The principal disadvantage of the GS process is the toxic and corrosive character of aqueous solutions of hydrogen sulfide. Extensive corrosion research and experience with the Dana and Savannah River plants has shown what materials of construction can be used to withstand corrosion, without prohibitive cost. The following summary of recommendations regarding materials of construction is condensed from reference [T4].

1. Carbon steel is used for a large part of the equipment in the heavy-water plants. This includes the shells of the exchange towers, the shells of most of the heat exchangers, and practically all the process piping. These items are protected from surface corrosion by a coating of iron sulfide that forms during the first few weeks of operating, after which further corrosion of the steel is so slight as to be negligible.

2. Bubble-cap trays in the exchange towers are made of stainless steel, preferably type 304 18-8. Carbon steel is unsuitable because the impingement of spray to which the trays are subjected prevents an iron sulfide layer from forming, and under these conditions carbon steel corrodes rapidly. The same considerations apply to other parts exposed to erosion by spray impingement or by high liquid velocity, such as heat exchanger tubes, centrifugal pumps, and throttle valves.

3. Carbon steel, “low-alloy” steel, and stainless steel must be suitably heat treated to relieve stresses that may result from fabrication procedures. If this is not done, failure may occur due to hydrogen embrittlement or to stress-corrosion cracking. Carbon steels are satisfactory if annealed according to the ASTM Boiler Code. Austenitic stainless steels that have been heavily cold worked must be quench annealed at 1800 to 2000°F.

4. Bolts (normally made of low-alloy steel) that are used at flanged joints (or for any other purpose) pose a special problem when handling H2 S-water. Even when such bolts are outside of the process equipment, they may be exposed to H2S because of leaks. A small leak of H2S in air will attack the surface of a bolt, causing hydrogen absorption into the metal. If such a bolt is stressed beyond a certain threshold value, dependent on its hardness, it will crack. For this reason, all bolts are heat treated, after machining, to reduce hardness below a critical maximum value and are installed to a predetermined stress level using torque wrenches. The unavoidable reduction in tensile strength resulting from the heat treatment is accepted.

5. In order to ensure that corrosion of process piping, if this should occur, would not result in a major release of H2 S, all piping above 3 in in diameter is provided with “minimum thickness holes.” These holes, about | in in diameter, are drilled from the outside to about half the wall thickness. Loss of metal on the inside of the pipe will result in a small but detectable leakage through the test holes, while the structural strength is still adequate to withstand the operating pressure.

Process description. Mass diffusion has one potential advantage over gaseous diffusion for separation of uranium isotopes, in that a special diffusion membrane with ultrafine holes is not required. Also, the energy input needed to effect separation can be provided by conventional refrigerant compressors rather than special compressors for UF6. To evaluate mass diffusion for uranium isotope separation, Forsberg [F2] carried out a detailed design and cost estimate of separation of uranium isotopes in a cascade of mass diffusion stages. Perfluorotributylamine, N(C4F9)3, trade name N43, was specified as separating agent. This compound was chosen as having the highest molecular weight of any commercially available substance that was thermally stable and not reactive with UF6 in the vapor phase at a pressure of 1200 Torr. This operating pressure was chosen as being sufficiently above the triple-point pressure of UF6, 1142 Torr, to prevent freezing during separation of N43 from UF6 by partial condensation at this pressure. The stage temperature was 194°C, slightly above the condensation temperature of any process mixture of N43 and UF6 at this pressure.

The mass diffusion screen used in the study was the electroformed nickel sheet referred to earlier, 3 pm thick, with holes 6.76 jum in diameter through 30 percent of its surface.

Because this method of separating uranium isotopes was found not to be economically competitive with gaseous diffusion, only a summary of Forsberg’s principal results will be given here.

Figure 14.35 shows the flow through a mass diffusion stage and the nomenclature to be used in characterizing its performance. Figure 14.36 shows how three stages are connected into a simple, ideal cascade and the location of equipment used to separate the mixture of UF6 and N43 leaving each stage into a UF6-rich stream and an N43-rich stream.

Physical separation. Figure 14.37 is a schematic flow sheet for the system used for the physical separation stage that prepares feed for each mass diffusion stage. The mixture of UF6 and N43

Optimum design conditions: Me = Mf = Ne = Nf *f=Yf Je = Tle = 0-47

If = 0.837 nf = 0.103

Figure 14.35 Nomenclature for mass diffusion stage.

to be fed to a stage, at the top center of Fig. 14.37, is cooled and partially condensed in the principal heat exchanger by separated UF6 — rich vapor and N43-rich liquid. Final cooling to condense the required fraction of feed is by heat exchange against boiling liquid refrigerant — il3 (R-113, C2Cl, Fj). The UF6-rich vapor and N43-rich liquid are reheated part way to process temperature in the principal heat exchanger. Heating of UF6 and evaporation of N43 is completed by heat exchange against condensing R-113 vapor in the final heaters.

Energy to drive the process is provided by the R-113 vapor compressor, which pumps heat from the lower temperature of the final cooler to the higher temperature of the final heaters. Most of this energy is removed in the R-.113 condenser as heat to cooling water. Because the heat-pump circuit operates between temperatures of 100 to 200°C, some energy is recovered in the power-recovery turbine.

Equations for separation performance of mass diffusion stage. At the bottom of Fig. 14.35, the stage conditions found to lead to minimum unit cost of separative work are tabulated. The condition that the UF6 content of the two effluent streams be equal,

|e = Ve (14.310)

is set so that the enriched stream leaving stage 1 + і can be mixed with the depleted stream from stage і — 1 without loss of thermodynamic efficiency before these are separated into the UF6-rich stream and the N43-rich stream to be fed to stage /.

The four molar flow rates Mf, Me, Ne, and Nf are equal for the following reasons. They are
necessarily related by the overall material balance

Mf + Nf = Me+ Ne (14.311)

The ideal cascade condition of a cut of 5 requires that

Nel-e=MeT, e (14.312)

Hence Ne and Me are equal. Forsberg found that a condition of zero net flow through the

screen led to minimum unit cost of separative work, so that

Mf = Me (14.313)

Hence Nf and Ne are equal.

The condition that the UF6 mole fraction of the effluent streams be

%e = 0.47 (14.314)

is the result of a detailed optimization study [F2], With a lower value (less UF6), more N43 would have to be circulated, heated, and cooled, with higher processing costs. With a higher

Figure 14.36 Cascade of mass diffusion stages.

value (less separating agent), the stage separation factor drops off rapidly, so that more stages and more UF6 reflux would be required.

After the above conditions are set, the UF6 content of the UF6-rich stream

%f= 0.837 (14.315)

and of the N43-rich stream

77/= 0.103 (14.316)

are equilibrium compositions that result from separation of the effluent stream containing 0.47 mole fraction UF6 into equimolal amounts of liquid and vapor by partial condensation at 1200 Torr [F2].

The mole fractions of 235U in UF6 in the two stage feeds are equal,

xf = y{ (14.317)

because these two streams came from the same physical separation stage, in which no isotope
separation occurs. Because of the ideal cascade requirement that the cut be the mole fractions of 235U in the feed and effluent uranium are related by

Xf~xe=ye-yf (14.318)

Equations (14.310) through (14.318) provide nine independent relations among the 12 variables Me, Mf, Ne, Nf, £e, %f, rje, ту, xe, X/, ye, and >y. For a given stage 23SU content (e. g., xe), the two remaining relations needed to specify completely all 12 variables are the interstage UF6 flow rate (e. g.,Ne%e) and the stage separation factor

_Уе( 1 ~xe) *e(l — ye)

The optimum interstage UF6 flow rate is that of an ideal cascade. For example, in the enriching section of a close-separation ideal cascade making product of composition yp at rate P, the UF6 flow rate in stage tails is given by Eq. (12.132). In the notation of this section,

_ Vjyp-x,)
eie (a — l)xe (1 —xe)

Forsberg [F2] has solved the differential equations for diffusion of 235UF6, 238UF6, and N43 through the holes of a mass diffusion screen and for material balances in countercurrent flow of the two streams in the mass diffusion stage of Fig. 14.35 to obtain Eq. (14.321) for the stage separation factor a. When there is no net flow through the screen,

а _ Щ — ke) {exp [fe — T)f)(l — Dp/Dn)] ~ 1) T 01 £e(l-Do/Da) Vf exp [(|e — r?/)(l — D0lDn)]} where y, the separability, is

The three diffusion coefficients are

£>oi, light component into separating agent Dm, heavy component into separating agent Dn, light component into heavy component

For an isotopic mixture with nearly equal molecular weights and m2,

mi — m2 1

T _ m, + m2 1 + (mi + m2)/2m0

и. — m2 , _ ,

Because, = a0 — 1 (14.325)

mi + m2

where a0 is the ideal separation factor in gaseous diffusion, the separability in mass diffusion is necessarily smaller than a0 — 1 in gaseous diffusion by the factor 1/[1 + (m2 + m2)/2m0]. This factor is closer to unity, the larger the molecular weight of the separating agent m0 is relative to the molecular weights of the isotopic compounds m2 and m2. This shows the

352 — 349 1

T — ІЇЇТЙ 1 4 (352 + 349)/(2)(671) " <0°0428)<0.657) — 0.00281 (14.326)

Thus, in separating uranium isotopes by mass diffusion with N43, the separability is less than two-thirds of a0 — 1 in gaseous diffusion.

For the ratio of diffusion coefficients in (14.321), for UF6-N43 mixtures, Forsberg recommended

With the optimum values of 0.103, 0.47, and 0.837 given previously for T)f, j-e, and

a — 1 = 0.882 = 0.00248 (14.328)

The coefficient of 7 in Eqs. (14.321) and (14.328) is analogous to the stage efficiency E in gaseous diffusion, Eq. (14.94).

The rate of production of separative work in this mass diffusion stage, with a cut of {, is

For the optimum conditions of Fig. 14.35,

0. 47Me (а — l)2

The mixing of a UF6-rich stream with a separating agent-rich stream as occurs in a mass diffusion stage results in an irreversible loss of availability analogous to the irreversible pressure drop in a gaseous diffusion stage. The rate of loss of availability in the adiabatic mass diffusion stage is

Q=T0(S ou«-Sta) (14.331)

where S is the rate at which entropy is carried by the indicated streams. Treating UF6-N43 mixtures as ideal solutions,

Q = RT0 [Nf[kf In if + (1 — *,) In (1 — *,)] + Mfr, f In vf + (1 — Vf) In (1 — П/))

— Ne [$e In %e + (1 — £«,) In (1 — £e)] — Me [ve In rie + (1 — Ve) In (1 — r? e)]}

(14.332)

For the optimum conditions of Fig. 14.35,

Q = RToMe (0.837ln 0.8374-0.163 In 0.163+0.103 In 0.103+0.897In 0.897

— 2(0.47 In 0.47 + 0.53 In 0.53)] = 0.6065 RT0Me

The rate of loss of availability per unit separative capacity is the ratio of (14.333) to (14.330),

Q _ 5.1бЛГо Д (а — l)2

With a — 1 from (14.328),

This is to be compared with 0.168 kW/(kg SWU/year) for the rate of loss of availability associated with pressure drop through the diffusion barrier of the optimized gaseous diffusion stage of Table 14.9.

In addition to this loss of availability resulting from mixing UF6 and N43 in each mass diffusion stage of Fig. 14.36, flow of heat through temperature differences of the heat exchanger, cooler, vaporizer, and heater of each physical separation stage of Fig. 14.37 results in even greater availability losses. Forsberg’s [F2] heat balances for an optimized plant predict an additional availability loss of 0.48 kW/(kg SWU/year) for a physical separation system consisting of two stages of partial condensation and evaporation, each with a minimum temperature difference of 5.5°C. With an allowance of 0.12 kW/(kg SWU/year) for other thermodynamic inefficiencies such as pressure drops, the total available energy consumption of an economically optimized mass diffusion plant was estimated to be 0.88 kW/(kg SWU/year). This is to be compared with

0. 266 kW/(kg SWU/year) for the U. S. gaseous diffusion plants and 0.366 for the gaseous diffusion design of Table 14.9.

This poor energy utilization compared with gaseous diffusion is inherent in the mass diffusion process. Using a thermodynamic argument similar to Sec. 4.8 for gaseous diffusion, Forsberg showed that the minimum ratio of availability loss rate to rate of production of separative work at any point in a mass diffusion screen is

(14.336)

For the UF6-N43 system, with у = 0.00281

(14.337)

This is to be compared with 0.0722 for gaseous diffusion. The minimum value of 0.168 is a theoretical lower limit, attained only by letting the UF6 content of the mixture with N43 approach zero, a condition that would require that the flow rate of N43, the amount of mass diffusion screen, and the size of physical separation equipment increase without limit.

Table 14.23 summarizes the foregoing comparison of gaseous diffusion and mass diffusion for uranium isotope separation. A mass diffusion plant would need about 1.2 times as many stages as a gaseous diffusion plant performing the same separation, and would consume about three times as much available energy. For this reason, and because the mass diffusion plant needs the complex physical separation system besides its diffusion separation stages, Forsberg [F2] has estimated that the capital cost of such a mass diffusion plant would be almost five times that of a gaseous diffusion plant of the same capacity.

Table 14.23 Comparison of mass diffusion with gaseous diffusion for uranium isotope separation

Process

Mass diffusion Gaseous diffusion

If the separation factor for the system is known and the variation of the reflux ratio is specified as a function of stage number in the cascade, the number of ideal stages required to separate feed into product and tails of specified composition can be calculated. For example, starting with the known tails composition хці, the heads composition from stage 1, jVi, is calculated using values of a and Eq. (12.18). This composition is used in Eq. (12.61) to calculate the tails composition from stage 2, x2. Equation (12.18) is again used to calculate y2, the heads composition from stage 2, and so on. Thus by a repetitive, stepwise, calculation involving the equilibrium expression (12.18) and the two difference equations (12.58) and (12.61), the compositions on each stage in the cascade can be calculated. Equation (12.61) is employed for compositions less than the feed composition and Eq. (12.58) for compositions greater than the feed composition. When the heads composition from a stage equals or exceeds the desired product composition, the required number of ideal stages has been calculated. This calculational method applies generally to all stage processes. Simplified or analytic methods of solution are available for special cases.

This chapter describes processes most suitable for separation of isotopes of light elements on an industrial scale. Principal emphasis is on separation of deuterium through production of heavy water, but some information on separation of isotopes of other light elements is also given. Processes to be discussed include distillation, electrolysis, and chemical exchange.

1 SOURCES OF DEUTERIUM

The most abundant source of deuterium, of course, is natural water. Other potential natural sources are natural gas and petroleum. Of these, natural water is by far the most significant. No economic method has been found for extracting deuterium from natural gas or petroleum without first converting them chemically to other materials. Industrial hydrogen and ammonia synthesis gas, produced by chemical conversion of natural gas and petroleum, are being used as sources of deuterium, but the amount of heavy water that can be produced from these industrial sources is small compared with the amount needed for heavy-water reactors. As shown in Chap. 12, a large plant producing 1000 short tons of synthetic ammonia per day could produce only around 75 short tons of heavy water per year, a small amount compared with around 500 short tons needed as the initial charge of a 600-MW heavy-water nuclear power plant.

Unlike other elements, the variability of isotopic composition of hydrogen from different sources is great enough to be a factor in the location, design, and economic performance of heavy-water plants.

The deuterium content of natural waters varies from place to place and from time to time because of isotopic fractionation which occurs when water evaporates from land or sea or is condensed from the air. The deuterium content of natural waters relative to standard water samples has been determined by a number of investigators; representative results of two workers are abstracted in Table 13.1. The percent differences from standards have been converted to atom percent deuterium by using the indicated deuterium content of the standards, which, however, are less accurately known than the differences.

Ocean water in the tropics contains around 0.0156 a/о (atom percent) deuterium. Water vapor in the air in equilibrium with the ocean has a deuterium content about 7 percent lower than seawater because H20 has a higher vapor pressure than HDO. Consequently, water vapor over the ocean should contain about 0.0156/1.07 = 0.0146 a/о deuterium. The first rain to fall out from this water vapor is richer in deuterium than 0.0146 percent, again because of the

Table 13.1 Deuterium content of natural waters

Percent difference Atom ppm

from standard deuterium

lower vapor pressure of HDO. As moisture-laden air from the ocean flows away from the tropics and over the continents, it becomes steadily depleted in deuterium. Rainfall on the leeward side of mountains and snowfall in the polar regions, where most of the moisture has already been condensed from the air, will contain less than 0.0146 a/о deuterium. This is shown in Table 13.1 for the Columbia, Missouri, and Colorado rivers, and for snowfall in Greenland, Antarctica, and, in an exceptional instance, in Chicago. For the same reason, rivers whose flow is substantially reduced by evaporation during passage through arid regions will contain more than 0.0146 a/о deuterium, as is shown in Table 13.1 for the Red, Arkansas, Rio Grande, and Nile rivers. Most of the differences in deuterium content given in this table can be explained by fractionation of deuterium during evaporation and condensation of water.

The difference in deuterium content of snow and rain at Chicago is an extreme example of the change in deuterium content with changes in conditions of precipitation.

The examples of this table have been selected to illustrate the variability of the deuterium content of natural waters. Actually, over large parts of the earth where conditions of precipitation are comparatively uniform and evaporation of groundwater unimportant, the variability is much less. For example, the deuterium content of river and lake waters in the eastern United States and Canada, where most of the world’s heavy water is now produced, is within 1 or 2 ppm of 148 ppm (0.0148 percent).

Because the cost of producing heavy water is roughly inversely proportional to the deuterium content of plant feed, local variations are of major economic importance. The low deuterium content of the Columbia River at Trail, British Columbia, 0.0133 percent, made the cost of producing heavy water at the U. S. Atomic Energy Commission’s (AEC) plant at this location higher than if the Columbia River had been as rich in deuterium as the Niagara or the Nile, for example.

The deuterium content of natural gas and petroleum is also variable. Values as low as 0.0107 percent have been found for Texas natural gas [HI 1].

When natural gas or petroleum is converted to hydrogen by reforming with an excess of steam, equilibrium is established in the reactions

CH4 + H20 * CO + 3H2 CO + H20 * C02 + H2 and HD + H20 H2 + HDO

The equilibrium constant for the third, deuterium exchange, reaction is around 2 at the temperature at which the second, water-gas shift, reaction is carried out. Because an excess of water is used to convert CO completely to C02, the deuterium content of hydrogen will be less than that of the methane and water fed, unless the excess water is fully recycled. Because water recycle is usually not practiced at ammonia synthesis plants, the deuterium content of synthesis gas at operating plants is sometimes as low as 0.009 percent [M7]. If the ammonia plant were specifically designed for deuterium recovery from its synthesis gas, the deuterium content could be increased to the average of the methane and water feeds by recycling all water and preventing losses.

During the period from 1943 to 1947 in the United States, the Manhattan Project carried four uranium enrichment processes through the large pilot stage and into production to the extent noted below.

The electromagnetic process, using the Calutron isotope separator in the Y-12 plant at Oak Ridge, Tennessee, produced the first kilogram quantities of highly enriched uranium in 1944. Because costs proved to be higher than in the gaseous diffusion process, separation of uranium isotopes by this method was terminated in 1946, with some of the equipment being converted to separating isotopes of other elements.

The thermal diffusion process, in the Oak Ridge S-50 plant, enriched natural uranium to

0. 86 percent 23SU, which was fed to the Y-12 plant to increase slightly the 23SU production rate of the latter. Its heat source was steam from the steam-electric power plant built to provide electricity for the K-25 gaseous diffusion plant. As the thermal diffusion process makes much less efficient use of energy for uranium enrichment than gaseous diffusion, the S-50 plant was shut down in 1945 when enough of the K-25 gaseous diffusion plant was operating to use productively the full electric output of the power plant. This process will be described briefly in Sec. 8.

The Oak Ridge K-25 gaseous diffusion plant was completed in sections in 1945 and 1946. When partially completed, its partially enriched Иіи product was fed to the Y-12 plant to increase the output of fully enriched uranium from the latter. After all sections of the K-25 plant were in operation, the Y-12 plant was shut down in 1946 because of the lower cost and more efficient energy use of the gaseous diffusion process. Later, Section K-27, containing larger gaseous diffusion stages than K-25, was brought into operation at Oak Ridge. By 1977 all of these Manhattan Project stages at Oak Ridge had been retired from operation because of the later construction of the more efficient gaseous diffusion stages of the K-29, K-31, and K-33 Sections at Oak Ridge and the Paducah and Portsmouth gaseous diffusion plants.

The gas centrifuge process was developed by the Manhattan Project through the construction and operation in 1944 at the Bayway, New Jersey, refinery of Standard Oil Company (N. J.) of a pilot plant of centrifuges 4 m long. After the gaseous diffusion process proved to be reliable, work on the gas centrifuge was suspended because of the low separative capacity of the individual centrifuges and the mechanical complexity of the machines then under development. With the advent of the simpler Zippe [Z2] centrifuge to be described in Sec. 5, development of the gas centrifuge for uranium enrichment was resumed in the 1960s, leading to its current industrial use.

In many isotope separation plants the initial cost of the plant is proportional to the separative capacity of the plant and the annual operating costs are proportional to the amount of separative work done per year. In such cases the annual charges for plant investment plus annual operating costs exclusive of feed, in dollars per year, equal Dcs, where D is the annual separative capacity in kilograms of uranium per year and cs is the unit cost of separative work, in dollars per kilogram of uranium of separative work units ($/kg SWU). If Fkg of feed is charged per year at a unit cost of cp S/kg, the total annual cost c is

Substitution of Eqs. (12.149) through (12.151) into (12.148) yields for the unit cost of product

The first term on the right gives the separative work component of the cost of product; the second term gives the feed component.

The exchange cascade of Fig. 13.17 is impractical because a volume of steam equal to the volume of hydrogen has to be evaporated and condensed on every exchange stage. The Ban — towers used in the Trail plant greatly reduced the heat load by permitting production and condensation of steam only once in an entire cascade. The principle of these towers is shown in Fig. 13.18. A gaseous mixture of steam and hydrogen flows up this column, passing alternately through a pair of bubble-plate absorption trays, a heater to vaporize entrained water, a chamber filled with catalyst, another pair of absorption trays, another catalyst chamber, and so on through the top pair of absorption trays. Water flows down the column through the top pair of absorption trays, then bypasses the catalyst chamber, and continues through the second pair of absorption trays, and so on through the bottom set of absorption trays. Each tower of the Trail plant contained 13 catalytic sections and 14 absorption sections.

In the gas flowing up through a catalyst chamber, deuterium is partially transferred from HD to HDO; as the gas next flows up through an absorption section, the HDO is partially absorbed from the gas phase by the downflowing water. The overall result is a transfer of deuterium from gas to liquid, so that as the gas flows up it is progressively depleted in HD, and as the liquid flows down it is progressively enriched in НЕЮ.

Steam is produced and condensed only once for an entire tower, and the ratio of steam to hydrogen may be varied at will. Steam consumption is therefore only a small fraction of that of Fig. 13.17, but more catalytic stages are required for a given change in deuterium content.

The primary heavy-water plant at Trail consisted of four groups of exchange towers and electrolytic cells connected in countercurrent cascade. Figure 13.19 shows the flow through one such group. At the top of the tower, vapor is cooled in a condenser; most of the steam is condensed and combined with water from the next lower group of electrolytic cells. Hydrogen from the condenser is returned to the next lower group of towers. At the bottom of the tower, steam is generated by vaporizing part of the water in a reboiler; hydrogen is generated by dissociating part of the water in a group of electrolytic cells with diaphragms to separate hydrogen from oxygen. Upflowing vapor consists of this steam and hydrogen, together with hydrogen from the next higher tower. Water fed forward to the next higher tower is obtained as condensate from the hydrogen and oxygen gases leaving the electrolytic cells.

Towers are operated at a pressure close to atmospheric and a temperature around 70°C, at which the steam-hydrogen ratio of the vapor is optimum.

The four groups of exchange towers and electrolytic cells at Trail produced partially

Figure 13.18 Section of exchange tower of Trail plant.

concentrated water containing 2.14 a/о deuterium. This water was concentrated further to 99.8 percent deuterium in the secondary electrolytic plant described in Table 13.13. The production rate was 6 Mg of heavy water per year.

Unit costs in 1945 were [M8]

Investment $500/kg D2 O/yr Operation $60/kg D20

Production costs in 1954, including overhead and profit to CM & S, were $133/kg D20 [S3].

The Trail plant was started up in 1943 and began producing heavy water in 1944. It was shut down in 1956 because of the high cost of its heavy water compared with that produced by the GS process (Sec. 11).

Details of the Trail plant have been given by Maloney et al. in [M8].

The two types of centrifuge whose features have been described most completely are the Groth and the Zippe machines. Figure 14.14 is a schematic drawing of Groth’s ZG5 machine [G3].

The aluminum alloy rotor R is suspended and driven from the top by an electric motor, not shown, within the vacuum case C. UF6 gas V is fed into the center of the rotor through the stationary tube R!. Heavy fraction is removed at the top through scoop, a stationary tube concentric with the feed tube, and outlet Zj. Light fraction is removed in similar fashion through scoop S2 and outlet Z2 at the bottom. Circulation of gas within the rotor is shielded from interference from the scoops by baffles B! and B2. Controlled countercurrent circulation of gas is effected by heating the top end cap by induction from the electromagnet E and cooling the bottom end cap by radiation to cooling coil K. Temperatures are measured by thermocouples Thj and Th2. Pressure at the axis is measured through connection M. The rotor is connected to hollow shafts at top and bottom, which rotate within oil-lubricated bearings, not shown. To keep oil and UF6 from mixing, labyrinth seals Di, D2, D3, and D4 are used on the top and bottom shafts. These are fed with hydrogen and discharge a mixture of hydrogen and UF6 to cold traps through Pi and P2, and a mixture of hydrogen and oil to other outlets, not shown.

A significant advantage of Groth’s machine is its control of internal circulation by convective heating and cooling; this permitted attainment of 75 percent of the maximum theoretical separative capacity, at least in the smaller machines. A serious disadvantage is the very complex construction associated with the oil-lubricated bearings and hydrogen-fed seals at top and bottom, which makes the machine expensive and complicates operation. The Zippe-type machine, free of these complications but with less flexibility in controlling internal circulation, is less costly and easier to operate.

Figure 14.15 is a cross section of one of the centrifuges tested by Zippe at the University of Virginia [Z2]. The rotor is a duraluminum cylinder 7.62 cm in diameter and 38 cm long. It

rotates inside a vacuum casing and is closed at the bottom by an end cap, which rests on a flexible steel needle. The needle spins in a bottom bearing supported by springs and oil-filled vibration dampers. The top of the rotor is covered by an end cap fitting with small clearance around a center post that carries three concentric tubes for withdrawing light fraction from the bottom of the rotor, admitting feed to the center, and withdrawing heavy fraction from the top. Leakage of UF6 between the top cap of the rotor and the center post is small because of the low pressure maintained at the axis by the centrifugal field. Any UF6 that leaks is kept out of the vacuum casing by the spiral grooves of a molecular pump that surrounds the top of the rotor. The rotor is positioned at the top by a magnet rotating on the top cap below a stationary magnet supported by flexible plastic strips and steel wires to provide positioning and damping.

Countercurrent circulation of UF6 is provided by the top scoop, which also serves to

Figure 14.14 Schematic of Groth ZG5 centrifuge. (Adapted from Shader et al. [S3].)

remove heavy fraction. Light fraction is removed by the bottom scoop, which is prevented from disturbing circulation within the rotor by the bottom baffle.

The rotor is driven by a planar induction motor whose armature plate is attached to the bottom end cap and whose stator is a flat winding with pole pieces outside the vacuum case. The motor is provided with cooling coils and a speed pickup.

The most useful methods mentioned above are recapitulated in Table 12.7.

This text is concerned primarily with methods used on a large industrial scale. Electrolysis, distillation, and chemical exchange, which are useful primarily for separating deuterium and isotopes of other light elements, will be described in Chap. 13. Diffusion methods, the gas centrifuge, and aerodynamic methods, which are used primarily for uranium but are applicable also to other heavy elements, will be described in Chap. 14.

The separation factor in all of these processes is so close to unity that production of separated isotopes requires repeated partial separations in a multistage cascade generally similar to the gaseous diffusion cascade of Fig. 12.2. The remainder of this chapter develops theoretical principles of isotope separation in such cascades.

To compare equilibrium times evaluated by approximate Eq. (12.204) and the lower bound Eq. (12.209), the example of an ideal cascade to perform the separation of Table 12.8 will be considered. It is assumed, in addition, that the stage holdup time A is 1 s and the stage separation factor is 1.0043, the nominal value for separating 235 UF6 from 238UF6. For this cascade,

^This disregards the slight difference in separation potential between stage feed, heads, and tails, which does not affect the final equation.

X ХкФк = 5.54 mol/day 2 Xiciiic = 802 mol/day

UF6 inventory (12.210): I = (5.008)(195) = 977 mol

HSUF6 inventory (12.211): їх = (5.008)(5.54) = 27.74 mol

Separative work inventory (12.212): /0 = (5.008)(802) = 4016 mol

With these inventories, the lower bound for the equilibrium time may be evaluated from Eq. (12.209).

t —L і ^-74 ГІ977І(0:0072)] (5.58273 -4,85551) + 4016 — (977)(4.85551)!

195 I 0.0072 — 0.0036

= 17.7 days (12.222)

The true value lies between 17.7 and 21.7 days.

This example shows that the equilibrium time in an ideal cascade with a — 1 < 1 may be relatively long, even when the stage holdup time h is very short. In a cascade that is not tapered at the product end, the equilibrium time will be even greater, because of the increased inventory of desired component in this part of the plant. Equation (12.197) may be used to estimate the equilibrium time of such a nonideal cascade; Eq. (12.209) is restricted to ideal cascades.