Fission Product Decay Heat Calculations for Neutron Fission of 232 Th

Transcription

1 Journal of Physcs: Conference Seres PAPER OPEN ACCESS Fsson Product Decay Heat Calculatons for Neutron Fsson of 3 Th To cte ths artcle: P N Son and N X Ha 016 J. Phys.: Conf. Ser Related content - The Manhattan Project: The background B C Reed - The Manhattan Project: Nuclear fsson B C Reed - Knetc Energy Effects n the Thermal Neutron Fsson of 35 U T J Goodng Vew the artcle onlne for updates and enhancements. Ths content was downloaded from IP address on 06/0/018 at 01:9

2 Fsson Product Decay Heat Calculatons for Neutron Fsson of 3 Th P N Son and N X Ha Nuclear Research Insttute, 01-Nguyen Tu Luc, Dalat, Vetnam E-mal: pnson.nr@gmal.com Abstract. Precse nformaton on the decay heat from fsson products followng tmes after a fsson reacton s necessary for safety desgns and operatons of nuclear-power reactors, fuel storage, transport flasks, and for spent fuel management and processng. In ths study, the tmng dstrbutons of fsson products' concentratons and ther ntegrated decay heat as functon of tme followng a fast neutron fsson reacton of 3 Th were exactly calculated by the numercal method wth usng the DHP code. 1. Introducton In a fsson reacton, fsson products (FP) are ntally formed wth known concentratons as ndependent fsson yelds, but ths data stll changes followng tmes after the fsson events. Ths s manly because of the natural decay of radoactve fsson products. In nuclear scence and technology, the concentratons of fsson products as functons of decay tme are the key data requred n aggregate decay heat calculatons for desgns and operatons of nuclear-power reactors, fuel storage, transport flasks, and for spent fuel management and processng [1, ]. Gamma and beta decay energes released from natural decay of the fsson products contrbute approxmately 7% to 1% of the total energy generated through the fsson process; ths component of power s called Decay Heat. After a reactor s shutdown, ths source of radoactve decay energy stll remans and cumulatvely ncreases that necessary to apply a heat removal system for mantanng the safety level of temperature nsde the reactor core. In nuclear reactor technology, thorum s consderng as a potental fuel materal that could possbly supplement or even replace natural uranum [3]. 3 Th s the naturally-occurrng sotope wth abundance of nearly 100%, and can be used as breedng-fuel materal by capturng neutrons n a thermal and epthermal neutron flux to form 33 Th sotope and subsequently decay to produce uranum-33 ( 33 U), whch s an excellent fssle materal for nuclear energy producton [4]. For fast reactors, n whch thorum-3 s used as the breedng-fuel component that drven by a fast neutron spectrum, 3 Th s also fssonable wth ncdent neutrons wth energy above one MeV; and the decay energes of ts fsson products would sgnfcantly contrbute to the decay heat power n the spend fuel. Accordngly, the updated knowledge of tmng dstrbutons or behavour of concentratons and decay heat energes by fsson products from fsson reacton of 3 Th s essental necessary n research and applcaton of fast reactor technology. In ths work, the DHP program [5], a numercal calculaton code, was used for calculaton of fsson products decay heat data for fast neutron fsson of 3 Th. The method used n ths calculaton s analyss procedure on the general solutons of the Bateman s Equatons [6] for every full complex decay chan, n whch the real-tme buld-up and decay of FP nucldes are determned. Based on the Content from ths work may be used under the terms of the Creatve Commons Attrbuton 3.0 lcence. Any further dstrbuton of ths work must mantan attrbuton to the author(s) and the ttle of the work, journal ctaton and DOI. Publshed under lcence by Ltd 1

3 decay and fsson yeld data from JENDL 4.0 [7], the concentraton of each FP nuclde s determned as functons of coolng tme after a fsson event. The dffcultes of the complex systems of the decaychans are solved by an addtonal computatonal algorthm mplemented n the DHP code.. Analyss of Decay and Buld-up Numbers The number of th nuclde at coolng tme t after a fsson burst can be calculated from the followng equaton: N ( t) = N (0) exp( λ t) + N ( t) n whch, N (0) s equal to the ndependent fsson yeld of the th nuclde; the component of N j-> (t) s the buld-up number of nuclde th at coolng tme t, that was formed n the system of decay chans orgnated from the nuclde j th. Ths term of the buld-up number can be obtaned by the general solutons of the Bateman s equaton for every partcular lnear decay chan. In ths work, we developed a numercal algorthm to calculate the term of N j (t) n equaton (1) drectly by usng the decay and fsson yeld data from JENDL4.0 [7] and/or the evaluated nuclear structure data fle ENSDF [8]. The calculaton procedure s generalzed as the followng steps [9]: For every nuclde j th, the decay net that started from the nuclde j th s separated to form equvalent sub-branches of lnear decay chans. For each lnear decay chan, f the nuclde th s a daughter nuclde n the decay chan, apply the general soluton of Bateman s equaton to calculate the buld up number of nuclde th due to the decay of nuclde j th through the current lnear decay chan, as of the coolng tme t. The total number N (t) can be obtaned by summng all the buld-up numbers of nuclde th from all the lnear decay chans n whch the buld-up numbers are calculated by apply the general soluton of Bateman s equaton [6] for every lner decay branch n a dfferental perod of tme Δt. Let consder to a lnear decay branch of n nucldes: M j j N1 N N3... N... N The buld-up number of nuclde N due to the decay of nuclde N -1 s calculated by the dfferental equaton: dn () t = λ 1N 1() t λn() t dt In case of {N j (t) 0 and all of the reman nucldes N 1,,...j-1,j+1,...,...M (t) = 0 at t = 0}, the soluton of buld-up number for N (t) contrbuted from nuclde N j at t > 0 s express as: n (1) () m N j () t Cme λ = m= j t (3) C m = k= j k m 1 k k= j. N j(0) ( λ λ ) k λ m (4)

4 In general case of {N j (t) 0 ; j = 1,, 3,... n at t = 0}, the total buld-up number of tme dependent N (t), at t > 0, contrbuted from all of other nucldes n a lner decay branch can be estmated as the followng general expresson. 1 λm e t N () t = N (0) ( λq λm) q= l q m j l j l= 1 k= l m= l A computatonal procedure for exact calculaton of the tme-dependent dstrbuton of fsson product concentraton, N (t), has been developed and ntegrated n the DHP code. In ths calculaton, all of decay chans and decay modes ncludng β - decay to ground state, frst and second somer states, double β - decay, electron capture decay to ground and somer states, alpha decay, delay β - decay, and nternal transtons n the fsson product system are taken nto consder n ths calculaton. The block dagram of the DHP computatonal algorthm and wndow nterface are shown n Fgure and Fgure 3, respectvely. The results of calculaton for tmng concentraton functons of several fsson product nucldes for tmes after a fsson reacton of 3 Th are shown n Fgure 1, n whch decay characterstcs for every fsson product and the ndependent neutron fsson yelds were extracted from JENDL4.0 [7]. (5) Fgure 1. Calculated Results of concentraton functons for a number selected fsson products after a fast neutron fsson reacton of 3 Th 3. Beta Decay Average Energes Calculatons The average energy values of beta and gamma-rays released from beta decay of ndvdual fsson product are the most mportant quanttes for nuclear decay heat summaton predcton. The expressons for average beta and gamma-ray energes based on the Gross theory of beta decay were appled n these calculatons [10, 11]. 3

5 E β = T 0 Eg / S β ( E) mc ( E 1) pe( Eg + 1 E) F( E) Q 1 dede g (6) E γ = T 0 Eg / S β ( E) mc ( Q + E g ) pe( E g + 1 E) F( E) Q 1 dede where: F(E) stands for the Ferm functon. E g s related to the exctaton energy E as E g = -(E -1); m, p and c denotes for electron rest mass, electron momentum and lght velocty, respectvely. The beta strength functon S β (E) can be determned from the beta feedng functon I β (E) as the followng formula: Sβ ( E) = I β ( E) f ( ZQ, ET ). f(z, Q β -E) s the ntegrated Ferm functon. Q, E and T 1/ are the beta decay energy, exctaton energy n the daughter nuclde and the half-lfe, respectvely. The functon I β (E) can be systematcally normalzed based on the beta branchng ntenstes adopted from the ENSDF data fle, or expermentally derved from measured dstrbutons of beta decay ntensty. The calculated results of average beta and gamma energes from beta decay for several selected fsson products are shown n Table 1. 1/ g (7) (8) Fgure. The block dagram of the computatonal procedure. 4

6 Fgure 3. The wndow nterface of the DHP program. Table 1. The calculated average beta and gamma energes for selected nuclde. Nuclde Q (MeV) T1/ (s) (a) (b) E β (MeV) E γ (MeV) E β (MeV) E γ (MeV) Rb Rb Rb-90m Rb Rb Sr Sr Sr Y Y Cs Cs-138m Cs Cs Cs Ba Ba Ba Ba Ba La La La La Ce Ce Ce Ce Pr

7 Pr Pr Pr-148m Pr Pr Nd Nd Nd Nd Nd Pm Pm Pm Pm Pm Pm Sm Sm Eu (a): Calculated wth I β (E) from ENSDF [8] (b): Calculaton wth I β (E) from expermental ntenstes [1] The average energes shown n Table 1 are calculated n two cases: (a) calculated based on the nput data of branchng ntenstes extracted from the ENSDF data fles; (b) calculated from the expermental beta decay ntenstes measured by Greenwood et al. [1] n whch a total absorpton gamma-rays spectrometer (TAGS) was used; TAGS s an effcent expermental method for average energes determnatons, that overcome the problem of pandemonum effects [13]. 4. Results of Calculatons The summaton model for decay heat calculatons s as the followng functon: M f () t = EλN() t = 1 where: M denotes the maxmum number of FP nucldes; E = E β + E γ stands for the mean energy per decay of the th nuclde, λ the decay constant, N (t) the correspondng concentraton functon for coolng tme f(t) s the burst functon of decay heat (MeV/Fsson/s). The physcal quantty equal to t f(t) s called decay heat power functon (MeV/Fsson). In ths work, the JENDL FP Decay Data Fle 011 [14] and fsson yeld data fle from JENDL 4.0 [7] have been appled for calculatons of fsson product concentratons as functons of coolng tme after fast neutron fsson reactons of 3 Th, and these results were adopted n decay heat calculatons. The results of calculatons for t f(t), as functons of tmes after a fsson event, are shown n Table and Fgure 4 n comparson wth measured values by Akzama 198 [15]. Table. Calculated fsson product decay heat for tmes after fast neutron fsson of 3 Th Decay Heat t f(t) Tme after Decay Heat t f(t) Tme after (MeV/Fsson) fsson burst (s) (MeV/Fsson) fsson burst (s) Beta Gamma Total Beta Gamma Total 1.10E E E E E E E E E E E E (9) 6

8 5.10E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E Fgure 4. Calculated fsson product decay heat after fast neutron fsson of 3 Th 5. Conclusons In the present work, the computer code DHP has been mproved for calculaton procedure and updated for new avalable nuclear databases. Calculatons have been carred out for the decay and growth dstrbutons of concentratons for fsson products from fast neutron fsson of 3 Th. The calculated data of fsson product concentratons were then ntroduced nto summaton calculatons of total and partal decay heat followng tmes after fsson burst. The decay and fsson yeld data used n ths work s extracted from JENDL FP Decay Data Fle and fsson yeld data fle 011 [14]. As shown n Table and Fgures 4, wthn the decay tme perod from 1 10 s to s, the present calculated 7

9 results are agreements wth the expermental values measured by Akzama [15]. It s also estmated that the updated DHP code can be used for calculatons of fsson product nventory concentratons and decay heat data exactly. Acknowledgments Ths research was partly funded by Vetnam Natonal Foundaton for Scence and Technology Development (NAFOSTED) under grant number References [1] Nchols A L 00 Nuclear Data Requrements for Decay Heat Calculatons Lectures gven at the Workshop on Nuclear Reacton Data and Nuclear Reactors: Physcs, Desgn and Safety, Treste, 00 [] Oyamatsu K 1999 Easy-To-Use Applcaton Programs to Calculate Aggregate Fsson Product Propertes on Personal Computers JEARI-Conf [3] Kazm M S, Czerwnsk K R, Drscoll M J, Hejzlar P and Meyer J E 1999 On the Use of Thorum n Lght Water Reactors MIT-NFC-TR-016 [4] OECD 015 Introducton of Thorum n the Nuclear Fuel Cycle, NEA No. 74 [5] Son P N and Katakura J 007 An Applcaton Program for Fsson Product Decay Heat Calculatons JAEA-Data/Code [6] Tobas A 1980 Prog. Nucl. Energy 5 1 [7] Shbata K O, et al 011 J. Nucl. Sc. Technol [8] Bhat M R 199 Evaluated Nuclear Structure Data Fle (ENSDF), Nuclear Data for Scence and Technology, Edted by Qam S M, Sprnger-Verlag, Berln, Germany, Page 817 [9] Son P N 014 Int. J. of Nucl. Ener. Sc. and Engnee [10] Katakura J, Yoshda T, Oyamatsu K, and Tachbana T 001 JENDL FP Decay Data Fle 000 JAERI-1343 (001) [11] Yoshda T and Katakura J 1986, Nucl. Sc Eng [1] Greenwood R C, Helmer R G, Putnam M H, and Watts K D 1997 Nucl. Instr. Meth. A [13] Hardy J C, Carraz L C, Jonson B and Hansen P G 1977 Phys. Letts. 71B() 307 [14] Katakura J 011 JENDL FP Decay Data Fle 011 and Fsson Yelds Data Fle 011 JAEA- Data/Code [15] Akyama M and An S 198 Measurement of fsson-product decay heat for fast reactors Proc. Int. Conf. on Nuclear Data for Scence and Technology, Antwerp Belgum (198): pp