Preliminary and Scoping Analysis for Uncertainty of HLW Geologic Repository Performance with Multiple Canister Repository Model by Earth Simulator

An uncertainty analysis of repository performance has been made by the VR code, which incorporates interference effects of multiple canisters in a repository. A problem of the previous study with the VR code is that the number of connected canisters was determined arbitrarily. In this study, first, the probability distribution functions for the number of canisters connected by the flow-bearing fracture clusters have been determined by the FFDF code, and then uncertainty associated with the peak fractional release rate of ²³⁷Np to the far field resulting from uncertainties with the buffer sorption coefficient, solubility, and the number of connected canisters has been numerically evaluated by the Latin-Hypercube Sampling method. The effects of uncertainty with the total number of connected canisters become less important as the number increases because the radionuclide concentration saturates in downstream compartments. Uncertainty with the buffer sorption and solubility shows an important contribution to that with the nuclide release rate.     

反应堆组件参数计算程序中燃耗方程数值解法研究

本文介绍了组件参数计算程序中燃耗计算理论模型,给出了求解燃耗方程的两种数值方法,编制了相应的计算程序,并将其计算结果与解析解的计算结果进行了对比分析,验证了两种数值方法的有效性。对两种数值方法的计算效率进行了比较,结果表明：两种数值方法均能取得较高的计算精度,但在计算速度及对初始时间步长取值的限制方面,Rosenbrock方法明显优于龙格库塔方法。     

The effect of the evolution of environmental conditions on the corrosion evolutionary path in a repository for spent fuel and high-level waste in Opalinus Clay

The corrosion evolutionary path (CEP) defines the time-dependent corrosion behaviour of canisters in a deep geologic repository. In turn, the CEP is largely determined by the evolution of the environmental conditions in the near- and far-fields. The evolution of environmental conditions in a repository for spent fuel and high-level waste in Opalinus Clay is described along with the impact on the corrosion behaviour of the canisters.     

裂隙水流-传热对高放废物处置库近场温度影响的三维离散元分析

裂隙水流-传热是高放废物处置库行为的重要影响因素。为研究裂隙水流-传热对高放废物处置库近场温度的影响,采用3DEC离散元软件计算分析了完整岩体模型和裂隙岩体水流模型对处置库近场温度分布和演变的影响。计算分析表明:由于裂隙水流的吸热降温作用,裂隙岩体模型的废物罐表面膨润土温度低于完整岩体模型的废物罐表面膨润土温度,并缩短了达到稳态所需要的时间;裂隙水流上游区域废物罐表面膨润土温度显著低于裂隙水流下游区域废物罐表面膨润土温度;在设定条件下,裂隙岩体模型的废物罐表面膨润土最高温度约为完整岩体模型废物罐表面膨润土最高温度的75%,裂隙水流速度从0.2mm/s增大到0.5mm/s,废物罐表面膨润土最高温度降低约4%。     

A New Mixed Method with Finite Difference and Finite Element Method for Neutron Diffusion Calculation

A new method for obtaining three-dimensional neutron flux distribution in a reactor has been developed by taking into account the fact that the X-Y planar geometry is generally complex but the geometry along Z-axis is simple. In this method, the finite element method is applied to the X-Y plane calculation and the finite difference method to the Z-axis. For solving a three-dimensional neutron diffusion equation, these two methods are iterated successively until a consistency of the leakage coefficients is attained between the two. The present method is embodied as a computer program FEDM for FACOM M200 computer. With this program, a three-dimensional diffusion calculation was performed for comparing some numerical results with those by a conventional standard computer code ADC. The comparison has shown that they agree well with each other. Computing time required for this problem by the FEDM was shorter than that by the ADC for obtaining same accuracy on the eigenvalue. To indicate usefulness of this method, a demonstration calculation for a reactor with a complex geometry was performed, which was a difficult case to calculate with a conventional finite difference code.     

Application of ‘natural coordinate system’ in the finite element solution of multigroup neutron diffusion equation

A simple method of generating stiffness matrices for the solution of multigroup diffusion equation by ‘natural coordinate system’ has been presented. A comparative study has been made using triangular elements with linear model, triangular elements with quadratic model and rectangular elements with bilinear model to demonstrate their relative efficiencies. The quadratic interpolation model has been shown to be superior to linear and bilinear models with respect to computing time, computer storage and relative error in K_eff for a two group diffusion example. The flexibility of the finite element treatment has been demonstrated by the calculation of the reactivity of a partially inserted control rod. Good agreement has been obtained with a perturbation calculation.     

Shell model calculation of enthalpy of solution of MgO in UO2+x

A computer program to evaluate the formation energies of defects in fluorite crystals is developed on the basis of the shell model Intrinsic defects of UO₂ are calculated with this program using the potential parameters reported by Catlow. The results are in agreement with those of Catlow. The present computer program is applied to a study of nonstoichiometry of the solid solutions of MgO and UO_2+x The calculation of the enthalpy of solution of MgO in UO_2+xis carried out on the basis of several defect models for charge compensation in the solid solution Mg_yU_1?yO_2±xThe calculated results are discussed in the light of our recent experimental work. It is proved that the present theoretical calculation predicts reasonably well the nonstoichiometric properties of the solid solution.     

Multiple lines of evidence for performance of the canister and waste form in long-term nuclear waste disposal: Reviews

The time scales required for nuclear waste disposal are very large compared with those for other engineering endeavors. Because of this, there are many uncertainties associated with the quantitative performance assessment of canisters containing high-level radioactive waste in a waste form. Multiple lines of evidence can be helpful in building confidence in the long-term behavior (corrosion and dissolution) of the canister and waste form. These lines of evidence are derived from long-term supports and probabilistic models and developed based on shorter term tests, bounding and conservative approaches, and available observations on natural analogs. This paper presents the progress made for important lines of evidence considered in quantitatively assessing radionuclide release behavior from canisters and waste forms. This paper considers risk-significant issues for canisters and waste forms (i.e., risk informed approach) in the probabilistic performance assessment of the disposal system which has also other components such as geology and hydrology.     

ORE Assessment Due to ACP in the PHTS of the Point Design Phase of the ITER Project

The work presented here dealt with the revision and the updating of the ORE (Occupational Radiation Exposure) assessment for the ITER PHTS (Primary Heat Transfer System). The data used come from the Point Design Documents and refers to the ITER design of the first half of 1996. The MCNP computer code was adopted to perform the shielding calculation. In addition, an accurate approach to evaluate the photon flux during maintenance and inspection activities was followed and recently published photon-flux-to-dose-rate conversion factors were applied to obtain the corresponding dose rate. The ACP inventory was taken from the relevant calculation performed with the PACTOLE code for the Point Design. A special ACP calculation was performed for each PHTS circuit and the related results are used in the respective dose rate calculations. The collective dose for the main activities performed to maintain the PHTS components is reported. The dose result for each activity type is shown and the comparison with a reference fission plant is discussed.     

On some matters concerning the backward and forward equations of probability balance for neutrons in a medium with randomly time-varying properties

The recent contributions to combined zero-power and at-power neutron noise analysis raises a number of interesting questions which deserve further discussion [Kitamura, Y., Pal, L., Pazsit, I., Yamamoto, A., Yamane, Y., Some properties of zero power neutron noise in a time-varying medium with delayed neutrons. Annals of Nuclear Energy, in press.]. It is shown, for example, by direct calculation, that the forward equation of probability balance is exact when combined with a dichotomic Markov process to describe the random physical behaviour of a medium, whereas the backward equation contains errors. This confirms and corroborates the assertions of Pal L. and Pazsit I. [2006. Neuron fluctuations in a multiplying medium randomly varying in time. Physica Scripta 74, 62.] who first pointed out this anomaly. Extensions to spatially random media are discussed, together with an application to the calculation of the extinction probability. Other methods of solution such as that of polynomial chaos are briefly touched upon. In order to carry out the calculations described we use the stochastic ansatz concept [Williams, M.M.R., 2008a. A stochastic ansatz and its relationship with the dichotomic Markov process. Physica A 387, 4997.].     

Analysis of the primary containment response using a hydrodynamic-elastic-plastic computer code

The dynamic response of the primary reactor containment system to a hypothetical core disruptive accident (HCDA) is determined from the basic equations of mass, momentum, and energy, and the equations of state of the medium. These equations are first expressed in material coordinates and then set into finite difference form solved numerically on the computer using a hydrodynamic-elastic-plastic computer code, REXCO-HEP developed at ANL. Propagation of pressure waves, loads imposed on different parts of the reactor components, and the resulting deformations are determined at every time step throughout the sequence of the calculation. As a sample calculation, the code was applied to analyze the response of the FFTF reactor to a 150 MWsec HCDA. The mathematical model is described in detail, particularly in the areas of modeling reactor internals and extending the time range to cover the entire excursion phenomenon. Finally, the results obtained from the computer analysis are discussed in detail.     

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.     

Vitrification of high-level wastes: A review of the computer thermal analyses for storage canisters

CANIST, a two-dimensional (r and θ) computer program that solves the unsteady-state, heat-conduction equation, was used to model the thermal behavior of canisters filled with waste glass. CANIST has been found to be a valuable analytical tool for predicting the temperature profile of a waste storage canister as a function of several variables, including the diameter of the canister, the placement of internal fins, the heat generation rate of the waste glass, and the thermophysical properties of the canister and the waste glass. Thus, temperature-dependent processes that may affect the integrity of the glass/canister unit, for example cracking, can be investigated using an analytical approach.     

Mathematical Simulation Procedure of Multicomponent Separating Cascade

A simulation procedure of multicomponent separating cascades is developed. This procedure is applicable and effective in such cases that the cut of mixture of each stage is prescribed and required to be independent of concentration, and the stage separation factors are given as input variables and very large. It can deal with cascades which have multiple feeds and sidestreams. The stage separation factors are allowed to be given as functions of compositions of down streams and up streams. The exact solutions are found out treating all the basic equations simultaneously by use of multi-dimensional Newton-Raphson method.

As an application of this procedure to actual cascade calculations, a computer simulation study is carried out for hydrogen isotope separation system by porous membrane method which consists of two cascades and two catalytic equilibrators. It is proved that the Newton-Raphson iterative calculation proceeds stably under the assumed input and output conditions, and the porous membrane method is worth while to investigate in further studies as one of promising methods for hydrogen isotope separation.     

Simulated model studies for solid waste storage surveillance facility

High level radioactive waste generated from reprocessing of spent fuel from nuclear reactors are encased in canisters after vitrification. They have high heat generation rate and need interim storage under surveillance and are to be cooled continuously until major portion of the heat is dissipated. Natural circulation air cooling (using suitable stack dimensions) has been considered to cool the overpacks containing canisters. Thermal analysis has been carried out for a reduced scale model of such a facility. Theoretical and experimental results have been compared.     

弥散颗粒型燃料特征线方法输运计算研究

弥散颗粒型燃料的中子输运问题因其特有的随机性和双重非均匀性难以直接使用现有输运方法进行求解。Sanchez-Pomraning方法借助更新方程,对特征线方法进行改进,使其能应用于弥散颗粒型燃料的输运计算中。本文对二维圆柱形弥散颗粒燃料输运问题进行了计算,数值结果表明：程序在不同颗粒填充率、不同颗粒尺寸、燃料颗粒与毒物颗粒共存的问题下均能保证较好的计算精度,反应性特征值绝对偏差大多低于100 pcm,仅在QUADRISO毒物颗粒填充时绝对偏差达到163 pcm。本文方法能满足弥散颗粒型燃料的输运求解要求,为新型燃料的设计研究工作提供了可靠的结果。     

Numerical Simulation for Chemical Reactions of Actinide Elements in Aqueous Nitric Acid Solution

A computer code REACT incorporating 30 rate equations of reactions, i.e. radiolytic formation and decomposition of HNO₂, redox and disproportionation reactions, was developed to simulate behavior of actinide elements in the aqueous nitric acid solution. Main aspects of REACT code were explained briefly and then calculated results were compared with reported data to evaluate the model in the systems of radiolytic accumulation of HNO₂, stabilization process of Pu solution. The study showed that some radiolytic products other than HNO₂ would play a significant role and should be taken into account for precise simulation of very slow valency change of Pu in the neat Pu solution particularly with high radiation power density. Some examples of calculation were also shown for systems of reduction of Pp and Np by uranous or HAN and oxidation of Np (V) to Np (VI).     

Development of a thermal-hydraulic analysis code TAC-DS for spent fuel dry-storage system for high-temperature pebble bed reactor

We report the development of a thermal-hydraulic analysis code (called TAC-DS: Thermal-hydraulic Analysis Code for Dry-storage System). The spent fuel dry-storage system of High-Temperature Reactor Pebble-bed Modules in China is simulated using the TAC-DS to confirm the design basis and to analyze the transient behavior following an accident involving blower failure. The TAC-DS includes mathematical models for the air-coolant system, heat conduction within spent fuel canisters, and thermal radiation between heat structures. The time-dependent hydrodynamic model of the TAC-DS is formulated using one-dimensional mass, momentum and energy equations, and solved using semi-implicit finite-difference scheme. The complicated heat transfer models of heat structure are incorporated into the hydrodynamic system implicitly with enclosure correlations. Code is written in Fortran 90. A validation calculation is performed by solving a simplified model. Thermal performance of the buffer storage region in the system under forced ventilation scenario is studied with TAC-DS to validate the design requirement, as well as to provide the initial condition for the transient analysis. Blower failure accident is studied to assess the performance of the safety features during the transient accident. Since the code is modular, TAC-DS can be easily modified and applied to other spent fuel dry-storage system in the future.     

Matrix calculation of radiant heat transfer in LWR fuel bundles under accident conditions

A computer code was developed for calculating the radiant heat transfer in a LWR fuel bundle under accident conditions. The calculation method is a modular one: a fuel bundle or its part is divided into unit cells, each of which is composed of a coolant subchannel surrounded by several segments of solid or imaginary faces. The view factor matrix in each cell is expanded over the whole bundle using the concept of ‘boundary face’ between cells, and the resultant heat transfer equations are simultaneously solved for solid wall temperatures. The geometrical flexibility of this method is suitable for treating various simulation experiments for accidents. The method is also effective for repeated calculations of the radiant heat transfer reflecting state or material property changes when analyzing fuel rod behaviour under accident conditions.