Uncertainties associated with the reliability of thermal-hydraulic nuclear passive systems

ABSTRACT

The increasing adoption of passive safety based front-line systems in advanced nuclear power reactors due to their simplicity, cost competitiveness and autonomous nature makes it very essential to carefully consider the uncertainties associated with their behaviour and the phenomena linked to their operations. The passive safety systems (PSSs) are known to be characterized with several uncertainties in their modelling and operations. These uncertainties are usually more pronounced than those of their active systems counterparts due to the stochastic nature of the associated phenomena, insufficient knowledge of their physics of operation and inadequacy of relevant real/experimental data. This paper thus focused on the uncertainty issues of the thermal-hydraulic (t-h) PSSs which influence their reliability analysis. In addition, the inadequacies of previous research, current research challenges and likely future research directions on uncertainties associated with the models and phenomena applicable to the t-h PSSs adopted in advanced reactors were discussed. For the purpose of illustration, Weibull distribution was adopted for the failures associated with a generic passively cooled steam generator and Bayesian approach applied to account for phenomenological uncertainty. The output of the approach justified the need to account for epistemic uncertainty in reliability analysis of such systems.     

Screening of critical parameters influencing thermal-hydraulic reliability of simple passive system

Robust safety nature of passive safety systems (PSSs) accounts for their increasing applications. Critical parameters (CPs) which influence reliability of thermal-hydraulic (t-h) PSSs are considered independent in most cases while considering their effects purposely for simplicity which may not be realistic. Findings affirmed reliability of t-h PSSs to be influenced by CPs that are dependent in most scenarios and thus, effects of CPs dependency which can directly/indirectly influence t-h reliability need to be considered. Reliability assessment methodologies (RAM) can thus be improved upon by considering the dependency of CPs in reliability analysis. In this regard, this paper considers the screening of CPs required to justify their dependency consideration in evaluating t-h reliability. The Pearson’s product moment correlation coefficient and covariance method were applied as illustration for the screening of the possible realistic CPs, which affect natural circulation of a passively water-cooled steam generator. The approach was used to determine the combinations of the CPs that are dependent and screens out those adjudged independent. Based on the results obtained, appropriate considerations (dependency/independency) can be made and further analysis of interest (failure/reliability) can be conducted for the system. Incorporation of this screening approach into the existing t-h RAMs will improve their efficiency.     

Estimation of the functional failure probability of a thermal-hydraulic passive system by Subset Simulation

In the light of epistemic uncertainties affecting the model of a thermal-hydraulic (T-H) passive system and the numerical values of its parameters, the system may find itself in working conditions which do not allow it to accomplish its function as required. The estimation of the probability of these functional failures can be done by Monte Carlo (MC) sampling of the uncertainties in the model followed by the computation of the system response by a mechanistic T-H code. The procedure requires considerable computational efforts for achieving accurate estimates. Efficient methods for sampling the uncertainties in the model are thus in order.In this paper, the recently developed Subset Simulation (SS) method is considered for improving the efficiency of the random sampling. The method, originally developed to solve structural reliability problems, is founded on the idea that a small failure probability can be expressed as a product of larger conditional probabilities of some intermediate events: with a proper choice of the conditional events, the conditional probabilities can be made sufficiently large to allow accurate estimation with a small number of samples. Markov Chain Monte Carlo (MCMC) simulation, based on the Metropolis algorithm, is used to efficiently generate the conditional samples, which is otherwise a non-trivial task.The method is here developed for efficiently estimating the probability of functional failure of an emergency passive decay heat removal system in a simple steady-state model of a Gas-cooled Fast Reactor (GFR). The efficiency of the method is demonstrated by comparison to the commonly adopted standard Monte Carlo Simulation (MCS).     

IPWRs非能动余热排出系统运行特性分析

由于结构紧凑和采用模块化及非能动安全技术,一体化压水堆(IPWRs)特别适合于舰船核动力装置的应用。本文研究对象为基于固有安全一体化动力堆UZrHx和俄罗斯一体化压水堆ABV-6M的运行特点而概念设计的一体化压水堆。堆芯采用弧形板状燃料元件,直流蒸汽发生器形式为套管式,利用3个回路的自然循环排出堆芯余热的非能动余热排出系统以及一套能动的停堆冷却系统。运用RE-LAP5/MOD3.4程序对该反应堆在全船断电事故工况下反应堆停堆,非能动余热排出系统和能动停堆冷却系统分别投入运行进行仿真计算,分析其热工水力动态特性,保证堆芯安全。     

The influence of ocean conditions on thermal-hydraulic characteristics of a passive residual heat removal system

There are many differences between the flow and heat transfer characteristics of nuclear reactors under ocean and land-based conditions for the effects of ocean waves. In this paper, thermal hydraulic characteristics of a passive residual heat removal system (PRHRS) for an integrated pressurized water reactor (IPWR) in ocean environment were investigated theoretically. A series of reasonable theoretical models for a PRHRS in an IPWR were established. These models mainly include the core, once-through steam generator, nitrogen pressurizer, main coolant pump, flow and heat transfer and ocean motion models. The flow and heat transfer models are suitable for the core with plate-type fuel element and the once-through steam generator with annular channel, respectively. A transient analysis code in FORTRAN 90 format has been developed to analyze the thermal–hydraulic characteristics of the PRHRS under ocean conditions. The code was implemented to analyze the effects of different ocean motions on the transient thermal-hydraulic characteristics of PRHRS. It is found that the oscillating amplitudes and periods of the system parameters are determined by those of the ocean motions. The effect of rolling motion is more obvious than that of pitching motion when the amplitudes and periods of rolling and pitching motions are the same. The obtained analysis results are significant to the improvement design of the PRHRS and the safety operation of the IPWR.     

非能动系统可靠性评价方法的研究

本文首先详细解释了非能动系统可靠性概念,分析各种非能动系统可靠性评价方法的特点,对比各种方法之间的区别,并指出这些可靠性评价方法共同存在的不足:没有一种方法可同时兼顾非能动系统设备可靠性与功能可靠性,不能科学地整合两者的可靠性,并且未将非能动系统整体可靠性融合进概率安全评价(PSA)模型;针对各种方法存在的不足,本文在国内外研究基础上提出研究问题与思路,而且展望了非能动系统可靠性评价方法未来的发展方向。     

The development and verification of thermal-hydraulic code on passive residual heat removal system of Chinese advanced PWR

1 Introduction The technology of passive safety is the trend of safety systems in nuclear power plant, and various novel reactor concepts, including AP600, EPP1000, SPWR, WWER1000, and MS600, have adopted pas- sive safety systems [1]. Passive safety system is one of the main features of Chinese advanced PWR, which is different from other conventional PWR [2]. Passive residual heat removal system (PRHRS), which ac- counts for the majority of passive safety systems of Chinese advanced…     

CFD modeling and thermal-hydraulic analysis for the passive decay heat removal of a sodium-cooled fast reactor

In this study, a pool-typed design similar to sodium-cooled fast reactor (SFR) of the fourth generation reactors has been modeled using CFD simulations to investigate the characteristics of a passive mechanism of Shutdown Heat Removal System (SHRS). The main aim is to refine the reactor pool design in terms of temperature safety margin of the sodium pool. Thus, an appropriate protection mechanism is maintained in order to ensure the safety and integrity of the reactor system during a shutdown mode without using any active heat removal system. The impacts on the pool temperature are evaluated based on the following considerations: (1) the aspect ratio of pool diameter to depth, (2) the values of thermal emissivity of the surface materials of reactor and guard vessels, and (3) innerpool liner and core periphery structures. The computational results show that an optimal pool design in geometry can reduce the maximum pool temperature down to ∼551 °C which is substantially lower than ∼627 °C as calculated for the reference case. It is also concluded that the passive Reactor Air Cooling System (RACS) is effective in removing decay heat after shutdown. Furthermore, thermal radiation from the surface of the reactor vessel is found to be important; and thus, the selection of the vessel surface materials with a high emissivity would be a crucial factor for consideration in safety design. This study provides future researchers with a guideline on designing safety measures for the fourth generation of the fast reactors with no particular reference to any specific manufacturer.     

Methodology for the reliability evaluation of a passive system and its integration into a Probabilistic Safety Assessment

A methodology has been developed to evaluate the reliability of passive systems characterised by a moving fluid and whose operation is based on thermal–hydraulic (T-H) principles. The methodology includes:

• identification and quantification of the sources of uncertainties and determination of the important variables;

• propagation of the uncertainties through T-H models and assessment of T-H passive system unreliability;

• introduction of passive system unreliability in the accident sequence analysis.

Each step of the methodology is described and commented and a diagram of the methodology is presented. An example of passive system is presented with the aim to illustrate the possibilities of the methodology. This example is the Residual Passive heat Removal system on the Primary circuit (RP2), an innovating system supposed to be implemented on a 900 MWe Pressurized Water Reactor.     

How to estimate reliability parameters

Two kinds of estimates are well known in order to evaluate reliability parameters from data concerning equipment: the maximum likelihood estimate — MLE, and the upper bound estimate — UBE, at a given confidence level. We intend in this paper to compare these two estimates in order to show that the MLE can be discarded and advantageously replaced by a better one derived from a 50% UBE. We also intend to show that the UBE can be handled just by using curves and numerical tables.     

Development of a multi-dimensional thermal-hydraulic system code, MARS 1.3.1

A multi-dimensional thermal-hydraulic system code MARS has been developed by consolidating and restructuring the RELAP5/MOD3.2.1.2 and COBRA-TF codes. The two codes were adopted to take advantage of the very general, versatile features of RELAP5 and the realistic three-dimensional hydrodynamic module of COBRA-TF. In the course of code development, major features of each code were consolidated into a single code first. The resulting source programs were rewritten in standard fortran 90, and then were restructured using modular data structures based on “derived type variables” and a new “dynamic memory allocation” scheme. In addition, the Windows graphics features were implemented for user friendliness. This paper presents the developmental activities up to mars version 1.3.1 including the code consolidation, the code restructuring and modernization, and the results of the developmental assessment.     

Some challenges to the thermal-hydraulic codes

The thermal-hydraulic codes were developed with the data and correlations obtained from separate effect tests. As such. There are some system-related phenomena which cannot be depicted properly by the codes. In this paper we discuss the difficulties encountered by code modeling for the following systems: feedback loop, multichannel system, multidimensional flow and multiloop circulation. The discussion shows that codes can only give probable answers; the difficulties encountered are due to maldistribution of heat and flow, primary-secondary interaction, feedback effect, instrumentation-control interaction and other unknown factors.     

紧凑型核动力系统的热工水力数值模拟

将多孔介质模型应用于紧凑型核动力系统的热工水力数值模拟,开发了计算程序,并以船用反应堆为例进行了初步的分析计算。为紧凑型核动力系统的热工水力特性整体多维模拟提供了可行的方案,也为紧凑型核动力系统综合分析平台的研制打下了基础。     

Multi-component nuclear energy system: How to meet requirements of self-consistency

Self-Consistent Nuclear Energy System simultaneously meets four requirements: energy generation, fuel breeding, burning of radionuclides and system safety. Multi-component nuclear energy system composed of fast and thermal reactors has a potential to approach to self-consistency provided external neutron sources are included in its structure. This paper deals with general analysis of such a system with focus on neutron production, minor actinide fissioning and plutonium vector at equilibrium stage.     

Dynamical reliability of the passive system in the very high temperature gas cooled reactor

A dynamic safety assessment has been developed for the passive system in the very high temperature gas cooled reactor (VHTR), when the operational data are insufficient. It was required to make use of the characteristics of the reactor in order to compensate for the data shortage and to treat the propagation of incidents. Therefore, this paper focuses on the failure frequency construction of the basic events and the advanced method of treating the propagation. The mass flow rate caused by the natural circulation in the passive system is related to the fuel temperature which affects the failure fraction of the fuel. These features are utilized for finding the failure frequency of the basic event. The non-linear string logic is used due to the simple and tractable algorithm of the passive system instead of the tree concept which is used in the event-fault tree based decision making. The time feedback is applied to the string concept, where the time weighting is adjusted by the operator’s judgment. Results are obtained for four cases. Among them, two cases are non-linear transition features of the events using feedback. The other two cases are based on linear propagations, which construct the characteristics of the dynamic resistance–stress method (DRSM). Using the string algorithm, one can successfully perform safety assessment for any other advanced reactor such as the VHTR.     

Stability of the water-chemistry regime in the loop of a passive safety system of nuclear power reactors

The organization of the water-chemistry regime in the loop of a passive safety system, whose purpose is emergency removal of heat from the core of a nuclear power reactor, is examined. It is shown that a selfregulated water-chemistry regime in which gaseous products of radiolysis can be dissolved in water coolant and recirculated into the irradiation zone, which will intensify liquid-phase radiation-chemical reactions of hydrogen with oxygen and organic release of gases from the liquid phase into the vapor-gas phase of the coolant, can arise in the loop of a passive safety system. This will result in the establishment in the loop of dynamic equilibrium between the release and dissolution of gases and will enable prolonged functioning of the safety system without intervention from the outside. The physicochemical and technical criteria for the appearance of a self-regulated water-chemistry regime for closed loops with natural circulation of the two-phase coolant are formulated and substantiated.     

Verification study of the FORE-2M nuclear/thermal-hydraulic analysis computer code

The verification of the LMFBR core transient performance code, FORE-2M, was performed in two steps. Different components of the computation (individual models) were verified by comparing with analytical solutions and with results obtained from other conventionally accepted computer codes (e.g., TRUMP, LIFE, etc.). For verification of the integral computation method of the code, experimental data in TREAT, SEFOR and natural circulation experiments in EBR-II were compared with the code calculations. Good agreement was obtained for both of these steps. Confirmation of the code verification for undercooling transients is provided by comparisons with the recent FFTF natural circulation experiments.     

Efficient reliability estimate of passive thermal hydraulic safety system with automatic differentiation

An approach for efficient estimation of passive safety system functional reliability has been developed and applied to a simplified model of the passive residual heat transport system typical of sodium cooled fast reactors to demonstrate the reduction in computational time. The method is based on generating linear approximations to the best estimate computer code, using the technique of automatic reverse differentiation. This technique enables determination of linear approximation to the code in a few runs independent of the number of input variables for each response variable. The likely error due to linear approximation is reduced by augmented sampling through best estimate code in the neighborhood of the linear failure surface but in a sub domain where linear approximation error is relatively more. The efficiency of this new approach is compared with importance sampling MCS which uses the linear approximation near the failure region and with Direct Monte-Carlo Simulation. In the importance sampling MCS, variants employing random sampling with Box-Muller algorithm and Markov Chain algorithm are inter-compared. The significance of the results with respect to system reliability is also discussed.     

User effects on the thermal-hydraulic transient system code calculations

Large thermalhydraulic system codes are widely used to perform safety and licensing analyses of nuclear power plants to optimize operational procedures and the plant design itself. Evaluation of the capabilities of these codes are accomplished by comparing the code predictions with the measured experimental data obtained from various types of separate effects and integral test facilities. During these comparisons of the code results, there has been a continuous debate on the way how the code user influences the predicted system behaviour. This rather subjective element might become a crucial point with respect to the quantitative evaluation of the code uncertainties which is essential if the “best estimate codes are used for licensing procedures”.The International Standard Problem Exercises (ISPs) proposed by the OECD/NEA-Committee for the Safety of Nuclear Installations (CSNI) and by IAEA (International Atomic Energy Agency) and thermalhydraulic code assessment activity undertaken by USNRC (US Nuclear Regulatory Commission) under International Code Assessment and Application Program (ICAP) demonstrate the large effort put in this framework by organizations all over the world. In recent years, some attempts have been made to establish methodologies to evaluate the accuracy and the uncertainty of the code predictions and consequently judgement on the acceptability of the codes. In none of the methodologies has the influence of the code user on the calculated results been directly addressed. In this paper, the results of the investigations on the user effects for the thermalhydraulic transient system codes will be presented and discussed on the basis of some case studies.The general findings of the investigations show that in addition to user effects, there are other reasons that affect the results of the calculations and which are hidden under user effects. Both the hidden factors and the direct user effects will be discussed in detail and general recommendations and conclusions will be presented to control and limit them.     

Practical reliability engineering applications to nuclear safety

PRA studies have been successful in providing a quantitative perspective on the important contributions to risk and on the relative impact of potential hardware modifications and procedural changes in reducing public risk. In addition it is the expectation that regulatory agencies will also use this technology to justify a relaxation in requirements that are too strict and the elimination of requirements that are irrelevant or counter to safety. This paper outlines several on-going application oriented R&D efforts that will improve safety in operation, lead to a continuing demonstration that nuclear plants are achieving acceptably low risk, and achieve a higher plant productivity.