1. Chapter 3Isotope Separation Methods for Nuclear FuelShuichi HasegawaGlossaryIsotope Nuclei of a chemical element which have the same number of protons but different number of neutrons. Some isotopes are stable; some are radioactive.Separation factor A ratio of a mole fraction of an isotope of interest to that of non-interest in an enriched ﬂow divided by that in a depleted ﬂow from a separation unit. The factor should be larger than unity for the unit to result in isotopic enrichment.Separation capability A measure of separative work by a cascade per unit time.Mean free path An average distance of a moving gas molecule between its collisions.Molecular ﬂow Low-pressure phenomenon when the mean free path of a gas molecule is about the same as the channel diameter; then a molecule migrates along the channel without inter- ference from other molecules present.This chapter was originally published as part of the Encyclopedia of Sustainability Science andTechnology edited by Robert A. Meyers. DOI:10.1007/978-1-4419-0851-3S. Hasegawa (*)Department of Systems Innovation, School of Engineering, The University of Tokyo,7-3-1 Hongo Bunkyo-ku, Tokyo, Japane-mail: hasegawa@sys.t.u-tokyo.ac.jpN. Tsoulfanidis (ed.), Nuclear Energy: Selected Entries from the Encyclopedia 59of Sustainability Science and Technology, DOI 10.1007/978-1-4614-5716-9_3,# Springer Science+Business Media New York 2013
2. 60 S. HasegawaDeﬁnition of the SubjectIsotope separation, in general, means enrichment of a chemical element to one of itsisotopes (e.g., 10B in B; 6Li in Li, 157Gd, etc). In the case of uranium, isotopeseparation refers to the enrichment in the isotope 235U, which is only 0.711% ofnatural uranium; today’s nuclear power plants require fuel enriched to 3–5%in 235U. Uranium enrichment is the subject of this article. Efﬁciencies of sorting out different isotopes of the element (separation factor)are usually very low. For practical enrichment plants, a gaseous diffusion processhas been successfully employed to obtain enriched uranium. A gas centrifugationprocess is the preferred method of enrichment today due to reduced energy con-sumption. A new process using lasers, which can have a high efﬁciency of separa-tion, is under development and has the potential to replace the current enrichmentmethods.IntroductionThe fuel used today by commercial nuclear power plants is the ﬁssile isotope 235U.Unfortunately, 235U is only 0.711% of natural uranium, the rest of which is,essentially, 238U. Light water reactors (LWR) operating dominantly all over theworld require isotope enrichment processes because the isotopic ratio of 235U fortheir fuels should be 3–5%. The processes used to elevate the 235U content from0.711% to 3–5% are called isotope separation or enrichment processes. Table 3.1shows the current trends of isotope separation capabilities of the world. The maincountries performing the process are Russia, France, US, and URENCO (Germany,Table 3.1 World Enrichment capacity (thousand SWU/year) [1]Country 2010 2015 2020France (Areva) 8,500* 7,000 7,500Germany, Netherlands, UK (Urenco) 12,800 12,200 12,300Japan (JNFL) 150 750 1,500USA (USEC) 11,300* 3,800 3,800USA (Urenco) 200 5,800 5,900USA (Areva) 0 >1,000 3,300USA (Global Laser Enrichment) 0 2,000 3,500Russia (Tenex) 23,000 33,000 30–35,000China (CNNC) 1,300 3,000 6,000–8,000Pakistan, Brazil, Iran 100 300 300Total approx. 57,350 69,000 74–81,000Requirements (WNA reference scenario) 48,890 55,400 66,535Source: WNA Market Report 2009; WNA Fuel Cycle: Enrichment plenary session WNFC April2011*Diffusion
3. 3 Isotope Separation Methods for Nuclear Fuel 61Netherland, and UK). A number of separation processes have been studied so far,but the principles of the current isotope separation processes mainly use gaseousdiffusion or gas centrifugation. The diffusion process was commercialized ﬁrst butthe centrifugation is taking over because of less energy consumption. This articlefollowing mainly [2, 3] describes the principles of the two processes and cascadetheory, which explains why it is required to repeat the process many times (usingsuccessive stages/cascades) to obtain a certain desired enrichment fraction such as3–5% because a single step provides only a small incremental enrichment. The newenrichment technology using lasers will be described at the end.Principles of the Separation ProcessesGaseous DiffusionFigure 3.1 shows the schematic diagram of the gaseous diffusion process. Considera chamber divided into two compartments by a porous membrane. When dilutegases are introduced into the bottom compartment of the chamber, the pores of themembrane (membrane) make dependency of the transmission of the gases on theirmolecular masses. If we have a mixture of two molecules in a gas with the same kinetic energy(kinetic energy is determined by kT, k = Boltzmann constant; T = temperature in K;(1/2 mv2 $ kT)), the lighter molecule is faster than the heavier one. Therefore, theirfrequencies of hitting the membrane is higher for the lighter than for the heaviermolecule. However, the mass preference phenomena occur only whenthe mean free path of the gas molecule is longer than the diameter of the pores 2rand the thickness of the membrane l. The mean free path, l of the molecule can bewritten as [2] kT l ¼ pﬃﬃﬃ (3.1) 4 2ps2 pwhere k is the Boltzmann constant, T is the absolute temperature, s is the radius ofthe molecule, and p is the gas pressure in the chamber. In this condition, a molecule Product p′ Feed Waste p′′Fig. 3.1 A single gaseousdiffusion stage
4. 62 S. Hasegawacannot collide with others during the transmission through the membrane so that itsdynamics can be considered as a single molecule process. This process is calledmolecular ﬂow. The ﬂux of the molecular ﬂow through the ﬂow path with circularcross section is derived by Knudsen as [3] 8rDp Gmol ¼ pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ (3.2) 3l 2pmRTwhere Gmol is the molecular ﬂow velocity, m is the molecular mass, R is the gasconstant, and Dp ¼ p00 À p0 is the pressure difference between the bottom and topcompartments of the chamber. Equation 3.2 shows that the ﬂow velocity dependson the mass of the gas molecules so that the ratio of the molecules in the mixturetransmitted to the upper compartment of the chamber is changed compared withthat of the feeding gas. The opposite condition where ﬂows do not depend on themolecular mass is called viscous ﬂow. We will derive the ideal separation factor in the case of 235UF6 and 238UF6 [3],the gas molecules used for uranium enrichment. On the ideal condition where p00 isvery small and p0 can be neglected compared with p00 , when we have a binarymixture of gases which consist of 235UF6 (molecular mass: m235 = 349, molefraction: x) and 238UF6 (molecular mass: m235 = 352, mole fraction: 1 À x), themolecular ﬂow velocities of 235UF6 and 238UF6 are 00 00 ð1ÀxÞ G235 ¼ pﬃﬃﬃﬃﬃﬃﬃ ; ap x m235 G238 ¼ ap ﬃﬃﬃﬃﬃﬃﬃ p m238 (3.3)where the constant a includes factors in Eq. 3.2. The ratio of the molecular ﬂow of235 UF6 to the whole can be written as pﬃﬃﬃﬃﬃﬃﬃﬃﬃ x x G235 m235 1 À x ﬃﬃﬃﬃﬃﬃﬃﬃﬃ s¼ ¼ ¼ r (3.4) x 1Àx G235 þ G238 pﬃﬃﬃﬃﬃﬃﬃﬃﬃ þ pﬃﬃﬃﬃﬃﬃﬃﬃﬃ x þ m235 m235 m238 1 À x m238 Therefore, the ideal separation factor a0 of the gaseous diffusion process can bederived as the separation factor of the molecular ﬂow of the porous media s rﬃﬃﬃﬃﬃﬃﬃﬃﬃ rﬃﬃﬃﬃﬃﬃﬃﬃ m238 352 a0 ¼ 1Às x ¼ ¼ ¼ 1:00429 (3.5) 1Àx m235 349 The separation factor depends on the ratio of the molecular masses so that thismethod is more effective for the isotope separation of lighter elements. For heavierelements, a larger number of repeated processes is required to obtain sufﬁcientlyenriched products. However, in reality, the real value of the separation factor is smaller than thatgiven by Eq. 3.5 due to reverse molecular ﬂow from the upper compartment to the
5. 3 Isotope Separation Methods for Nuclear Fuel 63bottom one and viscous ﬂow not depending on the molecular mass; these twophenomena work in a direction negating the enrichment process. Furthermoreoperating conditions (porous media performance, working pressures, etc.) affectthe value of the separation factor. The energy consumption to run the process isvery high due to pressure controlling of the gases, small separation factors and so on(see discussion about Separative Work Unit). Because of the relatively high energyconsumption, uranium enrichment by gaseous diffusion is on the way out and isreplaced by the gas centrifugation method.Gas CentrifugationThe principle of gas centrifugation is based upon centrifugal forces that are createdinside a rotating cylinder containing two different gas molecules, forces that dependon the molecular mass. Let’s see how it works in detail [2]. When we have a mixtureof two gas molecules in a rotating cylinder (centrifuge), pressure gradients developwith respect to the radial direction. The pressures can be written as dp ¼ o2 rr (3.6) drwhere p is the pressure, r is the radial distance, o is the angular frequency ofrotation, and r is the density of the gases. By substituting the equation of state r¼ pm=RT into the differential equation, we can derive the following equation, dp mo2 ¼ rdr (3.7) p RT When we integrate this differential equation from the radial distance r (pressurepr) to the inner radius of the cylinder a (pressure pa), we can obtain this expression, & r 2 ! pr 1 mv2 ¼ exp À a 1À (3.8) pa 2 RT awhere the speed of the outer circumference of the cylinder na = oa This equationshows that the ratio of the pressure at radius r to that of radius a depends on themolecular mass of the gases. If we have the gases which consist of 235UF6 (molecular mass: m235 = 349, molefraction: x) and 238UF6 (molecular mass: m235 = 352, mole fraction: 1 À x), theirratios of the partial pressures at the radius r to the radius a can be derived as r 2 ! pr x r 1 m235 v2 ¼ exp À a 1À (3.9) pa x a 2 RT a
6. 64 S. HasegawaTable 3.2 The local separation factor of 235UF6 and 238UF6 at r/a with T = 300K, ua = 700m/sr/a 0 0.5 0.8 0.9 0.95 0.98 0.99 1.0a 1.343 1.247 1.112 1.058 1.029 1.012 1.006 1.0 r 2 ! pr ð1 À xr Þ 1 m238 v2 ¼ exp À a 1À (3.10) pa ð1 À xa Þ 2 RT a Therefore, the local separation factor at radial distance r of radius a is given by xr r 2 ! 1 À xr ðm238 À m235 Þv2 a¼ xa ¼ exp a 1À (3.11) 2RT a 1 À xawhich depends on the difference of their molecular masses, Dm = m238Àm235 = 3.Values of the local separation factor of 235UF6 and 238UF6 with T = 300 K and na =700 m/s are given in Table 3.2. This feature is superior to the gaseous diffusionmethod when the difference of the masses is large, (e.g., for heavier elements). Theseparation factor increases as the speed of the outer circumference increases.However, the maximum speed vmax is limited by stresses created to the cylinderfrom the force of the centrifugation and can be written as [2] rﬃﬃﬃ s vmax ¼ (3.12) rwhere r is the density of the material of the cylinder, and s is the tensile strength.Although most molecular gases are localized at a % 1 because of the centrifugation, rthe values of the separation factor could be higher than those obtained from thegaseous diffusion method. These values can be enhanced if we make use ofa countercurrent ﬂow in the vertical direction. Figure 3.2 shows the schematicdiagram of countercurrent centrifugation method. Gernot Zippe performedpioneering work on the development of the centrifugation ﬁrst in the SovietUnion during 1946–1954, and from 1956 to 1960 at the University of Virginia.The countercurrent ﬂow can be induced by heating and cooling centrifuges, or pipesdrawing off ﬂows in centrifuges. The temperature control can adjust the ﬂowdeliberately but the equipment becomes more complicated than that of the ﬂowcontrol by the pipes (Fig. 3.2). This countercurrent ﬂow makes enrichment of thelighter isotopes at inner radius as the ﬂow descending along the axis direction, andthe heavier isotopes are being enriched at the circumference as the ﬂow ascending.These enriched gases are collected at different radial positions of the both ends (atouter radius for heavier isotope and at inner radius by bafﬂe for lighter isotope).When the centrifuge has a length L, the maximum separative power dUmax can bederived as [2, 4] 2 p Dmv2 dUmax ¼ LrD a (3.13) 2 2RT
7. 3 Isotope Separation Methods for Nuclear Fuel 65Fig. 3.2 Schematics of gascentrifuge with Heads (Product)countercurrent ﬂow Feed Tails (Waste) 238UF 238UF 6 6 238 UF6 235 UF6 235 238 UF6 UF6 235UF 235UF 6 6where D is diffusion coefﬁcient. The maximum separative power is proportional tothe height of the centrifuge. It is preferable to have a taller centrifuge in the verticaldirection, but the length is imposed on the resonant vibration of the centrifuge. Theresonant conditions can be written as [3] pﬃﬃﬃﬃrﬃﬃﬃﬃﬃﬃﬃ L 4 E ¼ li li ¼ 22:0; 61:7; 121:0; 200:0; 298:2;Á ÁÁ (3.14) a i 2s0where E is coefﬁcient of elasticity. A taller centrifuge can give a larger separativepower although excellent mechanical properties are required to overcome theresonant conditions.Cascade TheoryThe present isotope separation plants make use of these principles of enrichmentwith small separation factors. In order to obtain high enrichment ratios, cascadetheory is necessary [3]. According to the theory, we can enhance the ratios byiterating a single physical stage many times. Figure 3.3 shows a simple scheme
8. 66 S. Hasegawa Heads P1 Feed Fi Heads Pi Feed Fn xP 1 i xF i xP n xF Feed F Product P stage1 stage i stage n Feed xF Product xP Waste W1 Waste Wi Waste Wn xW1 xWi xWnFig. 3.3 Simple scheme of the cascadeof a cascade. An original material “feed” is provided to the system. The isotope ofinterest is enriched as going through many separation stages and a ﬁnal output“product” is obtained. Another output which mainly contains unnecessary isotopesis called “waste.” Each ﬂow F, P and W should have the following equation F¼PþW (3.15)and with mole fractions of the isotope of interest in each ﬂow xF , xP , xW , we canobtain FxF ¼ PxP þ WxW (3.16) In this system, we have four independent parameters to deﬁne. In order to obtainnecessary ﬂow of Product “P ” and mole fraction “xP” of the isotope of interest, weneed the design methodology to construct stages of separation units. The product ofa single stage (unit) is called heads and the waste of that is tails. The ratios of theisotope of interest in the product are usually most important. If, for instance, wehave two isotopes “1” and “2,” and want to enrich the “1” isotope, we would focuson the variation of the mole fraction ratio of the two isotopes, x1 , which can be x2 x1rewritten as 1Àx1 . The capability of each enrichment unit is described as separationfactor a. This factor is deﬁned as the ratios of the isotopes of interest to that ofnot-interest in the heads (product) divided by those in the tails (waste) xP 1 À xP a ¼ xW (3.17) 1 À xW In a similar way, we can deﬁne the ratio of the heads (product) to the feed asheads separation factor b, and that of the feed to the tails as tails separation factor g, xP xF 1 À xP 1Àx b¼ xF ; g ¼ xW F and a ¼ bg (3.18) 1 À xF 1 À xW
9. 3 Isotope Separation Methods for Nuclear Fuel 67 Feed Fi Heads Pi Feed Fi Heads Pi i xF i xP xF+ 1 i xP+ 1 i stage stage i i+1 Waste Wi Waste Wi xWi xW+ 1 iFig. 3.4 Simple cascade of the i and i + 1 th stages The ratio of the product to the feed is called “cut” y and deﬁned as P xF À xw y ¼ (3.19) F xP À xW The simplest design to accomplish enrichment is to accumulate separation stagesin a single line such as Fig. 3.4. This scheme is called simple cascade.Simple CascadeIn this scheme, the heads and the mole fraction of the i th stage are equal to the feedﬂow and the mole fraction of the i + 1 th stage (Fig. 3.4). Fiþ1 ¼ Pi ; xiþ1 ¼ xiP F (3.20) This cascade disposes of the tails of all stages so that the total amount of theisotope of interest in the waste should be given sufﬁcient attention. This can beevaluated by means of the recovery rate of the i th stage ri xiW 1À Pi xiP xi xiF À xiW xiP xiF a i À bi ri ¼ ¼ yi P ¼ ¼ i ¼ a À1 (3.21) Fi xiF xiF xiP À xiW xiF x i 1À W xiP When we have n stages in the cascade, the total recovery rate r can be expressed as P xP Pn xn P1 x1 P2 x2 Pn xn r¼ ¼ P ¼ P P ¼ P ¼ r1 r2 Á Á Á rn (3.22) F xF F1 x1 F1 x1 F2 x2 Fn xn F F F F The over-all separation factor of the cascade o can be derived as
10. 68 S. HasegawaFig. 3.5 Countercurrentrecycle cascade Stage n Heads Pi xP+ 1 i Feed Fi xF+ 1 i Stage i Heads Pns +1 Tails Wi xP s+ 1 n xW+ 1 i Feed F Stage xF ns + 1 Heads Pns n xP s Tails Wns+1 Stage ns xW s + 1 n Feed Fns Tails Wns n xF s n xW s Stage 1 xn P 1 À xn o¼ P ¼ b1 b2 Á Á Á bn (3.23) x1 F 1 À x1 F Therefore, if a, b do not depend on each stage, the total recovery rate can berewritten as !n a À o f ng 1 aÀb n r¼ ¼ (3.24) aÀ1 aÀ1 When the feed itself is available without any special cost, the simple cascade iseffective. But in case the wastes from each stage should not be disposed because,for instance, it is valuable or the recovery rate has to be increased, the waste ﬂowsare recycled as feed ﬂow, which is called countercurrent recycle cascade (Fig. 3.5).Countercurrent Recycle CascadeSince the simple cascade cannot improve the recovery rate, the tail ﬂow is recycledinto either stage to use it efﬁciently, which is called recycle cascade (Fig. 3.5). If b(heads separation factor) is equal to g (tails separation factor) in all stages, we canobtain xiþ2 ¼ xiþ1 ð¼ xiP Þ. So the tails ﬂow of the i + 2 th stage can be merged to the W F
11. 3 Isotope Separation Methods for Nuclear Fuel 69heads ﬂow of the i th stage and fed into the i + 1 th stage without any mixing loss.We will consider the case that the tails ﬂow of the second upper stage is reﬂuxed tothe i th stage. The ﬂows and the fractions of the isotope of interest in each stage of enrichingsections should have the following relationships. Pi ¼ Wiþ1 þ P; Pi xiP ¼ Wiþ1 xiþ1 þ PxP w (3.25) In a similar way, those in stripping sections can be expressed as Wjþ1 ¼ Pj þ W; Wjþ1 xjþ1 ¼ Pj xjP þ WxW W (3.26) Let’s estimate the number of stages. From these equations, we can derive xP À xiP xiP À xiþ1 ¼ W Wiþ1 (3.27) P At total reﬂux, where the reﬂux ratio is inﬁnity, Wiþ1 !1 (3.28) Pthe mole fraction of the heads ﬂow at the i th stage xiP becomes equal to that of thetails ﬂow at the i + 1 th stage xiþ1 and the number of the stages is minimal. W xiþ1 xiþ1 xi xiÀ1 P ¼ a W iþ1 ¼ a P i ¼ a2 P iÀ1 ¼ Á Á Á (3.29) 1 À xiþ1 P 1 À xW 1 À xP 1 À xPgives the following equation, xP xW ¼ an (3.30) 1 À xP 1 À xWand the minimum number of the stages at total reﬂux can be derived as 1 xP 1 À xW n¼ ln (3.31) ln a 1 À xP xW On the contrary, the reﬂux ratio becomes minimum when the mole fraction ofthe heads at the i + 1 th stage is equal to that of the heads at the i th stage ðxP ¼ xPÞ. iþ1 i
12. 70 S. HasegawaIdeal CascadeIdeal cascade satisﬁes the condition that the values of b (heads separation factor) atall stages are constant and the mole fraction of the heads ﬂow at the i + 1 th stage isequal to those of the tails ﬂow at the i À 1 th stage and of the feed ﬂow at the i thstage ðxiþ1 ¼ xiÀ1 ¼ xiF Þ . In this instance, each separation factor satisﬁes the p Wfollowing relationship. pﬃﬃﬃ b¼ a¼g (3.32) In a similar way to the previous section, we can obtain the total number of thestages for an ideal cascade 1 xP 1 À xW n¼ ln À1 ln b 1 À xP xW (3.33) 2 xP 1 À xW ¼ ln À1 ln a 1 À xP xW The number of stages in stripping nS and enriching nE = n À nS sections can bederived as 1 xF 1 À xW nS ¼ ln À1 (3.34) ln b 1 À xF xW 1 xP 1 À xF nE ¼ n À nS ¼ ln (3.35) ln b 1 À xP xF The reﬂux ratio Eq. 3.27 can be rewritten using xiP ¼ xiþ1 and b as F Wiþ1 xP À xiP 1 xP bð1 À xP Þ ¼ i ¼ À (3.36) P xP À xiþ1 b À 1 xiþ1 W W 1 À xiþ1 WMccabe–Thiele DiagramIt is useful to draw McCabe–Thiele diagram to investigate the design of thecascade, the mole fractions of the stages and so on. Figure 3.6 shows a typicalMcCabe–Thiele diagram. In this graph, the horizontal and vertical axes correspondto the mole fractions of the heads ﬂow xiP and of the tails ﬂow xiW , respectively.
13. 3 Isotope Separation Methods for Nuclear Fuel 71 1 xP Equilibrium line x P+1 i x iP x iW = α 1 x iP 1 x iW x iP Operating line Heads mole fraction i xP 1 x iP x P−1 i i +1 xW = α i +1 1 xW i +1 i −1 xW = x P xW 0 0 1 xW xW−1 i x iW xW+1 i xW+2 i xP Tails mole fractionFig. 3.6 McCabe-Thiele diagram First, the following equation is satisﬁed at the enrichment process of the i thstage because of the deﬁnition of the separation factor xiP xiW i ¼ a ðEquilibrium lineÞ (3.37) 1 À xP 1 À xiW Second, the condition that the tail (waste) ﬂow at the i + 1 th stage is the feed ofthe i th stage ðxiF ¼ xiþ1 Þ deﬁnes the relationship between the mole fractions of the Wtail (waste) and head (product) ﬂows at different stages as follows xiP xiF pﬃﬃﬃ xiþ1 i ¼ b i ¼ a W iþ1 ðOperating lineÞ (3.38) 1 À xP 1 À xF 1 À xW
14. 72 S. Hasegawa And third, the feed ﬂow at the i th stage consists of the tails ﬂow of the i + 1 thstage and the heads ﬂow of the i À 1 th stage and their mole fractions are the same. xiþ1 ¼ xiÀ1 W P (3.39) These three formulae can be shown in the McCabe–Thiele diagram as shown inFig. 3.6. We can estimate the number of necessary stages, mole fractions of thestages, and overview the total processes through the graphical construction.Separative Work UnitThe total ﬂow in the cascade can be derived as X bþ1 xW ðPi þ Wi Þ ¼ Wð2xW À 1Þ ln i ðb À 1Þ ln b 1 À xW ! xP xF þPð2xP À 1Þ ln ÀFð2xF À 1Þ ln (3.40) 1 À xP 1 À xF The ﬁrst term of Eq. 3.40 including b indicates the difﬁculty of the separationand increases as the value of b approaches to unity. The second term corresponds tothe amount of work for separation, and it has the same dimension as ﬂow rates andis called separative capacity or separative power. This value is important because itis considered to be proportional to the initial cost of the plant. When we use the unitof the amounts of material (mole, kg, etc.) instead of ﬂow rates, this is calledseparative work. The sum of the annual investment and operation costs can beexpressed by the product of the separative work SW (kg SWU/year) and unit priceof separative work cs ($/kg SWU). SWU is the abbreviation of Separative WorkUnit. The separative work is deﬁned as SW ¼ WfðxW Þ þ PfðxP Þ À FfðxF Þ (3.41)where f(xi) is called separation potential and written as xi fðxi Þ ¼ ð2xi À 1Þ ln (3.42) 1 À xi When we use kg SWU/year for the separative work, the unit of W, P, and Fshould be kg/year. For operating the plant, we need the raw materials, the amount of which is F (kg/year) and unit price of the raw materials cF ($/kg). The total cost per year c ($) canbe written as c ¼ SWcS þ FcF (3.43)
15. 3 Isotope Separation Methods for Nuclear Fuel 73 When the amount of the product per year is P (kg), the unit cost of the productcP ¼ P : could be derived as c SWcs FcF fðxF Þ À fðxW Þ cP ¼ þ ¼ ðfðxP Þ À fðxF ÞÞ À ðxP À xF Þ cs P P xF À xW xP À xW þ cF (3.44) xF À xWExampleWith the ideal cascade of the gaseous diffusion method (a = 1.00429), the molefraction of the feed ﬂow 0.711% (xF = 0.00711) would be enriched to 3% (xP = 0.03)and the mole fraction of the waste is planned to be 0.3% (xW = 0.003). In this case, thenecessary moles of the feed and the waste to obtain the product of 1 [mol] are PðxP À xW Þ 1 Â ð0:03 À 0:003Þ F¼ ¼ ¼ 6:569½mol xF À xW 0:00711 À 0:003 PðxP À xF Þ 1 Â ð0:03 À 0:00711Þ W¼ ¼ xF À xW 0:00711 À 0:003 ¼ 5:569ð¼ 6:569 À 1Þ½mol The total number of stages n and the number of stages in stripping section nS andin enriching section nE are calculated asStripping Section 2 xF 1 À xW nS ¼ ln À1 lna 1 À xF xW 2 0:00711 1 À 0:003 ¼ ln À 1 ¼ 404 ln 1:00429 1 À 0:00711 0:003
16. 74 S. HasegawaEnriching Section 2 xp 1 À xF nE ¼ ln ln a 1 À xp xF 2 0:03 1 À 0:00711 ¼ ln ¼ 683:5 ln 1:00429 1 À 0:03 0:00711The total number of stages 2 xp 1 À xW n¼ ln À1 ln a 1 À xp xW 2 0:03 1 À 0:003 ¼ ln À 1 ¼ 1087:5 ln 1:00429 1 À 0:03 0:003 The heads ﬂow rate in the enriching section can be written as Pi ¼ P þ Wiþ1 P ¼Pþ fxp ð1 À biÀn Þ þ ð1 À xp ÞbðbnÀi À 1Þg bÀ1and that in the stripping section W È É Pi ¼ xW bðbi À 1Þ þ ð1 À xW Þð1 À bÀi Þ bÀ1 These ﬂows as a function of the number of the stages can be shown as Fig. 3.7 inthis example. When we need higher concentration, such as 5%, F = 11.436[mol], W = 10.436[mol], n = 1336 and nE = 932.Laser Isotope Separation (LIS)The photon absorbing frequencies of isotopes show small differences caused byshifts of atomic electron energies due to the differences in the number of neutronsamong isotopes. This is called isotope shift. The invention and development oflasers enable to resolve the isotope shift sufﬁciently and make isotope-selectivephoto-chemical reaction possible. Laser Isotope Separation may lead to almost100% isotope separation in a single stage. Mainly, two methods such as AtomicVapor Laser Isotope Separation (AVLIS) and Molecular Laser Isotope Separation(MLIS) were intensively studied. AVLIS uses uranium atomic vapor that is struckby lasers of such wavelength that only 235U atoms are excited and then ionized;
17. 3 Isotope Separation Methods for Nuclear Fuel 75 Feed xF = 0.00711 1600 1400 1200Heads flow rate 1000 800 600 Product 400 Waste xP = 0.03 xW = 0.003 200 0 0 100 200 300 400 500 600 700 800 900 1000 1100 1200 number of stagesFig. 3.7 Heads ﬂow rateonce ionized, the 235U ions are collected by an electromagnetic ﬁeld. MLIS usesUF6, and vibrationally excites and multiphoton-dissociates only 235UF6 into235 UF5 by infrared lasers. The research to commercialize them has faded ona global scale. A new process called Separation of Isotopes by Laser Excitation (SILEX) isunder development. All details are not out in the open yet; but SILEX is consideredto be a kind of molecular LIS using UF6. The method only isotope-selectivelyexcites but not dissociates 235UF6. The separation factor announced by the companyhas been 2–20 [5]. Silex Systems Ltd was originally established as a subsidiary ofSonic Healthcare Limited of Australia in 1988. In 2007, the SILEX UraniumEnrichment project was transferred to GE’s nuclear fuel plant in the United States.Global Laser Enrichment (GLE) was formed as a subsidiary of GE-Hitachi in 2008[5]. In June 2009, GE-Hitachi submitted a license application to construct acommercial laser enrichment plant in Wilmington, NC. The NRC staff is currentlyreviewing that application. They announced that they succeeded the initial mea-surement program at Test Loop in 2010 and proceeded to evaluate the program todecide the commercialization of the process [6].
18. 76 S. HasegawaFuture DirectionsAs of today, the gaseous diffusion and centrifuge processes have been used on acommercial scale. For the future, it seems that laser enrichment (the SILEXprocess) may be the successor to current enrichment methods. Preliminary results,based on enrichment by lasers, are encouraging. However, considerableimprovements are needed before this method achieves commercial competitivestatus. Every uranium enrichment process is linked to nuclear proliferation issues.It would be very beneﬁcial for the world if a method of enrichment is devisedwhich inherently offers non- proliferation safeguards for nuclear materials.Bibliography1. World Nuclear Association, Uranium Enrichment, World Enrichment capacity - operational and planned. http://www.world-nuclear.org/info/inf28.html2. Villani S (1976) Isotope separation. American Nuclear Society, Hillsdale3. Benedict M, Pigford TH (1957) Nuclear chemical engineering. Mcgraw-Hill, New York; Benedict M, Pigford TH, Levi HW (1981) Nuclear chemical engineering (second edn.), (trans: by Kiyose R into Japanese)4. Kemp RS (2009) Gas centrifuge theory and development: a review of U.S. programs. Science and Global Security 17, 1; Wood HG, Glaser A, Kemp RS (2008) The gas centrifuge and nuclear weapons proliferation. Physics Today 405. Silex Systems Limited home page. http://www.silex.com.au/6. World Nuclear News (2010) Initial Success from SILEX test loop, 12 April 2010. http://www. world-nuclear-news.org/NN-Initial_success_from_SILEX_test_loop-1204104.html
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