Coolant void reactivity adjustments in advanced CANDU lattices using adjoint sensitivity technique

Coolant void reactivity (CVR) is an important factor in reactor accident analysis. Here we study the adjustments of CVR at beginning of burnup cycle (BOC) and k_eff at end of burnup cycle (EOC) for a 2D Advanced CANDU Reactor (ACR) lattice using the optimization and adjoint sensitivity techniques. The sensitivity coefficients are evaluated using the perturbation theory based on the integral neutron transport equations. The neutron and flux importance transport solutions are obtained by the method of cyclic characteristics (MOCC). Three sets of parameters for CVR-BOC and k_eff-EOC adjustments are studied: (1) Dysprosium density in the central pin with Uranium enrichment in the outer fuel rings, (2) Dysprosium density and Uranium enrichment both in the central pin, and (3) the same parameters as in the first case but the objective is to obtain a negative checkerboard CVR-BOC (CBCVR-BOC). To approximate the EOC sensitivity coefficient, we perform constant-power burnup/depletion calculations using a slightly perturbed nuclear library and the unperturbed neutron fluxes to estimate the variation of nuclide densities at EOC. Our aim is to achieve a desired negative CVR-BOC of −2 mk and k_eff-EOC of 0.900 for the first two cases, and a CBCVR-BOC of −2 mk and k_eff-EOC of 0.900 for the last case. Sensitivity analyses of CVR and eigenvalue are also included in our study.     

核电站循环停堆日期预测及循环长度的评价

核电站反应堆循环停堆日期预测及循环长度的评价都是为燃料管理提供设计输入.本文介绍了两种循环停堆日期预测方法,并指出了其适用范围;同时介绍了循环长度的标定方法,并用该方法评价了几个循环的理论循环长度,最后分析了标定误差.     

Sensitivity and uncertainty analysis for reactor stable period induced by positive reactivity using one-point adjoint kinetics equation

In order to better predict the kinetic behavior of a nuclear fission reactor, improvement of delayed neutron parameters is essential. Since it is required to establish a path from the microscopic nuclear data to the macroscopic delayed neutron parameters for the improvement, the present paper identifies important nuclear data for reactor kinetics. Sensitivities of the reactor stable period, which describes reactor kinetic behavior, to microscopic nuclear data such as independent fission yields, decay constants and decay branching ratios are calculated efficiently by using the adjoint kinetics equation. Furthermore, nuclide-wise and nuclear data-wise uncertainties of the reactor stable period are quantified using the variance data given in the nuclear data file, and the nuclear data that require further improvement are identified.

The results obtained through the present study are quite helpful, and can be a driving force for further nuclear physics studies.     

在蒙特卡罗程序中统计共轭通量并计算中子动力学参数的方法

文章介绍了在蒙特卡罗程序中,使用反复裂变几率的统计结果作为共轭通量的估计,并作为权重函数计算动力学参数β_eff和Λ的方法,阐释了在连续能量蒙特卡罗程序MCNP和多群蒙特卡罗程序MCMG中实现这种方法的过程。数值校验结果表明：在几乎不带来附加计算量的同时,在MCMG中使用该方法统计得到的共轭通量与ANISN的共轭通量计算结果符合较好,在MCNP中使用该方法计算得到的中子动力学参数与基准测量结果符合较好。在蒙特卡罗程序中实现了高效率计算中子动力学参数的功能,为蒙特卡罗程序进一步用于反应堆动态行为的分析奠定了基础。     

Science and Technology of Reactor Reactor Core Geometry Arrangement Research of Spent Fuel Critical Facility

With the development of nuclear power, the nuclear critical safety problem becomes more and more significant. The burnup credit technology has been applied to analysis of the nuclear critical safety. This has significantly enhanced the capacity of storing, transportation, reprocessing and improved the economy of back end fuel cycle. It is very important to carry out critical experiment on spent fuel for selecting calculation code packages and validating calculation methods using burnup credit technology. Before building the spent fuel critical experimental facility, massive detailed critical calculation should be performed.     

基于改进变分节块法的共轭中子通量密度计算技术

共轭中子通量密度对于核安全和压水堆（PWR）中的探测器计算有着重要的意义,为了消除现有节块方法在处理由于控制棒移动带来的非均匀节块（包括非均匀的截面和不连续因子）时所造成的较大误差,本文提出一种改进的变分节块法（VNM）。确定了不同于前向方程的共轭节块方法的连续条件,不同于传统VNM在全局建立泛函,本文方法为每一个节块建立泛函;构建了含非均匀不连续因子的乘子项,以显式处理表面不连续的共轭中子通量密度;除共轭体中子通量密度、截面和表面分中子流密度外,将表面不连续因子展开为分段正交多项式来构造响应矩阵。含有非均匀节块的BEAVRS基准题数值结果证明,同传统VNM相比,改进的VNM可以将非均匀问题的有效共轭增殖系数和燃料区共轭中子通量密度偏差降低2个量级,有利于实现前向与共轭中子通量密度的高精度内积计算。     

Effect of lattice-level adjoint-weighting on the kinetics parameters of CANDU reactors

Space–time kinetics calculations for CANDU^®1 reactors are routinely performed using the Improved Quasistatic (IQS) method. The IQS method calculates kinetics parameters such as the effective delayed-neutron fraction and generation time using adjoint weighting. In the current implementation of IQS, the direct flux, as well as the adjoint, is calculated using a two-group cell-homogenized reactor model which is inadequate for capturing the effect of the softer energy spectrum of the delayed neutrons. Additionally, there may also be fine spatial effects that are lost because the intra-cell adjoint shape is ignored. The purpose of this work is to compare the kinetics parameters calculated using the two-group cell-homogenized model with those calculated using lattice-level fine-group heterogeneous adjoint weighting and to assess whether the differences are large enough to justify further work on incorporating lattice-level adjoint weighting into the IQS method. A second goal is to evaluate whether the use of a fine-group cell-homogenized lattice-level adjoint, such as is the current practice for Light Water Reactors (LWRs), is sufficient to capture the lattice effects in question. It is found that, for CANDU lattices, the generation time is almost unaffected by the type of adjoint used to calculate it, but that the effective delayed-neutron fraction is affected by the type of adjoint used. The effective delayed-neutron fraction calculated using the two-group cell-homogenized adjoint is 5.2% higher than the “best” effective delayed-neutron fraction value obtained using the detailed lattice-level fine-group heterogeneous adjoint. The effective delayed-neutron fraction calculated using the fine-group cell-homogenized adjoint is only 1.7% higher than the “best” effective delayed-neutron fraction value but is still not equal to it. This situation is different from that encountered in LWRs where weighting by a fine-group cell-homogenized adjoint is sufficient to calculate the correct effective delayed-neutron fraction. It is concluded that lattice-level weighting with a detailed fine-group heterogeneous adjoint is desirable for the correct calculation of the effective delayed-neutron fraction in CANDU lattices.     

Necessity of nuclear fuel cycle closure

The results of a systems study confirming on a new level the need to develop fast reactors with a closed nuclear fuel cycle and the best transition times to a closed nuclear fuel cycle are presented. The results obtained show that nuclear fuel cycle closure is a necessary step for developing large-scale nuclear power in the country. Nuclear fuel cycle closure using fast reactors with inherent safety is justified economically even now.     

Automatic boiling water reactor loading pattern design using ant colony optimization algorithm

An automatic boiling water reactor (BWR) loading pattern (LP) design methodology was developed using the rank-based ant system (RAS), which is a variant of the ant colony optimization (ACO) algorithm. To reduce design complexity, only the fuel assemblies (FAs) of one eight-core positions were determined using the RAS algorithm, and then the corresponding FAs were loaded into the other parts of the core. Heuristic information was adopted to exclude the selection of the inappropriate FAs which will reduce search space, and thus, the computation time. When the LP was determined, Haling cycle length, beginning of cycle (BOC) shutdown margin (SDM), and Haling end of cycle (EOC) maximum fraction of limit for critical power ratio (MFLCPR) were calculated using SIMULATE-3 code, which were used to evaluate the LP for updating pheromone of RAS. The developed design methodology was demonstrated using FAs of a reference cycle of the BWR6 nuclear power plant. The results show that, the designed LP can be obtained within reasonable computation time, and has a longer cycle length than that of the original design.     

Uncertainty quantification of neutronic parameters of light water reactor fuel cells with JENDL-4.0 covariance data

Neutronic parameter uncertainty induced by nuclear data uncertainty is quantified for several light water reactor fuel cells composed of different combinations of fissile/fertile nuclides. The covariance data given in JENDL-4.0 are used as the nuclear data uncertainty, and uncertainty propagation calculations are carried out using sensitivity coefficients calculated with the generalized perturbation theory for burnup-related neutronic parameters.

It is found that main contributors of nuclear data uncertainty to the neutronic parameter uncertainty are the uranium-238 capture cross section in a uranium-oxide fuel cell, and the plutonium-240 and plutonium-241 capture cross sections and fission spectrum of fissile plutonium isotopes in a uranium–plutonium mixed-oxide fuel cell. It is also found that thorium-232 capture cross section uncertainty is a dominant source of neutronic parameter uncertainty in thorium–uranium and thorium–plutonium mixed-oxide fuel cells. It should be emphasized that precise and detail information of component-wise uncertainties can be obtained by virtue of the adjoint-based sensitivity calculation methodology. Furthermore, cross-correlations are evaluated for each fuel cell, and strong correlations among the same parameters at the beginning of cycle and at the end of cycle and among different parameters are observed.     

反应堆机组停堆检修后重返满功率运行的堆芯控制策略研究

核电站压水堆(PWR)在寿期末长时间停堆后重返满功率的运行过程中,堆芯控制存在困难,常常不能够安全快速地进入满功率运行。本文通过对影响堆芯控制的各种因素和物理过程进行分析,提出了一套基于临界点状态选择,在升功率期间采用提升功率控制棒和硼浓度稀释相结合的堆芯控制策略,并进行了实际验证。对重返临界点的选择和影响因素的分析直接影响后期操作,是堆芯控制策略的基础。策略对相同状况下的PWR堆芯控制有一定的指导意义。     

A sensitivity analysis of thermal lattices kinetic parameters with respect to the spectral weighting function using ultrafine BN method

Accurate calculation of kinetic parameters is of utmost importance in the safety analysis of a nuclear reactor. In the current paper, two approaches are investigated to evaluate these parameters in energy phase space. In the first approach, these parameters are derived from an energy-continuous form of the forward and adjoint transport equations and then integrals with respect to the energy variable are replaced by weighted summations over the energy groups, while in the second approach these parameters are extracted from the multi-group forward equation and its associate adjoint equation in which their multigroup constants are weighted by forward spectrum. The difference of weighting functions in these two approaches would naturally lead to different values for the kinetic parameters. This paper mainly compares the outcome of these two approaches in calculating kinetic parameters for two main types of thermal critical lattices: Mixed Oxide (MOX) and Uranium Oxide (UOX) using ultrafine B_N method. The results show that calculations which are based on using the forward weighted spectrum for generating the kinetic parameters underestimate prompt neutron generation time in both thermal lattices, while effective delayed neutron fraction is overestimated in UOX thermal lattice and underestimated in MOX one.     

A general survey of the potential and the main issues associated with the sulfur–iodine thermochemical cycle for hydrogen production using nuclear heat

The thermochemical sulfur–iodine cycle is studied by CEA with the objective of massive hydrogen production using nuclear heat at high temperature. The challenge is to acquire by the end of 2008 the necessary decision elements, based on a scientific and validated approach, to choose the most promising way to produce hydrogen using a generation IV nuclear reactor. Amongst the thermochemical cycles, the sulfur–iodine process remains a very promising solution in matter of efficiency and cost, versus its main competitor, conventional electrolysis. The sulfur–iodine cycle is a very versatile process, which allows lot of variants for each section which can be adjusted in synergy in order to optimise the whole process. The main part of CEA's program is devoted to the study of the basic processes: new thermodynamics data acquisition, optimisation of water and iodine quantity, optimisation of temperature and pressure in each unit of the flow-sheet and survey of innovative solutions (membrane separations for instance). This program also includes optimisation of a detailed flow-sheet and studies for a hydrogen production plant (design, scale, first evaluations of safety issues and technico-economic questions). This program interacts strongly with other teams, in the framework of international collaborations (Europe, USA for instance).     

基准模型keff对核数据的灵敏度分析及不确定度量化

为研究有效增殖因数（k_eff）对核反应数据的灵敏度,以科学量化核数据导致k_eff计算的不确定度,编制了输运计算积分量灵敏度及不确定度分析程序SURE。该程序采用多群S_N输运计算方法计算k_eff、角通量和伴随角通量,基于微扰理论确定k_eff对核数据的灵敏度,利用协方差数据量化评估k_eff计算的不确定度。利用ENDF/B-Ⅶ.1评价中子核数据库,制作了输运计算所需的多群核数据、灵敏度分析所需的各反应道多群截面和中子群转移矩阵、不确定度分析所需的多群协方差数据。采用上述数据,利用SURE分析了基准模型Godiva和Jezebel的k_eff计算值对核数据的灵敏度,以及核数据导致的模拟计算的不确定度。SURE的灵敏度计算结果与MCNP程序及FORSS程序计算结果符合较好。     

华龙一号平衡循环燃料管理策略研究

核电厂燃料管理的主要任务是在约定的限制条件下,为核电厂一系列的运行循环做出其经济安全运行的全部决策,确定最佳的各循环装料策略。一座核电厂从建成到退役期间要经历初始循环、过渡循环、平衡循环序列,平衡循环在理想情况下是一个无限的循环序列,一般认为平衡循环是性能指标最佳的循环方案,并为燃料管理人员定为目标运行循环。基于华龙一号百万千瓦级核电厂,通过对燃料组件和可燃毒物的合理布置及优化,采用了混合富集度燃料组件的换料策略,进行了平衡循环的燃料管理方案设计。结果表明,燃料管理方案在循环长度、核焓升因子、慢化剂温度系数、停堆裕量和组件卸料燃耗方面均满足预先设定的燃料管理目标。平均批卸料燃耗和燃料组件燃耗限值的比值约为0.92,与AP1000、EPR等三代核电站相当,具有非常好的燃料经济性。     

Development of two-energy group,two-dimensional,frequency dependent detector adjoint function based on the nodal method

A nodalization technique has been demonstrated to calculate the response of a detector to a vibrating absorber in a reactor core using a concept of local/global components, based on the frequency dependent detector adjoint function. The technique was developed for two-energy group one-dimensional or one-energy group two-dimensional reactor core geometry. The purpose of this research was to expand the applicability of a nodalization model technique to calculate the real and the imaginary parts of the detector adjoint function for two-energy group two-dimensional reactor geometry. The frequency dependent detector adjoint functions presented by complex equations were expanded into real and imaginary parts. In the nodalization technique, the flux or detector adjoint function is expanded into polynomials about the center point of each node. A computer code was developed to calculate static flux for two-energy group, two-dimensional reactor geometry. The eigen value (k_eff) and static flux were calculated for the Iowa State University UTR-10 reactor and the results were compared against the values calculated using the computer code exterminator. The eigen values were within less than 0.1% agreement. The phase angle and the detector adjoint function for the frequency of 10 rad/s were calculated for a detector located in the center of a 60×60 cm reactor. The phase angle calculated by the nodalization model technique varied from 0.2° near the source to 0.4° away from the source. These values are well within the range of the phase angle value of 0.2° calculated using the zero power transfer function. The thermal detector adjoint function peaked in the center as expected. The discontinuity in the current of the real thermal detector adjoint function at the detector position was observed as expected. The average current based on the polynomials on the left node of the interface and the right node of the interface matched within 1% of the average value at the interface. The current of the imaginary fast and thermal detector adjoint function on both sides of the interface varied ±2% from the average value at the interface. No discontinuity in the current was observed in the case of the fast real and imaginary and thermal imaginary components of the detector adjoint function at the detector location.     

自主化堆芯三维核设计软件COCO研发

中国广东核电集团正在开发的三维堆芯核设计软件COCO将具备堆内功率分布计算、精细功率分布计算、临界硼浓度搜索、控制棒临界搜索、核子密度计算等基本功能。COCO采用格林函数节块方法作为求解器计算堆芯的功率分布,采用单通道模型和棒传热模型来计算慢化剂的密度和燃料温度。COCO已实现从寿期初到寿期末的燃耗计算能力。通过与参考程序的数值比较发现,COCO采用的理论模型和耦合流程正确,计算精度可满足工程设计的需要。     

European new build and fuel cycles in the 21st century

Nuclear energy is back on the agenda worldwide. In order to prepare for the next decades and to set priorities in nuclear R&D and investment, it is important to assess the future nuclear fuel cycle. This allows to identify the triggers which influence the market penetration of future nuclear reactor technologies.To this purpose, fuel cycle scenarios for a future nuclear reactor park in Europe have been analysed applying an integrated dynamic process modelling technique. The assessment was undertaken using the DANESS code (Dynamic Analysis of Nuclear Energy System Strategies, developed by Argonne National Laboratory (US)). This code allows to provide a complete picture of mass flows and economics of the various nuclear fuel cycle scenarios.The present assessment recognizes the integrated nuclear fuel cycle and concentrates on the evolution under consideration of increased uranium prices, increased costs for geological disposal, lifetime extension of the current reactor park, and various nuclear energy demand scenarios. The analyses show that the future European nuclear park will consist of a mix of Gen-III and Gen-IV reactors. The relative shares of the reactor types in the total mix depend on the applied boundary conditions such as the future nuclear energy demand, the reactor characteristics, and the assumed economical factors. Furthermore, the analyses highlight the triggers influencing the choices between different nuclear energy deployment scenarios, and enable an evaluation of future types and amounts of nuclear waste. In addition, a dynamic assessment is made with regard to employment of manpower for a future nuclear fleet in the different scenarios. Finally an estimate is provided of the radiological impact on the regional population due to the release of potentially hazardous radionuclides during the different steps in the nuclear fuel cycle.     

Formulation of the two-group stochastic Feinberg-Galanin equations for heterogeneous lattices

The general problem of neutron noise in an infinite heterogeneous reactor consisting of plate-type fuel elements of identical nuclear properties embedded in a moderator is formulated in the two-group diffusion theory by using the source-sink method of Feinberg and Galanin.After linearizing the neutronic stochastic differential equations, the heterogeneous kinetic adjoint equations are formulated and solved by assuming that the detectors are only sensitive to thermal neutrons.It is shown that in a heterogeneous analysis, a localized noise source will give rise to additional local noise components in the response of a near-by detector. These components have very similar properties to the conventional local component of the homogeneous two-group theory but their existence is due to the attenuation of the signal in the pure moderator and is not directly related to the number of energy groups used in the analysis.     

蒙特卡罗共轭输运法计算反应堆压力容器快中子注量率

为了保证压力容器（RPV）在核电厂寿期内的安全,通过理论方法准确评估其受到的快中子积分注量率非常重要。本文提出了一种应用共轭输运理论解决深穿透问题的计算方法,并将该方法的计算结果与基准题HBR-2给出的实测值及确定论方法的结果进行了比较。结果表明：本文计算结果与基准题给出的实测数据吻合良好,大多反应率计算相对误差小于10%,最大相对误差不超过35%;70%以上的计算结果准确性优于确定论方法,表明本文提出的解决蒙特卡罗深穿透问题的方法是有效且准确的。