ibest: A Program for Burnup History Estimation of Spent Fuels Based on ORIGEN-S

Transcription

1 Accepted Mnuscript ibes: A Progrm or Burnup History Estimtion o Spent Fuels Bsed on ORIGE-S Do-Yeon Kim, Ser Gi Hong, Gil Hoon Ahn PII: S DOI: 1.116/j.net Reerence: E 6 o pper in: ucler Engineering nd echnology Received Dte: 29 Jnury 215 Revised Dte: 1 April 215 Accepted Dte: 12 April 215 Plese cite this rticle s: D.-Y. Kim, S.G. Hong, G.H. Ahn, ibes: A Progrm or Burnup History Estimtion o Spent Fuels Bsed on ORIGE-S, ucler Engineering nd echnology 215, doi: 1.116/j.net his is PDF ile o n unedited mnuscript tht hs been ccepted or publiction. As service to our customers we re providing this erly version o the mnuscript. he mnuscript will undergo copyediting, typesetting, nd review o the resulting proo beore it is published in its inl orm. Plese note tht during the production process errors my be discovered which could ect the content, nd ll legl disclimers tht pply to the journl pertin.

2 ACCEPED MASCRIP ibes: A Progrm or Burnup History Estimtion o Spent Fuels Bsed on ORIGE-S Do-Yeon Kim,, *Ser Gi Hong, nd b Gil Hoon Ahn Kyung Hee niversity, 1732 Deogyeong-dero, Giheung-gu, Yongin-si, Gyeonggi-do, Kore b Kore Institute o ucler onproliertion nd Control KIAC, 1534 Yuseong-dero, Yuseong-gu, Dejon, Kore Review ield: 2 ucler Fuel Cycle nd Rdioctive Wste Mngement umber o pges: 38 b umber o igures: 2 c umber o tbles: 11 ACCEPED MASCRIP * Corresponding uthor, E-mil ddress : sergihong@khu.c.kr Ser Gi Hong

3 ACCEPED MASCRIP ibes: A Progrm or Burnup History Estimtion o Spent Fuels Bsed on ORIGE-S Do-Yeon Kim,,* Ser Gi Hong, nd b Gil Hoon Ahn Kyung Hee niversity, 1732 Deogyeong-dero, Giheung-gu, Yongin-si, Gyeonggi-do, Kore b Kore Institute o ucler onproliertion nd Control KIAC, 1534 Yuseong-dero, Yuseong-gu, Dejon, Kore Abstrct In this pper, we describe computer progrm, ibes inverse Burnup ESimtor, tht we developed to ccurtely estimte the burnup histories o spent nucler uels bsed on smple mesurement dt. he burnup history prmeters include initil urnium enrichment, burnup, cooling time ter dischrge rom rector, nd rector type. he progrm uses lgebric equtions derived using the simpliied burnup chins o mjor ctinides or initil estimtions o burnup nd urnium enrichment, nd it uses the ORIGE-S code to correct its initil estimtions or improved ccurcy. Also, we newly developed stble bi-section method coupled with ORIGE-S to correct burnup nd enrichment vlues nd implemented it in ibes in order to ully tke dvntge o the new cpbilities o ORIGE-S or improving ccurcy. he ibes progrm ws tested using severl problems or veriiction nd well-known relistic problems with mesurement dt rom spent uel smples rom the Mihm-3 rector or vlidtion. he test results show tht ibes ccurtely estimtes the ACCEPED MASCRIP burnup history prmeters or the test problems nd gives n cceptble level o ccurcy or the relistic Mihm-3 problems. Keywords: Burnup History Estimtion, Forensics, ucler Spent Fuel, ORIGE-S

4 ACCEPED MASCRIP 1. Introduction he dnger is growing tht interntionl terrorist groups could use nucler mterils rom spent nucler uels rther thn nucler bomb becuse it would be diicult or smll group o terrorists to mnucture nucler bomb [1, 2, 3]. hereore, the bility to identiy the perpetrtors o such ttcks nd the origin o ny such nucler mteril is criticl. he methodology, inding the burnup history nd chrcteristics o the originl nucler mterils bsed on n nlysis o the post-event mterils, is considered necessry nd eective tool or interntionl nucler segurds. A similr methodology cn lso identiy the initil urnium enrichment nd burnup o spent nucler uels. he purpose o this work is to develop computer progrm tht cn ccurtely estimte the burnup histories o spent nucler uels bsed on smple mesurement dt within resonbly short time. Gmm-ry isotopic nlysis gives reltive isotopic rtios in spent uel smples, nd thus the estimtion o burnup history depends on the reltive isotopic rtios in the smples rther thn on the bsolute isotopic msses. he burnup history prmeters o spent uels include initil urnium enrichment, dischrge burnup, cooling time ter dischrge rom nucler rector, nd the type o nucler rector in which the spent uel ws burnt. Actully, the isotopic compositions o spent nucler uel in nucler uel ssemblies cn be ccurtely clculted using lots o lttice clcultion codes, such s HELIOS [4], CASMO [5], KARMA [6], nd DeCAR [7]. In those lttice codes, the isotopic compositions o uel regions ter burnup re determined by lterntively solving the neutron trnsport eqution ACCEPED MASCRIP nd the Btemn eqution describing the chnge o isotopic composition over speciied number o time steps. On modern computers, those codes typiclly tke severl tens o minutes to complete the isotopic composition determintion or singleuel ssembly model. But the inverse problem, to determine the burnup history prmeters such s initil urnium enrichment nd burnup, cn require mny itertions. he use o the lttice codes or tht purpose cn tke lots o computing time. Also, the lttice codes re typiclly pplicble only 2

5 ACCEPED MASCRIP or PWRs becuse their cross section librries were produced using the PWR spectrum. In 25, M. R. Scott proposed method tht used simpliied depletion chins to derive simple lgebric equtions to estimte the initil urnium enrichment nd burnup o spent uel rom its isotopic rtios [1]. He lso devised simple itertive lgorithm coupled with ORIGE-2 [8] to correct the initil estimtion o the burnup history prmeters. With his methods, burnup could be ound within 5% ccurcy, enrichment within 2.5% ccurcy, nd ge within 1% ccurcy or the nine smples tken rom the Mihm-3 rector. However, he reported tht the rector type i.e., PWR could not be correctly predicted nd his ppliction ws conirmed only to the Mihm-3 spent uel problems. We developed progrm clled ibes [9, 1] or the initil estimtion o burnup nd urnium enrichment bsed on the simple lgebric equtions developed by M. R. Scott, but we newly developed stble bi-section method to correct the initil urnium enrichment nd burnup becuse we ound tht the simple correction method used in Re. 1 cn be unstble. Also, we usedorige-s [11] rther thn ORIGE-2 in our progrm to ully tke dvntge o the burnup-dependent cross-section librries o ORIGE-S or improving ccurcy nd developed GI Grphic ser Interce or input nd output visuliztions, while the previous work given in Re. 1 used the old ORIGE2 code combined with simple correction method. For veriiction o ibes, we devised benchmrk problems using ORIGE-S or severl dierent types o rector nd the results o ibes tht were obtined with the input prmeters extrcted rom ORIGE-S outputs were compred with the initil conditions o ORIGE-S. hen, we tested the ibes progrm using the well-known relistic ACCEPED MASCRIP Mihm-3 problems [12], which hve mesurement dt rom spent uel ssys, or vlidtion. In Section 2, we review the methodologies or the initil estimtion o burnup nd enrichment nd describe the stble bi-section method developed in this work. Section 2 lso gives the correction methods or urnium nd burnup, s well s the computtionl procedure used in ibes. he veriiction nd vlidtion o ibes re given in Section 3. Section 4 gives the summry nd conclusions. 3

6 ACCEPED MASCRIP 2. heory nd Computtionl Method 2.1 Initil Estimtions o rnium Enrichment nd Burnup In this section, we irst review the method nd ormultions or the initil estimtion o burnup nd enrichment. he eqution tht cn estimte the burnup o spent uel is derived by considering tht the initil tom number density o urnium is equl to the sum o the remining tom number densities o urnium isotopes nd ll o the urnium rections undergone during irrdition t the mesurement time. he ollowing eqution gives the blnce reltion [1] : + = t φ t dt + γ t φ t dt + t φ t dt, where is the mesurement time o the spent uel smple, one-group eective ission cross section, cpture cross section, 235 γ 235 γ 235 t φ t dt ACCEPED MASCRIP is the microscopic is the microscopic one-group eective is the number density o the initil urnium toms, nd X is the number density o toms o nuclide X t mesurement time. Eq.1 lso ssumes tht the neutron spectrum does not chnge over time. he cpture terms o Eq.1 cn be decomposed into the cpture nd ission rtes o the corresponding cpture products. With those decompositions, Eq.1 cn be rewritten s: t φ t dt + t φ t dt + t φ t dt 2 + = Pu 235 Pu t φ t dt +..., Pu + Pu

7 ACCEPED MASCRIP where the delyed production o Pu rom the decy o nd p is ignored. At this point, the burnup monitor nuclides re considered to estimte the burnup. Actully, ny ission product produced directly proportionl to the burnup cn be used s burnup monitor, nd it is known tht burnup cn be mesured within one percent ccurcy coupled with mss spectrometry. But or our problems, the rector type is not given beore the problem is solved, nd so burnup monitors tht re produced t the sme rte regrdless o rector type should be chosen. Also, ission products tht hve constnt ission yield cross rector types nd long hl-lie re desirble or burnup monitoring, to simpliy the ormultion. For good burnup monitor, the ollowing eqution is stisied: d dt B Pu Pu = Y [ t φ t + t φ t +...] 3 B where the cumultive yield Y B or the burnup monitor is ssumed to be the sme or ll issionble nuclides nd to be independent o the incident neutron energy. In Eq.3, the right side should include ll o the issions contributed rom ll the issionble nuclides, nd the rdioctive decy o the burnup monitor is neglected by considering its long hl-lie. Also, in Eq.3, production rom rdioctive decy nd the rditive cpture o the preceding nuclides re not considered. he integrtion o Eq.3 over time gives: where R B = YB dt[ ρ = E R 235 Y B, B t 235 φ t + P ACCEPED MASCRIP t P φ t +...] ρ is the initil density o urnium in the uel, B is the burnup o the uel, nd E is the verge recoverble energy per ission. he substitution o Eq.4 into Eq.1 4 gives: = M E P R + B, P + P

8 ACCEPED MASCRIP where nd M re Avogdro s number nd the tomic weight o urnium, respectively. he division o Eq.5 by ter solving or gives the eqution relting the mesured quntities with burnup s ollows: P P =. 6 M 1 B E In this eqution, ll the quntities in the numertor cn be known rom the mesurements o spent uel smple, but the quntity on the let side is not mesurble. hereore, we need one dditionl eqution to determine the burnup. Dividing Eq.4 by the initil urnium tomic number density gives the dditionl eqution needed or burnup estimtion: R B ER B =. 7 Y M In Eq.7, the irst term on the right side is mesured quntity nd so, Eq.6 nd Eq.7 cn be used to estimte the burnup. ext, the eqution or the estimtion o initil urnium enrichment is derived by considering the blnce o the initil tomic density o 235. he blnce eqution is given by: 235 = ACCEPED MASCRIP γ B t φ t dt. 235 t φ t dt 8 In deriving the eqution or initil urnium enrichment estimtion, it ws ssumed tht p nd decy instntneously to Pu. he decy o ll issionble nuclides ws neglected or simplicity becuse the initil urnium enrichment will be improved by using the 6

9 ACCEPED MASCRIP correction step. he cpture term o Eq.8 is replced with the tomic number density o 236 i the ission o 236 is neglected, which gives: = + + t φ t dt. 9 hen, Eq.4 is used to eliminte the ission term rom Eq.9, which gives: 235 [ = 235 ACCEPED MASCRIP 236 ρ + + B ER 1 Pu Pu t φ t dt + t φ t dt +...]. Dividing Eq.1 by the initil urnium tomic number density gives the ollowing eqution: e = [ = φ t 236 t dt + ρ + E Pu R φ t B Pu t dt +...]. he next step is to use the depletion eqution without considertion o rdioctive decy or the ctinides tht pper in the lst term o Eq.11. For exmple, the depletion eqution or is given by: d dt 11 + o = φ t t dtφ t t =. 12 his eqution cn then be substituted into Eq.11 nd similr procedure cn be successively done or the other ctinides tht pper in the lst term o Eq.11. his procedure gives the ollowing eqution or the determintion o the initil urnium enrichment o the spent uel: 7

10 ACCEPED MASCRIP ACCEPED MASCRIP 8 ]]. [ ] [ ] [ ] [ [ P P P P P P P P P P P P P P R F F F B E e = ρ 13 In Eq.13, the ollowing deinitions or F were used: ]. [ ], [ ], [ P P P P P P P P P P P F F F F F + = + = = γ γ γ 14 I we ssume tht initil plutonium isotope msses re zero, Eq.14 cn be simpliied to:, ] [ P P P R G G G G B E M e + + = 15 where: ]. [ ], [ ], [ ], [ P P P P P P P P P P P P P P P P P P P P P P G G G G G G e G γ γ γ + = + = + = = 16

11 ACCEPED MASCRIP Eq.16 contins the rtio /, nd this quntity ws lredy determined during the estimtion o burnup. Our progrm uses n itertive lgorithm to solve Eq.15 nd Eq.16, nd we ound tht the lgorithm is lwys rpidly convergent. 2.2 Correction o rnium Enrichment nd Burnup he methods or the initil estimtion o urnium enrichment nd burnup described in Sec. 2.1 re reltively simple nd computtionlly eicient. However, the estimted vlues ound using Eq.6, Eq.7, Eq.15, nd Eq.16 re generlly inccurte. In prticulr, the estimted vlue o initil urnium enrichment is much less ccurte thn the estimted burnup, nd so correction o those initil estimtions is required to improve the ccurcy. For this purpose, correction method coupled with the ORIGE-2 orwrd depletion clcultion ws suggested or both burnup nd initil urnium enrichment in Re. 1. However, ORIGE-2 is very old code nd the ccurcy o its depletion clcultions re limited by its burnup-independent cross-section librries. Also, we hve ound tht the lgorithm given in Re. 1 to correct the urnium enrichment cn be unstble. In this work, we newly developed stble bi-section lgorithm to correct the initil urnium enrichment nd burnup. Also, we used ORIGE-S rther thn ORIGE-2 to improve the ccurcy becuse ORIGE-S provides severl new cpbilities, including burnup-dependent cross-section librry. ext, we describe enrichment correction using the bi-section method. he bi-section method strts with the initil estimtion o urnium enrichment by setting: ACCEPED MASCRIP X = XL = XR = e. 17 hen, our progrm utomticlly prepres n ORIGE-S input ile using the initil urnium enrichment nd burnup estimtions. At present, the ORIGE-S input ssumes n initil urnium mss o 1kg nd speciic power o 4W/g. ext, our progrm executes 9

12 ACCEPED MASCRIP ORIGE-S to perorm depletion clcultion up to the initilly estimted burnup nd then clcultes the ollowing unction vlue using the results o the ORIGE-S output: m 235 X where X represents urnium enrichment. In Eq.18, ORIGE ORIGE X = R A X A, 18 R m is the rtio o the number o 235 toms to the number o toms obtined rom smple mesurement, nd A is the ORIGE number o toms rom the ORIGE-S output t the burnup. We hope tht the unction given by Eq.18 is nerly zero when the enrichment correction is completed becuse the unction X indictes the dierence between the numbers o 235 toms obtined rom the ORIGE-S clcultion nd rom the mesurement rtio R m multiplied by the number o toms estimted by ORIGE-S. hus, i the unction X is positive, then XL is incresed by speciied vlue until XL becomes negtive. he lst XL t which the unction is negtive is then set to XR. On the other hnd, i the unction X is negtive, then XR is decresed by speciied vlue until XR becomes positive. he lst XR t which the unction is positive is then set to XL. Once the initil vlues o XL nd XR t which the unction hs dierent signs re determined, the conventionl bi-section method is used s ollows: 1 X = XL or XR depending on the initil sign o e 2 X 3 i old else X i = XL + XR / 2., else X X X old old Go o 2 ACCEPED MASCRIP = X old X * XR < XR = X XL = X, < ε SOP 19 In the irst step o the bove lgorithm, i the initil sign o e is positive, XR is set to X old nd otherwise, XL is set to X old. In Eq.19, ε is convergence criterion. he 1

13 ACCEPED MASCRIP bove enrichment corrections re done or ll o the cndidte rector types tht hve corresponding one-group cross-section librry. Ater the correction o urnium enrichment, similr procedure using the bi-section method is pplied to correct the burnup. In the correction o burnup, the unction given in Eq.18 is replced with: where m BM m, BM BM X ORIGE ORIGE X = R A X A, 2 R, is the rtio o the number o burnup monitor toms to the number o toms, ORIGE A BM is the number o burnup monitor toms clculted with ORIGE-S t the mesurement time, nd X is the burnup. hese sequentil corrections o enrichment nd burnup re ctully perormed two or three times in our progrm. 2.3 Determintion o Cooling ime nd Rector ype Ater the enrichment corrections re completed, the cooling time ter dischrge rom the rector is estimted. In generl, ission products with hl-lie vlue similr to the cooling time re desirble s the ge monitors, but the cooling time is unknown beore the problem is solved. Generlly, ission products with hl-lives o 1 yer 3 yers re recommended s ge monitors. ORIGE-S clcultions re perormed gin or ech type o rector, nd then the tomic number densities o the ge monitor nuclides t 3 dys ter dischrge re extrcted rom the ORIGE-S outputs to wit the decy out o the short-lived ission products tht led to the ge monitor. hose vlues re set to C,i. I the ge monitor nuclides re not produced rom the decy o other nuclides, their tomic number densities t cooling time ter dischrge re given by: ACCEPED MASCRIP C C C 1/ 2, i i C = ln, 21 C ln 2, i where λ i nd / 2, i 1 re the decy constnt nd hl-lie o the i th ge monitor, respectively. o use mesurble quntities, Eq.21 is chnged into: 11

14 ACCEPED MASCRIP C C 1/ 2, i i C / = ln[ ]. 22 C ln2 /, i In Eq.22, the denomintor is clculted rom the ORIGE-S clcultions, nd the numertor is rom the mesurements. When severl ge monitors re used, some monitors cn give lrger errors in cooling time thn others; thereore, the inl cooling time should be creully determined. We irst clculte the verge o the cooling times or ll the ge monitors nd select the two vlues closest to the verge vlue. hen, we select the verge vlue o those two vlues s the cooling time or ech rector type. Finlly, 3 dys should be dded to the cooling time determined by Eq.22 to give the inl cooling time becuse the tomic number densities t 3 dys ter dischrge were used in Eq.22. he estimtion o the rector type in which the spent uel ws burnt is lso done using ORIGE-S clcultions. he rector type monitor nuclides should be chosen such tht their depletion chrcteristics re distinctly dierent or dierent types o rectors. Also, to void the compliction o decy, stble or long-lived isotopes re desirble s rector type monitors. he method or determining rector type lso depends on the ccurcy o the depletion clcultions, which diminishes s the decy chin becomes more complicted. In prticulr, it is diicult to ccurtely determine rector type or spent uels with low burnup. he discrimintion between PWR nd BWR t low burnup is much more diicult thn other cses. o determine the rector type, ORIGE-S inputs re utomticlly prepred or ll rector ACCEPED MASCRIP type cndidtes using the previously estimted urnium enrichments, burnups, nd cooling times. hen, the ORIGE-S depletion clcultions re done with ll the inputs or ll the cndidte rector types. Ater the depletion clcultions, the tomic number density rtios o the rector type monitors to re clculted using the results o the depletion clcultions t the mesurement time. hen, the dierences between those rtios nd their mesured vlues re clculted, nd the rector type with the minimum dierence is selected. 12

15 ACCEPED MASCRIP 2.4. Computtionl Procedure in ibes We developed computer progrm clled ibes using the methodologies described in the previous sections to estimte the burnup history o spent uel. We wrote this progrm using C++ nd developed GI progrm or user convenience. he computtionl procedure using the methodologies given in Sec. 2.1, Sec. 2.2, nd Sec. 2.3 is shown in Fig. 1. First, the progrm estimtes the burnup nd xx_rtio = / by itertively solving Eq.6 nd Eq.7. ote tht only the ission yield vlues or the burnup monitors nd their isotopic rtios to re required to solve those equtions. hen, urnium enrichment is estimted by itertively solving Eq.15 nd Eq.16. Solving these two equtions requires the eective one-group ission, bsorption, nd cpture cross sections or the ctinides. hereore, ibes requires n xs.ile tht contins the eective one-group cross sections o the ctinides or ll o the cndidte rector types. rnium enrichment estimtion is done or ech o the cndidte rector types Fig rnium enrichment nd burnup correction re ollowed by the bi-section method described in Sec he urnium enrichment nd burnup corrections re repeted two or three times in ibes or ll the cndidte rector types. he next step is to estimte the cooling times or ll the cndidte rector types using Eq.22, nd 3 dys re dded to the ACCEPED MASCRIP cooling times, s explined in Sec Finlly, the rector type is determined ter the ORIGE-S depletion clcultions or ll the cndidte rector types using their burnup, urnium enrichment, nd cooling time estimtes. sers cn prepre the input ile or ibes using the GI, which lso provides output visuliztion. Fig. 2 shows the min window o the ibes GI. 13

16 ACCEPED MASCRIP Fig umericl Veriiction 3.1. umericl ests with ORIGE-S For veriiction, we irst pplied ibes to severl test problems prepred using ORIGE-S. he purpose o these test problems ws to show whether ibes gve the correct estimtions o burnup history prmeters. In these test problems, the burnup history prmeters re initilly speciied, nd the input prmeters or ibes were prepred by extrcting the tomic number densities o the monitor nuclides rom the ORIGE-S output iles. We considered our dierent types o test problems: 1 PWR test problems, 2 BWR test problems, 3 CAD test problems, nd 4 MAGOX test problems. he PWR tests were bsed on the Mihm-3 problems [12], which model nine spent uel smples rom the Mihm-3 rector. ble 1 speciies the tomic number density rtios o the monitor nuclides clculted using the tomic number densities rom the ORIGE-S outputs or these test problems. ble 2 summrizes the test results nd the speciictions o burnups, urnium enrichments, nd cooling times denoted s the reerence vlues or the nine test problems. As shown in ble 2, these nine test problems cover burnup rnge rom 8.3MWD/kg to 34.1MWD/kg. he considered cooling time is 5. yers. hree enrichments o 3.28%, 3.23%, nd 3.21% re considered or these problems ble ACCEPED MASCRIP ble he rector type monitors used in the PWR tests were 132 B nd 148 d, nd PWR nd BWR were the two cndidte rector types considered. he cross-section librries or PWR nd BWR provided by SCALE6.1 [13] or ORIGE-S re w15x15 nd ge7x7-, respectively. Our test problems were prepred using ORIGE-S clcultions with the 14

17 ACCEPED MASCRIP w15x15 librry. As shown in ble 2, ibes correctly identiied the rector type s PWR in ll cses. In generl, discrimintion between PWR nd BWR is quite diicult or smll burnup vlues. he mximum errors in urnium enrichment, burnup, nd cooling time were.26%,.22%, nd 1.39%, respectively. he results o these tests show tht ibes quite ccurtely predicted the speciied burnups, urnium enrichments, nd cooling times. he test problems or BWR were prepred bsed on the Cooper rector, BWR in the SA [14]. his rector uses 7x7 uel ssembly. he spent uel isotopic dt obtined through PIE post-irrdition exmintion o this rector re given in Re. 14. For this rector, six smple dtsets re vilble. nortuntely, the isotopic dt o the spent uel or this rector re insuicient to be used in the vlidtion o ibes, but we prepred the six test problems corresponding to the six smples using ORIGE-S depletion clcultions with the ge7x7- librry. ble 3 speciies the tomic number density rtios or the monitor nuclides. ble 4 shows the test results nd the speciictions o the burnups, urnium enrichments, nd cooling times denoted s reerence vlues. he enrichment or these six cses is 2.93%, nd the considered cooling times re 5.35 yers nd 5.28 yers. he burnups rnge rom 17.8MWD/kg to 33.9MWD/kg ble ble For these test problems, PWR nd BWR were lso used s the rector type cndidtes to ACCEPED MASCRIP see whether ibes cn correctly discriminte between PWR nd BWR. ble 4 shows tht ibes ccurtely estimted the burnups nd enrichments, with mximum errors o.34% nd.69%, respectively, or ll the cses. he mximum error or the cooling time ws 1.12%, which ws lrger thn those o the burnup nd enrichment. However, this level o mximum error is still smll nd cceptble. Also, using 132 B nd 148 d s rector type monitors, ibes correctly identiied the rector type s BWR in ll cses. 15

18 ACCEPED MASCRIP he next test problems modeled CAD rectors. We prepred six test problems using depletion clcultions with the cndu37 librry provided by SCALE6.1 or ORIGE-S. ble 5 describes the tomic number density rtios or the monitor nuclides prepred using the ORIGE-S outputs with the cndu37 librry ter the depletion clcultions. ble 6 summrizes the test results nd the speciictions o burnups, urnium enrichments, nd cooling times or these CAD test problems. In generl, the dischrge burnup o the CAD uels is much lower thn tht o PWR uels, bout 6.5MWD/kg 7.5MWD/kg. Also, CAD uel uses nturl urnium, in which only.711% o the totl urnium is 235 As shown in ble 5, the burnups rnge rom 1.5MWD/kg to 1.MWD/kg. he cooling times include 5 yers nd two extremely short cses o.1 nd.3 yers ble ble In these test problems, we considered lrger number o cndidte rector types thn in the PWR nd BWR test cses: PWR, BWR, CAD, nd MAGOX, whose librries provided by SCALE6.1 or ORIGE-S re w15x15, ge7x7-, cndu37, nd mgnox, respectively. he monitors or the rector type re 24 Pu, 148 d, nd 143 d or these test problems. ble 6 shows tht ibes correctly identiied the rector type s CAD in ll cses, even the very low burnup cses. he burnups were quite ccurtely predicted, within.7%, nd the urnium enrichment error ws within 1.4%. he urnium enrichment errors re ACCEPED MASCRIP lrger thn those in the BWR nd PWR cses becuse o the much lower 235 content thn in the previous cses. he cooling times were lso ccurtely predicted, within 1.8%, but the errors or the two extreme cses with very short cooling times were lrge, up to 16.7%. he diiculty in predicting the short cooling time is becuse the predicted cooling time cn be signiicntly inluenced by the contribution o the preceding ission products to the ormtion o ge monitors. 16

19 ACCEPED MASCRIP he lst test problems modeled MAGOX type rectors [15], which re gs CO 2 cooled rectors with grphite modertors. he uel is nturl urnium in metllic orm, cnned with mgnesium lloy clled Mgnox. In MAGOX rectors, the uel burnup is typiclly low becuse they use nturl urnium, s in CAD. So, we considered our dierent burnup cses o 2 MWD/kg, 3 MWD/kg, 4 MWD/kg, nd 8 MWD/kg. he considered cooling time ws 5 yers, nd very short cooling time o.1 yers ws lso considered. ble 7 describes the tomic number density rtios or the monitor nuclides prepred using ORIGE-S depletion clcultions rom the mgnox librry. he test results nd speciictions o the burnups, urnium enrichments, nd cooling times or these problems re summrized in ble 8. We used the sme rector type cndidtes nd their corresponding cross section librries or ORIGE-S s in the CAD test problems. As shown in ble 8, ibes correctly predicted the rector type s MAGOX in ll cses except or the one with.1 yers o cooling time. Also, the progrm ccurtely estimted the burnups nd urnium enrichments within.4% nd 1.1%, respectively. he cooling time hd slightly lrger errors thn the burnup nd urnium enrichment, nd the short cooling time.1 yers could not be ccurtely predicted, s in the CAD cses ble ble Mihm-3 est Problems with PIE Dt For this section, we pplied ibes to the nine smples rom the Mihm-3 rector. o our ACCEPED MASCRIP knowledge, these nine cses re the only vilble problems with suicient PIE mesurement dt or the vlidtion o ibes. he PIEs were conducted in JAERI. ine smples were tken rom three uel ssemblies irrdited in the Mihm nit 3 PWR rectors. ble 9 describes the tomic number density rtios or the monitor nuclides clculted using the dt 17

20 ACCEPED MASCRIP given in Re. 12. ble 1 summrizes the test results nd the speciictions, such s the burnups, urnium enrichments, nd cooling times, which re exctly the sme s those in ble 1. For these nine smples, we used 148 d s the burnup monitor nd considered 234, 235, 236,, Pu, 24 Pu, nd 241 Pu s the enrichment monitors. he rector type monitors were 143 d, 148 d, nd 24 Pu, exctly the sme s those in Re. 1, nd we used 16 Ru, 125 Sb, 134 Cs, nd 137 Cs s ge monitors. he results given in ble 1 were obtined without burnup correction only enrichment correction to see the eects o burnup correction coupled with enrichment correction ble ble In this test, we irst considered only two rector type cndidtes, PWR nd BWR. heir corresponding ORIGE-S librries re PWR_W15x15 nd BWR_GE7x7-, respectively. For ll the cses, ibes correctly identiied the rector type s PWR, wheres M. R. Scott reported tht his progrm, EMASYS, predicted PWR correctly only twice out o the nine smples. We ttribute our better perormnce in predicting the rector type to our use o ORIGE-S nd its burnup dependent librries rther thn ORIGE-2. ble 1 shows tht ibes ccurtely predicted urnium enrichment within 4.1% nd burnup within 2.5%. However, the cooling time ws predicted with lrger errors mximum error o 1.42% or the sixth smple. his lrger error does not relect the inbility o ibes, but it might stem rom ACCEPED MASCRIP mesurement uncertinties in the monitors becuse it gve quite ccurte predictions or ll the test problems in Sec For the irst nd second smples o the nine, we tested gin with our rector cndidtes PWR, BWR, CAD, MAGOX to show ibes s bility to correctly predict the rector type. ibes gin correctly identiied the rector type s PWR. We considered only the irst two smples, which hve low burnups, becuse the CAD nd MAGOX librries do not contin cross section dt or higher burnups. 18

21 ACCEPED MASCRIP ext, we tested the smples with corrections or both urnium enrichment nd burnup, with results given in ble 11. A comprison o the results in bles 1 nd 11 shows tht with the corrections, ibes returned lrger discrepncies between the predicted nd reported vlues o burnups thn without corrections. he burnups predicted with the corrections re within 5.%, nd tht error is considered cceptble or orensic pplictions. On the other hnd, s shown in ble 11, the discrepncies o urnium enrichment nd cooling time predicted with the corrections re reduced compred with the no correction cses. ble 11 lso reports the predicted vlues rom Re. 1 or comprison with our results. his comprison shows tht ibes predicted the burnups nd cooling times with similr discrepncies to those reported in Re. 1, wheres the discrepncies or urnium enrichments predicted by ibes re slightly lrger thn those given in Re. 1, but they remin within 3.4% ble Summry nd Conclusion We successully developed progrm clled ibes to predict burnup history prmeters, such s urnium enrichment, burnup, nd cooling time, using isotopic mesurement dt rom spent nucler uel. his progrm uses simple lgebric equtions or the initil estimtion nd burnup to reduce computing time. hen, it corrects those initil estimtions using newly developed stble bi-section method coupled with ORIGE-S depletion clcultions to ACCEPED MASCRIP improve the ccurcy. he use o ORIGE-S, with its burnup dependent librries, rther thn ORIGE-2, provides lexibility in the pplicble rector types nd improves the ccurcy. he vlidtion o ibes ws done using two-step procedure. In the irst step, we tested ibes with vrious test problems or dierent rector types: PWR, BWR, CAD, nd MAGOX. he test problems were prepred by extrcting the tomic number densities o the monitor nuclides rom ORIGE-S output iles ollowing depletion clcultions with the given 19

22 ACCEPED MASCRIP burnups, urnium enrichments, nd cooling times. he extrcted tomic number densities were then used s input iles or ibes. he results show tht ibes correctly predicted the rector types in ll cses except or one MAGOX cse with n extremely short cooling time. ibes lso estimted the given burnups, urnium enrichments, nd cooling times quite ccurtely or ll test cses. In the second step, ibes ws pplied to the nine smples o spent uel rom the Mihm-3 rector with PIE isotopic mesurement dt. With those relistic problems, ibes estimted the burnups, urnium enrichments, nd cooling times within 5.1%, 3.4%, nd 1.3%, respectively. In the results o test problems with known solutions, discrepncies between the vlues ibes estimted nd the mesured vlues re prtilly cused by uncertinties in the mesurements o the spent uel smples. he results o the test problems nd relistic Mihm-3 smples show tht ibes cn successully estimte burnup history prmeters nd be pplied to spent nucler uels rom vrious nucler rector types. Acknowledgements he work ws supported by KIAC Kore Institute o ucler onproliertion nd Control. Reerences [1] M. R. Scott, ucler Forensics : Attributing the Source o Spent Fuel used in n RDD ACCEPED MASCRIP Event, M. S. hesis, exs A&M niversity 25. [2] M. Wllenius, K. Myer, I. Ry, ucler Forensic Investigtions : wo Cse Studies, Forensic Science Interntionl, vol.156, pp [3] A. Glser nd. Bieleeld, ucler Forensics : Cpbilities, Limits, nd the CSI Eect, 2

23 ACCEPED MASCRIP Presenttion mteril t the Conerence on Science nd Globl Security, Msschusetts Institute o echnology, Cmbridge, MA, July 24, 28. [4] R. J. J. Stmm ler et l., HELIOS Methods, Studsvik Scndpower, [5] M. Edenius et l., CASMO-3 A Fuel Assembly Burnup Progrm Methodology, SDSVIK/FA-89/2. [6] K. S. Kim, KARMA 1.2 Code Methodology Mnul, S6X8-A-2-R-7 Rev.1, Kore Atomic Energy Reserch Institute, 211. [7] J. Y. Cho et l., DeCAR v.1.2 ser s Mnul, KAERI/R-3438/27, Kore Atomic Energy Reserch Institute, 27. [8] S. Ludwig, ORIGE : he ORL Isotope Genertion nd Depletion Code, CCC-371/17, Ok Ridge tionl Lbortory 22. [9] D. Y. Kim nd S. G. Hong, Development o Inverse Estimtion Progrm o Burnup Histories or ucler Spent Fuel Bsed on ORIGE-S, rnsctions o the Koren ucler Society Autumn Meeting, Pyeongchng, Kore, October 3-31, 214. ACCEPED MASCRIP [1] S. G. Hong et l., Development nd Vlidtion o A Code System nd Extended Librry or Burnup History Estimtion o Spent Fuel bsed on the Mesurement o Environmentl Smples, KIAC/CR-3/215 B4-811, Kore Institute o ucler onproliertion nd Control, 215. [11] O. W. Hermnn nd R. M. Westll, ORIGE-S : SCALE System Module to Clculte 21

24 ACCEPED MASCRIP Fuel Depletion, Actinide rnsmuttion, Fission Product Buildup nd Decy, nd Associted Rdition Source erms, ORL/REG/CSD-2/V2/R6, Ok Ridge tionl Lbortory, [12] OECD/EA, Post Irrdition Exmintion or Exmintion or Spent Fuel Smple Mihm-3, [13] RISCC, SCALE 6.1 : A Comprehensive Modeling nd Simultion Suite or ucler Sety Anlysis nd Design; Includes ORIGE, CCC-785, Rdition Sety Inormtion Computtionl Center. [14] OECD/EA, Post Irrdition Exmintion or Exmintion or Spent Fuel Smple Cooper, [15] S. E. Jensen nd E. onbel, Description o the Mgnox ype o Gs Cooled Rector MAGOX, ISB , Rise tionl Lbortory, ACCEPED MASCRIP 22

25 ACCEPED MASCRIP List o ble Cptions ble 1. Atomic number density rtios o the monitor nuclides or the Mihm-3 PWR test problems ble 2. est results or the Mihm-3 PWR test problems ble 3. Atomic density rtios o the monitor nuclides or the Cooper BWR test problems ble 4. est results or the Cooper BWR test problems ble 5. Atomic density rtios o the monitor nuclides or the CAD test problems ble 6. est results or the CAD test problems ble 7. Atomic rtios o the monitor nuclides or the MAGOX test problems ble 8. est results or the MAGOX test problems ble 9. Atomic number density rtios o the monitor nuclides or the Mihm-3 problems with PIE smple mesurement dt ble 1. est results or the Mihm-3 problems with PIE smple mesurement dt without burnup correction ble 11. est results or the Mihm-3 problems with PIE smple mesurement dt with ACCEPED MASCRIP the burnup correction 23

26 ACCEPED MASCRIP List o Figure Cptions Fig. 1. Clcultion procedure in ibes Fig. 2. Min window o ibes grphic user interce ACCEPED MASCRIP 24

27 ACCEPED MASCRIP ble 1. Atomic number density rtios o the monitor nuclides or the Mihm-3 PWR test Monitor type uclides Burnup Enrichment Rector type Age 148 d p Pu 24 Pu 241 Pu 242 Pu 132 B 148 d 16 Ru 125 Sb 134 Cs 137 Cs problems Problem o E E E E-3 1.E+ 6.23E-5 3.3E E E E-5 b 1.24E-7 1.E+ 2.73E-6 1.8E E-6 5.7E E E-3 1.E+ 5.29E E-3 3.5E E E-6 1.E-7 1.E+ 2.16E E-7 2.2E E-4 4.1E E E E E E E E E-3 1.E+ 2.59E E E E E E-7 1.E+ 8.73E-6 3.2E E E E E-3 1.E+ 1.64E E-3 1.6E-3 4.6E E E-7 1.E+ 5.89E E E E-4 Atomic density rtio to, b Atomic density rtio to 148 d 1.92E E E E-3 1.E E E-5 1.4E E-3 4.2E-4 5.7E-3 2.2E E E E E E E E-3 1.7E-3 5.6E-4 ACCEPED MASCRIP 8.57E-3 4.4E E E E E E E E-3 1.E+ 1.E+ 1.E+ 1.E+ 1.E+ 2.33E-7 5.3E E E E E E E-3 5.7E E-7 1.E+ 1.E+ 1.E+ 1.E+ 1.E+ 5.56E-6 2.2E E E E E-6 3.3E-5 1.8E E E E E E E E-5 2.6E-3 1.5E E E-5 2.9E-3 25

28 ACCEPED MASCRIP Problem R* o ble 2. est results or the Mihm-3 PWR test problems Burnup MWD/kg Enrichment % Cooling time yers Reerence Predicted Reerence Predicted Reerence Predicted / b / / / b / / / / / / / / / / /.14 ACCEPED MASCRIP / b / / / / / / / / / / /.31 * Is rector type predicted correctly?, Predicted vlue, b Discrepncy between the predicted nd reerence vlues % 26

29 ACCEPED MASCRIP ble 3. Atomic density rtios o the monitor nuclides or the Cooper BWR test problems Monitor uclides type Burnup Enrichment Rector type Age Problem o d 6.41E E E E E E p Pu 24 Pu 241 Pu 242 Pu 132 B 148 d 16 Ru 125 Sb 134 Cs 137 Cs 5.3E E-3 1.E+ 3.55E E E E E-4 b 4.67E-7 1.E+ 1.15E E E-5 2.5E E-3 4.1E-3 1.E+ 3.45E E E-3 7.4E E E-7 1.E+ 1.12E E-6 3.3E-5 2.E-3 1.3E-2 3.E-3 1.E+ 1.66E E E E E E-7 1.E+ 5.75E-6 2.4E E E-3 Atomic density rtio to, b Atomic density rtio to 148 d 6.21E E-3 1.E+ 3.18E E E-3 7.6E-4 4.8E E-7 1.E+ 1.9E E E E-3 7.2E E-3 1.E+ 2.95E E E E E E E E-3 1.E+ 1.5E E E E E E-7 1.E+ 1.E+ 1.1E E E E E E-6 1.4E-5 1.8E-3 ACCEPED MASCRIP 27

30 ACCEPED MASCRIP Problem *R o ble 4. est results or the Cooper BWR test problems Burnup MWD/kg Enrichment % Cooling time yers Reerence Predicted Reerence Predicted Reerence Predicted / b / / b / / / / / b / / / / / / / / / /1.12 * Is rector type predicted correctly?, Predicted vlue, b Discrepncy between the predicted nd reerence vlues % ACCEPED MASCRIP 28

31 ACCEPED MASCRIP ble 5. Atomic density rtios o the monitor nuclides or the CAD test problems Monitor type uclides Burnup Enrichment Rector type Age 148 d Pu 24 Pu 241 Pu 242 Pu 143 d 148 d 24 Pu 16 Ru 125 Sb 134 Cs 137 Cs Problem o E E E E E E-4 5.7E E-3 2.8E-3 1.5E-3 1.5E-3 1.5E E E E-4 9.1E-4 9.9E-4 9.9E-4 1.E+ 1.E+ 1.E+ 1.E+ 1.E+ 1.E+ 1.16E-3 3.2E E E E-3 7.4E E E E E-5 6.8E E E E E E-6 8.8E E E E E E E-4 ACCEPED MASCRIP 2.82E-3 b 3.9E+ 2.57E+ 2.23E+ 2.2E+ 1.99E+ 2.2E+ 1.E+ 1.E+ 1.E+ 1.E+ 1.E+ 1.E+ 3.14E+ 6.35E+ 7.21E+ 7.37E+ 7.37E+ 7.37E+ 5.6E-7 9.1E E E E-6 2.E E-4 1.8E E E E E-6 6.8E-6 1.2E E E E E E-5 Atomic density rtio to, b Atomic density rtio to 148 d 3.2E E-4 6.7E E E-4 29

32 ACCEPED MASCRIP Problem *R o ble 6. est results or the CAD test problems Burnup MWD/kg Enrichment % Cooling time yers Reerence Predicted Reerence Predicted Reerence Predicted / b / b / b / / / / / / / / / / / / /1.25 ACCEPED MASCRIP 5 5.5/ /6.25 * Is rector type predicted correctly?, Predicted vlue, b Discrepncy between the predicted nd reerence vlues % 3

33 ACCEPED MASCRIP ble 7. Atomic rtios o the monitor nuclides or the MAGOX test problems Monitor type uclides Burnup Enrichment Rector type Age 148 d Pu 24 Pu 241 Pu 242 Pu 143 d 148 d 24 Pu 16 Ru 125 Sb 134 Cs 137 Cs Problem o E E E E E E E E E E-3 8.1E E E E-4 8.7E-5 1.5E E E E E E-4 1.E+ 1.E+ 1.E+ 1.E+ 1.E+ 2.45E E E E E E E E E E-4 1.E+ 2.12E-5 1.2E E-6 1.5E-5 b 2.41E+ 2.83E+ 2.96E+ 3.1E+ 2.73E+ 4.42E-6 1.E+ 1.E+ 1.E+ 1.E+ 8.64E+ 7.49E+ 6.7E+ 5.44E+ 7.49E+ 5.62E E E E E E-6 6.4E E E E E-6 6.1E E E E E E-4 1.2E-4 2.7E-4 Atomic density rtio to, b Atomic density rtio to 148 d ACCEPED MASCRIP 31

34 ACCEPED MASCRIP Problem *R o ble 8. est results or the MAGOX test problems Burnup MWD/kg Enrichment % Cooling time yers Reerence Predicted Reerence Predicted Reerence Predicted 8 8.2/ b / b / b / / / / / / / /.97 o / / /41.18 ACCEPED MASCRIP 5 5.4/.79 * Is rector type predicted correctly?, Predicted vlue, b Discrepncy between the predicted nd reerence vlues % 32

35 ACCEPED MASCRIP ble 9. Atomic number density rtios o the monitor nuclides or the Mihm-3 problems Monitor type uclides Burnup Enrichment Rector type Age 148 d p Pu 24 Pu 241 Pu 242 Pu 143 d 148 d 24 Pu 16 Ru 125 Sb 134 Cs 137 Cs with PIE smple mesurement dt Problem o E E E E E E E-4 6.2E E E E-3 1.E+ 7.1E E E E E-6 b 3.1E+ 1.E+ 2.91E+ 2.61E E-7 3.8E E E E-3 1.E+ 5.78E E E-4 8.5E E E+ 1.E+ 2.82E+ 2.7E-6 9.2E E E E E-3 1.E E E E E-4 2.6E+ 1.E+ 3.99E+ 7.85E E E E-3 2.E E-3 1.E+ 1.65E E-3 1.8E E-4 7.6E E+ 1.E+ 3.86E+ 5.8E E-6 1.1E E E E E E-3 1.1E E E-5 1.8E E-3 ACCEPED MASCRIP E-3 2.2E E E E E E-3 2.4E E E E-3 4.9E E E-3 1.4E E E E-3 1.E+ 1.E+ 1.E+ 1.E+ 1.E+ 4.98E E E E E E+ 2.37E+ 2.3E+ 2.21E+ 2.2E+ 1.E+ 1.E+ 1.E+ 1.E+ 1.E+ 4.14E+ 4.6E+ 4.2E+ 3.93E+ 4.5E+ 5.77E E E E-4 Atomic density rtio to, b Atomic density rtio to 148 d 1.9E-5 3.6E E E E E-6 4.2E E E E-6 4.5E-5 2.1E E E E-5 2.3E-3 33

36 ACCEPED MASCRIP ble 1. est results or the Mihm-3 problems with PIE smple mesurement dt without burnup correction Problem Burnup MWD/kg Enrichment % Cooling time yers *R o. Reerence Predicted Reerence Predicted Reerence Predicted / b / / / / / / / / / b / / / / / / /1.34 ACCEPED MASCRIP / b / / / / / / / / /6.3 * Is rector type predicted correctly?, Predicted vlue, b Discrepncy between predicted nd reerence vlues % 34

37 ACCEPED MASCRIP ble 11. est results or the Mihm-3 problems with PIE smple mesurement dt with the burnup correction Problem Burnup MWD/kg Enrichment % Cooling time yers *R o. Reerence Discrepncy Reerence Discrepncy Reerence Discrepncy b 4.38/ c b.37/ c b 3.9/ c / / / / / / / / / / / /3.4.9/.96./ /1.4.31/2.42./.7 ACCEPED MASCRIP / / / / / / /2.2 * Is rector type predicted correctly?, Discrepncy between the predicted nd reerence vlues %, b exs A&M, c ibes 35

38 ACCEPED MASCRIP Input File &XS File Processing SOP Rector ype Determintion Age Determintion Burnup & Enrichment pdte Finl Enrichment & Burnup XX_rtio guess & Initil Burnup Estimtion Repet two or three times Initil Enrichment Estimtion Repet until it converges Repet until it converges Fig. 1. Clcultion procedure in ibes Initil Enrichment & Burnup ORIGE-S Adjust Enrichment ORIGE-S Adjust Burnup ACCEPED MASCRIP 36

39 ACCEPED MASCRIP Fig. 2. Min window o ibes GI ACCEPED MASCRIP 37