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

Transcription

1 materials Article Preliminary Assessment of Criticality Safety Constraints for Swiss Spent Nuclear Fuel Loading in Disposal Canisters Alexer Vasiliev 1, *, Jose Herrero 1, Marco Pecchia 1, Dimitri Rochman 1, Hakim Ferroukhi 1 Stefano Caruso 2 1 Paul Scherrer Institute (PSI), 5232 Villigen PSI, Switzerl; jjh@enusa.es (J.H.); marco.pecchia@psi.ch (M.P.); dimitri-alexre.rochman@psi.ch (D.R.); hakim.ferroukhi@psi.ch (H.F.) 2 National Cooperative for Disposal of Radioactive Waste (NAGRA), 5430 Wettingen, Switzerl; stefano.caruso@nagra.ch * Correspondence: alexer.vasiliev@psi.ch Received: 18 December 2018; Accepted: 28 January 2019; Published: 5 February 2019 Abstract: This paper presents preliminary criticality safety assessments performed by Paul Scherrer Institute (PSI) in cooperation Swiss National Cooperative for Disposal of Radioactive Waste (Nagra) for spent nuclear fuel disposal canisters loaded Swiss Pressurized Water Reactor (PWR) UO 2 spent fuel assemblies. The burnup credit application is examined respect to both existing concepts: taking into account actinides only taking into account actinides plus fission products. The criticality safety calculations are integrated uncertainty quantifications that are as detailed as possible, accounting for uncertainties in nuclear data used, fuel assembly disposal canister design parameters operating conditions, as well as radiation-induced changes in fuel assembly geometry. Furrmore, most penalising axial radial burnup profiles most reactive fuel loading configuration for canisters were taken into account accordingly. The results of study are presented help of loading curves showing what minimum average fuel assembly burnup is required for given initial fuel enrichment of fresh fuel assemblies to ensure that effective neutron multiplication factor, k e f f, of canister would comply imposed criticality safety criterion. Keywords: spent nuclear fuel; geological repository; criticality safety; burnup credit; loading curves 1. Introduction The Swiss National Cooperative for Disposal of Radioactive Waste (Nagra) plans to submit a general licence application for a deep geological repository for disposal of spent fuel high-level waste (HLW repository) for low- intermediate-level waste (L/ILW repository) by One of requirements for design of HLW repository is safety of installations (encapsulation facility repository) from point of view of a possible criticality excursion over a 1,000,000-year lifetime. Were it to occur, criticality would affect properties of engineered barrier system, namely canister, backfill material near-field of host rock. For above reasons, criticality safety issue for disposal of spent fuel canisters was preliminarily investigated by Nagra already in 2002 in context of safety assessment of a repository for spent fuel high-level waste in Opalinus Clay [1]. The results of that study were not considered sufficiently developed for detailed design of canisters for a systematic comprehensive application of burnup credit (BUC) to all Swiss spent nuclear fuel (SNF) assemblies. However, project came to important conclusion that a combination of burnup credit canister Materials 2019, 12, 494; doi: /ma

2 Materials 2019, 12, of 30 design modifications could ensure subcriticality in all cases. Furrmore, application of BUC was identified as necessary only for case of PWR SNF but not for case of Boiling Water Reactor (BWR) [2]. In fact, such findings were basically in line studies performed in USA in relation to Yucca Mountain deep geologic repository project, as can be seen in Reference [3]. Therefore, a detailed criticality safety analysis for BWR fuel was not considered in follow-up PSI/Nagra collaboration; however, internal Nagra activities were carried out to demonstrate compliance subcriticality criteria out application of a burnup-credit approach, namely by considering ideal fresh (un-irradiated) fuel, out any credit from burnable neutron poisons (e.g., gadolinium). Also, case of a degraded canister/fuel configuration was outside scope of project phase described in this paper. This is a certain limitation of preliminary results presented here since effects on criticality evaluations of such medium to very long-term processes as materials corrosion, alteration dissolution of fuel matrix [4], as well as canister deformation or even potential geochemical separation of Plutonium [5] have not been yet considered. Such studies are thus planned for investigations in subsequent phases of PSI/Nagra collaboration. At present stage, a dedicated calculation methodology for criticality safety evaluations (CSE) related to interim dry storage long-term waste disposal is under development at PSI. The CSE+BUC assessments require two coupled calculations: first, fuel depletion decay calculations to obtain isotopic compositions of fuel after discharge cooling period n, criticality calculations using se compositions, for different initial enrichments final burnups in order to create loading curves. All relevant details of calculation methodology applied of studies performed are reported below. The numerous validation studies that supported described methodology development qualification are not presented here in detail as y have been subject of many previous publications. In particular, validation studies for fuel depletion calculations st-alone CASMO code [6,7] CASMO/SIMULATE codes using PSI proprietary post-irradiation examination (PIE) data [8], for reactor core-follow simulations CASMO/SIMULATE codes using in-core reactor measurements [9] for criticality calculations Monte Carlo N-Particle MCNP or MCNPX Software (The registered trademarks are owned by Triad National Security, LLC, manager operator of Los Alamos National Laboratory (see assessed on 29 January 2019).) using criticality benchmark experiments [10,11] should be mentioned as examples. The paper is structured as follows. Section 2 presents approach used for defining bounding SNF case, including description of employed tools models, as well as criticality safety criterion selected for bounding case assessments. Section 3 presents discusses results obtained for bounding SNF case definition. Section 4 describes methodology applied for loading curve derivation. The integration of most penalising burnup profiles rom uncertainty components in CSE+BUC are demonstrated in Section 5. The loading curves for disposal canisters are finally derived in Section 6. These loading curves are preliminary, since re is still room for improvement, in particular, in relation to treatment of uncertainties, as discussed later. Furrmore, effect of degraded canister/fuel configurations on criticality has to be considered in future work for development of final loading curves. However, at same time, se preliminary loading curves can be used to guide future advanced studies to serve for verification of updated results. Sections 7 8 provide a discussion of results conclusions on work performed, respectively. 2. Definition of Bounding SNF Case for Loading in Disposal Canisters For specific case in h in this paper, namely application of burnup credit to long-term disposal of PWR spent nuclear fuel, this work was focused on simulation of Nagra conceptual canister model [12] loaded fuel assemblies (FAs) corresponding to Gösgen nuclear power plant (KKG) fuel designs. To be on a conservative side, optimum moderation conditions must be assumed in criticality safety assessments. The determination of most reactive moderation was done

3 Materials 2019, 12, of 30 in previous preliminary assessments [1] for canisters loaded PWR/BWR UO 2 or UO 2 /MOX Materials 2019, 12, of 30 (5% Pu-fiss) fuels when k e f f was calculated as a function of water density. It was found in those studies values. that Thus, maximum in given water work, density corresponds loaded canister to is highest also assumed k e f f values. to be flooded Thus, in given water work, entering through loaded canister a postulated is also breach, assumed as is to be flooded case for Swedish water entering design through related a postulated criticality breach, assessment as is [13]. Additional case for verification Swedish design of optimal related moderation criticality conditions assessment will [13]. be performed Additional at verification future stages of of optimal work moderation when canister conditions design will will be performed have been fixed. at future stages of work when canister The determination design will have of final been fixed. loading curves for SNF to be loaded in disposal canisters was preceded The determination by a preliminary of final loading study, namely curves for SNF evaluation to be loaded of in disposal bounding canisters fuel was type preceded /or by conservative a preliminary conditions, study, which namelyare discussed evaluation in of given bounding chapter. The fuelcses type were /or realised conservative for PWR conditions, FAs using realistic which are irradiation discussed conditions in given for different chapter. enrichments, The CSEs burnup were realised levels, FA for designs PWR FAs using fuel compositions. realistic irradiation Note conditions that KKG for different nuclear power enrichments, plant (NPP) burnup has levels, used FA designs highest possible fuel compositions. enrichment of Note fuel that as compared KKG nuclear two power or plant Swiss (NPP) PWR has reactors used Beznau highest possible 1 2 enrichment (KKB1 of KKB2). fuel as compared two or Swiss PWR reactors Beznau 1 2 (KKB1 KKB2) Calculation Tools 2.1. Calculation Tools For depletion phase, two-dimensional (2-D) fuel assembly depletion code CASMO5 [14] For depletion phase, two dimensional (2 D) fuel assembly depletion code CASMO5 [14] was employed feedback from three-dimensional (3-D) reactor code SIMULATE-3 [15] using was employed feedback from three dimensional (3 D) reactor code SIMULATE 3 [15] using in-house BOHR tool [8,16], as illustrated later in Section 2.3. in house BOHR tool [8,16], as illustrated later in Section 2.3. Between depletion calculations criticality calculations, a decay phase is introduced Between depletion calculations criticality calculations, a decay phase is introduced for study of long-term evolution of fuel composition. The decay module of code for study of long term evolution of fuel composition. The decay module of code SERPENT2 [17] has been selected as most preferable based on analysis of available SERPENT2 [17] has been selected as most preferable based on analysis of available options options [18]. [18]. For criticality calculation case, MCNP6 code [19] has been employed as most validated For criticality calculation case, MCNP6 code [19] has been employed as most among Monte Carlo codes available at PSI. validated among Monte Carlo codes available at PSI Development of Models 2.2. Development of Models The disposal canister is basically a carbon steel cylinder, is almost 5 metres long is designed The disposal canister is basically a carbon steel cylinder, is almost 5 metres long is designed to fit 4 PWR FAs in 4 separate inserted welded carbon steel boxes (see Figure 1). The preliminary to fit 4 PWR FAs in 4 separate inserted welded carbon steel boxes (see Figure 1). The preliminary dimensions selected for present analysis were R in = 41 cm, R out = 55 cm, box centre-centre (C-C) dimensions selected for present analysis were Rin = 41 cm, Rout = 55 cm, box centre centre (C C) separation = 17.9 cm, A 21.5 cm (side of FA top head) B 23.5 cm (inner side of FA box). separation = 17.9 cm, A 21.5 cm (side of FA top head) B 23.5 cm (inner side of FA The analysis performed refers entirely to this disposal canister concept. box). The analysis performed refers entirely to this disposal canister concept. Figure 1. A sketch of carbon steel disposal canister. Figure 1. A sketch of carbon steel disposal canister. No uncertainties related to underlying nuclear data, depletion calculations corresponding fuel compositions No uncertainties are considered related to at this stage, underlying but ynuclear will be data, included depletion later to develop calculations fuel loading corresponding curves. Three fuel compositions types of fuel assemblies are considered were at considered this stage, forbut y analysis: will be included later to develop fuel loading curves. Three types of fuel assemblies were considered for analysis: 1. UO w/o U 235

4 Materials 2019, 12, of UO w/o U-235 The UO 2 assembly is formed by a array of fuel pins ( 20 guide tubes) which contain fuel homogeneously enriched at 4.94 weight percent (w/o) of U-235 operated up to 5 cycles, reaching discharge burnups of 17.61, 33.82, 50.47, GWd/tHM. 2. Mixed Oxide Fuel (MOX) 4.80 w/o Pu fiss The MOX fuel assembly contains a distribution of three slightly different enrichments inside assembly, central rod empty, i.e., flooded water. The content of 239 Pu 241 Pu fissile isotopes in plutonium fuel fraction is approximately 64%. The chosen assembly was operated to burnups of 18.10, 34.78, GWd/tHM. 3. Enriched Reprocessed Uranium (ERU), w/o U-235 Equivalent The ERU fuel assembly is similar in structure to UO 2 fuel assembly was operated to burnups of 17.27, 34.58, 50.10, GWd/tHM. The following different loading configurations of canister were considered for bounding case analysis: 4 similar UO 2 FAs mixed burnup UO 2 fuel (3 FAs same burnup + 1 FA lower burnup) 4 similar ERU FAs 4 similar MOX FAs 1 MOX FA 3 similar UO 2 FAs 3 similar UO 2 FAs an empty position Configurations more than 1 MOX FA loaded in a canister are not considered feasible, as ir contributions to total heat load is too high according to repository constraints based on Nagra safety assessment. In fact, a heat load of 1.5 KW is considered maximum for disposal canister to ensure functionality of engineered barrier system (canister-bentonite-opalinus Clay). The mixed loading of one MOX 3 UO 2 is, however, considered possible for Nagra conceptual design. The calculational model is bounded by a 35 cm layer of bentonite clay, saturated water. Vacuum boundary conditions are employed at outer surface of bentonite clay. However, impact of bentonite on system k e f f is negligible for a flooded canister. Or conservative assumptions applied to model are low material temperature presence of water out diluted minerals (se assumptions lead to better neutron moderation less neutron absorption, both leading to an increasing k e f f value). The study was performed representative assemblies, selected arbitrarily from each assembly batch considered among assemblies reaching highest burnups at End of Life. The irradiation history was reconstructed using real plant operating data, as was described above, help of BOHR tool. Therefore, best estimate axial burnup profiles were utilised for bounding fuel case analysis. In this sense, bounding assessments performed, described in next section, are based on best estimate modelling of fuel operating history. Figure 2 shows MCNP model describing canister (not in full detail as compared Figure 6 given later; model s outer boundaries are cut as y are not significant for presentation) fuel assemblies discrete axial spent fuel specifications (see furr details in Section 4.2.1).

5 Materials 2019, 12, of 30 Materials 2019, 12, of 30 Figure 2. The axial (left) radial (right) views of canister MCNP model loaded fresh Figure 2. The axial (left) radial (right) views of canister MCNP model loaded fresh UO2 UO fuel. 2 fuel The Calculation Route 2.3. The Calculation Route The computational scheme developed implemented at PSI [16] is based on suite of reference The computational CASMO5/SIMULATE-3 scheme developed core models, continuously implemented developed at PSI [16] is validated based on for all suite Swiss of reference reactors CASMO5/SIMULATE 3 all operated cycles in core models, PSI Core continuously Management developed System (CMSYS) validated platform for [20]. all These Swiss reactors core models are all based operated on cycles real in reactor operating PSI Core histories. Management The core System nodal-wise (CMSYS) rmal-hydraulic platform [20]. These conditions core are models calculated are based on SIMULATE-3 real reactor code operating using histories. plant-provided The core boundary nodal wise conditions rmalhydraulic on inlet conditions coolant temperature are calculated core exit SIMULATE 3 coolant pressure code during using reactor plant provided cycle. boundary conditions A principal on limitation inlet coolant of temperature SIMULATE-3 core code exit is that coolant it is pressure not suited during for providing reactor detailed cycle. spent A fuel principal composition limitation (SFC), of which SIMULATE 3 is required for code is criticality that it is calculations, not suited for because providing such detailed data are spent not needed fuel composition for two-group (SFC), nodal which diffusion is required approximation for criticality employed calculations, in SIMULATE-3 because such for full data core are not neutron needed transport for calculations. two group nodal The detailed diffusion fuel approximation isotopic composition employed is actually in SIMULATE 3 required for at full stage core neutron of preparation transport of calculations. neutron cross The section detailed libraries fuel isotopic composition CASMO5 is code, actually which required involves at a higher stage of order preparation method of of characteristics neutron cross for section neutron libraries transport solution CASMO5 at code, spatial which level involves of FA a higher axial order slice. To method overcome of characteristics limitations for of neutron presently transport used CASMO5/SIMULATE-3 solution at spatial system level of of codes FA axial slice. respect To to overcome BUC application limitations calculation of presently needs for used which CASMO5/SIMULATE 3 this system of codes system was not of designed, codes a respect specific to calculation BUC scheme application was calculation developed called needs BOHR for which (which this sts system for of Bundle codes was Operating not designed, History a specific Reconstruction ). calculation BOHR scheme can provide was developed CASMO5 called BOHR realistic (which operating sts history for Bundle conditions, Operating which History can be retrieved Reconstruction ). from SIMULATE-3 BOHR full can core provide calculations, CASMO5 to rerun CASMO5 realistic depletion operating calculations history conditions, obtain pin-by-pin which can detailed be retrieved burnt fuel from isotopic SIMULATE 3 composition full core for an calculations, axial slice of to rerun fuel CASMO5 assembly. Thus, depletion CASMO5 calculations depletion calculations obtain pin by pin are performed detailed up to burnt discharge fuel isotopic burnup composition for each for particular an axial slice axial of FA slice, fuel assembly. actual Thus, operating CASMO5 history depletion which calculations is known are from performed SIMULATE-3 up to core-follow discharge burnup calculations for (when each particular conservative axial axial FA slice, burnup profiles actual are applied, operating history burnup which does is not known correspond from to SIMULATE 3 realistic discharged core follow burnup calculations but is defined (when based conservative on conservative axial burnup assumptions, profiles as explained are applied, later in burnup Section 4.2.1). does not Thus, correspond power to history realistic in discharged CASMO burnup calculations but is following defined based BOHR on procedures conservative (third assumptions, step in Figure as 3) explained is exactly later same in Section as was 4.2.1). used in Thus, original power SIMULATE history in calculations, CASMO i.e., calculations detailed (e.g., following daily-wise) BOHR power procedures history (third provided step in by Figure plant 3) is operator. exactly same as was used in original SIMULATE In next calculations, step, burnt i.e., detailed compositions (e.g., daily wise) are translated power into history input provided file of SERPENT2 by plant to operator. compute change In in next step, isotopic concentrations burnt compositions during are different translated decay into periods. input In or file of words, SERPENT2 fuel to compute depletion is simulated change in in isotopic given approach concentrations during CASMO different code, while decay discharged periods. spent In or fuel words, decay is done fuel depletion SERPENT is simulated (recall in Section given 2.1). approach The coupling between CASMO code, basic while MCNP discharged canister model spent fuel decay CASMO5/SERPENT is done SERPENT results (recall is performed Section 2.1). The coupling help of between COMPLINK basic tool MCNP [21], canister which model imports detailed CASMO5/SERPENT SNF compositions for results every is assembly performed to define a complete help of canister COMPLINK loading. tool [21], which imports detailed SNF compositions for every assembly to define a complete canister loading. The MCNP model of canister loaded burnt fuel assemblies is n used to compute of system at different time steps during decay, aiming to assess if system remains

6 Materials 2019, 12, of 30 The MCNP model of canister loaded burnt fuel assemblies is n used to compute Materials 2019, 12, of 30 k e f f of system at different time steps during decay, aiming to assess if system remains subcritical in postulated case of a flooded canister. In order to ensure criticality safety, calculated subcritical in postulated case of a flooded canister. In order to ensure criticality safety, k e f f must be assessed Nuclear Criticality Safety (NCS) Criterion. Figure 3 provides an calculated must be assessed Nuclear Criticality Safety (NCS) Criterion. Figure 3 illustration of scheme related processes described in following subsections. Here, provides an illustration of scheme related processes described in following subsections. symbols T f, T c, r c, C B P mean respectively fuel temperature, coolant temperature, coolant Here, symbols Tf, Tc, c, CB P mean respectively fuel temperature, coolant density, soluble boron concentration in coolant coolant pressure in computation temperature, coolant density, soluble boron concentration in coolant coolant node (i,j,k) ( axial slice of a fuel assembly in SIMULATE-3 full core 3-D model) in x,y,z system pressure in computation node (i,j,k) ( axial slice of a fuel assembly in SIMULATE 3 full of coordinates at time t. core 3 D model) in x,y,z system of coordinates at time t. Figure 3. The computational scheme for burnup credit in a disposal application Retrieval of Nodal History Figure 3. The computational scheme for burnup credit in a disposal application. The sequence of calculations begins generation of data library using CASMO5 2D latticeretrieval calculations. of The Nodal nuclear History data library employed in this step was based on ENDF/B-VII.0 library [22]. The spacers are smeared along full axial length of FA, which complies The sequence of calculations begins generation of data library using CASMO5 2D SIMULATE-3 model requirements. Every FA type is computed, initial isotopic composition is lattice calculations. The nuclear data library employed in this step was based on ENDF/B VII.0 taken from final state of previous cycle. library [22]. The spacers are smeared along full axial length of FA, which complies The reactor cycle operation is computed SIMULATE-3. From se results, values for SIMULATE 3 model requirements. Every FA type is computed, initial isotopic composition state parameters are retrieved for every FA axial elevation at different cycle instants. The explicit is taken from final state of previous cycle. spacer model for neutronics solution is activated in SIMULATE-3. The reactor cycle operation is computed SIMULATE 3. From se results, values for The BOHR tool is employed for extraction of required values from SIMULATE-3, which state parameters are retrieved for every FA axial elevation at different cycle instants. The provides values for nodal power, fuel temperature, coolant temperature density explicit spacer model for neutronics solution is activated in SIMULATE 3. boron concentration for every axial radial location in nodal calculation. The presence The BOHR tool is employed for extraction of required values from SIMULATE 3, which of inserted control rods during operation is also taken into account. provides values for nodal power, fuel temperature, coolant temperature density Lattice boron Calculations concentration for for Discharge every axial Composition radial Estimation location in nodal calculation. The presence of inserted control rods during operation is also taken into account. In order to extract make use of composition for every fuel pin at discharge burnups for Lattice everycalculations axial FA slice, for new Discharge 2-D lattice Composition calculations Estimation are performed CASMO5. During every time interval, actual irradiation history (fuel coolant temperatures densities, positions of control In order rods, to extract etc.) is employed make use based of on composition core cycle for every depletion/operation fuel pin at discharge calculations burnups SIMULATE-3. for every axial The FA nuclear slice, data new library 2 D lattice used calculations at this stage are was performed upgraded to ENDF/B-VII.1 CASMO5. During (The every new time release interval, of nuclear actual data irradiation library for history CASMO5 (fuel became coolant available temperatures at time densities, of study positions was of control refore rods, employed etc.) is for employed new calculations; based on however, core cycle original depletion/operation CASMO5/SIMULATE-3 calculations models SIMULATE 3. described in The previous nuclear section data library were based used at on this stage older was ENDF/B-VII.0 upgraded to version. ENDF/B VII.1 Neverless, b [23]. this inconsistency should not be of any practical significance for present analysis.) [23]. b The new release of nuclear data library for CASMO5 became available at time of study was refore employed for new calculations; however, original CASMO5/SIMULATE 3 models described in previous section were based on older ENDF/B VII.0 version. Neverless, this inconsistency should not be of any practical significance for present analysis.

7 Materials 2019, 12, of 30 The spacer mass is, again, smeared along whole axial length, introducing an approximation to realistic conditions. The additional approximations are that irradiation-induced changes of FA structures materials are currently not taken into account. More importantly, it must also be underlined that CASMO5 reconstructed depletion calculations are performed using single assembly reflected models, i.e., out accounting for a realistic leakage term representative of 3-D environment under which assembly was irradiated. The impact of this approximation ways to improve it still need to be analysed. It should be noticed, however, that effects of intra-fuel assembly pin-by-pin horizontal burnup distributions are taken into account later at stage of full-scale MCNP criticality calculations for loaded canister, as presented in Sections It is foreseen that application of newer Studsvik codes SIMULATE5 SNF may allow for improvement of presently developed BUCSS-R methodology (see later Section 7.1) Decay Calculations after Discharge From detailed burnup results, compositions obtained are decayed over a one-million-year period using Transmutation Trajectory Analysis algorithm programmed in burnup module of code SERPENT2 [17]. The decay data from ENDF/B-VII.1 were employed. The concentrations were computed at following times: 0, 1, 2, 5, 10, 20, 40, 60, 80, 100, 120, 150, 200, 300, 500, 1000, 2000, 5000, 8000, 10,000, 15,000, 20,000, 25,000, 30,000, 40,000, 45,000, 50,000, 100,000, 500,000 1,000,000 years. The fuel pin compositions in FA decay individually at every axial elevation Criticality Calculations for Disposal Canister Each particular MCNP model, which includes SFC for every discharge burnup at end of each fuel operation cycle for each decay period, is generated starting from a base input file canister model loaded FAs of equal uniform composition corresponding to fresh fuel (illustrated in Figure 2). The tool COMPLINK is used for this purpose. The SFC is provided at pin-by-pin axial node-wise level, as furr explained in Section Only isotopes usually accounted for in burnup credit calculations are included in fuel composition. Two sets of isotopes are considered following specifications given in Reference [24], customarily termed actinides only (AC) actinides plus fission products (AC+FP) groups. The AC group includes U-233, U-234, U-235, U-236, U-238, Pu-238, Pu-239, Pu-240, Pu-241, Pu-242, Am-241, Cm-242, Cm-243, Cm-244, Cm-245 Cm-246, AC+FP group includes in addition to isotopes in AC group Np-237, Am-242 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 Gd-155. Note that compared list of isotopes considered in Reference [24], here, curium isotopes are also taken into account. The nuclear data from ENDF/B-VII.1 coming MCNP6 software distribution have been used in calculations. The canister fuel geometry are considered to be constant over time, which is a common approach in this type of preliminary criticality safety assessments [13]. The material temperature is K everywhere, corresponding densities dimensions are employed. The MCNP criticality calculations for most of analysed cases were performed 80 inactive cycles 60 active cycles. The number of inactive cycles was chosen following MCNP recommendation based on Shannon entropy estimation of fission distribution [25] for AC+FP case mixed MOX UO 2 fuels, as this is most challenging in terms of initial fission source convergence. All cycles were run 200,000 neutron histories each. The resulting k e f f statistical uncertainty (k e f f stard deviation reported by MCNP code) was approximately ±25 pcm Criticality Criterion Selected for Bounding Case Assessments The criterion for nuclear criticality safety assessment, conventionally termed Upper Subcritical Limit (USL) hereafter, which accounts for burnup credit of spent nuclear fuel, is discussed in

8 Materials 2019, 12, of 30 detail later in Section 4.1. Here, it must only be mentioned that criticality safety criterion may vary depending on methodology definition on national regulatory requirements. However, one particular component is basically common to all countries methodologies, namely so-called administrative margin (also referred to as an arbitrary margin to ensure subcriticality [26]), which will be denoted here as ke AM f f. Normally this margin equals 0.05 in terms of absolute k e f f value [13,27], it is typically dominant compared to all or margins imposed uncertainty components. The last comment is especially true for fresh fuel case, but even in case of spent fuel, depletion-related uncertainties margins, e.g., assessed in Reference [13], are noticeably smaller as compared Thus, USL values obtained different methodologies by different organisations countries for same type of applications may vary but are normally not too far from k e f f = 0.95 value. Therefore, for sake of a better representability an easier comparison similar studies, it makes sense to consider k e f f = 0.95 value as simplified criticality criterion selected for consequent bounding case assessments, while for final loading curve derivations, PSI methodology-specific USL value will be employed. 3. Results of Bounding Fuel Case Assessments 3.1. Fresh Fuel To start, a set of calculations has been performed fresh fuel configurations. The configurations considered are following: The canister in dry conditions (actually filled helium gas) The canister flooded water at K The canister flooded FAs displaced diagonally towards centre of every fuel box (in design tolerances) The canister flooded FAs displaced diagonally towards outer part of fuel box When several assemblies of same type are considered (UO 2, ERU MOX), y are assumed to be fully identical (originating from same batch, i.e., same nuclear mechanical design). The calculated k e f f values for each of se cases are presented in Table 1. Table 1. The k e f f values for canister configurations fresh fuel. Assumed Conditions 4 UO 2 4 ERU 4 MOX 1 MOX + 3 UO 2 1 Empty + 3 UO 2 Helium filled Flooded/centred Flooded/inwards Flooded/outwards The canister in dry conditions is clearly subcritical for any combination of fresh fuel. However, in all or cases (except case of MOX/flooded outwards), calculated k e f f values are above 0.95 k e f f increases notably if a less favourable position of assemblies inside canister is considered (inwards). The importance of distance between assemblies for k e f f is clearly reflected in table. This also means that material of wall boxes has a small impact on decoupling neutron fluxes of each assembly, so loading position of assemblies into canister seems to be important for k e f f values in flooded conditions Discharged Fuel The burnup credit approach can reduce system k e f f (In fact, major change in system k e f f which occurs due to taking into account burned fuel composition is associated change in infinite multiplication factor of fuel lattice (k ), while changes in neutron leakage

9 Materials 2019, 12, of 30 should be effects of second order. Neverless, for sake of rigor, all presented evaluations were done for realistic 3-D canister models, refore, only results for system k e f f are Materials 2019, 12, of 30 discussed in this work.) as a consequence of presence of neutronic poisons (fission products some non-fissile actinides), as well as due to depletion of multiplicative materials (major actinides) The burnup credit approach can reduce system c as a consequence of presence of (Although some amount of fissile major minor actinides is produced in reactor operation, neutronic poisons (fission products some non fissile actinides), as well as due to depletion of net k e f f (primary k ) effect fuel burnup is negative.). The impact on k e f f has been evaluated for multiplicative materials (major actinides) both AC AC+FP cases. d. The impact on has been evaluated for both AC AC+FP cases. For se calculations, same configurations (as fresh fuel case) are used; however, in this For se calculations, same configurations (as fresh fuel case) are used; however, in this case, canister is loaded an SFC different burnups at different cooling times, covering case, canister is loaded an SFC different burnups at different cooling times, one-million-year period. covering one million year period. For burnt fuel configurations, analyses were conducted for each of assembly-averaged For burnt fuel configurations, analyses were conducted for each of assemblyaveraged burnup levels reached after every reactor cycle. The spent fuel compositions keep changing burnup levels reached after every reactor cycle. The spent fuel compositions keep changing after irradiation due to decay processes, refore, fuel neutronic properties ( reactivity ) are after irradiation due to decay processes, refore, fuel neutronic properties ( reactivity ) changing as well. The calculated curves of k e f f evolution are plotted in Figure 4 for a flooded are changing as well. The calculated curves of evolution are plotted in Figure 4 for a flooded canister at different instants during decay of isotopes for both AC AC+FP cases. canister at different instants during decay of isotopes for both AC AC+FP cases. k eff k eff 1.10 Fresh fuel GWd/t (AC) GWd/t (AC) GWd/t (AC) GWd/t (AC) GWd/t (AC) GWd/t (AC+FP) GWd/t (AC+FP) GWd/t (AC+FP) GWd/t (AC+FP) GWd/t (AC+FP) 1-adm.margin= '000 10' '000 1'000'000 Time (a) (a) 1.10 Fresh fuel GWd/t (AC) GWd/t (AC) GWd/t (AC) GWd/t (AC) GWd/t (AC) GWd/t (AC+FP) GWd/t (AC+FP) GWd/t (AC+FP) GWd/t (AC+FP) GWd/t (AC+FP) 1-adm.margin= '000 10' '000 1'000'000 Time (a) (c) k eff k eff 1.10 Fresh fuel GWd/t (AC) GWd/t (AC) GWd/t (AC) GWd/t (AC) GWd/t (AC) GWd/t (AC+FP) GWd/t (AC+FP) GWd/t (AC+FP) GWd/t (AC+FP) GWd/t (AC+FP) 1-adm.margin= '000 10' '000 1'000'000 Time (a) (b) 1.10 Fresh fuel GWd/t (AC) GWd/t (AC) GWd/t (AC) GWd/t (AC) GWd/t (AC+FP) GWd/t (AC+FP) GWd/t (AC+FP) GWd/t (AC+FP) adm.margin= '000 10' '000 1'000'000 Time (a) (d) Figure 4. Cont. c In fact, major change in system which occurs due to taking into account burned fuel composition is associated change in infinite multiplication factor of fuel lattice ( ), while changes in neutron leakage should be effects of second order. Neverless, for sake of rigor, all presented evaluations were done for realistic 3 D canister models, refore, only results for system are discussed in this work. d Although some amount of fissile major minor actinides is produced in reactor operation, net

10 Materials 2019, 12, of 30 Materials 2019, 12, of 30 k eff 1.10 Fresh fuel GWd/t (AC) GWd/t (AC) GWd/t (AC) GWd/t (AC) GWd/t (AC) GWd/t (AC+FP) GWd/t (AC+FP) GWd/t (AC+FP) GWd/t (AC+FP) GWd/t (AC+FP) 1-adm. margin= '000 10' '000 1'000'000 Time (a) (e) k eff 1.10 Fresh fuel GWd/t (AC) GWd/t (AC) GWd/t (AC) GWd/t (AC) GWd/t (AC) GWd/t (AC+FP) GWd/t (AC+FP) GWd/t (AC+FP) GWd/t (AC+FP) GWd/t (AC+FP) 1-adm. margin= '000 10' '000 1'000'000 Time (a) (f) Figure 4. The evolution of of k e f k feff for for intact intact canister canister loaded loaded (a) spent (a) UO spent 2 fuel; UO2 (b) fuel; mixed (b) burnup mixed UO burnup 2 fuel UO2 (fuel first( burnup first burnup value forvalue one position, for one position, second value second forvalue three for remaining); three remaining); (c) ERU fuel; (c) ERU (d) MOX fuel; (d) fuel; MOX (e) one fuel; low (e) burnup one low MOX burnup (18 MOX GWd/tHM) (18 GWd/tHM) three UOthree 2 fuel UO2 at different fuel at burnups; different burnups; (f) 3 UO 2 assemblies (g) 3 UO2 assemblies one empty one position. empty position. The results obtained are summarised belowin Sections It It should be be mentioned that observed behaviour is in line already published results for similar situations analysed discussed in in detail in in Reference [28]. [28]. In In brief, brief, it it can can be be recalled recalled here here that that decrease decrease of kof e f f kin eff in first first approximate approximate years years is mainly is mainly related related to to decay decay of 241 of Pu 241 Pu (T 1/2 (T1/ years), years), as as well well as as build-up of Am Am (in (in case case of of AC+FP, also build-up of of Gd Gdas a result of beta-decay of Eu Euis is important). Later, Later, increase increaseof of kk e eff f f up up to to around 30,000 years is is explained by decay of Am Am (T (T1/2 1/ years) Pu Pu (T (T1/2 1/2 6,560 6,560 years). years). At At a later a later time, time, kk eff e f f starts startsto to decrease decrease again mainly mainly due due to to Pu Pu decay decay (T (T1/2 1/2 24,100 24,100 years). years). The The given given explanations explanations half-life half-life (T1/2) (T 1/2 data ) data are are borrowed borrowed from from Reference Reference [28]. [28] UO Fuel Assemblies UO2 Fuel Assemblies Figure 4a shows k Figure 4a shows k e f f results as a function of decay time obtained for disposal canister eff results as function of decay time obtained for disposal canister loaded UO loaded 2 FAs of same burnup for both AC AC+FP approaches. It was UO2 FAs of same burnup for both AC AC+FP approaches. It was assessed using quadratic interpolation that spent fuel a burnup of less than 24 GWd/tHM assessed using quadratic interpolation that spent fuel burnup of less than 24 GWd/tHM (For bounding fuel case assessments reported in this section, a quadratic interpolation technique e (for AC+FP case) does not meet even limit of k eff = 0.95 for loading unless a mixed was applied to estimate limiting burnup values based on data illustrated in Figure 4. A more configuration higher burnup fuel was to be considered. If an AC approach was considered, a robust method explained in Section 6 was finally applied for derivation of limiting burnup burnup higher than approximately 38 GWd/tHM needs to be reached. The k eff of system after values for loading curves.) (for AC+FP case) does not meet even limit of k e f f = 0.95 for 10,000 years could reach a value above that of initial discharged fuel for AC approach. loading unless a mixed configuration 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 UO2 Fuel Assemblies of Mixed Burnups e f f of system after 10,000 years could reach a value above that of initial discharged fuel for AC approach. Next, a mixed burnup configuration was investigated, as reported in Figure 4b. One FA at low burnup (17.61 GWd/tHM) is considered in mixed loading or three FAs of higher burnups. UO 2 The Fuelresults Assemblies show of that Mixed high Burnups burnup fuels are needed (above 50 GWd/tHM) when taking credit Next, only a for mixed actinides. burnup configuration was investigated, as reported in Figure 4b. One FA at low burnup (17.61 GWd/tHM) is considered in mixed loading or three FAs of higher burnups. The results show that high burnup fuels are needed (above 50 GWd/tHM) when taking credit only for actinides ERU Fuel Assemblies The ERU FA corresponds to fuel enriched up to 4.6 w/o 235 U eq operated until GWd/tHM. The evolution of k e f f through time, shown in Figure 4c for both AC e AC+FP For cases, bounding is very fuel similar case assessments to that of UO reported 2 fuel. in this section, a quadratic interpolation technique was applied to estimate limiting burnup values based on data illustrated in Figure 4. A more robust method explained in Section 6 was finally applied for derivation of limiting burnup values for loading curves.

11 Materials 2019, 12, of MOX Fuel Assemblies The MOX FA corresponds to fuel enriched to 4.8 w/o Pu fiss operated until GWd/tHM. The evolution of k e f f through time in Figure 4d has stronger dip peak values around ,000 years (case AC+FP) or 45,000 years (case AC), respectively. Notable is that k e f f peak after thouss of years would be higher than any previous value calculated for AC case, meaning that using discharge compositions out decay would not be a bounding assumption for whole disposal period (moreover, taking only actinide changes into account leads to a remarkable case where k e f f of partly burned fuel can go above k e f f of fresh fuel; see Figure 4d case for 18.1 GWd/tHM (AC)). On or h, considering additional minor actinides fission products in fuel composition also has a stronger impact on k e f f than for UO 2 fuel, this impact is more important at later periods, thus reducing k e f f peak below former values in time. Therefore, use of discharge compositions would be bounding for AC+FP approach One MOX Three UO 2 Fuel Assemblies In this model, canister is loaded one MOX three UO 2 FAs. Figure 4e shows k e f f evolution for canister loaded low burnup MOX (18 GWd/tHM) toger three UO 2 assemblies at different burnup levels. The main findings from se graphs are as follows: For AC case, k e f f is increasing from 100,000 years keeps growing at end of period considered of 1 million years. At cooling time of 1 million years, k e f f values are greater than at zero cooling time. For AC+FP case, bounding value of k e f f corresponds to zero cooling time. The AC approach would require UO 2 fuel burnt to around 40 GWd/tHM, AC+FP approach would require burnup of approximately 20 GWd/tHM Empty Position Three UO 2 Fuel Assemblies The empty position is assumed to be also flooded water. The results plotted in Figure 4f show that fuel a limiting burnup of 19 GWd/tHM can be considered if using AC approach 10 GWd/tHM for AC+FP approach Findings from Bounding Fuel Case Analysis The bounding fuel case analyses consisted of assessing multiplication factor variation as a function of discharge burnup decay time, ranging between fresh fuel conditions best-estimate burnt fuel configurations. The main findings of analysis are that UO 2 fuel could be problematic if featuring low burnups, especially for AC case where all fuels suffer a rise in k e f f in later time periods after disposal, which may violate USL value. ERU fuel has a similar behaviour to UO 2 fuel. The mixing of UO 2 MOX fuel in canisters could be a good compromise to keep k e f f below safety margin while avoiding rmal limitations more easily violated by MOX fuel filled canisters. Figure 5 summarises minimum burnup credit which would be required for every type of loaded nuclear fuel considered in this study for both AC AC+FP cases.

12 Materials 2019, 12, of 30 Materials 2019, 12, of Minimum burnup (GWd/tHM) UO2 UO2 mixed empty-uo2 ERU MOX UO2-MOX low burnup UO2-MOX high burnup Minimum burnup (GWd/tHM) UO2 UO2 mixed empty-uo2 ERU MOX MOX low burnup-uo2 MOX high burnup-uo '000 10' '000 1'000'000 Time (a) '000 10' '000 1'000'000 Time (a) Figure Figure The The evolution of of minimum minimumburnup burnupcredit creditrequired requiredto tocomply comply a k e f f value value below below in in geological geological disposal disposal timeframe: timeframe: AC AC case case (left) (left) AC+FP AC+FP case case (right). (right). For AC case, loadings of UO For AC case, loadings of 2 fuel operated for just one cycle (17.61 GWd/tHM) could be UO2 fuel operated for just one cycle (17.61 GWd/tHM) could be allowed only if mixed 3 or UO allowed only if mixed 3 or 2 assemblies burnups above 45 GWd/tHM ( second UO2 assemblies burnups above 45 GWd/tHM ( second k e f f peak is decisive for AC approach). It can also be noted from Figure 5 for AC case that peak is decisive for AC approach). It can also be noted from Figure for AC case that minimum burnup required for a homogeneous UO minimum burnup required for homogeneous 2 fuel loading is not always above minimum UO2 fuel loading is not always above minimum burnup required for canisters filled MOX fuel (mixed UO burnup required for canisters filled MOX fuel (mixed UO2/MOX 2 /MOX case or full MOX case) since case or full MOX case) since second k second e f f peak in MOX cases is very high. peak in MOX cases is very high. For AC+FP case, mixed burnup loading (1 MOX + 3 UO For AC+FP case, mixed burnup loading (1 MOX UO2) 2 ) requires a minimum burnup of requires minimum burnup of 20 GWd/tHM for UO 20 GWd/tHM for 2 fuel (fuel operated at least for two operating cycles). In this case, burnup UO2 fuel (fuel operated at least for two operating cycles). In this case, burnup credit required for canisters loaded MOX fuel would be dominated by k credit required for canisters loaded MOX fuel would be dominated by e f f at discharge it at discharge will not be higher than corresponding UO it will not be higher than corresponding 2 case. UO2 case. Finally, it should be borne in mind that all se results imply that fuel matrix is still intact, Finally, it should be borne in mind that all se results imply that fuel matrix is still intact, maintaining actinide fission product mixture even after 100,000 years which is far from maintaining actinide fission product mixture even after 100,000 years which is far from normal FA design target, which ensures FA integrity during irradiation in core but not for normal FA design target, which ensures FA integrity during irradiation in core but not for geological timeframe. geological timeframe. The main driving parameter for criticality in current canister design is distance between The main driving parameter for criticality in current canister design is distance between FAs, due to compact configuration ( also because neutronic poisons are not present in FAs, due to compact configuration ( also because neutronic poisons are not present in canister basket material). Fresh fuel calculations indicate a difference of 2 5% in k canister basket material). Fresh fuel calculations indicate difference of 2 5% in e f f values between values between nominal displaced configurations, which is very important. nominal displaced configurations, which is very important. The results obtained are in line analyses performed for or canister designs [28] The results obtained are in line analyses performed for or canister designs [28] indicate that inclusion of fission products in burnup credit could allow 2-cycle-operated indicate that inclusion of fission products in burnup credit could allow 2 cycle operated FAs to be safely loaded into disposal canisters. However, margin is very close to limit, FAs to be safely loaded into disposal canisters. However, margin is very close to limit, once biases, uncertainties furr bounding assumptions are introduced for loading curves once biases, uncertainties furr bounding assumptions are introduced for loading generation, it will be furr reduced, as will be discussed in following sections. curves generation, it will be furr reduced, as will be discussed in following sections. Fuel low burnup (corresponding to one cycle of operation) cannot be loaded to fill all Fuel low burnup (corresponding to one cycle of operation) cannot be loaded to fill all positions of same canister. A dedicated study mixed UO positions of same canister. dedicated study mixed UO2 MOX 2 -MOX models demonstrated that models demonstrated that fuel low burnup could meet requirements in some mixed configurations or in empty fuel low burnup could meet requirements in some mixed configurations or in empty position configuration. position configuration. Finally, based on reported findings for currently considered canister design, canister Finally, based on reported findings for currently considered canister design, canister model loaded 4 similar PWR UO model loaded 4 similar PWR UO2 spent 2 spent FAs (i.e., type of fuel employed at KKG) will be FAs (i.e., type of fuel employed at KKG) will be used used for preliminary loading curve derivation as it is most problematic configuration among for preliminary loading curve derivation as it is most problematic configuration among those those studied. studied. 4. Methodology for Preliminary Loading Curve Derivation 4. Methodology for Preliminary Loading Curve Derivation As a main outcome of study outlined to this point, application of burnup credit to As a main outcome of study outlined to this point, application of burnup credit to criticality calculations for disposal canisters appears to be necessary for safe disposal of PWR criticality calculations for disposal canisters appears to be necessary for safe disposal of PWR spent FAs operated in Swiss reactors according to current design concept for Nagra spent FAs operated in Swiss reactors according to current design concept for Nagra disposal canister. disposal canister.

13 Materials 2019, 12, of 30 This section presents results of final stage of preliminary loading curve derivation. The application of a best-estimate computational route is now complemented conservative coverage in form of a stochastic analysis of main uncertainty components in combination application of bounding burnup profiles, as illustrated below. Furrmore, USL value considered in this final stage of work is now based on comprehensive validation study for LWR fuel performed at PSI for MCNP code in combination ENDF/B-VII.1 library, which has been selected for routine criticality calculations [10,11]. Note that general practice in burnup credit applications is based on choosing a set of bounding parameters for burnup calculations in terms of power density, fuel coolant temperatures, coolant densities, etc. so that k e f f at discharge for such conservative assumptions will be higher than k e f f obtained any possible real irradiation history. This path, however, was not adopted for BUCSS-R project. In fact, approach in BUCSS-R project is different because real operational data are employed (using SIMULATE-3 for accurate core-follow calculations) for FAs of different enrichments in order to estimate loading curves on basis of best-estimate assessments integrated a conservative but rational treatment of uncertainties. Therefore, at present, only some representative FAs operated at KKG could be considered explicitly analysed. It is foreseen that, in future, studies performed should be repeated for a statistically significant number of FAs, at least for most reactive design/enrichment types, to allow for statistically confident verification/updating of presently evaluated preliminary loading curves Chosen Criterion for Criticality Safety Accounting for Burnup Credit The criticality safety criteria applied for derivation of loading curves can be presented following relations (adapted from Reference [29]): Canister k e f f (BU) + kax e f f (BU) + krad e f f (BU) + 2σ tot(bu) <USL = K LTB e f f k AM Bounding FA pos AOA e f f, (1) where σ tot (BU) = σ 2 ND (BU) + σ2 BU e f f (BU) + σ2 OC (BU) + σ2 TP + σ2 T1/2 + σ2 MC ; (2) σ ND (BU) = σnd SNF CASMO (BU) + σmcnp ND Ke f f (BU); (3) Canister k e f f is neutron multiplication factor corresponding to disposal canister loaded Bounding FA pos SNF placed in most penalising positions considering canister technological tolerances (see Section 3.1 for details); ke Ax f f ke Rad f f are k e f f penalties to cover bounding axial radial burnup profiles, respectively; USL is Upper Subcritical Limit (see Reference [10] for details); σ ND, σ BU e f f, σ OP, σ TP, σ T1/2 σ MC are uncertainties at one stard deviation level respectively for nuclear data (ND), radiation/burnup-induced changes/effects (BU-eff ), operating conditions (OC), technological parameters components (TP), decay constants (T 1/2 ) Monte Carlo statistical uncertainty of employed MCNP code for criticality calculations. The listed components of σ tot (BU) uncertainty are assumed to be rom (not systematic) uncorrelated. The resulting σ tot (BU) is furr assumed to be normally distributed. Under se conditions, term 2σ tot (BU) in Equation (1) is assumed to represent 95% confidence interval for k e f f, which is, for instance, in line recommendations provided, e.g., in References [30,31]. The σnd SNF CASMO nuclear data-related component is responsible for k e f f uncertainty associated SFC (due to propagation of nuclear data uncertainties during depletion calculations), σnd Ke MCNP f f component is k e f f uncertainty due to nuclear data uncertainties mselves (see Section for furr details). The Ke LTB f f term sts for Lower Tolerance Bound for particular Area of Applicability AOA (AOA; here, this is limited to Swiss LWR fuel), its value was reported in Reference [10] as (following Gaussian-based derivation; see Reference [10] for details) for PSI CSE methodology

14 Materials 2019, 12, of 30 using MCNP code in conjunction ENDF/B-VII.1 library. As outlined in Section 2.4, ke AM f f is administrative margin normally imposed to cover unknown uncertainties to ensure subcriticality, which is assumed here to be (The administrative margin to criticality is normally set at 5000 pcm, i.e., k eff of system plus calculation bias uncertainty in bias should not exceed More recently, an administrative margin of 2000 pcm was suggested for very unlikely accident conditions [32].) (5000 pcm). Thus, for final loading curve derivations, USL = = is employed. As for above listed components of σ tot uncertainty, y are presented in more detail in Section Spatial Burnup Distribution Assumptions This section comprises most of modelling simulation assumptions employed. First of all, it addresses derivation of bounding burnup profiles assessment of ir impact on canister k e f f value, to derive ke Ax f f krad e f f penalties for Equation (1). The impact of cooling time is also addressed Axial Burnup Distribution Axial burnup profiles of spent fuel operated at KKG irradiated to different average burnups were retrieved from PSI CMSYS database, which includes all burnup values per fuel assembly at every axial node of SIMULATE-3 calculations, as described in Section 2. The burnup profiles were normalised se average values separated into two families corresponding to models 40 axial nodes in SIMULATE-3 active fuel regions between cm height models 38 axial nodes in SIMULATE-3 an active region of 340 cm height. The reason for having SIMULATE-3 models different numbers of axial layers of nodes fuel is that active fuel length of KKG FAs was changed from earlier cycles to later ones. The older FAs have reflector segments at 2 bottom nodes instead of fuel nodes. It can also be noted that older shorter FAs had lower fuel enrichment compared to later longer FAs. Therefore, it is important to take into account an actual axial burnup profile for every specific enrichment for correct derivation of loading curves. Following stard practice [33], approach was to choose lowest normalised burnup values of all profiles for first last 9 nodes highest normalised burnup values of profiles for remaining central nodes. This resulted in renormalised profiles shown later in Figure 6 ( average node burnup fraction is normalised to unity in both cases of axial nodes). The change in bounding axial profiles average assembly burnup was not considered could be a way of reducing conservatism if needed. Also, a mass calculation all profiles in database could be a different approach to deriving bounding profiles Radial Burnup Distribution For radial burnup profiles in FAs, re were no operational or CMSYS data available at time of study (such data could be obtained by upgrading reference CMSYS models also can be obtained in line discussions provided later in Section 7). Therefore, as an alternative solution, publicly open information on bounding horizontal burnup profile reported in Reference [34] was employed ( this is one of items requiring furr verification). The bounding profile is expressed Equations (4) (5), which were derived from real measurements (see Reference [34] references rein for details) to generate a radial burnup tilt varying for each assembly row: B rel = B H B av B av = (B av 10), (4)

15 Materials 2019, 12, of 30 B(n) = [ B rel ( N B rel n N + 2 )] B av (5) 4 where N is number of rows in square assembly, 15 in our case; B rel is relative difference between horizontally averaged burnup value for half of assembly (B H ) highest burnup horizontally averaged assembly burnup B av ; n is row number in assembly to which computed burnup B(n) corresponds (The second formula includes a correction of a sign from one in original report [34].). It must be underlined that, in fact, CASMO5 does not allow specification of burnup value desired for each row of FA. To overcome this difficulty, a surrogate approach was utilised: CASMO5 input file was modified such that fuel composition is printed at 15 burnup steps which correspond to desired burnups of each of fuel rod rows, as obtained Equations (4) (5). After this, fuel compositions from every burnup step were transferred to SERPENT later to MCNP6 models row by row, providing required intra-assembly fuel burnup horizontal distributions. In this sense, approach differs slightly from one described in Reference [34], where it was assumed that all fuel rods belonging to one same row have one same burnup. In present approach, each fuel rod has its own composition, but horizontally averaged burnup of entire row is preserved as defined by above procedure. However, an examination of typical ratios between burnup value of each pin average assembly burnup showed that, to avoid burning pins in regions of higher power above desired value for row, a factor of 0.93 should be applied to each B(n). This implies that assembly burnup is lowered by 7%, which introduces an additional conservatism in sequence as peripheral pins typically have already lower burnup than average. In addition, lowest burnup regions of assemblies are later faced in canister so as to produce highest k e f f. To illustrate outcome of employed methodology, Figure 6 below shows an example of radial (horizontal) U-235 concentration distribution on a pin-by-pin basis in a FA axial node Impact of Cooling Time The cooling time between cycles was explicitly considered in burnup calculations CASMO5. As it was illustrated in Section 3, in case of actinides only credit, impact of cooling time after discharge on system k e f f is characterised by an initial decrease in k e f f in first approximate 100 years n a steady increase which reaches its maximum at around 30,000 years after discharge. The important point is that k e f f value at that time for intact canister configurations could be higher than initial k e f f value just after discharge, so taking this initial value cannot be considered bounding in all cases that decay calculations up to 100,000 years also need to be considered to generate loading curves. Beyond that time, flooded intact canister approximation would be totally unrealistic for a canister a lifetime of approximately 10,000 years, degraded models should start to be considered in that range. The time positions where decay compositions have been used to compute k e f f values were 0, 5, 20,000, 30,000, 40,000 50,000 years Canister Modelling At stage of loading curve analyses, canister model was updated based on most detailed actual design information received by PSI from Nagra. The modelling included all details provided in Reference [12] as well as detailed structure of FAs, including heads, grids rods from internal documentation available at PSI. The illustration of final MCNP model indications of spatial burnup distributions employed in loading curve derivation analysis is shown in Figure 6.

16 Materials 2019, 12, of 30 Materials 2019, 12, indications 494 of spatial burnup distributions employed in loading curve derivation 16 of 30 analysis is shown in Figure 6. Figure Figure 6. The6. illustrative The illustrative MCNP MCNP model model (1/4th (1/4th symmetry sector; schematic not not to scale): to scale): axial axial (left) (left) radial radial (right) (right) view of view of refined refined canister canister model. model. The bounding The bounding axial burnup axial burnup profiles profiles (relative units) (relative for models units) for 38 models 40 axial 38 fuel nodes 40 axial fuel radial nodes burnup radial profiles burnup (here, profiles U-235 (here, atomic density U 235 is *10 atomic 24 at/cm density 3 ) are is illustrated. *10 24 at/cm 3 ) are illustrated. As outlined As outlined Section in Section 3, 3, fuel fuel assemblies were were conservatively placed towards centre of canister at canister storage at storage positions positions as thisas was this found was found to beto be most most reactive reactive configuration. 5. Quantification 5. Quantification of of Bounding Bounding Effects Effects Rom Uncertainties Components The results for criticality calculations of canister loaded same fuel assembly in The results for criticality calculations of canister loaded same fuel assembly in four four positions were compiled for different enrichments covering values employed from positions were compiled for different enrichments covering values employed from initial to initial to latest fuel cycles of KKG. In following sections, effects resulting from latest fuel cycles of KKG. In following sections, k substituting nominal burnup profiles by penalising e (conservative) f f effects resulting from substituting ones are quantified nominal reported. burnup profiles by penalising (conservative) ones are quantified reported Axial 5.1. Axial Burnup Burnup Effect Effect The results The results of substituting of original burnup profiles by penalising profiles while while keeping keeping average average assembly assembly burnup burnup are are illustrated in in Table 2 for highest considered fuel fuel enrichment of of 4.94 w/o w/o. Table Table 2. The2. k The penalty due to axial of 4.94 w/o, pcm. e f f penalty due to bounding axial burnup profiles for case of 4.94 w/o, pcm. Discharge Discharge Burnup Burnup (GWd/tHM) (GWd/tHM) 17.61* Time (a) * Time (a) AC AC+FP AC AC+FP AC AC+FP AC AC+FP AC AC+FP AC AC+FP AC AC+FP AC AC+FP AC AC+FP AC AC+FP ,792 2,359 3,390 3,604 4,880 4,737 6, , , , , , , , , , , , , , , , , , ,000 30, , , , , , , , , ,000 40, , , , , , , , , ,000 50, , , , , , , , , ,000 * At first - discharge - burnup 1213 of GWd/tHM, 2993 nominal 5154 axial 4901 burnup profile 7381 is actually 6693 more 9609 * At reactive first discharge than burnup penalising of one. GWd/tHM, nominal axial burnup profile is actually more reactive than penalising one. At first glance, it can be observed that impact on k e f f is stronger for following cases: AC+FP credit Longer decay periods Increasing burnup

17 Materials 2019, 12, of 30 Table 3 shows similar information for lower enrichment of 3.5 w/o. In this case, proposed profile is conservative even for lowest burnup, so impact of conservative axial burnup profile is apparently also stronger lower enrichments. As in previous case, added k e f f is notably larger in AC+FP approach. Time (a) Table 3. The k e f f penalty due to bounding axial burnup profiles for case of 3.5 w/o, pcm. Discharge Burnup (GWd/tHM) AC AC+FP AC AC+FP AC AC+FP AC AC+FP , , , , ,144 Finally, regarding effect for lowest enrichments of 1.9 w/o 2.5 w/o, impact of proposed profiles is not conservative k e f f from nominal profile is higher will be maintained for final loading curves. Or profiles could be proposed to create a unique bounding axial burnup profile for se enrichments Radial Burnup Effect In this section, impact is considered of intra-assembly burnup profiles obtained in accordance descriptions given in Section 4.2.2, in such a way that lowest radial burnup regions are facing centre of canister to raise k e f f. Results for cases of 4.94 w/o of 3.5 w/o are given respectively in Tables 4 5. Table 4. The k e f f penalty due to bounding radial burnup profiles for case of 4.94 w/o, pcm. Time (a) Discharge Burnup (GWd/tHM) AC AC+FP AC AC+FP AC AC+FP AC AC+FP AC AC+FP , , , , Table 5. The k e f f penalty due to bounding radial burnup profiles for case of 3.5 w/o, pcm. Time (a) Discharge Burnup (GWd/tHM) AC AC+FP AC AC+FP AC AC+FP AC AC+FP , , , ,

18 Materials 2019, 12, of 30 In general, k e f f impact is stronger for AC+FP credit; increasing from lower to higher burnups; mainly increasing during decay period up to 20,000 years n stabilising. As axial burnup profiles for lowest enrichments of w/o, proposed radial profiles are not conservative in any case so nominal profiles are kept Assessment of Uncertainties In following subsections, quantitative assessments are given for uncertainties components of σ tot (BU) from Equations (1) (3) listed in Section 4.1. It must be outlined that, at present, some of values provided are rar preliminary may require verification depending on availability of related information Reactor Operating Conditions Radiation-Induced Changes The impact of reactor operational parameter variations was estimated in a dedicated study help of CASMO-5 code ( results have been partly presented in Reference [8]). As mentioned, proprietary information on PIE data for various burned fuel rods from Swiss reactors is available at PSI toger detailed information on fuel operation fuel design parameters. This allows for validation of fuel burnup calculations toger an assessment of calculational vs. experimental uncertainty components of obtained C/E results. Such studies were conducted for a KKG fuel rod sample (from a fuel assembly irradiated during 3 cycles up to sample final burnup above 50 GWd/tHM), two types of uncertainties were assessed in this analysis: The uncertainties related to operating conditions, including boron concentration, moderator temperature, reactor power, etc. ( power moderator density were assumed fully correlated fuel moderator temperatures in underlying work described in Reference [8]) The radiation (BU-)induced changes in geometry (i.e., fuel pin position shift, moderator pin position shift, fuel pellet diameter increase, etc.) As can be seen, se uncertainties represent terms σ OC σ BU e f f of Equation (2). The final assessments accepted for given study are shown below in Table 6 (only first figures are deemed significant). It shall be noticed that at present stage, uncertainty components of Equation (2) are assumed to be uncorrelated. In reality, re might be some correlations between m, although y are not expected to be strong a priori, to best knowledge of authors. Stronger correlations would occur if one imposed into analysis certain reactor operational constraints, e.g., k e f f = 1, at reactor core follow simulations. However, in such cases posterior uncertainties of affected parameters are normally significantly reduced. Some representative illustrations on example of nuclear data evaluations can be found in References [35 37]. Furrmore, se types of uncertainties are most difficult for quantification are already quite conservative by mselves, refore, questions on uncertainties of se uncertainties or ir correlations go far beyond current work on preliminary loading curves development. Table 6. The available uncertainty data on operating conditions BU-induced geometry changes, pcm. Burnup (GWd/tHM) Operating conditions BU-induced changes

19 Materials 2019, 12, of Technological Tolerances Impact The impact of PWR fuel technological manufacturing parameter tolerances on criticality calculations was analysed in Reference [38] anor PSI in-house tool MTUQ (Manufacturing Technological Uncertainty Quantification). Taking into account only fuel assembly-related uncertainties from list of parameters used, total σ TP uncertainty component is assessed as only 10 pcm. In particular, uncertainty components from all parameters considered in Figure 9 of Reference [38], except parameters 11 (Absorber Box Inner boundary) 13 (FA rack Centre-to-centre distance), should be summed as rom uncorrelated uncertainties, thus leading to a total uncertainty value limited by 10 pcm Nuclear Data Uncertainty Impact The uncertainties in nuclear data employed in calculations contribute to uncertainty in computed canister k e f f values. Their impact was considered in CASMO5 burnup calculations using SHARK-X methodology (see References [39,40] references rein), providing σnd SNF CASMO (BU) estimation (uncertainties of cross sections fission yields were taken into account), in MCNP6 criticality calculations using Nuclear data Uncertainty Stochastic Sampling (NUSS) methodology to assess σnd Ke MCNP f f (BU) component (see References [39] [29]; uncertainties of rmal scattering (S(α,β)) data were ignored (see details discussions in Reference [41]). The approach to estimate σnd SNF CASMO (BU) was explained also in Reference [29]: The nuclear data uncertainty propagation in CASMO depletion calculations, resulting in spread of SNF composition, was done using SHARK-X tool. The obtained set of different SNF compositions was furr translated to SERPENT decay module for decay simulation finally provided to MCNP6 models of disposal canister to compute spread of k e f f values due to spread of SNF compositions, using nominal ENDF/B-VII.1 ND files. Interested readers can find alternative ways of assessing uncertainties associated depletion calculations, for example, in References [42,43]. For an additional illustration, Figure 7 shows scheme of ND-related uncertainties (given as covariance matrices (CM)) propagation in compliance flowchart in Figure 3. The Monte Carlo sampling method employed to obtain estimated uncertainty in k e f f requires a large number of calculations has thus been realised only for 4.94 w/o fuel enrichment case so far. Figure 8 shows estimated σnd SNF CASMO (BU) σmcnp ND Ke f f values for fuel just after discharge after 50,000 years of decay; uncertainties from all AC FP are considered. The direct effect from nuclear data in MCNP6 calculation, σnd Ke MCNP f f, is similar in both periods decreases slightly burnup level attained. The indirect effect of nuclear data contained in isotopic uncertainties, σnd SNF CASMO (BU), increases decay time grows burnup. These observations are valid for UO 2 fuel for employed ENDF/B-VII.1 CM. Details of calculations performed are given in Reference [39].

20 Materials 2019, 12, of 30 Materials 2019, 12, of 30 Materials 2019, 12, of 30 Figure 7. The presently employed nuclear data (ND) stochastic sampling methodology ( XS is cross sections). Figure 7. The presently employed nuclear data (ND) stochastic sampling methodology ( XS is Figure 7. The presently employed nuclear data (ND) stochastic sampling methodology ( XS is cross cross sections). sections). ND-related uncertainty of k eff, pcm ND-related uncertainty of k eff, pcm σ_(nd-snf)^casmo; 0a decay σ_(nd-keff)^mcnp; 0a decay σ_(nd-snf)^casmo; 50'000a decay σ_(nd-keff)^mcnp; 50'000a decay 800 σ_(nd-snf)^casmo; 0a decay σ_(nd-snf)^casmo; 50'000a decay 700 σ_(nd-keff)^mcnp; 0a decay σ_(nd-keff)^mcnp; 50'000a decay Burnup, GWd/tHM 0 Figure 8. 0 The estimated nuclear 30 data-related uncertainties 60 70of k e f f. Figure 8. The estimated nuclear Burnup, data related GWd/tHM uncertainties of. The decrease of σnd Ke MCNP f f uncertainty component burnup is consistent results presented The decrease earlier inof Reference [44], where uncertainty even component net effect (uncertainty burnup is propagations consistent through results both Figure 8. The estimated nuclear data related uncertainties of. presented depletion earlier criticality in Reference calculations) [44], where ofeven ND net uncertainties effect (uncertainty originating propagations from ENDF/B-VII.1 through both library The depletion was decrease also found of criticality to decrease calculations) uncertainty burnup of component for ND UO uncertainties 2 fuel (see burnup [44] originating is consistent notefrom that ENDF/B VII.1 impact results of fission presented library yields was earlier also uncertainties in found Reference to decrease was not [44], where accounted burnup for even for in UO2 [44], net effect fuel while (uncertainty (see in[44] given propagations note work that fission through impact yields both of contribution fission depletion yields is uncertainties taken into account criticality calculations) was not [39]). accounted The decreasing of ND for uncertainties [44], uncertainty while originating in can potentially given from work be explained ENDF/B VII.1 fission by yields decrease library contribution in was also is contribution found taken to into decrease account of U-235 [39]). cross burnup The section decreasing uncertainties for UO2 fuel uncertainty burnup (see [44] can note potentially probably that be impact explained some of by spectrum-related fission decrease yields uncertainties in effects contribution (see also was not of comments accounted U 235 cross provided for section in in [44], uncertainties Reference [29] while in for Figure given burnup 6 work of Reference fission probably [29]). yields contribution some It should spectrum related be noted that is taken into account effects uncertainty (see [39]). also The comments components decreasing provided σ uncertainty ND SNF CASMO in can Reference σmcnp potentially ND Ke f [29] f must be for be explained Figure correlated by 6 of since Reference underlying decrease [29]). nuclear data are same for independent estimations performed for in contribution of U 235 cross section uncertainties burnup probably both components. some spectrum related It should be noted However, effects that (see uncertainty correlation also comments components level has not been provided in Reference assessed. In [29] must ideal for Figure be correlated case, all 6 of calculations Reference since [29]). underlying should be nuclear done data in a single are set same using for independent same original estimations perturbation performed factors for both nuclear components. data in It should be However, both depletion noted that correlation uncertainty level criticality components has not calculations; been assessed. however, In this ideal will must case, require be all correlated calculations significant additional since should be underlying done computational in a nuclear single burdens. set data using are Therefore, same same original it will for perturbation be conservative independent factors estimations for assume performed nuclear a full data correlation for in both both between components. depletion both components However, criticality thus correlation calculations; to estimate level has not however, total ND-related been assessed. this will In require k e f ideal f component case, significant according all calculations additional to Equation should computational (3). More be done in burdens. advanced a single set Therefore, assessments using it same will are be planned original conservative for perturbation to near assume future factors a full for correlation latest release nuclear data between of in both both components depletion thus criticality to estimate calculations; total ND related however, this component will require according significant to Equation additional (3). computational burdens. Therefore, it will be conservative to assume a full correlation between both components thus to estimate total ND related component according to Equation (3).

21 Materials 2019, 12, of 30 Materials 2019, 12, of 30 More advanced assessments are planned for near future latest release of ENDF/B library (ENDF/B VIII), including analysis of ND related correlations, as proposed in ENDF/B References library [10,29]. (ENDF/B-VIII), including analysis of ND-related correlations, as proposed in References Next, [10,29]. to be on conservative side, total ND related uncertainty will be composed of Next, component to be on corresponding conservative side, to 50,000 total years ND-related of cooling uncertainty will be composed corresponding of to σzero ND SNF CASMO cooling component time (Figure corresponding 8). to 50,000 years of cooling σmcnp ND Ke f f corresponding to zero cooling time (Figure 8) Long Term Nuclide Evolution Long-Term Nuclide Evolution The performance of decay module of SERPENT2 code employed nuclear data library Thewas performance investigated of decay benchmarked module of in Reference SERPENT2 [18]. code Later, impact employed of nuclear data library uncertainty was investigated on decay calculations benchmarked realised in Reference SERPENT2 [18]. Later, code impact was studied of by nuclear perturbing data uncertainty decay data on decaya modified calculations version realised of ENDF2C SERPENT2 tool [39,45]. code was The studied main outcome by perturbing shows an decay impact data of a modified 15 pcm version of for ENDF2C studied tool load. [39,45]. The main outcome shows an impact / of σ T1/2 15 pcm on k e f f for studied load MCNP Monte Carlo Uncertainty MCNP Monte Carlo Uncertainty The Monte Carlo statistical uncertainty of calculations for loading curve analysis was The approximately Monte Carlo± statistical 25 pcm, which uncertainty is sufficiently σ MC of low. calculations for loading curve analysis was approximately ± 25 pcm, which is sufficiently low Summary of Bounding Burnup Distributions Rom Uncertainties 5.4. Summary of Bounding Burnup Distributions Rom Uncertainties The analysed rom uncertainty components are summarised in Table 7 (adapted from The analysed rom uncertainty components are summarised in Table 7 (adapted from Reference [29]) toger total sum of uncertainties,, which will be used in Equation Reference [29]) toger total sum of uncertainties, σ tot, which will be used in Equation (1). (1). It is important to note that total uncertainty is burnup dependent due to burnup It is important to note that total uncertainty is burnup-dependent due to burnup dependency dependency of components,. of components σ ND, σ OP σ BU e f f. Table 7. A summary of all rom uncertainty components, pcm. Table 7. A summary of all rom uncertainty components, pcm. Burnup (GWd/tHM) / 1 2 Burnup (GWd/tHM) σ ND σ OP σ BU eff σ TP σ T1/2 σ MC 1σ tot 2σ tot To better illustrate impact of considered burnup profile penalties uncertainty To better illustrate impact of considered burnup profile penalties uncertainty components, Figure 9 shows results obtained for case of AC+FP based on data reported in components, Figure 9 shows results obtained for case of AC+FP based on data reported in Table 6, Figure 8 Table 7 ( red line is direct sum of axial (Table 2) radial (Table 4) Table 6, Figure 8 Table 7 ( red line is direct sum of axial (Table 2) radial (Table 4) effects; adapted from Reference [29]). effects; adapted from Reference [29]). UO w/o, AC+FP Δk eff, [pcm] 12'000 10'000 8'000 6'000 4'000 2'000 0 impact of BU profiles impact of BU profiles + total uncertainty GWd/tHM Figure 9. The impact of burnup profiles total uncertainty on canister k e f f value. Figure 9. The impact of burnup profiles total uncertainty on canister value.

22 Materials 2019, 12, of Loading Curves Combined Uncertainties Effects The final target of this work was to assess a minimum average burnup for individual fuel assemblies required for a full loading of disposal canister out exceeding defined upper subcritical limit. This goal is accomplished by development of specific loading curves for discharged spent fuels, where initial enrichment final burnup of a fuel bundle will function as acceptance criteria for loading of disposal canister. The development of curve is done as follows: left part of Equation (1) is represented by a curve depending on burnup, while right part of Equation (1) is a constant corresponding to given USL value. If burnup-dependent curve of Equation (1) burnup-independent USL line intersect, burnup at point of intersection becomes point on loading curve corresponding to given fuel enrichment. If burnup-dependent curve of Equation (1) is always below USL value, n for given enrichment, minimum burnup equals zero on loading curve. As presented in Section 4.1, for PSI CSE methodology using MCNP code in conjunction ENDF/B-VII.1 assuming administrative margin equals 5000 pcm, USL value is defined according to Equation (1) as = To give an outlook on general behaviour of curve over burnup, Figure 10 shows examples for case of AC (left) AC+FP (right) corresponding to highest of all considered enrichments, 4.94 w/o. k eff UO w/o, AC GWd/tHM decay=0a decay=5a decay=20000a decay=30000a decay=40000a decay=50000a k eff UO w/o, AC+FP USL GWd/tHM decay=0a decay=5a decay=20000a decay=30000a decay=40000a decay=50000a USL Figure 10. An illustration of determination of minimum burnup required for fuel to meet Upper Figure Subcritical 10. An illustration Limit (USL) of criticality determination safety criteria of minimum for AC (left) burnup AC+FP required (right). for fuel to meet Upper Subcritical Limit (USL) criticality safety criteria for AC (left) AC+FP (right). It can be seen again that most conservative case for credit of AC+FP is zero cooling time after discharge, while in case of only AC, most conservative results generally correspond to cooling time of about 30,000 years (in particular, for AC cases 2.50 w/o 3.50 w/o enrichments, highest k e f f results took place at zero cooling time, in case of 3.50 w/o enrichment, at 20,000 years cooling time; in all or cases, most conservative cooling time was 30,000 years). The computed minimum required burnups for each particular enrichment are shown in Table 8. Table 8. The minimum burnup required for meeting criticality safety criteria. Enrichment w/o AC AC+FP ~6.0 * ~51.0 * ~51.7 * ~36.4 * 4.94 ~73.0 * 49.1 * These values are based on extrapolations or involve certain (minor) interpolations.

23 Materials 2019, 12, of 30 Materials 2019, 12, of 30 The The loading loading curves curves are are n n derived derived by by applying applying data data from from Table Table 8 as as shown shown in in Figure Figure (adapted (adapted from from Reference Reference [29]). [29]). 80 PWR UO2 discharged fuel AC+FP AC Linear (AC+FP) Linear (AC) Allowed loadings region Burnup (GWd/tHM) Eligible for a mix loading Enrichment (w/o) Figure 11. The preliminary loading curves all conservative effects for discharged spent fuel Figure 11. The preliminary loading curves all conservative effects for discharged spent fuel (valid only for criticality safety criteria, subject to discussed important assumptions). (valid only for criticality safety criteria, subject to discussed important assumptions). Some examples on KKG discharged fuel assemblies characteristics (viz., initial enrichment Some examples on KKG discharged fuel assemblies characteristics (viz., initial enrichment discharged burnup) are also demonstrated in Figure 11. From se results, it becomes clear discharged burnup) are also demonstrated in Figure 11. From se results, it becomes clear that that given canister design meets criticality safety criteria if burnup credit is based on given canister design meets criticality safety criteria if burnup credit is based on AC+FP AC+FP approach. A potential exception could be, for instance, 5 w/o enriched FAs if y approach. A potential exception could be, for instance, 5 w/o enriched FAs if y were irradiated were irradiated for a lower number of cycles than designed, e.g., discharged once-burned from a last for a lower number of cycles than designed, e.g., discharged once burned from a last operated core. operated core. In reality, last cycles can be loaded a lower enriched fuel to avoid inefficient In reality, last cycles can be loaded a lower enriched fuel to avoid inefficient use of fissile use of fissile material. material. It can be seen from Figure 11 that, for given USL value for case of UO 2, 4.94 w/o It can be seen from Figure 11 that, for given USL value for case of UO2, 4.94 w/o fuel, fuel, saving in terms of minimum required burnup as compared between cases of AC+FP saving in terms of minimum required burnup as compared between cases of AC+FP vs. vs. AC is about 24 GWd/tHM (this has been illustrated in more detail in Reference [29]). This result AC is about 24 GWd/tHM (this has been illustrated in more detail in Reference [29]). This result was was obtained by comparing cases which take into account bounding burnup profiles also obtained by comparing cases which take into account bounding burnup profiles also all all uncertainties listed in Table 7. Basically, same effect (23 GWd/tHM) can be observed for uncertainties listed in Table 7. Basically, same effect (23 GWd/tHM) can be observed for case case when only bounding burnup profiles are taken into account no uncertainties contribution. when only bounding burnup profiles are taken into account no uncertainties contribution. A A much weaker effect would be obtained (16 GWd/tHM) if calculations were done nominal much weaker effect would be obtained (16 GWd/tHM) if calculations were done nominal burnup profiles instead of bounding ones. Finally, a comparison between two values of burnup profiles instead of bounding ones. Finally, a comparison between two values of administrative margin was also shown in Reference [29]: for conventional value of 5000 pcm administrative margin was also shown in Reference [29]: for conventional value of 5,000 pcm for a reduced one of 2000 pcm. This illustration allowed prediction of what saving in minimum for a reduced one of 2,000 pcm. This illustration allowed prediction of what saving in burnup requirement could be achieved, provided administrative margin could hypotically be minimum burnup requirement could be achieved, provided administrative margin could relaxed to 2000 pcm. The extra saving for such a case was estimated as approximately 12 GWd/tHM. hypotically be relaxed to 2,000 pcm. The extra saving for such a case was estimated as approximately 7. Outlook 12 Discussion GWd/tHM. 7. Outlook The classical Discussion practice for criticality safety calculations for applications out of reactor has relied on fresh fuel assumption. The advantages of taking credit for changes in actinide compositions afterthe irradiation classical practice build-up for criticality of fission safety products calculations in spent for applications fuel, a net out effect of ofreactor decreasing has relied k on fresh fuel assumption. The advantages of taking credit for changes in actinide e f f of systems formed by burned fuel assemblies, have been given major attention during compositions last decades. Initially after irradiation applied to spent build up fuel pools of fission fuelproducts dissolution in facilities spent fuel, later toa transport net effect of decreasing dry storage, burnupof credit systems has also formed been used by inburned waste disposal fuel assemblies, applications have inbeen USA, given Sweden major attention during last decades. Initially applied to spent fuel pools fuel dissolution facilities later to transport dry storage, burnup credit has also been used in waste disposal applications in USA, Sweden Finl. The waste management applications in se three

24 Materials 2019, 12, of 30 Finl. The waste management applications in se three countries have been reviewed by regulators, are under review or are under development respectively. In line this, a preliminary criticality assessment study has been performed taking into account burnup credit in PSI/Nagra BUCSS-R research project recently conducted at PSI. Ways for furr methodological improvements verification of present results are discussed below Ways to Improve Reference BUCSS-R Methodology Based on analyses performed so far, it can be concluded that most significant uncertainty components at current stage are nuclear data (ND) combined impact (σ ND ), operating conditions (σ OC ), radiation-/burnup-induced geometry changes (σ BU e f f ). Obviously, it can be recommended at first to verify, in particular, most significant contributors to loading curve burnup penalties in future work (although future studies should not be limited to only listed components since or parameters can appear significant in more comprehensive simulations). Also, it would be relevant to assess SIMULATE-3/BOHR/CASMO5 methodology component approximations, namely infinite lattice calculations of pin-wise SNF compositions CASMO5 code. With respect to this limitation, transition to SIMULATE5 code in combination anor Studsvik code SNF (in quotation marks to distinguish from earlier spent nuclear fuel abbreviation) could provide intra-assembly pin-wise isotopic distributions from real core-follow calculations, as discussed in next section. Such work is currently ongoing at PSI outside present research collaboration NAGRA. Furrmore, a comparison of current methodologies, which can be classified as a combination of best estimate plus uncertainties (BEPU) approach certain conservative assumptions, against more traditional methodologies can be recommended. In particular, comparison of BEPU SNF compositions versus analogue data but application of so-called isotopic correction factors [13] obtained from validation studies post-irradiation examination (PIE) data should be considered. Finally, inclusion of correlation analysis in CSE methodology, as discussed in Reference [29], should be considered, since it would lead to more accurate probably less penalising loading curves Alternative Advanced Way to Derive Loading Curves under Development Verification The presently developed BUCSS-R calculation scheme is considered at PSI to be sufficiently detailed accurate for construction of BEPU-type loading curves, provided that statistically representative samples can be obtained for FAs all considered fuel types enrichments. A drawback of this system is that it is rar deming in terms of calculation resources. Important to mention is that SIMULATE/BOHR/CASMO calculations required for BUCSS-R scheme are basically not needed for any or type of simulation, so y are practically solely dedicated to BUCSS-R methodology for loading curve derivations (As outlined before, BOHR methodology is also useful for PIE data analysis, but in that case, only important FA segments can be calculated, which drastically reduces computational dems.). Since CASMO calculations generally have to be redone every time an updated/new version of CASMO code or/ its cross section library are released, such a method for derivation of loading curves becomes costly inefficient. However, an alternative way to derive loading curves recently became available based on exploitation of advanced features of additional CMS code SNF, which can be seamlessly integrated into PSI CMSYS system. A description of new methodology developed at PSI outside BUCSS-R project, which is based on CASMO/SIMULATE/SNF/COMPLINK/MCNP system of codes which was named CS 2 M method has been presented in Reference [46], toger

25 Materials 2019, 12, of 30 Materials 2019, 12, of 30 outside BUCSS-R project, which is based on CASMO/SIMULATE/SNF/COMPLINK/MCNP system of codes which was named CS2M method has been presented in Reference [46], toger examples of examples its trial application. of its trial application. Thus, concept Thus, of concept new of more new advanced more approach advanced for approach loadingfor curve derivation loading curve is to rely derivation nominal is to rely on validated nominal CMSYS CASMO/SIMULATE validated CMSYS core-follow CASMO/SIMULATE models core-follow calculations, models no need calculations, for complementary no need CASMO for complementary calculations tocasmo derive calculations SFC. All required to derive information SFC. All can required now be obtained information directly can from now be CASMO/SIMULATE obtained directly from results CASMO/SIMULATE help of SNF results code, as illustrated help of schematically SNF code, in Figure as illustrated 12 (see Reference schematically [47] for in details Figure on 12 (see relative Reference perturbation [47] for details factors). on relative perturbation factors). Figure 12. An alternative computational scheme based on SNF code integration into CMSYS system. Figure 12. An alternative computational scheme based on SNF code integration into CMSYS Furrmore, system. as already mentioned, it is recommended in future to use SIMULATE5 code, as it has a more accurate inter-assembly SFC characterisation capability. In doing so, it will be in Furrmore, as already mentioned, it is recommended in future to use SIMULATE5 principle possible to extract SFC for every individual fuel assembly ever operated in Switzerl code, as it has a more accurate inter-assembly SFC characterisation capability. In doing so, it will be thus to avoid all undesirable approximations to realise BEPU calculations. The uncertainty in principle possible to extract SFC for every individual fuel assembly ever operated in propagation can be done same tools as used before in BUCSS-R scheme. This is illustrated Switzerl thus to avoid all undesirable approximations to realise BEPU calculations. The shaded boxes in top part of Figure 12. uncertainty propagation can be done same tools as used before in BUCSS-R scheme. This Therefore, although new CS2M approach is also time-consuming, it does not require any is illustrated shaded boxes in top part of Figure 12. complementary unnecessary simplified assessments, for that reason, it is more efficient Therefore, although new CS2M approach is also time-consuming, it does not require any transparent for verification validation. complementary unnecessary simplified assessments, for that reason, it is more efficient Finally, since both approaches being developed at PSI to derive loading curves for transparent for verification validation. Swiss reactor spent fuel assemblies differ from more conventional conservative approaches Finally, since both approaches being developed at PSI to derive loading curves for Swiss (see Section 4 Group Discussions of Reference [48]), it is definitely an advantageous situation at PSI reactor spent fuel assemblies differ from more conventional conservative approaches (see that two different methods can be compared, in such way, resulting loading curves can be Section 4 Group Discussions of Reference [48]), it is definitely an advantageous situation at PSI that verified high confidence. In line this, results of work in Reference [46] of two different methods can be compared, in such way, resulting loading curves can be verified BUCSS-R assessments presented in this paper have been compared, as demonstrated in Figure 13. high confidence. In line this, results of work in Reference [46] of BUCSS-R For a consistent comparison, BUCSS-R results were reevaluated for this particular graph, using assessments presented in this paper have been compared, as demonstrated in Figure 13. For a same conditions as were applied in Reference [46]: no uncertainty components no bounding consistent comparison, BUCSS-R results were reevaluated for this particular graph, using burnup profiles are taken into account in this test exercise, i.e., only reference/nominal burnup same conditions as were applied in Reference [46]: no uncertainty components no bounding profiles are considered. As can be seen, results are in good agreement. Future work will be burnup profiles are taken into account in this test exercise, i.e., only reference/nominal burnup focused on extended more representative verification studies using both BUCSS-R CS2M profiles are considered. As can be seen, results are in good agreement. Future work will be calculation schemes. focused on extended more representative verification studies using both BUCSS-R CS2M calculation schemes.

26 Materials 2019, 12, of 30 Materials 2019, 12, of 30 AC; 'USL'= BUCSS-R CS2M Burn-up (GWd/tHM) U-235 Enrichement, w/o Figure 13. A comparison of test loading curves obtained reference BUCSS-R Figure 13. A comparison of test loading curves obtained reference BUCSS R advanced CS2M schemes (for same simplified conditions). advanced CS2M schemes (for same simplified conditions). 8. Conclusions 8. Conclusions This work was oriented towards deriving preliminary loading curves for SNF disposal canisters This to work be used was inoriented a Swiss towards deep geological deriving repository preliminary currentlyloading being planned curves for by Nagra. SNF This disposal paper canisters contains ato description be used in of a Swiss applied deep methodology geological repository presents currently main being findings planned by results. Nagra. This paper Incontains initiala description stage of of study, applied bounding methodology fuel type analyses presents using representative main findings fuel assemblies results. operated In ininitial Swiss stage PWR of plant study, KKG bounding were performed. fuel type analyses The UO 2 using, MOXrepresentative ERU fuelsfuel were assemblies analysed operated using in highest Swiss enrichments PWR plant used KKG to date were performed. operated to The UO2, highest MOX burnups ERU to properly fuels were assess analysed ir using behaviour. highest As detailed enrichments as possible, used intra-assembly to date operated SNF compositions to highest have burnups been used to properly in MCNP assess ir criticality behaviour. calculations As detailed based on as possible, resultsintra assembly of calculationssnf corresponding compositions to realistic have been cycle used operating MCNP conditions criticality extracted calculations from validated based on PSI core results management of calculations models. corresponding The case of PWR to realistic UO 2 hascycle been operating confirmedconditions to be most extracted limiting, from consequently, validated PSI core loading management curve analysis models. wasthe donecase for this of PWR fuel. UO2 The has been methodology confirmed applied to be for most loading limiting, curve derivation consequently, integrated loading outcome curve ofanalysis stard was done PSI criticality for this fuel. safety validation procedure estimated penalties on computed due to uncertainties The methodology in nuclear applied data, fuel for assembly loading design curve parameters derivation integrated operating conditions outcome as well of as stard radiation-induced PSI criticality changes safety in validation fuel assembly procedure geometry. Furrmore, estimated penalties boundingon axial computed radial burnup due profiles to uncertainties most reactive in nuclear fuel loading data, configuration fuel assembly indesign canister, parameters in terms of penalising operating conditions radial tilt, were as well takenas into radiation induced account accordingly. changes in fuel assembly geometry. Furrmore, bounding The loading axial curves radial obtained burnup for profiles reference disposal most reactive canister fuel (as illustrated loading configuration in Figure 11) in show canister, what minimum terms average of penalising fuel assembly radial tilt, burnup were taken is required into account for accordingly. given original fuel enrichment of fresh The fuel loading assemblies curves obtained so that for k e f f reference of canister disposal would canister comply (as illustrated imposed in Figure criticality 11) show what safetyminimum criterion. average fuel assembly burnup is required for given original fuel enrichment of fresh The fuel loading assemblies curves so that presented were of obtained canister forwould a reference comply disposal canister imposed design criticality provided safety by criterion. Nagra in course of project. However, Nagra is exploring various options for selection of materials The loading design curves concepts presented for were canister, obtained whichfor may a reference require adisposal reevaluation canister of design loading provided curves. by A preliminary Nagra in study course demonstrating of project. However, plausibility Nagra of is alternative exploring various canisteroptions designsfor can beselection found in of Reference materials [2]. design concepts for canister, which may require a reevaluation of loading curves. TheA loading preliminary curves study presented demonstrating this work plausibility show thatof AC alternative credit approach canister designs would not can be found sufficient in Reference to meet [2]. USL criticality safety criterion for a non-mixed loading fuel an initial enrichment The loading abovecurves approximately presented 3.5in w/o, this while work show AC+FP that approach AC credit justifies approach applicability would not of be sufficient canister design to meet considered USL criticality for safe safety disposal criterion of spent for a nuclear non mixed fuel loading all existing fuel enrichments an initial enrichment required above minimum approximately burnups. 3.5 w/o, while AC+FP approach justifies applicability of canister A postulated design considered hypotical for case safe consisting disposal of of FAs spent nuclear 5 w/ofuel initial enrichment all existing relatively enrichments low burnup required wouldminimum be onlyburnups. exception to fitting loading criteria; however, this case belongs only to a oretical A postulated last corehypotical discharge, where, case consisting in reality, aof lower FAs enriched 5 w/o fuelinitial shouldenrichment be employed. The relatively option low of some burnup canisters would being notonly fullyexception loaded could to fitting be an alternative loading approach criteria; however, but would this becase challenging belongs only to a oretical last core discharge, where, in reality, a lower enriched fuel should be employed. The option of some canisters being not fully loaded could be an alternative approach but would be challenging from anor point of view (logistics cost optimisation). Theoretically, mixed

27 Materials 2019, 12, of 30 from anor point of view (logistics cost optimisation). Theoretically, mixed configurations of SNF different burnup levels could also be a solution for most problematic cases. The loading curves must be treated as preliminary since re is still room for improvement in assessment of different components of Equations (1) (3). However, valuable findings have already been obtained concerning identification of most problematic scenarios loading schemes, which will serve as guiding information for next phases of research development at PSI Nagra, in particular for optimisation of canister design mixed burnup/fuel assembly design loading schemes. Among topics for furr improvement of BUCSS-R methodology ( respect to only criticality safety burnup credit assessments), or aspects can be proposed for consideration, such as extension of analysed FA sample to yield 95%/95% tolerance bounds for loading curves (i.e., to safely cover potential uncertainties from operating condition variations); a refinement of treatment of uncertainties respect to burnup axial radial profiles, allowing a consistent Total Monte Carlo assessment ( seamless calculations of both depletion/decay criticality models using same ND perturbation factors, as outlined in Figure 12); assessment of long-term scenarios canister fuel evolution degradation. In addition, an improvement of nuclear criticality safety criterion based on a detailed analysis of nuclear data-related uncertainties correlations, which can be done, e.g., NUSS [10,49], has been proposed in References [10,29] should be furr explored. In parallel, assessments of an alternative option for currently used BUCSS-R methodology are ongoing independently at PSI, for which Studsvik s code SNF is integrated into CS 2 M scheme [46] to substitute BOHR component of BUCSS-R scheme. At present, new approach is basically used for verification of base BOHR/BUCSS-R results; however, if confirmed to be more efficient, this new calculation scheme can replace original one in future studies at PSI. Author Contributions: Conceptualization, A.V., H.F. S.C.; data curation, H.F. S.C.; formal analysis, A.V., J.H. D.R.; funding acquisition, A.V., H.F. S.C.; investigation, J.H. D.R.; methodology, A.V., J.H., M.P., D.R. H.F.; project administration, A.V., H.F. S.C.; resources, H.F.; software, J.H., M.P., D.R. H.F.; supervision, A.V. H.F.; validation, A.V., J.H., M.P. D.R.; visualization, A.V., J.H., M.P. D.R.; writing original draft, A.V., J.H., M.P., D.R. S.C.; writing review editing, A.V., J.H., M.P., D.R., H.F. S.C. Funding: This research was partially funded by PSI Nagra in framework of bilateral collaboration on BUCSS-R project. Acknowledgments: The authors express ir gratitude to former Nagra collaborator L. Johnson former LRS/NES/PSI head M. Zimmermann for ir contributions to initiating joint PSI/Nagra BUCSS-R research project. The authors are also grateful to L. McKinley/Nagra for kindly provided comments English grammar check. Conflicts of Interest: The authors declare no conflict of interest. References 1. Kühl, H.; Johnson, L.H.; McGinnes, D.F. Criticality Canister Shielding Calculations for Spent Fuel Disposal in a Repository in Opalinus Clay; Nagra Technical Report NAB 12-42; Nationale Genossenschaft für die Lagerung radioaktiver Abfälle: Wettingen, Switzerl, Gutierrez, M.; Caruso, S.; Diomidis, N. Criticality Shielding Assessment of Canister Concepts for Disposal of Spent Nuclear Fuel. In Proceedings of International High-Level Radioactive Waste Management Conference, Charlotte, NC, USA, 9 13 April Scaglione, J.M.; Wagner, J.C. Burnup Credit Approach Used in Yucca Mountain License Application. In Proceedings of International Workshop on Advances in Applications of Burnup Credit for Spent Fuel Storage, Transport, Reprocessing, Disposition, Córdoba, Spain, October Ewing, R.C.; Weber, W.J. Nuclear-waste management disposal. In Fundamentals of Materials for Energy Environmental Sustainability; Ginley, D.S., Cahen, D., Eds.; Cambridge University Press: Cambridge, UK, 2011; pp

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