Luận án Study on fuel loading pattern optimization for vver-1000 nuclear reactor

In-core fuel management is a complicated multi-objective problem with a very large search space. Many methods have been investigated and applied to this problem, but none of them could definitely quarantine a global optimal solution. In this dissertation, the studies aim at developing advanced metaheuristics methods, i.e. ESA and SHADE, and applying to the ICFM problem of the VVER-1000 reactor. The three following studies have been carried out: (1) Development of a new core physics tool, LPO-V code, has been conducted to calculate the neutronic characteristics of VVER reactors with fast computational speed and acceptable accuracy. This tool is coupled with the newly developed optimization methods for solving the ICFM problem of VVER-1000 reactor. The PhD student developed the LPO-V based on the finite difference method for solving multi-group diffusion equations in hexagonal systems to calculate the neutronic characteristics of the VVER reactor core. Verification calculations of the LPO-V code have been performed based on a VVER-1000 MOX core benchmark and compared with MCNP calculations. Four-group cross-section set of the VVER-1000 MOX core was prepared using the PIJ module of the SRAC-2006 code system for the use in the LPO-V code. The results shown that the maximum deviation of keff is 102 pcm and the maximum deviation of the power distribution is 3.5%. Calculation speed of the LOP-V code was also tested and compared with the speed of the CITATION module of the SRAC-2006 code under the same conditions. The LPO-V code needs about 340 seconds to calculate 2000 LPs, while the CITATION needs 1040 seconds. It means that the LPO-V code can performs the core calculations for a large number of LPs (10000 to 100000) with a sufficient accuracy and reasonable computational time.

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than that of the reference core by about 1580 pcm. Whereas, the PPF is 89 smaller than the reference value by about 2.4%, and the flatness values are approximate. 90 Chapter 4 Conclusions and future work 4.1 Conclusions In-core fuel management is a complicated multi-objective problem with a very large search space. Many methods have been investigated and applied to this problem, but none of them could definitely quarantine a global optimal solution. In this dissertation, the studies aim at developing advanced metaheuristics methods, i.e. ESA and SHADE, and applying to the ICFM problem of the VVER-1000 reactor. The three following studies have been carried out: (1) Development of a new core physics tool, LPO-V code, has been conducted to calculate the neutronic characteristics of VVER reactors with fast computational speed and acceptable accuracy. This tool is coupled with the newly developed optimization methods for solving the ICFM problem of VVER-1000 reactor. The PhD student developed the LPO-V based on the finite dif- ference method for solving multi-group diffusion equations in hexagonal 91 systems to calculate the neutronic characteristics of the VVER reactor core. Verification calculations of the LPO-V code have been performed based on a VVER-1000 MOX core benchmark and compared with MCNP calculations. Four-group cross-section set of the VVER-1000 MOX core was prepared using the PIJ module of the SRAC-2006 code system for the use in the LPO-V code. The results shown that the maximum deviation of keff is 102 pcm and the maximum deviation of the power distribution is 3.5%. Calculation speed of the LOP-V code was also tested and compared with the speed of the CITATION module of the SRAC-2006 code under the same conditions. The LPO-V code needs about 340 seconds to calculate 2000 LPs, while the CITATION needs 1040 seconds. It means that the LPO-V code can performs the core calculations for a large number of LPs (10000 to 100000) with a sufficient accuracy and reasonable computational time. (2) Development of advanced optimization methods, ESA and SHADE, has been conducted and applied successfully to the LP optimization prob- lem of VVER-1000 reactor. The ESA is an improved version of the original SA method, that was proposed by the PhD student. Instead of using binary/ternary exchange operator to generate a new trial LP as in the SA, the ESA used a crossover of two base LPs for generating a new trial LP similar to that used in GA. Numerical calculations shown that this new improvement can enhance the performance of the SA method. In this study, the SHADE method, one of the current highest effi- ciency optimal search methods, was firstly applied to the ICFM problem. The SHADE method is an advanced version of the DE method with the 92 use of success-history based adaptation to determine the control param- eters F and CR automatically. The SHADE method is applied to opti- mization problems of continuous spaces, while the search space in the LP optimization problem is discrete. Therefore, the relative position indexing approach was deployed to convert real vectors to integer vectors in the discrete SHADE method. (3) Numerical calculations were performed for optimizing the LP of the reference VVER-1000 MOX core using the ESA and SHADE methods in comparison with other methods. The fitness function has been constructed based on the neutronic characteristics of the reactor core, i.e. keff , PPF and the flatness of power distribution. The fitness function was used to evaluate the optimization methods and find the optimal LP of the VVER-1000 reactor. A Mann- Whitney U Test was also introduced to evaluate statistical differences be- tween the optimization methods. Calculations for the VVER-1000 MOX core using the ESA method have been carried out in comparison with the original SA and ASA meth- ods. The results show that average fitness values and objective parameters obtained with ESA are better than those of SA and ASA. Whereas, the number of calculated LPs of ESA is smaller than that of SA and ASA by about 5–10%. Mann-Whitney U Test was also applied to evaluated statistical differences between the methods. The results show that ESA is advantageous over SA and ASA in the problem of fuel LP optimization. In case of the SHADE method, calculations based on the VVRE-1000 MOX core were performed and compared with the ESA and DE methods. The comparison shows that the three methods have comparable performance. 93 However, the advantage of SHADE is that the adaptive mechanism sim- plifies significantly the determination of the control parameters compared to DE. The optimal core LPs selected from the SHADE and ESA meth- ods were similar. This LP have a significant improvement of the keff value, which is greater than that of the reference core by about 1580 pcm. Whereas, the PPF is smaller than the reference value by about 2.4%, and the flatness values are approximate. The results demonstrate that the ESA and the discrete SHADE methods have been successfully developed and applied to the fuel loading optimization of the VVER-1000 reactor. The results also show that the efficiency of the two methods are compa- rable in the problem of this study. Nevertheless this is the first time the two methods have been applied to the ICFM problem, therefore further improvement and extensive application of the methods in the problem of fuel loading optimization are being continuously investigated. Comparison of the performance of the ESA and SHADE methods with other methods in the problem of fuel LP optimization will also be planned. 4.2 Future works (1) The current version of the LPO-V code can only handle 2D reactor core with triangular mesh and can not perform burn-up calculation. This code is being continuously upgraded to simulate 3D reactor with triangular and rectangular meshes and perform burn-up calculation. (2) Further investigation of the ESA and SHADE methods are being planned. Besides, new advanced methods will also be considered to apply 94 to the LP optimization problem. The extension of this study to multi-cycle optimization is also taken into account. (3) Extension of the application of these methods to the LP op- timization problem and core design for other reactor types is also being planned. 95 Papers published during the dissertation 1. Viet-Phu Tran, Giang T.T. Phan, Van-Khanh Hoang, Haidang Phan, Nhat-Duc Hoang, Hoai-Nam Tran; Success-history based adaptive differential evolution method for optimizing fuel loading pattern of VVER-1000 reactor; Nuclear Engineering and Design 377 (2021) 111125 2. Viet-Phu Tran, Giang T.T. Phan, Van-Khanh Hoang, Pham Nhu Viet Ha, Akio Yamamoto, Hoai-Nam Tran; Evolutionary simulated annealing for fuel loading optimization of VVER-1000 reactor; Annals of Nuclear Energy 151 (2021) 107938 3. Viet-Phu Tran, Hoai-Nam Tran, Akio Yamamoto, Tomohiro Endo; Automated Generation of Burnup Chain for Reactor Analysis Appli- cations; Kerntechnik, ISSN 0932-3902, 82 (2017 ) 2 196-205. 4. Viet-Phu Tran, Hoai-Nam Tran, Van Khanh Hoang; Application of Evolutionary Simulated Annealing Method to Design a Small 200 MWt Reactor Core; Nuclear Science and Technology, ISSN 1810-5408, Vol. 10, No. 4 (2020), pp. 16-23 5. Nguyen Huu Tiep, Nguyen Thi Dung, Tran Viet Phu, Tran Vinh Thanh and Pham Nhu Viet Ha; Burnup calculation of the OECD VVER-1000 LEU benchmark assembly using MCNP6 and SRAC2006; 96 Nuclear Science and Technology, ISSN 1810-5408, Vol. 8, No. 4 (2018), pp. 10-19 6. Tran Vinh Thanh, Tran Viet Phu, Nguyen Thi Dung; A study on the core loading pattern of the VVER-1200/V491; Nuclear Science and Technology, ISSN 1810-5408, Vol. 7, No. 1 (2017), pp. 21-27. 7. Tran Viet Phu, Tran Hoai Nam; Discrete SHADE method for in-core fuel management of VVER-1000 reactor; 45th Vietnam Conference on Theoretical Physics (VCTP-45), 2020 (Poster) 8. 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Assembly type Material name Material description UO2 assemblies type 1 U_4.2 Uranium fuel with 235U enrichment 4.2% wt. TVEG_5 Uranium-gadolinium fuel with enrichment 3.3% wt. on 235U and 5% wt. on Gd2O3 U_3.7 UO2 fuel with 235U enrichment 3.7% wt. MOX assemblies type 2 PU_3.6 MOX fuel with fissile plutonium isotopes enrichment 3.62% wt. TVEG_4 Uranium-gadolinium fuel with enrichment 3.6% wt. on 235U and 4% wt. on Gd2O3 PU_2.7 MOX fuel with fissile plutonium isotopes enrichment 2.69% wt. PU_2.4 MOX fuel with fissile plutonium isotopes enrichment 2.42% wt. Table A.3: Isotopic composition of fuel U_4.2, atoms/barn ∗ cm2 [5]. U_4.2 Burnup, MWd/kg 0 15 32 40 U235 9.0411E-04 5.8139E-04 3.2990E-04 2.4314E-04 U236 5.7700E-05 9.7452E-05 1.0890E-04 U238 2.0362E-02 2.0161E-02 1.9905E-02 1.9773E-02 NP37 3.7658E-06 1.0351E-05 1.3577E-05 PU38 4.5135E-07 2.7546E-06 4.6336E-06 PU39 9.6584E-05 1.2788E-04 1.3134E-04 PU40 1.7820E-05 4.4214E-05 5.4717E-05 PU41 7.8291E-06 2.4361E-05 3.0501E-05 PU42 8.5918E-07 6.9401E-06 1.1811E-05 AM41 9.6169E-08 5.7445E-07 8.2251E-07 O 4.2532E-02 4.2532E-02 4.2532E-02 4.2532E-02 SM49 9.1807E-08 8.9565E-08 8.5421E-08 SM51 3.8524E-07 4.9458E-07 5.3181E-07 TC99 1.9865E-05 4.0006E-05 4.8545E-05 RH03 1.1241E-05 2.2541E-05 2.6925E-05 CS33 2.1660E-05 4.3134E-05 5.2008E-05 ND43 1.7145E-05 3.0721E-05 3.5092E-05 ND45 1.2231E-05 2.3856E-05 2.8579E-05 PM47 5.1135E-06 7.0579E-06 7.2585E-06 SM52 2.0001E-06 4.0165E-06 4.7868E-06 119 Table A.4: Isotopic composition of fuel TVEG_5, atoms/barn ∗ cm2 [5]. TVEG_5 Burnup, MWd/kg 0 15 32 40 U235 6.6163E-04 4.8382E-04 2.6776E-04 1.9449E-04 U236 3.5164E-05 7.0094E-05 8.0032E-05 U238 1.9143E-02 1.8968E-02 1.8728E-02 1.8603E-02 NP37 2.5863E-06 7.7190E-06 1.0347E-05 PU38 2.9960E-07 2.0282E-06 3.5111E-06 PU39 8.8781E-05 1.1559E-04 1.1801E-04 PU40 1.5353E-05 4.1294E-05 5.1119E-05 PU41 6.2524E-06 2.2283E-05 2.8043E-05 PU42 6.0179E-07 6.3481E-06 1.1103E-05 AM41 6.9561E-08 4.9976E-07 7.2654E-07 O 4.1938E-02 4.1938E-02 4.1938E-02 4.1938E-02 GD52 3.2142E-06 2.2242E-06 1.1130E-06 7.6549E-07 GD54 3.4579E-05 3.1600E-05 2.7446E-05 2.5465E-05 GD55 2.3321E-04 3.2385E-07 1.5769E-07 1.4181E-07 GD56 3.2053E-04 5.4422E-04 5.3058E-04 5.2333E-04 GD57 2.4346E-04 1.8330E-07 1.6774E-07 1.5847E-07 GD58 3.8403E-04 6.3019E-04 6.3494E-04 6.3726E-04 GD60 3.3373E-04 3.3229E-04 3.3037E-04 3.2938E-04 SM49 8.0821E-08 8.0584E-08 7.7330E-08 SM51 3.1290E-07 4.0538E-07 4.4104E-07 TC99 1.2031E-05 3.0625E-05 3.8586E-05 RH03 7.4977E-06 1.8625E-05 2.2940E-05 CS33 1.3175E-05 3.3172E-05 4.1526E-05 ND43 1.0380E-05 2.3428E-05 2.7732E-05 ND45 7.3069E-06 1.8017E-05 2.2419E-05 PM47 3.3064E-06 5.7735E-06 6.1251E-06 SM52 1.2690E-06 3.2490E-06 3.9837E-06 120 Table A.5: Isotopic composition of fuel U_3.7, atoms/barn ∗ cm2 [5]. U_3.7 Burnup, MWd/kg 0 15 32 40 U235 7.9649E-04 4.8884E-04 2.6496E-04 1.9092E-04 U236 5.4042E-05 8.8494E-05 9.7726E-05 U238 2.0469E-02 2.0262E-02 2.0000E-02 1.9864E-02 NP37 3.7015E-06 9.9287E-06 1.2901E-05 PU38 4.6522E-07 2.7516E-06 4.5708E-06 PU39 9.5675E-05 1.2378E-04 1.2659E-04 PU40 1.9149E-05 4.5926E-05 5.6139E-05 PU41 8.3590E-06 2.4695E-05 3.0494E-05 PU42 1.0147E-06 7.7274E-06 1.2925E-05 AM41 1.0325E-07 5.7739E-07 8.0933E-07 O 4.2530E-02 4.2530E-02 4.2530E-02 4.2530E-02 SM49 8.3005E-08 8.2706E-08 7.9571E-08 SM51 3.4935E-07 4.5427E-07 4.9115E-07 TC99 1.9485E-05 3.8798E-05 4.6961E-05 RH03 1.1189E-05 2.2235E-05 2.6478E-05 CS33 2.1245E-05 4.1820E-05 5.0289E-05 ND43 1.6565E-05 2.9007E-05 3.2889E-05 ND45 1.1935E-05 2.2961E-05 2.7419E-05 PM47 4.9515E-06 6.7031E-06 6.8639E-06 SM52 2.0058E-06 3.9584E-06 4.6994E-06 121 Table A.6: Isotopic composition of fuel PU_3.6, atoms/barn ∗ cm2 [5]. PU_3.6 Burnup, MWd/kg 0 17 33 U235 4.3057E-05 3.0534E-05 2.0186E-05 U236 2.5385E-06 4.2696E-06 U238 2.0386E-02 2.0144E-02 1.9894E-02 NP37 2.4045E-06 4.2797E-06 PU38 1.0841E-06 1.3292E-06 2.7311E-06 PU39 7.5661E-04 4.7406E-04 2.9852E-04 PU40 5.3794E-05 1.4795E-04 1.7846E-04 PU41 9.5720E-06 5.7132E-05 8.3282E-05 PU42 3.5119E-06 9.8236E-06 2.5860E-05 AM41 1.3594E-06 2.9942E-06 O 4.2506E-02 4.2506E-02 4.2506E-02 SM49 1.4783E-07 1.2062E-07 SM51 7.7056E-07 7.6447E-07 TC99 2.2348E-05 4.0862E-05 RH03 2.2129E-05 3.6232E-05 CS33 2.4904E-05 4.4872E-05 ND43 1.5770E-05 2.7603E-05 ND45 1.1215E-05 2.0679E-05 PM47 5.0355E-06 6.6403E-06 SM52 3.2199E-06 5.2658E-06 122 Table A.7: Isotopic composition of fuel TVEG_4, atoms/barn ∗ cm2 [5]. TVEG_4 Burnup, MWd/kg 0 17 33 U235 7.3225E-04 5.4783E-04 3.4998E-04 U236 3.9989E-05 7.3537E-05 U238 1.9360E-02 1.9139E-02 1.8901E-02 NP37 3.7973E-06 9.6340E-06 PU38 4.9031E-07 2.5298E-06 PU39 1.2109E-04 1.5184E-04 PU40 1.7377E-05 4.4993E-05 PU41 7.0208E-06 2.4072E-05 PU42 5.4476E-07 5.0595E-06 AM41 8.8029E-08 5.5623E-07 O 4.2056E-02 4.2055E-02 4.2055E-02 GD52 2.5815E-06 1.8321E-06 1.0821E-06 GD54 2.7772E-05 2.5080E-05 2.2136E-05 GD55 1.8730E-04 1.0215E-06 1.6393E-07 GD56 2.5743E-04 4.3334E-04 4.2171E-04 GD57 1.9553E-04 2.5976E-07 2.0690E-07 GD58 3.0843E-04 5.0718E-04 5.1162E-04 GD60 2.6804E-04 2.6656E-04 2.6501E-04 SM49 1.0735E-07 1.0224E-07 SM51 4.0519E-07 5.0972E-07 TC99 1.2602E-05 2.9713E-05 RH03 7.9971E-06 1.8557E-05 CS33 1.3779E-05 3.2177E-05 ND43 1.0973E-05 2.3818E-05 ND45 7.6416E-06 1.7521E-05 PM47 3.2794E-06 5.5753E-06 SM52 1.2631E-06 3.0576E-06 123 Table A.8: Isotopic composition of fuel PU_2.7, atoms/barn ∗ cm2 [5]. PU_2.7 Burnup, MWd/kg 0 17 33 U235 4.3057E-05 2.8612E-05 1.7606E-05 U236 2.7944E-06 4.5372E-06 U238 2.0598E-02 2.0347E-02 2.0087E-02 NP37 2.4008E-06 4.2361E-06 PU38 8.0774E-07 1.0993E-06 2.5148E-06 PU39 5.6222E-04 3.3450E-04 2.1853E-04 PU40 3.9987E-05 1.2215E-04 1.4136E-04 PU41 7.1160E-06 4.9442E-05 6.9024E-05 PU42 2.6131E-06 9.5258E-06 2.5765E-05 AM41 1.1240E-06 2.3584E-06 O 4.2508E-02 4.2508E-02 4.2508E-02 SM49 1.1354E-07 9.8177E-08 SM51 5.8719E-07 6.0027E-07 TC99 2.0699E-05 3.7403E-05 RH03 2.0188E-05 3.2327E-05 CS33 2.3035E-05 4.0983E-05 ND43 1.4448E-05 2.4621E-05 ND45 1.0429E-05 1.9007E-05 PM47 4.6128E-06 5.9544E-06 SM52 3.0318E-06 4.7872E-06 124 Table A.9: Isotopic composition of fuel PU_2.4, atoms/barn ∗ cm2 [5]. PU_2.4 Burnup, MWd/kg 0 17 33 U235 4.3057E-05 2.7777E-05 1.6391E-05 U236 2.9076E-06 4.6650E-06 U238 2.0660E-02 2.0405E-02 2.0140E-02 NP37 2.3897E-06 4.1976E-06 PU38 7.2271E-07 1.0335E-06 2.4576E-06 PU39 5.0579E-04 2.9332E-04 1.9329E-04 PU40 3.5961E-05 1.1497E-04 1.3072E-04 PU41 6.4023E-06 4.6985E-05 6.4083E-05 PU42 2.3413E-06 9.6174E-06 2.6319E-05 AM41 1.0464E-06 2.1281E-06 O 4.2508E-02 4.2508E-02 4.2508E-02 SM49 1.0281E-07 9.0532E-08 SM51 5.3010E-07 5.4672E-07 TC99 2.0326E-05 3.6699E-05 RH03 1.9698E-05 3.1334E-05 CS33 2.2608E-05 4.0174E-05 ND43 1.4108E-05 2.3798E-05 ND45 1.0254E-05 1.8670E-05 PM47 4.5137E-06 5.7880E-06 SM52 2.9973E-06 4.6882E-06 Table A.10: Isotopic composition of the structural material, atoms/barn ∗ cm2 [5]. Material name Material zone Material isotopic composition Zirconium alloy Fuel cladding Zr 4.26E-02 Central tube Nb 4.22E-04 Guide tube Hf 6.59E-06 Steel Absorber cladding Fe 5.93E-02 Steel buffer Cr 1.69E-02 Steel barrel Ni 8.48E-03 Steel vessel Ti 9.90E-04 C 4.74E-04 B4C 80% enrichment of B10 Absorber rod B10 6.57E-02 B11 1.64E-02 C 2.05E-02 125 Table A.11: Moderator and water in reflector materials, atoms/barn ∗ cm2 [5]. Material name Material description Material isotopic composition M575B1.3 Moderator with boron content 1300 ppm, Tm = 575K, ρ = 0.7241g/cm3 H 4.8410E-02 O16 2.4205E-02 B10 1.0381E-05 B11 4.2049E-05 M575B0 Moderator without boron, Tm = 575K, ρ = 0.7241g/cm3 H 4.8410E-02 O16 2.4205E-02 B10 0.0 B11 0.0 M560B1.3 Moderator with boron content 1300 ppm, Tm = 560K, ρ = 0.7533g/cm3 H 5.0362E-02 O16 2.5181E-02 B10 1.0800E-05 B11 4.3744E-05 M560B0.6 Moderator with boron content 600 ppm, Tm = 560K, ρ = 0.7533g/cm3 H 5.0362E-02 O16 2.5181E-02 B10 4.9845E-06 B11 2.0190E-05 M560B0 Moderator without boron, Tm = 560K, ρ = 0.7533g/cm3 H 5.0362E-02 O16 2.5181E-02 B10 0.0 B11 0.0 M553B0 Moderator without boron, Tm = 553K, ρ = 0.7657g/cm3 H 5.1192E-02 O16 2.5596E-02 B10 0.0 B11 0.0 M300B2.8 Moderator with boron content 2800 ppm, Tm = 300K, ρ = 1.0033g/cm3 H 6.7076E-02 O16 3.3538E-02 B10 3.0981E-05 B11 1.2549E-04 Table B.1: Four groups structure with three fast groups and one thermal group. Group Energy (eV) Upper Lower 1 1.0000E+07 2.4788E+04 2 2.4788E+04 2.0347E+03 3 2.0347E+03 1.8554E+00 4 1.8554E+00 1.0000E-05 126 Table B.2: Four groups cross sections of fuel assemblies. Group PRODUCTION FISSION CAPTURE ABSORPTION FISS.SPCTR DIFFUSION1 g->1 g->2 g->3 g->4 * * A1B1A010 * * * * * * * * 1 4.14E-03 1.52E-03 1.01E-03 2.53E-03 9.98E-01 1.81E+00 1.43E-01 3.56E-02 3.07E-03 0.00E+00 2 2.31E-03 9.48E-04 5.42E-03 6.37E-03 1.48E-03 8.42E-01 0.00E+00 1.91E-01 1.99E-01 0.00E+00 3 1.53E-02 6.29E-03 2.31E-02 2.93E-02 3.32E-05 7.99E-01 0.00E+00 0.00E+00 3.17E-01 7.12E-02 4 1.36E-01 5.59E-02 2.68E-02 8.27E-02 0.00E+00 4.29E-01 0.00E+00 0.00E+00 2.62E-04 6.93E-01 * * A1B2A010 * * * * * * * * 1 4.05E-03 1.46E-03 1.00E-03 2.46E-03 9.98E-01 1.82E+00 1.42E-01 3.54E-02 3.05E-03 0.00E+00 2 1.70E-03 6.85E-04 5.36E-03 6.05E-03 1.51E-03 8.44E-01 0.00E+00 1.90E-01 1.99E-01 0.00E+00 3 1.27E-02 5.06E-03 2.40E-02 2.90E-02 3.37E-05 7.99E-01 0.00E+00 0.00E+00 3.17E-01 7.10E-02 4 1.40E-01 5.43E-02 3.69E-02 9.11E-02 0.00E+00 4.19E-01 0.00E+00 0.00E+00 2.88E-04 7.05E-01 * * A1B3A010 * * * * * * * * 1 3.90E-03 1.40E-03 9.90E-04 2.39E-03 9.98E-01 1.84E+00 1.41E-01 3.53E-02 3.04E-03 0.00E+00 2 1.19E-03 4.66E-04 5.30E-03 5.76E-03 1.53E-03 8.46E-01 0.00E+00 1.89E-01 1.99E-01 0.00E+00 3 1.01E-02 3.86E-03 2.48E-02 2.86E-02 3.43E-05 8.00E-01 0.00E+00 0.00E+00 3.17E-01 7.08E-02 4 1.27E-01 4.72E-02 4.42E-02 9.13E-02 0.00E+00 4.11E-01 0.00E+00 0.00E+00 2.87E-04 7.19E-01 * * A1B4A010 * * * * * * * * 1 3.84E-03 1.37E-03 9.84E-04 2.36E-03 9.98E-01 1.84E+00 1.41E-01 3.52E-02 3.04E-03 0.00E+00 2 1.01E-03 3.87E-04 5.27E-03 5.66E-03 1.54E-03 8.47E-01 0.00E+00 1.88E-01 1.99E-01 0.00E+00 3 9.00E-03 3.39E-03 2.51E-02 2.84E-02 3.45E-05 8.00E-01 0.00E+00 0.00E+00 3.17E-01 7.08E-02 4 1.19E-01 4.36E-02 4.60E-02 8.96E-02 0.00E+00 4.09E-01 0.00E+00 0.00E+00 2.80E-04 7.25E-01 * * A2B1A010 * * * * * * * * 1 4.61E-03 1.61E-03 9.99E-04 2.61E-03 9.98E-01 1.83E+00 1.41E-01 3.51E-02 3.02E-03 0.00E+00 2 1.61E-03 5.69E-04 5.49E-03 6.05E-03 1.52E-03 8.42E-01 0.00E+00 1.91E-01 1.99E-01 0.00E+00 3 1.64E-02 5.81E-03 2.41E-02 2.99E-02 3.39E-05 7.97E-01 0.00E+00 0.00E+00 3.17E-01 7.08E-02 4 2.36E-01 8.26E-02 8.04E-02 1.63E-01 0.00E+00 4.27E-01 0.00E+00 0.00E+00 5.13E-04 6.17E-01 * * A2B2A010 * * * * * * * * 1 4.30E-03 1.51E-03 9.93E-04 2.50E-03 9.98E-01 1.84E+00 1.41E-01 3.51E-02 3.03E-03 0.00E+00 2 1.24E-03 4.37E-04 5.38E-03 5.82E-03 1.54E-03 8.44E-01 0.00E+00 1.90E-01 1.99E-01 0.00E+00 3 1.34E-02 4.72E-03 2.45E-02 2.92E-02 3.45E-05 7.98E-01 0.00E+00 0.00E+00 3.18E-01 7.07E-02 4 1.96E-01 6.86E-02 7.28E-02 1.41E-01 0.00E+00 4.10E-01 0.00E+00 0.00E+00 4.43E-04 6.71E-01 * * A2B3A010 * * * * * * * * 1 4.07E-03 1.43E-03 9.87E-04 2.42E-03 9.98E-01 1.84E+00 1.40E-01 3.52E-02 3.03E-03 0.00E+00 2 9.84E-04 3.45E-04 5.31E-03 5.65E-03 1.57E-03 8.46E-01 0.00E+00 1.89E-01 1.99E-01 0.00E+00 3 1.11E-02 3.88E-03 2.52E-02 2.91E-02 3.51E-05 7.99E-01 0.00E+00 0.00E+00 3.18E-01 7.05E-02 4 1.60E-01 5.57E-02 6.82E-02 1.24E-01 0.00E+00 4.05E-01 0.00E+00 0.00E+00 3.86E-04 6.99E-01 127 Table B.3: Four groups cross sections of non fuel materials. Group PRODUCTION FISSION CAPTURE ABSORPTION FISS.SPCTR DIFFUSION1 g->1 g->2 g->3 g->4 * * STB1A080 * * * * * * * * 1 0.00E+00 0.00E+00 8.48E-04 8.48E-04 0.00E+00 1.40E+00 1.97E-01 3.69E-02 3.10E-03 0.00E+00 2 0.00E+00 0.00E+00 9.24E-04 9.24E-04 0.00E+00 5.14E-01 0.00E+00 5.28E-01 1.20E-01 0.00E+00 3 0.00E+00 0.00E+00 6.28E-03 6.28E-03 0.00E+00 4.71E-01 0.00E+00 0.00E+00 6.53E-01 4.87E-02 4 0.00E+00 0.00E+00 1.14E-01 1.14E-01 0.00E+00 3.02E-01 0.00E+00 0.00E+00 4.15E-04 9.89E-01 * * STB2A090 * * * * * * * * 1 0.00E+00 0.00E+00 2.15E-04 2.15E-04 0.00E+00 1.91E+00 5.35E-02 1.11E-01 9.74E-03 0.00E+00 2 0.00E+00 0.00E+00 8.83E-05 8.83E-05 0.00E+00 8.77E-01 0.00E+00 2.60E-02 3.54E-01 0.00E+00 3 0.00E+00 0.00E+00 9.13E-04 9.13E-04 0.00E+00 7.50E-01 0.00E+00 0.00E+00 3.00E-01 1.43E-01 4 0.00E+00 0.00E+00 1.72E-02 1.72E-02 0.00E+00 3.03E-01 0.00E+00 0.00E+00 1.65E-04 1.08E+00 * * STB3A0A0 * * * * * * * * 1 0.00E+00 0.00E+00 5.43E-04 5.43E-04 0.00E+00 1.58E+00 1.31E-01 7.33E-02 6.37E-03 0.00E+00 2 0.00E+00 0.00E+00 5.18E-04 5.18E-04 0.00E+00 6.36E-01 0.00E+00 2.89E-01 2.35E-01 0.00E+00 3 0.00E+00 0.00E+00 3.71E-03 3.71E-03 0.00E+00 5.74E-01 0.00E+00 0.00E+00 4.82E-01 9.51E-02 4 0.00E+00 0.00E+00 6.67E-02 6.67E-02 0.00E+00 2.95E-01 0.00E+00 0.00E+00 2.92E-04 1.06E+00 * * H2ORA0H0 * * * * * * * * 1 0.00E+00 0.00E+00 1.71E-04 1.71E-04 0.00E+00 1.97E+00 4.27E-02 1.16E-01 1.02E-02 0.00E+00 2 0.00E+00 0.00E+00 3.26E-05 3.26E-05 0.00E+00 9.24E-01 0.00E+00 -8.83E-03 3.69E-01 0.00E+00 3 0.00E+00 0.00E+00 5.41E-04 5.41E-04 0.00E+00 7.82E-01 0.00E+00 0.00E+00 2.76E-01 1.49E-01 4 0.00E+00 0.00E+00 1.08E-02 1.08E-02 0.00E+00 3.04E-01 0.00E+00 0.00E+00 1.49E-04 1.08E+00 * * STEAA0L0 * * * * * * * * 1 0.00E+00 0.00E+00 1.13E-03 1.13E-03 0.00E+00 1.32E+00 2.48E-01 2.29E-03 1.06E-06 0.00E+00 2 0.00E+00 0.00E+00 1.30E-03 1.30E-03 0.00E+00 4.40E-01 0.00E+00 7.47E-01 1.00E-02 0.00E+00 3 0.00E+00 0.00E+00 8.66E-03 8.66E-03 0.00E+00 3.99E-01 0.00E+00 0.00E+00 8.22E-01 4.53E-03 4 0.00E+00 0.00E+00 1.60E-01 1.60E-01 0.00E+00 3.10E-01 0.00E+00 0.00E+00 5.32E-04 9.15E-01 128

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