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Analisa Burnup Zaki Su’ud. Pengertian analisa burnup Analisa yang berkaitan dengan perubahan jangka panjang (hari-bulan-tahun) komposisi bahan-bahan dalam.

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Presentasi berjudul: "Analisa Burnup Zaki Su’ud. Pengertian analisa burnup Analisa yang berkaitan dengan perubahan jangka panjang (hari-bulan-tahun) komposisi bahan-bahan dalam."— Transcript presentasi:

1 Analisa Burnup Zaki Su’ud

2 Pengertian analisa burnup Analisa yang berkaitan dengan perubahan jangka panjang (hari-bulan-tahun) komposisi bahan-bahan dalam reaktor akibat berbagai reaksi nuklir yang terjadi saat pengoperasian reaktor nuklir Bahan-bahan pecahan reaksi fisi jumlahnya sangat banyak (lebih dari 1200 nuklida) dan karakteristiknya sangat beragam

3 Analisa burnup secara umum Proses burnup merupakan mekanisme yang sangat kompleks yang dipengaruhi berbagai faktor seperti komposisi bahan teras, distribusi fluks netron, temperatur, histori pengoperasian reaktor, dsb. Beberapa program analisis burnup telah disiapkan untuk operasi yang bersifat standar misalnya terkait PLTN yang banyak dioperasikan

4 Analisa Burnup secara umum(2) Akan tetapi untuk kasus-kasus khusus misalnya menyangkut advanced NPP yang memiliki skema fuel cycle yang cukup kompleks maka diperlukan program yang lebih komprehensif Dalam beberapa kasus program-program analisis yang ada pun perlu dimodifikasi agar cukup akuran dalam menganalisa kasus tersebut

5 Contoh rantai burnup

6 Persamaan Burnup terkait

7 CONTOH DERET BURNUP YANG DISEDERHANAKAN Am-241 ^ Pu-239  Pu-240  Pu-241  Pu-242 ^ Np-239 ^ U-238  U-239

8 Persamaan Burnup untuk deret yang disederhanakan

9 Persamaan Burnup untuk deret yang disederhanakan(2)

10 Solusi numerik Ada sangat banyak metoda yang dapat digunakan untuk memecahkan persamaan burnup Di sini diberikan contoh yang bersifat standar diantaranya metoda eksplisit berbasis finite difference dan metoda semi implisit berbasis finite difference juga Metoda eksplisit mudah dirumuskan hanyasaja mempunyai tingkat stabilitas yang lebih rendah dari metoda implisit

11 Solusi Numerik Finite difference Eksplisit

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15 Metoda Implisit Pada metoda implisit ruas kanan diisi dengan kombinasi duku pada iterasi waktu ke i dan i+1 dengan bobot yang dinyatakan dalam parameter tertentu Metoda numerik jauh lebih rumit perumusannya dari metoda eksplisit tetapi memiliki keunggulan stabilitas yang jauh lebih tinggi

16 Solusi Numerik Finite difference Implisit

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19 Solusi Numerik Finite difference Eksplisit

20 Metoda semi analitik Metoda analitik seperti yang dirumuskan dalam Bateman equation memiliki akurasi yang tinggi Kendalanya metoda ini sangat rumit untuk deret yang panjang, hanya dapat diterapkan dalam deret linier, serta tak dapat digunakan untuk rantai siklus Solusinya adalah dengan menggunakan metoda semi analitik

21 Metoda Semi analitik(2) Dalam metoda semi analitik maka rantai burnup dipotong-potong dengan panjang potongan yang diatur sesuai dengan kebutuhan/optimasi Selanjutnya dilakukan iterasi burnup untuk masing-masing potongan rantai secara pereodik Selanjutnya dilakukan updating nilai konsentrasi nuklida untuk tiap jenis nuklida

22 THEORY BURN UP EQUATION An explicit Burn Up equation for each nuclide is : where N i =concentration of ith nuclide λ i =decay constant of ith nuclide σ a,i =absorb microscopic cross section for ith nuclide Ф =neutron flux of nuclide S m,i =production speed of ith nuclide from mth nuclide

23 BATEMAN SOLUTION Bateman equation is one of analytic method to solve transmutation process in linear chain depend on time evolution General solution for linear chain of transmutation process

24 SIMULATION 192234922359223624942389223492235479524294242942439524395244 292235922369223793237259423994240942414895242962429624396244 39223692237932379323894238269424094241942424995242962429624394239 492237 932389323994239279424094241952415095242962429423894239 592237 93238942389423928942419424294243952435195242962429423892234 692237 932389423892234299424195241957425295243952449624496245 7922389223993239932409424030942419524195742962425395243952449624494240 892238922399323994239942383194241952419524294242549524496244 94246 99223892237932379323894241329424295241932375595244962449424094241 1092239932399324094240942413394243 95243952449624456962429624396244 119223993239942399424034942439524395244962449624557962429624394239 129323793238932399423935952419524395244962449424058962429423894239 13932379323894238942393695241957429524359962429423892234 1493237932389423892234379524195742952429424260962439624496245 1593238932399324094240389524195742952429624261962439624494240 169323893239942399424039952419524294242942439524362962439423994240 1793238942389423994240409524195242962429624363962449624596246 1893238942389223492235419524195242962429423864962449424094241 1993239932409424094241429524193237932389423865962459624696247 2093239942399424094241439574295243952449624466962469624796748 219324094240942419424244957429524294242942439524367962479624896749 22932409424094241952414595742952429624296243689624896249 2394238942399424046957429524296242962436996249 Linear series for analytical method

25 Burnup chain 1922349223592236 292235922369223793237 39223692237932379323894238 492237 932389323994239 592237 932389423894239 692237 932389423892234 79223892239932399324094240 89223892239932399423994238 99223892237932379323894241 109223993239932409424094241

26 Burnup chain(2) 1192239932399423994240 1293237932389323994239 1393237932389423894239 1493237932389423892234 1593238932399324094240 1693238932399423994240 1793238942389423994240 1893238942389223492235 1993239932409424094241 2093239942399424094241

27 Burnup chain (3) 2193240942409424194242 2293240942409424195241 23942389423994240 24942389223492235 25942399424094241 26942409424194242 27942409424195241 2894241942429424395243 29942419524195742 3094241952419574296242

28 Burnup chain (4) 3194241952419524294242 32942429524193237 3394243 952439524496244 349424395243952449624496245 359524195243952449624494240 36952419574295243 3795241957429524294242 3895241957429524296242 399524195242942429424395243 4095241952429624296243

29 Burnup chain (5) 4195241952429624294238 4295241932379323894238 4395742952439524496244 449574295242942429424395243 4595742952429624296243 4695742952429624296243 479524294242942439524395244 4895242962429624396244 4995242962429624394239 5095242962429423894239

30 Burnup chain (6) 5195242962429423892234 5295243952449624496245 5395243952449624494240 549524496244 94246 5595244962449424094241 56962429624396244 57962429624394239 58962429423894239 59962429423892234 60962439624496245

31 Burnup chain (7) 61962439624494240 62962439423994240 63962449624596246 64962449424094241 65962459624696247 66962469624796748 67962479624896749 689624896249 6996249

32 time Nuclide concentration (N U8 ) Nuclide concentration (N Pu239 ) time Nuclide concentration (N Pu240 ) time Nuclide concentration (N) time

33 BEBERAPA HAL PENTING TERKAIT ANALISA BURNUP Untuk reaktor cepat maka efek self shielding pada perubahan cross section microscopic tidak terlalu besar sehingga analisa burnup berbasis microscopic cross section dapat diterapkan Untuk reaktor thermal efek self shielding pada perubahan cross section microscopic cukup besar sehingga analisa burnup harus dilakukan dalam sel bahan bakar

34 BEBERAPA HAL PENTING TERKAIT ANALISA BURNUP(2) FP berjumlah lebih dari 1200 nuklida dan karakteristiknya bergantung jenis reaktor nuklir yang digunakan Untuk reaktor thermal ada beberapa FP yang sangat dominan sehingga dapat mewakili keseluruhan FP yang ada: misal Xenon, Sm, dll. Untuk reaktor cepat tak ada Fp yang terlalu dominan sehingga secara keseluruhan harus diperhitungkan

35 BEBERAPA HAL PENTING TERKAIT ANALISA BURNUP(3) Untuk reaktor cepat metoda yang biasa digunakan adalah menggunakan lumped FP atau menggunakan beberapa puluh nuklida FP dan sisanya menggunakan lumped FP Untuk perhitungan conversion/breeding ratio maka perlu dilakukan kalibrasi cross section fisi dan nilai v untuk masing-masing bahan fisil dominan Dalam hal digunakan sejumlah bahan fisil secara serempak maka dilakukan kalibrasi FP

36 Senstivitas Burnup pada Cross section

37 3/30/2015IAEA CRP RCM 21-25 Nov. 200537 Code Modification

38 3/30/2015IAEA CRP RCM 21-25 Nov. 200538 ParameterParameter Value/description SPINNOR ASPINNOR BVSPINNOR Installed capacity55 MWth / 20 MWe 27.5 MWth/ 10 MWe 17.5 MWth/ 6.25 MWe Operation life time (without refueling and fuel shuffling) 15 years25 years35 years Mode of operationBasic/load follow (selectable) Beyond 95% * Load factor Summary of major design characteristics - type of fuel - fuel enrichment - type of coolant/moderator - type of structural material UN-PuN** 10 – 12.5% Pb-Bi eutectic Stainless UN-PuN** 10 – 12.5% Pb-Bi eutectic Stainless UN-PuN** 10 – 12.5% Pb-Bi eutectic Stainless

39 3/30/2015IAEA CRP RCM 21-25 Nov. 200539 B1 B2 C1 C2 RR S RRR R R R R SS S S S S S SSS Radial direction

40 3/30/2015IAEA CRP RCM 21-25 Nov. 200540 outlet To stack Figure 1. Reactor assembly of SPINNOR AND VSPINNOR

41 3/30/2015IAEA CRP RCM 21-25 Nov. 200541 Burnup parametric study results: U238 fission 105% 102.5% 100% 97.5% 95%

42 3/30/2015IAEA CRP RCM 21-25 Nov. 200542 Burnup parametric study results:Pu-239 fission

43 3/30/2015IAEA CRP RCM 21-25 Nov. 200543 Burnup parametric study results:Pu-241 fission

44 3/30/2015IAEA CRP RCM 21-25 Nov. 200544 Burnup parametric study results: U-238 capture

45 3/30/2015IAEA CRP RCM 21-25 Nov. 200545 Burnup parametric study results: Pu-239 capture

46 3/30/2015IAEA CRP RCM 21-25 Nov. 200546 Burnup parametric study results: Pu-240 capture

47 3/30/2015IAEA CRP RCM 21-25 Nov. 200547 Burnup parametric study results: FP capture

48 3/30/2015IAEA CRP RCM 21-25 Nov. 200548 Burnup parametric study results: Pb capture

49 3/30/2015IAEA CRP RCM 21-25 Nov. 200549 Burnup parametric study results: Bi capture

50 3/30/2015IAEA CRP RCM 21-25 Nov. 200550 Burnup parametric study results: Pb transport

51 3/30/2015IAEA CRP RCM 21-25 Nov. 200551 Burnup parametric study results: Bi transport

52 3/30/2015IAEA CRP RCM 21-25 Nov. 200552 Burnup parametric study results: FP scattering

53 3/30/2015IAEA CRP RCM 21-25 Nov. 200553 Burnup parametric study results: Pb scattering

54 3/30/2015IAEA CRP RCM 21-25 Nov. 200554 Burnup parametric study results: Bi scattering

55 3/30/2015IAEA CRP RCM 21-25 Nov. 200555 Burnup parametric study results: Pu-239 fission  conversion ratio

56 3/30/2015IAEA CRP RCM 21-25 Nov. 200556 Burnup parametric study results: U-238 capture  conversion ratio

57 3/30/2015IAEA CRP RCM 21-25 Nov. 200557 Burnup parametric study results: FP capture  conversion ratio

58 3/30/2015IAEA CRP RCM 21-25 Nov. 200558 Burnup parametric study results: Pu239 fission  coolant void coefficient

59 3/30/2015IAEA CRP RCM 21-25 Nov. 200559 Burnup parametric study results: U-238 capture  coolant void coefficient

60 3/30/2015IAEA CRP RCM 21-25 Nov. 200560 Burnup parametric study results: FP capture  coolant void coefficient

61 3/30/2015IAEA CRP RCM 21-25 Nov. 200561 Burnup parametric study results: Pb scattering  coolant void coefficient

62 3/30/2015IAEA CRP RCM 21-25 Nov. 200562 Conclusion for Burnup parametric survey From the parametric survey results, we find that FP cross section is important to be considered to get reliable neutronic analysis results. Some other cross section is also critical such as U- 238 capture cross section and main fissile fission cross section, and Pb and Bi transport and scattering cross section. FP cross section is important to be treated in more accurate way to get better accuracy especially at the end of life.

63 INTRODUCTION:Background Small and very small nuclear power plant with moderate economical aspect is an important candidate for electric power generation in many part of the third world countries including outside Java- Bali area in Indonesia. The nuclear energy system with the range of 5-50 Mwe match with the necessity and planning of many cities and provinces outside Java-Bali islands. In addition to electricity, desalination plant or cogeneration plant is a good candidate for nuclear energy application

64 INTRODUCTION:Background Due to the difference of the load between afternoon and night the use of fast reactors is a better choice due to capability to follow the load. Lead and lead bismuth cooled nuclear power reactors is now considered as potential candidate of next generation nuclear power reactors in the 21th centuries. Various versions of lead cooled nuclear power reactors have been analyzed and safety analysis also have been applied to them. Accuracy of the simulation system need to be tested through international benchmark program under IAEA.

65 Introduction: Objective Solving FP treatment group constant with the following approach: First alternative: Rigorous treatment : We cover 165 nuclides with other relevant FP nuclides in direct individual burnup calculation. This method will give rigorous results but with considerable calculation time. However this method is important to test other simpler methods. Second alternative: Lumped FP treatment : We just build best FP lumped cross section for many general condition and use this FP group constant in burnup calculation. This method can give accurate results if the spectrum is same or near the spectrum to build the lumped FP cross section.

66 Introduction: Objective Third alternatives : Combination method: We treat some most important nuclides individually and treat the rest FP using lumped FP cross section. This method seems to be good alternative for general usage. Forth alternative : Lumped FP cross section with many interpolable parameter: We develop the concept similar to the back ground cross section in the Bondanrenko based cell calculation libraries. This will improve Lumped FP cross section results for general usage. Fifth alternative : We develop the few group effective FP similar to that in reactor kinetic problem. If we can get reasonable good few group effective FP then we can solve for all type of the core generally

67 METHODOLOGY Identifying the important FP nuclides which have strong influence to the overall FP cross section Identifying important FP decay chains relevant the important nuclides Analyzing the contribution of each FP nuclides to the overall FP crosssection based on the equilibrium model Analyzing the contribution of each FP nuclides to the overall FP crosssection based on the time dependent model

68 Identifying the important FP nuclides which have strong influence to the overall FP cross section Based on the study of Shiro TABUCHI and Takafumi AOYAMA we select 50 most important nuclides for fast reactors. Based on this selection we then identify relevant and important decay chains which should be considered. The 118 nuclides which has the contribution to the total FP cross section more than 0.01% are shown in the following table.

69 Table 1 118 Important FP Nuclides No Z A %X-sect Symbol 1 44 101 8.93 Ru 2 46 105 8.93 Pd 3 43 99 7.06 Tc 4 45 103 6.02 Rh 5 55 133 5.72 Cs 6 46 107 4.65 Pd 7 42 97 4.54 Mo 8 62 149 4.39 Sm 9 61 147 3.77 Pm 10 60 145 3.37 Nd 11 55 135 2.74 Cs 12 60 143 2.64 Nd 13 54 131 2.38 Xe 14 44 102 2.21 Ru 15 62 151 2.19 Sm 16 42 95 2.15 Mo 17 42 98 1.89 Mo 18 47 109 1.80 Ag 19 44 104 1.69 Ru

70 20 42 100 1.58 Mo 21 63 153 1.56 Eu 22 40 93 1.27 Zr 23 44 103 1.19 Ru 24 59 141 1.03 Pr 25 53 129 0.97 I 26 40 95 0.88 Zr 27 40 96 0.75 Zr 28 60 146 0.70 Nd 29 54 132 0.69 Xe 30 46 108 0.68 Pd 31 41 95 0.67 Nb 32 58 141 0.62 Ce 33 40 91 0.61 Zr 34 40 92 0.48 Zr 35 54 134 0.48 Xe 36 44 106 0.48 Ru 37 62 152 0.48 Sm 38 60 148 0.46 Nd 39 48 111 0.44 Cd 40 37 85 0.43 Rb41 53 127 0.42 I 42 57 139 0.42 La 43 46 106 0.41 Pd 44 63 155 0.35 Eu 45 40 94 0.32 Zr 46 62 147 0.31 Sm 47 58 142 0.29 Ce 48 60 150 0.28 Nd 49 60 147 0.26 Nd 50 55 137 0.25 Cs 51 39 91 0.20 Y 52 60 144 0.19 Nd 53 36 83 0.19 Kr 54 58 144 0.18 Ce 55 64 157 0.18 Gd 56 46 110 0.14 Pd 57 42 99 0.14 Mo 58 64 156 0.13 Gd 59 48 113 0.11 Cd

71 60 55 134 0.11 Cs 61 63 154 0.10 Eu 62 58 140 0.10 Ce 63 51 125 0.10 Sb 64 65 159 0.10 Tb 65 62 154 0.10 Sm 66 38 90 0.10 Sr 67 53 131 0.09 I 68 39 89 0.09 Y 69 56 138 0.08 Ba 70 59 143 0.08 Pr 71 35 81 0.08 Br 72 52 130 0.08 Te 73 49 115 0.08 In 74 52 128 0.07 Te 75 48 112 0.07 Cd 76 52 129m 0.07 Te 77 37 87 0.06 Rb 78 36 84 0.06 Kr 79 54 133 0.05 Xe 80 51 121 0.05 Sb81 52 127m 0.05 Te 82 61 148m 0.05 Pm 83 34 79 0.05 Se 84 45 105 0.05 Rh 85 62 150 0.04 Sm 86 51 123 0.04 Sb 87 64 155 0.03 Gd 88 50 117 0.03 Sn 89 61 149 0.03 Pm 90 54 136 0.03 Xe 91 46 104 0.03 Pd 92 64 158 0.03 Gd 93 44 100 0.03 Ru 94 36 85 0.03 Kr 95 38 89 0.03 Sr 96 48 114 0.02 Cd 97 38 88 0.02 Sr 98 50 119 0.02 Sn 99 62 148 0.02 Sm

72 100 34 82 0.02 Se 101 56 136 0.02 Ba 102 47 110m 0.02 Ag 103 34 77 0.01 Se 104 36 86 0.01 Kr 105 63 156 0.01 Eu 106 34 80 0.01 Se 107 63 151 0.01 Eu 108 48 116 0.01 Cd 109 50 118 0.01 Sn 110 48 110 0.01 Cd 111 34 78 0.01 Se 112 54 130 0.01 Xe 113 56 137 0.01 Ba 114 64 160 0.01 Gd 115 56 140 0.01 Ba 116 50 126 0.01 Sn 117 52 125 0.01 Te 118 50 120 0.01 Sn

73 Identifying important FP decay chains relevant the important nuclides (1) 84m Br 6.0m 84 Ga  84 Ge  84 As  84 Se 84 Kr 0.085s 0.95s 3.2s 3.1m stable 84 Br 31.8m (2) 85mKr 4.48h 85Ga  85Ge  85As  85Se  85Br 85Rb (0.09s) 0.54s 2.02s 31.7s 2.90mstable 85Kr 10.77y

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85 II.3 Analyzing the contribution of each FP nuclides to the overall FP crosssection based on the equilibrium model Based on the relevant and important decay chains, differential equation for the model can be derived. And using equilibrium approximation model we can obtain the formula for the contribution of each nuclide for certain flux level. Detail process will be discussed in the next part.

86 Analyzing the contribution of each FP nuclides to the overall FP cross section based on the time dependent model To see the process toward equilibrium, the time dependent change of each important nuclides is calculated. The calculation is performed based on the most important equation using analytical method or numerical methods

87 MATHEMATICAL MODEL DESCRIPTION AND THE METHODOLOGY OF SOLUTION 1. Simplification of Decay Scheme and Mathematical Model

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102 Table 2 Cumulative fission yield (Form JNDC) _______________________________ Kr-85m 6.10677000000000025E-1 Y -91 2.43774999999999986E+0 Zr-92 2.95633999999999997E+0 Zr-93 3.67079000000000022E+0 Zr-94 4.26259000000000032E+0 Zr-95 4.70092999999999961E+0 Zr-96 4.78516399999999997E+0 Mo-97 5.27359000000000044E+0 Mo-98 5.62816999999999990E+0 Tc-99 5.98852000000000029E+0

103 Mo-100 6.58037000000000027E+0 Ru-101 6.54110999999999976E+0 Ru-102 6.63984000000000041E+0 Ru-103 6.83164999999999978E+0 Ru-104 6.51982000000000017E+0 Pd-105 5.41333999999999982E+0 Ru-106 4.36779000000000028E+0 Pd-107 3.05134600000000011E+0 Pd-108 1.90365600000000001E+0 Ag-109 1.92017700000000002E+0 Cd-111 3.55362000000000011E-1 I -127 5.52984999999999949E-1 I -129 1.63166999999999995E+0 Xe-131 3.86864000000000008E+0 Xe-132 5.30914999999999981E+0 Cs-133 6.88192000000000004E+0

104 Xe-134 7.37063999999999986E+0 Cs-135 7.45038000000000000E+0 Cs-137 6.58718100000000018E+0 La-139 5.61065699999999978E+0 Ce-141 5.23207999999999984E+0 Ce-142 4.77627000000000024E+0 Nd-143 4.30201999999999973E+0 Nd-145 2.96883600000000003E+0 Nd-146 2.43299999999999983E+0 Nd-147 1.97354680000000005E+0 Nd-148 1.63632099999999991E+0 Sm-149 1.23951699999999998E+0 Nd-150 9.80944000000000038E-1 Sm-151 7.76606000000000018E-1 Sm-152 6.06010999999999966E-1 Eu-153 4.34675499999999992E-1 Eu-155 2.26013600000000009E-1

105 Results of EQUILIBRIUM APPROACH Nuclide Equilibrium atomic density 10 years fission yields Kr-85m 4.44770531791907562E+14 6.01822183500000051E+18 Kr-85 1.97633360887029606E+18 6.01822183500000051E+18 Rb-85 4.07118000000000076E+22 6.01822183500000051E+18 Y -91 5.56515074783236992E+17 2.40240262499999990E+19 Zr-91 1.87519230769230774E+23 2.40240262499999990E+19 Zr-92 2.69704499999999973E+24 2.91347307000000020E+19 Zr-93 7.22362078298686804E+23 3.61756354500000031E+19 Zr-94 1.44399416962568053E+25 4.20078244500000031E+19 Zr-95 4.42046908461249792E+18 4.63276651499999969E+19 Nb-95 2.41666241370500864E+18 4.63276651499999969E+19 Mo-95 4.77426312204802589E+23 4.63276651499999969E+19 Zr-96 5.52377933331738450E+24 4.71577912199999980E+19 Mo-97 7.48809471931197233E+23 5.19712294500000072E+19 Mo-98 2.84272507230397735E+24 5.54656153500000010E+19 Tc-99 5.80448830818055222E+23 5.90168646000000041E+19

106 Mo-100 6.50652098679982160E+23 6.48495463500000051E+19 Ru-101 1.64415151553121916E+23 6.44626390499999990E+19 Ru-102 1.11917766324970256E+24 6.54356232000000082E+19 Ru-103 4.07353193643529267E+18 6.73259107499999969E+19 Rh-103 3.62142075730733155E+23 6.73259107499999969E+19 Ru-104 1.90874718849906334E+24 6.42528261000000061E+19 Pd-105 3.71900383008765652E+23 5.33484656999999980E+19 Ru-106 6.23076879994554204E+19 4.30445704500000031E+19 Pd-106 2.80060091023820422E+24 4.30445704500000031E+19 Pd-107 7.33297125020930985E+23 3.00710148300000010E+19 Pd-108 3.10105667293295228E+24 1.87605298800000000E+19 Ag-109 1.16346325998803663E+24 1.89233443350000026E+19 Cd-111 4.33608363654999232E+21 3.50209251000000000E+18 I -127 8.31849101789200961E+21 5.44966717499999949E+18 I -129 3.96245109681555547E+22 1.60801078499999990E+19 Xe-131 1.21112624246693271E+23 3.81254472000000000E+19 Xe-132 1.20288420958816868E+24 5.23216732500000031E+19

107 Cs-133 3.62009300606139853E+23 6.78213216000000000E+19 Xe-134 4.91376000000000031E+24 7.26376572000000000E+19 Cs-135 7.45522158674253426E+23 7.34234948999999980E+19 Cs-137 2.82069197535739773E+20 6.49166687550000005E+19 La-139 1.65677159309021128E+24 5.52930247350000026E+19 Ce-141 1.51566891983954208E+17 5.15621484000000000E+19 Pr-141 9.13746420803279551E+22 5.15621484000000000E+19 Ce-142 2.51802498411755389E+23 4.70701408500000031E+19 Nd-143 4.34924587526784595E+23 4.23964071000000020E+19 Nd-145 5.88221448186497744E+22 2.92578787800000020E+19 Nd-146 7.71690857142856989E+23 2.39772150000000000E+19 Nd-147 1.02188351991170944E+17 1.94493037139999990E+19 Pm-147 8.89640490784821760E+18 1.94493037139999990E+19 Sm-147 2.20304355074652252E+22 1.94493037139999990E+19 Nd-148 1.32707108147550356E+23 1.61259434550000005E+19 Sm-149 1.43957988001329279E+22 1.22154400350000005E+19 Nd-150 3.06545000000000014E+22 9.66720312000000000E+18 Sm-151 8.09183452634436700E+15 7.65345213000000000E+18 Sm-152 1.42246774052948772E+22 5.97223840499999949E+18 Eu-153 4.44932410294246792E+22 4.28372705250000026E+18 Eu-155 1.53124322481422464E+18 2.22736402800000026E+18

108 Equilibrium results analysis Not all of the nuclides can be treated properly using equilibrium approach. The nuclides which need long time to reach the equilibrium are not appropriate for this approach. To investigate this we also show the yields of 10 years of burn- up using 100 W/cc power density and fission macroscopic cross section 0.01 cm-1. The equilibrium approach will be useful for nuclides in which equilibrium atomic density is much larger than the corresponding yields in the right column. Therefore we can find that Y-91, Zr-95, Nb-95, Ru-103, Ru- 106, Ce-141, and Nd-147 are nuclides which can be treated collectively using equilibrium approach. The verification of this can be found in the next session.

109 DIRECT NUMERICAL SOLUTION RESULTS

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162 Analysis The first pattern is about nuclides which soon reach asymptotic value, such as Nb-95, Y-91, Zr-95, Ru-103, Ru-106, Ce-141, Nd-147,and Sm-151. Such nuclides can be grouped together with certain weight which ma depend on some parameters such as flux, power density, etc. This results are also inline with the equilibrium model. The Ru-106 is may be in the boundary between first pattern and second pattern. The second pattern includes nuclides which change during burn-up include non-linear pattern. Such nuclides includes Kr- 85, Pd-106, Cs-137, Ce-142, Pm-147, Sm-147, and Eu-155. Such nuclides can be combined into one group or more with non linear wight (quadratic, cubic, quartic, etc.)

163 Analysis The third pattern is about nuclides which change almost linear during burnup. Such nuclides includes Rb-85, Zr-91, Zr-92, Zr-93, Zr, 94, Zr-96, Mo-95, Mo-97, Mo-98, Mo-100, Tc-99, Ru- 101, Ru-102, Ru-104, Rh-103, Pd-105, Pd-107, Pd- 108, Ag-109, Cd-111, I-127, I-129, Xe-131, Xe-132, Xe-134, Cs-133, Cs-135, La-139, Pr-141, Nd-143, Nd- 145, Nd-146, Nd-148, Nd-150, Sm149, Sm152, and Eu153. Such nuclides can be grouped into two or more group constants with flux level, power level and time.

164 CONCLUSION AND RECOMENDATION In this study we focus on the FP group constant treatment by considering around 50 most important nuclides. We then calculate the fission product effective yield for each modified chains and also generating one group constants using SRAC code system and other method (Origen etc.). We use two approach for investigating the important FP nuclides: using equilibrium model and using numerical solution for time dependent model. We found that we can separate the FP nuclides into three groups: which soon reach asymptotic value, which have non linear pattern and which have linear pattern

165 CONCLUSION AND RECOMENDATION In he future work we will complete the detail lumped FP model and include this in the full core benchmark calculation


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