Linking classical PRA models to a dynamic PRA
Introduction
Dynamic Probabilistic Risk Assessment (PRA) (Devooght, 1997, Devooght and Smidts, 1992) methods couple stochastic methods (Rutt et al., 2006, Hofer et al., 2002, Hsueh and Mosleh, 1996, Cojazzi, 1996, Alfonsi et al., 2014, Chraibi, 2014) (i.e., sampling methods) with system simulators (e.g., RELAP5-3D (RELAP5-3D Code Development Team, 2005) and MELCOR (Gauntt, 2000)) to determine the risks associated with complex systems such as nuclear power plants. Compared to classical PRA methods (NRC, 2005), they can evaluate with higher resolution the safety impacts of timing and sequencing of events on the progression of an accident without the need to introduce conservative modeling assumptions and success criteria.
As part of a dynamic PRA analysis, it is not uncommon that some components of the system under consideration might not require a complex and computationally expensive simulation model due to its intrinsic characteristics (e.g., no time or physics dependency). From a modeling point of view, such components could be actually included in the analysis by employing simpler classical PRA models such as Event Trees (ETs) or Fault Trees (FTs) (Lee and McCormick, 2011).
The objectives of this paper are twofold. The first objective is to present a set of methods to link classical PRA models into a dynamic PRA: a hybrid PRA. We consider not only ETs and FTs, but also Markov models (Aldemir, 1991) and Reliability Block Diagrams (RBDs) (Lee and McCormick, 2011) as possible modeling solutions (see Section 2). The created links (see Sections 3 Dynamic PRA, 4 Integration) are performed from a functional perspective by creating a common data communication flow among the sampled parameters, the classical PRA models and the safety analysis code. The second objective is to show how the generated hybrid PRA data can be employed to identify conservative assumptions in original PRA can be identified and how such original PRA can be modified by updating success criteria captured by the set of RELAP5-3D simulation runs. We apply the developed methods for the analysis of a Pressurized Water Reactor (PWR) Large Break Loss of Coolant Accident (LB-LOCA) accident scenario (see Sections 5). We link the main FTs from the original PRA directly to the RELAP5-3D code and perform a hybrid PRA. We then show how the hybrid PRA data are employed to update the success criteria of the original classical PRA.
Section snippets
Classical PRA models
PRA methods (Lee and McCormick, 2011) have been employed in the nuclear industry after the publication of the NRC document NUREG-1150 (NRC, 2005). Since then, each U.S. nuclear power plant has developed PRA models for each unit based on ETs, FTs, Markov models and RBDs.
ETs (Lee and McCormick, 2011) inductively model the accident progression using a tree structure with the goal of depicting all possible accident sequences. Starting from an initiating event, the accident progression evolves and
Dynamic PRA
In contrast to classical PRA, dynamic PRA approaches (Acosta and Siu, 1993, Mandelli et al., 2013) explicitly employ system simulation tools instead of complex logic structures (such as ETs and FTs). In fact, they can model in a single analysis: the thermal–hydraulic behavior of the plant, external events, and operators’ responses to the accident scenario. The probabilistic part of the analysis is performed by defining a set of stochastic parameters, which dictates the time dependent accident
Integration
The idea behind integrating classical PRA into a dynamic PRA is to replace an expensive physics model or a control logic model of Eq. (3) with a simpler classical PRA model such as a FT or an ET (see Section 2). By following the notation used in Section 3 we aim to replace a model of Eq. (3) with a new model as follows:or similarly:
As an example, the control logic of the LPI system could
Test case
The test case considered in this paper is a 3-loop PWR system of Westinghouse design with a large-dry containment. The initiating event is a LB-LOCA on the cold-leg RPV where the break occurs on the pressurizer loop. Under these accident conditions, the system experiences a sudden sub-cooled blowdown and primary system pressure drops from about 2,200 psi down to the saturation pressure (about 1,000 psi).
In order to compensate for the large loss of coolant inventory into the vessel and prevent
Analysis
In order to test the validity of the proposed PRA integration we coupled the RELAP5-3D PWR model with a set of FTs. The FTs that are part of the LB-LOCA initiating event are: the ACC FT (ACC-FT), the LPI FT (LPI-FT) and the LPR FT (LPR-FT). This analysis was performed by using the RAVEN framework and by employing the EnsembleModel feature. This feature allows the user to create connections among different models in terms of input and output data: output data generated by a model are passed as
Results
As described in Section 6, the generated database DB of the simulation data set has been processed by partitioning it (i.e., DB1, DB2, DB3, and DB4 of Fig. 7) accordingly to the LB-LOCA ET sequences (see Fig. 1). In this respect, Fig. 8 shows the plots of the temporal profile of PCT for the simulation runs belonging to the four LB-LOCA ET sequences of Fig. 1. Note that at the beginning for the transient, the PCT rapidly increases since a large amount of water inventory is lost due to the break.
Conclusions
This paper targets two objectives: to present a set of methods to link classical PRA models into a hybrid PRA and to demonstrate how hybrid PRA data can be employed to identify conservative assumptions in original PRA.
Regarding the first objective, we have summarized a series of methods and algorithms that can be employed to incorporate classical PRA models into dynamic PRA analyses. The objective is to model parts of the system not with advanced simulation tools but instead with classical PRA
CRediT authorship contribution statement
D. Mandelli: Software, Data curation, Writing - original draft. C. Wang: Software, Writing - review & editing. C. Parisi: Methodology, Writing - review & editing. D. Maljovec: Software. A. Alfonsi: Software. Z. Ma: Data curation, Writing - review & editing. C. Smith: Supervision.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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