RMPS methodology

In the late 1990s, a methodology known as REPAS was developed cooperatively by ENEA, the University of Pisa, the Polytechnic of Milan, and the University of Rome in Italy which was later incorporated into the European Commission’s reliability methodology for passive systems (RMPS) project within the European Commission’s 5th framework programme [12]. The RMPS methodology is based on evaluation of the failure probability of a system to carry out its desired function for a given set of scenarios, taking into account uncertainties of physical (epistemic) and geometric (aleatoric) parameters, deviations of which can lead to a failure of the system. The RMPS approach considers a probability distribution of failure to treat variations of the comparative parameters considered in the predictions of codes.

Schematics of the RMPS are shown in Fig. 1.

The RMPS methodology has been developed to evaluate reliability of passive systems incorporating a moving fluid and using natural convection as an operation mechanism. The reliability evaluation for such systems is based, in particular, on the results of thermal-hydraulic calculations. The RMPS methodology could be structured as follows:

— Identification and quantification of the sources of uncertainties;

— Reliability evaluation of a passive system;

— Integration of passive system reliability in PSA.

The methodology is applied to a specific accident scenario in which operation of a certain passive safety system is foreseen. When the scenario to be examined is specified, the first step — identification of the system — requires full characterization of the system under investigation be carried out. This step includes specifying the goals of the system, the modes via which it may fail, and providing the definition of a system failure, or more specifically the definition of success/failure criteria. Modelling of the system is also required, which is accomplished using best-estimate computer codes. Numerous sources of uncertainties present in the modelling process have to be identified. Such sources are related to approximations in modelling of physical processes and system geometry, and uncertainties in input variables, such as initial and boundary conditions. Identifying the most important thermal-hydraulic phenomena and parameters which have to be investigated for the system is an important part of the methodology. Such identification can be accomplished via a brainstorming session of experts with a good understanding of the system functions and best estimate code calculations, and through use of a method of the relative ranking of phenomena. The ranking technique implemented in the RMPS project is the analytical hierarchy process (AHP). After identifying important thermal-hydraulic parameters, the next step is to quantify their uncertainties. When experimental data are not available, expert judgement would be required to identify the range of uncertainties and select appropriate probability density functions for a given set of variables. The methodology incorporates a sensitivity analysis, which is to determine, among all uncertain parameters, the main contributors to the risk of a system failure.

The second part of the methodology requires evaluating uncertainty in the expected performance of the passive system as predicted by the thermal-hydraulic code and according to the studied scenario. Such uncertainty evaluation could be performed using confidence intervals or probability density functions. Within RMPS studies, it has been found that methods providing an uncertainty range of system performance are not very efficient for reliability estimation. Therefore, use of a probability density function was selected as an approach to be implemented. The probability density function of system performance can be directly used for reliability estimation once a failure criterion is given. The existing methods for such quantitative reliability evaluation are generally based on Monte Carlo simulations. Monte Carlo simulations consist of drawing samples of the basic variables according to their probabilistic density functions and then feeding them into the performance function evaluated by a thermal-hydraulic code. An estimate of the probability of failure can then

be determined by dividing the number of simulations leading to a failure of the system by the total number of simulation cycles. Monte-Carlo simulations require a large number of calculations; as a consequence, the technique can be prohibitively time consuming. To avoid this problem, two approaches are possible: (i) application of variance reduction techniques used in Monte-Carlo methods, or (ii) the use of response surfaces. It is also possible to use approximate methods, such as first and second order reliability methods (FORM/ SORM).

The final part of the methodology focuses on the development of a consistent approach for quantitative reliability evaluations of passive systems, which would allow introducing such evaluations in the accident sequence of PSA. In the PSA of innovative reactor projects carried out until recently, only the failures of passive system components (valves, pipes, etc.) was taken into account and not failures of combinations of physical phenomena on which system performance is based. It is a difficult and challenging task to examine this aspect of passive system failure within PSA models, because there are no commonly accepted practices available.

Different options have been discussed within the framework of the RMPS project, but no real consensus between partners has been found. In line with the standards in place for Level 1 PSA models, the approach currently followed by the CEA and Technicatome of France is based on accident scenarios being presented in the form of static event trees. The event tree technique makes it possible to identify the whole variety of chains of accident sequences, deriving from initiating events and describing different basic events corresponding to a failure or a success of the safety systems. This method has been applied to a fictitious PWR type reactor equipped with two types of passive safety systems. The analyses of failures carried out for this reactor made it possible to characterize both technical failures (those of valves, heat exchanger pipes, etc.), and ranges of variation of uncertain parameters affecting the physical process. A simplified PSA has been performed starting from a single initiating event. The majority of sequences addressed by this event tree were analysed by deterministic evaluations, using enveloping values of the uncertain parameters. For some sequences, where definition of the enveloping cases was impossible, basic events corresponding to the failure of physical processes were added to the event tree, and quantitative reliability evaluations, based on Monte Carlo simulations and on thermal-hydraulic code analyses, were carried out to evaluate corresponding failure probability. Failure probabilities obtained by these reliability analyses were fed into the corresponding sequences. Such an approach allows for evaluation of the impact of a passive safety system on the accident scenario. In particular, for the example studied, a new design basis for the system has been proposed in order to meet in full the global safety objective assigned to the reactor.

The RMPS methodology has been applied to three types of passive safety systems, including the isolation condenser system of a boiling water (BWR) reactor, the residual heat removal system on the primary circuit of a PWR reactor, and the hydro-accumulator (HA) systems of PWR and WWER type reactors.

In RMPS applications performed by the CEA and Technicatome of France, the thermal-hydraulic passive system acts as an ultimate system in the management of an accident scenario. Under this assumption, characteristics of the current Level 1 PSA models remain adequate.

A test case using the RMPS methodology is currently underway for a CAREM like passive residual heat removal system within the ongoing IAEA coordinated research project “Natural circulation phenomena, modelling and reliability of passive systems that utilize natural convection”.