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The Separation Nozzle Process
Evolution of process. The separation nozzle process has evolved through a number of forms. The first process tested experimentally by Becker [B6] is illustrated schematically in Fig. 14.20, with dimensions for one of the devices tested on UF6. UF6 feed at a pressure p of around 20 Torr flows through a slit-shaped nozzle 0.045 mm wide into a region at much lower pressure p’, where a fraction в, about 0.2, of the feed diverges from the feed jet and is somewhat enriched in the light isotope. The remaining fraction of the feed jet, 1—6, somewhat enriched in the heavy isotope, passes through a wider separator slit, where its pressure p" is somewhat higher than p’ because of deceleration. London [L4] gives examples of the separation factor, cut, and UF6 feed rate observed by Becker [B6]. Optimum pressure conditions at which power consumption, compressor capacity, and nozzle length per unit separative capacity were smallest are listed in the first column of Table 14.18, together with the minimum values of these performance indices.
Comparison with corresponding performance indices for gaseous diffusion, taken from
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Light fraction Figure 14.20 First form of separation nozzle process. |
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Table 14.18 Comparison of operating conditions and performance indices of two forms of nozzle process and gaseous diffuaon process
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Table 14.9, shows that in this early version of the separation nozzle process, the separation factor was slightly better than for gaseous diffusion, but the power consumption, Q/Д, the rate of loss of availability, was four times as great as in gaseous diffusion, and the compressor capacity, V/A, was ISO times as great. The high power consumption was a consequence of the high pressure ratio through which both light and heavy fractions were expanded in this early version of the nozzle process, and the very high compressor capacity was caused both by the high pressure ratio and the low operating pressure level.
Two modifications of the process developed by Becker and his associates have greatly improved these process characteristics. (1) Dilution of UF6 feed with a gas of lower molecular weight, helium in early developments [B7] and hydrogen in later developments [Gl], has had two beneficial effects. Sonic velocity in the nozzle is increased, with accompanying increase in separation factor, and diffusion rates are increased, permitting operation at higher pressure and higher uranium throughout without impairment of separation. (2) The radical change in nozzle geometry illustrated in Fig. 14.21 adds the relatively large separation caused by centrifugal acceleration to the smaller separation accompanying expansion through the slit.
Improved nozzle process. In Fig. 14.21, a dilute mixture of / mole fraction UF6 in hydrogen at upstream pressure p is expanded through a convergent-divergent slit with a throat spacing s into a curved groove of radius a. After being deflected through 180° by the wall of the curved groove, the gas stream at lower pressure p traveling at high speed is separated by a flow divider set at radius c into an outer heavy fraction depleted in 23SUF6 and hydrogen and an inner light fraction enriched in these components. The cut в is determined by the position of the flow divider. The separation factor a (1) is higher the higher the speed attained by the gas, which is higher the higher the pressure ratio р/р’ and the lower the UF6 content of the feed gas; (2) has a maximum value at an optimum pressure level, which is inversely proportional to the dimensions s and a; and (3) is higher the lower the cut в.
Figure 14.22 shows the dependence of separation factor on cut. The lower lines show the separation factor calculated by assuming that the 23SUF6 and 238UF6 density distribution in the curved groove reaches centrifugal equilibrium at the indicated peripheral speed v, using the theory to be derived later in this section. The top line shows the highest values of the separation factor reported in Becker’s papers [BIO], at a pressure ratio of 8 and a low UF6 content, 1.6 m/o (mole percent) in hydrogen, at which the calculated outlet gas velocity for reversible expansion is 1042 m/s. Because these extreme conditions result in gas-compression energy consumption per unit of separative work produced much greater than optimum, they are not recommended for a commercial plant. They do indicate, however, that values of a — 1 in the current version of the nozzle process can be 10 times as high as in the early, linear nozzle process of Fig. 14.20 or in the gaseous diffusion process of Table 14.9. ■
Design studies for a commercial plant by Geppert and associates [Gl] indicate that optimum conditions are feed composition f = 0.042 mole fraction UF6 in hydrogen, pressure ratio р/р = 2.1, and a cut в = at which a — 1 = 0.0148, still four times that in gaseous diffusion, and somewhat higher than what would be predicted for centrifugal equilibrium at the speed attainable from expansion through this pressure ratio. The cut of j necessitates use of a three-up, one-down cascade, as shown in Sec. 14.2 of Chap. 12.
Attainment of separation factors higher than predicted for equilibrium in a centrifugal field have been explained by Becker and associates [B10] as follows. Before the mixture of hydrogen, 235UF6, and 238UF6 enters the curved groove, the concentration of each is spatially uniform. While undergoing linear and centrifugal acceleration, the heaviest component, 238UF6, experiences the highest forces and migrates more rapidly toward the outer wall than the lighter component, 235UF6. Thus, there is a transient time during flow along the curved wall when the 238UF6/23sUF6 concentration ratio is a maximum, after which the ratio decreases toward the limiting, equilibrium value. This transient phenomenon is enhanced by high dilution by hydrogen, which reduces the frequency of collisions between 235UF6 and 238UF6 molecules, which otherwise would speed attainment of centrifugal equilibrium between these species. Maximum benefit from this transient phenomenon for a given pressure ratio is obtained at an optimum pressure level for a given set of nozzle dimensions. At a pressure level lower than
optimum, diffusion rates, which are inversely proportional to pressure, cause attainment of centrifugal equilibrium before the gas mixture reaches the flow divider. At a pressure level higher than optimum, diffusion rates are too slow to permit the initially spatially uniform 238UF6/235UF6 ratio to reach its maximum transient value.
The left half of Fig. 14.23 shows the dependence of separation factor, expressed as a — 1, on pressure ratio р/р’ and upstream pressure p, for a cut в = 3 and / = 0.04 mole fraction UF6 in hydrogen, as reported by Becker et al. [В10]. At each pressure ratio р/р’ there is an
Seporotion factor separative capacity, Q/й
optimum inlet pressure p at which the separation factor is a maximum. At high pressure ratios, the separation factor is higher than predicted by Fig. 14.22 for centrifugal equilibrium at a cut of 3, for any speed. At each pressure ratio, i. e., at each speed, there is an inlet pressure at which the separation factor is a maximum; this inlet pressure is higher the higher the pressure ratio and the higher the speed.
The right half of Fig. 14.23 shows the dependence of power consumption per unit separative capacity Q/A on the same pressure variables. The power consumption has been calculated as the rate of loss of availability, so that Q/A is given by
Q 2RT0]np/p’
Д ~ (a — l)20(1 — в)
Optimum pressure conditions for minimum Q/A are inlet pressure p = 22 Torr, and pressure ratio р/р = 2.1, at which a — 1 = 0.0148 and the power consumption is 0.31 kW/(kg SWU/year).
The nozzle dimensions a and s with which the pressure level of Fig. 14.23 was associated were not stated in reference [В10]. Dimensions and related operating pressures reported [VI] as optimum for UF6-helium mixtures are
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Throat spacing s, mm |
0.4 |
0.2 |
0.03 |
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Groove radius a, mm |
0.1 |
||
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Downstream pressure p’, Torr |
12 |
20 |
ISO |
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Upstream pressure p, Torr |
48 |
80 |
600 |
Because the diffusion coefficient of UF6 into hydrogen is about 20 percent higher than into helium, optimum pressures for UF6-hydrogen mixtures would be about 20 percent higher than the foregoing values. The inference then is that the data of Fig. 14.23 were obtained with a nozzle with a throat spacing around 0.4 mm.
Operation at the highest feasible pressure is economically desirable because the volumetric flow rate is lower and compressors and piping are smaller. Later design studies for a commercial plant by Geppert et al. [Gl] selected optimum outlet and inlet pressures of 138 and 290 Torr, respectively. These are for 4.2 m/o UF6 in hydrogen feed, presumably with nozzle dimensions of
Throat spacing s = 0.03 mm Groove radius a = 0.1 mm
the smallest dimensions reported [VI]. This lower pressure ratio of 2.1 was chosen to reduce the specific power consumption and to permit operation with a single stage of compression without intercooling.
The second column of Table 14.18 summarizes characteristics of the improved nozzle plant whose design was described by Geppert et al. [Gl], The slit length, power, and compressor capacity per unit separative capacity are greatly improved over the early process because of the much higher separation factor and operating pressures. However, the last two are still not as small as those for the gaseous diffusion process, restated from Table 14.9 in the third column. The higher compressor capacity and power consumption of the nozzle process compared with gaseous diffusion results from the 24-fold dilution of UF6 with hydrogen and the need to recompress both light and heavy fractions through the full pressure ratio in the nozzle process. However, the much higher separation factor of the nozzle process causes the number of stages it requires to be only 40 percent of those needed by gaseous diffusion for the same separation,
despite the smaller cut used in the nozzle process. When all sources of process inefficiency, such as pressure drops and compressor inefficiency, are taken into account, Geppert [Gl] has estimated that the actual power consumption of a complete nozzle plant with capacity of
5,045,0 kg SWU/уеаг would be 2520 MW, for a specific power consumption of 0.50 kW/(kg SWU/уеаг). This may be compared with the capacity of the gaseous diffusion plants of the U. S. DOE, 17,230,000 kg SWU/уеаг and their power consumption of 6,060 MW, for a specific power consumption of 0.352 kW/(kg SWU/уеаг). These actual power consumptions are in approximately the same ratio as the values of Q/A in Table 14.18.
Equipment of nozzle plants. Becker [Bll] has described two types of separating elements with the cross-section contour shown in Fig. 14.21. The more fully developed type, produced by mechanical means by Messerschmidt-Bolkow-Blohm Gmbh, Munich, is illustrated in Fig. 14.24. This consists of a cylindrical aluminum tube 2 m long, whose outer surface carries 10 semicircular longitudinal grooves, through each of which a portion of the feed gas flows circumferentially. The convergent-divergent nozzle contour and flow divider are provided by properly shaped strips fitted into 10 dovetail-shaped notches cut into the aluminium tube. The aluminum tube is divided into 10 radial sectors which carry, alternately, inflowing feed gas and outflowing heavy fraction. The light fraction flows into the space outside the tube through a slot between the dovetail strips, which are held in position by small spherical spacers at regular intervals. A complete separation stage contains 80 or more of these separating tubes mounted vertically, with appropriate headers for admitting feed and withdrawing light and heavy fractions. Their predicted separating capacity when operated on 4.2 percent UF6 in hydrogen and pressures of 290 and 138 Torr is 0.48 kg SWU per year per meter slit length [Gl]. A separating element of this type has been run on UF6 for over 30,000 h without change in measured separation factor [В11]. The cost of mass-produced separating tubes of this type predicted in 1971 [B9] was less than $16/(kg SWU/year).
A second type of separating element, developed by Siemens AG, is fabricated by photoetching of metal foils by techniques used in miniaturizing electronic circuits. The left side of Fig. 14.25 is an enlarged contact print of such an etched foil. The middle of Fig. 14.25 shows how these foils are stacked into chips held by cover plates pierced with holes in register with the feed and heavy fraction passages. The right side of Fig. 14.25 shows assembly of chips into a tube.
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Light fraction Figure 14.24 Tubular separation element for nozzle process. (Courtesy of Dr. E. W. Becker.) |
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Figure 14.25 Separation nozzle element made by stacking photoetched metal foils. (Courtesy of Dr. E. W. Becker. Reproduced with permission of the copyright holder, American Institute of Chemical Engineers.) |
Figure 14.26 is a partially cutaway side view of a small prototype separation nozzle stage that has been run [Gl] on total recycle with UF6 and hydrogen. The stage contains 54 of the 10-sector elements 1 m long. The separating elements are mounted vertically inside a metal tank from which is suspended a two-stage gas cooler and a two-stage radial centrifugal compressor. The two-stage arrangement was necessitated by design for a compression ratio of 4. Stages for a larger production plant, based on later designs, will use a compression ratio of 2.1, and a single-stage cooler and axial-flow compressor.
Theory of separation. Theoretical analysis of the current form of the separation nozzle process is very difficult because of the presence of three components of widely different molecular weight, the complex flow geometry, and the importance of transient diffusion effects during the brief exposure of the mixture to centrifugal acceleration. A simplified, approximate analysis of the effect of cut and gas velocity on separation factor, separative capacity, and power consumption will be given by assuming (1) that 23SUF6 and 238UF6 attain their equilibrium concentration distribution at the end of the 180° rotation the expanded gas undergoes, and (2) that gas motion is in “wheel flow” at uniform angular velocity со. Finally, the effect of factors neglected in this simplified treatment will be discussed qualitatively. Mailing and Von Halle [М2] made similar assumptions in their simplified analysis of the nozzle process.
The flow geometry assumed is illustrated in Fig. 14.21. The gas mixture is assumed to be rotating at uniform angular velocity со in a semicircular groove of radius a. Centrifugal equilibrium is established where the mixture is separated by the flow divider at radius c into an inner, light fraction enriched in hydrogen and 23SUF6 and an outer, heavy fraction depleted in these components relative to 238UF6.
From the treatment of the gas centrifuge in Sec. 5.5, the dependence of concentration of
light isotope (e. g., 23SUF6) on radius r at centrifugal equilibrium is
where Pi(0) is the density of component (1) of molecular weight m, at the center of rotation (r = 0). A similar equation for the density of component 2 (e. g., J38UF6) is
(14.265)
Ґ is the absolute temperature of the mixture after acceleration to angular velocity u>. If the flow divider is set at r = c, the mass flow rate of component 1 in the light fraction per unit length is
Ґ fc /m1wJr! RT’pM
= u>rpi(r) dr = / ojrpі (0) exp I dr =————-
Jo Jo 2RT J m, w
(14.266)
Similarly, the mass flow rate per unit length of component 2 in the light fraction is fc RT’pi(0) Г /т2ш2<^ "І
=l wrp’(r)dr = _^T (14-267)
The mass flow rate of component 1 in the heavy fraction flowing between radius c and the outer wall at radius a is
and that of component 2 in the heavy fraction is
Let
(14.270)
as in Sec. 5.5. In the low-enrichment case, when зЯі < 3R2 and 3t, < , the cut в is
_ _JKj______ exp (A2c2/a2) — 1
зи2 + aij exp A2 — 1
Hence, the fraction of the total flow area used for the light fraction to provide a cut of в is
2 = 1 + ~ In [в + (1 — в) exp (-Л5)]
The fraction of the flow area used for the light fraction has a lower limit of в when the speed is low (A -*■ 0) and approaches unity as the speed increases (A -* °°), as in the countercurrent centrifuge, because all flow is compressed against the outer wall.
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<*o = |
The separation factor a is
This notation is used to facilitate comparison with gaseous diffusion, for which the ideal separation factor is
(14.275)
With cJ/e2 from (14.272),
1—6 ([6 + (1 — 0) exp (—A2)1>a’ — exp (—A3/aJ) в / l-[6 + (l-0) exp(-A2)],/a5
At low speed (A -*■ 0), a approaches unity. At high speed,
1-е Є*/“«
When a0 — 1 < 1, as in uranium isotope separation,
The corresponding expression for a cross-flow gaseous diffusion stage, from Eqs. (14.92) and (14.93), is
, («о “ ln(l — Є)
<“ — Ода =———————- fl—————
Hence, in the nozzle process at high speed, the separation factor at cut Є is 2ШмЕв times as great as in gaseous diffusion at cut 1 — Є.
In Fig. 14.22 the curves of separation factor versus cut for centrifugal equilibrium were calculated from Eq. (14.276) for 235UF6 (m, = 349) and 238UF6 (m2 = 352). oj = 1.008596.
The temperature Ґ and peripheral speed coa = v occurring in the definition of A2, Eq. (14.270), are for the mixture of UF6 and hydrogen after expansion to speed v. The nozzle process ordinarily is operated at a known constant temperature T before expansion. T, Ґ, and v are related by the enthalpy balance
CP(T (14.280)
where Cp is the molar specific heat at constant pressure and m is the molecular weight. At T = 313 K, assumed [Gl] as the temperature at which the mixture of UF6 and H2 enters the nozzle separator,
Cp{H2) = 6.874 cal/(g-mol-K) [P2]
CP(UF6) = 31.3 cal/(g-mol-K) [D6]
and Cp(mixture) = 6.874(1 — f) + 31.3/ cal/(g-mol • K) (14.281)
where / is the mole fraction of UF6. In dealing with gas expansion processes, it is conventional to use the heat capacity ratio
Cv 1 — R/Cp
The molecular weight m of a mixture of UF6 and hydrogen is m = 2.016(1 — Л + 352.02/
On the assumption that и = сое, from Eqs. (14.270), (14.280), and (14.282),
Values of и calculated from Eq. (14.284) for the values of A2 shown in Fig. 14.22 are tabulated at the bottom of Fig. 14.27 for several mole fractions of UF6,/. The equilibrium separation factor increases rapidly between 100 and 250 m/s and approaches a limiting value
A 9(1-9X<*-1)2 Z 2
from Eqs. (12.169) and (12.172). Figure 14.27 shows the dependence of this separative capacity on cut for the peripheral speeds used in Fig. 14.22. The important point to note is that the cut at which separative capacity is highest for a given speed shifts from в = 5 at low speed to в = I at the highest speeds. Because both the light and heavy fractions have to be recompressed in this version of the nozzle process, the cut at which the separative capacity is highest is the cut at which power consumption is lowest for a given speed.
Power requirement. In the separation nozzle elements shown in Figs. 14.24 and 14.25, the kinetic energy of the expanded gas is dissipated after separation. Then the minimum net power to recompress the gases leaving the separator at pressure p to the feed pressure p is
ZRTp In (р/р1) 238/
The minimum power consumption per unit separative capacity is obtained from (14.290) and (14.285):
The dependence of a on A2 and 0 is given by (14.276).
For every feed composition / and cut 0, there will be an optimum value of ^42, because the numerator of (14.291) increases continuously with A2, whereas the denominator approaches a limit. As a practical matter, values of A2 are limited to those corresponding to the speed of sound because expansion through the curved nozzle becomes very irreversible at higher speeds. Because the sonic speed is
(14.292)
(14.293)
(14.294)
The lower curve of Fig. 14.28 is a plot of (Q/A)s versus mole fraction UF6 in feed,/, for 0 =
5. The minimum value of (Q/A)s is 0.072 kW/(kg SWU/уеаг) at a feed composition of 0.18 mole fraction UF6. This is to be contrasted with the optimum value of 0.31 kW/(kg SWU/year) reported by Geppert et al. [Gl] for experiments with a feed composition of 0.04 mole fraction UF6, and a design value of 0.287 kW/(kg SWU/year) for a commercial plant with a feed composition of 0.042 mole fraction (Table 14.18).
Part of the lack of agreement can be explained by the fact that flow in the curved groove in which separation takes place is quite different from the wheel flow assumed in the foregoing derivation. Instead of v at the wall (r = a) being a maximum as assumed, v actually drops to zero there because of wall friction. Also, flow through the curved nozzle cannot be perfectly reversible, so that the speed of the mixture after expansion will be lower than calculated for reversible expansion through a given pressure ratio. Justification for the choice of a feed
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Figure 14.28 Power per unit separative capacity for nozzle process with UF$-hydrogen mixtures expanded through critical pressure ratio. Cut = 5. |
composition of 0.042 fraction UF6 and agreement with Geppert’s reported Q/A of 0.31 kW/(kg SWU/уеаг) can be obtained by assuming that the effective peripheral speed и of the gas after expansion through the pressure ratio corresponding to sonic speed is one-half the sonic speed. The upper curve of Fig. 14.28 was calculated for this condition. The minimum value of 0.308 at a feed composition of 0.042 mole fraction UF6 in hydrogen is close to the values cited by Geppert [Gl].