Although the isotopes of an element have very similar chemical properties, they behave as completely different substances in nuclear reactions. Consequently, the separation of isotopes of certain elements, notably 235 U from 238 U and deuterium from hydrogen, is of great importance in nuclear technology. The fact that isotopes of an element have such similar gross physical and chemical properties, however, makes their separation unusually difficult and has necessitated the development of processes and concepts especially adapted to this purpose. Despite the novelty of some of these isotope separation techniques, they have features in common with distillation and other familiar separation methods, and study of isotope separation is helpful in under­standing more conventional separation methods.

1 USES OF STABLE ISOTOPES

Table 12.1 lists separated isotopes that are being produced on a significant industrial scale. In addition to these, separated isotopes of practically all natural elements are being produced in research quantities by the U. S. Department of Energy (DOE) and by the atomic energy agencies of England, France, the Soviet Union, and other nations.

1.1 235 U

23SU is the separated isotope of by far the greatest industrial importance, with the value of annual production throughout the world of the order of a billion dollars. Uranium enriched from the natural level of 0.7 percent to from around 1.5 to 4 percent is used as fuel in power reactors moderated by natural water or graphite.

235 U enriched to 90 percent or higher, mixed with thorium, is proposed as fuel for the high-temperature gas-cooled reactor, the light-water breeder reactor, and the thorium-fueled CANDU type of heavy-water reactor, and as an alternative fuel for light-water reactors. In these reactor systems fission of 235 U is supplemented by five times or more as many fissions from 233U produced by neutron absorption in thorium, as outlined in Chap. 3. Highly enriched 233U is used as fuel for research or testing reactors, where the highest attainable neutron flux is wanted, and in compact power reactors, where high power density is needed.

Figure 12.23 shows the nomenclature to be used in describing the operation of an isotope separation plant during the transient period in which it is approaching steady-state performance. Figure 12.24 represents qualitatively the way tails and product flow rates and compositions will change with time during this transient period. Compositions are represented by a scale linear in In [x/(l -*)].

At time zero, all stages of the plant contain material of feed composition, zP. Initially the plant is operated with no feed supply and no tails or product withdrawal. As the plant operates, the fraction of desired isotope in material at the tails end of the plant decreases and the fraction of desired isotope in material at the product end increases. At time tx material at the tails end of the plant reaches the desired steady-state level xw. At this time tails withdrawal is started at such a rate W(t) as to keep the composition at this point constant at xw. Feed is supplied at a rate equal to tails withdrawal. At first, tails withdrawal is at a rate below the steady-state value W because the compositions elsewhere in the stripping section have not yet reached steady-state values. The tails rate increases and may temporarily exceed the steady-state value for a time, until product withdrawal can be started.

The fraction of desired isotope in material at the product end of the plant continues to increase, reaching the steady-state value yP at time t2. Product withdrawal is then started at such a rate P(t) as to keep product composition constant at yP. Feed is supplied at the rate P(t) + Wt). At first, product withdrawal is at a rate below the steady-state value P because the compositions elsewhere in the enriching section have not yet reached steady-state values. As time goes on, P(f) approaches P asymptotically.

The equilibrium, or start-up, time for product withdrawal tP is defined as the number of days of equivalent production lost during the approach to steady state. In Fig. 12.24, the area of the rectangle between the vertical line at tP and the horizontal line at unity equals the area between this horizontal line and the curve for P(t)/P. Mathematically,

(12.188)

к Фе

ls4>s

Іф

(12.189)

Although most isotope separation problems involve only two components, it is occasionally necessary to consider the effect of one or more additional components on cascade design or performance. Examples are the effect of the 0.0058 percent 234 U present in natural uranium, the 236 U present in uranium recovered from a nuclear fuel reprocessing plant, the three isotopes found naturally in oxygen, or the five isotopes occurring in natural tungsten, de la Garza and co-workers have extended the theory of the close-separation, ideal cascade to multicomponent mixtures. In this section, their development is used to derive equations that describe the effect of small amounts of 236 U on the performance of a cascade designed to separate 235 U and 238 U. For extension of the theory to systems containing large amounts of a third component and to multicomponent systems, de la Garza’s papers [Dl, D2] and Pratt’s [P2] summary of them may be used.

Figure 12.27 Nomenclature for stage processing mixture of 23SU, 236U, and 238U.

Saito [SI] has patented separation of lithium isotopes by countercurrent exchange between lithium amalgam and lithium chloride or bromide dissolved in dimethyl formamide or other organic solvent. Arkenbout [A2] has measured a separation factor of 1.05 for this process, with 6 Li concentrating in the amalgam phase. With countercurrent flow through a packed column, natural lithium (7.5 percent 6Li) was separated into 5.8 percent 6Li at the top of a 1-m column and 12 percent 6 Li at the bottom. Reflux at the bottom was obtained by making the amalgam the anode (positive electrode) of an electrolytic cell in contact with the organic solution of the lithium salt. Reflux at the top was obtained by crystallizing lithium salt from organic solvent, dissolving it in water, and electrolyzing the aqueous solution at a mercury cathode.

Saito and Dirian [S2] have patented separation of lithium isotopes by countercurrent exchange between lithium amalgam and an aqueous solution of lithium hydroxide, with 6 Li concentrating in the amalgam phase. Reflux at the bottom is obtained by making the amalgam the anode of an electrolytic cell against an aqueous solution of LiOH. Reflux at the top is obtained by the reverse reaction, which takes place spontaneously between lithium amalgam and water. The simpler cathodic process is an advantage of this system compared with the previous one using an organic solvent. A disadvantage is the spontaneous transfer of lithium from amalgam to aqueous phase by chemical reaction that takes place as amalgam flows through the column. This has to be reversed by applying a negative potential to the amalgam either continuously or at intervals. Saito and Dirian report a separation factor of 1.06 to 1.07. Collin [CIO] reports 1.069 ± 0.004. A process like this was used in the Y-12 plant of the U. S. AEC.

A cascade like Fig. 12.12, in which no attempt is made to reprocess the partially depleted tails streams leaving each stage, will be called a simple cascade. In a simple cascade the feed stream for one stage is the heads stream from the next lower stage of the cascade. This type of cascade connection is used in the lower stages of the Norsk Hydro electrolytic heavy-water plant where the tails streams have too little deuterium to warrant processing for deuterium recovery. The theory of such a cascade is developed in Sec. 6.

When partially depleted tails have sufficient value to warrant reprocessing, a countercurrent recycle cascade like Fig. 12.13 may be used. This cascade flow scheme is by far the most

Stage heads

Froction

desired component

Stage toils

Figure 12.12 Simple cascade, no reprocessing of tails.

common. It is approached, for example, in a bubble-plate distillation column and is used in a battery of series-connected solvent extraction mixer-settlers or in the gaseous diffusion cascade of Fig. 12.2.

Such a countercurrent cascade separates feed containing zp fraction of desired component flowing at rate F into product containing yp fraction of desired component flowing at rate P and waste, or tails, containing хц/ fraction of desired component flowing at rate W. These six compositions and flow rates are called the external variables of the cascade.

Feed for each stage consists of heads from the next tower stage and tails from the next higher stage. These interstage flow rates and compositions will be called the internal variables of the cascade.

The portion of the cascade between the feed point and product end is called the enriching section; the portion between the feed point and waste end is called the stripping section. The purpose of the enriching section is to make material of product composition; the purpose of the stripping section is to increase the recovery of desired isotope from feed. The enriching section is essential in making product of the desired grade; the stripping section is used only to reduce the amount of feed required to make a given amount of product. When feed has no value, as with water feed for a deuterium plant, the stripping section may be eliminated altogether.

Stages of the cascade are numbered consecutively from 1 at the waste end of the plant to n at the product end. The highest stage of the stripping section is numbered rtg.

The streams that move away from the ends of the cascade, that is, the tails stream in the enriching section and the heads stream in the stripping section, are known as reflux.

The theory of a recycle cascade is developed in Sec. 7.

Although water distillation is not competitive with other processes for primary concentration of deuterium from natural water, owing to the high energy consumption and the large number of towers used by this process, it is the preferred method for final concentration of deuterium from water previously enriched to several percent deuterium. In this high-enrichment range, energy consumption or equipment size is only a small fraction of that needed for primary concentration, and the reliability and simplicity of water distillation make it the process preferred for final concentration. Almost all final concentration water distillation plants installed since 1960 have been built by Sulzer Brothers, of Winterthur, Switzerland, including the final concentration sections of plants 1, 10, 12, 13, 15, 19, and 20 of Table 13.2.

Water distillation is also generally used for purifying D20 that may have become contaminated in use by H2 О through dilution or DTO through neutron absorption.

The design of Sulzer water distillation plants for these purposes, described in references [B2], [Dl], [H7], [M5], and [Zl], has evolved through several stages. The most recent plants use Sulzer CY packing made of copper, chemically treated to improve wettability. As shown in Fig. 13.10, this packing consists of parallel strips of wire mesh with oblique corrugations, arranged vertically. The slopes of adjacent strips are in opposite directions. The packing is fabricated in cylindrical cartridges about 160 mm high. Successive cartridges are turned 90° from adjacent ones. Because of the 90° displacement and the oblique corrugations, the gas
stream is well mixed at each elevation, and the liquid trickles down in a zigzag motion. After flowing through 3 to 4 m of packing, the liquid is collected, mixed, and redistributed over the top of the next packed section. Because of these means to keep gas and liquid well mixed, no increase in transfer unit height has been noted in column diameters up to 2 m.

Figure 13.11 shows the principal characteristics of Sulzer CY packing for water distillation service [M6]. The optimum throughput is said to be at 75 percent of flooding, at which the F factor is 1.7. At this load, the gas-phase pressure drop is about 4 Torr/m, the liquid holdup is about 6 percent of the packed volume, and the observed height of a transfer unit (htu) has been found to be between 6.5 and 12 cm. The observed variations in htu are attributed to variations in the wetting of the packing, which is impaired by traces of oil and other hydrophobic impurities in the water.

At an F factor of 1.7, the water vapor throughput at several pressures is as follows:

5.2 Separation of 18 О by Distillation of Water

Water distillation has been used by Dostrovsky [D4] to produce 13 g/day of D218 О containing

99.8 percent 180 from natural water containing 0.204 a/о 180. Figure 13.12 shows external flows between stages in this water distillation plant; reboilers and condensers are not shown. Table 13.12 summarizes process conditions in this plant. This plant has the stepped-down tapered shape characteristic of a squared-off cascade.

The columns are packed with Dixon [D3] rings made from 100-mesh phosphor bronze wire gauze. The columns are operated at a mean pressure of approximately 0.5 atm, with a pressure drop of 130 Torr. Under these conditions, Dostrovsky and co-workers [D5] have found the 160-180 separation factor to be 1.0064, and the height of a transfer unit in the larger columns to be about 2 cm.

Because the atom fraction of light component in the net transport of gas through the barrier, v, is greater than the atom fraction of light component in the gas at the high-pressure face of the barrier, x", there must be a difference between the average composition of the gas flowing past the high-pressure side of the barrier, x(, and the gas at the barrier face, x", to maintain the required transport of light component to the barrier surface. The local barrier mixing efficiency is defined as

(14.64)

The purpose of this section is to show how this mixing efficiency depends on conditions on the high-pressure side of the barrier.

Figure 14.5 is a transverse section of a circular barrier tube of diameter d with high-pressure flow along the inside of the tube. With turbulent flow of gas inside the tube, molar velocity is practically uniform at a value slightly above the average, H, over most of the tube diameter, but drops to zero at the tube wall. Atom fraction light component is practically constant at a value slightly above the average, X{, over most of the tube diameter owing to turbulent mixing where the velocity is uniform, but drops to a lower value of x" adjacent to the tube wall to provide the required transport through the poorly mixed gas adjacent to the

tube wall. The molar velocity of gas flow through the barrier is G, with i> atom fraction light component.

Bilous and Counas [B17] have used an equation derived originally for wetted-wall gas-absorption towers to evaluate as a function of the molar velocities G and H. The basic assumption is that the actual gas flow pattern behaves as if there were a stagnant film of thickness t adjacent to the tube wall, through which light component is transported by molecular diffusion, with diffusion coefficient D. As will be shown later, EM in this model is given by

(14.65)

Here 352 is the molecular weight of UF6 and p is the mass density. The empirical correlation for the thickness of the stagnant film t, obtainable from standard chemical engineering texts such as [S4], is

Here pD/p has the value for UF6, and Re is the Reynolds number on the high-pressure side of the barrier:

p is the viscosity of UF6, Eq. (14.4).

Equation (14.65) for the composition gradient in mass transfer through a stagnant film of thickness t may be derived with the aid of Fig. 14.6. At a distance tj into the film, where the atom fraction of light component is Xf, the required net transport of Gv mol of light component per unit area per second is the resultant of that due to flow, Gxj, and that due to diffusion:

r r Dp dxf Gv =Gxf~ 352 dFf

The solution of this equation, with boundary condition Xf — x{ at tf — 0, is

In —^- = -352Gt/Dp

V—Xf r

At the barrier surface, where // = f and Xf = x",

which is (14.65).

The molar velocity H of the gas along the high-pressure side of the barrier may be obtained from the dimensions of the barrier as follows: The total number of moles of gas flowing through a barrier tube d in diameter and L long is ■ndGL. In a well-designed diffusion stage, one-half of the gas entering the stage is diffused. The molar velocity of gas at the inlet end of each tube of the stage then is

r _ 2 ndGL 8 GL, n 77<f2/4 d

Figure 14.6 Nomenclature for de­riving Eq. (14.65) for mixing ef­ficiency.

For a rough estimate of average mixing efficiency, the value of H at midlength of the tube may be used, at which

For a barrier tube of given diameter and permeability, the mixing efficiency is higher the longer the barrier tube, because the molar velocity along the tube is proportional to the length. However, the pressure drop experienced by the gas flowing along the tube is greater the longer the tube, both because of the increased flow path and the increased molar velocity. This pressure drop is detrimental for three reasons: The barrier separation efficiency is decreased, more barrier area is needed, and more energy must be expended to restore the pressure drop. Determination of optimum tube length requires an economic balance among the gain in mixing efficiency, the loss of barrier efficiency, and the cost of increased energy input. Such detailed balance is beyond the scope of this text. Instead, calculations will be given for the mixing efficiency and pressure drop for several tube lengths, and an arbitrary choice of length will be made for subsequent design examples.

The pressure gradient in a circular tube of diameter d through which turbulent flow at molar velocity H is taking place is

dp _ 0.046m2H2 dz (Re)02 dp

Here p is the gas density:

Tube lengths of 2, 4, and 6 m will be considered. A specific high-side inlet pressure of 1 atm (101,325 Pa) and low-side pressure of 0.25 atm (25,331 Pa) will be used.

For the example of the French aluminum barrier with у — 15.6 X 10_s, the molar velocity G of UF6 through the barrier at 358 K, an upstream pressure of p" = 1.0 atm (101,325 Pa), and a downstream pressure of p’ = 0.25 atm (25,331 Pa), from (14.14), is

For this barrier at 358 K, in general, when pressures p" and p are expressed in atmospheres,

G = 14.61 X 10’s = 19.48 X 10’5 (p" — p) kg-mol/(m2-s) (14.77)

Table 14.7 gives the mixing efficiency and pressure gradient at the inlet, midlength, and outlet of barrier tubes of these three lengths, and the overall pressure drop in the direction of flow down the tube. The overall pressure drop is approximated by multiplying the average of the pressure gradient at the three calculated points by the length of the tube.

Table 14.7 shows that increasing the tube length from 2 to 4 m increases the mixing efficiency at midlength by 9 percent with an increase in pressure drop under 1 percent. Further increase in tube length to 6 m increases mixing efficiency by less than 4 percent, with an increase in pressure drop of 2 percent. Determination of the optimum tube length would require an economic balance that is beyond the scope of this text. A length of 4 m will be used

^Tube diameter d, 0.014 m; barrier specific permeability 7, 15.6 X 10”s; temperature T, 358 K; high-side pressure p”, 101,325 Pa; low-side pressure p’, 25,331 Pa.

in Sec. 4.7 in examining the effect of various combinations of high-side and low-side pressures on stage design and plant requirements.

Table 14.7 also shows that the mixing efficiency at midlength is close to the average value over the tube length. To simplify the calculations to be made in Sec. 4.7, the mixing efficiency will be treated as if constant at its value at midlength, and the pressure drop along the tube will be neglected. In accurate design calculations, point-by-point calculations along the barrier tube should be made of pressure drop, flow through the barrier, flow along the tube, and mixing efficiency, refinements that are neglected in the remaining treatment of gaseous diffusion.

To illustrate the shape of a typical ideal cascade, we shall work out the variation of interstage flow with stage number for an ideal cascade to separate natural uranium (zp = 0.0072) into enriched uranium with yp = 0.90 and depleted uranium tails with дсц/ = 0.003 by gaseous diffusion, with a = 1.00429.

To produce 1 mol of product, the amount of feed, from (12.54), is

and the amount of tails, from (12.55), is

The heads separation factor is given by (12.90), with

/3 = V1.00429 = 1.00214 (12.110)

The total number of stages n is twice the minimum, given by (12.74), less 1, or 3738. The number of stages in the stripping section n$ is given by (12.94), with

The heads flow rate in the enriching section, from (12.106), is

(1 -1.00214′-3738X050)

0. 00214

+ (ййщ) d -002143738 -‘ — 1 X0.10) (410 < і < 3738)

The heads flow rate in the stripping section, from (12.107), is

Mj = ^^[(1.00214X1.00214/ — 1X0.003) + (1 — 1.00214’/’X0.997)] (0 </ < 410)

(12.113)

Figure 12.17 is a plot of these equations represented as a tapered column whose height is proportional to stage number above tails and whose width is proportional to heads flow rate.

The large interstage flow rate at the feed point (М410//>= 58,229) and its rapid decrease as the product and tails ends of the plant are approached are characteristic of an ideal cascade.

The exchange reaction between water and hydrogen sulfide was one of a number of reactions investigated by Urey and co-workers at Columbia University from 1940 to 1943 for possible

T

1 HYDROGEN I SULFIDE I RECYCLE

I 7c

I

Figure 13.26 Simplified illustration of dual-temperature principle.

use by the Manhattan District for heavy-water production. During this time, Spevack [S6] conceived and patented the dual-temperature process and suggested its use with the water- hydrogen sulfide system. Because of concern about corrosion by aqueous solutions of hydrogen sulfide, the process was not used by the Manhattan District.

In 1949, when the need for large amounts of heavy water for the Savannah River reactors of the U. S. AEC was recognized, E. I. du Pont de Nemours and Company selected this process as the most economical means for producing heavy water on the large scale then required.

Spevack [S7] had developed improvements in the process that reduced its energy consumption, and corrosion research established where it was necessary to use stainless steel and where carbon steel could be used without undue corrosion by hydrogen sulfide. Under duPont direction the Girdler Corporation designed a plant to produce heavy water at Dana, Indiana, where some of the equipment formerly used for the Manhattan District’s water distillation plant was available. The process came to be known as the GS process, for Girdler-Sulfide. Lummus designed and du Pont built a second GS plant at Savannah River, of about the same capacity as the Dana plant. Both plants came into operation in 1952. By 1957, production rates were 490 MT/year at Dana and 480 MT/year at Savannah River. At this time the demand for heavy water began to decrease; the Dana plant was shut down and dismantled, and two-thirds of the GS units at Savannah River were shut down and put into standby condition. In 1977 the production rate from the operating portion of the Savannah River plant was 69 MT/year.

At both Dana and Savannah River the GS process was used for primary concentration of deuterium to 15 percent, with the remaining concentration being effected by distillation of water and electrolysis.

Pilot-plant investigations of the GS process have been carried out in France [R4] and in Sweden [E2], and a thorough analysis of the process has been published by Weiss [W3].

The stage type of mass diffusion was patented by Hertz [H4], who used this method to separate the isotopes of neon [H5, H6]. The means by which separation is effected in a mass diffusion stage are shown in Fig. 14.33, which illustrates the type of equipment used by Maier [Ml] to separate hydrogen from other gases.

The heart of this apparatus is the mass diffusion stage, in this case of cylindrical cross section, which is divided into two annular chambers by the mass diffusion screen. Feed gas is brought to the top of the inner compartment by a riser. As this stream flows down through the inner chamber, it gives up a portion of the feed, which diffuses through the screen into the outer chamber against the inward-diffusing separating agent. Because the light component of the feed diffuses at a higher speed than the heavy, the stream in the inner chamber is progressively depleted in the light component relative to the heavy.

Steam or other separating-agent vapor is admitted at the bottom of the outer chamber. As this stream flows upward it gives up separating agent to the heavy stream and picks up from it a portion of the feed, enriched in the light component.

After the light and heavy streams leave the diffusion stage, they are cooled to condense the separating agent. After separation of the condensate, they leave the apparatus as the light and heavy fractions.

For the mass diffusion screen, Maier used a variety of materials, such as plates perforated with 0.4-mm holes, fine-mesh wire screen, or alundum filter plates. Very fine holes, such as is needed in gaseous diffusion, are not required, although holes with diameter under 10 цтп are preferred because control of mass flow through the screen is easier. In the uranium isotope separation design example to be given in Sec. 7.4, electroformed nickel screen with holes 6.76 Mm in diameter and 30 percent free area was specified.

The main requirements of the separating agent are that it be selective, be readily separable from the components of the mixture to be separated, and be chemically inert to it. For isotopic mixtures in the form of a permanent gas, such as neon or methane, a readily condensible vapor such as steam or mercury has been used. For UF6 feed neither of these can be used because of chemical reactivity, and fluorocarbon vapor is specified. Selectivity is enhanced by using a separating agent of appreciably higher molecular weight than the components to be separated.

Table 14.21 gives examples of isotope separation reported for this type of apparatus.