Luận án Tiến sĩ Nghiên cứu tối ưu thay đảo nhiên liệu lò phản ứng hạt nhân VVER1000

MINISTRY OF EDUCATION AND TRAINING MINISTRY OF SCIENCE AND TECHNOLOGY VIETNAM ATOMIC ENERGY INSTITUTE TRAN VIET PHU STUDY ON FUEL LOADING PATTERN OPTIMIZATION FOR VVER-1000 NUCLEAR REACTOR DISSERTATION FOR THE DOCTOR DEGREE OF PHYSICS Hanoi - 2022 BỘ GIÁO DỤC VÀ ĐÀO TẠO BỘ KHOA HỌC VÀ CÔNG NGHỆ VIỆN NĂNG LƯỢNG NGUYÊN TỬ VIỆT NAM TRẦN VIỆT PHÚ NGHIÊN CỨU TỐI ƯU THAY ĐẢO NHIÊN LIỆU LÒ PHẢN ỨNG HẠT NHÂN VVER-1000 LUẬN ÁN TIẾN SĨ VẬT LÝ Chuyên ngành: Vật lý Nguyên tử Hạt nhân Mã số: 9.44.01.06 Giáo viên hướng dẫn: o PGS TS TRẦN Hoài Nam GS TS YAMAMOTO Akio Hà Nội - 2022 MINISTRY OF EDUCATION AND TRAINING MINISTRY OF SCIENCE AND TECHNOLOGY VIETNAM ATOMIC ENERGY INSTITUTE TRAN VIET PHU STUDY ON FUEL LOADING PATTERN OPTIMIZATION FOR VVER-1000 NUCLEAR REACTOR DISSERTATION FOR THE DOCTOR DEGREE OF PHYSICS Major: Nuclear and Atomic Physics Code: 9.44.01.06 Supervisors: o Assoc Prof Dr TRAN Hoai Nam Prof Dr YAMAMOTO Akio Hanoi - 2022 Contents Declaration of Authorship iii Acknowledgements iv Dedication v Tóm tắt vi Abstract viii List of Abbreviations x List of Figures xii List of Tables xiv Introduction 1.1 General introduction 1.2 Description of fuel LP optimization problem 1.3 Overview of methods applied to fuel LP optimization 1.4 Overview of VVER reactor 1.5 Purposes of this dissertation 1.6 Dissertation outline Methods and development 2.1 Introduction 2.2 VVER-1000 MOX core benchmark 2.3 Data preparation for core calculations 2.4 Development of LPO-V code for core physics calculations 2.4.1 Steady-state multi-group diffusion equations 2.4.2 Finite difference method for spatial discretization 2.4.3 Boundary conditions 2.4.4 Successive over-relaxation method 2.4.5 Core modeling by LPO-V code 2.4.6 Verification of core calculations i 1 12 18 19 21 21 22 25 28 28 30 34 36 41 43 ii Contents 2.5 2.6 2.7 2.8 2.9 Development of ESA method 2.5.1 SA and ASA methods 2.5.2 ESA method Development of a discrete SHADE method 2.6.1 Classics Differential Evolution 2.6.2 SHADE operators 2.6.3 Success-history based adaptation 2.6.4 Discrete SHADE method Fitness functions Mann-Whitney U Test Conclusions 46 46 48 52 52 54 57 60 62 65 67 Loading pattern optimization of VVER-1000 reactor 3.1 Introduction 3.2 LP optimization of VVER-1000 core using ESA method 3.2.1 Selection of ESA method 3.2.2 Comparison among SA, ASA and ESA 3.2.3 LP optimization of the VVER-1000 MOX core using ESA method 3.3 LP optimization of VVER-1000 reactor using SHADE method 3.3.1 Determination of control parameters 3.3.2 LP optimization of the VVER-1000 MOX core using SHADE method 3.4 Optimal core loading pattern of SHADE and ESA 3.5 Conclusions of Chapter 68 68 69 69 71 76 77 77 Conclusions and future work 4.1 Conclusions 4.2 Future works 91 91 94 Papers published during the dissertation 96 REFERENCES 98 APPENDICES 118 A VVER-1000 MOX core Benchmark specification 118 B Cross sections of materials 118 79 87 88 Declaration of Authorship I certify that this dissertation entitled "STUDY ON FUEL LOADING PATTERN OPTIMIZATION FOR VVER-1000 NUCLEAR REACTOR" is my own original work except where otherwise clearly indicated I confirm that the dissertation submitted to the Nuclear Training Center, Vietnam Atomic Energy Institute was mainly done during my candidature for a PhD degree under the supervision of Assoc Prof Dr Tran Hoai Nam and Prof Dr Yamamoto Akio TRAN VIET PHU iii Acknowledgements This dissertation presents a long-term work in an interesting field of nuclear and atomic physics The dissertation was performed with great supports from my colleagues and the encouragements of my relatives together with my individual endeavor iv Dedication To my wife and sons, who have constantly supported me throughout challenging years To my parents, my younger sister, who are always next to me with love v Tóm tắt Luận văn trình bày nghiên cứu tối ưu thay đảo nhiên liệu cho lò phản ứng VVER Một chương trình mơ vùng hoạt (LPO-V) phát triển cho lò phản ứng VVER, với phương pháp tìm kiếm tối ưu hóa Chương trình giải phương trình khuếch tán ô mạng tam giác dựa phương pháp sai phân hữu hạn Việc xác minh chương trình LPO-V thực dựa tốn chuẩn lị VVER-1000 nạp tải nhiên liệu MOX Kết cho thấy chương trình có độ xác đảm bảo hiệu suất tốt mơ-đun CITATION Hai phương pháp tối ưu hóa tiên tiến phát triển cho toán tối ưu nạp tải nhiên liệu lò phản ứng VVER-1000: Phương pháp mơ tơi kim tiến hóa (ESA) phương pháp tiến hóa vi phân dựa lịch sử thành công (SHADE) Phương pháp ESA cải tiến từ phương pháp mô kim nguyên (SA) cách sử dụng toán tử trao đổi chéo đột biến để tạo cấu hình nạp tải thử nghiệm Phương pháp SHADE sử dụng chế thích ứng dựa lịch sử tham số điều khiển thành công, tức tỷ lệ đột biến F tỷ lệ trao đổi chéo CR, để cải thiện thuật tốn tiến hóa vi phân (DE) ban đầu Do đó, thay ba tham số điều khiển DE ban đầu, phương pháp SHADE bao gồm hai tham số kích thước quần thể N P kích thước nhớ lịch sửH Để áp dụng phương pháp SHADE cho toán tối ưu thay đảo nhiên liệu, phương pháp tiếp cận số vị trí tương đối triển khai để chuyển đổi biến thực thành biến số ngun Các tính tốn thực để chọn thông số điều khiển phù hợp SHADE cho toán tối ưu thay đảo nhiên liệu lò phản ứng VVER-1000 nạp tải MOX vi vii Tóm tắt Các tính tốn số cho bải tốn tối ưu thay đảo nhiên liệu lị VVER-1000 nạp tải MOX thực phương pháp ESA SHADE, có so sánh với SA, mơ tơi kim thích ứng (ASA) DE Một hàm mục tiêu chọn để tối đa hóa kef f , đồng thời làm phẳng phân bố công suất hướng tâm Kết cho thấy kef f cấu hình tối ưu lớn cấu hình tham chiếu khoảng 1580 pcm Trong đó, hệ số đỉnh cơng suất xuyên tâm (P P F ) cấu hình tối ưu nhỏ khoảng 2,4 % so với cấu hình tham chiếu Sự khác biệt thống kê phương pháp đánh giá dựa phương pháp Mann-Whitney U-test Kết cho thấy phương pháp ESA SHADE có hiệu suất tương đương với DE lợi so với SA ASA Việc phát triển thêm phương pháp mở rộng ứng dụng chúng cho vấn đề khác tối ưu thay đảo nhiên liệu tiếp tục nghiên cứu tương lai [94] A Glebov, A Klushin, Y Baranaev, 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Appendix B Cross sections of materials 118 Radius (cm) 0.386 0.455 0.55 0.63 0.35 0.41 0.55 0.63 Table A.2: Material names used in the fuel assemblies [5] Assembly type Material name U_4.2 U O2 assemblies type TVEG_5 U_3.7 PU_3.6 MOX assemblies type TVEG_4 PU_2.7 PU_2.4 Material description Uranium fuel with 235U enrichment 4.2% wt Uranium-gadolinium fuel with enrichment 3.3% wt on 235U and 5% wt on Gd2O3 U O2 fuel with 235U enrichment 3.7% wt MOX fuel with fissile plutonium isotopes enrichment 3.62% wt Uranium-gadolinium fuel with enrichment 3.6% wt on 235U and 4% wt on Gd2O3 MOX fuel with fissile plutonium isotopes enrichment 2.69% wt MOX fuel with fissile plutonium isotopes enrichment 2.42% wt Table A.3: Isotopic composition of fuel U_4.2, atoms/barn ∗ cm2 [5] Burnup, MWd/kg U_4.2 U235 U236 U238 NP37 PU38 PU39 PU40 PU41 PU42 AM41 O SM49 SM51 TC99 RH03 CS33 ND43 ND45 PM47 SM52 9.0411E-04 2.0362E-02 4.2532E-02 15 5.8139E-04 5.7700E-05 2.0161E-02 3.7658E-06 4.5135E-07 9.6584E-05 1.7820E-05 7.8291E-06 8.5918E-07 9.6169E-08 4.2532E-02 9.1807E-08 3.8524E-07 1.9865E-05 1.1241E-05 2.1660E-05 1.7145E-05 1.2231E-05 5.1135E-06 2.0001E-06 119 32 3.2990E-04 9.7452E-05 1.9905E-02 1.0351E-05 2.7546E-06 1.2788E-04 4.4214E-05 2.4361E-05 6.9401E-06 5.7445E-07 4.2532E-02 8.9565E-08 4.9458E-07 4.0006E-05 2.2541E-05 4.3134E-05 3.0721E-05 2.3856E-05 7.0579E-06 4.0165E-06 40 2.4314E-04 1.0890E-04 1.9773E-02 1.3577E-05 4.6336E-06 1.3134E-04 5.4717E-05 3.0501E-05 1.1811E-05 8.2251E-07 4.2532E-02 8.5421E-08 5.3181E-07 4.8545E-05 2.6925E-05 5.2008E-05 3.5092E-05 2.8579E-05 7.2585E-06 4.7868E-06 Table A.4: Isotopic composition of fuel TVEG_5, atoms/barn ∗ cm2 [5] Burnup, MWd/kg TVEG_5 U235 U236 U238 NP37 PU38 PU39 PU40 PU41 PU42 AM41 O GD52 GD54 GD55 GD56 GD57 GD58 GD60 SM49 SM51 TC99 RH03 CS33 ND43 ND45 PM47 SM52 6.6163E-04 1.9143E-02 4.1938E-02 3.2142E-06 3.4579E-05 2.3321E-04 3.2053E-04 2.4346E-04 3.8403E-04 3.3373E-04 15 4.8382E-04 3.5164E-05 1.8968E-02 2.5863E-06 2.9960E-07 8.8781E-05 1.5353E-05 6.2524E-06 6.0179E-07 6.9561E-08 4.1938E-02 2.2242E-06 3.1600E-05 3.2385E-07 5.4422E-04 1.8330E-07 6.3019E-04 3.3229E-04 8.0821E-08 3.1290E-07 1.2031E-05 7.4977E-06 1.3175E-05 1.0380E-05 7.3069E-06 3.3064E-06 1.2690E-06 120 32 2.6776E-04 7.0094E-05 1.8728E-02 7.7190E-06 2.0282E-06 1.1559E-04 4.1294E-05 2.2283E-05 6.3481E-06 4.9976E-07 4.1938E-02 1.1130E-06 2.7446E-05 1.5769E-07 5.3058E-04 1.6774E-07 6.3494E-04 3.3037E-04 8.0584E-08 4.0538E-07 3.0625E-05 1.8625E-05 3.3172E-05 2.3428E-05 1.8017E-05 5.7735E-06 3.2490E-06 40 1.9449E-04 8.0032E-05 1.8603E-02 1.0347E-05 3.5111E-06 1.1801E-04 5.1119E-05 2.8043E-05 1.1103E-05 7.2654E-07 4.1938E-02 7.6549E-07 2.5465E-05 1.4181E-07 5.2333E-04 1.5847E-07 6.3726E-04 3.2938E-04 7.7330E-08 4.4104E-07 3.8586E-05 2.2940E-05 4.1526E-05 2.7732E-05 2.2419E-05 6.1251E-06 3.9837E-06 Table A.5: Isotopic composition of fuel U_3.7, atoms/barn ∗ cm2 [5] Burnup, MWd/kg U_3.7 U235 U236 U238 NP37 PU38 PU39 PU40 PU41 PU42 AM41 O SM49 SM51 TC99 RH03 CS33 ND43 ND45 PM47 SM52 7.9649E-04 2.0469E-02 4.2530E-02 15 4.8884E-04 5.4042E-05 2.0262E-02 3.7015E-06 4.6522E-07 9.5675E-05 1.9149E-05 8.3590E-06 1.0147E-06 1.0325E-07 4.2530E-02 8.3005E-08 3.4935E-07 1.9485E-05 1.1189E-05 2.1245E-05 1.6565E-05 1.1935E-05 4.9515E-06 2.0058E-06 121 32 2.6496E-04 8.8494E-05 2.0000E-02 9.9287E-06 2.7516E-06 1.2378E-04 4.5926E-05 2.4695E-05 7.7274E-06 5.7739E-07 4.2530E-02 8.2706E-08 4.5427E-07 3.8798E-05 2.2235E-05 4.1820E-05 2.9007E-05 2.2961E-05 6.7031E-06 3.9584E-06 40 1.9092E-04 9.7726E-05 1.9864E-02 1.2901E-05 4.5708E-06 1.2659E-04 5.6139E-05 3.0494E-05 1.2925E-05 8.0933E-07 4.2530E-02 7.9571E-08 4.9115E-07 4.6961E-05 2.6478E-05 5.0289E-05 3.2889E-05 2.7419E-05 6.8639E-06 4.6994E-06 Table A.6: Isotopic composition of fuel PU_3.6, atoms/barn ∗ cm2 [5] PU_3.6 U235 U236 U238 NP37 PU38 PU39 PU40 PU41 PU42 AM41 O SM49 SM51 TC99 RH03 CS33 ND43 ND45 PM47 SM52 Burnup, MWd/kg 4.3057E-05 2.0386E-02 1.0841E-06 7.5661E-04 5.3794E-05 9.5720E-06 3.5119E-06 4.2506E-02 17 3.0534E-05 2.5385E-06 2.0144E-02 2.4045E-06 1.3292E-06 4.7406E-04 1.4795E-04 5.7132E-05 9.8236E-06 1.3594E-06 4.2506E-02 1.4783E-07 7.7056E-07 2.2348E-05 2.2129E-05 2.4904E-05 1.5770E-05 1.1215E-05 5.0355E-06 3.2199E-06 122 33 2.0186E-05 4.2696E-06 1.9894E-02 4.2797E-06 2.7311E-06 2.9852E-04 1.7846E-04 8.3282E-05 2.5860E-05 2.9942E-06 4.2506E-02 1.2062E-07 7.6447E-07 4.0862E-05 3.6232E-05 4.4872E-05 2.7603E-05 2.0679E-05 6.6403E-06 5.2658E-06 Table A.7: Isotopic composition of fuel TVEG_4, atoms/barn ∗ cm2 [5] TVEG_4 U235 U236 U238 NP37 PU38 PU39 PU40 PU41 PU42 AM41 O GD52 GD54 GD55 GD56 GD57 GD58 GD60 SM49 SM51 TC99 RH03 CS33 ND43 ND45 PM47 SM52 Burnup, MWd/kg 7.3225E-04 1.9360E-02 4.2056E-02 2.5815E-06 2.7772E-05 1.8730E-04 2.5743E-04 1.9553E-04 3.0843E-04 2.6804E-04 17 5.4783E-04 3.9989E-05 1.9139E-02 3.7973E-06 4.9031E-07 1.2109E-04 1.7377E-05 7.0208E-06 5.4476E-07 8.8029E-08 4.2055E-02 1.8321E-06 2.5080E-05 1.0215E-06 4.3334E-04 2.5976E-07 5.0718E-04 2.6656E-04 1.0735E-07 4.0519E-07 1.2602E-05 7.9971E-06 1.3779E-05 1.0973E-05 7.6416E-06 3.2794E-06 1.2631E-06 123 33 3.4998E-04 7.3537E-05 1.8901E-02 9.6340E-06 2.5298E-06 1.5184E-04 4.4993E-05 2.4072E-05 5.0595E-06 5.5623E-07 4.2055E-02 1.0821E-06 2.2136E-05 1.6393E-07 4.2171E-04 2.0690E-07 5.1162E-04 2.6501E-04 1.0224E-07 5.0972E-07 2.9713E-05 1.8557E-05 3.2177E-05 2.3818E-05 1.7521E-05 5.5753E-06 3.0576E-06 Table A.8: Isotopic composition of fuel PU_2.7, atoms/barn ∗ cm2 [5] PU_2.7 U235 U236 U238 NP37 PU38 PU39 PU40 PU41 PU42 AM41 O SM49 SM51 TC99 RH03 CS33 ND43 ND45 PM47 SM52 Burnup, MWd/kg 4.3057E-05 2.0598E-02 8.0774E-07 5.6222E-04 3.9987E-05 7.1160E-06 2.6131E-06 4.2508E-02 17 2.8612E-05 2.7944E-06 2.0347E-02 2.4008E-06 1.0993E-06 3.3450E-04 1.2215E-04 4.9442E-05 9.5258E-06 1.1240E-06 4.2508E-02 1.1354E-07 5.8719E-07 2.0699E-05 2.0188E-05 2.3035E-05 1.4448E-05 1.0429E-05 4.6128E-06 3.0318E-06 124 33 1.7606E-05 4.5372E-06 2.0087E-02 4.2361E-06 2.5148E-06 2.1853E-04 1.4136E-04 6.9024E-05 2.5765E-05 2.3584E-06 4.2508E-02 9.8177E-08 6.0027E-07 3.7403E-05 3.2327E-05 4.0983E-05 2.4621E-05 1.9007E-05 5.9544E-06 4.7872E-06 Table A.9: Isotopic composition of fuel PU_2.4, atoms/barn ∗ cm2 [5] PU_2.4 U235 U236 U238 NP37 PU38 PU39 PU40 PU41 PU42 AM41 O SM49 SM51 TC99 RH03 CS33 ND43 ND45 PM47 SM52 Burnup, MWd/kg 4.3057E-05 2.0660E-02 7.2271E-07 5.0579E-04 3.5961E-05 6.4023E-06 2.3413E-06 4.2508E-02 17 2.7777E-05 2.9076E-06 2.0405E-02 2.3897E-06 1.0335E-06 2.9332E-04 1.1497E-04 4.6985E-05 9.6174E-06 1.0464E-06 4.2508E-02 1.0281E-07 5.3010E-07 2.0326E-05 1.9698E-05 2.2608E-05 1.4108E-05 1.0254E-05 4.5137E-06 2.9973E-06 33 1.6391E-05 4.6650E-06 2.0140E-02 4.1976E-06 2.4576E-06 1.9329E-04 1.3072E-04 6.4083E-05 2.6319E-05 2.1281E-06 4.2508E-02 9.0532E-08 5.4672E-07 3.6699E-05 3.1334E-05 4.0174E-05 2.3798E-05 1.8670E-05 5.7880E-06 4.6882E-06 Table A.10: Isotopic composition of the structural material, atoms/barn ∗ cm2 [5] Material name Zirconium alloy Steel B4C 80% enrichment of B10 Material zone Fuel cladding Central tube Guide tube Absorber cladding Steel buffer Steel barrel Steel vessel Absorber rod 125 Material isotopic composition Zr 4.26E-02 Nb 4.22E-04 Hf 6.59E-06 Fe 5.93E-02 Cr 1.69E-02 Ni 8.48E-03 Ti 9.90E-04 C 4.74E-04 B10 6.57E-02 B11 1.64E-02 C 2.05E-02 Table A.11: Moderator and water in reflector materials, atoms/barn ∗ cm2 [5] Material name Material description M575B1.3 Moderator with boron content 1300 ppm, Tm = 575K, ρ = 0.7241g/cm3 M575B0 Moderator without boron, Tm = 575K, ρ = 0.7241g/cm3 M560B1.3 Moderator with boron content 1300 ppm, Tm = 560K, ρ = 0.7533g/cm3 M560B0.6 Moderator with boron content 600 ppm, Tm = 560K, ρ = 0.7533g/cm3 M560B0 Moderator without boron, Tm = 560K, ρ = 0.7533g/cm3 M553B0 Moderator without boron, Tm = 553K, ρ = 0.7657g/cm3 M300B2.8 Moderator with boron content 2800 ppm, Tm = 300K, ρ = 1.0033g/cm3 Material isotopic composition H 4.8410E-02 O16 2.4205E-02 B10 1.0381E-05 B11 4.2049E-05 H 4.8410E-02 O16 2.4205E-02 B10 0.0 B11 0.0 H 5.0362E-02 O16 2.5181E-02 B10 1.0800E-05 B11 4.3744E-05 H 5.0362E-02 O16 2.5181E-02 B10 4.9845E-06 B11 2.0190E-05 H 5.0362E-02 O16 2.5181E-02 B10 0.0 B11 0.0 H 5.1192E-02 O16 2.5596E-02 B10 0.0 B11 0.0 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 1.0000E+07 2.4788E+04 2.0347E+03 1.8554E+00 126 Lower 2.4788E+04 2.0347E+03 1.8554E+00 1.0000E-05 Table B.2: Four groups cross sections of fuel assemblies 127 Group * * * * * * * PRODUCTION * 4.14E-03 2.31E-03 1.53E-02 1.36E-01 * 4.05E-03 1.70E-03 1.27E-02 1.40E-01 * 3.90E-03 1.19E-03 1.01E-02 1.27E-01 * 3.84E-03 1.01E-03 9.00E-03 1.19E-01 * 4.61E-03 1.61E-03 1.64E-02 2.36E-01 * 4.30E-03 1.24E-03 1.34E-02 1.96E-01 * 4.07E-03 9.84E-04 1.11E-02 1.60E-01 FISSION A1B1A010 1.52E-03 9.48E-04 6.29E-03 5.59E-02 A1B2A010 1.46E-03 6.85E-04 5.06E-03 5.43E-02 A1B3A010 1.40E-03 4.66E-04 3.86E-03 4.72E-02 A1B4A010 1.37E-03 3.87E-04 3.39E-03 4.36E-02 A2B1A010 1.61E-03 5.69E-04 5.81E-03 8.26E-02 A2B2A010 1.51E-03 4.37E-04 4.72E-03 6.86E-02 A2B3A010 1.43E-03 3.45E-04 3.88E-03 5.57E-02 CAPTURE * 1.01E-03 5.42E-03 2.31E-02 2.68E-02 * 1.00E-03 5.36E-03 2.40E-02 3.69E-02 * 9.90E-04 5.30E-03 2.48E-02 4.42E-02 * 9.84E-04 5.27E-03 2.51E-02 4.60E-02 * 9.99E-04 5.49E-03 2.41E-02 8.04E-02 * 9.93E-04 5.38E-03 2.45E-02 7.28E-02 * 9.87E-04 5.31E-03 2.52E-02 6.82E-02 ABSORPTION * 2.53E-03 6.37E-03 2.93E-02 8.27E-02 * 2.46E-03 6.05E-03 2.90E-02 9.11E-02 * 2.39E-03 5.76E-03 2.86E-02 9.13E-02 * 2.36E-03 5.66E-03 2.84E-02 8.96E-02 * 2.61E-03 6.05E-03 2.99E-02 1.63E-01 * 2.50E-03 5.82E-03 2.92E-02 1.41E-01 * 2.42E-03 5.65E-03 2.91E-02 1.24E-01 FISS.SPCTR * 9.98E-01 1.48E-03 3.32E-05 0.00E+00 * 9.98E-01 1.51E-03 3.37E-05 0.00E+00 * 9.98E-01 1.53E-03 3.43E-05 0.00E+00 * 9.98E-01 1.54E-03 3.45E-05 0.00E+00 * 9.98E-01 1.52E-03 3.39E-05 0.00E+00 * 9.98E-01 1.54E-03 3.45E-05 0.00E+00 * 9.98E-01 1.57E-03 3.51E-05 0.00E+00 DIFFUSION1 * 1.81E+00 8.42E-01 7.99E-01 4.29E-01 * 1.82E+00 8.44E-01 7.99E-01 4.19E-01 * 1.84E+00 8.46E-01 8.00E-01 4.11E-01 * 1.84E+00 8.47E-01 8.00E-01 4.09E-01 * 1.83E+00 8.42E-01 7.97E-01 4.27E-01 * 1.84E+00 8.44E-01 7.98E-01 4.10E-01 * 1.84E+00 8.46E-01 7.99E-01 4.05E-01 g->1 * 1.43E-01 0.00E+00 0.00E+00 0.00E+00 * 1.42E-01 0.00E+00 0.00E+00 0.00E+00 * 1.41E-01 0.00E+00 0.00E+00 0.00E+00 * 1.41E-01 0.00E+00 0.00E+00 0.00E+00 * 1.41E-01 0.00E+00 0.00E+00 0.00E+00 * 1.41E-01 0.00E+00 0.00E+00 0.00E+00 * 1.40E-01 0.00E+00 0.00E+00 0.00E+00 g->2 * 3.56E-02 1.91E-01 0.00E+00 0.00E+00 * 3.54E-02 1.90E-01 0.00E+00 0.00E+00 * 3.53E-02 1.89E-01 0.00E+00 0.00E+00 * 3.52E-02 1.88E-01 0.00E+00 0.00E+00 * 3.51E-02 1.91E-01 0.00E+00 0.00E+00 * 3.51E-02 1.90E-01 0.00E+00 0.00E+00 * 3.52E-02 1.89E-01 0.00E+00 0.00E+00 g->3 * 3.07E-03 1.99E-01 3.17E-01 2.62E-04 * 3.05E-03 1.99E-01 3.17E-01 2.88E-04 * 3.04E-03 1.99E-01 3.17E-01 2.87E-04 * 3.04E-03 1.99E-01 3.17E-01 2.80E-04 * 3.02E-03 1.99E-01 3.17E-01 5.13E-04 * 3.03E-03 1.99E-01 3.18E-01 4.43E-04 * 3.03E-03 1.99E-01 3.18E-01 3.86E-04 g->4 * 0.00E+00 0.00E+00 7.12E-02 6.93E-01 * 0.00E+00 0.00E+00 7.10E-02 7.05E-01 * 0.00E+00 0.00E+00 7.08E-02 7.19E-01 * 0.00E+00 0.00E+00 7.08E-02 7.25E-01 * 0.00E+00 0.00E+00 7.08E-02 6.17E-01 * 0.00E+00 0.00E+00 7.07E-02 6.71E-01 * 0.00E+00 0.00E+00 7.05E-02 6.99E-01 Table B.3: Four groups cross sections of non fuel materials 128 Group * * * * * PRODUCTION * 0.00E+00 0.00E+00 0.00E+00 0.00E+00 * 0.00E+00 0.00E+00 0.00E+00 0.00E+00 * 0.00E+00 0.00E+00 0.00E+00 0.00E+00 * 0.00E+00 0.00E+00 0.00E+00 0.00E+00 * 0.00E+00 0.00E+00 0.00E+00 0.00E+00 FISSION STB1A080 0.00E+00 0.00E+00 0.00E+00 0.00E+00 STB2A090 0.00E+00 0.00E+00 0.00E+00 0.00E+00 STB3A0A0 0.00E+00 0.00E+00 0.00E+00 0.00E+00 H2ORA0H0 0.00E+00 0.00E+00 0.00E+00 0.00E+00 STEAA0L0 0.00E+00 0.00E+00 0.00E+00 0.00E+00 CAPTURE * 8.48E-04 9.24E-04 6.28E-03 1.14E-01 * 2.15E-04 8.83E-05 9.13E-04 1.72E-02 * 5.43E-04 5.18E-04 3.71E-03 6.67E-02 * 1.71E-04 3.26E-05 5.41E-04 1.08E-02 * 1.13E-03 1.30E-03 8.66E-03 1.60E-01 ABSORPTION * 8.48E-04 9.24E-04 6.28E-03 1.14E-01 * 2.15E-04 8.83E-05 9.13E-04 1.72E-02 * 5.43E-04 5.18E-04 3.71E-03 6.67E-02 * 1.71E-04 3.26E-05 5.41E-04 1.08E-02 * 1.13E-03 1.30E-03 8.66E-03 1.60E-01 FISS.SPCTR * 0.00E+00 0.00E+00 0.00E+00 0.00E+00 * 0.00E+00 0.00E+00 0.00E+00 0.00E+00 * 0.00E+00 0.00E+00 0.00E+00 0.00E+00 * 0.00E+00 0.00E+00 0.00E+00 0.00E+00 * 0.00E+00 0.00E+00 0.00E+00 0.00E+00 DIFFUSION1 * 1.40E+00 5.14E-01 4.71E-01 3.02E-01 * 1.91E+00 8.77E-01 7.50E-01 3.03E-01 * 1.58E+00 6.36E-01 5.74E-01 2.95E-01 * 1.97E+00 9.24E-01 7.82E-01 3.04E-01 * 1.32E+00 4.40E-01 3.99E-01 3.10E-01 g->1 * 1.97E-01 0.00E+00 0.00E+00 0.00E+00 * 5.35E-02 0.00E+00 0.00E+00 0.00E+00 * 1.31E-01 0.00E+00 0.00E+00 0.00E+00 * 4.27E-02 0.00E+00 0.00E+00 0.00E+00 * 2.48E-01 0.00E+00 0.00E+00 0.00E+00 g->2 * 3.69E-02 5.28E-01 0.00E+00 0.00E+00 * 1.11E-01 2.60E-02 0.00E+00 0.00E+00 * 7.33E-02 2.89E-01 0.00E+00 0.00E+00 * 1.16E-01 -8.83E-03 0.00E+00 0.00E+00 * 2.29E-03 7.47E-01 0.00E+00 0.00E+00 g->3 * 3.10E-03 1.20E-01 6.53E-01 4.15E-04 * 9.74E-03 3.54E-01 3.00E-01 1.65E-04 * 6.37E-03 2.35E-01 4.82E-01 2.92E-04 * 1.02E-02 3.69E-01 2.76E-01 1.49E-04 * 1.06E-06 1.00E-02 8.22E-01 5.32E-04 g->4 * 0.00E+00 0.00E+00 4.87E-02 9.89E-01 * 0.00E+00 0.00E+00 1.43E-01 1.08E+00 * 0.00E+00 0.00E+00 9.51E-02 1.06E+00 * 0.00E+00 0.00E+00 1.49E-01 1.08E+00 * 0.00E+00 0.00E+00 4.53E-03 9.15E-01