The MELCOR code as a severe accident simulation tool does not have the capability to capture the quench process of a debris bed which may form in the wet cavity during a severe accident of light water reactors (LWRs). Although the coupled MELCOR/COCOMO simulation could overcome the limitation (Chen et al., 2022), the calculation time was explosively escalated due to mechanistic modeling of debris bed thermal-hydraulics in COCOMO. To suppress the computational cost, a surrogate model (SM) was developed in our previous study (Wang et al., 2023), and its coupling with MELCOR could realize a quick estimation of the quench process of one-dimensional debris beds. The present study is an extension of the previous work, aiming at the development of a new surrogate model for the quench process of two-dimensional conical debris beds. The new surrogate model (SM) was based on artificial neural networks (ANNs) and trained by the database from COCOMO calculations of various conical debris beds quenched in the reactor cavity of a Nordic boiling water reactor (BWR). The MELCOR was then coupled with the new SM to simulate a postulated station blackout (SBO) scenario in the BWR. The results show that the coupled MELCOR/SM simulation could provide similar ex-vessel debris bed quench period and containment pressure/temperature trends as the coupled MELCOR/COCOMO. Compared with the MELCOR standalone calculation, the coupled calculations predicted earlier points of time for water pool saturation and containment venting, since the heat transfer from conical debris bed to water pool is faster in the coupled simulations.

This study is concerned with uncertainty analysis of MELCOR simulation of a hypothetical severe accident initiated by station blackout (SBO) in a Swedish pressurized water reactor (PWR). 9 input parameters are chosen, and 12 safety-related output parameters are selected as the figures of merit (FOMs). In random sampling (RS) method, 800 MELCOR cases are run to produce empirical cumulative distribution functions (CDFs) and empirical 95th percentiles of FOMs. Given this sufficient sample size, uncertainty analyses through statistical analysis, can be performed to obtain the first two statistical moments and 95/95 estimates from the first order Wilks' method. However, RS method including Wilks' method turns out to be time consuming and computationally expensive since many MELCOR cases require iterative tuning of MELCOR input to restart and finish calculations. To overcome this issue encountered in RS method, in the present study three deterministic sampling (DS) methods are applied to uncertainty analyses, and a coupled approach by combining DS methods with a coverage factor 1.65 is proposed. Comparable results show that DS methods can generally capture the first two statistical mo-ments quickly, and acceptably accurate 95th percentiles can be calculated by the coupled approach when the output parameters can be described as normal distributions. Besides, estimated 95th percentiles from the coupled approach are covered by estimates (boxplots) from the first order Wilks' method. Hence, it can be concluded that the coupled approach has its potential to work as an alternative in engineering to RS method including Wilks' method for numerically equivalent estimates of 95/95 tolerance limit with an acceptable accuracy and a significantly less computational cost in MELCOR severe accident simulation.

Analytical simulation using best-estimate codes were suggested to be extended for the elaboration and improvement of SAMG in current PWRs. This work is about to perform an assessment work using MELCOR for the effectiveness of safety injection to achieve the PBF strategy in SAM following a BDBA scenario, that is LOCA with concurrent SBO. In the simulations, the safety injection is assumed to be retrieved with the postulated power recovery at different timing during core relocation. The simulation results illustrates that the grace period of preventing vessel failure varies with LOCA break size and locations. The safety injection implemented in grace period is capable of retarding or ceasing the core relocation, sequentially avoiding the massive core relocation into lower plenum, mitigating the hydrogen generation and fission product release from core. Meanwhile, the injection later than grace period would be failed to prevent RPV failure, and it negatively affects hydrogen generation in some scenarios. The results also indicate that the smallest injection capacity of HPSI system in Swedish PWR is sufficient to achieve the effective mitigation.

This study is concerned with uncertainty analysis of MELCOR simulation of a hypothetical severe accident initiated by station blackout (SBO) in a Nordic boiling water reactor (BWR). The hydrogen mass from cladding oxidation and the vessel failure timing in the accident are selected as the figures of merit (FOMs) in this study. As a conventional approach of uncertainty analysis, 456 cases with random sampling of 31 MELCOR input pa-rameters are executed by the code to produce the empirical cumulative distribution functions (CDFs) and the empirical 95th percentiles of the FOMs. Given the sufficient sample cases, uncertainty analyses through two nonparametric methods at various orders, i.e., the Wilks' method and the Wald & Guba's method, can then be performed to obtain the distributions of 95/95 estimates (95th percentiles estimated at a 95% confidence level) of single FOM and two FOMs. However, the conventional approach turns out to be time consuming and computationally expensive since many sample cases require iterative tuning of MELCOR input to restart and finish calculations. To overcome this issue encountered in the conventional approach of uncertainty analysis, an alternative approach is developed in the present study, in which 150 and 170 MELCOR calculation cases are used to develop bootstrapped artificial neural network (ANN) models which predict single FOM and two FOMs, respectively. The bootstrapped ANN models are then employed in uncertainty analyses through the two nonparametric methods of 95/95 estimates mentioned above. The comparative results show that the alternative approach can reproduce the distributions of 95/95 estimates for both single FOM and two FOMs with less computational costs. Moreover, while the Wilks' method or the Wald & Guba's method at a very high order (e.g., 100th order) can be used in the alternative approach to produce 95/95 estimates closer to the empirical 95th percentile, it is practically impossible to do so in the conventional approach due to unaffordable computational cost of excessive MELCOR runs. Hence, it can be concluded that the alternative approach of uncertainty analysis is not only effective (much less MELCOR cases with least fixing of unsuccessful runs), but also enabling high -order nonparametric methods for 95/95 estimates.

This study proposed a modified uncertainty quantification (UQ) approach which couples deterministic sampling (DS) methods with dynamic coverage factors, to overcome the disadvantage of the previous UQ approach (Wang and Ma, 2023b) in obtaining numerically equivalent estimates of 95/95 tolerance limits for MELCOR simulations of postulated severe accidents in a Swedish pressurized water reactor (PWR). In the modified UQ approach two deterministic sampling (DS) methods were used to obtain the first two statistical moments, and dynamic coverage factors calculated from fitted beta distributions are employed to extend the moment information to the 95th percentile. The modified UQ approach was compared with the previous UQ approach (coupling DS methods with a fixed coverage factor) and conventional UQ approach of the first order Wilks' method. The comparative results showed that the modified UQ approach not only enabled eliminating unrealistic estimates in the previous UQ approach, but also offered estimates that are covered by boxplots from the first order Wilks' method with a significant reduction of computational cost. In the modified UQ approach 10-18 samples were sufficient, while at least 59 samples were required for the first order Wilks' method. In the scope of the present study, DS-Standard method was recommended in the modified UQ approach in view of conservatism, while DS-Simplex method was preferred in view of accuracy and computational cost. Since the behavior of a DS method is dependent of time and outputs, in practice different DS methods should be integrated to the modified UQ approach for numerically equivalent estimates of 95/95 tolerance limits in MELCOR severe accident simulations.

In the severe accident management (SAM) strategy for Nordic boiling water reactors (BWRs), a flooded reactor cavity is conceived to receive corium in case of vessel failure, with the hope that the discharged corium will fragment and form a coolable particulate debris bed in the deep water pool. The so-formed debris bed on the cavity basement is supposed to be very hot at the beginning and therefore its quenching is a prerequisite for long-term coolability. In previous study the coupled MELCOR/COCOMO simulation was employed to simulate quench process of ex-vessel debris beds in severe accident scenarios. Although it successfully extended the MELCOR capability, the calculation was dramatically slowed down by explosive computational cost of COCOMO. To overcome the limitation, the present study is to develop a surrogate model (SM) which can replace the me-chanical code COCOMO and realize quick estimations of the quench process of ex-vessel debris beds. It was then coupled with MELCOR code for integral severe accident analyses of a Nordic BWR with cooling of ex-vessel debris beds. The SM was developed based on a database generated from COCOMO calculations of various one-dimension (1D) debris beds quenched in the reactor cavity, using artificial neural networks (ANNs). Finally, the coupled MELCOR/SM simulation was applied to safety analyses of postulated severe accident scenarios due to station blackout (SBO) in the BWR, where MELCOR performs integral analysis of accident progression while SM predicts the consequences (e.g. energy transfer) of debris bed quench. The simulation results show that the coupled MELCOR/SM simulation can predict the trends of containment pressure and pool temperature similar to those of the coupled MELCOR/COCOMO simulation. Compared with MELCOR standalone simulation, the coupled MELCOR/SM simulation predicted earlier pool saturation and containment venting.

Different uncertainty analysis methods are applied to MELCOR simulation of two postulated severe accidents in a Nordic boiling water reactor (BWR): (i) station blackout (SBO) accident, and (ii) large break loss-of-coolant accident (LBLOCA) combined with SBO, with the objective to compare their performances in the estimates of 95/95 tolerance limits of two figures of merit (FOMs) - the hydrogen mass produced from core degradation and the timing of vessel failure. Given 17 uncertain input parameters of MELCOR with probability density functions (PDFs), the 95/95 estimates of the two FOMs are obtained through the uncertainty analysis. From the uncertainty analysis results, it is found that for the quantification of single FOM a larger sample size leads to a much more accurate and stable 95/95 estimate at a higher computational cost, and the three nonparametric methods (Wilks' method, Beran and Hall's linear interpolation method as well as Hutson fractional statistics method) behave similarly in both accidents, while the goodness-of-fit test method performs differently and tends to provide a more realistic 95/95 estimate in both accidents. For the quantification of multiple FOMs the bracketing method tends to provide a smaller 95/95 estimate than the Wald and Guba method does, in consistent with their mathematical definitions. The Wald and Guba method is more stringent than the bracketing method when all percentiles (coverage) are set as the same. The sensitivity analysis results show that the several most significant input parameters are ranked almost identically by Spearman rank correlation coefficient (SRCC) and Pearson correlation coefficient (PCC), but these coefficients are dependent on accident scenarios and output parameters. Among the 17 parameters chosen, molten cladding drainage rate is the most influential to the output parameters (timing of initial melt relocation, timing of vessel failure, residual heat, etc.) considered in the present study, probably due to its impacts on molten Zr exposure to steam and resulting oxidation.