Reliability analysis of a passive cooling system using a response surface with an application to the flexible conversion ratio reactor

Abstract

A comprehensive risk-informed methodology for passive safety system design and performance assessment is presented and demonstrated on the Flexible Conversion Ratio Reactor (FCRR). First, the methodology provides a framework for risk-informed design decisions and as an example two design options for a decay heat removal system are assessed and quantitatively compared. Next, the reliability of the system is assessed by quantifying the uncertainties related to system performance and propagating these uncertainties through a response surface using Monte Carlo simulation. Finally, a sensitivity study is performed to measure the relative effects of each parameter and to identify ways to maintain, improve, and monitor system performance. A common characteristic of passive safety systems is that their driving force tends to be weak and therefore adverse or off-normal conditions may substantially degrade system performance [2]. Under certain conditions, system performance may be degraded to a level that results in unacceptable consequences. These consequences are typically identified by the system designer and are referred to as failure criteria. Failure criteria can be defined at the system level (e.g., flow rate, fluid temperature) or at a higher level (e.g., peak cladding temperature, containment pressure). Therefore, the conditional failure probability of a passive system can be defined as the probability that, given an initiating event, a set of thermal-hydraulic conditions will exist that cause the system to exceed one or more failure criteria. System conditions leading to failure are the result of adverse combinations of system parameter values such as pressure, temperature, and void fraction. Prediction of the exact values of these parameters is made difficult by several sources of uncertainty and typically, we can only assume a range of expected values and a corresponding probability distribution. We will refer to this type of uncertainty as parametric uncertainty. Second, there are uncertainties associated with the models used to predict system behavior. These can involve equations or empirical correlations used to model various phenomena or may stem from the numerical methods employed by computer codes. We will refer to this type of uncertainty as model uncertainty. Both parametric and model uncertainties are classified as epistemic since they are related to a lack of knowledge as opposed to aleatory uncertainty, which is related to randomness [3]. An estimate of system reliability can be obtained by quantifying parametric and model uncertainty and observing their effect on system performance. Further insights can be gained by evaluating the sensitivity of system performance to each parameter, and we will demonstrate several ways in which this can be done.The reliability of passive safety systems has been the subject of a great deal of research this decade both in the United States and internationally. System failure is assumed to occur when a physical quantity such as temperature exceeds a value th...

How to effectively compute the reliability of a thermal–hydraulic nuclear passive system

“…A future improvement in the state of knowledge, e.g. due to the collection of data and information useful to improve the characterization of the heat transfer phenomenon, would lead to a change in the epistemic uncertainty distribution describing the likelihood of the various values of heat transfer coefficient and eventually to a more accurate estimate of the system reliability/failure probability [Pagani et al, 2005;Bassi and Marques, 2008;Mackay et al, 2008;Mathews et al, 2008 andPatalano et al, 2008;Fong et al, 2009].…”

“…Estimation of the functional failure probability of the passive system conditional on the current state of knowledge about the phenomena involved (step 2. above) [Pagani et al, 2005;Bassi and Marques, 2008;Mackay et al, 2008;Mathews et al, 2008 andPatalano et al, 2008;Fong et al, 2009;Pedroni, 2009a-c and. Formally, let Y( x ) be a single-valued scalar …”

“…In [Bucher and Most, 2008;Gavin and Yau, 2008;Liel et al, 2009], polynomial Response Surfaces (RSs) are employed to evaluate the failure probability of structural systems; in Fong et al, 2009;Mathews et al, 2009], linear and quadratic polynomial RSs are employed for performing the reliability analysis of T-H passive systems in advanced nuclear reactors; in [Deng, 2006;Hurtado, 2007;Cardoso et al, 2008;Cheng et al, 2008], learning statistical models such as Artificial Neural Networks (ANNs), Radial Basis Functions (RBFs) and Support Vector Machines (SVMs) are trained to provide local approximations of the failure domain in structural reliability problems; in [Volkova et al, 2008;Marrel et al, 2009], Gaussian meta-models are built to calculate global sensitivity indices for a complex hydrogeological model simulating radionuclide transport in groundwater.…”

“…It has also been used to evaluate the failure probabilities of decay heat removal systems in Gas-cooled Fast Reactors (GFRs) [Pagani et al, 2005;Bassi and Marquès, 2008;Mackay et al, 2008;Patalano et al, 2008;Pedroni, 2009b, c and, sodium-cooled Fast Breeder Reactors (FBRs) [Mathews et al, 2008 and and the lead-cooled, fast spectrum Flexible Conversion Ratio Reactor (FCRR) [Fong et al, 2009]. In all these analyses, the passive system is modeled by a detailed, mechanistic T-H system code and the probability of not performing the required function is estimated based on a Monte Carlo (MC) sample of code runs which propagate the epistemic (stateof-knowledge) uncertainties in the model describing the system and the numerical values of its parameters.…”

“…Second, long calculations (several hours) are typically necessary for each run of the detailed, mechanistic T-H code (one code run is required for each sample of values drawn from the uncertainty distributions) [Fong et al, 2009;Pourgol-Mohamad et al, 2010] 3 .…”