Analisa Burnup Zaki Su’ud

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

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

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

Contoh rantai burnup

Persamaan Burnup terkait

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

Persamaan Burnup untuk deret yang disederhanakan

Persamaan Burnup untuk deret yang disederhanakan(2)

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

Solusi Numerik Finite difference Eksplisit

Solusi Numerik Finite difference Eksplisit

Solusi Numerik Finite difference Eksplisit

Solusi Numerik Finite difference Eksplisit

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

Solusi Numerik Finite difference Implisit

Solusi Numerik Finite difference Implisit

Solusi Numerik Finite difference Implisit

Solusi Numerik Finite difference Eksplisit

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

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

THEORY BURN UP EQUATION An explicit Burn Up equation for each nuclide is : where Ni = concentration of ith nuclide λi = decay constant of ith nuclide σa,i = absorb microscopic cross section for ith nuclide Ф = neutron flux of nuclide Sm,i = production speed of ith nuclide from mth nuclide

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

SIMULATION Linear series for analytical method 1 92234 92235 92236 24 94238 47 95242 94242 94243 95243 95244 2 92237 93237 25 94239 94240 94241 48 96242 96243 96244 3 93238 26 49 4 93239 27 95241 50 5 28 51 6 29 95742 52 96245 7 92238 92239 93240 30 53 8 31 54 94246 9 32 55 10 33 56 11 34 57 12 35 58 13 36 59 14 37 60 15 38 61 16 39 62 17 40 63 96246 18 41 64 19 42 65 96247 20 43 66 96748 21 44 67 96248 96749 22 45 68 96249 23 46 69

Burnup chain 1 92234 92235 92236 2 92237 93237 3 93238 94238 4 93239 94239 5 6 7 92238 92239 93240 94240 8 9 94241 10

Burnup chain(2) 11 92239 93239 94239 94240 12 93237 93238 13 94238 14 92234 15 93240 16 17 18 92235 19 94241 20

Burnup chain (3) 21 93240 94240 94241 94242 22 95241 23 94238 94239 24 92234 92235 25 26 27 28 94243 95243 29 95742 30 96242

Burnup chain (4) 31 94241 95241 95242 94242 32 93237 33 94243 95243 95244 96244 34 96245 35 94240 36 95742 37 38 96242 39 40 96243

Burnup chain (5) 41 95241 95242 96242 94238 42 93237 93238 43 95742 95243 95244 96244 44 94242 94243 45 96243 46 47 48 49 94239 50

Burnup chain (6) 51 95242 96242 94238 92234 52 95243 95244 96244 96245 53 94240 54 94246 55 94241 56 96243 57 94239 58 59 60

Burnup chain (7) 61 96243 96244 94240 62 94239 63 96245 96246 64 94241 65 96247 66 96748 67 96248 96749 68 96249 69

Nuclide concentration (NPu239 ) time time Nuclide concentration (NU8 ) Nuclide concentration (NPu240 ) time Nuclide concentration (N) time

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

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

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

Senstivitas Burnup pada Cross section

Code Modification 4/8/2017 IAEA CRP RCM 21-25 Nov. 2005

Parameter Value/description SPINNOR A SPINNOR B VSPINNOR Installed capacity 55 MWth / 20 MWe 27.5 MWth/ 10 MWe 17.5 MWth/ 6.25 MWe Operation life time (without refueling and fuel shuffling) 15 years 25 years 35 years Mode of operation Basic/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 4/8/2017 IAEA CRP RCM 21-25 Nov. 2005

B1 B2 C1 C2 R S Radial direction 4/8/2017 IAEA CRP RCM 21-25 Nov. 2005

outlet To stack Figure 1. Reactor assembly of SPINNOR AND VSPINNOR 4/8/2017 IAEA CRP RCM 21-25 Nov. 2005

Burnup parametric study results: U238 fission 105% 102.5% 100% 97.5% 95% 4/8/2017 IAEA CRP RCM 21-25 Nov. 2005

Burnup parametric study results:Pu-239 fission 4/8/2017 IAEA CRP RCM 21-25 Nov. 2005

Burnup parametric study results:Pu-241 fission 4/8/2017 IAEA CRP RCM 21-25 Nov. 2005

Burnup parametric study results: U-238 capture 4/8/2017 IAEA CRP RCM 21-25 Nov. 2005

Burnup parametric study results: Pu-239 capture 4/8/2017 IAEA CRP RCM 21-25 Nov. 2005

Burnup parametric study results: Pu-240 capture 4/8/2017 IAEA CRP RCM 21-25 Nov. 2005

Burnup parametric study results: FP capture 4/8/2017 IAEA CRP RCM 21-25 Nov. 2005

Burnup parametric study results: Pb capture 4/8/2017 IAEA CRP RCM 21-25 Nov. 2005

Burnup parametric study results: Bi capture 4/8/2017 IAEA CRP RCM 21-25 Nov. 2005

Burnup parametric study results: Pb transport 4/8/2017 IAEA CRP RCM 21-25 Nov. 2005

Burnup parametric study results: Bi transport 4/8/2017 IAEA CRP RCM 21-25 Nov. 2005

Burnup parametric study results: FP scattering 4/8/2017 IAEA CRP RCM 21-25 Nov. 2005

Burnup parametric study results: Pb scattering 4/8/2017 IAEA CRP RCM 21-25 Nov. 2005

Burnup parametric study results: Bi scattering 4/8/2017 IAEA CRP RCM 21-25 Nov. 2005

Burnup parametric study results: Pu-239 fission conversion ratio 4/8/2017 IAEA CRP RCM 21-25 Nov. 2005

Burnup parametric study results: U-238 capture conversion ratio 4/8/2017 IAEA CRP RCM 21-25 Nov. 2005

Burnup parametric study results: FP capture conversion ratio 4/8/2017 IAEA CRP RCM 21-25 Nov. 2005

Burnup parametric study results: Pu239 fission coolant void coefficient 4/8/2017 IAEA CRP RCM 21-25 Nov. 2005

Burnup parametric study results: U-238 capture coolant void coefficient 4/8/2017 IAEA CRP RCM 21-25 Nov. 2005

Burnup parametric study results: FP capture coolant void coefficient 4/8/2017 IAEA CRP RCM 21-25 Nov. 2005

Burnup parametric study results: Pb scattering coolant void coefficient 4/8/2017 IAEA CRP RCM 21-25 Nov. 2005

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. 4/8/2017 IAEA CRP RCM 21-25 Nov. 2005

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

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.

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.

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

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

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.

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 Table 1 118 Important FP Nuclides

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 Rb 41 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

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 Sb 81 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

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

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

Detail process will be discussed in the next part. 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.

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

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

Differential Equation

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

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

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

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

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

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

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.

DIRECT NUMERICAL SOLUTION RESULTS

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.)

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.

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

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