Conditional Core Damage Probability Research Articles

Dynamic Seismic Probabilistic Risk Assessment of Nuclear Power Plants Using Advanced Structural Methodologies

The conditional core damage probability (CCDP) of a representative nuclear power plant is estimated for a beyond design basis earthquake (BDBE) using state-of-the-art structural models within a dynamic probabilistic risk assessment (DPRA) framework. Randomness of seismic excitation and uncertainty of structural parameters are considered using a simulation-based approach. Finite element models are developed for the structure and a liquid container (hydro-accumulator), and fluid–structure interaction is considered with the arbitrary Lagrangian-Eulerian method. The CCDP is evaluated through a time-dependent event tree. Also, correlation among multiple hydro-accumulators is investigated. The results show that operator action and implementation time of mobile safety equipment are critical under BDBE in case of loss of offsite power following an earthquake. It was also found necessary to adopt a DPRA approach to determine the available time for action and core damage timing probabilistically.

Impact of choice of fragility approaches on seismic risk quantification of nuclear power plants

Development and evaluation of seismic fragility of structures and components is crucial in seismic probabilistic risk assessment of nuclear power plants. Simulation-based fragility approaches are a prevailing trend in the literature, while industry-recommended methodologies rely heavily on engineering judgment and deterministic analysis. In this paper, four critical components are selected, modeled and analyzed as a case study. Their fragilities are evaluated using both state-of-the-art fragility methods and code-recommended methods with approximate models. The impact of the choice of fragility approaches on the fragilities of the components and conditional core damage probability of the plant are assessed. The findings reveal that the recommended approaches employed with approximate models have limitations in estimating the median capacity of complex equipment. While there is a notable variance in the treatment of uncertainty among fragility approaches, its influence on core damage probability remains limited unless the component is the primary contributor to core damage.

On the use of time-dependent success criteria within risk-informed analyses. Application to LONF-ATWS sequences in PWR reactors

The classical Probabilistic Safety Analysis (PSA) does not include any time dependence explicitly. However, the success criteria (SC) could evolve during the cycle for some initiating events. In that sense, there is a type of sequence in which this time-dependency is quite important, the family of Anticipated Transient without Scram (ATWS) sequences in Pressurized Water Reactors. Therefore, a new risk-informed approach is proposed in this paper, which makes it possible to obtain the time-dependent SC evolution of the safety functions affected by the Moderator Temperature Coefficient (MTC) value. Then, the evolution of the ATWS conditional core damage probability (CCDP) could be obtained using a PSA model. To quantify the CCDP, the average values of the time-dependent failure probabilities must be computed. Finally, the comparison between the CCDP obtained through the application of the classical PSA approach and the new one makes it possible to quantify the impact of time-dependence on the SC of the headers that this new risk-informed ATWS approach can provide.

Simulation-based dynamic probabilistic risk assessment of an internal flooding-initiated accident in nuclear power plant using THALES2 and RAPID

Probabilistic risk assessment (PRA) is a method used to assess the risks associated with large and complex systems. However, the timing at which nuclear power plant structures, systems, and components are damaged is difficult to handle explicitly if the risk of an external event is evaluated using conventional PRA based on event trees and fault trees. A methodology coupling thermal-hydraulic analysis with external event simulations using Risk Assessment with Plant Interactive Dynamics (RAPID) is therefore proposed to overcome this limitation. A flood propagation model based on Bernoulli’s theorem was applied to represent internal flooding in the turbine building of the pressurized water reactor. Uncertainties were also taken into account, including the flow rate of the floodwater source and the failure criteria for the mitigation systems. The simulated recovery actions included the operator isolating the floodwater source and using a drainage pump; these actions were modeled using several simplifications. Overall, the results indicate that combining isolation and drainage can reduce the conditional core damage probability upon the occurrence of flooding by approximately 90%.

Proposal of inspection and evaluation rules of the Rules on Fitness-for-Service to eliminate the circumferential crack angle limitation of class 1 piping

The Rules on Fitness-For-Service (the Rules on FFS) of the Japan Society of Mechanical Engineers (JSME) limits the circumferential crack angle to 60 degrees or less for Class-1 piping. This limitation was based on a deterministic evaluation because of the concern about fracture that would occur if the measurement error of the crack size was taken into consideration. However, ASME Section XI, which is a standard similar to the Rules on FFS, has no limitation on the circumferential crack angle, and the crack angle limitation is unique to the Rules on FFS. After the first edition of the Rules on FFS was published in 2000, some research on crack size measurement were performed. The number of inspections according to the measurement error that satisfy the target fracture frequency regardless of the crack angle can be evaluated by using probabilistic evaluation. In this study, the number of measurements of the crack size required to satisfy the target fracture frequency is determined based on the thickness of pipes, crack size measurement error, the fracture frequency according to the number of crack size measurements, and the conditional core damage probability due to pipe fracture. Based on this result, the requirement for inspection and evaluation of the Rules on FFS was proposed.

Investigation on risk-informed uncertainty method and its application in PWR LBLOCA

The mainstream deterministic and probabilistic methods for safety analysis of the nuclear power plant (NPP) are the best estimate plus uncertainty (BEPU) analysis and probabilistic safety analysis (PSA), respectively. With the development of techniques, a more “realistic” simulation of the NPP has become a long-term goal to improve the economic efficiency. Nowadays, the combination of BEPU and PSA, also known as the risk-informed uncertainty method, is under development. In this paper, the cold leg double-ended break accident of a typical pressurized water reactor was selected to be the target scenario for a preliminary study of the combined method. A failure analysis of the emergency core cooling system based on PSA was carried out first, and the failure probability of each event sequence was determined. Then the conditional core damage probability of each event sequence was evaluated through BEPU analysis, and the core damage frequency of the reactor was finally determined.

Assessment of Terrorist Attack Risk of a BWR Nuclear Power Plant Using Monte Carlo Simulations

The security of nuclear power plants becomes an ever more important issue after the tragedy of the World Trade Center of New York City on September 11, 2000. Utilities around the world have significantly increased the resources used to enhance the security of nuclear power plants. In this study, a mathematical model based on Monte Carlo simulations is developed to calculate the probability of invaders being located in a building in the vital area, on a floor of the building, and in a region of the floor when invaders break into the vital area successfully. In the model, it is assumed that invaders have no specific target to sabotage and they have no prior knowledge of the layout of the plant. Invaders are running around randomly in the vital area, and Monte Carlo simulations are used to trace their paths on a floor. The results can help the security of a nuclear power plant locate invaders in the vital area. If it is assumed that the damage caused by the invaders is similar to the damage induced by a fire, the product of the probability of invaders being located in a region and the fire conditional core damage probability of the region ijk (CCDPF,ijk) from a fire hazard probabilistic safety assessment can be used to prioritize the importance of the region to the risk of terrorist sabotage and to allocate resources that enhance physical protection. The summation of the product for all the region is the conditional core damage probability of terrorist attack (CCDPS). The surrogate plant used in the present study is a typical General Electric–designed Boiling Water Reactor-6 with Mark III containment. The vital area in this study has six entrances and three buildings: turbine, control, and auxiliary. Among the 196 regions considered in the analysis, the majority (between 85% and 92% for different entrances) have the Pijk of locating terrorist probability of less than 10−2. The top three average Pijk regions are located in the turbine building. The eight regions with CCDPF,ijk equal to 1.0 of the plant contribute 86.8% of the total average CCDPS. Region AUX56, which is the corridor on the third floor of the auxiliary building, contributes 33.9% of the risk of core damage. Region AUX14, which is the corridor on the first floor of the auxiliary building, contributes 17.1% of this risk.

Development of a multi-unit seismic conditional core damage probability model with uncertainty analysis

Various studies about multi-unit probabilistic safety assessment (PSA) have been conducted following the Fukushima accident. In this paper, an intuitive and simple model is developed to supplement the disadvantages of huge models that integrate all units in the same site. Through this framework, pre-assessment can be made for multi-unit events, the results of which can assist risk-informed decision making in a relatively short time. The model deducts multi-unit seismic conditional core damage probability (MUSCCDP) with a Bayesian belief network, and by including seismic inter-unit correlation factors, the model can also represent the extent of simultaneous and identical core damage in multiple units at the same site due to an earthquake. The outcome of the model confirms the impact that seismic intensity and seismic correlation have on MUSCCDP. Moreover, it provides an importance analysis of the components in the units and represents which components are the most vulnerable in multiple units. As the uncertainty analysis of the input data for the model is conducted by changing the distribution of the variables, the results raise the necessity for further uncertainty analyses in multi-unit seismic PSA before accepting the PSA results.

Probability subtraction method for accurate quantification of seismic multi-unit probabilistic safety assessment

Single-unit probabilistic safety assessment (SUPSA) has complex Boolean logic equations for accident sequences. Multi-unit probabilistic safety assessment (MUPSA) model is developed by revising and combining SUPSA models in order to reflect plant state combinations (PSCs). These PSCs represent combinations of core damage and non-core damage states of nuclear power plants (NPPs). Since all these Boolean logic equations have complemented gates (not gates), it is not easy to generate exact Boolean solutions.Delete-term approximation method (DTAM) has been widely applied for generating approximate minimal cut sets (MCSs) from the complex Boolean logic equations with complemented gates. By applying DTAM, approximate conditional core damage probability (CCDP) has been calculated in SUPSA and MUPSA. It was found that CCDP calculated by DTAM was overestimated when complemented gates have non-rare events. Especially, the CCDP overestimation drastically increases if seismic SUPSA or MUPSA has complemented gates with many non-rare events.The objective of this study is to suggest a new quantification method named probability subtraction method (PSM) that replaces DTAM. The PSM calculates accurate CCDP even when SUPSA or MUPSA has complemented gates with many non-rare events. In this paper, the PSM is explained, and the accuracy of the PSM is validated by its applications to a few MUPSAs.

Development of an optimal mitigation strategy by estimating the conditional core damage probability with time-dependent recovery actions

The optimization of an emergency operating strategy necessitates the risk quantification of mitigation action. However, there are challenges associated with plant risk estimation: 1) there are thousands of accident scenarios in given conditions that will cause core damage, and 2) the time-dependent recovery probability and various available times of component recovery according to plant conditions increase the complexity of risk assessment. To address these challenges, the functional modeling method and the concept of the mitigation success domain are applied to the risk quantification methodology proposed in this study. The functional modeling method can systematically reduce the number of component configurations that cause core damage before and after recovery actions, and the mitigation success domain can determine an available time range for the recovery actions with the given accident conditions. In this paper, the mitigation strategy that minimizes the plant risk under a small break loss of coolant accident is developed based on the risk quantification results.

Emergency core cooling system performance criteria for Multi-Layered Silicon Carbide nuclear fuel cladding

Multi-layered Silicon Carbide (SiC) cladding has been proposed to replace the current Zircaloy (Zr) cladding in existing nuclear power plants. Due to its ceramic property, SiC may have a different failure mechanism from that of metallic Zr clad. This characteristic should be considered in designing the plant’s safety system performance, such that the fuel’s integrity is reasonably assured during accident scenarios.This paper aims at optimizing the Emergency Core Cooling System (ECCS) performance criteria in mitigating LBLOCA accidents at a Pressurized Water Reactor (PWR) using the uranium dioxide fuel and duplex or triplex SiC cladding structures. Clad failures by brittle fractures and thermal degradation were modeled in a fuel analysis code. This fuel model was coupled with the RELAP5 plant model by adapting the fuel’s mesh configuration and formulating the effective heat transfer coefficients. A model to quantify the likelihood of clad functional failure as a combination of individual layer fractures at various axial positions was proposed. Updated SiC material properties were gathered from recent reference studies. Clad reliability estimates using the proposed model were compared with the estimates obtained using other models. The results were used to relax the criterion of required actuation timing of ECCS, such that the risk of the new plant design is less or equal to that of the initial plant configuration.Triplex clad was more reliable than duplex clad and Zr, reducing the conditional core damage probability by three orders of magnitude in the reference LBLOCA scenario. Compressive stresses due to irradiation swelling played the determining role in the vulnerabilities of each clad design. The duplex clad was vulnerable to pressure-loading stresses while triplex clad was prone to fail due to thermal shocks experienced during the LOCA reflood phase. Additionally, it was concluded that the most vulnerable axial fuel rod location in the reference LBLOCA scenario was located at the highest axial power peaking location.A sensitivity study on the ECCS timing density was conducted. The results showed that ECCS actuation timing could be extended from the initial technical specification, without increasing the fuel damage likelihood. The time extension was distributed in the order of several hundreds of seconds, which was comparable with time extensions offered by FeCrAl and Cr-coated-Zr clad designs in LBLOCA scenarios. This time extension may potentially reduce the failure probabilities of EDGs and pumps, hence improving the plant safety further.

The safety assessment of OPR-1000 nuclear power plant for station blackout accident applying the combined deterministic and probabilistic procedure

Station blackout (SBO) is a typical beyond design basis accident (BDBA) and significant contributor to overall plant risk. The risk analysis of SBO could be important basis of rulemaking, accident mitigation strategy, etc. Recently, studies on the integrated approach of deterministic and probabilistic method for nuclear safety in nuclear power plants have been done, and among them, the combined deterministic and probabilistic procedure (CDPP) was proposed for safety assessment of the BDBAs. In the CDPP, the conditional exceedance probability obtained by the best estimate plus uncertainty method acts as go-between deterministic and probabilistic safety assessments, resulting in more reliable values of core damage frequency and conditional core damage probability. In this study, the safety assessment of OPR-1000 nuclear power plant for SBO accident was performed by applying the CDPP. It was confirmed that the SBO risk should be reevaluated by eliminating excessive conservatism in existing probabilistic safety assessment to meet the targeted core damage frequency and conditional core damage probability. By estimating the offsite power restoration time appropriately, the SBO risk was reevaluated, and it was finally confirmed that current OPR-1000 system lies in the acceptable risk against the SBO. In addition, it is concluded that the CDPP is applicable to safety assessment of BDBAs in nuclear power plants without significant erosion of the safety margin.

A combined deterministic and probabilistic procedure for safety assessment of beyond design basis accidents in nuclear power plant: Application to ECCS performance assessment for design basis LOCA redefinition

The concept and assessment approach of nuclear safety in nuclear power plants (NPPs) have been evolved with the technological progress and the lessons learned from the major events. Recently, studies on the integrated approach of deterministic and probabilistic method have been done. In this study, a combined deterministic and probabilistic procedure (CDPP) is proposed for safety assessment of the beyond design basis accidents (BDBAs). In the CDPP, the conditional exceedance probability obtained by the best estimate plus uncertainty method acts as go-between deterministic and probabilistic safety assessments, resulting in more reliable values of core damage frequency and conditional core damage probability. To verify applicability of the methodology, performance of the APR-1400 emergency core cooling system is assessed against large break loss of coolant accident (LOCA), under the premise that LOCAs for any breaks larger than transition break size would be regarded as BDBA. In addition, discussions are made for analysis results for allowable NPP changes of emergency diesel generator start time extension and power uprating. It is concluded that the proposed CDPP is applicable to safety assessment of BDBAs in NPPs without significant erosion of the safety margin.

06/00400 Study of liquid CO 2 droplet formation under simulated mid-depth ocean conditions : Nishio, M. et al. Energy, 2005, 30, (11–12), 2284–2297

A part of managing nuclear power plant operations is the control of plant risk over time as components are taken out of service or plant upsets are caused by initiating events. Unfortunately, measuring risk over time proves to be challenging, even with modern probabilistic risk analyses (PRAs) and PRA tools. In general, the process of measuring the operational risk would satisfy three desires: (1) the measurement would provide the risk magnitude for a particular event or over a period of time; (2) the risk results could be summed for a period of time to obtain a cumulative risk profile; and (3) the measurement process would be tractable while still using the current modeling techniques and tools. This paper demonstrates the calculation of the conditional core damage probability (CCDP) for the two cases of component outages and initiating events. In addition, two potential complications were identified that must be addressed when performing a CCDP calculation. The first complication, determining the appropriate nonrecovery probabilities to be applied to an inoperable component or initiating event, addresses the possibility of the plant operators preventing damage to the plant from their actions. The second complication, adjusting common-cause probabilities specific to the plant configuration, accounts for the fact that the PRA common-cause probabilities built into the model are applicable only during nominal conditions. The examples presented in the paper illustrate the potential under-estimation in CCDP when modifications to common-cause probabilities are ignored. These underestimation errors ranged from a factor of two to over a factor of six underestimation in CCDP.

06/00398 Risk-informed design guidance for future reactorsystems: Delaney, M. J. et al. Nuclear Engineering and Design, 2005, 235, (14), 1537–1556

A part of managing nuclear power plant operations is the control of plant risk over time as components are taken out of service or plant upsets are caused by initiating events. Unfortunately, measuring risk over time proves to be challenging, even with modern probabilistic risk analyses (PRAs) and PRA tools. In general, the process of measuring the operational risk would satisfy three desires: (1) the measurement would provide the risk magnitude for a particular event or over a period of time; (2) the risk results could be summed for a period of time to obtain a cumulative risk profile; and (3) the measurement process would be tractable while still using the current modeling techniques and tools. This paper demonstrates the calculation of the conditional core damage probability (CCDP) for the two cases of component outages and initiating events. In addition, two potential complications were identified that must be addressed when performing a CCDP calculation. The first complication, determining the appropriate nonrecovery probabilities to be applied to an inoperable component or initiating event, addresses the possibility of the plant operators preventing damage to the plant from their actions. The second complication, adjusting common-cause probabilities specific to the plant configuration, accounts for the fact that the PRA common-cause probabilities built into the model are applicable only during nominal conditions. The examples presented in the paper illustrate the potential under-estimation in CCDP when modifications to common-cause probabilities are ignored. These underestimation errors ranged from a factor of two to over a factor of six underestimation in CCDP.

Accident sequence precursor analysis: level 2/3 model development

The US Nuclear Regulatory Commission’s Accident Sequence Precursor (ASP) program currently uses simple level 1 models to assess the conditional core damage probability for operational events occurring in commercial nuclear power plants (NPP). Not all accident sequences leading to core damage will result in the same radiological consequences. Therefore, it is necessary to develop simple level 2/3 models that can be used to analyze the response of the NPP containment structure in the context of a core damage accident, estimate the magnitude of the resulting radioactive releases to the environment, and calculate the consequences associated with these releases. This level 2/3 model development work was initiated in 1995, and several prototype models have been completed. Two versions of these prototype level 2/3 models have been developed. Simple level 2/3 models have been linked to the simple level 1 models to provide risk perspectives for operational events. Additionally, very complex and detailed models have been developed that take provide much greater flexibility in accommodating a much wider range of level 1 core damage accident sequences. These detailed models also make possible assessments that are integrated with the level 1 model, on the importance of different severe accident phenomena and containment performance characteristics. This paper describes the development and capabilities of these level 2/3 ASP models, and the linkage to the level 1 models.

Calculating conditional core damage probabilities for nuclear power plant operations

A part of managing nuclear power plant operations is the control of plant risk over time as components are taken out of service or plant upsets are caused by initiating events. Unfortunately, measuring risk over time proves to be challenging, even with modern probabilistic risk analyses (PRAs) and PRA tools. In general, the process of measuring the operational risk would satisfy three desires: (1) the measurement would provide the risk magnitude for a particular event or over a period of time; (2) the risk results could be summed for a period of time to obtain a cumulative risk profile; and (3) the measurement process would be tractable while still using the current modeling techniques and tools. This paper demonstrates the calculation of the conditional core damage probability (CCDP) for the two cases of component outages and initiating events. In addition, two potential complications were identified that must be addressed when performing a CCDP calculation. The first complication, determining the appropriate nonrecovery probabilities to be applied to an inoperable component or initiating event, addresses the possibility of the plant operators preventing damage to the plant from their actions. The second complication, adjusting common-cause probabilities specific to the plant configuration, accounts for the fact that the PRA common-cause probabilities built into the model are applicable only during nominal conditions. The examples presented in the paper illustrate the potential under-estimation in CCDP when modifications to common-cause probabilities are ignored. These underestimation errors ranged from a factor of two to over a factor of six underestimation in CCDP.

Semi-Markov reliability analysis of three test/repair policies for standby safety systems in a nuclear power plant

Abstract During the course of efforts in re-examining the technical specifications for nuclear power plants, particular attention has been paid to the ‘additional test’ requirement on the redundant components in a standby safety system. When a failure of one part is detected by the scheduled test, the following three test/ repair policies are considered on the other redundant parts during the allowed outage time of the first failed component: (1) Policy 1—a prompt additional test, (2) Policy 2—no additional test, and (3) Policy 3—an additional test after repairing the first failed one. For the analysis of the three test/repair policies, a computer program MARADD ( Mar kov R eliability Analysis for the Add itional Test Requirement) was developed in the present study, based on semi-Markov reliability analysis. The allowed outage time (AOT) is usually larger than the calculation time step required by acceptable accuracy. A component can change its state from repair to operable state during the AOT according to the assumed Poisson repair process. However, some system states make forced transitions to other system states due to the additional test requirement, and to the plant shutdown state on exceeding the AOT that is a deterministic parameter. Thus, the three test/repair policies have semi-Markovian characteristics. The methodology was applied to the diesel generator system on which Policy 1 is currently performed. For the three test/repair policies, the system unavailability, the core damage frequency, and the plant shutdown probability in 1 year of plant operation were calculated for several AOTs and STIs using the nominal input data and also using various input data for sensitivity studies. The current test/repair procedure, i.e. Policy 1, has no advantage over Policies 2 and 3 in a nuclear power plant with relatively large conditional core damage probability given a reactor trip and with a diesel generator system that has short repair time, and low failure rate. Furthermore, the allowed outage time could be extended to improve the core damage frequency when the plant has large conditional core damage probability given a reactor trip. However, there is significant benefit in plant availability resulting from extending the allowed outage time, independently of the magnitude of the conditional core damage probability given a reactor trip.