# Validation of the MORET 5 Monte Carlo Transport Code on Reactor Physics Experiments

^{*}

## Abstract

**:**

_{eff}multiplication factor used in criticality studies as well as for other parameters commonly used in reactor physics applications. Special attention will be paid on commission tests performed in the CABRI French Reactor (CABRI is a pool-type research reactor operated by CEA and located in the Cadarache site in southern France used to simulate a sudden and instantaneous increase in power, known as a power transient, typical of a reactivity-initiated accident (RIA).) and the IPEN/MB-01 LCT-077 benchmark.

## 1. Introduction

^{1}Water Loop reactor prior to the CIP-Q program [6]. Around 175 experimental cases corresponding to 20 IRPhEP evaluations are available so far in the MORET validation database. For these benchmarks, reference values of k

_{eff}, reaction rates ratios, spectral indices, reactivity coefficients of control rods, reflector and kinetics parameters are provided, allowing comparison with calculated values from the MORET 5 code. This paper presents calculations performed with the MORET 5.D.1 code using the JEFF-3.1.1, JEFF-3.2 and ENDF/B-VII.1 libraries. For most of the cases, a good agreement is obtained with the benchmark values, taking into account experimental uncertainties, which validates the developments performed in the MORET 5 code and allows confidence in the reported results using various nuclear data libraries. Moreover, sensitivity calculations with the Iteration Fission Probability method (IFP [7]) recently implemented in the MORET 5 code were also performed in order to discriminate elements for which a feedback on nuclear data could be done.

## 2. Selection of Criticality and Reactor Physics Benchmarks

#### 2.1. Selection of Benchmarks

#### 2.2. Methodology for Validation

_{eff}, kinetics parameters, reactivity worth…) of the benchmark was systematically compared to the benchmark experimental parameter. When the $\left|\frac{\mathrm{C}-\mathrm{E}}{\mathrm{E}}\right|$ difference between the calculated value (C) and the benchmark experiment parameter (E) exceeded three times the square root of the sum in quadrature of the experimental uncertainties and the Monte Carlo standard deviation, a bias was identified. Otherwise, a good agreement was considered between the calculation and the benchmark.

_{eff}as well as quantities used in reactor physics such as kinetics parameters, reaction rates and fluxes, but also all kinds of tallies that can be defined by the user.

^{−5}) and 3σ experimental uncertainties are reported in black dashed lines. The nomenclature used to name the experiments is taken from the ICSBEP Handbook.

## 3. Analysis of K_{EFF} Results

_{eff}results are compared with benchmark k

_{eff}in Figure 1 for criticality experiments and in Figure 2 for reactor physics experiments. When looking at Figure 1, one can conclude that, for most cases, there is a good agreement between the calculated k

_{eff}and the benchmark k

_{eff}. However, for four series (HMI-001, HMF-067, HMF-070, PMI-004), discrepancies stand outside the 3σ uncertainty margins for JEFF-3.1.1 and JEFF-3.2 evaluation of nuclear data. The HMF-067 and HMF-070 are ZPR experiments involving highly enriched uranium cylinders with large quantities of tungsten in the fissile and aluminum reflectors. The overestimation is mainly due to the JEFF-3.1.1 and JEFF-3.2 evaluations of tungsten cross sections. The ENDF/B-VII.1 evaluation leads to satisfactory results for all experiments, except for HMF-07-001 and HMF-070-003.

^{239}Pu in the epithermal energy spectrum.

^{56}Fe in the iron reflector and to the evaluation of

^{235}U in epithermal energy range.

_{eff}with respect to the library can be explained by the evaluation of

^{232}Th.

^{233}U, being different between the JEFF-3.1.1 and JEFF-3.2 or ENDF/B-VII.1 evaluation, it is not surprising that we detect significant k

_{eff}discrepancies between libraries for U233-CT-001 and all libraries leading to C-E values in the uncertainty margins.

_{eff}and the benchmark k

_{eff}. Marginal discrepancies between libraries can be pointed out, except for SNEAK and ORSPHERE experimental programs, for which up to 400 pcm discrepancies can be highlighted. For ORSPHERE, the increase of k

_{eff}is mainly due to the new evaluation of

^{235}U in JEFF-3.2 and ENDF/B‑VII.1, which differs from the one in JEFF-3.1.1 evaluation. As for SNEAK, the 300 pcm discrepancy between JEFF-3.2 and JEFF-3.1.1/ENDF/B-VII.1 is due to the evaluations of

^{239}Pu and

^{238}U which strongly differ between JEFF-3.2 and less recent evaluations.

## 4. Sensitivity/Uncertainty Analysis

_{eff}using the TSUNAMI sequence [10] of the SCALE 6.2 package [11]. To compute the so called “prior uncertainty”, the TSUNAMI sequence uses sensitivity coefficients produced by the MORET 5.D.1 continuous energy code based on the IFP methodology (which is also implemented in the MCNP6.2 code [12]) but also covariance matrices. The covariance matrices express the uncertainty of nuclear data (diagonal terms) and the cross correlated uncertainties between isotopes and reactions (anti-diagonal terms). Two covariance matrices available in the SCALE 6.2 package were used in this study: the 44groupcov based on ENDF/B‑VII.0 and the 56groupcov7.1 based on ENDF/B-VII.1. The prior uncertainty for our selection of reactor physics experiments is reported in Table 2. The uncertainty can vary depending of the fissile media and reflectors. For KRITZ and EOLE experimental programs, which involve plutonium, higher prior uncertainty values are obtained with the 44groupcov covariance matrix. It is quite understandable since the

^{239}Pu nubar has been strongly unrealistically reduced between the ENDF/B-VII.0 and ENDF/B‑VII.1 evaluations of nuclear data. For other series, the overall uncertainty is quite comparable. However, when looking at the main contributors to the uncertainty, the hierarchy depends of the covariance library. We chose to make the comparison for the 4–6 major contributors determined with the 44groupcov covariance library. Generally,

^{239}Pu nubar,

^{238}U (n,n′),

^{239}Pu fission,

^{235}U fission and

^{238}U (n,gamma) are in the top list. However, this analysis allows for showing the impact of other nuclides (

^{56}Fe for IPEN and CABRI,

^{232}Th for HCT-018,

^{167}Er for CROCUS) as can be seen in Figure 3.

## 5. Other Parameters

_{eff}are necessary to validate the use of a code for reactor physics applications. For that purpose, benchmarks from the IRPheP database were used for the calculation of dedicated parameters by the MORET 5.D.1 transport code. Moreover, results from the CABRI reactor commissioning tests are reported in this paper.

#### 5.1. Kinetics Parameters

^{+}is the adjoint flux, P

_{eff}and P

_{effd}are, respectively, calculated using formulas (3) and (4).

#### 5.2. Reactivity Parameters

## 6. Conclusions

_{eff}calculations. More than 200 experiments contribute to the validation of reactor physics applications through the calculation of reactivity coefficients, control rods reactivity worth, etc. Recent developments allowed for introducing the calculation of kinetics parameters for IRSN use but also for the production of sensitivity coefficients. This is an important step in the development of the code for it gives us an opportunity to prioritize between reactivity effects, and also to have feedback on nuclear data. Comparisons made between calculated values and benchmark values, and especially on the French CABRI commissioning experiments, showed that the MORET 5.D.1 code is generally in very good agreement with the benchmark within the uncertainty margins. Future works will consist of extending the validation database for reactor physics, selecting other parameters and trying to have feedback on nuclear data using other covariance matrices through the use of in-house sensitivity/uncertainty tool MACSENS [13].

## Author Contributions

## Funding

## Informed Consent Statement

## Acknowledgments

## Conflicts of Interest

## References

- Cochet, B.; Jinaphanh, A.; Heulers, L.; Jacquet, O. Capabilities overview of the MORET 5 Monte Carlo code. Ann. Nucl. Energy
**2015**, 82, 74–84. [Google Scholar] [CrossRef] - Sanchez, R.; Zmijarevic, I.; Coste-Delclaux, M.; Masiello, E.; Santandrea, S.; Martinolli, E.; Villate, L.; Schwartz, N.; Guler, N. APOLLO2 year 2010. Nucl. Eng. Technol.
**2010**, 42, 474–499. [Google Scholar] [CrossRef] [Green Version] - Gomit, J.M.; Duhamel, I.; Richet, Y.; Entringer, A.; Magnaud, C.; Malouch, F.; Carmouze, C. CRISTAL V2: New package for criticality calculations. In Proceedings of the Nuclear Criticality Safety Division Topical Meeting (NCSD 2017), Carlsbad, CA, USA, 11–14 September 2017. [Google Scholar]
- International Criticality Safety Benchmark Evaluation Project. International Handbook of Evaluated Criticality Safety Benchmark Experiments, Organization of Economic Cooperation and Development-Nuclear Energy; NEA/NSC/DOC(95)03; United States Department of Energy: Washington, DC, USA, 2016. [Google Scholar]
- International Reactor Physics Experiment Evaluation Project. International Handbook of Evaluated Reactor Physics Benchmark Experiments, Organization of Economic Cooperation and Development-Nuclear Energy; NEA/NSC/DOC(2006)01; United States Department of Energy: Washington, DC, USA, 2018. [Google Scholar]
- Ritter, G.; Rodiac, F.; Beretz, D.; Jammes, C.; Guéton, O. Neutron Commissioning in the new CABRI Water Loop Facility. In Proceedings of the International Group on Research Reactors 13th Conference, Knoxville, TN, USA, 19–23 September 2010. [Google Scholar]
- Jinaphanh, A.; LeClaire, N.; Cochet, B. Continuous-Energy Sensitivity Coefficients in the MORET Code. Nucl. Sci. Eng.
**2016**, 184, 53–68. [Google Scholar] [CrossRef] - Ichou, R.; Jeannesson, C.; Haeck, W. Feedback on JEFF-3.3 Processing with GAIA 1.1; JEFDOC 1930; OECD: Paris, France, 2018. [Google Scholar]
- MacFarlane, R.; Kahler, A. Methods for Processing ENDF/B-VII with NJOY. Nucl. Data Sheets
**2010**, 111, 2739–2890. [Google Scholar] [CrossRef] - Rearden, B.T.; Reed, D.A.; Lefebvre, R.A.; Mueller, D.; Marshall, W. SCALE/TSUNAMI Sensitivity Data for ICSBEP Evaluations. In Proceedings of the International Conference on Nuclear Criticality 2011, Edinburgh, UK, 19–22 September 2011. [Google Scholar]
- Petrie, L.M.; Jordon, W.C.; Edwards, A.L.; Williams, P.T.; Ryman, J.C.; Hermann, O.W.; Landers, N.F.; Bucholz, J.A.; Knight, J.R.; Parks, C.V.; et al. SCALE: A Modular Code System for Performing Standardized Computer Analyses for Licensing Evaluations; NUREG/CR-0200, Rev. 7 (ORNL/NUREG/CSD-2/R7); Radiation Safety Information Computational Center: Oak Ridge, TN, USA, 2004; Volume 1–3. [Google Scholar]
- Brown, F.; Kiedrowski, B.; Bull, J. MCNP5-1.60 Release Notes; LA UR 10 06235; US Department of Energy: Washington, DC, USA, 2010. [Google Scholar]
- Jinaphanh, A.; Fernex, F.; Leclaire, N. Uncertainty and Bias Quantification with the MACSENS Software; EGUACSA-2017; OECD NEA: Paris, France, 2017. [Google Scholar]

**Figure 2.**Calculated k

_{eff}vs. benchmark k

_{eff}for reactor physics experiments. No uncertainty is available for CABRI and CROCUS experiments.

Series of Experiments | Description | Parameter of Interest |
---|---|---|

IPEN1—LCT-077 | Critical loading configurations of the IPEN/MB-01 reactor | k_{eff,} spectral indices, reactivity coefficients, reaction rates |

SNEAK-LMFR-EXP-001 | SNEAK 7A and 7B Pu-fueled fast critical assemblies in the Karlsruhe fast critical facility | k_{eff,} spectral indices, reactivity coefficients, kinetics parameters |

CROCUS-LWR-RESR-001 | Benchmark on Kinetics Parameters in CROCUS | k_{eff,} reactivity coefficients, kinetics parameters |

CABRI | Studies on the French CABRI reactor to determine the behavior of fuel rods (cladding) during a reactivity insertion accident in PWR | k_{eff,} kinetics parameters, control rods’ reactivity worth, isothermal temperature coefficient |

ORSPHERE-FUND-EXP-001—HMF-100 | Physics measurements for bare, HEU(93.2)-metal sphere | k_{eff}, reactivity effects, kinetics parameters |

EOLE-PWR-EXP-001—MCI-005 | Under-moderated MOX (11 wt.% PuO_{2}) lattice in the EOLE reactor | k_{eff} |

KRITZ-LWR-RESR-001 | KRITZ-2:19 experiment on regular H_{2}O/fuel pin latticeswith mixed oxide fuel at temperatures 21.1 °C and 235.9 °C | k_{eff,} reaction rates distribution |

DIMPLE-LWR-EXP-001—LCT-048 | Light water moderated and reflected low Enriched uranium (3 wt.% ^{235}U) dioxide rod lattices DIMPLE s01 | k_{eff,} reaction rates distribution |

Benchmarks | Total Prior Uncertainty 44groupcov (pcm) | Total Prior Uncertainty 56groupcov7.1 (pcm) |
---|---|---|

HCT-018-001 | 506 | 555 |

KRITZ-LWR-RESR-001 (cold) | 1160 | 720 |

IPEN1—LCT-077-001 | 655 | 671 |

EOLE-PWR-EXP-001 | 976 | 735 |

CABRI program | 518 | 553 |

CROCUS—Erbium | 553 | 597 |

DIMPLE—LCT-048-005 | 578 | 616 |

SNEAK A | 1150 | 872 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Leclaire, N.; Duhamel, I.
Validation of the MORET 5 Monte Carlo Transport Code on Reactor Physics Experiments. *J. Nucl. Eng.* **2021**, *2*, 65-73.
https://doi.org/10.3390/jne2010007

**AMA Style**

Leclaire N, Duhamel I.
Validation of the MORET 5 Monte Carlo Transport Code on Reactor Physics Experiments. *Journal of Nuclear Engineering*. 2021; 2(1):65-73.
https://doi.org/10.3390/jne2010007

**Chicago/Turabian Style**

Leclaire, Nicolas, and Isabelle Duhamel.
2021. "Validation of the MORET 5 Monte Carlo Transport Code on Reactor Physics Experiments" *Journal of Nuclear Engineering* 2, no. 1: 65-73.
https://doi.org/10.3390/jne2010007