Tuyển tập báo cáo Hội nghị Khoa học Công nghệ hạt nhân toàn quốc lần thứ 14 Proceedings of Vietnam conference on nuclear science and technology VINANST-14 PHÂN TÍCH ĐỘ NHẠY VÀ ĐỘ BẤT ĐỊNH CỦA MỘT SỐ ĐỒNG VỊ ĐỐI VỚI HỆ SỐ KEFF CỦA QUÁ TRÌNH KHỞI ĐỘNG LÒ PHẢN ỨNG HẠT NHÂN ĐÀ LẠT VỚI NHIÊN LIỆU HEU SỬ DỤNG CHƯƠNG TRÌNH MCNP6 VÀ THƯ VIỆN ENDF/B-VIII.0 SENSITIVITY AND UNCERTAINTY ANALYSIS OF MAJOR ISOTOPES ON THE KEFF OF THE STARTUP DNRR CORE WITH HEU FUEL USING MCNP6 AND ENDF/B-VIII.0 LIBRARY CHU THOI NAMA, VU THANH MAIA, AND TRAN HOAI NAMB a VNU University of Science, Vietnam National University, Hanoi, 334 Nguyen Trai, Thanh Xuan, Hanoi 10000, Vietnam b Institute of Fundamental and Applied Sciences, Duy Tan University, Ho Chi Minh city, Vietnam Tóm tắt: Mục tiêu nghiên cứu đánh giá độ nhạy độ bất định hệ số nhân hiệu dụng keff q trình khởi động lị với 88 nhiên liệu độ giàu cao (HEU) lò phản ứng hạt nhân Đà Lạt từ thư viện liệu hạt nhân ENDF/B-VIII.0 Các đồng vị có độ nhạy cao tính tốn bao gồm U-235, H-1, Al-27, U-238, B-10, C-12 Fe-56 Từ cấu trúc độ nhạy 44 nhóm kết hợp với ma trận phương sai xử lý mơ-đun ERRORR từ chương trình xử lý liệu NJOY2016 sử dụng để phân tích độ định Kết tính tốn thu độ bất định lớn với đồng vị H-1 cho phản ứng bắt neutron (0.3094%) tán xạ đàn hồi (0.2384%), sau đến đồng vị U-235 cho phản ứng phân hạch (0.1641%) Từ khóa: Độ nhạy, độ bất định, DNRR, ENDF/B-VIII.0 Abstract: This study presents the evaluation of the sensitivity and uncertainty of major isotopes on the effective multiplication factor (keff) of the startup core with 88 HEU fuel bundles of the Dalat Nuclear Research Reactor (DNRR) on the ENDF/B-VIII.0 nuclear data The calculations were performed some high sensitivity isotopes including U-235, H-1, Al-27, U-238, B-10, C-12 and Fe-56 using the MCNP6.1 code The structural sensitivity of 44 groups and the covariance matrices obtained by the ERRORR module of the NJOY2016 code were used in the uncertainty analysis The results show that the greatest uncertainty was found with the isotope H-1 for neutron capture (0.3094%) and elastic scattering (0.2384%), then U-235 for fission reaction (0.1641%) Keywords: Sensitivity, uncertainty, DNRR, ENDF/B-VIII.0 INTRODUCTION Dalat nuclear research reactor (DNRR) is a pool-type research reactor loaded with Russian VVR-M2 fuel type The DNRR plays an important role in the generation of neutron sources for the purpose of isotope production in industry, radiopharmaceuticals in medicine, research and development in nuclear technology, and training reactor operators [1, 2] The core region consists of interstitial 121 cells, control rods, beryllium rods, neutron trap regions, horizontal beam tubes, etc This complicated core components and structure can only be simulated precisely using a Monte Carlo simulation code In previous works, the DNRR cores have been extensively simulated using a number of codes, such as SRAC, MCNP5, etc [3-5] However, the computational codes also produce certain errors in the results due to numerical algorithms, simulation models, design data, and nuclear data libraries Therefore, it is necessary to evaluate the reliability of the calculated data, including the uncertainty from the isotopic reaction cross-sections caused by the nuclear data library [6, 7] In this study, sensitivity and uncertainty analysis of some major isotopes in the fuel, coolant and structural materials on the effective multiplication factor of the startup DNRR core has been performed using the MCNP6 code and the ENDF/B-VIII.0 nuclear data library [8] METHODOLOGY 2.1 Description of the DNRR The DNRR is a pool-type research reactor with the power output of 500 kWt The DNRR core was loaded with Russian VVR-M2 fuel type with high enrichment uranium (HEU) 36 wt% before converting to low enrichment uranium (LEU) fuel in 2011 The DNRR core consists of 121 regular hexagonal grid cells to place fuel bundles, control rods, neutron traps, aluminum rods, beryllium blocks and irradiation channels [3-5] Table describes the detailed specifications of the DNRR The startup core configuration consists of 52 Tiểu ban A: Lò phản ứng, Điện hạt nhân Đào tạo nguồn nhân lực Section A: Nuclear reactor, Nuclear power and Human resource training 88 HEU fuel bundles and control rods, including one automatic regulating rod (AR), four shim rods (ShR) and two safety rods (SR) The automatic regulating rod (AR) is made of stainless steel, while other rods are made of B4C [9] In this study, the sensitivity and uncertainty analysis has been performed for the startup core of 88 fuel bundles Figure depicts the MCNP6 model of the startup DNRR core a Vertical cross section b Horizontal cross section of core Figure 1: MCNP6 model of the DNRR core with 88 HEU fuel bundles Table 1: Specification of the DNRR with HEU fuel [1] Specification Reactor type Nominal thermal power Moderator and Coolant Cooling mechanism Reflector Active core height Active core diameter Fuel bundle pitch Fuel HEU type Fuel cladding Number of control rods Neutron measuring channels Irradiation channel Horizontal channel Description Pool type 500 kW Light water Natural convection Graphite, Beryllium and water 60 cm 44,2 cm 3,2 cm VVR-M2 type U-Al alloy, 235U enrichment 36 wt% Aluminum alloy SAV-1 (2 safety rods, shim rods, regulating rod) (3 fission chamber detector, ionization chamber detector) (1 neutron trap, wet channel, dry channels) (1 tangential channel, radial channels) 2.2 Method for sensitivity and uncertainty analysis Calculation scheme of sensitivity and uncertainty of some isotopes on the effective multiplication factor keff of the DNRR core based on the ENDF/B-VIII.0 nuclear data library with 44 energy groups [6] is depicted in Figure The sensitivity coefficient represents the effect of some reactions (such as elastic, inelastic, capture, fission, total ν ) on keff The sensitivity of isotopes according to 12 types of reactions performed by the KSEN mode of the MCNP6 code [10] The sensitivity coefficient of the keff is structured according to the sensitivity matrix S as follows: 53 Tuyển tập báo cáo Hội nghị Khoa học Cơng nghệ hạt nhân tồn quốc lần thứ 14 Proceedings of Vietnam conference on nuclear science and technology VINANST-14 𝑆1 𝑆2 𝑆=[ ] ⋮ 𝑆44 (1) The covariance matrix of the reactions of each isotope was processed with the ERRORR card by NJOY2016 [11] with 44 corresponding energy groups Then, the resulting sensitivity matrix has the form: 𝐶1,1 𝐶1,2 ⋯ 𝐶1,44 𝐶2,2 ⋯ 𝐶2,44 𝐶 (2) 𝐶 = 2,1 ⋮ ⋮ ⋮ ⋱ [𝐶44,1 𝐶44,2 ⋯ 𝐶44,44 ] The uncertainty (U) is then calculated according to the “Sandwich Rule” [12, 13] as follows: (3) U=√𝑆 𝐶 𝑆 𝑇 From Eq (3), it is seen that the uncertainty of some isotopes according to the reaction depends on the corresponding sensitivity If the sensitivity is high, the uncertainty of the results will be large Therefore, it is necessary to reduce the statistic error of the sensitivity calculation using the MCNP6 code In this study, the MCNP6 calculations were performed with 106 neutrons of neutron of neutron history per cycle and run for 250 cycles with 50 inactive cycles to ensure a statistic error of the keff within 6pcm Figure 2: Sensitivity and uncertainty calculation scheme [7] RESULTS AND DISCUSSION 3.1 Sensitivity analysis The sensitivities with the absolute values greater than 0.1% obtained from KSEN mode of MCNP6 with 44 energy groups of the ENDF/B-VIII.0 nuclear data library are summarized in Tables and The reactions of some major isotopes with positive sensitivities are shown in Table Six reactions with the largest contribution are total ν and fission reactions of U-235, elastic scattering of H-1, C-12, Be-9, Al-27 and O-16 Meanwhile, the negative sensitivity is mainly due to neutron absorption reactions such as neutron capture of H-1, U-235, Al-27, U-238 or alpha production of B-10 Thus, the isotopes U-235, H-1, C-12, Be-9, B-10, Al-27, U-238 expected to cause the main influence on the system calculation results keff of the core DNRR Figures to show the energy-dependent sensitivity of the reaction cross-sections of each some isotopes We see that the light isotopes including H-1, Be-9, C-12, O-16, Al-27 have large positive sensitivity for elastic scattering in the fast neutron energy region The positive sensitivity peaks of the isotopes range from about 2.3 MeV to 2.5 MeV In addition, the isotopes H-1, Be-9, Al-27 have negative sensitivities for neutron capture in the thermal neutron energy region from 0.0075 eV to 0.2 eV, with a concave of sensitivity at an energy of 0.045 eV corresponding to minimum sensitivities -6.02E-02 (H-1), 54 Tiểu ban A: Lò phản ứng, Điện hạt nhân Đào tạo nguồn nhân lực Section A: Nuclear reactor, Nuclear power and Human resource training 1.12E-03 (Be-9) and -2.50E-02 (Al-27) Meanwhile, for B-10, because of the characteristics of the alpha production reaction, the negative sensitivity is found in the energy region from 30 eV to 17 keV Besides, Fe-56 has a negative sensitivity for the (n,γ) reaction in the energy region similar to that of H-1, Be-9 and Al-27, with a minimum sensitivity of -8.77E-04 However, the positive sensitivity of elastic scattering is significant from thermal neutron energies (0.0253 eV) to the fast neutron energy region Table 2: Positive sensitivities of keff in the increasing direction Table 3: Negative sensitivities of keff in the decreasing direction Isotopes U-235 U-235 H-1 C- 12 Be-9 Al-27 O-16 C-nat (S(𝛂,𝛃)) Reaction Total ν Fission Elastic Elastic Elastic Elastic Elastic Elastic Sensitivity 9.98E-01 3.52E-01 2.89E-01 4.50E-02 4.40E-02 3.84E-02 3.76E-02 7.74E-03 Isotopes Reaction Sensitivity H-1 Capture -1.48E-01 U-235 Capture -1.24E-01 Al-27 Capture -6.00E-02 U-238 Capture -2.30E-02 B-10 n-α -1.10E-02 Be (S(𝛂,𝛃)) Elastic -4.08E-03 C-nat (S(𝛂,𝛃)) Fe-56 U-238 Be (S(𝛂,𝛃)) Inelastic Elastic Total ν Inelastic 6.93E-03 2.65E-03 2.12E-03 Be-9 Capture -2.66E-03 Fe-56 Capture -2.11E-03 U-234 Capture -2.10E-03 U-238 Fission 1.46E-03 1.82E-03 Figure shows the energy sensitivity dependence for U-235 The positive sensitivities of total ν and fission reactions have a peak in the thermal neutron region from 0.0003 eV to eV, with maximum value at 0.045 eV Also, there is a minimum for the negative sensitivity of the gamma capture in this thermal energy region From Fig and 5, it can be seen that the negative sensitivity of the neutron capture starts from 0.00253 eV, and has a large value in the energy regions of - 8.1 eV for U-238 and 4.75 - eV for U-234, which corresponds to the first resonance peak of U-238 of 6.67 eV and U-234 of 5.2 eV, respectively 55 Tuyển tập báo cáo Hội nghị Khoa học Cơng nghệ hạt nhân tồn quốc lần thứ 14 Proceedings of Vietnam conference on nuclear science and technology VINANST-14 Figure 3: Energy dependent sensitivities of k to H-1, Be-9, B-10 and C-12 cross sections Figure 4: Energy dependent sensitivities of k to O-16, Al-27, Fe-56 and U-234 cross sections 56 Tiểu ban A: Lò phản ứng, Điện hạt nhân Đào tạo nguồn nhân lực Section A: Nuclear reactor, Nuclear power and Human resource training Figure 5: Energy dependent sensitivities of k to U-235 and U-238 cross sections Figure 6: Energy dependent sensitivities of k to Be-9 S(α,β) (be-met.40t) and C-12 S(α,β) (grph.40t) Figure shows the energy-dependent sensitivities of Be-9 S(α,β) and C-12 S(α,β) The negative sensitivity for the elastic scattering response of Be-9 S(α,β) lies on the thermal neutron energy range from 7.5x10-3 eV to 0.0325 eV Meanwhile, the negative sensitivity of inelastic scattering from 2.53x10-2 to 0.225 eV and a positive sensitivity from 0.25 eV to eV For the sensitivity of C-12 S(α,β), both elastic scattering and elastic scattering have positive sensitivities The positive sensitivity of elastic scattering is in the range of 0.01 eV to 0.15 eV, while the sensitivity of inelastic scattering is further extended from 0.01 eV to 4.76 eV 3.2 Uncertainty analysis Table 4: The uncertainty of keff due to the uncertainty of the reaction cross-sections of some isotopes Isotopes H-1 Reaction Capture Uncertainty 0.3094% Isotopes C-12 Reaction Elastic Uncertainty 0.0233% H-1 Elastic 0.2384% U-238 Capture 0.0221% U-235 Fission 0.1641% O-16 Elastic 0.0168% Al-27 Capture 0.1373% Be-9 Capture 0.0135% Al-27 Elastic 0.1206% Fe-56 Capture 0.0048% Be-9 Elastic 0.0466% U-238 Fission 0.0017% U-235 Capture 0.0339% Table shows the uncertainty of some isotopes according to the reactions based on Eq (3) The uncertainty of the isotopes according to the reaction is less than 0.35% of reactivity effect In which, the highest uncertainty values of H-1 are found with capture reaction (0.3094%) and elastic scattering (0.2384%) The next isotope that affects to the keff uncertainty is U-235 due to the uncertainty of the fission 57 Tuyển tập báo cáo Hội nghị Khoa học Cơng nghệ hạt nhân tồn quốc lần thứ 14 Proceedings of Vietnam conference on nuclear science and technology VINANST-14 and neutron capture reaction cross-sections The Al-27 isotope also contributes to significant uncertainty of keff, resulting from the inaccuracy of the data of neutron capture and elastic scattering cross sections of approximately 0.14% and 0.12%, respectively CONCLUSION Sensitivity and uncertainty of some major isotopes in the fuel, coolant and structural materials on the effective multiplication factor keff of the startup DNRR core with 88 HEU bundles have been analyzed using the MCNP6 code and the ENDF/B-VIII.0 nuclear data library The high positive sensitivities are found with the total ν and fission reaction of U-235, elastic scattering of H-1, C-12, B-9, Al-27, O-16 The largest negative sensitivities are from neutron captures of H-1, U-235, Al-27, U-238 or alpha production reaction of B-10 Based on the sensitivity profile and 44-group covariance matrix of ENDF/B-VIII.0 from the nuclear data processing system NJOY, the uncertainty of the keff for some isotopes according to the reaction is also 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