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Uncertainty of a severe accident code output needs to be handled reliably considering its use in safety regulation of nuclear industry. In particular, severe accident codes are utilized for probabilistic safety assessment (PSA), where the uncertainty of severe accident progress should be considered carefully due to its influence on human reliability analysis. Therefore, in this study, the uncertainty analysis of severe accident progress was performed using MELCOR code, and a total of 200 data sets of in-vessel uncertainty parameters were generated by Latin hypercube sampling method. The rank regression analysis was also performed to investigate the effect of uncertainty parameters on the severe accident progress. Sensitivity coefficients (SCs) in MELCOR such as molten clad drainage rate and zircaloy melt breakout temperature showed significant influence on relocation time and dryout time of lower plenum. However, the influence of uncertainty parameter diminished as the accident progressed.

Since Fukushima accident in 2011, numerous studies about the severe accident (SA) phenomena and their progress have been investigated experimentally and numerically. However, due to the large scale of nuclear power plants, not many experimental studies were conducted for the accident sequence. Therefore the researches about the SA progress were conducted mostly by the numerical analysis [

Among the code outputs, identifying timing of certain SA sequence is important in terms of human reliability analysis (HRA). As a practical example, the success probability of human related actions can be defined as a function of available time in HRA [

MELCOR code is an integrated SA code for various kinds of nuclear power reactors. Since 1982, MELCOR code has been developed by Sandia National Laboratories (SNL) and used for plant risk assessment and source term analysis. To simulate various SA phenomena, a number of modular packages were coupled in a unified frame. By the interaction of each modular package, MELCOR code can simulate thermal-hydraulic response of the plant, heat-up, oxidation, degradation and relocation of the core, and fission product release and transport. Because of the lack of knowledge about the SA phenomena and the interest of quick code execution time, parametric equations were used to model complicated physical processes in the past. However most recent MELCOR models are mechanistic thank to the improved calculation speed of modern computers. In many of the mechanistic models, adjustable optional parameters can be also available for uncertainty analyses and sensitivity studies. For that reason, MELCOR version 2.1.6342 was used.

As a reference plant, Optimized Power Reactor 1000 MWe (OPR1000), which consists of majority of Korean operating NPP, was selected. The nodalization of OPR1000 input model is shown in Figure ^{3}. Figure

The nodalization of OPR1000 MELCOR input model.

The core nodalization of OPR1000 MELCOR input model.

In SOARCA project [

The information of PDF about selected uncertainty parameters.

Uncertainty parameter | Distribution type | Distribution parameters | Lower bound | Upper bound |
---|---|---|---|---|

Zircaloy melt breakout temperature (SC1131(2)) | Scaled beta | 2,100 K | 2,540 K | |

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Molten clad drainage rate (SC1141(2)) | Log triangular | Mode: 0.2 | 0.1 kg/m-s | 2.0 kg/m-s |

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Radial solid/molten debris relocation time constant (SC1020(1)/SC1020(2)) | Uniform | - | Molten: 10 s | Molten: 100 s |

| ||||

Effective temperature at which the eutectic formed from UO2 and ZrO2 melts (SC1132(1)) | Normal | Mean: 2,479 K | - | - |

Symbolic nuclear analysis package (SNAP) is a graphical user interface for simplifying the task of creating input files for the analytic codes and helping to visualize code results [

To investigate the uncertainty of SA progress, the aforementioned STSBO was selected as a base case. All of safety features were assumed to fail by losing AC power, and steam driven auxiliary feed water (AFW) pump was also modeled to fail. Table

The accident sequence of base case.

Accident sequence | Time (s) |
---|---|

Reactor trip | 0 |

RCP trip | 0 |

MFW trip | 0 |

SG dryout | 3,762 |

PSRV open | 4,881 |

Core exposure | 5,359 |

Oxidation start | 8,991 |

Core dryout | 9,990 |

Cladding melt | 10,297 |

Initial melt relocation | 10,441 |

First LP dryout | 12,866 |

RPV failure | 14,462 |

CNMT over-pressurization | 60,100 |

RCS pressure in the base case (STSBO).

Core water level in the base case (STSBO).

When the RPV failure was initiated, the RCS pressure reached to 16.25 MPa (Figure

Ejected debris mass after RPV failure.

CNMT pressure in the base case (STSBO).

Among a total of 200 sample cases, only 162 cases were calculated until 259,000 s (72 hrs). Because of COR or CAV package errors, 37 cases were stopped as soon as the RPV failure was reported. A case was calculated until the initial melt relocation. However, it was terminated before the RPV failure. For that reason, the statistics of accident progress such as mean, coefficient of variance (C.V.), median, 5th percentile (P5), and 95th percentile (P95) were calculated through the available cases. Table

The statistics values of accident progress.

Accident progression phenomena | # of cases | Base case | Mean (s) | C.V. | Median (s) | P5 | P95 |
---|---|---|---|---|---|---|---|

Initial melt relocation | 200 | 10,441 | 10,445 | 0.013 | 10,491 | 10,244 | 10,601 |

First LP dryout | 199 | 12,866 | 13,421 | 0.023 | 13,466 | 12,831 | 13,811 |

RPV failure | 199 | 14,462 | 15,850 | 0.047 | 15,731 | 14,911 | 17,253 |

CNMT over-pressurization | 162 | 60,100 | 60,779 | 0.075 | 58,932 | 55,882 | 69,272 |

Histogram of major accident progress.

Relocation time

First LP dryout time

RPV failure time

CNMT overpressurization time

Although the ordinary linear regression can show the potential relations between input and output values, capturing any complex relationship is challenging in reality [

Linear regression results of accident progress.

Relocation time (Adj. R^{2} = 0.612)

First LP dryout time (Adj. R^{2} = 0.467)

RPV failure time (Adj. R^{2} = 0.125)

CNMT overpressurization time (Adj. R^{2} = 0.186)

The coefficient of determination values shows how the regression model explains the relationship between input and output parameters. In this study, adjustable R square (Adj. R^{2}) was used for the coefficient of determination. The Adj. R^{2} values of the regression model about initial melt relocations show that the in-vessel uncertainty parameters explain the potential relationships about initial melt relocation in a limited way. However, as the accident progressed, the influence of in-vessel uncertainty parameters on the regression model decreased. In cases of RPV failure and CNMT overpressurization, Adj. R^{2} values were significantly low (Adj. R^{2} < 0.3). Thus the regression model could not explain the relationship between input and output. These results might be caused by the complex behavior of molten corium relocation. In this case, although the uncertainty parameters affected the tendency of molten corium behavior, the effect on the results can be insignificant due to the cumulative random variation.

In case of initial melt relocation, SRRC and PRCC show strong negative correlation (r < -0.7) between SC1141(2) and the timing of initial melt relocation. Figure

The scatter plot of relocation time versus SC1141(2).

SRRC of first LP dryout shows that SC1141(2) and SC1131(2) were the most significant parameters affecting the first LP dryout. SRRC and PRCC indicated moderate negative relationship (-0.3 > r > -0.7) between these two uncertainty parameters and first LP dryout time. Figure ^{2} value (Adj. R^{2} > 0.7) shows that the rank regression model can properly explain the relationship between uncertainty parameters and hydrogen production and relocated mass. PRCC indicated strong negative correlation between SC1141(2) and in-vessel hydrogen production and strong positive correlation between SC1141(2) and relocated mass before first LP dryout. While the lower hydrogen production reduced the total heat accumulated in the core, the higher relocated mass transferred more heat to water in LP. Therefore, the effect of SC1141(2) on first LP dryout can be reduced by the countering effect. In case of SC1131(2), only moderate positive correlation between SC1131(2) and in-vessel hydrogen production was observed. For that reason, the effect of SC1131(2) on in-vessel hydrogen production directly influenced the first LP dryout time.

The scatter plot of first LP dryout time versus SC1141(2).

Linear regression results of potential factor about first LP dryout time.

In-vessel hydrogen production (Adj. R^{2} = 0.704)

Relocated mass before first LP dryout (Adj. R^{2} = 0.756)

To investigate the uncertainty of accident progress induced by in-vessel uncertainty parameters, uncertainty quantification was performed with regard to the timing of initial melt relocation, first LP dryout, RPV failure, and CNMT overpressurization. A total of 200 data sets of sensitivity coefficients in COR package were generated by SNAP-DAKOTA plugin using the LHS method. 5th/95th range of initial melt relocation, first LP dryout, RPV failure, and CNMT overpressurization were 10,244 s/ 10,601 s, 12,831 s/13,811 s, 14,911 s/17,253 s, and 55,882 s/69,272 s, respectively. The rank regression analysis was also performed to investigate the effect of in-vessel uncertainty parameters. The regression results show that zircaloy melt breakout temperature (SC1131(2)) and molten clad drainage rate (SC1141(2)) exhibited significant influence on initial melt relocation time and first LP dryout time, respectively. Although only in-vessel uncertainty parameters among input parameters were modified, the effect on RPV failure and CNMT overpressurization time could not be described by the rank regression model. To clearly understand the effect of in-vessel uncertainty on accident progress, various regression techniques and the stochastic studies about the core behavior should be performed for the future work.

^{2}:

Adjustable R square

Auxiliary feed water

Coefficient of variance

Containment

Control volume

Direct containment heating

High pressure melt ejection

Human reliability analysis

Latin hypercube sampling

Lower plenum

Molten corium concrete interaction

Main feed water

5th percentile

95th percentile

Probability distribution function

Partial rank correlation coefficient

Probabilistic safety assessment

Pressurizer safety relief valve

Value of coefficient

Reactor coolant system

Reactor coolant pump

Reactor pressure vessel

Severe accident

Sensitivity coefficient

Safety depressurization system

Steam generator

Symbolic nuclear analysis package

Sandia national laboratories

Standardized rank regression coefficient

Short term station black out.

The data used to support the findings of this study are available from the corresponding author upon request.

The authors declare that there are no conflicts of interest regarding the publication of this paper.

This work was supported by the National Research Foundation of Korea (NRF) funded by the Ministry of Science & ICT (MSIT, Korea) [Grant no. NRF-2017M2A8A4018213] and the Nuclear Safety Research Program through the Korea Foundation of Nuclear Safety (KoFONS) using the financial resource granted by the Nuclear Safety and Security Commission (NSSC) of the Republic of Korea (no. 1805001).