# Preliminary Assessment of Criticality Safety Constraints for Swiss Spent Nuclear Fuel Loading in Disposal Canisters

^{1}

^{2}

^{*}

## Abstract

**:**

_{2}spent fuel assemblies. The burnup credit application is examined with respect to both existing concepts: taking into account actinides only and taking into account actinides plus fission products. The criticality safety calculations are integrated with uncertainty quantifications that are as detailed as possible, accounting for the uncertainties in the nuclear data used, fuel assembly and disposal canister design parameters and operating conditions, as well as the radiation-induced changes in the fuel assembly geometry. Furthermore, the most penalising axial and radial burnup profiles and the most reactive fuel loading configuration for the canisters were taken into account accordingly. The results of the study are presented with the help of loading curves showing what minimum average fuel assembly burnup is required for the given initial fuel enrichment of fresh fuel assemblies to ensure that the effective neutron multiplication factor, ${k}_{eff}$, of the canister would comply with the imposed criticality safety criterion.

## 1. Introduction

^{®}MCNP

^{®}or MCNPX Software (The registered trademarks are owned by Triad National Security, LLC, manager and operator of Los Alamos National Laboratory (see https://mcnp.lanl.gov/; assessed on 29 January 2019).) using criticality benchmark experiments [10,11] should be mentioned as examples.

## 2. Definition of the Bounding SNF Case for Loading in Disposal Canisters

_{2}or UO

_{2}/MOX (5% Pu-fiss) fuels when ${k}_{eff}$ was calculated as a function of the water density. It was found in those studies that the maximum water density corresponds to the highest ${k}_{eff}$ values. Thus, in the given work, the loaded canister is also assumed to be flooded with water entering through a postulated breach, as is the case for the Swedish design and related criticality assessment [13]. Additional verification of the optimal moderation conditions will be performed at future stages of the work when the canister design will have been fixed.

#### 2.1. Calculation Tools

#### 2.2. Development of Models

_{in}= 41 cm, R

_{out}= 55 cm, box centre-centre (C-C) separation = 17.9 cm, A ≈ 21.5 cm (side of the FA top head) and B ≈ 23.5 cm (inner side of the FA box). The analysis performed refers entirely to this disposal canister concept.

_{2}4.94 w/o U‑235

_{2}assembly is formed by a 15 × 15 array of fuel pins (with 20 guide tubes) which contain fuel homogeneously enriched at 4.94 weight percent (w/o) of U-235 and operated up to 5 cycles, reaching discharge burnups of 17.61, 33.82, 50.47, 61.92 and 72.75 GWd/tHM.

_{fiss}

^{239}Pu and

^{241}Pu fissile isotopes in the plutonium fuel fraction is approximately 64%. The chosen assembly was operated to burnups of 18.10, 34.78, 44.96 and 51.72 GWd/tHM.

_{2}fuel assembly and was operated to burnups of 17.27, 34.58, 50.10, 56.04 and 61.72 GWd/tHM.

- 4 similar UO
_{2}FAs - mixed burnup UO
_{2}fuel (3 FAs with the same burnup + 1 FA with lower burnup) - 4 similar ERU FAs
- 4 similar MOX FAs
- 1 MOX FA and 3 similar UO
_{2}FAs - 3 similar UO
_{2}FAs and an empty position

_{2}is, however, considered possible for the Nagra conceptual design.

#### 2.3. The Calculation Route

_{f}, T

_{c}, r

_{c}, C

_{B}and P mean respectively the fuel temperature, the coolant temperature, the coolant density, the soluble boron concentration in the coolant and the coolant pressure in the computation node (i,j,k) (the axial slice of a fuel assembly in the SIMULATE-3 full core 3-D model) in the x,y,z system of coordinates at time t.

#### 2.3.1. Retrieval of the Nodal History

#### 2.3.2. Lattice Calculations for Discharge Composition Estimation

#### 2.3.3. Decay Calculations after Discharge

#### 2.3.4. Criticality Calculations for the Disposal Canister

^{m}, Am-243, Mo-95, Tc-99, Ru-101, Rh-103, Ag-109, Cs-133, Nd-143, Nd-145, Sm-147, Sm-149, Sm-150, Sm-151, Sm-152, Eu-151, Eu-153 and Gd-155. Note that compared with the list of isotopes considered in Reference [24], here, the curium isotopes are also taken into account.

_{2}fuels, as this is the most challenging in terms of initial fission source convergence. All the cycles were run with 200,000 neutron histories each. The resulting ${k}_{eff}$ statistical uncertainty (${k}_{eff}$ standard deviation reported by the MCNP code) was approximately ±25 pcm.

#### 2.4. Criticality Criterion Selected for the Bounding Case Assessments

## 3. Results of the Bounding Fuel Case Assessments

#### 3.1. Fresh Fuel

- The canister in dry conditions (actually filled with helium gas)
- The canister flooded with water at 293.16 K
- The canister flooded with the FAs displaced diagonally towards the centre of every fuel box (within the design tolerances)
- The canister flooded with the FAs displaced diagonally towards the outer part of the fuel box

_{2}, ERU and MOX), they are assumed to be fully identical (originating from the same batch, i.e., with the same nuclear and mechanical design). The calculated ${k}_{eff}$ values for each of these cases are presented in Table 1.

#### 3.2. Discharged Fuel

_{∞}), while the changes in the neutron leakage should be the effects of the second order. Nevertheless, for the sake of rigor, all presented evaluations were done for realistic 3-D canister models, and therefore, only the results for the system ${k}_{eff}$ are discussed in this work.) as a consequence of the presence of neutronic poisons (fission products and some non-fissile actinides), as well as due to the depletion of multiplicative materials (major actinides) (Although some amount of fissile major and minor actinides is produced in the reactor operation, the net ${k}_{eff}$ (primary k∞) effect with fuel burnup is negative.). The impact on ${k}_{eff}$ has been evaluated for both the AC and AC+FP cases.

^{241}Pu (T

_{1/2}≈ 14.4 years), as well as the build-up of

^{241}Am (in the case of AC+FP, also the build-up of

^{155}Gd as a result of the beta-decay of

^{155}Eu is important). Later, the increase of ${k}_{eff}$ up to around 30,000 years is explained by the decay of

^{241}Am (T

_{1/2}≈ 432 years) and

^{240}Pu (T

_{1/2}≈ 6,560 years). At a later time, ${k}_{eff}$ starts to decrease again mainly due to

^{239}Pu decay (T

_{1/2}≈ 24,100 years). The given explanations and the half-life (T

_{1/2}) data are borrowed from Reference [28].

#### 3.2.1. UO_{2} Fuel Assemblies

_{2}FAs of the same burnup for both the AC and the AC+FP approaches. It was assessed using quadratic interpolation that the spent fuel with a burnup of less than 24 GWd/tHM (For the bounding fuel case assessments reported in this section, a quadratic interpolation technique was applied to estimate the limiting burnup values based on the data illustrated in Figure 4. A more robust method explained in Section 6 was finally applied for the derivation of the limiting burnup values for the loading curves.) (for the AC+FP case) does not meet even the limit of ${k}_{eff}$ = 0.95 for loading unless a mixed configuration with higher burnup fuel was to be considered. If an AC approach was considered, a burnup higher than approximately 38 GWd/tHM needs to be reached. The ${k}_{eff}$ of the system after 10,000 years could reach a value above that of the initial discharged fuel for the AC approach.

#### 3.2.2. UO_{2} Fuel Assemblies of Mixed Burnups

#### 3.2.3. ERU Fuel Assemblies

^{235}U

_{eq}and operated until 61.72 GWd/tHM. The evolution of ${k}_{eff}$ through time, shown in Figure 4c for both the AC and AC+FP cases, is very similar to that of UO

_{2}fuel.

#### 3.2.4. MOX Fuel Assemblies

_{fiss}and operated until 51.72 GWd/tHM. The evolution of ${k}_{eff}$ through time in Figure 4d has stronger dip and peak values around 100 and 30,000 years (case AC+FP) or 45,000 years (case AC), respectively. Notable is that the ${k}_{eff}$ peak after thousands of years would be higher than any previous value calculated for the AC case, meaning that using the discharge compositions without decay would not be a bounding assumption for the whole disposal period (moreover, taking only actinide changes into account leads to a remarkable case where ${k}_{eff}$ of partly burned fuel can go above the ${k}_{eff}$ of fresh fuel; see the Figure 4d case for 18.1 GWd/tHM (AC)).

_{2}fuel, and this impact is more important at later periods, thus reducing the ${k}_{eff}$ peak below former values in time. Therefore, the use of the discharge compositions would be bounding for the AC+FP approach.

#### 3.2.5. One MOX and Three UO_{2} Fuel Assemblies

_{2}FAs. Figure 4e shows the ${k}_{eff}$ evolution for the canister loaded with low burnup MOX (18 GWd/tHM) together with the three UO

_{2}assemblies at different burnup levels. The main findings from these graphs are as follows:

- For the AC case, ${k}_{eff}$ is increasing from 100,000 years and keeps growing at the end of the period considered of 1 million years. At the cooling time of 1 million years, the ${k}_{eff}$ values are greater than at the zero cooling time.
- For the AC+FP case, the bounding value of ${k}_{eff}$ corresponds to zero cooling time.

_{2}fuel burnt to around 40 GWd/tHM, and the AC+FP approach would require burnup of approximately 20 GWd/tHM.

#### 3.2.6. Empty Position and Three UO_{2} Fuel Assemblies

#### 3.3. Findings from the Bounding Fuel Case Analysis

_{2}fuel could be problematic if featuring low burnups, especially for the AC case where all fuels suffer a rise in ${k}_{eff}$ in later time periods after disposal, which may violate the USL value. ERU fuel has a similar behaviour to the UO

_{2}fuel. The mixing of UO

_{2}and MOX fuel in the canisters could be a good compromise to keep ${k}_{eff}$ below the safety margin while avoiding the thermal limitations more easily violated by MOX fuel filled canisters.

_{2}fuel operated for just one cycle (17.61 GWd/tHM) could be allowed only if mixed with 3 other UO

_{2}assemblies with burnups above 45 GWd/tHM (the second ${k}_{eff}$ peak is decisive for the AC approach). It can also be noted from Figure 5 for the AC case that the minimum burnup required for a homogeneous UO

_{2}fuel loading is not always above the minimum burnup required for the canisters filled with MOX fuel (mixed UO

_{2}/MOX case or full MOX case) since the second ${k}_{eff}$ peak in the MOX cases is very high.

_{2}) requires a minimum burnup of 20 GWd/tHM for the UO

_{2}fuel (fuel operated at least for two operating cycles). In this case, the burnup credit required for canisters loaded with MOX fuel would be dominated by the ${k}_{eff}$ at discharge and it will not be higher than the corresponding UO

_{2}case.

_{2}-MOX models demonstrated that the fuel with low burnup could meet the requirements in some mixed configurations or in the empty position configuration.

_{2}spent FAs (i.e., the type of fuel employed at KKG) will be used for the preliminary loading curve derivation as it is the most problematic configuration among those studied.

## 4. Methodology for Preliminary Loading Curve Derivation

#### 4.1. Chosen Criterion for Criticality Safety Accounting for Burnup Credit

_{1/2}) and the Monte Carlo statistical uncertainty of the employed MCNP code for the criticality calculations. The listed components of the ${\sigma}_{tot}^{}\left(BU\right)$ uncertainty are assumed to be random (not systematic) and uncorrelated. The resulting ${\sigma}_{tot}^{}\left(BU\right)$ is further assumed to be normally distributed. Under these conditions, the term $2{\sigma}_{tot}^{}\left(BU\right)$ in Equation (1) is assumed to represent the 95% confidence interval for ${k}_{eff}$, which is, for instance, in line with the recommendations provided, e.g., in References [30,31].

_{eff}of the system plus the calculation bias and uncertainty in the bias should not exceed 0.95. More recently, an administrative margin of 2000 pcm was suggested for very unlikely accident conditions [32].) (5000 pcm). Thus, for the final loading curve derivations, USL = 0.99339 − 0.05000 = 0.94339 is employed. As for the above listed components of the ${\sigma}_{tot}^{}$ uncertainty, they are presented in more detail in Section 5.4.

#### 4.2. Spatial Burnup Distribution Assumptions

#### 4.2.1. Axial Burnup Distribution

#### 4.2.2. Radial Burnup Distribution

#### 4.3. Impact of Cooling Time

#### 4.4. Canister Modelling

## 5. Quantification of the Bounding Effects and Random Uncertainties Components

#### 5.1. Axial Burnup Effect

- AC+FP credit
- Longer decay periods
- Increasing burnup

#### 5.2. Radial Burnup Effect

- stronger for the AC+FP credit;
- increasing from lower to higher burnups; and
- mainly increasing during the decay period up to 20,000 years and then stabilising.

#### 5.3. Assessment of Uncertainties

#### 5.3.1. Reactor Operating Conditions and Radiation-Induced Changes

- The uncertainties related to operating conditions, including boron concentration, moderator temperature, reactor power, etc. (the power and the moderator density were assumed fully correlated with the fuel and moderator temperatures in the underlying work described in Reference [8])
- The radiation (BU-)induced changes in the geometry (i.e., fuel pin position shift, moderator pin position shift, fuel pellet diameter increase, etc.)

#### 5.3.2. Technological Tolerances Impact

#### 5.3.3. Nuclear Data Uncertainty Impact

_{2}fuel and for the employed ENDF/B-VII.1 CM. Details of the calculations performed are given in Reference [39].

_{2}fuel (see [44] and note that the impact of the fission yields uncertainties was not accounted for in [44], while in the given work the fission yields’ contribution is taken into account [39]). The decreasing uncertainty can potentially be explained by the decrease in the contribution of U-235 cross section uncertainties with burnup and probably with some spectrum-related effects (see also comments provided in Reference [29] for Figure 6 of Reference [29]).

#### 5.3.4. Long‑Term Nuclide Evolution

#### 5.3.5. MCNP Monte Carlo Uncertainty

#### 5.4. Summary of Bounding Burnup Distributions and Random Uncertainties

## 6. Loading Curves with Combined Uncertainties Effects

_{2}, 4.94 w/o fuel, the saving in terms of the minimum required burnup as compared between the cases of AC+FP vs. AC is about 24 GWd/tHM (this has been illustrated in more detail in Reference [29]). This result was obtained by comparing the cases which take into account the bounding burnup profiles and also all uncertainties listed in Table 7. Basically, the same effect (23 GWd/tHM) can be observed for the case when only bounding burnup profiles are taken into account with no uncertainties contribution. A much weaker effect would be obtained (16 GWd/tHM) if the calculations were done with nominal burnup profiles instead of the bounding ones. Finally, a comparison between two values of the administrative margin was also shown in Reference [29]: for the conventional value of 5000 pcm and for a reduced one of 2000 pcm. This illustration allowed the prediction of what saving in the minimum burnup requirement could be achieved, provided the administrative margin could hypothetically be relaxed to 2000 pcm. The extra saving for such a case was estimated as approximately 12 GWd/tHM.

## 7. Outlook and Discussion

#### 7.1. Ways to Improve the Reference BUCSS-R Methodology

- the nuclear data (ND) combined impact (${\sigma}_{ND}^{}$),
- the operating conditions (${\sigma}_{OC}^{}$), and
- the radiation-/burnup-induced geometry changes (${\sigma}_{BU-eff}^{}$).

#### 7.2. Alternative Advanced Way to Derive the Loading Curves under Development and Verification

_{2}M method has been presented in Reference [46], together with examples of its trial application. Thus, the concept of the new and more advanced approach for the loading curve derivation is to rely on the nominal and validated CMSYS CASMO/SIMULATE core-follow models and calculations, with no need for complementary CASMO calculations to derive the SFC. All required information can now be obtained directly from the CASMO/SIMULATE results with the help of the “SNF” code, as illustrated schematically in Figure 12 (see Reference [47] for details on the relative perturbation factors).

## 8. Conclusions

_{2}, MOX and ERU fuels were analysed using the highest enrichments used to date and operated to the highest burnups to properly assess their behaviour. As detailed as possible, intra-assembly SNF compositions have been used in the MCNP criticality calculations based on the results of calculations corresponding to realistic cycle operating conditions extracted from the validated PSI core management models. The case of PWR UO

_{2}has been confirmed to be the most limiting, and consequently, the loading curve analysis was done for this fuel.

_{2}M scheme [46] to substitute the BOHR component of the BUCSS-R scheme. At present, the new approach is basically used for the verification of the base BOHR/BUCSS-R results; however, if confirmed to be more efficient, this new calculation scheme can replace the original one in the future studies at PSI.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 2.**The axial (

**left**) and radial (

**right**) views of the canister MCNP model loaded with fresh UO

_{2}fuel.

**Figure 4.**The evolution of ${k}_{eff}$ for the intact canister loaded with (

**a**) spent UO

_{2}fuel; (

**b**) mixed burnup UO

_{2}fuel (the first burnup value for one position, the second value for the three remaining); (

**c**) ERU fuel; (

**d**) MOX fuel; (

**e**) one low burnup MOX (18 GWd/tHM) and three UO

_{2}fuel at different burnups; and (

**f**) 3 UO

_{2}assemblies and one empty position.

**Figure 5.**The evolution of minimum burnup credit required to comply with a ${k}_{eff}$ value below 0.95 within the geological disposal timeframe: AC case (

**left**) and AC+FP case (

**right**).

**Figure 6.**The illustrative MCNP model (1/4th symmetry sector; schematic and not to scale): the axial (

**left**) and radial (

**right**) view of the refined canister model. The bounding axial burnup profiles (relative units) for the models with 38 and 40 axial fuel nodes and radial burnup profiles (here, the U‑235 atomic density is *10

^{24}at/cm

^{3}) are illustrated.

**Figure 7.**The presently employed nuclear data (ND) stochastic sampling methodology (“XS” is cross sections).

**Figure 9.**The impact of the burnup profiles and the total uncertainty on the canister ${k}_{eff}$ value.

**Figure 10.**An illustration of the determination of the minimum burnup required for fuel to meet the Upper Subcritical Limit (USL) criticality safety criteria for AC (

**left**) and AC+FP (

**right**).

**Figure 11.**The preliminary loading curves with all the conservative effects for discharged spent fuel (valid only for the criticality safety criteria, and subject to discussed important assumptions).

**Figure 12.**An alternative computational scheme based on the “SNF” code integration into the CMSYS system.

**Figure 13.**A comparison of the test loading curves obtained with the reference BUCSS-R and the advanced CS2M schemes (for the same simplified conditions).

Assumed Conditions | 4 UO_{2} | 4 ERU | 4 MOX | 1 MOX + 3 UO_{2} | 1 Empty + 3 UO_{2} |
---|---|---|---|---|---|

Helium filled | 0.21146 | 0.20772 | 0.26259 | 0.20743 | 0.17861 |

Flooded/centred | 1.09513 | 1.08022 | 0.96180 | 1.07035 | 1.02971 |

Flooded/inwards | 1.12903 | 1.11227 | 0.98601 | 1.10079 | 1.04864 |

Flooded/outwards | 1.04355 | 1.02920 | 0.91990 | 1.02301 | 0.99541 |

**Table 2.**The $\Delta {k}_{eff}$ penalty due to the bounding axial burnup profiles for the case of 4.94 w/o, pcm.

Discharge Burnup (GWd/tHM) | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|

Time (a) | 17.61 * | 33.82 | 50.47 | 61.92 | 72.75 | |||||

AC | AC+FP | AC | AC+FP | AC | AC+FP | AC | AC+FP | AC | AC+FP | |

0 | - | - | 983 | 1792 | 2359 | 3390 | 3604 | 4880 | 4737 | 6223 |

5 | - | - | 1273 | 2203 | 2752 | 4042 | 4141 | 5642 | 5322 | 7144 |

20,000 | - | - | 1209 | 2445 | 2886 | 4946 | 4571 | 7113 | 6210 | 9078 |

30,000 | - | - | 1197 | 2445 | 2930 | 4968 | 4675 | 7218 | 6414 | 9236 |

40,000 | - | - | 1225 | 2544 | 2950 | 5064 | 4729 | 7307 | 6538 | 9493 |

50,000 | - | - | 1213 | 2533 | 2993 | 5154 | 4901 | 7381 | 6693 | 9609 |

**Table 3.**The $\Delta {k}_{eff}$ penalty due to the bounding axial burnup profiles for the case of 3.5 w/o, pcm.

Discharge Burnup (GWd/tHM) | ||||||||
---|---|---|---|---|---|---|---|---|

Time (a) | 18.9 | 33.66 | 45.25 | 56.15 | ||||

AC | AC+FP | AC | AC+FP | AC | AC+FP | AC | AC+FP | |

0 | 401 | 1037 | 1703 | 2306 | 3711 | 4705 | 4910 | 6211 |

5 | 592 | 1387 | 1931 | 2860 | 4129 | 5575 | 5484 | 7252 |

20,000 | 587 | 1769 | 2143 | 3603 | 4904 | 7184 | 6808 | 9472 |

30,000 | 577 | 1905 | 2248 | 3698 | 4974 | 7258 | 6982 | 9647 |

40,000 | 674 | 1919 | 2274 | 3760 | 5064 | 7411 | 7271 | 9944 |

50,000 | 634 | 2026 | 2350 | 3826 | 5294 | 7593 | 7401 | 10,144 |

**Table 4.**The $\Delta {k}_{eff}$ penalty due to the bounding radial burnup profiles for the case of 4.94 w/o, pcm.

Discharge Burnup (GWd/tHM) | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|

Time (a) | 17.61 | 33.82 | 50.47 | 61.92 | 72.75 | |||||

AC | AC+FP | AC | AC+FP | AC | AC+FP | AC | AC+FP | AC | AC+FP | |

0 | 1380 | 1729 | 2008 | 2230 | 2100 | 2656 | 2449 | 2829 | 2375 | 2820 |

5 | 1464 | 1947 | 2187 | 2475 | 2364 | 3016 | 2584 | 3268 | 2548 | 3103 |

20,000 | 1246 | 1832 | 2194 | 2743 | 2553 | 3550 | 2917 | 3959 | 2926 | 3858 |

30,000 | 1202 | 1831 | 2185 | 2821 | 2601 | 3652 | 3009 | 3952 | 3040 | 3883 |

40,000 | 1208 | 1860 | 2225 | 2815 | 2630 | 3663 | 3028 | 3976 | 3121 | 3973 |

50,000 | 1260 | 1860 | 2219 | 2888 | 2670 | 3751 | 3073 | 3997 | 3102 | 4045 |

**Table 5.**The $\Delta {k}_{eff}$ penalty due to the bounding radial burnup profiles for the case of 3.5 w/o, pcm.

Discharge Burnup (GWd/tHM) | ||||||||
---|---|---|---|---|---|---|---|---|

Time (a) | 18.9 | 33.66 | 45.25 | 56.15 | ||||

AC | AC+FP | AC | AC+FP | AC | AC+FP | AC | AC+FP | |

0 | 1966 | 2339 | 2278 | 2511 | 2866 | 3210 | 2780 | 3163 |

5 | 2140 | 2575 | 2248 | 2975 | 2928 | 3710 | 2972 | 3617 |

20,000 | 2150 | 2761 | 2633 | 3553 | 3567 | 4429 | 3642 | 4601 |

30,000 | 2107 | 2799 | 2603 | 3657 | 3577 | 4572 | 3701 | 4617 |

40,000 | 2151 | 2770 | 2666 | 3677 | 3586 | 4624 | 3851 | 4750 |

50,000 | 2198 | 2911 | 2754 | 3733 | 3754 | 4638 | 3879 | 4826 |

**Table 6.**The available uncertainty data on the operating conditions and the BU-induced geometry changes, pcm.

Burnup (GWd/tHM) | 0.0–17.6 | 17.6–33.8 | 33.8–50.5 |
---|---|---|---|

Operating conditions | 100 | 400 | 500 |

BU-induced changes | 200 | 200 | 700 |

Burnup (GWd/tHM) | ${\mathit{\sigma}}_{\mathit{N}\mathit{D}}^{}$ | ${\mathit{\sigma}}_{\mathit{O}\mathit{P}}^{}$ | ${\mathit{\sigma}}_{\mathit{B}\mathit{U}-\mathit{e}\mathit{f}\mathit{f}}^{}$ | ${\mathit{\sigma}}_{\mathit{T}\mathit{P}}^{}$ | ${\mathit{\sigma}}_{{\mathit{T}}_{1/2}}$ | ${\mathit{\sigma}}_{\mathit{M}\mathit{C}}^{}$ | $1{\mathit{\sigma}}_{\mathit{t}\mathit{o}\mathit{t}}^{}$ | $2{\mathit{\sigma}}_{\mathit{t}\mathit{o}\mathit{t}}^{}$ |
---|---|---|---|---|---|---|---|---|

0 | 367 | 0 | 0 | 10 | 15 | 25 | 368 | 737 |

17.61 | 560 | 100 | 200 | 10 | 15 | 25 | 604 | 1208 |

33.82 | 700 | 400 | 200 | 10 | 15 | 25 | 831 | 1662 |

50.47 | 834 | 500 | 700 | 10 | 15 | 25 | 1199 | 2397 |

61.92 | 930 | 500 | 700 | 10 | 15 | 25 | 1267 | 2534 |

72.75 | 1026 | 500 | 700 | 10 | 15 | 25 | 1339 | 2679 |

Enrichment w/o | AC | AC+FP |
---|---|---|

1.90 | 0 | 0 |

2.50 | ~6.0 * | 3.7 |

3.20 | 21.5 | 13.8 |

3.50 | 33.9 | 21.4 |

4.10 | ~51.0 * | 31.5 |

4.30 | ~51.7 * | ~36.4 * |

4.94 | ~73.0 * | 49.1 |

© 2019 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**

Vasiliev, A.; Herrero, J.; Pecchia, M.; Rochman, D.; Ferroukhi, H.; Caruso, S.
Preliminary Assessment of Criticality Safety Constraints for Swiss Spent Nuclear Fuel Loading in Disposal Canisters. *Materials* **2019**, *12*, 494.
https://doi.org/10.3390/ma12030494

**AMA Style**

Vasiliev A, Herrero J, Pecchia M, Rochman D, Ferroukhi H, Caruso S.
Preliminary Assessment of Criticality Safety Constraints for Swiss Spent Nuclear Fuel Loading in Disposal Canisters. *Materials*. 2019; 12(3):494.
https://doi.org/10.3390/ma12030494

**Chicago/Turabian Style**

Vasiliev, Alexander, Jose Herrero, Marco Pecchia, Dimitri Rochman, Hakim Ferroukhi, and Stefano Caruso.
2019. "Preliminary Assessment of Criticality Safety Constraints for Swiss Spent Nuclear Fuel Loading in Disposal Canisters" *Materials* 12, no. 3: 494.
https://doi.org/10.3390/ma12030494