A Limited-Scope Probabilistic Risk Assessment Study to Risk-Inform the Design of a Fuel Storage System for Spent Pebble-Filled Dry Casks

Round 1

Reviewer 1 Report

No Comments and Suggestions

Author Response

We appreciate the support provided by the esteemed reviewers.

Reviewer 2 Report

The application of PRA for Fuel Storage System for Spent Pebble-Filled Dry Casks is presented in this manuscript. New generations of the Nuclear Power Plant might impose additional  risk to the public so looking beyond the conventional assessments are necessary. This paper applies the standard steps of PRA for the Fuel Storage System for Spent Pebble-Filled Dry Casks. Although the application is clearly demonstrated step by step, its contribution to the topic is minimal. The authors are profficient with several  computation tools needed to complete the required  calculations. I think this will be useful for the readers in this area to see how different elements of PRA are applied. Below are my comments:

1. Language: The authors should revise the manuscript for clarity and readability to ensure that all sentences are easily understood.

2. Scope and Objective: The authors should clearly state their research contributions, whether this is a novel methodology or an application of existing methodologies.

3. Abbreviations: The authors should provide a table of all abbreviations to assist readers in understanding the text.

4. Methodology: The authors should consider removing the elements of existing methodologies from the "2. methodology" section and instead provide references to the original resources.

5. Alternative approaches: The authors should avoid discussing alternative approaches that were not utilized, as this is not a review paper. The methodology should be discussed around Figure 3.

6. Results: The authors should provide justification for the use of CAFTA PRA Module UNCERT with 10,000 sampling, and discuss how this might impact the end results.

7. Probabilistic validity: The authors should discuss the challenges in probabilistic validation and provide some verification that the results are valid.

8. Sensitivity analysis: The authors should present tabular results for sensitivity analysis instead of the section 4.6.3. This will make the results clearer and easier to understand.

Overall, the manuscript should be revised for clarity and readability, and the authors should clearly state their research contributions. Abbreviations should be defined, and the methodology should be presented in a clear and concise manner. The authors should provide justification for their methods and discuss the validity of their results. Sensitivity analysis should be presented in a clear and organized manner.

1. The language is overall good. Some of the sentences are difficult to be understood. A fine look is recommended. 

Author Response

We appreciate the invaluable feedback provided by the esteemed reviewers. With deep gratitude, we submit the following responses to address your concerns regarding the manuscript. This letter includes the reviewer's comments and our corresponding answers.

 

Reviewer’s comment:

The application of PRA for Fuel Storage System for Spent Pebble-Filled Dry Casks is presented in this manuscript. New generations of the Nuclear Power Plant might impose additional risk to the public so looking beyond the conventional assessments are necessary. This paper applies the standard steps of PRA for the Fuel Storage System for Spent Pebble-Filled Dry Casks. Although the application is clearly demonstrated step by step, its contribution to the topic is minimal. The authors are proficient with several computation tools needed to complete the required calculations. I think this will be useful for the readers in this area to see how different elements of PRA are applied. Below are my comments:

 

Comment #1)

Language: The authors should revise the manuscript for clarity and readability to ensure that all sentences are easily understood.

Answer)

Thank you for your comment. We revised introduction and conclusion for better understanding.

 

Comment #2)

Scope and Objective: The authors should clearly state their research contributions, whether this is a novel methodology or an application of existing methodologies.

Answer)

Thank you for your comment. We revised the section 1.2. (Research Objective) and added more sentences to clarify the contribution with the solid objective.

 

Comment #3)

Abbreviations: The authors should provide a table of all abbreviations to assist readers in understanding the text.

Answer)

Thank you for your comment. The table of abbreviations can be found at the end of the manuscript.

 

Comment #4)

Methodology: The authors should consider removing the elements of existing methodologies from the "2. methodology" section and instead provide references to the original resources.

Answer)

Thank you for your comment. We have addressed it in the manuscript.

Comment #5)

Alternative approaches: The authors should avoid discussing alternative approaches that were not utilized, as this is not a review paper. The methodology should be discussed around Figure 3.

Answer)

Thank you for your feedback. We would like to emphasize the importance of Section 2, which outlines the methodology used in this study. The paper discusses the commonly used PRA elements for non-LWR systems, which can be applied not only to this study but also to future research. Therefore, Section 2 is crucial in describing the techniques utilized in each PRA element process. In particular, a concise explanation of the methods used to identify initiating events, such as master logic diagrams, heat balance fault trees, and others, assists the reader in understanding why this study selected the master logic diagram and its advantages over other methods. However, in response to your concern, we clarified the reasons for including the general PRA elements in Section 2 when demonstrating Figure 3.

Comment #6)

Results: The authors should provide justification for the use of CAFTA PRA Module UNCERT with 10,000 sampling and discuss how this might impact the end results.

Answer)

A sample size of 10,000 has been arbitrarily selected, but it is a reasonable number considering the balance between computational cost and output from the UNCERT module. As shown in the table and figure below, the mean frequency tends to converge to a point value (indicated by the black dashed line) as the sample size increases. However, beyond a certain point (5,000 sample size in this study), it is not guaranteed that the mean value from a larger sample size will always be closer to the real value than one from a smaller sample size due to the inherent randomness of Monte Carlo methods. Moreover, a larger sample size will certainly require more computational cost. Although the case study we have presented is not complicated to calculate the uncertainty in event sequences, choosing an appropriate sample size is crucial from a cost perspective when dealing with a large event tree for future work. Therefore, we have chosen a sample size of 10,000 for this study as a proper showcase. The section 4.4 is revised to reflect this concern.

 

Release Category: Direct Exposure (Point Value = 2.021E-06)
Sample Size	Mean	5th percentile	Median	95th percentile
100	2.385E-6	8.777E-10	7.683E-7	7.846E-6
1,000	1.909E-6	3.501E-9	5.759E-7	9.030E-6
3,000	2.090E-6	2.792E-9	5.694E-7	9.317E-6
5,000	2.068E-6	4.124E-9	5.651E-7	9.077E-6
10,000	1.971E-6	3.977E-9	5.705E-7	8.682E-6
20,000	2.045E-6	4.118E-9	5.712E-7	8.924E-6
50,000	2.059E-6	4.192E-9	5.703E-7	9.13E-6

 

Comment #7)

Probabilistic validity: The authors should discuss the challenges in probabilistic validation and provide some verification that the results are valid.

Answer)

Challenges in verifying probabilistic results arise from the uncertainty in both event sequence frequencies and consequences. To properly qualify the findings of the case study, it is crucial to take into account two types of uncertainties: epistemic uncertainty and aleatory uncertainty. Epistemic uncertainty pertains to the estimation of frequency and can be minimized through further investigations that offer supporting evidence to examine the probability of failure. Because of a lack of information, the failure probability for event sequence quantification contains the epistemic uncertainty, thus, the CNID is used to minimize the impact of prior input and maximize the influence of the likelihood function. In conclusion, the challenge for validation occurs due to the lack of information.

Moreover, the pebble failure probability data used in this study has been validated through experimentation [1]. The study acknowledges the discrepancy between the simulation result obtained from the finite element model and the experimental result as an aleatory uncertainty.

In response to your concern, we have added the challenges of this study that the paper reader needs to be aware of in the conclusion.

[1]     M. Lin, J. Wang, B. Wu, and Y. Li, “Dynamic analysis of dry storage canister and the spent fuels inside under vertical drop in HTR-PM,” Annals of Nuclear Energy, vol. 154, p. 108030, May 2021, doi: 10.1016/j.anucene.2020.108030.

 

Comment #8)

Sensitivity analysis: The authors should present tabular results for sensitivity analysis instead of the section 4.6.3. This will make the results clearer and easier to understand. - Done

Answer)

We appreciate your comment. Table 11 has been partitioned into two distinct tables, one presenting the outcomes of the ordinary least square (OLS) method and the other exhibiting the impact results obtained through sensitivity analysis. The OLS method results reveal the goodness of fit of the OLS model for the case studies, ascertained by the R-squared and P-values. Conversely, the impact results through sensitivity analysis provide a comparative analysis of the impact of variables in each case. By utilizing the split tables, the detailed demonstrations of the results have been revised.

 

Overall Comment)

Overall, the manuscript should be revised for clarity and readability, and the authors should clearly state their research contributions. Abbreviations should be defined, and the methodology should be presented in a clear and concise manner. The authors should provide justification for their methods and discuss the validity of their results. Sensitivity analysis should be presented in a clear and organized manner.

Answer)

Thank you for your comment. We have addressed it in the manuscript.

 

Reviewer 3 Report

The authors conduct the PRA study to the spent pebble dry cask and spent TRISO particle fuel. The methods and analyses are sound and clear. The study is meaningful to show the risk-informed designs. The manuscript can be accepted by checking some minor suggestions listed below. 

1. Check the format of citing references in the contexts, such as [31] on Page 3.

2. Check typos, such as “section 2” on Page 3 should be “Section 2”. 

3. Check figures and tables. For instance, in Table 2, inputs of Heat Exchanger and Blower in the row of Open Loop Active Cooling Mode should be No and Yes.

4. Check abbreviations, such as HAZOP. The full name should be given at the first time and it is only necessary to be indicated once. 

Author Response

We appreciate the invaluable feedback provided by the esteemed reviewers. With deep gratitude, we submit the following responses to address your concerns regarding the manuscript. This letter includes the reviewer's comments and our corresponding answers.

 

Reviewer’s comment:

The authors conduct the PRA study to the spent pebble dry cask and spent TRISO particle fuel. The methods and analyses are sound and clear. The study is meaningful to show the risk-informed designs. The manuscript can be accepted by checking some minor suggestions listed below.

 

1. Check the format of citing references in the contexts, such as [31] on Page 3.

Thank you for your comment. We have addressed it in the manuscript.

2. Check typos, such as “section 2” on Page 3 should be “Section 2”.

Thank you for your comment. We have addressed it in the manuscript.

3. Check figures and tables. For instance, in Table 2, inputs of Heat Exchanger and Blower in the row of Open Loop Active Cooling Mode should be No and Yes.

Thank you for your comment. We have addressed it in the manuscript.

4. Check abbreviations, such as HAZOP. The full name should be given at the first time and it is only necessary to be indicated once.

Thank you for your comment. We have addressed it in the manuscript.

Round 2

Reviewer 2 Report

The reviewer evaluated the responses to the comments. The manuscript will be very informative for the readers if it is published in high quality of content, language and structure. There are a few concerns:

1.     1.  The authors have not provided a change track or highlighted the revision areas, making it difficult for the reviewer to evaluate the sufficiency of the actions taken. It is requested that the authors provide it with the next revision for comments of v1 and v2.

2.     2.   The reviewer attempted to track the changes made in the manuscript but was unsuccessful. Having a change track or highlighting would greatly help the reviewer in examining the revisions. For example, when trying to track the change made for comment 4, it was not possible to identify the specific changes.

3.       The aim of the review is not just a rebuttal. If the authors agree with the comments, they should clearly demonstrate how each comment has been addressed in the manuscript, rather than only in the response to reviewers.

4.   3.    In relation to Comment 5, there are numerous developed methodologies for risk and hazard assessment. The reviewer is aware of the merits, limitations, and interconnections of these methodologies. If the submitted manuscript is a research paper, the authors should limit their focus to the elements of the developed methodologies. For example, the reviewer could not find any trace of using HAZOP and FMEA in the research. The reviewer understands that some elements can be replaced with others, but there is no guideline provided to explain how the elements were selected. It is suggested that the authors focus only on the utilized elements. It would be acceptable if the authors review the merits and limitations of elements outside of the application.

5.     4.  Regarding the sample size for the Monte Carlo simulation, the reviewer agrees with the authors that the sample size can be determined using convergence criteria. However, the reviewer could not find evidence of this convergence in the "Release Category" table. While it is understood that random sampling will provide different results in each simulation trial, a meaningful convergence for the mean, 5th percentile, median, and 95th percentile is not apparent. It is advised to review the results again.

6.     5.   Comment 7: The reviewer is aware of the uncertainty sources and categories of aleatory and epistemic uncertainties. By using probabilistic validation, the aim is to assure the readers that the obtained results are reasonably accurate. However, it is unclear how we can determine that the CDF frequency is not underestimated or overestimated by several orders of magnitude.

The overall language is ok. Some minor edits can improve the readability of the manuscript. 

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Round 3

Reviewer 2 Report

The authors have addressed the concern of the reviewer properly.