A summary of the electronic structures of plutonium (in addition to the Rn core) is given in Table 9.16.

1.4 Plutonium Metal

The phases of plutonium metal and their transition temperatures at atmospheric pressure are shown in Table 9.17. The delta-prime phase exists only in high-purity plutonium; as little as 0.15 w/o (weight percent) impurities results instead in a continuous delta phase [C4]. Because of the high densities of the metallic states of uranium and plutonium, there is considerable incentive to use metal fuel in fast-breeder reactors to obtain high breeding ratio. However, the solid-phase transformations in uranium and plutonium and the susceptibility of these metals to radiation damage have resulted in greater emphasis on nonmetallic forms for high-bumup breeder fuel. The large density changes of plutonium metal, particularly between the alpha and beta plutonium, and the large thermal expansion coefficients, as shown in Table 9.17, can result in serious distor­tion and deformation of the fuel elements when subjected to internal stresses from repeated thermal cycling and from radiation damage. Solutions of molten uranium and plutonium have been considered as a fluid fuel for breeder reactors, but the extensive corrosion of structural materials by this molten metallic fuel is a formidable problem.

Plutonium metal is prepared by calcium reduction of plutonium fluorides or oxides in induction-heated MgO crucibles, under an inert atmosphere of helium or argon. The thermo­dynamics of plutonium reduction are discussed later in this chapter.

Plutonium metal oxidizes readily in the presence of humid air at elevated temperatures. The massive metal is relatively inert to atmospheric oxidation at room temperature, although the presence of water vapor causes unalloyed plutonium metal to disintegrate over long periods even with relatively little oxidation [K2]. The finely divided metal is pyrophoric. Plutonium reacts with halogens at moderate temperatures to form the trihalides. The metal is readily soluble in

Table 9.16 Electronic structures of plutonium ions

Plutonium

valence

Shell

6s

6 P

5/

6 d

Is

0

2

6

6

0

2

2

6

5

1

2

+3

2

6

5

0

0

+4

2

6

4

0

0

+ 5

2

6

3

0

0

+6

2

6

2

0

0

Table 9.17 Properties of plutonium metal

Phase

Temperature

ranged

°С

Crystal

structure*

Density,*

g/cm3

Linear expansion coefficient, § per °С (X 106)

a

25-122

Simple

monoclinic

19.86

59

p

122-205

Body-centered

monoclinic

17.70

30.3

7

205-318

Face-centered

orthorhombic

17.14

33.3

8

318-452

Face-centered cubic

15.92

-8.8

8′

452-476

Body-centered

tetragonal

16.00

-63

Є

476-640

Body-centered

cubic

16.51

25.6

Liquid

*From Rand [R2].

*From Miner and Schonfeld [M5].

^ Mean value over the indicated temperature range (25 to 122° C for a phase) [C4].

HC1 of all concentrations and dissolves also in 72% HC104, 85% H3PO4, and concentrated tri­chloroacetic acid. Nitric acid shows no visible attack on massive plutonium over a period of several hours. Plutonium reacts slowly with H2 S04 of moderate concentrations, but with concentrated H2 S04 it forms a protective coating that resists further attack.

Uranium Purification

Uranium leaving the partitioning step in the organic phase is back extracted to the aqueous phase by 0.01 M HN03. It is then purified by one or more additional cycles of solvent extraction by TBP, while plutonium is kept in the inextractable trivalent state. To purify this uranium sufficiently to permit its use as feed to a UF6 plant, the U. S. DOE requires that the total beta-gamma activity be less than twice that of aged natural uranium and that the alpha activity be less than 1500 disintegrations per minute per gram of uranium, corresponding roughly to a plutonium-uranium ratio less than і X 10"8. To meet these strict specifications, a final cleanup step is usually needed. The first Purex plants passed the concentrated uranyl nitrate solution through a silica gel bed, which adsorbs fission products, primarily zirconium and niobium. A recent, more versatile process [B4, SI], developed in Italy, removes zirconium, niobium, and tetravalent neptunium and plutonium from aqueous nitrate solution by batch extraction with a 0.4 M solution of oleyl hydroxamic acid in 20 v/o octyl alcohol, 80 v/o n-dodecane. Distribution coefficients for these contaminants in this solvent are very high. When the solvent becomes too contaminated it is regenerated by washing with aqueous oxalic and nitric acids.

Factors Affecting Criticality Safety

The principal factors that must be taken into account in assessing criticality safety are as follows: [32] [33] [34] [35] [36] [37] [38] [39] [40] [41] [42]

For given fuel composition (factors 1 and 2 specified), the simplest but most restrictive condition to ensure subcriticality is one of items 3, 4, 5, or 6 (limitation of mass, dimensions, volume, or concentration of fissile material). These so-called single-parameter limits for fissile nuclides are spelled out in American National Standard ANSI N16.1-1975 [А4]. They were abstracted in Table 4.11 of Chap. 4 and are amplified somewhat in Sec. 8.2, following. These single-parameter limits give the largest mass, size, volume, or concentration that will be safely subcritical no matter what other criticality-limiting conditions may be present.

Use of a single-parameter limit often leads to an inconveniently small size of batch or equipment. To permit safe operation on a larger scale, combinations of two parameters that together are safely subcritical are sometimes specified, provided that the simultaneous presence of both parameters can be assured. For example, if the maximum concentration of plutonium in aqueous solution can be limited to 20 g/liter, the maximum safe diameter of a cylinder may be increased from the single-parameter limit of 15.7 cm (Table 4.11 or 10.25) to 25 cm (Fig. 10.35).

By restricting the concentration of moderators (item 7) or the presence of reflectors (item 8), the dimensions or concentrations of safely subcritical systems may be increased further. The presence of neutron-absorbing poisons such as boron, cadmium, or gadolinium (item 9) also sometimes permits such increase. On the other hand, heterogeneity (item 10, such as lumping of fuel containing 238U or interaction between two systems containing fissile material (item 11, such as adjacent pipes carrying fissile material) reduce the dimensions, mass, or concentration of safely subcritical systems.

236 U and 237U

236 U and 237 U are produced by successive neutron captures in fuel containing 238 U. Both isotopes are detrimental contaminants. Long-lived 236 U is a neutron absorber that reduces the fuel’s reactivity. It has an atomic mass between 23SU and 238 U, which makes subsequent isotopic reenrichment more difficult, as described in Sec. 15 of Chap. 12. The 6.7-day half-life of 237 U necessitates storage of irradiated uranium for around 150 days if its radioactivity is to be no higher than that of natural uranium, as explained in Chap. 8. И7и decays to 2.14- million-year 237 Np, the longest-lived member of the 4л + 1 radioactive decay series.

1.3 239U

239U is produced by neutron capture in fuel containing 238 U. It decays to 239 Pu through two successive beta emissions, as described in Fig. 3.1. Because of its short, 23.5-min half-life, it is not present after irradiated fuel has been stored. It is, however, a significant contributor to decay heat production immediately after reactor shutdown.