百万千瓦级压水堆核电站长燃耗堆芯钆可燃毒物优化研究

对百万千瓦级参考核电站长燃耗堆芯（１８个月换料）采用的可燃毒物（钆）含量与堆芯燃料管理主要结果进行了分析研究。该研究采用先进的燃料管理程序系统,对不同可燃毒物含量和不同可燃毒物棒根数的燃料组件进行了计算,给出了组件无限增殖因子（ｋｉｎｆ）随燃耗的变化关系,据此对参考堆芯采用相同的装载进行了４种方案燃料管理计算。计算结果表明,对于堆芯燃料管理,采用低可燃毒物含量、含可燃毒物棒数多的装载方案明显优于高可燃毒物含量、含可燃毒物棒少的堆芯装载方案。     

长寿期压水堆板状燃料组件可燃毒物选型研究

可燃毒物在长寿期压水堆中起着至关重要的作用,板状燃料组件在长寿期压水堆中具有较好的应用前景。本文开展长寿期压水堆板状燃料组件可燃毒物选型及中子学特性研究,对含不同可燃毒物的板状燃料组件进行输运-燃耗计算,筛选出中子学性能较好的可燃毒物。结果表明,采用富集同位素157Gd、167Er和B4C作为可燃毒物时,几乎无反应性惩罚;当采用PACS-J和231Pa作为可燃毒物时,因其自身特性,在寿期末不仅未造成反应性惩罚,且延长了组件寿期,提高了燃料利用率;PACS-J与慢燃耗可燃毒物组合,可获得更优的反应性曲线。由本文结果可知,板状燃料组件可以选用富集同位素157Gd、富集同位素167Er、B4C、231Pa和PACS-J作为可燃毒物,可燃毒物组合可以选用PACS-Er和PACS-Pa两种组合方案。     

Core reload optimization for equilibrium cycles using simulated annealing and successive linear programming

An algorithm is developed to determine directly all the parameters of the optimal equilibrium cycle. The core reload scheme is described by discrete variables, while the cycle length, as well as uranium enrichment and loading of burnable poison in each feed fuel assembly, are treated as continuous variables. An important feature of the algorithm is that all these parameters are determined by the solution of one big optimization problem. To search for the best reload scheme, simulated annealing is applied. The optimum cycle length as well as uranium enrichment and loading of burnable poison in each feed fuel assembly are determined for each reload pattern examined using successive linear programming. The uranium enrichments and loadings of burnable poison are considered to be distinct in different feed fuel assemblies. The number of batches and their sizes are not fixed, and also determined by the algorithm. As the first step of the numerical investigation of the algorithm, a problem of feed fuel cost minimization for a target equilibrium cycle length and fixed batch sizes is considered. The algorithm developed is demonstrated to provide about 2% less feed fuel cost than the ordinary simulated annealing algorithm.     

锕系可燃毒物板状燃料组件燃耗特性研究

为研究锕系可燃毒物在板状燃料组件的燃耗特性和延长寿期的适用性,本研究以不同富集度的板状燃料为对象,计算分析了相同初始组件无限增殖因数(k_inf)情况下的锕系可燃毒物装载量、燃耗深度、²³⁵U利用率等。结果表明,在低富集度(4%～7%)情况下,240Pu可燃毒物在寿期内表现出较好的转换效应,²³⁵U利用率高,可起到延长堆芯寿期的作用;在中等富集度(25%～40%)情况下,240Pu可燃毒物的转换效应减弱,而²³¹Pa可燃毒物表现出较好的转换效应;在高富集度(70%～97%)情况下,²³¹Pa可燃毒物的转换效应减弱,但含²³¹Pa组件的²³⁵U利用率和达到的燃耗深度在所选锕系核素中最大;240Pu可作为长寿期低富集度燃料可燃毒物的选择,²³¹Pa可作为长寿期中等、高富集度燃料可燃毒物的选择。     

Local power peaking factor estimation in nuclear fuel by artificial neural networks

This paper presents the training of an artificial neural network (ANN) to accurately predict, in very short time, a physical parameter used in nuclear fuel reactor optimization: the local power peaking factor (LPPF) in a typical boiling water reactor (BWR) fuel lattice. The ANN training patterns are distribution of fissile and burnable poison materials in the fuel lattice and their associated LPPF. These data were obtained by modeling the fuel lattices with a neutronic simulator: the HELIOS transport code. The combination of the pin U²³⁵ enrichment and the Gd₂O₃ (gadolinia) concentration, inside the 10 × 10 fuel lattice array, was encoded by three different methods. However, the only encoding method that was able to give a good prediction of the LPPF was the method which added the U²³⁵ enrichment and the gadolinia concentration. The results show that the relative error in the estimation of the LPPF, obtained by the trained ANN, ranged from 0.022% to 0.045%, with respect to the HELIOS results.     

华龙一号“177堆芯”特点分析

华龙一号（HPR1000）压水堆核电厂最显著的技术特征是反应堆采用由177个燃料组件构成的堆芯（简称“177堆芯”）,具有完全的自主知识产权。为深入分析其特点,本文介绍了“177堆芯”的主要技术特征,并在燃料组件及控制棒组件数目方面与157个燃料组件构成的堆芯（简称“157堆芯”）进行了对比分析;对2种典型反应堆堆芯（“177-A堆芯”与“177-B堆芯”）装载方案的异同进行了叙述和评价。结果表明,与“157堆芯”相比,“177堆芯”在安全性和经济性方面更有优势;2种典型堆芯的首循环装载布置各有所长,在可燃毒物选材上,“177-B堆芯”优于“177-A堆芯”。最后,从取消堆芯中央位置控制棒组件、设置堆芯径向金属反射层、实施无中子源启动、分批装载自主化燃料组件以及优化堆芯活性段长度等5个方面给出了HPR1000反应堆堆芯的优化建议。      

含有可燃毒物的压水堆核电站堆芯装料设计优化研究

含可燃毒物的压水堆装料优化是燃料管理优化研究中的难点,应用通常的脱耦方法和优化算法效率低、全局性差。研究提出局部脱耦方法用以简化问题规模、缩小搜索空间,选择特征统计算法进行优化方案的搜索。利用局部脱耦方法结合特征统计算法研制出压水堆核电站堆芯LP和BP耦合装料优化程序CSALPBP。使用该程序对大亚湾第10循环和第12循环进行了装料优化计算。结果表明CSALPBP程序在求解含可燃毒物的压水堆装料优化问题方面具有很高的搜索效率和很好的全局性,能够较好地解决含可燃毒物的压水堆堆芯装料优化难题。     

Technetium transmutation in thin layer coating on PWR fuel rods

Based on the EFTTRA-T2 experiment results, we study the transmutation characteristics of pressurized water reactors (PWR) after coating a thin layer of Tc-99 on the fuel rods. Our calculation shows that for the same Tc-99 loading amount, the effect on the PWR k_eff after coating Tc-99 on the PWR fuel rods is much less than that of the homogeneous addition of Tc-99 to uranium dioxide nuclear fuel. If we just coat 0.2λ_c (0.0065 mm) thickness Tc-99 on PWR fuel rods, the total Tc-99 coating amount is about 291.37 kg, this is approximately equivalent to the 4 PWR Tc-99 annual outputs, and the system k_eff merely decreases to 0.98530.Loading Tc-99 to the PWR is equivalent to introducing extra poisons to PWR system to control excess reactivity, some control poisons like boric acid concentration in primary coolant or burnable poison rods in fuel assemblies are needed to be removed to keep the reactor in criticality. As Tc-99 coating thickness increases from 0.05λ_c to 0.2λ_c, no matter which substitution pattern is used, B16→12 or C16→12, the system k_eff variations are almost the same and can return to criticality again after removing corresponding burnable poison rods from fuel assemblies. For coating 0.15λ_c or 0.2λ_c thickness on the fuel rods of PWR, the system k_eff is slightly below the criticality either in B16→12 or C16→12 substitution pattern, we may reduce the concentration of the boric acid slightly to let the system in criticality again.Our calculation results indicate that the optimal coating thickness of Tc-99 on PWR fuel rods is probably between 0.15λ_c to 0.2λ_c, i.e. 0.00488–0.0065 mm.     

Design studies of a typical PWR core using advanced computational tools and techniques

This study deals with the design and development of calculational techniques and evaluation of key neutronic parameters of a typical PWR core having a total reactor power of 2652 MW_t (890 MW_e). The PWR core consists of 157 fuel assemblies containing a total of ∼72 tons of uranium arranged vertically in a concentric square array within the core shroud. Each fuel assembly contains 264 UO₂ fuel pins with various enrichments (2.1, 2.6 and 3.1%), 24 control rods of Gd₂O₃ and one central water channel and all are arranged in a 17 × 17 array of matrix. Different computer codes including WIMS, TWOTRAN, CITATION and MCNP have been employed to develop a versatile and accurate reactor physics model of the PWR core. The computational methods, tools and techniques, customization of cross section libraries, various models for cells and super cells, and a lot of associated utilities have been standardized and established/validated for the overall core analysis. The analyses were performed in 3 steps: firstly for fuel pincells, then for the fuel assemblies and finally for the whole core. The WIMS and MCNP calculated infinite multiplication factors for fuel pincells having 2.1% enriched ²³⁵U were found to be 1.23393 and 1.23654, for 2.6% enrichment 1.28635 and 1.28887, and finally for 3.1% enrichment 1.32481 and 1.32812, respectively. For fuel assembly, WIMS and MCNP calculated infinite multiplication factors having 2.1% enrichment were found to be 1.24853 and 1.25445, for 2.6% enrichment 1.30372 and 1.30992, and for 3.1% enrichment 1.34424 and 1.35041, respectively. The effective multiplication factor calculated by CITATION, TWOTRAN and MCNP for whole core were found to be 1.25580, 1.25909 and 1.26382, respectively. The peak thermal neutron flux in the core calculated by MCNP was found to be 5.0298 × 10¹⁴ neutrons/cm² s and the average core power density was 17.1 kW/cm³. The calculated results from different codes were found to be very good agreement for different moderator conditions. The choice of computer codes like WIMSD, TWOTRAN, CITATION and MCNP which are being used in nuclear industry for many years were selected to identify and develop new capabilities needed to support PWR analysis. The ultimate goal of the validation of the computer codes for PWR applications is to acquire and reinforce the capability of these general purpose computer codes to perform the core design and optimization study.     

Optimization studies of fuel loading pattern for a typical Pressurized Water Reactor (PWR) using particle swarm method

A three dimensional multi-energy group computer model PRISHA, which solves the neutron diffusion equations using finite difference method is developed for Pressurized Water Reactor (PWR). This computer code can find an optimum loading of a group of fresh fuel assemblies along with fuel assemblies of different exposures. The successive line over relaxation (SLOR) method is used to solve neutron diffusion equations. After validation of this part of computer code against an IAEA – PWR benchmark problem with 177 fuel assemblies in the core, particle swarm optimization (PSO) method is incorporated in the code for finding the optimum fuel loading pattern. A typical PWR core with 157 fuel assemblies, where 289 fuel pins are arranged in 17 × 17 rectangular arrays in a fuel assembly, was analyzed using this computer model for two cycles using PSO method. Different numbers of particles and iterations were used in PSO method. The results are found to be not very sensitive to either the number of particles or the number of iterations used in PSO method for considered case. However, a number of experiments have to be performed to arrive at the best global fitness parameter. Reasonably low power peaking factors were obtained for both the cycles.     

Burnup characteristics and performance of boron nitride and boron coated urania and urania-gadolinia fuels

In this research the burnup performance of (1) boron nitride (BN) and (2) boron nitride-boron (B), hybrid coated urania (UO₂) and urania-gadolinia (Gd₂O₃) fuels were studied. The behavior of fuel burnup, depletion of BN and B, the effect of coating thickness and also Gd₂O₃ content on the burnup performances of the fuels were found by using the code WIMS-D/5 for pressurized water reactor (PWR) and boiling water reactor (BWR) fuel assemblies. The optimum thickness ratio of B to BN was found as 4 and their thicknesses were chosen as 4 and 1 μm, respectively. Based on this observation, calculations were performed for the standard fuel assemblies with and without burnable poison and similar assemblies with BN-B hybrid coating with the desired BN-B thicknesses. Results are discussed to make an assessment of the effect of such hybrid coating on fuel cycle characteristics.     

Development of enriched Gd-155 and Gd-157 burnable poison designs for a PWR core

In this study, a genetic algorithm developed by the authors was applied to design the optimal enriched Gd-155 and Gd-157 burnable poisons in a reference PWR TMI-1 core. The CASMO-4/TABLES/SIMULATE-3 package calculated the neutronic performance of the enriched UO₂/Gd₂O₃ fuel pin configurations. These configurations included different fractions of neutron absorbing isotopes Gd-155 and Gd-157, and 100 w/o enriched Gd-155 designs. Fuel cost analysis was performed to evaluate the economical benefits of these optimized enriched gadolinium designs. The break-even point for unit Gd-155 enrichment cost was determined to be around ∼$30/gram-Gd-155 with current unit cost scenario. The projected savings were 3.13% in gross and 2.08% in net compared to total fuel cycle cost of a reference TMI-1 core loading, if all of the 68 feed assemblies would be replaced with the optimized designs.     

Fuel lattice design in a boiling water reactor using an ant-colony-based system

This paper presents a new approach to deal with the boiling water reactor radial fuel lattice design. The goal is to optimize the distribution of both, the fissionable material, and the reactivity control poison material inside the fuel lattice at the beginning of its life. An ant-colony-based system was used to search for either: the optimum location of the poisoned pin inside the lattice, or the U²³⁵ enrichment and Gd₂O₃ concentrations. In the optimization process, in order to know the parameters of the candidate solutions, the neutronic simulator CASMO-4 transport code was used. A typical 10 × 10 BWR fuel lattice with an initial average U²³⁵ enrichment of 4.1%, used in the current operation of Laguna Verde Nuclear Power Plant was taken as a reference. With respect to that reference lattice, it was possible to decrease the average U²³⁵ enrichment up to 3.949%, this obtained value represents a decrease of 3.84% with respect to the reference U²³⁵ enrichment; whereas, the k-infinity was inside the ±100 pcm’s range, and there was a difference of 0.94% between the local power peaking factor and the lattice reference value. Particular emphasis was made on defining the objective function which is used for making the assessment of candidate solutions. In a typical desktop personal computer, about four hours of CPU time were necessary for the algorithm to fulfill the goals of the optimization process. The results obtained with the application of the implemented system showed that the proposed approach represents a powerful tool to tackle this step of the fuel design.     

轻水堆含钆燃料棒稳态辐照行为分析

国内外的压水堆燃料组件最新设计中,广泛采用钆燃料（UO₂-Gd₂O₃）作为可燃毒物来控制初始反应性和展平堆芯功率分布。钆燃料棒的性能与普通燃料棒存在较大差异,本文利用燃料元件性能分析程序FRAPCON-3.5对BR3堆内含钆燃料棒性能进行计算,并与实验测量值进行比较。结果表明：FRAPCON-3.5对含钆燃料棒的计算结果与实验测量值符合较好;含钆燃料棒在辐照初期强化了燃料棒自屏效应,对燃料的径向功率分布影响显著;在平均功率密度相同的情况下,燃料中加入钆会导致热导率降低,芯块温度升高;钆含量不同,裂变气体释放及燃料和包壳的变形略有差异。     

Recommended strategy and limitations of burnable absorbers used in VVER fuel assemblies

There is an obvious effort to increase the burn up of used fuel assemblies in order to improve fuel utilization.A more effective operation can be realized by extending the fuel cycles or by increasing the number of reloadings.This change is nevertheless connected with increasing the uranium enrichment even above 5% of 235 U. Burnable absorbers are widely used to compensate for the positive reactivity of fresh fuel. With proper optimization, burnable absorbers decrease the reactivity excess at the beginning of the cycle, and they can help with stabilization of power distribution. This paper describes properties of several materials that can be used as burnable absorbers. The change in concentration or position of the pin with a burnable absorber in a fuel assembly was analyzed by the HELIOS transport lattice code. The multiplication factor and power peaking factor dependence on fuel burn up were used to evaluate the neutronic properties of burnable absorbers. The following four different materials are discussed in this paper: Gd_2O_3, IFBA, Er_2O_3,and Dy_2O_3.Gadolinium had the greatest influence on fuel characteristics. The number of pins with a burnable absorber was limited in the VVER-440 fuel assembly to six. In the VVER-1000 fuel assembly, 36 pins with a burnable absorber can be used as the assembly is larger. The erbium depletion rate was comparable with uranium burn up.Dysprosium had the largest parasitic absorption after depletion.     

含可燃毒物的压水堆堆芯装料优化

含可燃毒物的压水堆堆芯装料优化是燃料管理优化研究中的难点。应用通常的优化算法效率低、全局性差,特征统计算法更适合求解该优化问题。本研究克服了原特征统计算法装料优化将组件布置(LP)优化和新组件可燃毒物配置(BP)优化脱耦处理的缺陷,对LP和BP同时进行优化,结合堆芯分析程序CYCLE2D,成功地研制了压水堆LP和BP耦合优化程序CSALPBP。用该程序对大亚湾2号机组第10循环进行了堆芯装料优化计算。结果表明：CSALPBP程序具有很高的搜索效率和很好的全局性。     

可燃毒物提高小型压水堆堆芯寿期研究

针对长寿期堆芯的应用需求,开展了提高小型压水堆堆芯寿期研究。以棒状燃料为对象,对不同栅格尺寸和不同可燃毒物的选取进行计算,得出小型压水堆堆芯寿期相关影响因素。通过对不同尺寸的燃料栅格进行输运 燃耗计算,得到燃耗最佳栅格尺寸。以燃耗最佳栅格尺寸建立组件,并选择转换性能好的锕系核素²⁴⁰PuO₂作为可燃毒物,利用²⁴⁰Pu吸收中子转换成易裂变核素²⁴¹Pu的特性,对堆芯实现反应性控制和寿期延长。本研究通过对燃料栅格尺寸和可燃毒物的合理选择,提高了燃料利用率,达到延长堆芯寿期的目的。     

压水堆堆芯换料设计优化的研究

讨论压水堆堆芯换料设计优化问题，并研制一套实用的换料优化软件包，可用于低泄漏、外－内和改进的外－内装料方案的优化。在低泄漏方案优化时，利用哈林原理将燃料组件布置与可燃毒物配置的优化问题脱耦成两步优化问题。先用线性规划方法进行无可燃毒物时燃料组件布置的优化，然后再用可变容差法寻找可燃毒物的优化布置。应用该软件对秦山核电厂首次难芯换料方案进行了优化，提出了可供参考的一些优化布置方案。     

Optimization of BWR fuel lattice enrichment and gadolinia distribution using genetic algorithms and knowledge

An optimization methodology based on the Genetic Algorithms (GA) method was developed for the design of radial enrichment and gadolinia distributions for boiling water reactor (BWR) fuel lattices. The optimization algorithm was linked to the HELIOS code to evaluate the neutronic parameters included in the objective function. The goal is to search for a fuel lattice with the lowest average enrichment, which satisfy a reactivity target, a local power peaking factor (PPF), lower than a limit value, and an average gadolinia concentration target. The methodology was applied to the design of a 10 × 10 fuel lattice, which can be used in fuel assemblies currently used in the two BWRs operating at Mexico. The optimization process showed an excellent performance because it found forty lattice designs in which the worst one has a better neutronic performance than the reference lattice design. The main contribution of this study is the development of an efficient procedure for BWR fuel lattice design, using GA with an objective function (OF) which saves computing time because it does not require lattice burnup calculations.