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.

Figure 12.12 illustrates flow through a simple cascade, fed at rate F with material containing zp fraction of desired component, to produce product at rate P containing yp fraction of desired component. Feed for one stage consists of heads from the next lower stage, so that

In a cascade in which 04 and & are independent of stage number, (12.43) and (12.44) reduce to

n

and (12.47) to

co = /3"

The relation between recovery, overall enrichment, and number of stages then is

/a — uvnn Г = — )

Figure 12.14 illustrates the variation of r with co for a simple cascade of electrolytic cells with a = 7 and n = 1, 2, or 3. The recovery is greater the greater the number of stages. In the limit, as the number of stages increases indefinitely, the recovery from Eq. (12.50) approaches

lim r =

n-> «О

The line for л-к» is also shown in Fig. 12.14. This is the highest recovery that can be obtained in a simple cascade, with a = 7.

Such a simple cascade, with an infinite number of stages each performing an infinitesimal amount of separation, is equivalent to type A differential stage separation. Equation (12.51) is equivalent to the form of the Rayleigh equation (12.35), when one recognizes that ш in the simple cascade is equivalent to the heads separation factor 0 in differential stage enrichment, and a in the simple cascade is equivalent to the local separation factor a.

We wish to find a value function V, a generalization of the separation potential ф for a two-component mixture, now a function of xs and x6, which can be used to evaluate the separative capacity, and from it, the total flow rate. The difference equation (12.313) for V is obtained by writing a V balance for the stage, in which the difference between the separation potential carried by the stage effluents and the stage feed is equated to the separative capacity of the stage, given by Eq. (12.174) а&Мф2І4:

MV(ys, y6) + MV(xs, x6) — 2AfV(zs, z6) = (12.313)

For a close-separation cascade with a cut of |,

(12.314)

When Eq. (12.313) is expanded in a Taylor series about xs and x6, the following differential equation is obtained:

^ -*s)2 0 + 20,5 “*5)(Уб ~*б) гВк + 0,6 ~X6? U = ф2 (12-315)

Terms in V, dV/bXs, and bV/bx6 have dropped out because of material-balance relations. Substitution of ys — xs from (12.311) and y6 —x6 from (12.312) into (12.315) leads to

We wish to find a solution of Eq. (12.316) that can be used to evaluate total flow rates, as was done for two components in Sec. 11. To do this, it is necessary to arrange that there be no loss of V when two streams are mixed. In a two-component system this was done by requiring the two streams to have the same composition. In a three-component system this is not generally possible. The mole fractions of only one component in the two streams may be made equal, or one function of the mole fractions in the two streams may be made equal. For the present derivation, we shall require that the abundance ratio R of the two principal components, 235 U and 238 U, be equal whenever two streams are mixed.

== *5

1 — XS — x6

de la Garza et al. [Dl, D2] have shown that this leads to a cascade with nearly the minimum total internal flow as long as the fraction of other components is small, and have called such a cascade a matched R cascade. We then need to find the most general solution of Eq. (12.316) that has the property that when two streams are mixed, V is conserved.

If the streams being mixed have flow rates M1 and M" and compositions (R, x’6) and (R, х’б), the condition that V be conserved is

{M’ + M") V(R, x6)=M’V(R, x’f) + M"V(R, xl) (12.318)

with the 236 U fraction in the mixed stream x6 given by material balance

M’x6 + M"x’s *6 M’ + M"

To satisfy (12.318) and (12.319), V(R, x6) must be a linear function of x6:

V(R, xt) = a(R) + b(R)x6 (12.320)

The most general solution of (12.316) of the form (12.320) is

V(R, x6) = k0 + ksxs + k6x6 + + (2×5 + 4×6 — 1) In R (12.321)

К

к0, к5, к6, and к are arbitrary constants. The fact that (12.321) satisfies the differential equation (12.316) may be verified by direct substitution.

When interstage flows are adjusted so that the abundance ratios R of 235 U to 238 U of each pair of streams being mixed are equal, the separative capacity D of an entire cascade whose feed, product, and tails are

is

D = PV(RP, y6J>) + WV(Rw, x6<w) — FV(Rf, zttF) (12.322)

This may be shown by a development similar to that of Sec. 11.

When Eqs. (12.321) for feed, product, and tails are substituted into (12.322), the coefficients of к0, k5, and k6 vanish because of material-balance relations. The coefficient of the remaining arbitrary constant к in Eq. (12.321) for the separative capacity may be made to vanish by requiring that

Equation (12.323) and the material-balance equation for 236 U make possible evaluation of the distribution of 236 U between product and tails in terms of the specified fraction of 236 U in feed z6F and the specified abundance ratios RP, Rw, and Rp of “U to 238U in product, tails, and feed, respectively. It should be noted that it is not possible to specify in advance the distribution of the third component, 236 U in this case. The distribution of only two components, called key components, 235 U and 238 U in this case, are the only ones that can be specified in advance.

With the distribution of 236 U between product and tails thus determined, the separative capacity of the entire cascade, from Eqs. (12.321) and (12.322), becomes

D = P{2y%j> + 4y6J> — 1) In RP + W(2×5>w + 4x6jW — 1) In Rw — F(2zStp + 4z6fF — 1) In Rp

Thus, it has been shown that the separation potential, or value function, for an ideal cascade treating a mixture of 235 U, 236 U, and 238 U in which the ratios of 235 U to 238 U in each pair of streams being mixed are made equal, is

To give an example of one of the most successful applications of chemical exchange to separation of isotopes of an element heavier than hydrogen that may have industrial application, a brief description will be given of the process and equipment used by Taylor and Spindel [T2] to product 15 N 99.8 percent pure. This separation depends on the exchange reaction

15NO + H14N03 *= 14N0 + H15N03

which takes place in the gas phase because of the presence there of the species NO, N02, N203, N204, H20, HN02i and HN03. These interact at acceptably high rates at temperatures of 25°C or higher. The separation factor for this process, defined as the ratio of ISN/14N in the liquid phase to 1SN/14N in the gas phase, was found by Taylor and Spindel to be 1.055 at 25°C in 10 M HN03, and to decrease with increasing acid concentration and increasing temperature. Because the value of the equilibrium constant for the foregoing reaction calculated from spectroscopic data is 1.096, it appears that isotopic exchange reactions between species other than HN03 and NO enter into the observed overall exchange equilibrium. This reaction, however, may be used to characterize the process.

Taylor and Spindel found that the optimum conditions for operating this process on the laboratory scale were 8 to 10M HN03, 25 to 50°C, and atmospheric pressure. Although a higher temperature speeds up attainment of exchange equilibrium, a is lower, and more N02 is present with a lower exchange equilibrium constant.

The process used by Taylor and Spindel is illustrated in Fig. 13.41. liquid aqueous HN03 flows downward through a packed column countercurrent to an upflowing gas stream consisting largely of NO with lesser amounts of other nitrogen compounds. Nitric acid containing the
normal abundance of 1SN, 0.365 a/о, is fed at the top of the larger column, no. 1, and is enriched in 1SN by the foregoing exchange reaction as it flows down this column. At the foot of the column, where its 15N content is around 7 percent, the reflux ratio of NO vapor to product may be substantially reduced. This is done by diverting 4 percent of the acid downflow to the smaller column, no. 2. The remaining 96 percent of the acid downflow is sent to NO reflux generator no. 1, where it is reduced to NO by reaction with S02:

НгО + HN03 + f S02 — f H2S04 + NO

The NO is returned to column no. 1 as reboil vapor.

The HN03 flowing down through the smaller column, no. 2, countercurrent to NO is enriched further in 1SN to 99.8 percent at the foot of the column. At this point some of the downflowing HNO3 is withdrawn as plant product, and the remainder of the HN03 is reduced to NO with S02 in reflux generator no. 2. This NO is used to reboil column no. 2.

NO vapor depleted in 1SN leaving column no. 1 at the top of the plant is converted to HNO3 depleted in 15 N by mixing it with air and passing the mixture counter to downflowing water in a packed column, where the reaction

——- H20

——- S02

-► H2S04

Figure 13.41 Plant used for production of 1SN by Taylor and Spindel.

NO + fOj +|HjO-*-HN03

takes place.

The net result of the process, then, is to separate HN03 containing the natural abundance of, SN into product HN03 highly enriched in 1SN and waste HN03 slightly depleted in 15 N, while converting S02 and air to H2S04. The minimum ratio of H2S04 to 1SN is | times the minimum molal reboil vapor ratio, which is given by Eq. (12.80), or

3Xp-xF g _ 3 0.998 — 0.00365 1.055 2 xF a— 1 2 0.00365 0.055

This high reflux requirement is not a complete economic drain because H2S04 is a more valuable material than S02. In this respect, Taylor and Spindel’s process is in a more favorable economic position than the chemical exchange system of Fig. 13.24 to concentrate deuterium, which consumes aluminum to make less valuable A1203.

In their engineering analysis of the HN03-NO process, Garrett and Schacter [G2] considered a plant to produce 30.2 g-mol lsN/day while simultaneously producing 239,670 g-mol H2S04/day. They recommended use of substantially the same conditions employed by Taylor and Spindel and estimated that 1SN could be produced at a cost of $4/g. This relatively low cost is due to the credit for converting S02 to H2S04.

It is important to note that the use of a cascade of columns of decreasing size, such as in Fig. 13.41, does not affect the consumption of chemicals for reflux, because this depends on the interstage flow required at the feed point. The cascade of columns of decreasing size does, however, reduce the total volume and the holdup of desired isotope. If the cascade of columns were not used for the 15 N separation example, with its low feed concentration and separation factor close to unity, the holdup would be so great that product concentration would not reach

99.8 percent in any practical time.

NOMENCLATURE

a defined by Eq. (13.34)

A annual cost, $/year A tower cross-sectional area b defined by Eq. (13.36) c defined by Eq. (13.35) c unit cost D separative capacity E efficiency F molar feed rate

F’ molar flow rate of supplementary feed to hot tower g ratio of steam rate to minimum rate G vapor molar flow rate h height of transfer unit H moles of hydrogen

H humidity, mol water/mol noncondensible gas I inventory, mol / annual charge against investment к equilibrium constant for gas-phase exchange reaction К total tails flow rate

К equilibrium constant for gas-liquid exchange reaction

L liquid molar flow rate M molecular weight n number of stages p pressure

P mol product (or molar product flow rate)

P kg D2 O/year Q rate of loss of availability r fractional recovery

R gas constant

s entropy per mole

S entropy

5 solubility, mol dissolved gas/mol water t time

T absolute temperature

T0 absolute temperature at which heat is rejected v vapor velocity, cm/s

V tower volume

V vapor molar flow rate

W moles of tails (or molar tails flow rate)

W power

x atom fraction or mole fraction in liquid

у atom fraction or mole fraction in vapor

z distance from top of tower

Z height of tower

a stage separation factor

a* relative volatility, separation factor in distillation /3 heads separation factor 7 relative volatility of H2 S to HDS r relative abundance in vapor

£ relative abundance in liquid

?r vapor pressure

p density

со overall separation factor

Subscripts

a stream produced in heating liquid or cooling gas b bottom of tower c cold tower

F feed stream

h hot tower

і stage number

m stage number

P product stream Q turbine work

S supplementary feed point t top of tower

V tower volume W tails stream

0 gas stream from cold tower to hot tower, Fig. 13.34

(a) Find the number of theoretical plates in the cold stripping section ncS, the cold enriching section n^, and the hot tower nh.

(b) Compare this process with the methylamine process of Fig. 13.40 and the ammonia process of Fig. 13.37 with respect to:

(1) Number of cold-tower plates

(2) Number of hot-tower plates

(3) Flow ratio, hydrogen to D2 0

(4) Flow ratio, liquid to D2 0

CHAPTER

The total interstage flow rate of heads or tails is a measure of the size of the separation plant. In a distillation plant, for example, the total volume of column internals is proportional to the total interplate vapor flow rate. In a gaseous diffusion plant, the total amount of power expended in pumping gas from one stage to the next is proportional to the total heads flow rate.

An expression for the total flow rate of heads or tails in stripping or enriching section may be derived by summing the appropriate Eq. (12.106) or (12.107). For example, the total heads flow rate in the stripping section J$ is

(12.121)

Terms in yp—zp and zp—хщ have canceled out because of the material-balance relations (12.52) and (12.53). Also, because of these material-balance relations, (12.121) may be written

output

input

(12.122)

This result is of great importance for isotope separation plants. It states that the total flow in the plant is the product of two factors, the first a function only of the heads separation factor 0, and the second a function only of the flow rates and composition of feed, product, and tails.

The first factor is a measure of the relative ease or difficulty of the separation; it is large when 0 is close to unity and small when /3 differs markedly from unity. The second factor is a measure of the magnitude of the job of separation; it is proportional to the throughput, and is large when product and tails differ substantially in composition from feed, and small when these compositions are nearly equal. The second factor has been termed the separative capacity, because it is a measure of the rate at which a cascade performs separation. It equals the sum of two output terms, each the product of an output flow rate and a function of the corresponding output condition, minus an input term that is the product of the feed rate and a function of the input condition. The separative capacity is discussed in more detail in Sec. 10.

6.1 Electrolysis of Water

History of process. Until 1943, all the heavy water produced commercially was made by electrolysis. The largest single producer of heavy water was the Norsk Hydro Company, which operated the world’s largest electrolytic hydrogen plant at Rjukan, Norway. In 1942, this plant was making about 1.5 MT of heavy water per year as a by-product of the production of 17,300 nm3 of electrolytic hydrogen per hour, used for ammonia synthesis. The average power consumption of this plant was 91,000 kW, or 5.2 kWh/nm3 of hydrogen.

The primary plant at Rjukan made water containing 15 a/о deuterium. The electrolytic cells were of the Pechkranz [М2] type, with steel cathodes and diaphragms to prevent mixing of hydrogen and oxygen. Nine stages of parallel-connected cells were used, with the number of
і Figure 13.11 Characteristics of Sul — zer CY packing for water distilla­tion service.

cells per stage decreasing as the deuterium content increased. The stages were connected in a series cascade, without recycle of partially enriched hydrogen, and the cascade was operated in steady flow. A schematic flow sheet for this kind of plant is shown in Fig. 13.13. About 73 percent of the water fed to each stage was electrolyzed; and 27 percent was carried from the stage by the products of electrolysis as water vapor, condensed, and fed to the next higher stage of the cascade. The fraction of water fed forward was controlled by the vapor pressure of water; 27 percent forward feed requires an electrolyte temperature of 60°C.

The product of the primary plant was refined to pure D2 О in a small, nine-stage secondary plant, also operated with steady flow, but with the partially enriched hydrogen burned and recycled, as shown in Fig. 13.14. The secondary electrolytic plant has since been replaced by a water distillation plant.

During World War II heavy-water production at Rjukan was increased by addition of steam-hydrogen deuterium exchange equipment, to be described in Sec. 7. In 1943 operation was interrupted by a series of commando raids, but production was resumed after the war and was at the rate of 6.5 Mg/year in 1975 [R3]. A second electrolysis and exchange plant at Glomfjord, Norway, was then producing 5.9 Mg/year.

The steady-flow electrolytic process without recycle, shown in Fig. 13.13, was also used at the plant of Emswerke AG at Ems, Switzerland, to produce 400 nm3/h of hydrogen enriched

Figure 13.12 Dostrovsky’s [D4] water distillation plant for concentration of 180.

sixfold in deuterium over natural abundance [H3] and is being used at the Indian government’s fertilizer plant at Nangal, India, to produce 5,000 nm3/h of hydrogen containing 3.1 times the natural abundance of deuterium [Gl]. In each case the partially enriched hydrogen goes to a hydrogen distillation plant for final concentrations of deuterium, as was described in Sec. 13.4.

At the Manhattan District’s heavy-water plant at Trail, British Columbia, primary concen­tration of deuterium was effected by the combination of electrolysis and steam-hydrogen

exchange, to be described in Sec. 7. The plant made use of hydrogen produced electrolytically by the Consolidated Mining and Smelting Company for ammonia synthesis. This was the largest electrolytic hydrogen plant in North America. In 1945 the average hydrogen production rate was 14,000 nm3/h, almost as great as at Rjukan. The electrolytic cells used at Trail have been described by Mantell [М2]. The cells were operated with steady flow. Because the principal means for isotope separation in the primary plant at Trail was by the exchange process rather than by electrolysis, no special efforts were made to obtain a high separation factor in the primary plant. .

The electrolytic process was also used by the Manhattan District, at Morgantown, West Virginia, and at Trail, British Columbia [M8], to refine crude heavy water from a primary plant where some process other than electrolysis was employed. These electrolytic plants were operated batchwise. The cells had no diaphragm, so the product was a mixture of hydrogen and oxygen. The gases were recombined in a burner, and the water was recycled to the primary plant when its deuterium content was leaner than primary-plant product or to the next batch of the electrolytic plant when its deuterium content was richer than primary-plant product.

Details of the Manhattan District’s secondary electrolytic plants are given by Maloney et al. [М8].

Batch electrolysis was used to concentrate deuterium from 90 to 99.87 percent at the large Savannah River heavy-water plant of the U. S. Atomic Energy Commission, at Aiken, South Carolina [B7, B8], but this final concentration step is not needed when the plant is operated at reduced capacity.

Separation factors. Deuterium separation factors in the electrolytic plants described above, together with the types of cells used and operating conditions that may have had an effect on separation factor, are listed in Table 13.13. Separation factors of from 6 to 10 have been reported for the secondary plants, and from 3.8 to 7.0 for the primary plants. The lower values for the primary plants are attributed to their higher cell temperatures, their use of diaphragms, and the greater difficulty of keeping large equipment clean.

In a detailed laboratory investigation of the effect of cell variables on the deuterium separation factor in electrolysis of water, Brun and co-workers [ВІЗ] have found that a depends on the cathode material, electrolyte composition, and cell temperature, generally as follows. The separation factor is higher for an alkaline electrolyte than for an acid. With KOH, at 15°C, a pure iron cathode gave the highest value reported, 13.2. The separation factor for mild steel, the material used in most commercial electrolyzers, was 12.2. Values as low as 5 were reported for tin, zinc, and platinized steel. At 25°C the separation factor with a steel cathode was 10.6, and at 75°C it had dropped to 7.1.

Because the equilibrium constant for the reaction

H2 O(0 + HDfe) «* HDO(0 + H2 (?)

is 3.81 at 25°C and 2.95 at 75°C, it is evident that the much higher separation factors obtained in electrolysis must be due to some mechanism other than establishment of equilibrium in this reaction at the cathode surface. One plausible explanation is that the hydrogen ion is discharged more readily at the cathode than the deuterium ion.

Stage separation efficiency. Figure 14.7 illustrates the nomenclature to be used in describing flow rates, compositions, and degree of separation in a cross-flow gaseous diffusion stage, with v = y. The stage separates feed containing Xp mole fraction light component into a light fraction containing у mole fraction and a heavy fraction containing x mole fraction.

X <xF <y

The separation factor of the stage a is defined as

*0-y>

A stage separation efficiency E, analogous to the overall Murphree plate efficiency in distillation, may be defined as

where x0 is the composition of gas that, on the high-pressure side of an ideal barrier, would give low-pressure gas of composition у. From (14.23) it follows that

_ _ (a0 ~ l)y(l ~y)

y x° y + Mi-y)

In the close separation case,

, У-x

a — 1 = —r.—- г

*0 — x)

Our problem is to determine the relationship between the stage separation efficiency, given by (14.82), the barrier separation efficiency EB, defined by (14.26), and the local mixing efficiency EM, defined by (14.64). The stage separation efficiency depends on the relative direction of flow of the high-pressure and low-pressure streams and the degree of mixing of these streams.

No mixing, cross flow. In a common type of gaseous diffusion stage, high-pressure gas flows along the inside of a number of barrier tubes in parallel without significant mixing in the direction of flow, and the low-pressure gas that has passed through the barrier is removed in cross-flow paths approximately perpendicular to the barrier tubes. With cross flow on the low-pressure side, the composition of the gas at each point on the low-pressure side of the barrier, /, equals the composition of the net flow through the barrier at the point, v. This

Light

fraction

Figure 14.7 Cross-flow gaseous diffusion stage. Stage separation factor a = y( — x)/x( — y) stage efficiency E = (y — x)/(y — x0); Np, Nt, N, M = molar flow rates; xF, xf, x, y, v = mole fraction light component.

practically important condition obtains in most barrier testing experiments and is a condition for Eqs. (14.47) and (14.55) for barrier separation efficiency. When у = v, there is no mixing efficiency correction on the downstream side of the barrier.

Figure 14.7 shows the nomenclature to be used in deriving an equation relating the stage separation efficiency to the barrier efficiency EB and the local mixing efficiency Em for the above kind of cross-flow diffusion stage. A material balance on light component over the portion of the high-pressure side of the stage in which the flow rate decreases by dN{ may be expressed as

vdNi = NfCf — (Nt — dN,) (xf + dxt)

This leads to the differential equation

(14.85)

In the close-separation case, from (14.65),

from (14.27). In the close-separation case v changes so little from point to point in a diffusion stage that v in (14.87) may be replaced by x, the outlet heavy fraction composition. With this substitution, Eqs. (14.87) and (14.85) become

xF-x = (a0- l)x(l — x)EMEB In ^ The fraction diffused is the stage cut в:

(14.90)

By material balance,

From (14.82), the stage separation efficiency is

Because — [ln(l — 0)] /0 is greater than unity, the stage efficiency in cross flow exceeds the local efficiency Em^b — a similar result is found in distillation, where the plate efficiency is greater than the point efficiency when there is cross flow of liquid without mixing across the plate.

In an ideal cascade in which 0 = |,

E= 13&6EMEB (14.94)

Stage performance equations for a mixture in which a0 differs substantially from unity have been derived by Weller and Steiner [Wl].

Stage design variables. The principal independent variables involved in designing a gaseous diffusion stage to serve in an ideal cascade are as follows:

1. The product rate P and product composition yp of the cascade of which the stage is a member

2. The fraction of light component у in the stage of interest

3. The quality of the barrier selected, as measured by its characteristic pressure pc and its permeability у

4. The diameter d and length L of barrier tubes

5. The high-side pressure p" and low-side pressure p’

6. The barrier absolute temperature T

The principal stage characteristics that depend on the choice of the above independent variables are as follows: [47] [48] [49] [50] [51] [52] [53] [54] [55]

a — 1 = 1.386(ao — 1 )EMEB (14.95)

from (14.83) and (14.94).

For a barrier whose separation performance on UF6 is given by the Bosanquet equation (14.58),

1 _ ‘ j "

о -1 = 1.386(«o — l)EM J — . (14.96)

1 + ІР ~P )IPc

where Oo — 1 = 0.00429 (14.97)

and Em is given by (14.65) and (14.66).

Heads flow rate. The flow rate M of stage heads of composition у in the enriching section of a close-separation ideal cascade producing product at rate P and composition yP is

_2P(yP-y)_ M (a — l)y(l —y)

as can be seen by a development similar to Eq. (12.125).

Stage separative capacity. The separative capacity Д of a stage in a close-separation cascade with a cut of is

from Eq. (12.174).

Compressor volumetric capacity. The volumetric capacity V of the compressor for the heads stream at pressure p and absolute temperature T flowing at molar rate M is

v_ MRT
P

The ratio of compressor capacity to separative capacity is

V = ART = ART [1 +(p"-P’)/Pc]2

Д (a-l)V (1.386)2(a0 — 1)2£m j p’(l-p’lp")2

This ratio is independent of isotopic composition. Because EM is only slightly dependent on p’ and p", the pressures p’ and p" that would result in minimum compressor capacity for a given separative capacity are close to those that minimize the term in braces in (14.101). These are found to be

p" = 2pc and p’ = pc (14.102)

at which the term in braces in (14.101) has the value 16lpc, so that the minimum compressor capacity is

Fmin _ 33.3RT

A (a0 — l)2Elfpc

Barrier area. The barrier area A required for a heads stream flowing at molar rate M between pressures of p" and p is

M j2mnRf M A G 7ІР”-РГ)

from (14.14). Hence the ratio of barrier area to separative capacity is

A ^ M _ 4V2nmRT___________ Ay/2mnRT [1 + 0" ~p’)/pc]2 / ri4 1ПЧ7

Д СД (a-l)W’-p-) (1.386)2(a0-l)2^7 )(p"-p’Xl-p7p")2i 1*

The pressures p and p" that would result in minimum barrier area for a given separative capacity are close to those that minimize the term in braces in (14.105). These are

p" = pc and p = 0 (14.106)

at which the term in braces in (14.105) has the value 4lpc, so that the minimum barrier area is

Amin 8.33 j2mnRT Д (<*o — 1)2£mPc7

This indicates the desirability of having a high value of the characteristic pressure pc (hence small pores) and a high value of у (hence many pores per unit area).

Power. Flow of gas through the barrier at rate M is accompanied by loss of availability at rate

Q = MRT0 In

where T0 is the temperature of heat rejection to the environment. This represents the minimum net power needed to recompress the gas from p to p" when the heat of compression at temperatures above T0 is converted to work in a reversible heat engine. Hence the ratio of this net power to separative capacity is

Q 4RT0]n(p"lp’) _ 4RT0 j[l +(p"-p’)/pc]2 (p_

Д (a-D2 (1.386)2(a0-l)2f& ( (l-p’/p")2 U

Minimum power results when both p and p" approach zero, with their ratio q = p’/p" selected to make [ln(l/p)]/(l — qf a minimum. This occurs at q = 0.285, at which the term in braces in (14.109) has the value 2.455. EM at zero pressure equals 1.0. Hence the minimum power per unit separative capacity is

5A1RT0 («о — l)2

This important result is independent of the type of barrier and isotopes being separated. For ^UFe and 23®UF6. with T0 = 300 K,

___________ (5,11) [8314 J/(kg-mol-K)] (300 K)_________

mi„ “ (0.00429)2(3.6 X 106 J/kWhX8760 h/yrX238 kg U/kg-mol)

= 0.0923 kW/(kg SWU/yr)

The pressure conditions that minimize compressor capacity, barrier area, and power consumption are listed in part 1 of Table 14.8. Part 2 of Table 14.8 gives for a diffusion plant with a separative capacity of 1 kg uranium/year, using anodized aluminum barrier tubes 0.014 m in diameter and 4 m long, the compressor capacity, barrier area, and power for the conditions that minimize these three plant requirements. Since these conditions are different, no one design can minimize simultaneously compressor capacity, barrier area and power.

The appropriate criterion to optimize the design of a gaseous diffusion stage is that the

Minimum Minimum

compressor barrier Minimum

capacity area power

^Diameter, 0.014 m; length, 4 m; permeability y, 15.6 X 10’5; pc, 1.974 atm; T, 358 K.

unit cost of separative work produced by the stage be a minimum. To illustrate how Eqs. (14.101), (14.105), and (14.109) may be used to select optimum values of the stage pressures p’ and p" that minimize the unit cost of separative work, specific assumptions will be made about the unit cost of the principal stage characteristics on which the cost of separative work depends. The unit costs assumed for this purpose are listed below:

Direct capital costs

Compressors and piping Converters and barrier Electrical equipment and cooling system Indirect capital costs Capital charge rate Electric power

Ratio of actual power to power for isothermal compression at T0

Other costs that make small additional contributions to the cost of separative work, which are to be disregarded in this example, include costs of operation, maintenance, and supervision; fixed stage costs for such components as instruments; and the cost of enriched UF6 inventory. With the above assumptions, the unit cost of separative work eg is

Table 14.9 gives the characteristics of a diffusion stage using these optimum conditions of p" = 0.55 atm and p’lp" = 0.32 for anodized aluminum barrier tubes 0.014 m in diameter and 4 m in length, with pc — 1.974 atm and 7 = 15.6 X 10"s.

The unit cost of $110/kg SWU is not far from the value of $100 anticipated for 1980 delivery. The power consumption of (2X0.16776) = 0.336 kW/(kg SWU/уеаг) may be com­pared with the power of 6,060,000 kWe consumed by U. S. ERDA’s diffusion plants when operating at their full capacity of 17,230,000 kg SWU/year [U1 ]: 6,060,000/17,230,000 = 0.352 kW/(kg SWU/year).

After the cascade improvement and cascade operating programs planned by U. S. DOE have been completed, their power consumption will be increased to 7,380,000 kW and their separative capacity to 27,700,000 kg SWU/year, equivalent to a specific power consumption of 0.266 kW/(kg SWU/year).

6 Li may be used in fusion power systems, as noted above, and is the starting material for producing tritium by neutron absorption:

|Li+ &n->-?T + $He

In some types of thermonuclear power systems it is desirable to use a blanket of lithium enriched in 6 Li to increase the volumetric rate of neutron capture to produce tritium.

7 Li hydroxide is now used in some water-cooled reactors to inhibit corrosion by control of hydrogen ion concentration. Because the thermal-neutron absorption cross sections of the lithium isotopes are 6 Li, 940 b, and 7Li, 0.037 b, it is necessary to use 7 Li containing less than

0. 01 percent 6 Li. 7Li metal, which melts at 180°C, was proposed as coolant for an aircraft — propulsion reactor, because of its low vapor pressure at high temperature and low neutron — absorption cross section.

1.2 10B

The thermal-neutron absorption cross section of natural boron, which contains 19.61 percent 10B, is 759 b, whereas that of separated I0B is 3837 b. Thus, enriched 10B is useful in applications where the highest volumetric rate of neutron absorption is wanted. Examples are compact shielding for thermal neutrons and control rods for fast reactors.

Neutron-capture therapy is an experimental technique for selective destruction of cancerous tissue surrounded by healthy tissue. In this technique a compound of 10 В that is selectively absorbed by the cancer is injected into the bloodstream, followed by irradiation of the cancerous tissue by a beam of neutrons. Energetic alpha particles, produced by the reaction

*?B + Jn^-fHe + ^y

where the neutron beam reacts with the boron compound in the cancer, destroy the cancer while leaving the neighboring healthy tissue, containing less boron, less affected.

1.3 13C

Carbon, hydrogen, oxygen, and nitrogen are the elements that occur in greatest abundance in living systems. Tracer experiments using either radioactive isotopes or separated natural isotopes are of great importance in understanding biochemical reactions. Although with carbon there is the possibility of using the short-lived radioisotope "C or the very long-lived 14 C, for many experiments it is preferable to avoid radioactivity and use separated stable 13 C. Another important use of 13 C is in nuclear magnetic resonance experiments on the structure of carbon compounds. By synthesizing a compound with a 13 C atom in a known location, it is possible to draw conclusions about the configuration of the molecule, because 13 C has a nuclear magnetic moment and 12 C has none.

1.4 15 N

1SN can be used in very much the same way as 13C, as a tracer for nitrogen compounds and in nuclear magnetic resonance experiments. The fact that the longest-lived nitrogen radioisotope, 13 N, has a half-life of only 10 min gives 15 N added significance.

An additional possible use suggested for 15 N is in U15N fuel material for a fast reactor. 15 N has a lower absorption and inelastic scattering cross sections for fast neutrons than the more abundant 14 N. Its use avoids 14 C production from the reaction 14 N + ln -* 14 C + 1H.

1.5 Oxygen Isotopes

Because the longest-lived oxygen radioisotope, 15 0, has a half-life of only 124 s, the separated isotopes 17 0 and 18 О are valuable in tracer experiments. The nuclear magnetic moment of 17 0 gives it application in determining molecular structure by nuclear magnetic resonance measurements.

The total inventory IE and the inventory of desired component IExE may be evaluated if the inventory per stage is known. The stage inventory Ht may be related to the stage feed rate M(+Nt by

Ht = h(Mt + TV,) (12.198)

where h is the stage holdup time, the time it takes material to flow through one stage. We shall assume that h is constant throughout the cascade. This will be strictly true of an ideal cascade made up of identical separating units and is often approximately true of an ideal cascade made up of stages of decreasing size.

The total inventory of the enriching section IE then is just h times the total flow rate in the enriching section; for a close-separation, ideal cascade,

as may be seen from Eq. (12.137) and the fact that heads and tails flow rates are approximately equal in a close-separation, ideal cascade.

The inventory of desired component in the enriching section is

di,

di — —— dx =
dx

from (12.134). this inventory is given by

With Eqs. (12.199) and (12.203), approximate equation (12.197) for the start-up time of a close-separation, ideal cascade becomes