Computational Analysis of Signatures of Highly Enriched Uranium Produced by Centrifuge and Gaseous Diffusion

Transcription

1 Computatonal Analyss of Sgnatures of Hghly Enrched Uranum Produced by Centrfuge and Gaseous Dffuson Houston G. Wood * and Alexander Glaser ** * Mechancal & Aerospace Engneerng, Unversty of Vrgna 122 Engneer s Way, Charlottesvlle, VA ** Program on Scence and Global Securty, Prnceton Unversty 221 Nassau St, Fl 2, Prnceton, NJ ABSTRACT. Dfferent enrchment processes have been used hstorcally to produce hghly enrched uranum (HEU) for weapon purposes. The most relevant ones are the gaseous dffuson process and the gas centrfuge. The two explot dfferent physcal prncples to separate sotopes of dfferent molecular weght. It could therefore be expected that HEU mght carry an sotopc sgnature that s unque to the enrchment process used to produce the materal. Mult-sotope enrchment cascades are generally modeled usng the matched-abundance-rato approach. In ths paper, we wll present comparsons of the sotopc sgnatures predcted n gas centrfuge cascades wth those predcted n gaseous dffuson cascades by usng a modfed verson of the matchedabundance-rato cascade code, MSTAR, whch accounts for the physcal dfferences n the stage separaton factors n the two processes. Addtonally, we wll present the methodology used by the modfed code and dscuss representatve results for HEU produced from both natural and reprocessed uranum. We fnd that essentally complete nowledge of the enrchment technologes employed, of the cascade desgn, and of the mode of operaton s requred n order to mae meanngful (quanttatve) statements about expected HEU sgnatures. Introducton Uranum can be used as fuel for nuclear power reactors and for nuclear weapons. As uranum occurs n nature, t has three sotopes: 234 U, U, and 238 U. The abundance of these sotopes s shown n Table 1. The sotope of nterest for producng fsson reactons s U, and the uranum must be enrched n that sotope to ~ 3 5% for lghtwater-cooled power reactors and to ~ 90% for weapons. There are a number of dfferent ways of separatng or enrchng sotopes, but the two processes used for large-scale enrchment of uranum are gaseous dffuson and gas centrfuge. Uranum that has been used as fuel n a nuclear reactor, for example, n a plutonum producton reactor, can be reprocessed and re-enrched n U, but ths rradated uranum contans addtonal sotopes, whch are produced by the nuclear reactons n the reactor. These sotopes nclude 232 U, 233 U, and 236 U, n addton to the 234 U already present. Understandng the unt separaton factors for these mnor sotopes s mportant n the enrchment of reprocessed uranum.

2 Table 1. Isotopc concentratons of natural and Hanford-type rradated uranum. 1 Natural Uranum Hanford-type RepU U E-10 at% U E-09 at% U at% at% U at% at% U at% The unt separaton n gaseous dffuson s a functon of the square root of the rato of the molecular weghts of the components beng separated n contrast wth the unt separaton n a gas centrfuge, where t s a functon of the dfference of the molecular weghts. 2 When analyzng cascades beng fed reprocessed uranum for producton of low enrched uranum (LEU, less than 20% U), ths dstncton may be small, but n the case of producng HEU (greater than 20% U), one mght reasonably expect the two processes to produce rather dfferent concentratons of the mnor sotopes. For desgnng cascades for enrchng mult-component mxtures of uranum, the dfference n assays of mnor sotopes may be of lttle mportance. However, one mght be nterested n ascertanng how a partcular sample of enrched materal was produced. In that case, the mnor sotopes mght provde forensc sgnatures, whch could dentfy the separaton process or ultmately even the orgn of the materal. In ths paper, we explore how the separaton factors of mnor sotopes may dffer between gaseous dffuson and gas centrfuge, and we present example calculatons of enrched LEU and HEU. For the mathematcal and numercal analyss, the matched abundance rato or M* (read M-star) cascade theory s used. Ths theory was frst suggested by de la Garza. 3,4 Matched-Abundance-Rato Cascades In a cascade separatng a bnary mxture, the assay of the desred sotope n the up-flowng stream from a stage s matched to the assay of the down-flowng stream from the stage above. Ths results n a no-mxng cascade or deal cascade, whch has the desrable feature of mnmum nter-stage flow. In a mult-component mxture, the deal cascade s generalzed to a matched-abundance-rato cascade, whch wll become an deal cascade when the mxture s bnary. Followng Von Halle, 5 n a mult-component mxture of J components, let the th component be desgnated the ey component, and let the abundance rato of each component be defned n terms of the ey component by x R = ; = 1,2,..., J, (1) x

3 where R desgnates the abundance rato of the th component and x denotes the mole fracton of the th component n the mxture. The overall separaton factor for a stage n a cascade s defned as ' R = ; = 1, 2,..., J, (2) '' R where the superscrpt (') denotes a quantty n the up-flowng stream leavng a stage and the superscrpt ('') denotes a quantty n the down-flowng stream leavng a stage. Ths concept s llustrated n Fgure 1, whch depcts two adjacent stages n the enrchng secton of a cascade. In the fgure, L n s the up-flow from stage number n. From the defnton, the overall stage separaton factor for the ey component,, s unty. In gas centrfuge plants, t s common for cascades to be comprsed of centrfuges of the same desgn and each would be operated at feed flow rates producng the same separaton factor. In ths analyss, the overall stage separaton factors are assumed to be constant throughout the cascade. That s, all are assumed to be ndependent of the stage number. Fgure 1. Two adjacent stages n the enrchng secton of a cascade. The enrchng secton of the cascade s comprsed of all the stages above the feed pont, and the strppng secton all stages below the feed pont. Materal balances are taen about both the enrchng and strppng sectons to descrbe ther performances. The resultng equatons are then used to descrbe the performance of the overall cascade.

4 Computer programs, wrtten n Vsual Basc, have been developed by Von Halle to solve these M* cascade equatons. 6 The followng nput s requred: (1) the concentratons of all the sotopes n the feed stream, (2) the concentraton of U n the both the product and tals stream, (3) ether the feed rate or the product rate, and (4) the overall stage separaton factor for each sotope. The program then calculates the number of requred stages n both the enrcher and the strpper, and the nterstage flow rates. In the orgnal verson of the M* program, the overall stage separaton factor,, for U s gven as nput, and the stage separaton factor per unt mass dfference s calculated as = 1/(238 ) 0. (3) Then the overall stage separaton factor for the th component s calculated as ( ) M M = 0. (4) For both gaseous dffuson and gas centrfuge, the process gas s UF 6, and the molecular weghts of UF 6 and 238 UF 6 are 349 and 352, respectvely. For gaseous dffuson, the overall stage separaton factor for U, not ncludng any neffcences, s = 352 / 349 = (5) For a gas centrfuge, the fundamental separaton due to the centrfugal force s gven by the expresson 2 M 2 exp[ M V 2RT ] = exp A M, (6) where A 2 2 = M V 2RT s the stratfcaton parameter, M s molecular weght, T s absolute temperature, M s the dfference n molecular weghts of the speces, and R s the unversal gas constant ( J/(g mole K)). For the hypothetcal Iguaçu centrfuge, 7 the perpheral speed s 600 m/s and T = 300 K, Equaton (6) yelds A 2 = 25.4 for UF 6. The overall separaton factor of a gas centrfuge s determned not only by Equaton (6) but by the feed rate, length of the centrfuge, and other parameters of the countercurrent flow n the centrfuge. Typcal centrfuges reported n the lterature have overall separaton factors on the order of 1.6, consderably larger than gaseous dffuson. However, f these two values of overall separaton factor are used n the classcal M* code, the product and tals concentratons of all the sotopes are exactly the same. The only dfference s n the number of stages requred n the two cascades. Ths result s due to the calculaton of the overall stage separaton factor for the mnor sotopes through Equaton (4). Therefore, the M* code was modfed so the user can prescrbe all n a manner consstent wth the separaton process beng modeled.

5 Determnaton of Separaton Factors for Gas Centrfuges Enrchment of spent reactor fuel by gas centrfuge has been reported n whch the Iquaçu centrfuge parameters were used. 8 In that study, a sngle gas centrfuge was numercally optmzed for enrchment of U from a bnary mxture of natural uranum. Then, numercal smulatons were performed wth spent reactor fuel as feed materal. The separaton factors were computed as functons of feed rate where the concentraton of U was maxmzed wth respect to the gradent of the temperature on the rotor wall and drag power of the tals removal scoop. Usng the concentratons of the sotopes calculated n the wthdrawals streams, the followng results were obtaned: = 1.97, = 1.32, = (7) These ratos were found to vary by less than 1% as the feed rate was vared from 1 to 100 mg/s. Expandng the rght-hand sde of Equaton (6) n a Taylor seres eepng only the frst two terms yelds M M M M = 1 + A 1 = A, (8) where M s the dfference n molecular weght between sotope and the ey sotope, n ths case 238 U. Use Equaton (8) for the sotopes 232 U, 234 U, U, 236 U, 238 U, so J = 5, and tae the ey component to be 238 U, wth = 5 : = 1 M 1 M M M M = 3, = 1, 2,..., 5. (9) More terms could be taen n the Taylor seres, but ths equaton predcts values of 2, 4/3, and 2/3, whch compares very well wth the results of the numercal study presented n Equaton (7). If the separaton factor for U s gven, the separaton factors for the other components can be determned from ths equaton as follows: M = 1+ ( 1), = 1, 2,..., 6. (10) 3 So we see the separaton factors are proportonal to mass dfferences, whch s consstent wth results reported elsewhere. 9 Equaton (10) wll be used to smulate enrchment by gas centrfuge. Determnaton of Separaton Factors for Gaseous Dffuson For gaseous dffuson, we use Equaton (5) to determne the separaton factors for all the sotopes:

6 = M M, = 1,..., J, (11) where M s the molecular weght of each sotope and M s the molecular weght of the ey component. For 238 UF 6, M = 352. Equatons (4) and (11) yeld almost exactly the same values for, and ether may be used to smulate enrchment by gaseous dffuson. Results of Calculatons We performed M* calculatons to smulate enrchng natural uranum and reprocessed uranum to 93% U by both gaseous dffuson and gas centrfuge as descrbed earler. The concentratons of the feed materal for the two cases are gven n Table 1. In all calculatons, the U tals concentraton was 0.3%. For the gas centrfuge calculatons, we have chosen =1.60, and we have used Equaton (10) for the separaton factors for the other sotopes. Ths gves results dfferent from tradtonal M* calculatons, whch used Equaton (4). The net effect s shown n Fgure 2 for the sotope 232 U enrched n a centrfuge cascade usng the tradtonal and the modfed M* code. Counterntutvely, the 232 U concentraton at frst ncreases faster for the lower separaton factor because t s closer to the value the cascade s optmzed for (1.60 for U). Ths trend reverses only n the fnal stages of the cascade, when the U enrchment s already about 90%. In ths example, the fnal concentraton of 232 U s about 10% lower for the modfed M* calculaton, whch uses the smaller separaton factor (2.20 vs. 2.56) for ths sotope. Note that about 80% of the total 232 U present n the feed s extracted n a cascade desgned producton of weapon-grade uranum, compared to only about 50% of the ntal U that leaves the cascade n the product. Fgure 2. U-232 vs U- n a centrfuge cascade usng the tradtonal and the modfed M* code. Smlarly, Fgure 3 shows the concentraton of several uranum sotopes relatve to the fnal concentraton of the respectve sotope n the product stream of the centrfuge cascade as a functon of the stage number n the enrchng secton. These smulatons, carred out wth the modfed M* code, predct that the relatve ncrease of concentraton per stage behaves qute dfferently for the varous sotopes. Agan, snce the cascade s

7 optmzed for U enrchment, the concentraton of other sotopes ncreases less effectvely n the lower stages of the enrcher. Only once the effcency of U enrchment,.e. or 238 U depleton, drops n the fnal stages of the cascade, the enrchment of the lghter sotopes becomes much more effcent. In Table 2, the product concentratons of weapon-grade uranum (93% U) enrched by gas centrfuge and gaseous dffuson are presented. In the case of naturaluranum feed, the dfference for 234 U concentraton between the two methods s shown to be on the order of 5%. In the case of rradated uranum from a Hanford-reactor-type producton reactor, the dfferences for the mnor sotopes concentratons range from 5% to more than 20%. The dfference for the lghter sotopes ncreases wth decreasng molecular weght and are all much smaller than the dfference for the heaver sotope 236 U, whch features the most sgnfcant sgnature n our smulatons. Fgure 3. Relatve concentraton of varous uranum sotopes as a functon of stage number. Table 2. Product concentratons n gas centrfuge and gaseous dffuson cascades producng HEU from natural uranum (top) and reprocessed Hanford-reactor-type uranum (bottom). Isotope Gas Centrfuge Gaseous Dffuson Dfference U at% at% -4.7% U at% 93.0 at% - Isotope Gas Centrfuge Gaseous Dffuson Dfference U E-08 at% 5.49E-08 at% -8.14% U E-07 at% 8.88E-07 at% -7.65% U at% at% -5.68% U at% 93.0 at% - U at% at% %

8 Conclusons We have extended the functonalty of the cascade code MSTAR, whch smulates multsotope enrchment cascades usng the matched-abundance-rato technque. In the modfed code, the separaton factors for all sotopes can be specfed ndependently, allowng the user to determne the mpact of dfferent enrchment processes on the abundance of the mnor uranum sotopes. We have proposed expressons to determne sets of separaton factors for the gas centrfuge and the gaseous dffuson process and used those wth MSTAR to determne sotopc sgnatures for weapons-grade uranum produced from natural and rradated uranum. The most sgnfcant sgnature s obtaned for the 236 U concentraton n weapons-grade uranum produced from reprocessed uranum. Our smulatons predct that the 236 U content should be about 20% hgher for materal enrched wth centrfuge technology, whch could be a relevant ndcator for an assessment of the potental orgn of the sample. The results of our smulatons should be benchmared aganst (or valdated wth) expermental data, whch would however requre nowledge of all relevant sample propertes and process characterstcs that were used at the tme of producton. Acnowledgement The frst author (HGW) receved partal support for ths wor from UT-Battelle, LLC (ORNL) under contract number to the Unversty of Vrgna. 1 Adapted from Sgnatures of Plutonum and Uranum, Appendx F n Nuclear Forenscs: Role, State of the Art, Program Needs, report by the Jont Worng Group of the Amercan Physcal Socety (APS) Panel on Publc Affars and the Amercan Assocaton for the Advancement of Scence (AAAS), Center for Scence, Technology and Securty Polcy, Washngton, D.C., February 2008, Table F.2. 2 J. Shacter, R. L. Hoglund, E. Von Halle, Dffuson Separaton Methods, Encyclopeda of Chemcal Technology (1965) John Wley & Sons, Inc.: A. De La Garza, G. A. Garrett, J. E. Murphy, Multcomponent sotope separaton n cascades, Chemcal Engneerng Scence, 15 (1961): A. De La Garza, A generalzaton of the matched abundance-rato cascade for multcomponent sotope separaton, Chemcal Engneerng Scence, 18 (1963): E. Von Halle, Multcomponent Isotope Separaton n Matched Abundance Rato Cascades Composed of Stages Wth Large Separaton Factors n Proceedngs of the 1st Worshop on Separaton Phenomena n Lquds and Gases, edted by K. G. Roesner, Insttut für Mechan, Darmstadt, Germany (1987): E. Von Halle, personal communcaton, 2007, and D. F. Starr, MSTAR-IAEA Enrchment Code User Gude, K/NSP-386, U.S. Department of Energy, June C. Schwab, N. A.S. Rodrgues, and H.G. Wood, edtors, Ffth Worshop Proceedngs Separaton Phenomena n Lquds and Gases, Centro Técnco Aeroespacal, Insttuto de Estudos Avançados, Mnstéro da Cênca e Tecnologa, Insttuto Naconal de Pesqusas Espaca, Foz do Iguaçu, Brasl, (1996). 8 F. Doneddu, P. Robln, and H. G. Wood, Optmzaton Studes for Gas Centrfuges, Separaton Scence and Technology, 35(8), (2000): R.S. Kemp, Gas Centrfuge Theory and Development: A Revew of the U.S. Approach, Scence & Global Securty, n revew.