keff uncertainty quantification and analysis due to nuclear data during the full lifetime burnup calculation for a small-sized prismatic high temperature gas-cooled reactor

To benefit from recent advances in modeling and computational algorithms,as well as the availability of new covariance data,sensitivity and uncertainty analyses are needed to quantify the impact of uncertain sources on the design parameters of small prismatic high-temperature gas-cooled reactors(HTGRs).In particular,the contribution of nuclear data to the keff uncertainty is an important part of the uncertainty analysis of small-sized HTGR physical calculations.In this study,a small-sized HTGR designed by China Nuclear Power Engineering Co.,Ltd.was selected for keff uncertainty analysis during full lifetime burnup calculations.Models of the cold zero power(CZP)condition and full lifetime burnup process were constructed using the Reactor Monte Carlo Code RMC for neutron transport calculation,depletion calculation,and sensitivity and uncertainty analysis.For the sensitivity analysis,the Contribution-Linked eigenvalue sensitivity/Uncertainty estimation via Track length importance Characterization(CLUTCH)method was applied to obtain sensitive infor-mation,and the"sandwich"method was used to quantify the keff uncertainty.We also compared the keff uncertainties to other typical reactors.Our results show that 235U is the largest contributor to keff uncertainty for both the CZP and depletion conditions,while the contribution of 239Pu is not very significant because of the design of low discharge burnup.It is worth noting that the radioactive capture reaction of 28Si significantly contributes to the keff uncer-tainty owing to its specific fuel design.However,the keff uncertainty during the full lifetime depletion process was relatively stable,only increasing by 1.12％owing to the low discharge burnup design of small-sized HTGRs.These numerical results are beneficial for neutronics design and core parameters optimization in further uncertainty prop-agation and quantification study for small-sized HTGR.     

确定论数值反应堆程序NECP-X的开发及应用

数值反应堆是基于大规模并行计算平台,利用先进的物理模型和数值模拟算法,采用精细化建模,从而精确模拟反应堆在正常运行与事故工况中发生的各类物理现象的模拟技术。西安交通大学NECP团队基于自研的多群和连续能量数据库,提出了全局 局部耦合输运计算方法、大规模并行的2D/1D耦合输运方法等,开发了基于确定论方法的数值反应堆物理程序NECP X,并在此基础上实现了物理 热工 燃料性能分析的多物理耦合模拟计算。基于该程序及其耦合系统,在商用大型压水堆、研究堆和实验堆中进行了验证应用。数值结果表明,NECP X程序及其耦合系统可准确预测反应堆在运行过程中的关键安全参数随时间的演变情况,如有效增殖因数、功率、温度、应力、间隙宽度等,可为商用大型压水堆、研究堆和研究堆的设计及安全分析提供可靠的工具。     

Development of a method of evaluating an inventory of fission products for a pebble bed reactor

The design of the high temperature gas-cooled reactor (HTGR) has evolved and the relevant safety requirements have been defined; accordingly, the source term to be used as the basis for licensing must also be developed. However, analysis of the source term in the HTGR has not been adequately investigated and there has not been definite improvement in this respect. Because radioactivity in normal operation must be well understood, the purpose of this study is to establish a method for activity evaluation by the code combination MCNP-ORIGEN-MONTEBURNS-MOTEX. The sophisticated method, which constructs the HTR-10 core by using the unit lattice of a hexagonal prism, is developed for core modeling. The MCNP modeling is used to simulate the generation of fission products with an increase of burnup, and ORIGEN is utilized for depletion calculation of each fission product. Continuous fuel management is divided into five discrete periods for the feeding and discharging of fuel pebbles. MONTEBURNS is used for discrete fuel management. In short, this work by aid from MOTEX traces 41 isotope nuclides, the results of which seem highly probable. In addition, the inventory of actinides at the end of each cycle is also investigated. It would be informative when the waste management of spent fuel of HTGRs would be taken into account. This article lays the foundation for future work on the analysis of the source term in HTGRs and will hopefully serve as a platform from which the safety assessment of radioactive material release during accidents can be undertaken in future.     

基于灵敏度对比分析SCALE 6.1自带库与CENDL-TMSR-V1数据库

为满足钍基熔盐堆物理设计和钍铀燃料循环物理分析对核数据的需求，中国核数据中心研制了一套钍铀燃料循环专用数据库CENDL-TMSR-V1。本文利用SCALE程序，针对熔盐堆开展了SCALE 6.1自带数据库和CENDL-TMSR-V1库对比分析。结果显示，针对1 GWt钍增殖熔盐堆，利用两个数据库的238群数据计算的不同燃耗下k_eff最大差异约1 200 pcm。结合核数据对keff的灵敏度分析显示，其差异主要由石墨的核数据不同引起的。宏观检验结果显示，CENDL-TMSR-V1库中石墨数据更合理。同时，基于CENDL-TMSR-V1 44群协方差数据，计算得到核数据对初始时刻k_eff总不确定度为1.03%，约为SCALE 6.1自带44群协方差数据库计算结果的2倍，其差异主要由²³³U、²³²Th等核素的协方差数据不同导致。     

Long life small CANDLE-HTGRs with thorium

CANDLE (constant axial shape of neutron flux, nuclide densities and power shape during life of energy producing reactor) burnup strategy is applied to small (30 MWth) block-type high temperature gas-cooled reactors (HTGRs) with thorium fuel. The CANDLE burnup is adopted in this study since it has several promising merits such as simple and safe reactor operation, and the ease of designing a long life reactor core. Burnup performances of thorium fuel (²³³U, ²³²Th)O₂ are investigated for a range of enrichment ⩽15%. Discharged fuel burnup and burning region motion velocity are major parameters of its performances in this study. The reactors with thorium fuel show a better burnup performance in terms of higher discharged fuel burnup and slower burning region motion velocity (longer core lifetime) compared to the reactors with uranium fuel.     

基于精细燃耗历史及精细燃耗链的球床高温气冷堆燃耗不确定性分析

球床高温气冷堆的燃料管理具有燃料球多次通过堆芯的特点,使得燃料元件经历的燃耗历史十分复杂。球床高温气冷堆堆芯物理设计程序VSOP可以提供燃料元件的精细燃耗历史,但仅包含少量燃耗链和核素种类。而清华大学自主开发的燃耗计算程序NUIT可实现精细燃耗计算,且包含完整燃耗链和核素信息,但不具备精细燃耗历史跟踪功能。本文基于NUIT,结合VSOP提供的球床高温气冷堆精细燃耗历史,开发了球床高温气冷堆堆芯的精细燃耗计算功能,搭建了带有精细燃耗历史模拟和精细燃耗链核素的燃耗分析流程,并实现燃耗不确定性分析功能。在此基础上研究了裂变产额不确定性对球床高温气冷堆燃耗计算不确定性的贡献,并与VSOP的计算结果进行对比。计算分析结果显示,基于NUIT的精细燃耗计算结果和VSOP的燃耗计算结果得到了相互验证,且可以得到更多的核素浓度信息,该计算结果是开展球床高温气冷堆衰变热不确定性研究的基础。     

Experimental validation of effectiveness of rod-type burnable poisons on reactivity control in HTTR

In block-type high temperature gas-cooled reactors (HTGRs), insertion depth of control rods (CRs) into a core should be retained shallow to keep fuel temperature below 1495 °C through a burnup period, and hence excess reactivity should be reduced through a different method. Loading burnable poisons (BPs) into the core is considered as a method to resolve this problem as in case of light water reactors (LWRs). Effectiveness of BPs on reactivity control in LWRs has been validated by experimental data, however, this has not been done yet for HTGRs, because there was not enough burnup characteristics data for HTGRs required for the validation. The High Temperature Engineering Test Reactor (HTTR) is a block-type HTGRs and it adopts rod-type BPs to control reactivity. The HTTR has been operated up to middle burnup, and thereby the experimental data was expected to show effect of the BPs on the reactivity control. Hence, in order to validate effectiveness of rod-type BPs on reactivity control in the HTTR, we investigated on the HTTR results whether the BPs have functioned as designed. As a result, the CRs insertion depth has been retained shallow within allowable range, and then effectiveness of rod-type BPs on reactivity control in the HTTR was validated.     

球床式高温气冷堆MOX燃料循环优化

与压水堆相比,球床式高温气冷堆能在堆芯结构不做明显改变的情况下采用全堆芯装载混合氧化物（MOX）燃料元件。基于250 MW球床模块式高温气冷堆堆芯结构,设计了4种球床式高温气冷堆下MOX燃料循环方式,包括铀钚混合的燃料球和独立的钚球与铀球混合装载的等效方式,采用高温气冷堆设计程序VSOP进行分析,比较了初装堆的有效增殖因数、燃料元件在堆芯内滞留时间、卸料燃耗、温度系数等主要物理特性。结果表明：采用纯铀和纯钚两种分离燃料球且铀燃料球循环时间更长的方案,平均卸料燃耗较高,总体性能较其他循环方式优越。     

Development of a Method for Evaluation of Pin-wise Power Distribution in Fuel Assemblies of Fast Reactors

In the design of fast reactor core with higher burnup and higher linear power, prediction accuracy of burnup history of fuel pin should be upgraded so as to assure fuel integrity without extra design margin under increased neutron fluence and burnup. A method is studied to predict fuel pin-wise power and its burnup history in fast reactors accurately based on an analytic solution of diffusion theory equation on hexagonal geometry with boundary condition from core calculation by finite-differenced diffusion calculation code. The present method is applied to a fast reactor core model, and its accuracy in predicting fuel pin power is tested. The result is compared with the reference solution by the finite difference calculation with very fine mesh. It is found that the present method predicts the power peaking factors in fuel assemblies accurately. The fuel pin-wise nuclide depletion calculation is also done using neutron fluxes for each fuel pin. The result shows that the fuel pin-wise depletion calculation is very important in predicting the burnup history of the fuel assembly in detail.     

Prediction of Nongaseous Fission Products Behavior in the Primary Cooling System of High Temperature Gas-Cooled Reactor

In high temperature gas-cooled reactors (HTGRs), some amounts of fission products (FPs) are released mainly from fuel with failed coatings and are transported in the primary cooling system with the primary coolant during normal operation. In that case, condensable FPs plateout on the inner surface of components in the primary cooling system. On the other hand, since the HTGRs use helium gas as primary coolant, the primary coolant is not activated itself and very small amount of corrosion products is generated. Then, γ-ray emitted from the FPs becomes main source in shielding design of the HTGRs, and not only release amount from fuel but also plateout distributions of the FPs should be properly evaluated. Therefore, prediction of plateout behavior in the primary cooling system of HTGRs was carried out based on the calculation result of plateout distribution in High Temperature Engineering Test Reactor. Before the calculation, analytical model was verified by comparison with experimentally obtained plateout distributions and the applicability of the model to predict the plateout distributions in the primary cooling system of HTGR was certified.

This report describes the predicted result of plateout distribution in the primary cooling system of HTGR together with the verification result of the analytical model.     

Safety design

JAERI established the safety design philosophy of the HTTR based on that of current reactors such as LWR in Japan, considering inherent safety features of the HTTR. The strategy of defense in depth was implemented so that the safety engineering functions such as control of reactivity, removal of residual heat and confinement of fission products shall be well performed to ensure safety. However, unlike the LWR, the inherent design features of the high-temperature gas-cooled reactor (HTGR) enables the HTTR meet stringent regulatory criteria without much dependence on active safety systems. On the other hand, the safety in an accident typical to the HTGR such as the depressurization accident initiated by a primary pipe rupture shall be ensured. The safety design philosophy of the HTTR considers these unique features appropriately and is expected to be the basis for future Japanese HTGRs.This paper describes the safety design philosophy and safety evaluation procedure of the HTTR especially focusing on unique considerations to the HTTR. Also, experiences obtained from an HTTR safety review and R&D needs for establishing the safety philosophy for the future HTGRs are reported.     

HTGR experience, programs, and future applications

This paper reviews the current status of the programs for the development of high-temperature gas-cooled reactors (HTGRs) in the major industrial countries of the world. Existing demonstration plants and facilities are briefly described, and national programs for exploiting the unique high-temperature capabilities of the HTGR for commercial production of electricity and in process steam/heat applications are discussed.     

Small high temperature gas-cooled reactors with innovative nuclear burning

Since the innovative concept of CANDLE (Constant Axial shape of Neutron Flux, nuclide densities and power shape During Life of Energy producing reactor) burning strategy was proposed, intensive research works have been continuously conducted to evaluate the feasibility and the performance of the burning strategy on both fast and thermal reactors. We learned that one potential application of the burning strategy for thermal reactors is for the High Temperature Gas-Cooled Reactors (HTGR) with prismatic/block-type fuel elements. Several characteristics of CANDLE burning strategy such as constant reactor characteristics during burn-up, no need for burn-up reactivity control mechanism, proportionality of core height with core lifetime, sub-criticality of fresh fuel elements, etc. enable us to design small sized HTGR with a high degree of safety, easiness of operation and maintenance, and long core lifetime which are required for introducing the reactors into remote areas or developing countries with limited infrastructures and resources. In the present work, we report our evaluation results on small sized block-type HTGR designs with CANDLE burning strategy and compared with other existing small HTGR designs including the ones with pebble fuel elements, under both uranium and thorium fuel cycles.     

Small PWRs using coated particle fuel for district heating, PFPWR50

It has been said that nuclear energy is an important option for especially developing countries to satisfy their increasing energy demand. However, it will be difficult to deploy first of a kind nuclear power plant in developing countries because extensive safety demonstration has to be conducted in industrialized countries. On the other hand, it will be essential to present rigid proof of reliable operational experience to develop proper understanding of the safety features of new reactor systems among the people around the demonstration plant sites. One of the ways to solve the issue is to integrate existing technologies supported by a great deal of data and experience into a new reactor design. Based on the consideration, a small-sized district heating reactor system based on the pressurized water reactor (PWR) technologies combined with the fuel concept of high temperature gas cooled reactors (HTGRs) has been studied. The purpose of the combination of these two existing concepts is to take the best advantages of both excellent operational experience of PWRs and the integrity of HTGR fuel, coated particle fuel, against fission products release even at high temperature. We expect that this approach will help create a breakthrough to the current stagnation of nuclear power deployment.     

Validation of IRBURN calculation code system through burnup benchmark analysis

Assessment of the reactor fuel composition during the irradiation time, fuel management and criticality safety analysis require the utilization of a validated burnup calculation code system. In this work a newly developed burnup calculation code system, IRBURN, is introduced for the estimation and analysis of the fuel burnup in LWR reactors. IRBURN provides the full capabilities of the Monte Carlo neutron and photon transport code MCNP4C as well as the versatile code for calculating the buildup and decay of nuclides in nuclear materials, ORIGEN2.1, along with other data processing and linking subroutines. This code has the capability of using different depletion calculation schemes.     

Modeling spent TRISO fuel for geological disposal: corrosion and failure under oxidizing conditions in the presence of water

High temperature gas reactors (HTGRs) are being considered for near term deployment in the United States under the GNEP program and farther term deployment under the Gen IV reactor design (U.S. DOE Nuclear Energy Research Advisory Committee, 2002). A common factor among current HTGR (prismatic or pebble) designs is the use of TRISO coated particle fuel. TRISO refers to the three types of coating layers (pyrolytic carbon, porous carbon, and silicon carbide) around the fuel kernel, which is both protected and contained by the layers. While there have been a number of reactors operated with coated particle fuel, and extensive amount of research has gone into designing new HTGRs, little work has been done on modeling and analysing the degradation rates of spent TRISO fuel for permanent geological disposal. An integral part of developing a spent fuel degradation modeling was to analyze the waste form without taking any consideration for engineering barriers. A basic model was developed to simulate the time to failure of spent TRISO fuel in a repository environment. Preliminary verification of the model was performed with comparison to output from a proprietary model called GARGOYLE that was also used to model degradation rates of TRISO fuel. A sensitivity study was performed to determine which fuel and repository parameters had the most significant effect on the predicted time to fuel particle failure. Results of the analysis indicate corrosion rates and thicknesses of the outer pyrolytic carbon and silicon carbide layers, along with the time dependent temperature of the spent fuel in the repository environment, have a significant effect on the time to particle failure. The thicknesses of the kernel, buffer, and IPyC layers along with the strength of the SiC layer and the pressure in the TRISO particle did not significantly alter the results from the model. It can be concluded that a better understanding of the corrosion rates of the OPyC and SiC layers, along with increasing the quality control of the OPyC and SiC layer thicknesses, can significantly reduce uncertainty in estimates of the time to failure of spent TRISO fuel in a repository environment.     

Neutronic and thermo-hydraulic analyses of a small,long-life HTGR for passive decay-heat removal

Since the accident at Fukushima Daiichi Nuclear Power Plant in 2011, design concepts for nuclear reactors have been reconsidered with much greater emphasis placed upon passive systems for decay-heat removal. By considering this issue, the design parameter conditions for high temperature gas-cooled reactors (HTGRs) with passive safety features of decay-heat removal were obtained by residual-heat transfer calculation using equations for fundamental heat transfer mechanisms in our previous works. In the present study, the appropriate size of reactor core for a 100 MW_t reactor operating at 1123 K of the initial core temperature was found using the conditions. Consequently, neutronics and thermo-hydraulic analyses for the proposed reactor core were performed and the proper optimizations to control the excess reactivity and flatten the change in power peaking factor during operation were done successfully. By the systematic method to decide the core design which satisfies the condition for passive decay-heat removal, a long-life small HTGR concept whose excess reactivity was small during the operation was shown. The small excess reactivity is a significant advantage from the view point of safety in reactivity accident.     

Relation between static and dynamic Young's modulus of nuclear graphites and carbon

In order to evaluate precisely the stresses and strains generated in the graphite structures of high temperature gas-cooled reactors (HTGRs), it is necessary to use not only correct stress-strain relationships but also proper values of the Young's modulus of HTGR graphites. In this study the relation between the Young's modulus obtained from the slope of the stress-strain curve at the origin and that measured by the ultrasonic wave propagation method was examined on two grades of HTGR graphites (IG-110 and PGX) and a grade of carbon materials (ASR-ORB). One of the main conclusions obtained here is that the ratio of the static Young's modulus to the dynamic one depends upon the accuracy of the strain measurement. If the Young's modulus which is evaluated from the secant at 0.01 to 0.05% strain is taken as the static modulus, the dynamic Young's modulus measured using a 5-MHz transducer is approximately equal to the static one.     

燃耗信任制下燃耗计算对临界计算的偏差及不确定度的研究

为量化燃耗信任制中燃耗计算传递给临界计算的不确定度,本文基于参数统计法对燃耗计算的核素偏差及偏差不确定度展开分析,并以蒙特卡罗（MC）抽样方法计算的kinf不确定度为基准,比较不同抽样方法对临界计算不确定度的影响。结果表明,核素偏差与偏差不确定度是随样品燃耗变化的分段函数。对于临界计算,拉丁超立方抽样（LHS）方法与MC抽样方法的kinf不确定度计算结果吻合较好,且LHS方法可考虑参数间的相关性,计算结果更真实,可进一步提升电厂的经济性。     

Desirability of small reactors, HTGR in particular

Small reactors of about 100–300 MWe, High Temperature Gas Cooled Reactors (HTGRs) in particular, are considered desirable in future, based on the following ways of thinking;

Global scale enhancement of nuclear energy is considered necessary from reduction of environment impact point of view.

Small reactors are desirable, due to (a) enhanced safety in terms of fuel inventory and inherent safety, then (b) easier plant siting, near populated or industrial area, (c) more flexible development, planning and construction than larger reactors by finer adjustment with demand, and (d) economic competitiveness attainable by means of adoption of more rationalized systems categorization, simpler and modularized design, mass production in factory, less work at construction site, and marketability including that of developing countries.

In such ways, small reactors can be economically designed, constructed and operated, by conquering “scale de-merit”, in contrast with scale merit of larger reactors as seen in current LWRs.

Small HTGRs, in particular, are mostly desirable and promising, from view points of wider applications, such as electricity use, wide range of heat uses and/or cogenaration, Pu burning with high efficiency, wider fuel cycle options, using U, Pu and/or Th, with or without reprocessing, and development stages, where not only test reactor programs for development & demonstration but also realization programs are already going on towards commercial operation start in 2005–2010.

Development programs on small HTGR, related global activities and cost evaluations by developers and JAPC are shown, and steps towards their global scale commercializations are proposed.