Criticality assessments for long-term post-closure canister corrosion scenarios in a deep geological repository

and investigated in collaboration with the Paul Scherrer Institute (PSI). The reactivity effects of the postulated ELB corrosion scenarios were studied at PSI by means of detailed criticality simulations carried out with the MCNP ® code. This paper presents the conservative ELB corrosion scenarios considered in the analysis and their implementation. The observed relative impact on the system reactivity is then discussed. Additional preliminary considerations concerning the expected variability in porewater composition and canister manufacturing tolerances are also addressed.


Introduction
The criticality safety assessment of the final disposal concept for spent nuclear fuel (SNF) in a deep geological repository is a regulatory requirement in Switzerland (Eidgenössisches Nuklearsicherheitsinspektorat (ENSI), 2020) and in many other countries.One of the main challenges stems from the very long timescales (one million years in Switzerland) that have to be considered in the assessment, which are orders of magnitude larger than in any other area of the fuel cycle.
Over this very long timeframe, interactions between the engineered and/or natural barriers can occur.At a later stage in the assessment period, effects such as alteration of the geometry of the SNF final disposal canister (ELB), corrosion of the ELB, etc. have to be considered.These effects are investigated in the criticality safety analysis to determine whether their occurrence may impact the reactivity of the system and, if yes, to evaluate the potential change in reactivity.
Nagra, the Swiss National Cooperative for the Disposal of Radioactive Waste, is presently elaborating the technical and scientific foundation for a criticality safety assessment for the Swiss spent fuel and high-level waste repository concept.The Paul Scherrer Institute (PSI), the largest research institute for natural and engineering sciences in Switzerland, is the national competence centre for nuclear safety.Over decades, PSI has maintained in-house development, validation and qualification of methodologies for nuclear criticality safety evaluations (CSE) and, based on this, has acquired a set of state-of-the-art tools for best estimate plus uncertainty (BEPU) CSE (Pecchia et al., 2015;Vasiliev et al., 2018;Rochman et al., 2016;Vasiliev et al., 2008;Pecchia et al., 2019;Zhu et al., 2015).
An important part of the RD&D activities pursued by Nagra in collaboration with PSI addresses the impact of the near-field evolution in the post-closure phase.The first preliminary study carried out in this context had two main objectives: (i) to analyse various implementation aspects for different ELB degradation processes, potentially relevant for criticality safety, by defining simplified scenarios and (ii) to determine the potential relative change in the system reactivity by evaluating the effective neutron multiplication factor (k eff ) for each of the previously implemented simplified scenarios.The scenario definition, formulated by Nagra, aimed to capture and illustrate certain aspects of a potential ELB evolution in the repository post-closure phase.It must be noted that the simplified scenarios do not necessarily reflect a realistic or even probable evolution of the ELB over the safety assessment period.Instead, they were deliberately defined for the sake of simplicity and to enable a direct evaluation of the postulated ELB degradation effects on the computed k eff value.The simplified scenarios were jointly translated into models which were implemented and analysed at PSI, as a first proof-of-concept.
The work presented here comprises explicit Monte Carlo simulations addressing specific aspects of spent fuel final disposal.In-depth analyses of the obtained results are beyond the scope of this paper and can be addressed in subsequent studies.

Engineered barrier system
The geological disposal scenario considered in this study is based on the repository concept for disposal of spent nuclear fuel (SNF) developed by Nagra (Patel et al., 2012).This concept envisages horizontal emplacement of disposal canisters in tunnels excavated in the Opalinus Clay (OPA) host rock and backfilling of the voids around and between the canisters with bentonite.The repository will be situated at a depth of 400 m to 900 m.In the long term, the bentonite is expected to gradually resaturate with porewater from the host rock, swell and form a low permeability barrier around the canisters.
The preliminary reference disposal canister design (Patel et al., 2012) consists of a carbon steel cylinder almost 5 m long, with an outer diameter of 105 cm and an initial wall thickness of 14 cm and accommodates four pressurised water reactor (PWR) fuel assemblies (FA) in a carbon steel basket designed accordingly (see Fig. 1).By design, no strong neutron absorbers are included.Furthermore, the final disposal concept foresees the evacuation and filling of the canisters with inert gas.Helium is considered as the base scenario in the following.
The effects of variations in the canister design parameter values on the system reactivity were analysed (Section 4.3).In particular, the wall thickness of the FA boxes and the inner radius of the canister shell as the parameters with the presumably highest impact on the reactivity were of primary interest.

Monte Carlo model
For the criticality calculations of this study, MCNP6.2 has been employed as one of the most validated Monte Carlo (MC) codes (Werner et al., 2017).The fully-three-dimensional MCNP6 model consists of the disposal canister loaded with 4 FAs surrounded by a 35 cm thick layer of water-saturated bentonite clay, although the effect of the bentonite on the criticality is negligible for all the scenarios considered in this study.The remaining volume of the bentonite backfill and the host rock formation are not part of the MCNP model, i.e. it is modelled as a void.

Intact canister
The basis of the Monte Carlo model is an intact canister.No corrosion and consequently no formation of corrosion products have taken place yet.The interior of the canister is modelled to be under a helium atmosphere.Fig. 2 shows a quarter sector in the transversal plane of the canister model in the base scenario.

Canister degradation and water ingress
Following a postulated breach of the disposal canister, the MC model assumes that the FAs are fully immersed in water from the surrounding host rock formation.The water properties such as composition, density and temperature are modelled as optimal for neutron moderation: • The water is modelled as pure H 2 O, ignoring the presence of dissolved minerals.This leads to a better simulated neutron moderation and lower neutron absorption, eventually resulting in higher k eff values • In previous preliminary assessments for canisters loaded with UO 2 FAs, higher water densities have been found to correspond to higher k eff values (Kühl et al., 2012).A conservative pressure and temperature regime in the envisioned deep geological repository was assumed, resulting in a water density of 1.005 g/cm 3 .This density has therefore been set in the MCNP model • The material temperatures of all model components are required information in the neutron transport calculations, i.e. for the selection of nuclear data (ND) libraries employed by the MCNP model.In the present model, these temperatures were all assumed to be equal to 293 K.This rather low temperature leads to better neutron moderation in the MC simulations.A comparison of these conservative assumptions for the properties of water with more realistic conditions in terms of their effects on the system criticality is the subject of Section 4.2.Different possible porewater chemistries were investigated, also taking into account the effect of the dissolved constituents of the porewater on neutron absorption and moderation.Furthermore, a wide range of possible water densities has been considered in the k eff eigenvalue calculations as specific porewater densities are unknown.Further specifications are provided in Section 2.2.4.

Nomenclature
Despite the postulated canister breach, the canister model geometry remains unchanged, i.e. no damage details of any kind are modelled, apart from the transformation of steel to magnetite due to corrosion.The same is true for the structure of the FAs: it is considered as intact, and the model geometry is identical in all simulations of this work.Also, degradation issues and damage of the FAs, which are inevitable over longer post-closure timescales, and corresponding changes in the geometry or the materials are not taken into account by the MC model.

Canister loading
A preliminary bounding fuel case assessment in the context of criticality safety for Swiss PWR SNF loading in disposal canisters showed that loadings exclusively with UO 2 FAs and the highest enrichment of 4.94w/o 235 U are the most critical ones (Vasiliev et al., 2019).The comparison covered loadings with all relevant PWR FA types: UO 2 fuel, MOX as well as Enriched Reprocessed Uranium (ERU), but also mixed loadings with FAs of different type.With UO 2 FAs of 4.94w/o 235 U enrichment being the most critical type of loading, only this type was chosen for a more detailed analysis of the reactivity changes induced by long-term canister corrosion.In this study, the canister is considered to be loaded with 4 PWR FAs having the same nuclear and mechanical design.The FA model has a 15x15 array of fuel pins containing UO 2 enriched to 4.94w/o 235 U and 20 guide tubes; see also Fig. 2.
For simplicity, only canister loadings with fresh FAs, i.e. without any burnup were simulated.It should be noted that the final disposal of fresh nuclear fuel is not intended and is of no practical relevance whatsoever.In this sense, the simulated k eff eigenvalues of these configurations represent purely theoretical upper limits for the system criticality.Furthermore, with its independence from possible operation histories, burnups and decay times for each single FA, the fresh fuel assumption facilitates the comparison of k eff values for different canister degradation scenarios and makes a comparison possible in the first place.a

Material compositions and nuclear data
In the base scenario, upon canister emplacement in the repository the compacted MX-80 bentonite buffer is assumed to be already fully saturated with porewater as in all subsequent canister corrosion scenarios.Density and material composition were adopted from (Kühl et al., 2012).
The material of the disposal canister plays an essential role in the overall performance of the disposal system and has to fulfill the requirements for the canister formulated in (Patel et al., 2012).These requirements are related to the long-term performance, as well as to operational aspects and the final sealing weld.Based on these requirements, a bespoke low-carbon steel alloy has been selected (Patel et al., 2012).The material composition for the present canister model was implemented accordingly.
The main corrosion product of the selected carbon steel under the conditions in a deep geological repository is magnetite (Smart et al., 2017;Reddy et al., 2021).However, the magnetite can be nonstoichiometric, incorporating elements from the porewater, such as carbonates, or corrosion products of the alloying elements.For simplicity, it is assumed that canister corrosion leads to pure magnetite with a density of 5.17 g/cm 3 (Haynes et al., 2012) and a Pilling-Bedworth ratio of 2. Thus, each amount of wall thickness loss is replaced by the double amount of magnetite (i.e. 1 cm of steel leads to the formation of 2 cm of magnetite).
The present study includes an investigation of different realistic porewater types and their effect on the canister reactivity in the cases where the canister integrity was affected and water ingress has occurred.The porewater types considered and specifications regarding their elemental composition are listed in the following: • Opalinus Clay porewater.Information about the elemental composition of the porewater constituents has been taken from Appendix 1 in (Mäder, 2009).• Two different bentonite backfill porewaters.Their elemental compositions, indicative of the expected variability in the water composition, are specified in the second columns of Tables 1 and 2, respectively.• For each of the "free" bentonite porewaters, two canister water cases.
In these cases, the water is assumed to be in chemical equilibrium with magnetite, the main corrosion product of the carbon steel.The two different cases, a "high" and a "low" corrosion case, take into account possible differences in the porewater chemistries, namely the H 2 concentration and the redox potential.The elemental compositions of canister waters are specified in columns 3 and 4 of Tables 1 and 2.
The ND library release ENDF/B-VII.1 (Chadwick et al., 2011) was applied in all MC calculations of the present study.Furthermore, all simulations used ND values at room temperature (293 K) at this stage of the project.

Canister corrosion scenarios
Nagra considers a lifetime requirement of 10,000 years for SNF and HLW canisters (Patel et al., 2012).The simplified scenarios defined for this study are based on the reference canister design (Patel et al., 2012) and the ELB corrosion is the only degradation process taken into account.
For the sake of simplicity, the effects of the corrosion of canister a A CSE methodology taking into account burnup credit (BUC) for the FAs is currently being developed at PSI.It is used for an assessment of Nagra's disposal concept addressing the criticality safety requirements for such an installation (Vasiliev et al., 2019).See Section 5 for more details.
components are modelled and investigated in a highly abstract manner to demonstrate the applicability of the method.Furthermore, even though a more realistic description of the evolution of the canister after breaching is likely to include plastic collapse and significant deformations under lithostatic loads, only the change in geometry and composition due to corrosion is considered here.The corrosion of spent fuel (stainless steel, zircaloy, UO 2 ) leading to geometry or other material changes in the spent fuel itself are also not included in this study.These simplifications were made to allow a direct and straightforward evaluation of the impact of the postulated ELB corrosion on its reactivity.
For the calculation of wall thickness loss due to corrosion, a steel corrosion rate of 2 μm/y is used.For simplification, the magnetite growth was modelled such that, once it reaches another solid, it is spatially redistributed in the model, to avoid any geometric distortions while keeping the total magnetite volume in accordance to the amount of corroded steel at the chosen points in time.
Two postulated canister corrosion cases were defined and assessed: 1. a canister without flaws, and 2. a canister with a postulated unidentified critical flaw leading to early failure.
It is worth noting that the second case represents a what-if scenario and was investigated to demonstrate the evaluation methodology.
Several simplified scenarios were defined for each of the two ELB corrosion cases, as described hereafter.Each scenario comprises specific aspects related to the canister corrosion, representing various stages in a hypothetical ELB evolution with time.However, it must be emphasised that the configurations described by the simplified scenarios do not necessarily illustrate a realistic time evolution of the system.
For illustration purposes, schematic visualisations of the canister corrosion scenarios are provided in addition to their description.These illustrations are by no means drawn to scale but efficiently highlight major modelled developments in the canister evolution.Table 3 contains an illustration of a canister directly after emplacement, i.e. at the beginning of all possible degradation scenarios.At this stage, no corrosion has taken place yet and the canister is intact, i.e. no canister breach and water ingress has occurred.However, porewater and magnetite are already part of the colour legend to make it applicable also to all the following scenario illustrations.Furthermore, it is important to note that the interstitial spaces in the fuel assemblies are always filled with their surrounding medium, i.e. helium when the canister is intact and porewater in the case of water ingress.For the sake of simplicity, the visualisations do not take this into account and the fuel assemblies are always illustrated in the same way (as yellow squares).
In this scenario it is assumed that the fabrication of the disposal canister has been performed according to specifications and the canister lifetime thus reaches the design target of 10,000 years.Upon breaching corrosion" canister water composition as compared to the "free" bentonite porewater composition.  of the canister, the following phases are assessed: Canister with unidentified critical flaws (Case 2).
In this what-if scenario, it is assumed that the fabrication of the disposal canister has not been performed according to specifications, and a canister breaching immediately upon emplacement in the repository is modelled.The following phases are assessed:

Corrosion scenarios
The effects of corrosion on the criticality of a disposal canister are presented in the following.Fig. 3 shows the reactivity change b in each phase of the evolution scenarios as described in Tables 4 and 5 relative to the base case of a freshly emplaced canister in the repository as in Table 3.For both scenarios, the development is shown until the point in time when all the carbon steel of the ELB is corroded.The jump in reactivity after 10,000 years in scenario 1 or immediately after emplacement in scenario 2 is caused, as expected, by the immersion of the fuel assemblies in water and the associated increase in neutron moderation.The following 2,500 years mark a further increase in reactivity of about 3,000 pcm mainly due to the corrosion of the steel basket and formation of magnetite; see transition from 1.1 to 1.2 and from 2.1 to 2.2 in Fig. 3.The replacement of steel and the displacement of water by magnetite alters the neutron absorption and scattering regime inside the canister, further enhancing the reactivity.This development, now driven by the corrosion of the canister wall, continues at a much lower rate in the years directly after the complete corrosion of the steel basket, gaining more momentum again as the magnetite front approaches the fuel assemblies and finally ending with scenarios 1.3 and 2.3, respectively, representing a complete consumption of carbon steel in the ELB by corrosion.The reactivity changes reached in scenarios 1.3 and 2.3 amount to 93,640 and 95,910 pcm, respectively.The statistical uncertainty in the Monte Carlo calculation results, as well as in all other results presented in this section unless stated otherwise, is approximately 25 pcm.An example of other typical calculation uncertainties in connection with CSEs can be found in (Frankl et al., 2021).
Scenarios 1.3 and 2.3 represent cases with the maximum possible amount of magnetite based on the initial amount of carbon steel and the given Pilling-Bedworth ratio.As can be seen by the corresponding illustrations in Tables 4 and 5, the simulation models for these scenarios still contain cavities filled with water.An investigation of the reactivity change in the case where these cavities were also filled with magnetite is of interest, although such scenarios have to be considered as hypothetical since more magnetite is taken into account than could be produced given the initial amount of carbon steel in the ELB and a Pilling-Bedworth ratio of 2. For this reason, two more hypothetical scenarios, 1.H and 2.H, were modelled in which the remaining water volumes in scenarios 1.3 and 2.3, respectively, were replaced by magnetite.The simulations indicated reactivity changes of 97,750 and 97,800 pcm for scenarios 1.H and 2.H compared to the base case (0).
It is important to note for scenarios 1.H and 2.H that, although the space surrounding the FAs is completely filled with magnetite, the free space inside the FAs, i.e. between the fuel rods, the gaps inside the fuel rods as well as the space inside the guide tubes, is still considered to be filled with water.An intrusion of magnetite into those spaces, and hence a displacement of the water therein, would lead to a reduction of the overall reactivity with respect to scenarios 1.H and 2.H.The model for 1. H was modified filling only the spaces between the fuel rods with magnetite -again leaving water inside the fuel rod gaps and guide tubes and the reactivity change with respect to the base case (0) was found to be 47,220 pcm.This finding is consistent with results obtained for the KBS-3 canister design published by the Swedish Nuclear Fuel and Waste Management Company (SKB) (Agrenius and Spahiu, 2016).

Realistic porewater compositions
Monte Carlo simulations of the disposal canister filled with porewater and thus considering more realistic compositions of the water possibly present in the repository revealed that dissolved minerals can have an impact on the criticality.The k eff value has been calculated for all the porewater compositions specified in Section 2.2.2 and for two extreme scenarios of canister corrosion: Scenario 1.1 without relevant magnetite formation as defined in Table 4 and scenario 1.H in which the FAs are completely surrounded by magnetite.The k eff values obtained for pure water at a density of 1.0 g/cm 3 served as reference values.Fig. 4 shows the k eff results obtained for all porewater compositions, putting them directly in relation to the corresponding reference values for pure water.In scenario 1.1., the difference in k eff between Opalinus Clay porewater and pure water is about 1,500 pcm, assuming the same water density, with a similar result for bentonite porewater 1, while for bentonite porewater 2 the reactivity is more than 3,500 pcm lower than for pure water.These differences are in general slightly lower in scenario 1.H due to the lower amount of water present in the model.c Δk eff is about 1,300 pcm for OPA porewater and bentonite porewater 1 and 3,100 pcm for bentonite porewater 2. The assumption of porewater with a realistic composition having the same density as pure water is made here for comparison purposes only.Under the same boundary conditions of temperature and lithostatic pressure, a different porewater density has to be expected.
Simulation results for the canister water cases "low corrosion" and "high corrosion" are not shown in Fig. 4 as the differences in k eff are negligible (<25 pcm) when compared to the corresponding "free" bentonite porewater cases.3-5.The reactivity change between points (0) and ( 1) is caused by the corrosion of the external canister wall, leading to the formation of a 2 cm thick layer of magnetite.At point (1) the canister is modelled as filled with inert gas.
b It has to be noted that the term "reactivity" is not used according to the canonical definition of reactivity in reactor physics theory (reactivity = (k eff -1)/ k eff ).The expression "reactivity change" here and in the following rather denotes a change in the effective neutron multiplication factor (Δk eff ).
c Although the FAs are completely surrounded by magnetite, their interstitial spaces are still filled with water.
M. Frankl et al.

Variations in canister design parameter values
Potential effects of variations in the canister design parameter values on the reactivity were also part of the analyses in this study.These effects are of interest as the canister design is still preliminary, however corresponding investigations also cover possible uncertainties in the manufacturing of the ELB.The wall thickness of the steel basket boxes and the inner radius of the canister wall were analysed as parameters with the supposedly highest impact on the reactivity.Nominal values for the box wall thickness and the inner canister radius in the preliminary design are 10 mm and 385 mm, respectively.The models of scenarios 0 and 2.1 (see Tables 3 and 5) were modified, changing these values independently of each other, i.e. just one parameter was changed at a time, within an interval of ±5 mm.Simulation results are shown in Figs. 5 and 6.
A thicker wall for the steel baskets would marginally increase the reactivity in the base case of an intact canister filled with helium, see Fig. 5.In the case of scenario 2.1, on the other hand, thicker FA boxes lead to a lower amount of water between the FAs and consequently to reduced neutron moderation and reactivity.
Changes in the inner canister wall radius within an interval of ±5 mm, on the other hand, do not play any role in the reactivity of the FAs in scenario 2.1.Instead, the water directly surrounding the FAs is the determining factor for the neutron multiplication inside the canister.Fluctuations in the graph for scenario 2.1 depicted in Fig. 6 are merely of a statistical nature due the MC calculations.In the base case 0, however, a small increase in the reactivity can be observed for smaller radii due to slightly enhanced backscattering from the canister wall.The helium atmosphere does not significantly shield the FAs from the backscattered neutrons so that they can contribute further to the overall reactivity.The canister is still intact after having reached its design target lifetime of 10,000 years.It is assumed to be still filled with helium, while the outer 2 cm of the steel have corroded to form magnetite.

1
(1.1) 10,000 Full water ingress upon breaching.This phase assumes that the canister is immediately filled with porewater upon breaching.No internal corrosion has taken place yet.

(1.2) 12,500
The basket is fully corroded.This phase describes the potential state of the canister at 12,500 years after emplacement (2,500 years after breaching).At this time, the 1 cm thick steel basket holding the fuel assemblies has completely corroded to form magnetite.Furthermore, 0.5 cm of steel from the canister wall thickness has corroded internally and a total of 2.5 cm of the wall thickness have corroded externally.

(1.3) 40,000
The canister wall is fully corroded.This phase describes the potential state of the canister at 40,000 years after emplacement (30,000 years after breaching).At this time, all steel components of the canister (wall and basket) are fully corroded.This means an external corrosion of the canister wall of 8 cm and an internal corrosion of 6 cm.
Neither case, the base case 0 or scenario 2.1, includes any magnetite.Reactivity changes due to canister degradation in the long term were not investigated for canisters with modified design parameter values.The basket is fully corroded.This phase describes the potential state of the canister at 2500 years after emplacement.At this time, the 1 cm thick steel basket holding the fuel assemblies has completely corroded to form magnetite.Furthermore, 0.5 cm of steel from the canister wall thickness has corroded internally and 0.5 cm of the wall thickness has corroded externally.

(2.3) 35,000
The canister wall is fully corroded.This phase describes the potential state of the canister at 35,000 years after emplacement.At this time, all steel components of the canister (wall and basket) are fully corroded.This means an internal and external corrosion of the canister wall of 7 cm respectively.Although a different development of the reactivity has to be expected for modified canisters than that seen for scenarios 1 and 2 in Fig. 3, the hypothetical extreme, a fully corroded canister with FAs entirely surrounded by magnetite would be similar to scenarios 1.H or 2.H as defined in Section 4.1.Thus, also for canisters with modified steel basket wall thickness and inner canister wall radius, a maximum reactivity change of about 97,800 pcm can be assumed due to post-closure canister corrosion.

Conclusions and outlook
The study described in this work was developed as a proof-of-concept and comprised: (i) the preliminary definition of abstract simplified scenarios, illustrating aspects relevant for the corrosion of the final disposal canister in the post-closure phase and (ii) the implementation of the simplified scenarios as computational models and the subsequent k eff determination.
The key parameters of the scenarios investigated in this study were deliberately chosen for the sake of simplicity and to enable direct comparisons.Thus, for instance, the canister was assumed to be filled with four fresh UO 2 fuel assemblies, i.e. with the initial highest enrichment.The fresh fuel assumption is very conservative (bounding) and unrealistic since no fresh fuel would be directly disposed of.Nevertheless, it was deliberately selected not only in view of the conventional assumptions but also since it allows a first direct comparison of k eff values for different canister degradation scenarios.The results of this comparison were presented in terms of the relative reactivity change caused by the canister corrosion.
This work focused on investigating the impact of the potential ELB corrosion on k eff , taking into account aspects relevant specifically for the post-closure phase of a deep geological repository.It must be noted that these differ significantly from the traditional criticality safety applications, especially in terms of the considered timeframes, material compositions and the materials' distribution within the system.Consequently, no direct conclusions regarding the effects of geometry and material changes on the effective neutron multiplication factor should be formulated from these preliminary results.A further study of the neutron physical background with a particular focus on configurations relevant for the post-closure phase, especially in view of the relative reactivity changes observed in this study, would be therefore highly valuable for all potential future investigations.
However, various approaches for further investigating the impact of the ELB degradation on its reactivity can now be formulated, based on this preliminary study.Thus, additional simplified scenarios that reflect other relevant degradation processes and cases such as e.g. the deformation of the canister under lithostatic loads as well as backfilled canisters where the water has access only to a small fraction of the total space in the canister could be defined and investigated.
In addition, expanding the methodology presented here to include the irradiation history of the FAs could be considered.This could be achieved by applying the CSE approach currently under development at PSI in collaboration with Nagra.The criticality evaluations are performed by means of a computational scheme called BUCSS-R (BUrnup Credit System for the Swiss Reactors -Repository case), complemented by a comprehensive quantification of uncertainties from a variety of sources, e.g. from nuclear data (Frankl et al., 2021).

Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Fig. 2 .
Fig. 2. Rendering of a quarter sector of the MCNP model in the transversal plane.

Fig. 3 .
Fig. 3. Reactivity changes for canister evolution scenarios 1 and 2. Major steps in the development are labelled as defined in the first columns of Tables3-5.The reactivity change between points (0) and (1) is caused by the corrosion of the external canister wall, leading to the formation of a 2 cm thick layer of magnetite.At point (1) the canister is modelled as filled with inert gas.

Fig. 4 .
Fig. 4. Change in k eff eigenvalues for scenarios 1.1 (top) and 1.H (bottom) considering different water specifications over a wide range of density.Reference is the respective k eff of a disposal canister filled with pure water at 1.0 g/ cm 3 .The smoothness of the displayed curves is slightly affected by the MC calculation uncertainty of 25 pcm in the supporting data points.

Fig. 5 .
Fig. 5. Reactivity changes for a modified thickness of the steel basket walls.Reference are k eff values for the base case (0) and scenario 2.1, respectively, with a nominal wall thickness of 10 mm.The statistical uncertainty in the data points for the graph of the base case is about 4 pcm, and about 25 pcm in the data points for scenario 2.1.

Fig. 6 .
Fig. 6.Reactivity changes for a modified inner canister wall radius.Reference are k eff values for the base case (0) and scenario 2.1, respectively, with a nominal inner wall radius of 385 mm.The statistical uncertainty in the data points for the graph of the base case is about 4 pcm, and about 25 pcm in the data points for scenario 2.1.

Table 1
Bentonite backfill porewater composition no. 1 and corresponding canister water cases.Differences between canister and porewater compositions in bold.

Table 2
Bentonite backfill porewater composition no. 2 and corresponding canister water cases.Differences between canister and porewater compositions in bold.

Table 3
Base case of intact and uncorroded canister.

Table 4
Canister lifetime reaching design target.

Table 5
Canister breach upon emplacement.Full water ingress upon emplacement.This phase corresponds to the abstract scenario which assumes that the canister is immediately filled with porewater upon emplacement.No internal or external corrosion has taken place yet.