## Separation Factors

The degree of separation achieved by a single stage is known as the stage separation factor, or amply the separation factor a. This is defined as the weight, mole, or atom ratio in the heads stream divided by the corresponding ratio in the tails. For a two-component mixture,

_ t) у/(1-у) a~ t x/(l-x)

The separation factor defined in this way is useful because in many isotope separation processes, it is independent of composition. The ratio y/x, on the other hand, may vary strongly with composition.

Other useful measures of the degree of separation effected by a stage are the heads separation factor /3, defined by

n y/O-y)

І x/(i-*)

and the tails separation factor y, defined by

f x/(l-i) 7 І */(!-*)

The composition differences measured by a, /3, and у are indicated in Fig. 12.9 by the curved lines. From the definitions of a, (3, and y, it follows that

_ flz = ax
y~ Pz+l-z~ax+l-x

ax________ У

ax+ (3(1 — x)~y + /3(1 — y)

У _ i
y + a(l — y) z+y(l—z)

A relation between /3, a, and в may be obtained from (12.12), (12.15), and (12.16):

(a-1X1-0)

1 +0(a-lXl -У)

## Special Cases

Standard ideal cascade, p = q = 1. For the standard ideal cascade, p — q= 1. From Eqs. (12.242) and (12.243),

/3 = 7 = a}n

and the coefficient of z in Eq. (12.254) is identically zero. Hence which is equivalent to Eq. (12.142a).

Close-separation case. In many multistage isotope separation processes a — 1 < 1, so that /3—1^1 and 7 — 1 < 1. The gaseous diffusion process for separating uranium isotopes and the water distillation process for enriching deuterium are examples.

Define

То the second order in 5 and e this reduces to

Z6e _ ZQ3 — lXy ~ 1) 2 2

which is independent of z. Hence, the concept of separative capacity may be used to evaluate the total flow rate in a close-separation, ideal cascade for all values of p and q.

Low-enrichment case, z<£l. In the largest and most important stages of a deuterium enrichment or uranium isotope separation plant z < 0.03. For this low-enrichment case z[((3 + 1X7 ~ l)ln(3 — (7 + 1)03—l)ln7] in Eq. (12.254)is small compared with7ОЗ— 1)In 7 — (7 — 1) In 6 and may be neglected for values of (3 and 7 under 2.

## METHY LAM IN E-HYDROGEN EXCHANGE PROCESSES

The deuterium exchange reaction between liquid methylamine and gaseous hydrogen, CH3NH2(0 + HDC^CHjNHDCO + H2(g)

is catalyzed by potassium methylamide, CH3NHK. This reaction proceeds with sufficient speed at —50°C to permit operation of a cold tower at this temperature, where the equilibrium constant, 7.9, is the highest known for any practical, deuterium exchange reaction. The optimum hot-tower temperature for a dual-temperature process using this reaction is +40°C, a limit set by thermal decomposition of potassium methylamide at higher temperatures. At +40°C the deuterium exchange equilibrium constant is 3.6. The ratio of these two separation factors, 7.9/3.6 = 2.19, is also higher than the ratio for any other practical system (Tables

12.17 and 13.18). For this reason, Atomic Energy of Canada, Limited (AECL), has undertaken a development program for a dual-temperature process using methylamine and hydrogen from a synthetic ammonia plant with a flow sheet similar to Fig. 13.37.

Sulzer Brothers Canada, Ltd., working with AECL, has given a partial description [W6] of a dual-temperature flow sheet modified from Fig. 13.37 proposed for use in recovering deuterium from ammonia synthesis gas made from Alberta natural gas containing 135 ppm deuterium. Figure 13.40 is a material flow sheet for the synthesis-gas generation section and first deuterium-enrichment stage of such a heavy-water plant. Deuterium contents have been given as [xN], where x is the ratio of the deuterium content to that of Alberta water containing 135 ppm deuterium. The deuterium contents of methane, water, and hydrogen are those given by Wynn [W6]. The deuterium contents of methylamine streams have been assumed to give a plausible number of stages in the various towers. Total flow quantities

 Atom fraction D in liquid Figure 13.39 McCabe-Thiele diagram for Fig. 13.38.
 Transfer 0 from MA liquid to MA vgpor «*-D ;

 Natural gos 1270.8 CH4 _[0.9N]_____ ^ " д/Г"* 1440 N2 381.6 02

 Transfer D from MA vapor] a=| to water D —*■

assumed for this flow sheet are those for a plant permitting production of 1150 MT ammonia/day, after allowing for losses in the ammonia plant. The net deuterium extraction of

0. 422 kg-mol/h would produce 66.8 MT D2 О in 330 operating days per year.

The novel feature of this flow sheet is the production of synthesis gas enriched threefold relative to natural water to provide enriched feed for the exchange plant and thus reduce its size. In the synthesis-gas generator (A), natural gas whose deuterium content is 0.97V is re-formed with air and enriched steam, 5.7N, to produce threefold-enriched synthesis gas and unreacted enriched water, whose enriched deuterium content is recycled. Enriched synthesis gas is the vapor feed to the hot tower (C) of the first dual-temperature exchange stage. Here the deuterium content of synthesis gas is raised from 3N to 207V, while that of counterflowing methylamine and catalyst is reduced from 9151N to 10.916.V. In the cold tower (D), the deuterium content of synthesis gas is decreased from 20N to 0.2Л’ while that of methylamine is increased from 1.061V to 9SN. A portion of the 95-fold-enriched methylamine is fed to the second enriching stage, and an equal amount of partially depleted methylamine is returned; the resultant net flow of 0.422 kg-mol D/h, after further enrichment in higher stages, provides the plant’s heavy-water product.

Enriched steam for the synthesis-gas generator (A) is produced in the series of sieve-plate contactors (E), (F), and (G). In (E) deuterium is transferred from methylamine liquid to methylamine vapor, reducing the deuterium content of the liquid from 10.9167V to 1.061V while increasing that of the vapor from 1.02TV to 107V. In (F) deuterium is transferred from methylamine vapor to water, increasing the deuterium content of the latter from IN to 81V. This two-step transfer of deuterium from liquid methylamine leaving (C) to water leaving (F) is necessary to prevent chemical reaction between water and the catalyst dissolved in liquid methylamine.

Deuterium in enriched water (81V) leaving (F) and unreacted enriched water (5.5N) leaving (B) is transferred to steam in step G, producing enriched steam (5.7N) for the synthesis-gas generator from natural steam. This transfer step is used instead of simply recycling the water leaving (B) and (F) to avoid returning nonvolatile impurities to the synthesis-gas generator.

Because of the reduced rate of the deuterium exchange reaction at —50°C, the stages of the cold tower (D) are to be of the type developed by Sulzer [LI ] for the ammonia-hydrogen exchange process and used in the Mazingarbe plant, Sec. 9.1. For the methylamine-hydrogen system at —50°C, a stage efficiency of 70 percent has been obtained [W6].

At the temperature of the hot tower, 40°C, potassium methylamide slowly decomposes into potassium dimethyl formamidide:

2CH3NHj + CH3NHK -*■ CH3(NKXCH)NCH3 + 2H2 + NH3

This reaction is suppressed by addition of an equimolal amount of lithium methylamide, which has little catalytic activity but inhibits decomposition of the potassium compound.

The great advantage of this methylamine-hydrogen exchange process compared with the dual-temperature ammonia-hydrogen system is the much smaller number of stages needed with methylamine. Intratower flow rates relative to product D20 with methylamine are also smaller than with ammonia. Table 13.27 compares the two processes. The lower internal flow rates with methylamine also lead to lower utility requirements. A disadvantage of this methylamine — hydrogen flow sheet is the need to operate the synthesis-gas-generating section of the ammonia plant with enriched water. This necessitates recycle and strict control of losses of unreacted deuterium-enriched steam and water.

## Laser Isotope Separation of UF6

The absorption spectrum of UF6 is far more complex even than that of uranium metal, because the spectrum of the UF6 molecule involves transitions between many vibrational and rotational states that are absent in the uranium atom. Absorption bands of the 235UF6 molecule overlap those of 238UF6, so that highly selective absorption by one isotope is seldom found. This is illustrated by Fig. 14.43, which shows the absorption by 235UF6 and 238UF6 at four different pressures at room temperature at an infrared wavelength around 16 /tan at which the difference between the spectra of the two compounds is greatest. The peak in the 23SUF6 absorption band is displaced 0.55 cm-1 from the peak in the 238UF6 band at a wave number (reciprocal wavelength) of 625 cm’1, about 1 part in 1000. However, the absorption by 238UF6 at the peak absorption by 235UF6 is so great as to preclude selective absorption under these conditions.

It has been predicted theoretically by Sinha et al. [S5] and observed experimentally by Jensen and Robinson [J4, R2] that if UF6 is cooled to 55 К and its absorption spectra measured with high resolution, wavelengths can be found at which selective absorption by 235UF6 takes place with relatively little absorption by 238UF6. The reason for this is as follows.

Uranium in the UF6 molecule is at the center of an octahedron, with the six fluorine atoms equally spaced at the comers. Such a molecule can vibrate in six different modes, of which the uranium atom moves in only two, the only ones with an isotopic shift. In the v3 mode to which Fig. 14.43 is attributed, the uranium and two opposite fluorine atoms move up and down together out of the plane of the other four fluorine atoms. The absorptions of Fig. 14.43 are caused by transitions in which the vibrational quantum number increases by unity, while the rotational quantum numbers change by plus or minus unity. If all transitions were

Table 14.27. Estimated characteristics of uranium metal laser isotope separation plants

 Source of estimate Osaki et al. [03] Janes et al. [J2] Capacity, million kg SWU/yr 8.75 3 Specific electric power, kW/(kg SWU/yr) 0.20 0.02 Unit investment cost, \$/(kg SWU/yr) 36 195

from the lowest vibrational level, the fine structure of the absorption bands would be as shown qualitatively in Fig. 14.44, where the individual peaks are due to transitions from different rotational levels. Under such conditions, a 23SUF6 absorption maximum might be found that occurred at a 238UF6 absorption minimum, as shown in the figure. Then a tuned laser beam with a frequency spread narrower than the line spacing of 0.1 cm-1 might be able to excite 235UF6 to the first vibrational level without exciting 238UF6.

Such selective absorption is not possible at room temperature. There, only about 1 percent of the UF6 molecules are in their lowest vibrational state, so that the observed absorption spectrum is a composite of vibrational transitions from the ground state and many excited states, in each case to the next higher vibrational quantum number. These excited-state absorption frequencies are displaced somewhat from the ground state, so that 238UF6 lines from an excited state overlap 23SUF6 lines from the ground state, thus destroying selectivity.

There is another difficulty with working at room temperature. In the photochemical method, a second light beam would be used to dissociate vibrationally excited 23SUF6 molecules into a physically separable, nonvolatile lower fluoride and fluorine, while leaving unexcited 238 UF6 molecules with too little energy to be dissociated. However, because most of the 238 UF6 molecules at room temperature are already in excited states, many of these would necessarily also be dissociated.

For these two reasons, two-step photochemical dissociation of UF6 at room temperature would yield only very partial separation and would make very inefficient use of laser energy. At very low temperatures, the fraction of UF6 in the lowest vibrational state increases, reaching 69 percent at 77 К and 85 percent at 55 K. However, the vapor pressure of UF6 at 77 K, extrapolated from measurements at higher temperature, is only 5 X 10-25 Torr.

Jensen and Robinson [J4] have described an experiment at Los Alamos in which a dilute mixture of UF6 in hydrogen was cooled to ЗО К by expansion to high speed through a hypersonic nozzle. In this experiment, subcooled UF6 molecules remained uncondensed long enough to assume the low-temperature energy distribution and display an absorption spectrum in which 235UF6 lines and 238UF6 lines were separate and did not overlap.

In the proposed separation process, this high-speed, subcooled gas mixture would be irradiated first by 16-/ли light of a frequency absorbed by 23SUF6 and not by 238UF6 and then by additional light of sufficient energy to dissociate the excited 23SUF6, but insufficient to dissociate the unexcited 238UF6. The dissociated lower fluoride of 23SU and undissociated 238UF6 would then be separated in one of several possible ways. If condensation of subcooled UF6 could be delayed long enough, the solid lower fluoride of 23SU might be separated mechanically from the still gaseous 238UF6. Or both might be condensed and the 238UF6 leached with water from the insoluble lower fluoride of 23SU. In either method, transfer of a fluorine atom from undissociated 238UF6 to the possibly unstable lower fluoride of 23SU would impair selectivity. Because of classification, information is not available on how successful this postirradiation separation step has been.

A possible simplification of the photochemistry of this process is afforded by the discoveries of multistep photon absorption by Lyman et al. [L5] and by Ambartzumian et al. [A3]. An intense laser beam of the frequency absorbed by 235UF6 will deliver a sufficient number of photons successively to a 235UF6 molecule to dissociate it, while hopefully leaving 238UF6 unaffected. This would permit a single laser to do the job.

 parameter Av = 0.002 cm Figure 14.44 Schematic representation of unresolved structure of absorption spectra of,3SUF6 and 238UF6.

[1]In this text each nuclide, such as uranium-235, is referred to by its chemical symbol, in this case 235U.

*The mass of the electrons is not included in this calculation because the electrons emitted from the nucleus in radioactive decay ultimately return as orbital electrons surrounding the nucleus of a neutral atom.

t Ratio based on 235U thermal fission for 4 years, no depletion, typical spectrum for light-water reactor.

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

and by continuous processing. Examples of continuous-processing removal are the vaporization of one or more gaseous elements from a solid or liquid at high temperature or the continuous separation of one or more chemical elements from a well-stirred fluid mixture. Nuclides within the chain under consideration are linked by radioactive decay or neutron reactions. In the present analysis for batch operation we assume that there is a finite initial amount of only the first member of the chain, that there is no source for continuous formation of this first member, and that there is no source of any other member of the chain other than its precursor in the chain itself.

*Calculated for the neutron spectrum of a typical pressurized-water reactor.

[4] Bennett [ВЗ].

[5]In reality, the neutron flux varies spatially throughout the reactor. The method of calculating effective xenon poisoning for spatially varying flux is developed in texts on reactor theory, such as Weinberg and Wigner [W3].

[6] Requires information from cycle 4.

Requires information from cycle 5. ® Requires information from lot 5.

10.027 weight fraction 235 U in U. ^ In spaces between assemblies.

[8] 53.9 kg Cm 949 8 kg FP

Figure 3.32 Fuel-cycle flow sheet for 1000-MWe LWR fueled with natural uranium, recycle plutonium, and plutonium recovered from reactor fueled with enriched uranium. Basis: 1 year, 80 percent capacity factor.

[9] і = Dixi

[10]Data from American National Standard for Nuclear Criticality

Safety in Operations with Fissionable Materials Outside Reactors [A2] and J. T. Thomas [Tl].

* The fissile material is subcritical if any one of the listed conditions is met, with no other fissile species present.

[13] Provided the nitrogen-to-plutonium atom ratio is equal to or greater than 4.0.

“Height of mixer-settler limited to 7.6 cm. Not amenable to efficient neutron poisoning for criticality control.

* Built of stainless steel containing a neutron poison such as gadolinium or boron.

“Sieve plates or packing constructed of “poisoned” stainless steel, thus allowing large-diameter columns.

[15]With variable-speed drive and replaceable impellers.

“With variable-speed drive.

Source: Adapted from M. W. Davis and A. S. Jennings, “Equipment for Processing by Solvent Extraction,” in Chemical Processing of Reactor Fuels, J. F. Flagg (ed.), Academic, New York, 1961, by permission.

[16] Ores containing tetravalent uranium

Uraninite (pitchblende) U3 О 8

Uranothorite Th! _жих8Ю4

Coffinite U(Si04 )i _j.(OH)4j

[17] Hydrated ores containing hexavalent uranium

Gummite U03"nH20

Camotite K20’2U03,V205’3H20

Tyuyamunite CaO-2U03 •V205’8H20

Autunite CaO*2U03,P2Os‘8H20

Torbernite Cu0*2U03 •P205 "8^0

Uranophane Ca0’2U03’2Si02‘6H20

[18] Refractory minerals containing tetravalent uranium

Davidite UFe5 Ti8 Ом

Brannerite (U, Th, Ca2 ,Fe2 )Ti2 06

Pyrochlore (Na4 ,Ca2 ,U, Th)(Nb, Ta)4 012

a 1 M SO4; pH = 1; ~1 g metal/liter; 0.1 M amine in kerosine; 1:1 phase ratio. b Trialkylmethylamine, homologous mixture, 18-24 carbons.

"Mixed Си alkyls from tetrapropylene by oxo process. dDodecenyl-trialkylmethylamine, homologous mixture, 24-27 carbons.

"Trialkylamine with mixed п-octyl and n-decyl radicals.

■^Kerosine diluent modified with 3 v/o (volume percent) tridecanol.

[20] Mixed Cg alkyls from oxo process.

Source: D. J. Crouse and К. B. Brown, “Recovery of Thorium, Uranium, and Rare Earths from Monazite Sulfate Leach Liquors by the Amine Extraction (Amex) Process,” Report ORNL-2720, July 16, 1959.

* 1000-MWe reactor, 80% capacity factor.

\$33 MWd/kg, 32.5% thermal efficiency, calculated for 150 days after discharge, equilibrium fuel cycle.

§ Core: 67.6 MWd/kg, 41.8% thermal efficiency, calculated for 60 days after discharge, equi­librium fuel cycle. Residence time of radial blanket = 2120 days.

[22] The decay of 8.05-day 1311 avoids troublesome quantities of gaseous and dissolved radioiodine in fuel reprocessing.

[23] The decay of 6.75-day 237U eliminates the need for remote handling of the purified

uranium recovered by fuel reprocessing. Also, presence of high activities of 237 U would

interfere with monitoring for fission-product decontamination of the recovered uranium.

^Each light-element concentration is calculated on the basis of no other light elements present,

[27] Includes 232 U daughters present after 100 days of postprocessing storage.

*From references [B4, G1, N2, N3, R2].

[29] Gaseous state.

® Sublimes.

to chlorinate any Pu02 impurity. Fresh РиСІз containing as much as 15 percent Pu02 is added continuously, with the molten plutonium product drawn off continuously at the cathode at demonstrated rates of 300 to 400 g/h. Another process demonstrated on a laboratory scale in­volves PuCl3 in a mixture of 28 percent BaClj and 42 percent KC1 at 800°C, also in a MgO-TiOj crucible [C2].

Electrodeposition as a means of reducing plutonium to the metal has been limited by the corrosiveness of the chlorine and fused chloride environment. It also provides relatively little separation from impurities, except for those elements that form volatile chlorides [C2].

^SF, spontaneous fission. *’24201 Am.

I = = 0.1475; *Йі0 = 0.01; 4,0 = 4u, o = 0.

[31] Given concentrations.

[32] Fissile nuclide (23SU, 233 U, or 239 Pu)

[33] Proportion of fertile nuclide (238U, 232 Th, or 240 Pu) diluting fissile nuclide

[34] Mass of fissile nuclide

[35] Geometry (shape and dimensions) of region holding fissile material

[36] Volume of region holding fissile material

[37] Concentration of fissile material

[38] Nature and concentration of moderators

[39] Nature and thickness of reflectors surrounding fissile material

[40] Nature and concentration of neutron-absorbing poisons, such as nitrate ion or gadolinium nitrate

[41] Homogeneity or heterogeneity of fuel-moderator-poison mixture

[42] Degree of interaction between two or more regions containing fissile material

[43]From California University Cyclotron.

*See, for example, papers presented by Dr. E. W. Becker and his associates at the International Conference on Uranium Isotope Separation of the British Nuclear Energy Society, London, March 1975.

[44]For consistency with the original references, conditions in U. S. heavy-water plants have been expressed in English units. Conversion tables to SI units are given in App. B.

[45] The deuterium content ym at and above which hydrogen is burned and recycled

[46] The increase in deuterium content taken per stage

[47] The stage separation factor a

[48] The heads flow rate M

[49] The stage separative capacity Д

[50] The compressor volumetric capacity V

[51] The stage barrier area A

[52] The stage power requirement Q

[53] The initial cost of the stage Co

[54] The annual cost charged to the stage C

[55] The unit cost of separative work cs = Cl A

The objectives of this section are as follows:

1. To develop equations for the dependence of these stage characteristics on the independent variables

2. To show how the stage design may be optimized for various criteria

3. To work out the stage design conditions that lead to minimum unit cost of separative work for a specific barrier type

[56] The flow pattern efficiency decreases from 0.56 at va = 400 m/s to 0.19 at 700 m/s. When combined with the v% in the first factor of Eq. (14.226), the overall effect is to cause the separative capacity per unit length to vary as vl’02 over this range of ua, instead of as v%.

and 700 m/s. These parameters have been cast in the present dimensionless form from numerical integrations carried out by May [M6].

As this table shows, concentration of counterflow near the outer wall of the centrifuge in the Berman-Olander profile has these principal effects compared with the optimum uniform mass velocity distribution:

[58] In the circulation efficiency, Eq. (14.228), the factor [/(rj/a)]2/4/3, which has the value unity for the uniform mass velocity profile, increases rapidly with va, thus reducing the circulation efficiency.

[59] The radial separation factor, expressed as a — 1, is nearly independent of va over this range, instead of varying as vl as would be the case for a uniform mass velocity profile, and is much smaller than the local separation factor between the center and outer radius of the centrifuge, given in Table 14.13.

Overall separation performance. To evaluate the overall separative performance of a gas centri­fuge from the preceding results for the local separative performance at particular height z and composition y, it is necessary to integrate the differential enrichment equations (14.181) for the enriching section and (14.182) for the stripping section. Because the parameters Cj and Cs are functions of the circulation rate N for a given axial velocity profile, it is necessary to know how N varies with z before these integrations can be carried out. A qualitative description can be given of the dependence of N on z for the principal means used to drive the circulation.

Scoop and baffle. With an unbaffled scoop at one end and a rotating baffle at the other, such as shown in Figs. 14.10 and 14.15, the circulation rate will decrease exponentially from the

The above condition for an ideal cascade may also be expressed in terms of abundance ratios:

їі’+i ~Vt-i — it

Figure 12.15 shows three stages of an ideal cascade in which this condition holds. From the
definition of the heads separation factor,

Vi = Ki

In an ideal cascade, because of (12.84),

Vi ~ РІі+i

Similarly, Vi*i=PVi

By multiplying these two equations together,

Vi+i = P2£i+i

But, from the definition of the separation factor,

Vi* і =

so that /3 = y/a = у

This relation between the heads and tails separation factors and the stage separation factor is the key property of an ideal cascade.

In the close-ftactionation case, in which (3—1 and a — 1 are small compared to unity,

An equation for the cut б in an ideal cascade is obtained from Eq. (12.12) by substituting for у and x their values in terms of z from Eqs. (12.18) and (12.20) and using the condition P = y:

## DISTILLATION OF WATER

Distillation of water was used in the early plants of the Manhattan Project [M8] for primary concentration of deuterium. It is now the method generally used for final concentration of deuterium and for reconcentration of heavy water that has picked up light water during use. Distillation of water has been used by Dostrovsky [D4, D5] to produce 180.

## French Process Equipment

Stages in the Eurodif gaseous diffusion plant contain the same components in the same process sequence as Fig. 14.1, but they are arranged more compactly, as shown in Fig. 14.3, with converter, cooler, compressor, and motor mounted vertically on the same axis. This arrange­ment greatly reduces the length of interconnecting piping and the required floor area and build­ing space.

Charpin et al. [C3] and Massignon [M5] have described several types of diffusion barrier developed in France and given examples of their characteristics. Materials from which these barriers were made include sintered alumina, oxidized aluminum, Teflon, and nickel. Pore radii were in the range of 0.01 to 0.05 pm. Barriers developed in Sweden have been described by Martensson et al. [М3].

## Significant Period of the Hazard

In analyzing the safety of a waste repository, it is crucial to know the time period under consideration. A number of geologic processes and events are relevant for the safety analysis only if the time frame exceeds a certain range. As it is obvious that the hazard of a waste repository due to the decrease of its radioactive inventory will eventually approach a level that is no longer significant, it will be feasible to estimate a time frame for the safety analysis. This time frame will be called the significant period of the waste repository hazard. The estimation of

Figure 11.29 Radioactivity of in­dividual radionuclides in HLW from the LWR uranium fuel cycle. Re­processing, 150 days after reactor dis­charge; enrichment, 3% 23SU; burnup,

30,0 MWd/MT heavy metal; resi­dence time, 1100 days; 0.5% uranium and 0.5% plutonium remaining in HLW.

such a significant period of hazard may be considered the first step in an iteration that may need refinement before the safety analysis is completed.

Definition of a significant level. To define a level of significance for the geologic waste repository hazard, a point of reference is required. The hazard of naturally occurring uranium in equilibrium with its daughters is frequently used as such reference. This choice implies the reasonable assumption that an artificial hazard equal to that of naturally occurring uranium is not considered significant because the natural uranium hazard is inevitable and people have been living with it all the time.

Such a comparison of hazards is meaningful only for similar chemical species and if the barriers protecting people from the hazards are at least qualitatively similar. This is true for a geologic waste repository as compared to a uranium deposit. The locations are similar, that of waste is even likely to be more favorable, and the key radionuclides involved, particularly 226 Ra and its parents, behave similarly.

As for the location, many uranium deposits occur considerably closer to the surface than a waste repository is supposed to be located. Therefore, radionuclides from uranium deposits may have to travel a shorter distance than those from waste repositories. Moreover, groundwater at greater depth is usually less mobile. The geologic containment of the waste repository is not taken into account as a barrier because the significant period of the hazard is supposed to be the period for which the integrity of the geologic containment is to be analyzed. Even disregarding this barrier, it is reasonable to consider the remaining barriers of a waste repository similar to those of a natural uranium deposit.

The specific radionuclides reponsible for the waste hazard are important because of their different mobilities when migrating with groundwater. Figures 11.29 and 11.30 show the long-term radioactivities and ingestion hazard indices of the most significant radionuclides in LWR uranium waste versus time. Beyond 500 years, the ingestion hazard is controlled by americium, plutonium, and eventually by radium as a uranium daughter. The neptunium itself contributes to the ingestion hazard, but less than 10 percent. The ingestion hazard of natural uranium is that of its daughter radium, and consequently over a long period of time is identical

Figure 11.30 Ingestion hazard index (defined in Sec. 2.1) of individual radio­nuclides in HLW from the LWR uranium fuel cycle. Reprocessing, 150 days after reactor discharge; enrichment, 3% 235U; bumup, 30,000 MWd/MT heavy metal; residence time, 1100 days; 0.5% uranium and 0.5% plutonium remaining in HLW.

Figure 11.31 Range of ingestion hazard index of HLW and range of reference in­gestion hazard index of naturally occur­ring uranium.

with the ingestion hazard of waste. Plutonium and americium have essentially the same mobility as uranium. The mobility of radium is correlated with that of its parent uranium. Only the not very abundant neptunium is faster by a factor of 100 [B8].

The conclusion is that a comparison of ingestion hazard indices of waste in a geologic repository and of naturally occurring uranium is a reasonable basis for the definition of a significant level of the waste hazard.

Estimation of the significant period of the waste hazard. Figure 11.31 shows a band of long-term ingestion hazard indices of HLW from various fuel cycles and a line corresponding to unreprocessed LWR fuel versus time. It shows also a horizontal band representing various reference levels [L4, L5].

Reference level means the quantity of natural uranium whose ingestion hazard index is used as a reference to which that of the waste from 1 MT of heavy metal reprocessed is compared. These quantities according to different approaches are as follows:

The quantity of natural uranium to be mined for the production of the heavy metal reprocessed. This type of reference has already been used in Chap. 8 because it is the most general one with no special assumption about the form of the natural uranium involved. Its disadvantage is the strong dependence on fuel-cycle type. With an equilibrium LMFBR fuel cycle, for instance, the quantity of uranium to be mined becomes close to zero and, consequently, the period of significance of the waste hazard becomes extremely long. To maintain its applicability, the uranium equivalent must always be calculated on the virtual basis that all power has been generated from freshly mined uranium.

The volume of natural U308 equal to the volume of solidified waste from reprocessing 1 MT of heavy metal. This volume is assumed to be 80 liters as an average. For unreprocessed fuel 120 liters have been used. U308 has been chosen as the standard uranium species because this is the radioactive concentrate in a uranium ore just as solidified waste is the radioactive concentrate in a waste repository. Moreover, it is a sufficiently generalized uranium species. This reference leads to a dependence of the significant period on the waste oxide concentration in the waste form.

The waste from 1 MT of heavy metal is assumed to be evenly distributed in that volume of rock which is required to accommodate the boreholes for the corresponding number of waste blocks, disregarding rock above and beneath the boreholes. The waste blocks are assumed to have 20 w/o waste oxides and to be arranged in a hexagonal array with 10-m distances. The ingestion hazard index of a unit volume of this homogenized disposal field is compared to the ingestion hazard index of the same volume of 0.2 percent uranium ore. This approach leads to a dependence of the significant hazard period on the density of waste in the host rock of the geologic repository.

The range of intersection between the ingestion hazard index band and the horizontal band indicates the range of significant periods of the hazard. These significant periods vary in a relatively narrow range, namely, between 500 and 10,000 years for the whole variety of waste from different fuel cycles except for unreprocessed fuel.

## EQUILIBRIUM TIME FOR ISOTOPE SEPARATION PLANTS

One of the most striking aspects of plants for producing heavy water or 235 U is the long time they must be operated when first started before it is possible to withdraw enriched material of specified product composition from them. This is because the amount of desired isotope held up in the plant may represent many days or even months of normal production, and at start-up the plant must be run without product withdrawal for a time sufficient to produce the plant’s working inventory of desired isotope. The purpose of this section is to derive approximate relations that may be used to estimate the so-called equilibrium, or start-up, time of an isotope

## Monothermal Water-Hydrogen Sulfide Exchange

The deuterium exchange reaction between water and hydrogen sulfide,

H2 0(0 + HDS(g) * HDO(0 + H2 S(g)

proceeds rapidly without catalysis and has an equilibrium constant of 2.32 at 32°C. A monothermal process using this reaction, thus, could concentrate deuterium without the need for the complicated catalyst-recovery steps used in the ammonia-hydrogen exchange process, Fig. 13.23. Moreover, a water-hydrogen sulfide exchange plant can use natural water as feed and thus, unlike hydrogen-fed processes, is not limited in capacity to the amount of deuterium present in other industrial operations.

Despite these advantages of the water-hydrogen sulfide deuterium exchange reaction, it is not economical to use it in a monothermal flow sheet to produce heavy water because of the high cost of chemical reflux in this system. This may be shown by reference to Fig. 13.24.

In this monothermal, water-hydrogen sulfide flow sheet, natural water is fed at the top of a bubble-plate exchange column, and the water becomes progressively enriched in deuterium as it flows down the column in countercurrent contact with upflowing hydrogen sulfide gas. Heavy-water product is drawn off the bottom of the column and hydrogen sulfide gas depleted in deuterium is drawn off the top.

 Figure 13.24 Example of reflux by chemical conversion for water-hydrogen sulfide exchange process.

The critical and essential feature of this flow sheet is the D2 S generator at the bottom of the column in which deuterium is transferred from D20 to D2S to provide reflux. Various means for effecting this chemical transfer can be imagined; all are costly. The means assumed here is the reaction between water and aluminum sulfide,

3Dj О + 2AljS3 «*= 3Dj S + Al2 03

Aluminum sulfide may be made by reacting aluminum metal with sulfur:

2A1 + 3S -»■ A12S3

The sulfur needed for this step may be reclaimed from the depleted hydrogen sulfide leaving the top of the column by partial combustion with air:

H2S + j02 ->H20 + S

 G _xp~xf a _ 1 2.32 P) mm* xf «-I 0.000149 1.32

The overall effect is to separate natural water into D20 and water depleted in hydrogen, with reflux provided by consumption of aluminum metal and production of aluminum oxide. Sulfur and hydrogen sulfide circulate internally and are not consumed by the process. The minimum molar ratio of D2S reflux G to D20 product P may be evaluated from Eq. (12.80):

Because this reflux ratio is much lower than the reflux ratio in the distillation of water derived in Eq. (13.11), the towers of a hydrogen sulfide exchange plant could be much smaller in diameter than the towers of a water distillation plant. Because the separation factor for the exchange process (2.32) is much greater than for water distillation (—1.05), the towers could contain a much smaller number of plates.

However, the cost of providing chemical reflux is so high as to preclude the use of the flow sheet of Fig. 13.24 for heavy-water production. From the preceding chemical reactions it is seen that I mol of aluminum metal is consumed for each mole of D2S reflux. Because aluminum metal costs around \$0.50/lb, the minimum cost of aluminum (MW = 27) per pound of heavy-water product (MW = 20) is

Even without allowing for the additional costs of the conversion operations themselves, this is clearly prohibitive. Other possible chemical conversion schemes are similarly uneconomical.