End Of Cycle Research Articles

A sensitivity study of BWR instability over global and regional modes at different exposures

Boiling water reactors have unique mechanisms coupling between neutronic and two-phase flow thermalhydraulic behaviors, and may exhibit in-phase (global mode) instability and out-of-phase (regional mode) instability. In some observation modes, the regional mode instability is associated with an increase in power in one half of the core and a simultaneous decrease in power in the other half, such that the average power remains essentially constant. Yet in practice, sometimes the real situation is hidden, the neutron flux may oscillate more vigorously than expected. To investigate the stability behavior at the stability boundary from BOC (beginning of cycle) to EOC (end of cycle), fractional changes of the decay ratio are used to evaluate the parametric sensitivity of the global mode and the regional mode at different exposures. Decay ratios for regional mode oscillations are much less than those under core-wide conditions. Current studies demonstrated that for some of the parameters under particular conditions, the variation in the regional mode decay ratio exceeded that in the global mode. In this work, the thermalhydraulic parameters (such as flow rate and system pressure) exhibit a more sensitive regional variation than global. Moreover, some parameters (density reactivity coefficient and delayed-neutron fraction, for example) depend on the shape of the axial power shape; for the bottom peak axial power shape, the regional mode decay ratio variation is more sensitive than global; for the top peak axial power shape, the opposite is true.

Application of minimum plutonium criteria at EOC to optimize the fuel loading pattern in VVER-1000 reactors

Most of the strategies yet implemented to optimal fuel loading pattern design in nuclear power reactors, are based on maximizing the core effective multiplication factor ( K eff) to extract maximum energy and lowering the local power peaking factor ( P q) from a predetermined value. However, a new optimization criterion could be of interest, aiming at maximum burn-up of the plutonium content in fuel assemblies, i.e., minimization of remaining plutonium in spent fuel at the end of cycle (EOC). In this research, we developed a new strategy for optimal fuel core loading pattern of a VVER-1000 reactor, based on multi-objective optimization: lowering the P q, maximization of the K eff and minimization of remaining plutonium ( Pu) in fuels at EOC. This strategy has been implemented considering exact calculations of fuel burn-up during the equilibrium cycle using WIMSD and CITATION calculation codes. We used the genetic algorithm to find the optimum fuel loading pattern. Simulation results show that this strategy can reduce the remaining Pu of the fuels at EOC while considering limitations on core power peaking and multiplication factor.

Design and analysis of HYPER

KAERI (Korea Atomic Energy Research Institute) has been developing an accelerator driven transmutation system called HYPER (hybrid power extraction reactor). It is designed to transmute long-lived TRU and fission products such as Tc-99 and I-129. HYPER is a 1000 MW th system with k eff = 0.98 which requires 17 mA proton beam for an operation at EOC (end of cycle). Pb–Bi is used as the coolant and target material at the same time. HYPER core has 186 ductless hexagonal fuel assemblies. The fuel blanket is divided into three TRU (transuranic elements) enrichment zones to flatten the radial power distribution. The core height of HYPER was compromised at 150 cm, and the power density was determined such that the average coolant speed could be about 1.64 m/s. The inlet and exit coolant temperatures are 340 and 490 °C, respectively, in the core. The cylindrical beam tube and spherical window is adopted as the basic window design of HYPER. We have also introduced an Lead–Bismuth eutectic injection tube to maximize the allowable proton beam current. A metallic alloy of U-TRU-Zr is considered as the HYPER fuel, in which pure lead is used as the bonding material. As a result, a large gas plenum is placed above the active core. TRU transmutation rate is 282 kg/yr. In the case of a FP transmutation, 28.0 kg of Tc-99 and 7.0 kg of I-129 are incinerated per year. The MACSIS-H (metal fuel performance analysis code for simulating the in-reactor behavior under steady-state conditions-HYPER) for an metallic fuel was developed as the steady-state performance computer code. The MATRA (multichannel analyzer for transient and steady-state in rod array) code was used to perform the thermal-hydraulic analysis of HYPER core.

Genetic Algorithm to Optimize the UO2/Gd2O3 Fuel Pin Designs in a Pressurized Water Reactor

An efficient and practical genetic algorithm (GA) was developed to optimize the UO2/Gd2O3 fuel pin burnable poison (BP) configurations for fresh fuel assembly (FA) designs loaded in a pressurized water reactor core. The objective of the optimization was to minimize the residual binding due to residual Gd isotopes in the fuel at the end of cycle (EOC). The GA process for creating new BP designs in a coded form called genotypes is generated randomly resulting in a large number of invalid designs. Each new BP design or genotype created by the new GA must be decoded into its corresponding phenotype so that it can be evaluated with a coupled fuel lattice and core depletion calculation. It is essential that most of the invalid designs be eliminated before performing the precise coupled fuel lattice calculation because of the long CPU time that it takes for this calculation. The elimination was accomplished in the new GA by incorporating a beginning-of-cycle (BOC) Kinf filter. The BOC Kinf filter eliminated most of the invalid new genotypes by assigning a high negative penalty to all genotypes that have a BOC Kinf greater than some limit (1.065) for the reference TMI-1 FA. This filter eliminates the need for performing coupled lattice and core depletion calculations for these genotypes. It accelerated the solution process and allowed evaluation of all new genotypes within one day. In this way, the GA minimized the residual binding using an objective function, which maximized the EOC soluble boron (SB) concentration. In essence, the EOC SB or its equivalent EOC keff was maximized.

Developing a Tool for Simulating the Behavior of Axial Flux Difference during Power Reduction for Maanshan Pressurized Water Reactor Units

A tool, AFDCONTROL, is developed to help the operators of pressurized water reactors predict axial flux difference (AFD) and find the control rod positions for power maneuvers. AFDCONTROL has used an off-line procedure to simulate AFD.After adopting a long-cycle strategy as the fuel management policy of Maanshan nuclear power plant (MNPP), AFD control during the power reduction near end of cycle (EOC) becomes more difficult than before. In this study, we have used AFDCONTROL to simulate this trend. AFDCONTROL suggests that AFD (even at higher burnup conditions) can be controlled by extending the power reduction rate. After implantation of the AFDCONTROL tool in MNPP, the operators of MNPP units have used AFDCONTROL to find the control rod sequences and positions under certain power reduction rates to control AFD without violating limits, especially at EOC of the high-burnup cycle.

Genetic Algorithm Application for Burnable Poison Placement in PWRs with Optimized UO2/Gd2O3 Fuel Pin Configurations

In this paper, an efficient genetic algorithm has placed burnable poisons (BPs) into all of the fresh fuel positions in the core employing the optimized BP configurations and techniques developed in two previous papers. Of importance was the previous development of a Kinf filter, which greatly reduced the computational time. The Kinf filter eliminated many of the invalid genotypes/phenotypes before making a precise core depletion analysis. An extensive BP library was generated by the CASMO-4/TABLES-3 codes. The process was automated with a user-friendly program developed for this purpose. The BPs were vendor UO2/Gd2O3 fuel assembly designs used in a reference Three Mile Island Unit 1 core. The optimized UO2/Gd2O3 fuel pin configurations have small residual binding at end of cycle (EOC), and BP loading optimization results with 97.2 ppm soluble boron at EOC while it was 94.4 ppm with the available vendor designs. The result was that optimized UO2/Gd2O3 fuel pin configurations were developed with unique self-shielding properties and residual binding that also provided a 6.89% reduction in the total required Gd amount, providing extra savings in fuel cost.

Use of 240Pu Waste as a Burnable Absorber in Light Water Reactors

Current burnable absorbers such as boron carbide placed in the control rod guide tubes of fresh fuel assemblies create a water displacement penalty at end of cycle (EOC) that reduces the overall maximum cycle length of the reactor. Other burnable absorbers such as gadolinium-oxide mixed in the fuel do not create the water displacement penalty but create a lower centerline melt temperature for the fresh fuel and reduce the overall enrichment for the assembly. This research proposes using a transuranic (TRU) isotope with a relatively high absorption cross section such as 240Pu to reduce excess criticality within the reactor at beginning of cycle. The added benefit of using this TRU isotope over a standard burnable absorber is that when it absorbs a neutron it no longer negatively affects the criticality of the reactor, and it will transmutate into a fissile material that will add to the overall criticality of the reactor at EOC.

Application of genetic algorithms to optimize burnable poison placement in pressurized water reactors

An efficient and a practical genetic algorithm (GA) tool was developed and applied successfully to Burnable Poison (BP) placement optimization problem in the reference Three Mile Island-1 (TMI-1) core. Core BP optimization problem means developing a BP loading map for a given core loading pattern that minimizes the total Gadolinium (Gd) amount in the core without violating any design constraints. The number of UO 2/Gd 2O 3 pins and Gd 2O 3 concentrations for each fresh fuel location in the core are the decision variables. The objective function was to minimize the total amount of Gd in the core together with the residual Gd reactivity binding at the End-of-Cycle (EOC). The constraints are to keep the maximum peak pin power during the core depletion and soluble boron (SOB) concentration at the Beginning of Cycle (BOC) both less than their limit values. The innovation of this study was to search all of the possible UO 2/Gd 2O 3 fuel assembly designs with variable number of UO 2/Gd 2O 3 fuel pins and concentration of Gd 2O 3 in the overall decision space. The use of different fitness functions guided the solution towards desired (good solutions) region in the solution space, which accelerated the GA solution. The main objective of this study was to develop a practical and efficient GA tool and to apply this tool to designing an optimum BP pattern for a given core loading.

Sensitivity analysis for AHWR fuel cluster parameters using different WIMS libraries

India is presently engaged in the design of an advanced heavy water reactor (AHWR) which utilises thorium as fuel. The AHWR is a boiling light water cooled heavy water moderated reactor where the heat is removed through natural convection. Dysprosium is used as burnable absorber to get a reduction in void reactivity. The design needs to be well validated. The 69 group old WIMS library distributed by NEA in 1980′s is presently being used for the design and analysis of AHWR. We have now undertaken an exercise to study the sensitivity of the design parameters, such as k-infinity and void reactivity with respect to the various datasets which have been made available as part of the IAEA CRP on the final stage of the WIMS library update project (WLUP). The k-infinity variations are within 1% both at the beginning of cycle (BOC) and at the end of cycle (EOC). The results for the coolant void reactivity, however, show significant differences between the different datasets at BOC itself which increases further with burnup. In comparison, the differences for natural uranium fuelled pressurised heavy water reactor (PHWR) lattice are relatively lower. Major source of variations in AHWR lattice are probably coming from Th- 233U data.

Online Higher-Order Error Correction of Nonlinear Diffusion Generalized Perturbation Theory Using Neural Networks

An online scheme has been developed for the reduction of errors associated with a second order generalized perturbation theory (GPT) approximation of the neutron diffusion fundamental-mode eigenvalue (1/keff.). The primary application of this work is nuclear fuel loading optimization, where the noted calculation estimates the eigenvalue response as a function of fuel material perturbations (i.e., fuel assembly shuffles) relative to a reference (unperturbed) core loading pattern. The implementation of GPT for approximating keff can reduce the computational time requirements by a factor of 10 or greater, however, the nature of GPT is such that the errors in the second order approximation grow as the perturbations get larger. Therefore, the main emphasis of this study is to achieve improved approximations of the End-of-cycle (EOC) keff with minimal increase in the computational time. Specifically, this study shows that an online neural network-based scheme can be applied to reduce the average errors while still maintaining a computational edge over direct eigenvalue calculations.

Mixed Integer Programming for Pressurized Water Reactor Fuel-Loading-Pattern Optimization

A new optimization method is presented for determining the optimized pressurized water reactor (PWR) fuel-loading pattern in the maximization principle of the end-of-cycle (EOC) core reactivity. The new method utilizes the point reactivity model in deriving the objective function corresponding to the EOC core reactivity as a linear function of the fuel-loading binary variables. It also uses a mixed integer programming algorithm consisting of the branch and bound method and dual linear programming algorithm in order to maximize the EOC core reactivity. The utility of the new optimization method is discussed in terms of numerical examples for the fuel-loading-pattern optimization of the cycle 4 core of the Yonggwang unit 2 PWR plant.

Design of a gadolinia bearing mixed-oxide fuel assembly for pressurized water reactors

A study on neutronics design of a gadolinia (Gd2O3) bearing mixed-oxide (MOX) fuel assembly (MOX-UO2 (Gd2O3) assembly) was performed for the purpose of suppressing the use of fresh lumped burnable poison rods (BPRs). The MOX-UO2 (Gd2O3) assembly investigated consists of MOX and UO2 (Gd2O3) fuel rods, which have already been verified through both fabrication and irradiation experiences. In all, 16 UO2 (10 wt% Gd2O3) fuel rods are located at every corner and the peripheral region of the MOX-UO2 (Gd2O3) assembly in order to reduce the power peaking of MOX fuel rods due to the thermal neutron inflow, and to reduce the reactivity penalty at the end of cycle (EOC). Since fresh BPRs are not expected to be inserted and UO2 (Gd2O3) fuel rods are located at every corner of the assembly, the number of splits in plutonium (Pu) content can be only two, which is less than three splits required for a standard MOX assembly. Core characteristics of an equilibrium core loaded with MOX-UO2 (Gd2O3) assemblies are evaluated and it is verified that adoption of the MOX-UO2 (Gd2O3) assembly is effective to avoid the use of fresh BPRs with securing both the core safety and cycle length. The simplication of the splits in Pu content is also supposed to be beneficial, since it has the possibility of reduce MOX fuel fabrication costs.

In-Core Nuclear Fuel Management Optimization for Pressurized Water Reactors Utilizing Simulated Annealing

AbstractAn in-core nuclear fuel management code for pressurized water reactor reload design has been developed that combines the stochastic optimization technique of simulated annealing with a computationally efficient core physics model based on second-order accurate generalized perturbation theory. The approach identifies the placements of feed fuel, exposed fuel with assembly orientations, and burnable poisons within the core lattice that optimize fuel cycle performance or thermal margin according to one of the following objectives: maximization of keff at a target end-of-cycle (EOC) burnup, minimization of the maximum radial power peaking over the cycle, or maximization of region average discharge burnup, and subject to constraints on radial power peaking, discharge burnup, and moderator temperature coefficient. Each objective examined for a typical cycle 2 reload indicated the existence of multiple optimal solutions. A comparison of the loading patterns obtained for the same fuel inventory shows that...

Optimization of axial enrichment and gadolinia distributions for BWR fuel under control rod programming.

The axial enrichment and gadolinia distributions of BWR (boiling water reactor) fuel are optimized under control rod programming. The objective of the problem is to minimize the average enrichment required to reach a planned EOC (end-of-cycle) with criticality condition and axial power peaking constraint. A method of approximation programming is employed as the basis for the solution method. Resulting linear programming problem at each iteration step is solved by means of goal programming algorithm. The method is applied to the initial fuel for a typical BWR/5 represented by an axial one-dimensional core model Two-region analysis leads to the conclusion that the core bottom should be depleted during the cycle so that the power shifts to the core top at EOC. The enrichment and gadolinia distributions are determined to maximize EOC power peaking within a limit. The optimal solution of a 24-region fuel with a power peaking limit of 1.4 saves 10.6% in uranium ore compared with a uniform fuel depleted with a H...

Optimization of Core Reload Design for Low-Leakage Fuel Management in Pressurized Water Reactors

A method was developed to optimize pressurized water reactor low-leakage core reload designs that features the decoupling and sequential optimization of the fuel arrangement and control problems. The two-stage optimization process provides the maximum cycle length for a given fresh fuel loading subject to power peaking constraints. In the first stage, a best fuel arrangement is determined at the end of cycle (EOC) in the absence of all control poisons by employing a direct search method. The constant power, Haling depletion is used to provide the cycle length and EOC power peaking for each candidate core fuel arrangement. In the second stage, the core control poison requirements to meet the core peaking constraints throughout the cycle are determined using an approximate nonlinear programming technique.

The Benefits of Cycle Stretchout in Pressurized Water Reactor Extended-Burnup Fuel Cycles

Nuclear reactors are inherently capable of operating for a substantial period beyond their nominal end of cycle (EOC) as a result of negative moderator and fuel temperature coefficients and the decrease in xenon poisoning with lower core power levels. This inherent capability can be used to advantage to reduce annual uranium makeup requirements and cycle energy costs by the use of planned EOC stretchout. This paper discusses the fuel utilization efficiency and economics of both the five-batch, extended-burnup cycle and the three-batch, standard-burnup cycle, which can be improved by employing planned EOC (end of cycle) stretchout. 11 refs.

Enrichment Zoning and Control Rod Programming for Reactivity and Power Shape Control

An efficient optimization method has been developed that determines simultaneously beginning-of-cycle (BOC) enrichment distribution and the control rod programming in reactors that lose reactivity during burnup such that (a) reactor criticality and a desired power distribution are satisfied throughout the cycle and (b) all the control rods are withdrawn at end-of-cycle (EOC). The method uses (a) an iterative scheme of uncontrolled burnup calculations (and linear programming (LP) for more than two enrichment zones) to determine a good approximation of the EOC reactor composition that satisfies reactor criticality and the desired power distribution and (b) LP in a reversed burnup process starting from the EOC conditions to determine the control rod programming and the BOC enrichment distribution.

Optimization of Refueling Schedule for Light-Water Reactors

A stagewise optimization of the refueling schedule for light-water reactors has been developed with emphasis on the nuclear model. The decision variables to be determined are end-of-cycle (EOC) rea...