To show the main features of the GS process, a simplified analysis is first given, in which the complications introduced by the solubility of hydrogen sulfide in liquid water and the vaporization of water into hydrogen sulfide gas are neglected. The effects of the solubility of hydrogen sulfide and the volatility of water on the process are considered in Sec. 11.7. Figure 13.27 shows the flow of gas and liquid assumed and the nomenclature to be used. Figure 13.28 is a McCabe-Thiele diagram for the process. The analysis is formally similar to that given for solvent extraction with constant distribution coefficients in Chap. 4.

To simplify the treatment further, only low deuterium abundances are considered, so that the atom fractions of deuterium in liquid x and in vapor у in the streams leaving stage і are related by

ya = f — (1359)

UC

in the cold tower and

Уы = ~ (13.100)

ah

in the hot tower. These are the equations for the equilibrium lines of the McCabe-Thiele diagram, which pass through the origin with slope jac and 1/ал.

For the cold tower, the overall deuterium material balance is

F{xp-xF) = G(yP-yF)

Figure 13.27 Nomenclature for simplified treatment of dual­temperature process.

This is the equation for the operating line in the cold tower, which passes through the points (yp, xF) and (yp, xp) and has the slope

F _yp~yF G Xp — Xp

Similarly, in the hot tower, the equation for the operating line is

or Уы=Ур + 2—— —(хН’Ц1-XW) (13.107)

Xp-X w •

because

W _ Ур ~yF G Xp —Xyj

This line passes through the points (yF, Xy>) and (yP, xP) and has the slope W/G given by (13.108).

Because the deuterium content of water leaving the cold tower (xp) equals that entering the hot, and the deuterium content of hydrogen sulfide leaving the hot tower (yP) equals that entering the cold, the two operating lines end in a common point at top right. Because the deuterium content of hydrogen sulfide leaving the cold tower (yF) equals that entering the hot, the left end of each operating line is at the same value of y.

It is thus possible to draw the McCabe-Thiele diagram with equilibrium lines established from the separation factors ac and ah, and the operating lines established from specified values of feed, product, and waste compositions xF, xP, and Ху/ and assumed values of the gas-phase compositions yF and yP. The number of theoretical stages needed in the cold tower for a given set of conditions is then determined by the number of horizontal steps required to go from xF to Xp the number of stages in the hot tower, from the number of steps to go from Ху/ to xP. For the separation example of Fig. 13.28, the number of stages in each tower is 16.

The McCabe-Thiele diagram can be used to demonstrate two important characteristics of a dual-temperature plant.

1. If xF, Xyr, and yF are held constant and the number of plates in both towers is increased, the deuterium content of product Xp can be increased to any desired degree.

2. If xp, xF, and yp are held constant and the number of plates is increased, yp decreases and the lower end of each operating line approaches the corresponding equilibrium line. The maximum spread between xw and Xp occurs with an infinite number of plates, at which

(13.109)

The fractional recovery of deuterium is

PxP _ 1 — xw/xF Fxp 1 —x-w/xp

The maximum deuterium recovery possible is

1-— (13.111)

because usually xw/xP < 1.

This shows the importance of using a reaction in which the separation factor in the hot tower differs substantially from that in the cold; in fact, separation is possible only because the slopes of the two equilibrium lines in Fig. 13.28 are different. For the GS process example of Fig. 13.25, the maximum recovery of deuterium possible is

It is found in practice [B7] that the minimum number of stages for a given separation, or the maximum production rate for a given number of stages, is realized where two conditions are satisfied:

1. The approach to equilibrium at the top of the cold tower equals that at the bottom of the hot:

xf _ F ~ xw

and

2. The ratio of the slope of the equilibrium line to the slope of the operating line in the hot tower equals the ratio of the slope of the operating line to the slope of the equilibrium line in the cold tower:

l/a<i _F/G W/G /ac

The approximate validity of these two conditions can be seen qualitatively by considering the effect on the number of stages of changing the location of the operating lines in Fig. 13.28, while keeping xp and Хц> constant.

The diameter of the towers of a GS plant, the principal heat exchanger duties, and the heat consumption are determined mainly by the ratio of gas flow rate to product rate, G/Pxp. The optimum value of G is, from (13.114),

G = y/FWacah (13.115)

When F ** W, and

(13.116)

The gas flow rate per unit product is

| (xp/xF){[ac(F/G) -1](G/W)[(G/Wah)”*-!] + gJfrcW* — l][(G/№h) — 1]} ac МСГ’ — 1 ] l(G/WahT» +I -1]

(13.126)

(Cont.)

Because G/W depends on xw/xF through

G FG (xp/xF) — (xw/xF) g.

W WF (xP/xF)~ 1 F (.13.127)

Eq. (13.126) is implicit in Xy/xF and must be solved by trial. Figure 13.29 shows values of Xw/xF calculated for the specific case of nc = nh = 16; xP/xF = 4, for a range of values of G/F.

This figure brings out an important characteristic of dual-temperature exchange processes: The recovery (or production rate) of a given plant is very sensitive to the gas-to-liquid flow ratio. There is only a narrow range of flow ratios within which optimum performance is obtained. In the example of Fig. 13.29, the minimum value of xwjxFt 0.8563, is obtained at G/F= 2.03. If G/F is less than 1.85 or greater than 2.25, xw/xF becomes greater than 0.90, and the recovery of deuterium is decreased by 30 percent or more.

At the optimum value of G/F = 2.03, G/W = 2.127 and yF = 0.4558xF. The approach to equilibrium is

At top of cold tower: ^ = (132)^4558) = O’946 (13’128>

At bottom of hot tower: °^- = —= °-958 (13.129)

Хці U. oDo.5

The McCabe-Thiele diagram, Fig. 13.28, is drawn for this separation at the optimum flow ratio G/F — 2.03. At this optimum condition, the size of each step in the cold tower is approximately equal to the size of the step in the hot tower at the corresponding plate. In operating the Savannah River plant [B7], the flow ratio of gas to liquid is controlled to give optimum performance by setting it so that the deuterium content of corresponding streams at the middle of the hot and cold towers are equal. In Fig. 13.28 this is illustrated by the fact that the deuterium content of vapor flowing between the eighth and ninth plates of the hot tower (step A) is approximately equal to the deuterium content of vapor flowing between the eighth and ninth plates of the cold tower (step B). Use of this principle greatly simplified what would otherwise be a difficult problem in flow control.

Because the separation obtainable in a mass diffusion stage is even smaller than in a gaseous diffusion stage, a practical degree of separation requires either a multistage cascade, such as the 48-stage cascade used by Hertz [H3] to separate neon isotopes, or a mass diffusion column.

The mass diffusion column, devised by Benedict [ВІЗ, B15] to provide a greater degree of separation than attainable from a single mass diffusion stage, is shown in Fig. 14.34. The main differences from a mass diffusion stage are as follows: (1) Separating agent is charged to the light stream at a uniform rate over the entire length of the column, instead of at one end of a stage. (2) Separating agent is condensed at a uniform rate over the entire length of the column instead of just from the streams leaving the column. To permit uniform charging and condensation of separating agent, this mass diffusion column contains four compartments instead of the two used in the stage type. These may take the form of cylindrical shells (Fig. 14.34) or parallel ducts.

In Fig. 14.34 the innermost chamber carries separating agent and distributes it at uniform rate over the length of the column; the second chamber carries the light stream; the third chamber, the heavy stream; and the fourth chamber, cooling water. Separating agent vapor flows radially through holes in the central tube and diffuses through the chambers carrying light and heavy streams to the cooling surface, where it is condensed.

The mass diffusion screen divides the second chamber, carrying the light stream, from the third chamber, carrying the heavy. As the light stream flows up, it is progressively enriched in the light isotope, which diffuses through the screen against the separating agent. As the heavy stream flows down, it is progressively enriched in the heavy isotope, which is carried through the screen with the separating agent.

By proper control of flow rates of separating agent and light — and heavy-stream feed rates, it is possible to make the molar velocity of light component inward just equal to the molar velocity of heavy component outward, a preferred condition for isotope separation in this equipment.

In the simple cascade of Fig. 12.12, whose performance was illustrated in Fig. 12.14, it is impossible to obtain high recovery of desired component because of losses in the tails streams leaving every stage. Desired component in these streams can be recovered by recycling these

streams to a lower stage in the cascade. Figure 12.13 illustrates the simplest type of recycle cascade, in which the tails stream from stage і +1 is recycled to become part of the feed to stage і from which stage / + 1 received part of its feed. This recycle flow scheme is by far the most common in countercurrent separation processes. 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. More complex recycle flow schemes will be treated in Sec. 14.

As an example of the use of these equations, we shall calculate the distribution of 236 U and the amount of separative work expended in a matched 23SU/238U cascade producing 1000 kg/day of uranium containing 3.2 w/o 233U from feed containing 0.711 w/o 235U and 0.4 w/o 236U, while stripping tails to 0.3 w/o 23S U. External conditions specified for the cascade are listed in Table 12.13.

Distribution of 236U is evaluated from the material-balance equation

(l) y6>F + 6.056 x6iW — 7.056 z6yF = 0 (12.326)

and application of Eq. (12.323):

__________ (1)Уб. р + 6.056 x6’W 7.056 z6J — =

[0.032/(0.968 — y6j)]1/3 [0.003/(0.997 — *«,„,)]173 [0.00711/(0.99289 — z6>F)]1/3

(12.327)

Values of y6j> and x6 w obtained from these equations using z6F =0.004 are tabulated below, together with weight fractions of 235 U and 238 U.

The amount of separative work expended per day in making 1000 kg/day of product, from Eq. (12.324) with these values of y6j> and х6 ц> is 3813.4 kg SWU/day. This may be compared with the amount of separative work needed in the absence of 236 U with the same weight fractions of 235U in product, tails, and feed and the same quantities of these streams:

D = 1000 0(0.032) + 6056 <K0.003) — 7056 0(0.00711) = 3787.5 (12.328)

using values of the separation potential 0 from Eq. (12.144).

Thus, the presence of 0.004 weight fraction 236 U in the feed increases the amount of

separative work needed for this example by 3813.4 — 3787.5 = 25.9 kg SWU/day, or 25.9/(7056X0.004) = 0.918 kg SWU/kg 236U in feed. This could serve as the basis for a penalty to be charged for 238 U present in feed to a uranium enrichment plant operating between the 235 U concentrations of this example. It should be noted that these results for the effect of 236 U on separative capacity are independent of the separation process under consideration.

1 INTRODUCTION

Because of the importance of M5U at compositions above natural abundance, originally for military purposes and more recently for nuclear electricity generation, great effort has gone into investigation and development of many processes for enriching 23SU. This chapter deals only with those processes that have been used on an industrial scale, those that seem likely to become of future industrial importance, and those that illustrate the shortcomings of the processes used industrially for separating the isotopes of light elements when applied to heavy elements such as uranium.

Discussion of processes for industrial separation of uranium isotopes cannot be as complete as the discussion of deuterium separation in Chap. 13. The detailed technology of the most economical and most promising processes is subject to security classification and to proprietary restrictions. Nevertheless, processes for enriching uranium can be described in sufficient detail to make their principles clear and to illustrate the similarities and differences between them and processes for separating isotopes of light elements.

For a more detailed discussion of uranium isotope separation than is possible in this chapter, reference may be made to papers on this subject presented at the four International Conferences on the Peaceful Uses of Atomic Energy sponsored by the United Nations at Geneva, to the Proceedings of the International Conference on Uranium Isotope Separation sponsored by the British Nuclear Energy Society in London in April 1975 [B20], to the Chemical Engineering Progress Symposium Series volume on uranium enrichment [B14], the articles on diffusion separation methods [Hll, S3] in the Encyclopedia of Chemical Technology, informative reports ORO-684, 685, 690, and 694 on uranium enrichment activities of the U. S. Atomic Energy Commission (AEC), and the authoritative monograph on uranium enrichment edited by Villani [Via].

The processes used most extensively for separating isotopes of light elements, distillation and chemical exchange, become progressively less selective as the atomic weight increases and are ineffective for uranium.

The processes used most extensively for separating uranium isotopes, gaseous diffusion and the gas centrifuge, are much less efficient than distillation for light elements, but are impaired less by an increase in molecular weight, so that they are the preferred methods for uranium. Table 14.1 compares the separation factors for these four processes when applied to mixtures

Table 14.1 Representative separation factors for isotope separation processes

Separation factor for isotopic mixture: Process Property* H2-HD 14NO-1sNO “’UFg-^F*

+a*, relative volatility. K, exchange equilibrium constant: * for HD-H2 О exchange; § for 14NO — H1SN03 exchange;* for 235UF6-23&UF5 NOF exchange. m2,m!, molecular weight of heavy, light component. va, peripheral speed, 500 m/s. R, 8314 J/(kg-mol’K). T, 300 K.

of H2 and HD, 14NO and 15NO, and J35UF6 and 238UF6. Although many features besides separation factor enter into choice of the preferred process, it is clear that the higher values for gaseous diffusion and the gas centrifuge give these processes a substantial advantage over distillation and chemical exchange for uranium isotope separation.

Section 2 of this chapter deals with the isotopic content of uranium. Section 3 lists the principal processes for separating uranium isotopes on an industrial scale and describes briefly projects using these processes. Section 4 gives a detailed description of the gaseous diffusion process, which until now has produced almost all of the world’s enriched uranium. Section 5 is a parallel treatment of the gas centrifuge process, which is emerging as an effective competitor of gaseous diffusion. Section 6 describes aerodynamic processes that separate uranium isotopes through composition differences developed when mixtures of 23SUF6 and 238UFe are subjected to high linear or centrifugal accelerations in flowing gas streams. Such processes are in an advanced stage of development and are to be used industrially in Brazil and possibly South Africa. The remainder of this chapter discusses in less detail other processes not yet ready for industrial use. Mass diffusion (Sec. 7) and thermal diffusion (Sec. 8) are clearly not economical for uranium isotope separation but are described briefly because they illustrate isotope separation principles in the comparison with gaseous diffusion, and have been used to advantage for other elements. Laser-based processes (Sec. 9) appear very promising and may, with sufficient development, become the most economical means of separating uranium isotopes.

A close-separation cascade is one in which a — l < 1. In such a cascade, the condition 0 = /a for an ideal cascade, in which heads and tails fed to a stage have the same composition, may be approximated by

(12.123)

Equation (12.102) for the tails flow rate in an ideal cascade may be approximated by

Р(УР ~ x)
СЗ-1Ж1-Х)

because of (12.123). We shall now show that when the total tails flow rate of a dose-separation cascade is a minimum, the tails flow rate at each stage is given by (12.125).

The difference in composition between stage heads and stage tails, given by (12.76), may be approximated by

Уі+і -*/+1 =(«-1)Уї+і(1 ~Уі+і) (12.126)

in the close-separation case. A relation for the change in heads composition between adjacent stages is obtained by combining this with the material-balance equation (12.62):

Уі+1 ~Уі = (а — 1)У/+і(1 — Л+і)-дА (Ур-Уі) (12.127)

Jvi+i

Because Уі+І, у і, and х,- are nearly equal, this difference equation may be approximated by the differential equation

^ = (a-l)x(l — x)-^(yP-x)

The total tails flow rate in the enriching section is

is a minimum at all x. The optimum value of N that makes this a minimum is that at which the derivative of the denominator vanishes, or at which

This is just twice the minimum tails flow rate at which dx/di = 0.

This is identical with (12.125). Thus it has been shown that in the dose-separation case an ideal cascade may be defined in any one of the three following equivalent ways:

РІУР-Х)

" (p-iyxil-x)

N is so chosen that total interstage flow is a minimum

In such a cascade, the heads and tails fed to each stage have the same composition, and the cut в is I. The last may be seen from (12.21), which becomes

13-І =(а-1Х1 — в) (a-l<l) (12.133)

At the optimum flow rate, the change in composition per stage, from (12.128), is

§ = ^*0-*) (12-134)

which is just half the change at total reflux at which P/N = 0. The total number of stages in the enriching section is

Equation (12.95) reduces to this expression, except for terms of the order of unity.
The total tails flow rate in the enriching section at the optimum flow rate is

(12.136)

With-Nop, from (12.132) and dijdx from (12.134), this becomes

The total heads flow rate, from (12.120), reduces to the same expression.

The total flow rate in both stripping and enriching sections, from (12.122), becomes

(12.139)

The total heads flow rate or total tails flow rate in both sections is one-half this value.

These formulas are extraordinarily useful in roughing out the characteristics of an isotope separation plant without the necessity of designing every one of its stages, which often number in the thousands. As an illustration, the total heads flow rate in the uranium isotope separation example considered in Fig. 12.17 is

-213.57[(2X0.0072) — 1] In ^||j-= (217,343X191.57) = 41,636,000

(12.140)

This is the area within Fig. 12.17. Around 42 million moles of UF6 must be pumped for every mole of 90 percent 235UF6 separated.

In this analysis of electrolysis, the somewhat optimistic assumption will be made that a separation factor of 7 can be obtained at a cell voltage of 2.1. At 95 percent current efficiency, the power consumption per gram-mole of water electrolyzed is then

of hydrogen produced.

Let us first consider the production of heavy water in a simple cascade of electrolytic cells, without recycle, as in Fig. 13.13. Such a cascade, used at Ems and Nangal, preconcentrates deuterium prior to final concentration by distillation of hydrogen. With a sufficient number of stages, such a cascade could be used to produce pure heavy water in low yield from natural water.

If the heads separation factor (3 is constant throughout such a simple cascade, the fraction of deuterium that may be recovered depends on the number of stages n and the overall enrichment ш in accordance with

/а-ы^Л"

r" V «“I /

as has been shown in Eq. (12.50).

As an example of the recovery of deuterium obtainable in a simple electrolytic cascade without recycle, production of heavy water containing 99.693 a/о deuterium from natural water containing 0.0149 a/о will be considered. The overall enrichment w is

A high, but attainable, overall separation factor of a = 7 will be used. A heads separation factor such as the one that would be used in an ideal recycle cascade of (3 = s/a = fl = 2.646 will be assumed. Then the number of stages n is given by

The recovery of deuterium, from Eq. (13.51), is

Г7 —(2,176,168)ms] 15

r = |——— —-—I = 0.00816 (13.54)

The reason for this low recovery, of course, is that most of the deuterium is carried off by the hydrogen produced during electrolysis, and only a small fraction is left in the residual water.

The maximum amount of heavy water that could be produced in this way as the by-product of 10,000 g-mol of hydrogen would be

(10,000X0.000149X0.00816) = 0.0122 g-mol (13.55)

or 0.244 g. The electric power consumption is 1180 kWh, or 4836 kWh/g D20. Because electric power costs of the order of $0.02/kWh, this corresponds to $100/g D20. It is evident that a profitable use must be made of the hydrogen, because the value of the heavy water is only a small fraction of the cost of power.

The recovery of deuterium can be increased substantially by burning deuterium-rich hydrogen from the upper stages of the plant and recycling the water to the electrolytic cells, as in Fig. 13.14. Figure 13.15 shows a generalized flow sheet for such a plant, with hydrogen from the lower stages being used as the principal plant product and with hydrogen from the upper stages being burned and recycled to increase recovery of heavy-water by-product. The principal variables in such a flow sheet are [46] 2

The increase in deuterium content per stage is measured by the heads enrichment factor /3, defined in terms of the atom fraction deuterium in the heads water leaving this stage xm and the atom fraction deuterium in the water leaving the next lower stage xm _ j, as

*m0 xm-1) xm — i(l xm)

In stages m — 1 and higher, the optimum enrichment per stage is that of an ideal cascade, in which

xm -1 — Ут+1 (13.57)

and P = >/a (13.58)

We shall use condition (13.58) to set the enrichment per stage in the lower stages in which hydrogen is not recycled, also. The total number of stages n is then given by Eq. (13.53).

As a specific example, we may consider a plant designed to produce 10,000 g-mol of hydrogen per minute, while recovering as a by-product as much heavy water as can be economically justified. The atom fraction D in feed water x0 will be taken as the natural value of 0.000149, and the atom fraction D in the heavy-water product xp will be taken as 0.99693 (to make the number of stages exactly 15.00). The deuterium content of hydrogen and water leaving the lower stages of this cascade is given in Table 13.14.

It evidently would not pay to bum and recycle hydrogen from stages 1 and 2, because it is no richer in deuterium than feed. To determine at which stage it would pay to begin to bum and recycle hydrogen, a number of alternative flow sheets have been worked out, with the most significant results summarized in the last four columns of Table 13.14. In the first case listed, hydrogen is burned and recycled on stage 3 and all higher stages, in the second case on stage 4 and higher, etc. In each case, the unbumed hydrogen production rate has been held constant at 10,000 mol. For each case there has been evaluated:

1. The deuterium recovery, from (13.51)

2. The moles of heavy water produced, P

3. The moles of hydrogen burned and recycled, H, the total tails flow of the recycle portion of the cascade, from (12.119)

To determine which of these cases is best economically, it is necessary to set a value on the hydrogen that is burned and therefore lost. A representative value for hydrogen produced commercially by reforming naphtha is $1.50/1000 ft3; an electrolytic plant would probably not be built unless it could sell hydrogen for this figure. Because 0.5 mol of oxygen is consumed per mole of hydrogen burned, it is necessary to set a value on this, too. A value of $20/short ton, or $0.80/1000 ft3, will be used. The value of hydrogen and oxygen consumed is therefore $1.90/1000 ft3 or $1.59/kg-mol of hydrogen burned.

The next-to-the-last column of Table 13.14 gives AH/AP, the ratio of the additional hydrogen that must be made to the additional heavy water produced when hydrogen from an additional stage is burned and recycled. The last column gives the value of the additional hydrogen and the associated oxygen required to produce 1 kg of additional D20. This is obtained as ($1.59/2Q)(AH/AP). Because of the high value of $ 196/kg of incremental D20 made by burning hydrogen from stage 4, it is evident that it would not be economical to bum hydrogen from this stage. The incremental value of $74/kg for hydrogen from stage 5 is under the cost of heavy water in competing processes. Burning hydrogen from stage 5 to increase heavy-water production therefore might be justified.

The average cost of hydrogen and oxygen from stage 5 and higher burned to make heavy water in the most favorable case is

Although the need for efficient condensers and the complications of connecting electrolytic cells in series cascade would add something to the cost, it is evident that electrolysis provides a way of making small amounts of heavy water at a very low cost as a by-product of hydrogen and oxygen.

Figure 13.16 is a flow sheet for a plant for the case in which hydrogen from stage 5 and higher is burned and recycled. The fraction of deuterium in the feed that is recovered is only 0.238. This low recovery is characteristic of the electrolytic process when used as the sole means of concentrating deuterium. As a result, the amount of heavy water that could be produced by electrolysis alone, even at a large electrolytic plant, is small.

Although the recovery of heavy water is better than in the simple cascade without recycle,

Figure 13.16 Optimum electrolytic cascade for production of 10,000 mol hydrogen and heavy — water by-product, a = 7; (3 = /T.

In Fig. 13.15, stages 1 to m-2 constitute a simple cascade, without recycle, and the remaining stages, from m — 1 to n, constitute an ideal, recycle cascade. We shall show how flow quantities may be derived for this flow sheet.

The deuterium content of water heads leaving stage m is

IF’xf + 1 — xF

The deuterium content of hydrogen tails from the same stage is

Compositions in Fig. 13.16 were obtained in this way.

The total amount of hydrogen formed from stages m to n is given by (12.119), for the total tails flow in the enriching section of an ideal cascade, with xm. x replacing zF. In the plant shown in Fig. 13.16, the total number of moles formed is

0,3553 99%y/T + 1) —VT [7 0.997 / 0.993 N yJT-) In VT [Уо.00725/ Vo.00313/

Hydrogen from stage m — 1 constitutes tails from the ideal cascade section, whose quantity relative to product is given by

Р{хр~хт_г)

xm — 2 Ут-І

In the plant shown in Fig. 13.16, the tails quantity is

The feed rate to stage 4 is W + P= 206.93.

In Fig. 13.15, the first m— 2 stages constitute a simple cascade, operated without recycle, with constant heads separation factor p. The recovery of deuterium from a simple cascade of m—2 stages operated at constant P is

(13.66)

from Eq. (12.48).

In the flow sheet of Fig. 13.16, the recovery of deuterium from the three stages of the simple cascade is

(13.67)

The number of moles of natural water fed to stage 1 required to get 206.93 mol of water

containing 0.2752 percent deuterium from stage 3 is then

„ (206.93X0.002752) _____

(0.38220X0.000149) ~ 10,000

6.2 Electrolytic Separation of Other Elements

Separation factors in electrolysis for other elements are much lower than for hydrogen. A few values that have been reported are listed in Table 13.15. These values are so low, and the cost of electric energy per unit electrolyzed is so high, that electrolysis is uneconomical for separating isotopes of any element other than hydrogen. Some concentration of 18 О takes place in an electrolytic deuterium plant.

Equation (14.111) for the minimum power of 0.0923 kW to produce 1 kg of separative work per year in uranium isotope separation was derived for cross flow on the low-pressure side of the barrier, with the composition of gas on that side y’ equal to the composition of the net flow u. The purpose of this section is to show that the minimum power requirement could be reduced further by having и greater than у by an appropriate amount and to derive an expression for the optimum difference between v and у and the corresponding power consump­tion per unit separative capacity. For this minimum-power case, pressures on the high-pressure and low-pressure sides of the barrier must be so low the only flow through the barrier is of the separating, molecular type, and the mixing efficiency on each side of the barrier is unity.

A stream containing x mole fraction light component flowing at molar rate N carries separative work at the rate

N(2x — 1) In = (Nt — N2) In ^ (14.118)

where N і and N2 are the molar flow rates of light and heavy components, respectively.

Consider the small element of barrier area dA shown in Fig. 14.9, at which the flow rates of light and heavy components are as follows:

High-pressure stream

Low-pressure stream

(14.125)

In terms of the molar velocity G of both components through the barrier and the mole fraction v of light component in the net flow through the barrier,

For uranium isotope separation, є < 1 and и — x ” <в 1. Hence, to the second order in є and v — x”, Eq. (14.130) reduces to

dA e(v — x") є2 GdA~x"( 1-х") 2

For the present assumption of pure molecular flow, и — x" from Eq. (14.30) is

_ " s*"0 -*”) + д(х" — У) ~ 6<?У(1 ~У)

V X 1 + 5x" — q( 1 + §У)

where 5 = 0!o — 1 (14.133)

To the first order in 5 and У — x", Eq. (14.132) reduces to

v — x" = 5x"(l — x")———- — Cv’-x”) (14.134)

1 “<?

To the first order in є, Eq. (14.129) reduces to

У — X = ex (1 — X )

With Eqs. (14.134) and (14.135), Eq. (14.131) becomes

dA ca(l+<?)

GdA Є 2(1 — q)

The optimum value of є is the one that makes (14.136) a maximum, at which

de GdAJ 1 ~q

„ «О-<7)

Hence eop, = ————-

1 + q

„d (^)

GdA/ max 2(1 +q)

From (14.129), (14.134), and (14.138), it is found that

5x"(l — x")q
ГТ~q

The minimum power required to recompress GdA moles flowing through pressure ratio q is

(14.141)

From (14.139) and (14.141), the ratio of minimum power to maximum separative capacity is

dQ = 2RT0 (1 + g) ln(!Ajr) dA/„и,, (a0 — 1)J 1 ~q

where (do — 1) has been substituted for 6. Values of 2[(1 + q) ln(l/г?)]/(1 — q) are tabulated below.

Pressure ratio q 0.2 0.3 0.4 0.6 0.8 1.0

2[(1 +<?)ln(l/q)]/(l-<?)] 4.83 4.47 4.28 4.09 4.02 4.00

Hence the minimum value occurs at a ratio of 1.0, as the low-side pressure becomes equal to the high-side pressure. At this limiting condition, the minimum ratio of power to separative capacity is

,dQ =JRh_

q-*-0v^/min («0 1)

The coefficient 4 in Eq. (14.143) for optimum counterflow is to be compared with 5.11 in Eq. (14.110) for cross flow. The minimum possible power input to produce 1 kg of separative work per year is

ART0 _ (4)[0.002310 kWh/(kg-mol-K) (300 K)

m(a0 -1)2~ [238 kg U/(kg-mol)] (0.00429)J(8760 h/yr)

= 0.0722 kW/(kg SWU/yr)

This result is to be compared with 0.0923 kW for the minimum with cross flow.

Because this minimum value with counterflow is obtained in the limit of zero pressure difference across the barrier, it would require use of an infinite amount of barrier surface. This condition is analogous to the familiar thermodynamic condition that the loss in availability in a heat exchanger is a minimum when an infinite amount of surface is used.

The foregoing tabulation shows, however, that even at a practical pressure ratio of 0.3, the coefficient of RT0/(uo — l)2 would be 4.47, substantially less than 5.11 with cross flow. However, this result would be somewhat offset by mixing inefficiency on the low-pressure side when v differs from y’, and by the need to use a counterflow, p-up, one-down cascade to obtain the optimum difference at as many points as possible in the cascade.

2.1 235 U

Table 12.2 lists methods that have been used on an industrial or large pilot-plant scale to enrich uranium in 235 U.

Gaseous diffusion process. Figure 12.1 illustrates the principle of one stage of the gaseous diffusion process. Stage feed gas, UF6, flows past a diffusion barrier made of porous material with very fine holes, smaller than the mean free path of the UF6 molecules. About half of the feed gas flows through the barrier to a lower-pressure region. The gas passing through the barrier is slightly richer in 235 U than the gas remaining on the high-pressure side, because the mean speed of 235 UF6 molecules is slightly higher than that of 238 UF6 molecules. These mean speeds are in the inverse ratio of the square roots of the molecular weights of the two molecules. Under practical operating conditions the ratio of 235 UF6 atoms to 238 UF6 atoms in the enriched UF6 fraction passing through the barrier, yj(l —у), to the corresponding ratio in the depleted UF6 fraction remaining behind, x/(l — x), is in the ratio of their mean speeds:

The ratio [v/( 1 —y)]/[x/( 1 —x)] is called the stage separation factor and is denoted by a. Analogous separation factors are used to characterize all separation processes. A value of a close to unity indicates that the separation is difficult; a value far from unity, easier. For gaseous diffusion of UF6, a is so close to unity that the process must be repeated many times for a useful degree of separation. To do this, the low-pressure enriched UF6 must be recompressed to the feed pressure and cooled. The depleted UF6, which experiences some pressure loss, must also be recompressed (not shown).

Because of the small change in enrichment from a single stage, for a useful degree of enrichment, it is necessary to use many stages in series in countercurrent cascade. Figure 12.2 shows how stages are connected together in such a cascade. On each stage a motor-driven compressor takes partially depleted gas from the next higher stage and partially enriched gas from the next lower stage and recompresses them before passage through a cooler and the diffusion barrier. To separate natural uranium feed containing 0.00711 fraction 235 U into product containing 0.03 and tails 0.002 fraction 23SU requires 1272 stages. The minimum total

interstage flow in such a cascade is obtained when the compositions of the streams mixed at each point A are equal. Such a cascade is called an ideal cascade. In such a cascade, the interstage flow rate M from a stage where the 235 U fraction is у is

2РІУР-У)

(а — 1>(1 — У)

where P is the flow rate of product containing yp fraction 235 U. The theory of such an ideal cascade is developed later in this chapter, and details of the gaseous diffusion process are given in Chap. 14.

Figure 123 is a photograph of the large gaseous diffusion plant of the U. S. Department of Energy at Portsmouth, Ohio, which use 4080 stages to enrich 233U to 97 percent.

The gas centrifuge. Figure. 12.4 shows the principle of the type of countercurrent gas centrifuge proposed 20 years ago by the German engineer, Gernot Zippe [Zl], and now generally adopted by groups continuing development of this promising method of isotope separation. Such a centrifuge consists of a rapidly rotating cylindrical bowl made of a material with high strength-to-density ratio. The UF6 gas rotating inside in this bowl is subjected to centrifugal accelerations thousands of times greater than gravity. This makes the pressure at the outer radius of the bowl millions of times greater than at the axis and causes the concentration of 238 UF6 relative to 235 UF6 to be appreciably higher at the outer radius than at the axis. In a machine made of fiberglass running at the highest speed possible without mechanical failure, the 233 U content at the center of the bowl can be as much as 18 percent higher than at the

Figure 12.4 Zippe gas centrifuge sche­matic.

outside. In addition, longitudinal countercurrent flow of UF6 is induced by a system of rotating baffles and stationary scoops. In Fig. 12.4, gas enriched in 235UF6 at the center flows downward and gas enriched in 238 UF6 at the outside flows upward. Under these conditions the gas toward the bottom of the bowl becomes progressively richer in 235 UF6 and the gas at the top richer in 238 UF6. By making the bowl sufficiently long, the concentration difference between top and bottom can be made many times greater than between center and outside.

Gas centrifuges of greater capacity than described by Zippe have been developed in the United States, England, Germany, and Holland. Commercial centrifuge plants are operating in England and Holland and are planned in the United States. The power consumption of the centrifuge process is much lower than gaseous diffusion, and it is expected that separation costs will become lower. The process is described in more detail in Chap. 14.

Thermal diffusion of UF6. The thermal diffusion process makes use of the small difference in 23SU/238U ratio that is established when heat flows through a mixture of 23SUF6 and 238 UF6. The principle of the process is described in Chap. 14. The process was used [Al] in 1945 in the United States by the Manhattan Project to enrich uranium to 0.86 percent 235U. This slightly enriched material was used as feed for an electromagnetic separation plant. Although the process could be put into production quickly because of the simplicity of the equipment, it
was very inefficient, with very high heat consumption per unit of output. Consequently, when the more efficient gaseous diffusion plant came into operation at Oak Ridge, the thermal diffusion plant was dismantled. Thermal diffusion is a useful method, however, for separating small amounts of isotopes for research purposes. It is used, for example, at the Mound Laboratory to enrich 13C from 90 to 99 percent.

Electromagnetic processes. The possibility of using electromagnetic means for separating isotopes was established by Thomson [T5] in 1911. When Thomson passed a beam of positive neon ions through electric and magnetic fields, two traces were produced on a photographic plate, one for 20 Ne and the other for 22 Ne. The modem mass spectrometer works on the same general principle. With it, the existence of naturally occurring isotopes of 61 elements has been established, and isotopic abundances and masses have been determined (App. C).

In 1940, Nier and co-workers [N2] used a mass spectrometer to separate around 0.01 /Jg of

235 U from 238 U, to show that 235 U was the fissionable isotope of uranium. Because of its demonstrated ability to separate 235 U, the electromagnetic method was the first one selected by the Manhattan District for large-scale production of this isotope [S5]. Under the direction of Lawrence [LI ] at the University of California, mass spectrometers of greatly increased capacity were developed. The end result was the calutron[43] electromagnetic isotope separator used in the Y-12 plant at Oak Ridge, in which, in 1944, the first kilograms of 235U were produced.

When the gaseous diffusion plant came into operation, the cost of separating MSU electromagnetically was found to be higher, and in 1946, the Y-12 plant was taken off uranium-isotope separation. Some of this equipment is now being used to produce gram quantities of partially separated isotopes of most of the other polyisotopic elements, for research uses. These units have also been used to separate artificially produced isotopes, such as

236 U from irradiated uranium, and the various plutonium isotopes.

Large-capacity electromagnetic isotope separation equipment has also been developed in Russia [Z2], and at Harwell [S4], Amsterdam [K2], and other centers of nuclear research

[K5] •

Becker separation nozzle process. Recently there has been increased interest in aerodynamic processes in which partial separation of isotopes is obtained in flowing gas streams subjected to high linear or centrifugal acceleration. The aerodynamic process about which most information is available is the Becker separation nozzle process.* This originally employed linear acceleration of UF« through a divergent nozzle, but now uses a combination of linear and centrifugal acceleration through a curved slit.

Figure 12.5 is a cross section of the slit-shaped separation element used in the most fully tested form of the Becker nozzle process. Feed gas consists of a mixture of about 5 m/o (mole percent) UF6 and 95 m/o hydrogen at a pressure of around 1 atm. This flows into a low-pressure region through a long curved slit, or “nozzle” (perpendicular to the plane of the figure), with first a convergent, then a divergent cross section. The change in cross section accelerates the gas mixture to supersonic speed, and the curved groove downstream of the slit produces a centrifugal field. This sets up a concentration gradient in the mixture, with the gas adjacent to the curved wall enriched in 238 U relative to 235 U. A knife-edge downstream from the slit divides the stream into a more-deflected light fraction and a less-deflected heavy fraction.

Dilution of UF6 with hydrogen has two beneficial effects. The mixture has a much higher sonic velocity than pure UF6, so that much higher flow velocities are attainable, and inert gas makes the isotope separation factor greater than would be predicted for the prevailing centrifugal field. A separation factor of 1.015 can be obtained with a mixture of 5 percent UF6-95 percent H2 flowing through a pressure ratio of 3.5.

A more complete description of the process is given in Chap. 14. A semicommercial plant using this process is being built in Brazil.

UCOR process. The UCOR process, developed by the Uranium Enrichment Corporation of South Africa, Ltd., also makes use of high-speed flow of UF6-hydrogen mixtures through sharply curved ducts. By using a new cascade technique, called the Helikon, in which an axial-flow compressor handles several streams simultaneously without mixing, it is expected that natural uranium can be enriched to 3 percent 235 U with from 90 to 115 multistage compressor modules. A partial description of a South African pilot plant using this process was given by Roux and Grant [R2].

Laser-based processes. In addition to the processes listed in Table 12.2, intensive research is being conducted on using high-intensity, tunable lasers to separate uranium isotopes by making use of the small differences in absorption spectra of 235 U and 238 U or one of their compounds. Laser-based processes have demonstrated capability for selective separation of isotopes of many elements on a small scale and are considered promising candidates for eventual large-scale economic production of enriched uranium. Letokhov and Moore [L3] provide a good review of laser isotope separation work through 1976.

2.2 Deuterium

Commercial production of deuterium has been almost universally in the form of heavy water, DjO. Table 12.3 lists processes that have been used for production of heavy water at rates above a ton per year. These processes are divided into two classes. Parasitic processes take feed

from a primary plant producing hydrogen or ammonia synthesis gas (75 percent H2, 25 percent N2), extract deuterium from it, and return the depleted hydrogen for commercial use, usually ammonia synthesis. Self-contained processes have heavy water as their sole product and use natural water as feed. Generally speaking, the parasitic processes produce heavy water at lower cost, but their output is limited to the deuterium contained in the feed gas, which seldom contains more than 0.013 a/о (atom percent) deuterium. Even with complete deuterium extraction, a large plant producing 1000 short tons (t) of ammonia synthesis gas per day and operating 330 days/year could yield only

/10001 NH3 /330 days / 3 atoms H /0,00013 atoms D /20tD2Q / day / yr / molecule NH3/ atom H /t-molD20//

2 atoms 1

Concentration of deuterium by the electrolysis of water was proposed by Washburn and Urey [Wl], used by Lewis [L4] to make the first samples of pure D20, and employed for the first production of heavy water on a large industrial scale by the Norsk Hydro Company, at Rjukan, Norway. The Rjukan plant makes use of cheap hydroelectric power to produce electrolytic hydrogen for ammonia synthesis and by-product heavy water.

When Germany occupied Norway in World War II, this plant was producing 1.5 MT/year of heavy water, and around 90,000 MT/year of ammonia. The water being electrolyzed contained 21 MT/year of heavy water, of which 10 could have been recovered by burning hydrogen enriched in deuterium from the higher stages of the plant and recycling the deuterium-rich water. This, however, would have reduced the ammonia output by 23/300 MT/year. The German scientists Harteck, Hoyer, and Suess [C2] conceived the ingenious idea of recovering deuterium from the hydrogen gas by absorption in water, by making use of the exchange reaction

HD + H2O^HDO + H2 A= 3.0

in which deuterium concentrates in the water. A nickel catalyst for carrying out this reaction in the gas phase was developed. One catalytic reactor was installed at Rjukan, and others to bring the heavy-water production up to 5 MT/year were planned, but the plant was destroyed in 1943 in a series of daring commando raids. It was rebuilt after the war and has been in operation since then.

At about the same time, a similar exchange process was developed by Urey and Taylor [M5, S2, Tl], working under the Manhattan Project in the United States. The Standard Oil Development Company designed the exchange equipment [Bl] and installed it in the electrolytic hydrogen plant of the Consolidated Mining and Smelting Company, at Trail, British Columbia, where it was operated until 1955. This plant produced 6 MT D20/year at a concen­tration of 237 w/o (weight percent) D20. Final concentration to 99.7 w/o D20 was by elec­trolysis. The cost was $ 130/kg D20.

A second method for the industrial production of heavy water, used by the Manhattan Project in the United States [M5], was the distillation of water. Three plants having a total capacity of 13 MT D20/year were built at Army Ordinance plants. Because the relative volatility for separating H2 О from НЕЮ is only 1.03 at atmospheric pressure, the size of equipment and the heat consumption of these plants per unit of D2 О produced was very high, and the cost of heavy water was greater than in other processes. Nevertheless, the distillation of water was attractive as a wartime production method because the process needed little development work and used standard equipment. These plants were shut down after the war. More recently, distillation of water has come to be one of the most satisfactory methods for final concentration of heavy water.

Because the relative volatility for separation of deuterium by the distillation of liquid hydrogen is around 1.5 at atmospheric pressure, the size and heat consumption of a hydrogen distillation plant would be much smaller than that of a water distillation plant producing the same amount of deuterium. Plants to concentrate deuterium by the distillation of liquid hydrogen were designed by German engineers [C2] and by the Manhattan Project [M5] during World War II, and by Hydrocarbon Research, Inc. [H6], in the United States, but none of these plants was built because of uncertainty about the performance of industrial equipment operating at the very low temperatures needed to liquefy hydrogen. In 1949 a group of Soviet engineers undertook the development work necessary to ensure success of this type of plant, and in 1958 announced [Ml] that a plant producing deuterium by distillation of electrolytic hydrogen had been in operation in the Soviet Union for some years. The plant consists of multiple units, each with a capacity of around 4 MT D2 O/year.

In 1958, two companies specializing in cryogenic engineering put into operation experi­mental plants for concentrating deuterium by distillation of ammonia synthesis gas (75 percent H2, 25 percent N2). Socifte de Г Air Liquide designed and built one at the ammonia plant of Office National Industriel de l’Azote (ONIA), at Toulouse, France, which is operated by Compagnie Fran$aise de l’Eau Lourde, jointly owned by Air Liquide and ONIA. Gesellschaft fur Iinde’s Eismaschinen designed and built a second deuterium plant at the ammonia plant of Farbwerke Hoechst, at Hoechst, Germany. The production rates of the plants were roughly 2 and 6 MT D2 О/year, respectively. Because of the small size of these plants, the high local cost of electric power, and the less-than-natural deuterium content of the available synthesis gas, the cost of heavy water produced in these plants was high. After sufficient information had been obtained to permit design of larger plants at other locations where local conditions were more favorable, both plants were shut down in 1960.

In 1959, Sulzer Brothers designed and built a plant to distill electrolytic hydrogen enriched to six times the natural abundance of deuterium, which was available at the ammonia plant of Emswerke AG, at Ems, Switzerland [HI]. At this plant, about 2 MT/year of heavy water were

produced at a cost near $62/kg. The cost at Ems was lower than at Toulouse or Hoechst because of the higher deuterium content of feed and the low content of nitrogen and other condensable impurities in electrolytic hydrogen. This plant has been shut down because production of the electrolytic hydrogen that fed the heavy water plant has become too costly. In 1961, a 14 MT/year plant of this type was built by Linde to distill electrolytic hydrogen enriched to three times the natural abundance of deuterium, which was available at the Indian government’s ammonia plant at Nangal, India.

Another process that has been used to extract deuterium from ammonia synthesis gas is the deuterium-exchange reaction between liquid ammonia and gaseous hydrogen:

NH3(I) + HDfc) — NH2D(0 + HjGO

In the presence of potassium amide, KNH2, as catalyst dissolved in liquid ammonia, equilibrium favors concentration of deuterium in the liquid phase. A 26 MT/year plant using this process was operated at Mazingarbe, France, in the late 1960s, and three larger plants with a combined capacity over 200 MT/year are being built in India.

All of the previously mentioned plants except those employing distillation of water were parasitic to a synthetic ammonia plant. Their deuterium-production rate is limited by the amount of deuterium in ammonia synthesis gas. To produce heavy water at a sufficient rate, a growing industry of heavy-water reactors requires a deuterium-containing feed available in even greater quantity than ammonia synthesis gas. Of the possible candidates, water, natural gas, and petroleum hydrocarbons, water is the only one for which an economic process has been devised, and the dual-temperature hydrogen sulfide-water exchange process is the most economic of the processes that have been developed.

This process, invented by Spevack [S7] and developed independently by Geib [C2] in Germany, makes use of the fact that the separation factor a for exchange of deuterium between liquid water and gaseous hydrogen sulfide,

H2 0(/) + HDSfe) — HDO(0 + H2 ЗД is etc = 2.32 at 32°C and ah = 1.80 at 138°C

By running liquid water countercurrent to recycled gaseous hydrogen sulfide through first a cold tower and then a hot tower, as shown schematically in Fig. 12.6, water enriched in deuterium may be withdrawn from the water leaving the cold tower. The principle of the process and process flow sheets are described in detail in Chap. 13.

The first plant of this type, designed by the Girdler Corporation and operated by E. I. du Pont de Nemours and Company, built at the Wabash Ordnance Plant at Dana, Indiana, in 1952 but later shut down, gave this process the name the G-S process, for Girdler-Sulfide. Three improved units, each with a capacity of 160 MT/year, were designed, built, and operated by du Pont at Aiken, South Carolina [B2]; one is still in operation at a reduced capacity of 69 MT/year.

Figure 12.7 is a photograph of this plant. The world’s principal heavy-water production capacity is found in Canada, where G-S plants with a total capacity of 4000 MT/year are in operation or under construction.

2.3 Lithium Isotopes

Many methods have been used to achieve partial separation of lithium isotopes on a small scale. Examples of processes and reported separations are listed in Table 12.4. A process somewhat similar to the last one listed in this table, involving countercurrent exchange of lithium isotopes between aqueous lithium hydroxide and lithium amalgam, is to be used in a plant being built

Figure 12.6 Dual-temperature water-hydrogen sulfide process.

by Eagle Kcher Industries, Inc., at Quapaw, Oklahoma, to produce 1000 kg 99.99 percent 7 Li per year at an approximate price of $3/g.

2.4 10 В

Table 12.5 compares four processes that have been used for concentrating 10B. The research that led to the first commercial production of 10 В was carried out by Crist and Kirshenbaum [C5] in the laboratory of H. C. Urey at Columbia University in 1943. As reported-by Kilpatrick and co-workers [Kl], it was concluded that the most satisfactory process consisted in the equilibrium distillation of the complex of boron trifluoride and dimethyl ether, BF3-(СНз^О. When this substance vaporizes, it dissociates partially according to the reaction

BF3 -(СН3)а О — BF3 + (СН3)г О

The isotopic exchange equilibrium

10BF3C?) + UBF3 -(CH3)20(1) * nBF3(g) + I0BF3 ’(СН3)20(Г)

is then established, with an equilibrium constant of 1.027 at 100°C [К2]. When the liquid is distilled at 100°C, the vapor phase is 60 percent dissociated.

(1.027X0.6) + (1.000X0.4) = 1.016 (12.4)

This value has been confirmed experimentally [Kl].

A semicommercial plant based on this process was built and operated for the Manhattan Project by the Standard Oil Company of Indiana [C4]. In 1953, the U. S. Atomic Energy Commission authorized construction of a larger plant at Niagara Falls, New York, with the Hooker Electrochemical Company as operating contractor [Ш]. This plant produced 460 kg/year of 10B at an enrichment of 92 a/о 10B. The plant was shut down in January 1958. Eagle Picher Industries, Inc., has been producing 10В at Quapaw, Oklahoma, by this process since 1973 and is expanding capacity to 1000 kg/year. The cost is from $5 to $15/g.

A plant producing 2 kg of 10 В per year by equilibrium distillation of the complex of BF3 and diethyl ether, BF3 *(Сг H5 X O, was operated by 20th Century Electronics, Ltd., in New Addington, England [Е1]. The process, developed by the U. K. Atomic Energy Authority (UKAEA), is generally similar to the U. S. process using the dimethyl ether complex. Both plants are operated at subatmospheric pressure, to minimize irreversible decomposition of the complex.

Distillation of BF3 is another process that has been used to concentrate I0B. This has the advantage over the processes using ether complexes of BF3 that decomposition is not a problem, so that the plant can be operated at atmospheric pressure and can be scaled up without special concern about increased column pressure drop. Disadvantages of BF3, however, are that the separation factor is only 1.0075 [Nl], and the reflux condenser must be operated

at temperatures in the inconvenient range between the melting point of BF3 (—127°C) and its normal boiling point (—101°C). Despite these difficulties, the process was used successfully in the Soviet Union [M4] to produce O. S kg/year of 10 В enriched to 83 percent, and in England by the UKAEA [Nl] to produce 26.5 kg/year enriched to 95 percent. I0B concentrates in the liquid phase, as in the exchange equilibrium.

2.5 13C

Natural carbon contains 1.11 percent 13 C. This isotope was first produced commercially at a rate of around 1 g/day by the Eastman Kodak Company [S8], using the exchange reaction between HCN gas and NaCN solution developed in 1940 by Urey and co-workers [H5]. The separation factor is 1.013.

13 C has also been produced by the low-temperature distillation of carbon monoxide, in a process developed by London and co-workers [Jl, L6]. A carbon monoxide distillation plant has been in operation at Harwell since 1949, producing 0.4 g/day of 13 C at 60 to 70 percent enrichment. Simultaneously, the plant produces 0.045 g/day of 18 О at 5 to 6 percent enrichment. The separation factors for these two separations are

12C160/13C160: 1.011

12CI60/12C180: 1.008

A carbon monoxide distillation plant at Los Alamos Scientific Laboratory produces 4 kg 13C/year [A2] at 90 percent enrichment.

2.6 15 N

Natural nitrogen contains 0.365 percent 15 N. Methods that have been used for separating 15 N on a small scale are listed in Table 12.6.

The exchange reaction between NH3 gas and NH4NO3 in aqueous solution was used by Thode and Urey in 1939 to obtain the first samples of enriched 1SN, and was employed by the Eastman Kodak Company to produce 15N at a rate of around 1 g/day. The only production of ls N in the United States at present is by distillation of NO at Los Alamos [М2].

A lower bound for the equilibrium time of an ideal cascade may be found by determining the length of time it would take the plant to produce its own steady-state composition gradient if at all times during the start-up period it was possible to prevent loss of separative work through mixing of streams of different composition. Conceptually, this might be done if the plant consisted of a large number of small separating units whose connection in parallel and in series could be changed continuously during the start-up period. We assume that no product is withdrawn until the steady-state composition gradient has been established. Then product withdrawal may be started at the steady-state rate.

During the start-up period prior to product withdrawal it is necessary to bring in enough feed of composition zF and withdraw enough tails of composition Хці to provide the increase in inventory of desired component from its initial value of IzF to its steady-state value of lx. By material balance, the required amount of feed EF is

Z7 _ f(x ~ zf)

bp—————-

Zp-Xy,

During the start-up period, the change in the plant’s inventory of separative work is /(0 — фр), where

all

/0= ) 7(0 0i

If the duration of the start-up period is t, the amount of separative work S done by a plant whose separative capacity is D is

Dr = Ef(4>w — фр) + І(ф — фр) (12.208)

This may be solved for the equilibrium time r, with EF given by (12.205):

This expression gives a lower bound for the equilibrium time, which can be attained only if mixing of streams of different composition can be prevented during the entire start-up period. It provides a lower bound for the equilibrium time in somewhat the same way that consideration of a thermodynamically reversible process provides a lower bound for the amount of work needed to carry out a given change of state.