8.1 Principle of Process

To circumvent the high cost of chemical reflux, Geib [C3] in Germany and Spevack [S6] in the United States conceived of the dual-temperature system for providing reflux by purely physical means. The principle of the dual-temperature process using the water-hydrogen sulfide reaction is shown in Fig. 1325. The cold tower of Fig. 13.25 performs the same function as the tower of Fig. 1324; it operates at 32°C with a separation factor of 2.32 in this example, and it enriches deuterium from feed concentration to product concentration by exchanging deuterium from upflowing hydrogen sulfide to downflowing water.

The D2 S reflux needed for the cold tower is provided by the hot tower. This operates at a

Figure 13.25 Dual-temperature reflux for water-hydrogen sulfide process.

high temperature, 138°C in this example, at which the separation factor is lower, 1.80 in this example.

With a proper flow ratio of hydrogen sulfide to water, this lower separation factor makes possible transfer of deuterium from water to hydrogen sulfide in the hot tower and thus converts the H2 S entering the hot tower into the D2 S needed for refluxing the cold tower.

Hydrogen sulfide is conserved by returning depleted H2 S from the top of the cold tower to the bottom of the hot. Heat is conserved by heat exchange between hot and cold liquid and between hot and cold vapor. In principle, no materials other than feed water are consumed in the dual-temperature system; energy consumption can be reduced by efficient heat exchange, with a lower bound set by the minimum required by thermodynamics for the separation.

The detailed manner in which the dual-temperature system effects separation will be explained in Sec. 113. That separation is possible can be made plausible by the simple qualitative considerations of Fig. 13.26. This represents one vessel containing cold water and a second containing hot water through which water flows in series and through which hydrogen sulfide may be recirculated.

Deuterium exchange equilibrium at the appropriate temperature is established between the
hydrogen sulfide leaving each vessel and the water contained in it. The separation factor in the cold vessel ac is greater than that in the hot vessel ah. The deuterium-to-hydrogen abundance ratio in the water in the cold vessel is related to the abundance ratio in the gas leaving the cold vessel by

$c = <V? c 0357)

Similarly, the abundance ratio in the water in the hot vessel is related to the abundance ratio in the gas leaving the hot vessel by

Іл=адл (1358)

Imagine that water containing the normal abundance ratio of deuterium to hydrogen ip is started flowing through the system before hydrogen sulfide is charged. At this time product, waste, and feed water all have the same deuterium abundance ip. Then assume that the hydrogen sulfide is charged and its circulation started. Because ic = £/, at this time, because olc > ah, and because of Eqs. (13.97) and (13.98), T)h > tjc; that is, the hydrogen sulfide leaving the hot vessel is richer in deuterium than that leaving the cold vessel. Therefore, there will be a net transport of deuterium from the hot vessel to the cold vessel; when a steady state is reached, £e must be greater than ip, and ih must be less than ip. Partial separation of the deuterium in the feed is effected. Addition of more cold and more hot contacting stages, as in Fig. 13.25, makes possible more complete separation.

In mass diffusion, separation of isotopes occurs through diffusion of the light isotope of a gas mixture into a condensible vapor at higher rate than diffusion of the heavy isotope. Mass diffusion separation has been carried out in a cascade of individual mass diffusion stages and in a mass diffusion column.

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 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.

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.

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.

Of the three moderators that make possible a fission chain reaction in natural uranium, heavy water, graphite, or beryllium, heavy water has become the preferred material. It is used both as coolant and moderataor in heavy-water reactors, which are the exclusive source of nuclear power in Canada, Argentina, and Pakistan, are being used in India, and are being considered in other countries wishing to have a nuclear power system not dependent on a source of enriched uranium.

Deuterium, either mixed with tritium or in the form of 6 Li deuteride, 6 LiD, is an essentia] ingredient in the fuel proposed for fusion power reactors. In the magnetically confined type of fusion power system, the working substance is a plasma mixture of fully ionized deuterium and tritium. In the laser or electron beam imploded type of system, the fuel form is a small sphere containing deuterium and tritium or 6 LiD. Although power systems of these types have not yet been proved feasible, their successful development would create a market for deuterium and 6 Li as great as the current market for enriched uranium.

A simple relation between tp, tw, and the cascade inventory may be derived as follows. The inventory of both components in the plant is assumed to remain constant at I during the start-up period. The average fraction of desired component in the plant changes from zF, the value throughout the plant at time zero, to x when the steady state is reached. The material-balance equation for desired component during the transient period is

F(t)zP — P[t)yp — = I f-

F(t) = P(t) + W(t)

In the limit, as T -*■ °°,

Of — zF)PtP — (zF — xw)Wtw = I(x — zF) (12.195)

where the limit of the integrals have been expressed in terms of the equilibrium times through (12.188) and (12.189).

Hence tP = ^+ tw (12.196)

*ХУр ~ Zf)

This equation is a consequence of material-balance relations and is exact.

Its usefulness for evaluating the equilibrium time of the enriching section tP is diminished, however, because fjy is usually not known exactly. Nevertheless, an approximate equation for tP can be developed by considering the result of decreasing the size of the stripping section of the plant until only the enriching section is left. The inventory of desired component at steady state then becomes IFxF, that of the enriching section alone. The equilibrium time for waste withdrawal ty/ becomes small, because tails withdrawal may be started at time zero, so that

<ш97>

This is the equation usually used to estimate the start-up time of a separation cascade. In most cases, it overestimates the time somewhat, because ty/ for a plant without stripping section is usually negative.