Operations with fissile materials may be performed safely by complying with any one of the subcritical limits given in Sec. 8.2 provided the conditions under which it applies are maintained. A limit shall be applied only when the effects of neutron reflectors and of other nearby fissionable materials are no greater than reflection by an unlimited thickness of water, t The limits shall not be applied to mixtures of 235U, and 233U, and 239Pu.

Process specifications shall incorporate margins to protect against uncertainties in process variables and against a limit being accidentally exceeded

Uniform aqueous solutions. Any one of the limits of Table 10.25 is applicable provided a uniform aqueous solution is maintained and provided, for 239Pu, at least four nitrate ions are present for each plutonium ion. The 239 Pu limits apply to mixtures of plutonium isotopes provided the concentration of 240Pu exceeds that of 241 Pu and provided 241 Pu is considered to be M9Pu in computing mass or concentration.

Uniform slurries. The limits of Table 10.25 may be used for macroscopically uniform slurries, provided:

1. There are at least four nitrate ions intimately associated with each plutonium atom, and

2. For the dimensional and volume limits, the ratio of hydrogen-to-fissionable material does not exceed that in an aqueous solution having the same concentration of fissionable material.

^Section 8.2 is taken verbatim from Sec. 5 of [A4] except for footnotes and changes in references to tables, sections, and literature citations. Extracted from American National Standard N-16.1-1975 (ANS-8.1), with permission of the publisher, the American Nuclear Society.

*The limits do not apply to reflection by graphite, beryllium, or heavy water.

The limit on the 1.00 wt % enrichment of uranium is valid only for the slurries in which the ratio of surface-to-volume of the particles is at least 80 cm"1.

Nonuniform slurries. The limits on cylinder diameter and slab thickness in Table 10.25 may be used for nonuniform slurries provided:

1. Four nitrate ions are intimately associated with each plutonium atom,

2. The restriction on the ratio of hydrogen-to-fissionable atoms, specified in Condition 2 for uniform slurries is met everywhere throughout the system,

3. For cylinders, the concentration gradient is only along the length, and

4. For slabs, the concentration gradient is only parallel to the faces.

For 239Pu in the absence of nitrate ions, but with the proviso that no localized regions of density greater than 0.25 g of 239Pu/cm3 are permitted, limits of 15.1 and 5.4 cm on cylinder diameter and slab thickness, respectively, are applicable under Conditions 2, 3, and 4 above.

The areal densities given in Table 10.25 are valid for nonuniform slurries provided these densities are uniform.

The subcritical mass limits for 235U, 233U, and 239Pu in nonuniform slurries are 0.70, 0.52, and 0.45 kg, respectively. Nitrate ions need not be present.

Metallic units. The enrichment limit for uranium and the mass limits given in Table 10.26 apply to a single piece having no concave surfaces. They may be extended to an assembly of smaller units provided there is no inter-unit moderation.

The 235 U and 233 U limits apply to mixutres of either isotope with 234 U, 236 U, or 238 U provided all isotopes except 238 U are considered to be 235 U or 233 U, respectively, in computing mass. The 239Pu limits apply to isotopic mixtures of plutonium provided the concentration of ^Pu exceeds that of 241 Pu, all plutonium isotopes are considered to be 239 Pu in computing mass, and no more than 1% 238Pu is present.

550 NUCLEAR CHEMICAL ENGINEERING Table 10.26 Single-parameter limits for metal units

Each of the uranium isotopes is a member of one of the four possible radioactive decay series involving successive alpha and beta decay reactions. 238 U is the longest-lived member and the parent of the An + 2 series, which includes 234 U as a member. 235 U is the longest-lived member and the natural parent of the An + 3 series. 236 U decays by alpha emission to 232 Th, the longest-lived member and natural parent of the An series, to be described in Chaps. 6 and 8. 232U decays by alpha emission to 228 Th, also a member of the An series. Problems arising from the radioactivity of 232U and its daughters are discussed in Chap. 8. 237U decays by beta emission to 237Np, the longest-lived member of the An + 1 series, the only one not of natural occurrence. 233 U is an intermediate member of this series.

1.4 238 U Decay Series

Figure 5.1 shows the nuclear reactions that occur successively as 238U decays into its stable end product 206 Pb. As is conventional in such decay diagrams, each nuclide is plotted on a grid, with the mass number A vertical and the atomic number Z horizontal. Table 5.2 gives the half-lives of these radioactive species and their principal decay radiations. The last column of Table 5.2 gives the ratio of the number of atoms of each nuclide to the number of uranium atoms in natural uranium, assuming that the uranium in the ore has been undisturbed long enough to be in decay equilibrium with all its decay products. At equilibrium, the activity of each of these nuclides is the same. Per megagram of contained uranium, the activity of 238 U and each of its daughters is

(0.9927 238U/U)(106 g U/Mg)(6.0225 X 1023/g-atom)(0.693)

(238 g U/g-atom)(4.51 X 109 yr)(3.154X 107 s/yr)[3.7 X 1010/(Ci-s)]

Hie daughters of 338 U of principal radiological concern in uranium mills and refineries are the long-lived nuclides 330Th and 336 Ra (radium) and gaseous 333 Rn (radon). The amount of these nuclides in uranium mills and tailings pfles is discussed in Sec. 8.9; their occurrence in uranium refineries is discussed in Secs. 9.2 and 9.7.

In the U. S. Department of Energy (DOE) plant at Paducah and the Comurhex plant at Pierrelatte [B5], UF4 is converted to UF6 by reaction with fluorine in a tower reactor. Solid UF4 and a slight excess of fluorine gas are fed at the top of a monel tower with walls cooled to around 500°C. Most of the UF4 reacts almost instantaneously with a flame temperature of around 1600°C. Small amounts of unreacted UF4 and uranium oxides are removed from the bottom of the tower and recycled to the hydrofluorination step.

The effluent gases containing UF6, fluorine, and diluent gases such as oxygen and nitrogen are cooled to around 150°C and passed through filters to remove entrained solids. Most of the UF6 is condensed as solid in cold traps cooled to -10° C. Residual fluorine in the gases leaving the cold trap is removed by reaction with additional UF4 in a fluid-bed reactor which forms additional UF6 and nonvolatile intermediate fluorides such as UF5. Solids from this bed are fed to the primary fluorination reactor.

Exhaust gases from the second reactor go to a second cold trap at — 50° C, which condenses most of the UF6. The last traces of UF6 are removed by a second UF4 fluid-bed reactor, which reduces the UF6 content of exhaust gases to less than 10 ppm.

UF6 produced in this way is exceptionally pure. The UF6 content is above 99.97 percent, and the overall process yield exceeds 99.5 percent. Table 5.28 summarizes U. S. DOE specifications that UF6 must meet to be fed to U. S. gaseous diffusion plants.

1.1 Phases

The phases of metallic zirconium and hafnium and their transition temperatures are listed in Table 7.2.

Zirconium and hafnium form nearly ideal solid solutions, with melting and transition temperatures between those of the pure components.

Equations for the vapor pressure of zirconium are [II]

Source: International Atomic Energy Agency, “Zirconium: Physico-Chemical Properties of Its Compounds and Alloys,” Atomic Energy Rev., Special Issue No. 6, 1976.

Contrasted to benefits from reduction in “Th activity, preprocessing cooling increases the 228Th content of irradiated thorium. The amount Noe (7) of 228Th present at the end of an irradiation period TR, due to 232 U decay, is given by applying Eq. (2.106):

Nm 1 — ■Tr 1 —

N02 ^ 21 Мп(М22 —МпХМов “Ми) M2211 — M22XM08 ~M22)

1 — Tr

Мов(Мі1 ~ МовХМ22 ~ Мов)

where Мов = 0008 + Хов (8.35)

During the preprocessing cooling period, the atom ratio of 232 U to 232 Th remains essentially constant because of the long half-life of 232 U. An equation for the activity osNos(Tc) of 228Th present after a time Tc of preprocessing cooling is obtained by applying Eqs. (2.13) and (2.27):

Хов^ов(Гс) = obNq&(Tr) е-кхтс + 0 _e-wrc) (g 36)

Nm Nm Nm

where the activities XoeN0b(Tr) and 22N22(Tr) at the end of the irradiation are obtained from Eqs. (8.34) and (8.19), respectively.

The growth of 228 Th activity during irradiation at various neutron fluxes is shown in Fig.

8.14. At a given flux time of irradiation, the 228Th activity is lower at the higher flux levels. This is because the actual time since the beginning of irradiation is shorter at the higher fluxes and less of the 232 U formed has undergone radioactive decay.

Because 228 Th is usually not in secular equilibrium with 232 U, its activity continues to grow during preprocessing cooling. Although the total of the 228 Th and 234 Th activities decreases with time, the activity from 228 Th daughters is the most troublesome when chemically purified thorium is being refabricated. The highly energetic betas from both 228 Th and 234 Th chains give large skin doses on surface contact with separated thorium, but the hard (i. e., highly energetic) gammas (2.3 MeV) from the 228 Th chain can result in serious dose rates even with semiremote fabrication techniques.

When the separated thorium is eventually to be recycled and blended with low-activity uranium streams, such as makeup 235 U, the activity of 228 Th after a preprocessing cooling time Tc and a postprocessing storage time Ts is given by

(ХЛОов = [N13(r*)XM(l — e-K«Tc)+Nm(TR)Ховє’т’]е-^т* (8.37)

where N22(Tr) = quantity of 232U in discharge fuel Noe(TR) = quantity of 228Th in discharge fuel

Thorium can be recycled for fabrication with low-activity uranium if the 228 Th activity is no more than a factor ф greater than the 228 Th activity in natural thorium,

(XN) 08 — 0(XjV)o2

Arnold [Al] suggests a value of ф = 5 for thorium to avoid the requirement of semiremote fabrication. Combining Eqs. (8.37) and (8.38), we obtain

For an HTGR [HI, P3] with discharge concentrations of (XN)22/(XN)o2 = 4.04 X 103, (XN)oe/(XN)o2 = 2.54 X 103, Tc = 150 days, and ф = 5, we obtain

T, = 21.3 years

for thorium to be used when fabricating fuel with makeup 23SU. In the HTGR about two-thirds of the thorium is used to fabricate fuel containing makeup or recycled uranium containing no 332 U, so about two-thirds of the separated thorium would be subjected to the storage time estimated above.

For that portion of the separated thorium that is eventually to be recycled and blended with the recycled bred uranium, less time for thorium storage is possible. A reasonable criterion is that the thorium be stored for a sufficient period such that its 228 Th activity is equal to the activity of 228 Th in the recycled uranium at the time of fabrication. Ignoring process losses, the recycled bred uranium contains all of the 232 U that was present in the discharge thorium. If this recovered uranium has been stored for a time Tp prior to fuel fabrication, the activity of 228 Th in the uranium is

(Хов^м)и=^22Х22(1-е-х«г^) (8.40)

Applying the above criterion, we equate the 228 Th activity in the bred uranium to the activity

Figure 8.14 228 Th concentration in irradiated thorium. Basis: ОщСп, 2n) = 0.010 b.

of 228 Th in the fraction /3 of the recovered thorium that is eventually to be recycled for fabrication with the bred uranium, i. e.,

(Ьт#ш)и = №т#я)п (8.41)

where (XoejVog)Th is given by Eq. (8.34). Combining Eqs. (8.34), (8.36), (8.40), (8.41), and

(8.37) , we obtain

, 1 , Г„ 1 — (1 “

‘ = 5£1п[/——————— i-e-КЪ——————

For the HTGR, /3 = 0.36. Assuming that Tc — ISO days and 7> = 60 days, we obtain

Ts = 4.2 years

As the prefabrication time of uranium storage increases, less time is required for thorium storage. For the parameters listed above, if the recovered uranium is stored for 312 days before fabrication, the 228 Th activity in the uranium becomes equal to that in 36 percent of the separated thorium, so no thorium storage is then required to meet the 228Th criterion.

As described in Chap. 3, fuel discharged from a nuclear reactor after irradiation to the end of its useful life still contains most of the fertile material (238U or thorium) that was present in the fuel when charged, appreciable concentrations of valuable fissile nuclides (235 U, plutonium, and/or 233U) and large amounts of radioactive, neutron-absorbing fission products. The principal objectives of reprocessing are (1) to recover uranium and plutonium, and thorium if present, for reuse as nuclear fuels; (2) to remove radioactive and neutron-absorbing fission products from them; and (3) to convert the radioactive constituents of spent fuel into forms suitable for safe, long-term storage. There may be some interest in recovering individual fission products such as 90Sr or 137Cs for use as radiation sources or in recovering by-product transuranic elements such as neptunium, americium, or curium.

The thorium nitrate solution from the dissolver will be about 9 Af in nitric acid. To obtain satisfactory decontamination of thorium from fission-product protactinium, ruthenium, and zirconium-niobium, it was found necessary to remove all of the nitric acid from the solution and make the solution around 0.15 Af acid-deficient in nitrate ion by converting a fraction of the A1(N03)3 to a water-soluble basic nitrate. This also converts the readily hydrolyzed nitrates of these fission products to basic nitrates that are less extractable than the species present in the acid dissolver solution.

In the initial development of the Thorex process [S9], the feed was made acid-deficient by evaporation until the boiling point reached 155°C. Trouble was experienced with corrosion and with precipitation of solids. The procedure finally adopted [R2] is shown in Fig. 10.20. The dissolver solution is evaporated until its boiling point reaches 135°C, at which point about 70 percent of the original volume has been evaporated and the nitric acid concentration is down to 3 M. Further stripping at constant volume and a constant temperature of 135°C is carried out by adding water and boiling off aqueous nitric acid until the solution is 0.2 M acid-deficient. The solution is finally diluted with water to make it around 0.15 M acid-deficient.

Prior to solvent extraction, the solution is treated with 0.02 M NaHS03 at 55°C for 1 h to convert ruthenium to a less extractable form.

If the irradiated thorium to be processed still contains appreciable protactinium activity from 27-day 233Pa, 97 percent of this can be removed and recovered by adsorption on unfired, porous Vycor glass [G10], At a flow rate of 1.57 ml/(min-cm2), columns containing 100-120 mesh Vycor, water-cooled to prevent boiling, could be loaded with 3.1 g protactinium per kg glass with only 3 percent break-through. Washing with eight volumes of 10 M HN03, 0.1 M A1(N03)3 removed most of the uranium and thorium. Then, elution with 0.5 M oxalic acid recovered 98.5 percent of the protactinium at an average concentration of 1.46 g/liter.

It has been an attractive idea for some time to reduce the long-term potential hazard of the waste by chemical removal of the actinides and subsequent transmutation in a neutron flux. The overall incentive for actinide partitioning is not very great. The reduction of the ingestion hazard after recycling equilibrium has been reached will be only modest, and the technical effort will be enormous. The technology for actinide partitioning is not available as yet, and considerable development will be required to make it available. Moreover, it has to be considered that part of the actinides are transferred from the waste to the fuel cycle on recycling, where they may create an even greater hazard than in the waste.

The overall effect of actinide partitioning depends not only on the degree of chemical separation but also on the efficiency of transmutation. At present transmutation would have to be performed by recycling the separated actinides to LWRs, where it will be less effective than in a LMFBR. The reduction of the potential hazard achieved by actinide removal will decrease with repeated recycling of these actinides as a result of the buildup of the higher actinides and will eventually attain an equilibrium value. Figure 11.17 is a plot of equilibrium hazard index reduction factors in LWR uranium waste versus age of the waste for 99.5 and 99.9 percent chemical separation efficiency. Between 100 and 50,000 years, reduction factors are found of not more than 5 and 30, respectively [С2]. Any actinide separation higher than 99.9 percent makes it necessary to consider 99 Tc as well and seems out of reach, as presently nothing even close to 99.9 percent is technically feasible.

Figure 11.17 reflects the effect that actinide partitioning and transmutation has on the actin­ide hazard index of only the HLW itself. If the total quantity of actinides accumulated in the HLW and in the fuel cycle is considered, the same equilibrium reduction factor will eventually be at­tained provided that a constant nuclear power level is assumed, but it will take a very long time. In the fuel-cycle study performed for the American Physical Society [P2], an example with recycling the actinides to a LMFBR has been calculated that is shown in Fig. 11.18.

It should also be obvious that actinide reduction in HLW is reasonable only if an equivalent reduction of actinides in non-high-level waste, such as refabrication waste, can also be achieved. Also, 129 I must be considered in a long-term hazard balance.

Chemical separation. Current concepts for high-efficiency separation of actinides call for improved plutonium recovery, coextraction of uranium and neptunium with subsequent partitioning by valence control, and extraction of amercium and curium from the HAW stream. There are a number of major problems to be solved before a technically feasible process will be available.

Actinide losses to undissolved residues of fuel and to solids generated in the process have to be eliminated. To improve the recovery of plutonium, inextractable forms have to be identified and means have to be found to recover them.

For the recovery of americium and curium from the waste stream, cation-exchange and extraction processes appear most promising. The outstanding problem is a highly effective separation of actinides from lanthanides. The latter would be harmful upon transmutation in thermal reactors because of the high-neutron-capture cross sections of some of them. An actinide/lanthanide fraction would probably have to be separated first from the other fission products and waste components and then the actinides would have to be recovered with high purity. Also, by taking into account that substantial additional waste streams would have to be managed without significantly increasing the overall waste quantity, it is obvious that the recovery of americium and curium will be the most difficult task in waste partitioning [B5].

Transmutation. Recycling actinides to the LWRs will decrease the average material neutron multiplication factor by only 0.8 percent, provided that they are of high purity [C2]. Recycling to LMFBRs, however, will be preferred. There will be less neutron capture in impurities, such as lanthanides, and the average fission-to-capture ratio of the actinides should be higher in a fast spectrum than in a thermal one.

Recycling of actinide waste will increase radiation problems associated with processing of fuel. After a few cycles, for example, 552 Cf builds up to the strongest neutron source and reaches 1012 njs per MT of heavy metal at 150 days after discharge.

Figure 11.19 is a schematic flow sheet for actinide recycling.

Assuming that at equilibrium all aqueous HN03 is fully ionized and all organic HN03 is in the form of HN03 "TBP, the distribution coefficient of nitric acid is

о = [HNOsjTBPCg)] (4.19)

H [H+(*?)3

and combining with Eq. (4.16),

DH = KH [N03′(«?)] [TBP(o)] (4.20)

For a uranium-nitric acid system, the concentration of uncombined TBP in terms of concentrations of uranium and acid in the organic phase is

[TBP(o)] = C — [HN03 — TBP(o)] — 2 [U02 (N03 )2-2TBP(o)] (4.21)

where C is the concentration of total TBP, both combined and uncombined, in the organic phase. The distribution coefficient of uranium in terms of total TBP concentration and aqueous concentrations is obtained by combining Eqs. (4.16), (4.18), and (4.21):

Dy________ = Ац [МОГИ)]2

(С — 2DV [U(V+(<zq)] Г (1 + AH [H>?)] [N03 ‘(aq)] f ‘ ‘

and solving for Dy,

Only the negative sign of the square root is used in Eq. (4.23); the positive value of the root yields a trivial solution that implies negative concentrations of uncombined TBP in the organic phase.

The extraction of nitric acid with TBP from aqueous solutions free of other extractable species has been studied by several investigators [G7, М2], and the equilibrium data lead to an average value of 0.145 for the acid equilibrium constant, assuming activity coefficients of unity. The correlation of nitric acid on the basis of Eq. (4.16) is poor when the acid concentration in the aqueous phase is greater than about 7 Af, possibly because of the formation of the dinitrato and trinitrato complexes 2HN03*TBP and 3HN03*TBP or possibly because of solution of nitric acid in the organic without complexing [S4].

The uranium distribution data in Table 4.3 can be correlated reasonably well by using the following equilibrium constants in Eq. (4.23) and assuming activity coefficients of unity:

KH = 0.145

Au = 5.5

The concentration C of total TBP is obtained from the volume percent (v/o) TBP in the organic phase by

where 0.972 is the density of pure TBP [G4, Ml, S4] and 266.3 is the molecular weight of TBP, which has the chemical formula (C4H9)3P04. Equation (4.25) neglects the small volume change resulting from water solubility in the organic phase and from extraction of the uranium and acid complexes, and it neglects the solubility of TBP in the aqueous phase [S4]. At 40 percent TBP by volume, the total TBP molar concentration Cis 1.464 mol/liter.

Uranium distribution coefficients calculated from Eq. (4.23) and from the above data are listed in Table 4.3.

The close agreement between observed and calculated distribution coefficients in Table 4.3 is surprising in view of the wide range of aqueous concentration and the assumption of unity for the activity coefficients. Distribution coefficients for an even greater range of parameters in the TBP extraction system are given in Chap. 10.

A number of attempts have been made to establish correlations of distribution coefficients in the U0j(N03)2-HN03-TBP system on a more fundamental thermodynamic basis. One approach [Bl, H2, R4] has been to correlate on the basis of ionic strength in the aqueous
phase, with assumed constant activity coefficients in the organic phase. A more advanced approach by Goldberg et al. [G2a] involved the correlation of distribution data based on the ratio of the activity of the U02(N03)2 ‘2TBP complex to the activity of free TBP in the organic phase, using activity coefficients derived from experimental data for the partial pressure of HN03 over aqueous solutions of HNO3 and иОзСЮз^. With this approach the data of Codding et al, [C3] for the distribution coefficients of UC^CNCb^ in TBP extraction were correlated over a wide range of concentrations, with an average deviation of 5.8 percent.

1.11Oxidation States of Uranium in Aqueous Solution

In aqueous solution, uranium may occur as trivalent U3+, the tetravalent uranous ion U4+, pentavalent Uv02V or the hexavalent uranyl ion UVI022+. However, U3+ is unstable, reducing water with production of hydrogen, and Uv02+ is unstable, disproportionating into U,+ and UV1022+:

2Uv02+ + 4H+ -+ U4* + UVI023+ + 2H20 Thus, only the uranous and uranyl ions are of practical importance.

1.12 Uranium(IV) Solutions

Solutions of tetravalent uranium salts are usually prepared by reduction of the corresponding uranyl compounds. Reduction may be effected by metallic zinc or at the cathode of an electrolytic cell:

U022+ + 4H+ + 2e — -* U4* + 2H20

Pure uranous compounds may be prepared by precipitating U(OH)4 from aqueous solution with ammonium hydroxide and dissolving the precipitate in the appropriate acid. Uranous sulfate, the most common salt, is soluble in water, as are the chloride, bromide, and iodide. Uranous nitrate is unstable, gradually undergoing oxidation to uranyl nitrate with liberation of oxides of nitrogen.

Tetravalent uranium can be precipitated from aqueous solution as the insoluble oxalate, fluoride, or phosphate. UF4 precipitated from aqueous solution contains water of crystal­lization. When this compound is heated to drive off the water, it is partially hydrolyzed to an oxyfluoride. The phosphate U3(P04)4 is soluble in hot, concentrated phosphoric acid and appears in this form when uranium in phosphate rock, Ca3(P04)2, is dissolved in sulfuric acid.