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Monte Carlo Variance Reduction for SNF Cask Radiation Shielding Analyses

사용후핵연료 운반/저장용기에 대한 몬테칼로 방사선 차폐 해석의 분산감소기법에 관한 연구

  • 박민호 (Minho Park, 포항공과대학교)

초록/요약

본 연구는 사용후핵연료 수송/저장 용기의 안전성 평가 중 몬테칼로 방사선 차폐계산의 분산을 효과적으로 감소시키기 위한 방법을 도출하기 위하여 수행되었다. Hi-star100 캐스크 시스템의 안전성 분석 보고서를 벤치마킹하고, MCNP5와 MAVRIC 코드의 계산결과를 비교하는 방법을 통하여 ORIGEN-APP, MCNP, MAVRIC 코드에 대한 검증계산이 먼저 수행되었으며, 그 결과 코드운용의 적절성을 검증하였다. MCNP5 코드의 WWG 기법과 SCALE 코드 내 MAVRIC 모듈의 CADIS 기법이 용기의 차폐평가시에 몬테칼로 분산감소기법으로써 이용되었으며, 정확성과 효율성에 대한 비교가 이루어졌다. 이 비교검증을 통하여 CADIS 기법의 정확성 및 적절성이 확인되었다. 계산 효율성 지표로서 Convergence time을 제시하고, 사용함으로써 계산효율의 비교가 효과적임을 보였으며, 실제로 수행한 MCNP5 WWG, MCNP5 Empirical, analog MCNP5, CADIS, FW-CADIS, MONACO analog 계산의 효율이 정량적으로 비교되었다. WWG 기법을 사용한 계산에서 아날로그 몬테칼로 계산에 비하여 5배의 계산효율 상승을 확인할 수 있었다. 또한 WWG의 약점들을 정성적으로 분석하였으며, 개선을 위한 방법들이 제시되었다. CADIS 기법을 이용한 계산에서는 아날로그 몬테칼로에 비하여 효율이 3500배 증가함을 확인할 수 있었다. 여러개의 탤리를 갖는 차폐계산의 효율향상을 위해 FW-CADIS 기법이 적용되었다. 여덟 개의 탤리를 갖는 차폐계산에 대하여 FW-CADIS 기법을 적용함으로써 CADIS 기법을 적용하였을 때 보다 4배 가량 계산효율이 증가함을 확인할 수 있었다. CADIS 기법 및 FW-CADIS를 적용한 계산에서 탤리의 숫자가 증가할 때 계산효율이 감소하는 현상이 발생하였으며, 이론적으로 설명되었다. 본 연구를 통하여 분산감소기법들의 강점 및 약점들이 분석되었으며, 효과적으로 분산을 감소시킨 사용후핵연료 운송/저장 용기에 대한 몬테칼로 차폐계산이 이루어졌다.

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초록/요약

This research is performed to effectively reduce the variance of the Monte Carlo (MC) radiation shielding calculation for the spent nuclear fuel (SNF) cask radiation safety analysis. Validation works for the ORIGEN-ARP, MCNP5, and MAVRIC codes are performed by benchmarking the safety analysis report of the Hi-star100 cask and comparing the shielding calculation results from the MCNP5 and MAVRIC codes. Comparisons in benchmarking calculations have shown reasonable agreements so that the validity of codes are verified. Based on the validation study, comparisons of VRTs, the weight window generator technique (WWG) in the MCNP code and the constant adjoint driven importance sampling (CADIS) technique in the MAVRIC module, are utilized for the MC cask radiation shielding calculation. Through these calculations, dose rates are compared to examine the accuracy and validity of the CADIS technique. A computing efficiency index, convergence time is suggested for the comparison of biased MC and analog MC calculations. The MC calculation efficiencies are qualitatively examined by comparing the convergence time of the analog, empirically biased, and WWG MCNP5 calculations and analog, CADIS, FW-CADIS MAVRIC calculations. Compared to the analog MC calculation, the efficiency has been enhanced by factor of 5 both for the WWG and empirical biasing. Weak points of the WWG technique are qualitatively analyzed and improvement suggestions for the technical drawback have been made for the WWG technique. The biased MC calculation using the CADIS technique has shown an enhanced efficiency by 3500 times than the analog case. The efficiency of using the FW-CADIS technique for a calculation having 8 tally points has been enhanced by factor of 4 compared to the case the CADIS technique is used. Both the CADIS and FW-CADIS techniques has shown to be decelerated for multiple tally problems and the reason for the efficiency degenerations are investigated. Advantages and disadvantages of various VRTs are investigated while efficient cask radiation shielding calculations are performed and validated through this research.

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목차

Contents

1. Introduction ····························································································· 1

2. Cask Radiation Shielding Analysis Methodology and Benchmarking 2
2. 1. Cask Radiation Shielding Overview ············································· 2
2. 1. 1 Source Term Generations ····················································· 5
2. 1. 2. Shielding Calculations ··························································· 7
2. 2. Benchmarking Calculations ························································· 13
2. 2. 1. ORIGEN-ARP Source Term Generation Benchmarking ·· 13
2. 2. 2. MCNP5 Shielding Benchmarking ······································· 20

3. Variance Reduction Techniques for Monte Carlo Calculations ······· 24
3. 1. Monte Carlo Methods and Statistical Uncertainties ················· 24
3. 1. 1. Central Limit Theorem and MC Estimation of the True Mean ···················································································· 25
3. 1. 2. Figure of Merit as an Index for the Calculation Efficiency ······························································································· 28
3. 2. Biased MC and The Variance Minimizing PDF ······················· 29
3. 3. Variance Reduction Techniques ················································· 31
3. 3. 1. Implementation Techniques of Biased MC ······················· 31
3. 3. 2. Derivation of Importance Map ··········································· 36
3. 4. Adjoint Flux as The Importance Function ································· 38
3. 4. 1. Description on the Adjoint Flux ········································· 38
3. 4. 2. Adjoint Property of the Importance Function ···················· 40
3. 4. 3. CADIS Technique and Implementation in MAVRIC ········· 41
3. 4. 4. FW-CADIS Method ······························································ 42

4. Efficient Cask Radiation Shielding Calculations ································ 45
4. 1. Model Description and an Efficiency Index Suggestion ··········· 45
4.1.1. MCNP5 and SCALE/MAVRIC Shielding Model Description 45
4.1.2. An Efficiency Index Suggestion ············································· 50
4.2. Weighting by Stochastic Importance Estimation ························· 51
4.2.1. MCNP5 Stochastic Importance Estimation ···························· 51
4.2.2. Weak Points of Weight Window Generator ·························· 54
4.3. Weighting by Deterministic Adjoint Calculation ··························· 57
4.3.1. SCALE/MAVRIC Benchmarking ·············································· 57
4.3.2. Efficiency Increase Using the CADIS Technique ················· 58
4.3.3. Biasing for Multiple Tally Problems ······································· 63

5. Concluding Remarks ············································································ 72

REFERENCES

Summary in Korean

Acknowledgements

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