WHY A CRITICALITY EXCURSION WAS POSSIBLE IN THE FUKUSHIMA SPENT FUEL POOLS

PHYSOR 014 The Role of Reactor Physics Toward a Sustainable Future The Westin Miyako, Kyoto, Japan, September 8 October 3, 014, on CD-ROM (014) WHY CRITICLITY EXCURSION WS POSSIBLE IN THE FUKUSHIM SPENT FUEL POOLS G. Caplin,. Sargeni * Institut pour la Radioprotection et la Sûreté Nucléaire (IRSN) BP 17 960 Fontenay-aux-Roses - FRNCE gregory.caplin@irsn.fr antonio.sargeni@irsn.fr BSTRCT During the Fukushima event, IRSN performed some calculations to assess whether a criticality excursion was likely to occur in case of a loss of coolant of the spent fuel pools (dry-out). The results of these calculations show that the k-eff of the spent fuel pool can increase when a water-air mixture is modeled within the storage (with subsequent water density decrease), compared to the k-eff value with a full water density within the pool. This k-eff increase reaches more than 5% for an optimal range of water-air mixture, which is more than usual safety margins kept to demonstrate the safety of the spent fuel pools. This initial study showed that the pitch between the fuel assemblies, the materials (steel with more or less boron) composing the storage rack and the water densities are the main parameters driving the magnitude of the k-eff increase. ll the above calculations were performed with the standard route of the CRISTL package [1] and, in order to interpret and understand the here-above results, investigations were performed in parallel using pure Monte-Carlo pointwise calculations and pure deterministic calculations so as to first confirm, then to explain the observed results using a reactivity splitting via the four factors formula. This paper presents these complementary studies showing how, when water density decreases and inter-assembly gap increases, the balance between increasing fast fissions and water absorption may justify a reactivity increase. Key Words: Fukushima, spent-fuel-pools, loss-of-coolant, reactivity, criticality 1. INTRODUCTION During the Fukushima event, IRSN performed some calculations to assess whether a criticality excursion was likely to occur in case of a loss of coolant of the spent fuel pools (dry-out). The results of these calculations show that the k-eff of the spent fuel pool can increase when a water-air mixture is modeled within the storage, compared to the k-eff value with a full water density within the pool. This k-eff increase reaches more than 5% for an optimal range of water-air mixture, which is more than usual safety margins kept to demonstrate the safety of the spent fuel pools. This effect was first demonstrated for fuels for Boiling Water Reactors (BWR) and for various designs of storage racks. In order to identify the main parameters and conditions leading to such a k-eff increase, and in order to show if this effect is specific to BWR fuels, the calculations performed during the Fukushima crisis were supplemented by a textbook case based on fuels for Pressurized Water Re- * Corresponding author

G. CPLIN &. SRGENI actors (PWR). It was shown that the k-eff of a spent fuel pool also increases in the case of PWR fuels. Moreover, the main parameters driving the magnitude of the k-eff increase were proved to be the pitch between the fuel assemblies, the materials (steel with more or less boron) composing the storage rack and the water densities. ll the above calculations were performed with the standard route of the CRISTL package (version 1.) [1]. This route consists in a first deterministic (Pij) calculation of the fissile material (lattice of cells modeling spent fuel rods) to get homogenized multi-group cross-sections (performed by the POLLO code), followed by a 3D Monte-Carlo k-eff calculation (performed by the MORET 4 code) of the spent fuel pool including several assemblies made of the above homogenized lattice of spent fuel rods. In order to interpret and understand the here-above results, investigations are performed in parallel using pure Monte-Carlo pointwise calculations and pure deterministic calculations in order to first confirm, then to explain the observed results using a reactivity splitting via the four factors formula. This paper presents these complementary studies.. DESCRIPTION OF THE STUDIED CSE The textbook case used for the study of the decrease of the water density in a spent fuel pool is based on an infinite array of undamaged 17x17 fuel assemblies in water, Uranium OXyde (UOX) fuels for PWR, initial enrichment in 35 U is 3.7 %. Preliminary studies showed that the studied behavior does not depend at first order on the fuel design. For this array of fuels: - the distance between the assemblies is made varying from 1 so-called Water Gap (the nominal distance between assemblies in a PWR reactor core, i.e. 0.1558 cm) to 00 Water Gaps (i.e. 31.1704 cm), - the water density (within the assemblies and between them) is made varying (homogeneously) to simulate the water-air mixture in case of a heating leading to an uncover of the fuel or a refilling of the pool, - there is no boron in the water (as for Fukushima s spent fuel pools and to account for a potential non borated water injection during an accident). The impacts of the fuel burn-up and of the neutron leakage (finite array) have also been studied. Only the general conclusions of these studies are presented in this paper. These very simple assumptions (infinite model, no account taken for a structural material between the assemblies, no water density variation along the assemblies, etc.) were chosen in order to: 1. see if the effect, observed in the more realistic calculations performed during the Fukushima event, is due to a particular design effect or is an intrinsic physical phenomenon for fuel pool storages,. ease the interpretation of the results. Nevertheless, more complete studies (with structural materials, presence of boron within the water, varying height of low water density, varying number of fuel assemblies, etc.), not presented in this paper, were performed to identify the main conditions driving the behavior of the storage reactivity in case of an accidental scenario. / 13 PHYSOR 014 The Role of Reactor Physics Toward a Sustainable Future Kyoto, Japan, September 8 October 3, 014

Why a criticality excursion was possible in the Fukushima Spent Fuel Pools 3. MONTE-CRLO CLCULTIONS Monte-Carlo calculations were performed with the MORET (version 5..1) 3D pointwise Monte-Carlo code, [3], associated with the JEFF3.1.1 nuclear library. The following picture shows the k-inf curves as a function of the inter-assembly distance (from WG 1 = 0.1558 cm up to WG 00 = 31.16 cm) and the moderator density, going from the nominal value of 1 g/cm 3 to 0. 1.50 1.45 1.40 1.35 1.30 1.5 1.0 1.15 1.10 1.05 1.00 0.95 0.90 WG 1 WG 10 WG 30 WG 70 WG 100 WG 150 WG 00 0.85 0.80 0.75 0.70 0.65 1.00 0.95 0.90 0.85 0.80 0.75 0.70 0.65 0.60 0.55 0.50 0.45 0.40 0.35 0.30 0.5 0.0 0.15 0.10 0.05 0.00 g/cm 3 Figure 1: K-inf behavior of a submerged fuel assemblies array when water density decreases for various distances between assemblies Figure 1 shows three types of k-inf behaviors with the moderator decreasing, which are in agreement with the results of the calculations made during and after the Fukushima event with the standard calculation route of the CRISTL package: a) a constant k-inf decrease for inter-assembly gap until, about, 3 cm (WG 0); b) an initial k-inf increase followed by a decrease for inter-assembly gap from 3 cm to about 15 cm (WG 100); c) an initial k-inf decrease followed by an increase and again a decrease for an inter-assembly gap bigger than 15 cm. The first behavior (a) is quite usual regarding fuel assemblies in a nuclear reactor core (a loss of reactivity in case of a decrease of the water density, due to the under-moderation -by design- of the fuel assemblies). Both other behaviors (b) and (c) are specific of storage in pools and need some investigations to be interpreted. PHYSOR 014 The Role of Reactor Physics Towarda Sustainable Future Kyoto, Japan, September 8 October 3, 014 3 / 13

G. CPLIN &. SRGENI 4. PHYSICL INTERPRETTION To try to understand the behaviors different from the usual reactor core behavior, idea was to analyze the k-inf variations using the classical 4 factors formula in order to separate the different physical effects and to grasp the origin of these behaviors. The code used for this analysis is the DRGON deterministic code [4] (computation scheme: JEFF3.1 library, 81 groups SHEM [6] energy meshing, a first step using a Pij technique to compute the flux, collapsing to 6 energy groups, and finally a k-inf computation by the Method of Characteristics MOC [7]). The method used for this study has been to repeat all the Monte-Carlo computations in order a) to check that we were able to reproduce these results and b) to be able to compute the 4 factors and the variations of the 4 factors when we changed the water density and the inter-assembly distance. The 4 factors formula [5] is: k = P, F P P = = p f η ε, where: P P = total neutron production - = total neutron absorption = thermal absorption (thermal cut-off at 0.65 ev),f = thermal fuel absorption; P = thermal production, F p = = resonance escape probability; f = = thermal utilization factor P P η = = reproduction factor; ε = = fast fission factor, F P δ k δ p δ f δη δε t first order, the k-inf variation is: + + + and, in such a way, it is possible to grasp the origin of a k-inf variation; in other words, what we want to understand are the k p f η ε physical reasons for such reactivity variations. Starting from the nominal moderator density of 1 g/cm 3, we have decreased the density by steps of 0.05 g/cm 3 and, for each step, we have analyzed the relative k-inf variation as a sum of the 4 factors relative variations. The modeled assembly has zero Burn-Up (BU) and no leakage. Some complementary studies have been executed to take into account the effects of not zero BU and leakage (see 3.5). The three types of k-inf behaviors above-mentioned are separately analyzed in the next sub-sections. 4.1. K-inf behavior between 0 and 3 cm of inter-assembly distance In the range from 0 to 3 cm of inter-assembly distance, k-inf acts towards the moderator decreasing density in a classical way: k-inf decreases as moderator density decreases. Figures and 3 show the k-inf, the 4 factors and their relative variations as functions of the water density in the reference case (inter-assembly distance equals to 0.1558 cm)., F 4 / 13 PHYSOR 014 The Role of Reactor Physics Toward a Sustainable Future Kyoto, Japan, September 8 October 3, 014

Why a criticality excursion was possible in the Fukushima Spent Fuel Pools Figure : Inter-assembly gap lower than 3 cm: k-inf and 4 factors Figure 3: Inter-assembly gap lower than 3 cm: k-inf and 4 factors variations s seen in the above pictures, k-inf decrease is mainly due to the p factor decrease that overwhelms the fast fissions factor increasing. This is due, of course, to the water density diminishing that, at the same time, decreases the slowing down and increases the fast neutron number. 4.. K-inf behavior between 3 and 15 cm of inter-assembly distance The behaviors of the k-inf, the 4 factors and their variations, for an inter-assembly distance between 3 and 15 cm, are shown in the Figures 4 and 5 (in the case of 50 water gaps between assemblies, i.e. 7.79 cm). PHYSOR 014 The Role of Reactor Physics Towarda Sustainable Future Kyoto, Japan, September 8 October 3, 014 5 / 13

G. CPLIN &. SRGENI Figure 4: Inter-assembly gap between 3 and 15 cm: k-inf and 4 factors Figure 5: Inter-assembly gap between 3 and 15 cm: k-inf and 4 factors variations In this configuration, k-inf always grows until, about, 0.3 g/cm 3 where it starts decreasing. s seen in the previous pictures, k-inf relative variation is the sum of 3 components (analyzed in the following): 1. f : always positive and slightly increasing from 1 to 0.5 g/cm 3. p : always negative 3. ε : positive and increasing 4..1. Thermal utilization factor (f) The f factor variation is, in turn, divided into its components variations (at first order): fuel thermal absorption (,F ) and total thermal absorption ( ), whose variations are shown in the Figure 6. δf δ, F δ f, F 6 / 13 PHYSOR 014 The Role of Reactor Physics Toward a Sustainable Future Kyoto, Japan, September 8 October 3, 014

Why a criticality excursion was possible in the Fukushima Spent Fuel Pools Figure 6: Inter-assembly gap between 3 and 15 cm: variations of f factor and its components On the above picture, the positive f variation is a sum of an always negative contribution of the fuel thermal absorption (explained by a decrease of the thermal neutron number due to the water density decrease) and of an always more negative contribution of the total thermal absorption, i.e. and F decrease but decreases faster, thus their ratio increases. 4... Resonance escape probability factor (p) The escape factor p and its two components (thermal absorption) and (total absorption) variations are represented in the Figure 7. Figure 7: Inter-assembly gap between 3 and 15 cm: variations of p factor and its components Escape factor constantly decreases with the water density decrease.what we note is that the total absorption increases quickly in the low density region and this is due to the increase of the fast fissions. PHYSOR 014 The Role of Reactor Physics Towarda Sustainable Future Kyoto, Japan, September 8 October 3, 014 7 / 13

G. CPLIN &. SRGENI 4..3. Fast fission factor ( eps, ε) The fast fission factor ε relative variation and the relative variation of P (total production) and P (thermal production) are reproduced in Figure 8. Figure 8: Inter-assembly gap between 3 and 15 cm: variations of eps factor and its components These curves highlight the big increase of fast fissions when the water density decreases. Explanation is, probably, simply due to the growth of the fast neutrons population with the moderation decrease. 4.3 K-inf behavior for more than 15 cm of inter-assembly distance The infinite assemblies array with a total water gap equivalent to 100 nominal water gaps (inter-assembly distance of 15.6 cm) has the k-inf and 4-factor curves shown in the Figure 9. Figure 9: Inter-assembly gap higher than 15 cm: k-inf and 4 factors This picture shows how the k-inf follows the f factor s curve. Both parameters have first a tendency to slightly decrease with the water density decrease and then to increase. The relative 8 / 13 PHYSOR 014 The Role of Reactor Physics Toward a Sustainable Future Kyoto, Japan, September 8 October 3, 014

Why a criticality excursion was possible in the Fukushima Spent Fuel Pools variations of k-inf and of the 4 factors are presented in the Figure 10.,0 1,5 1,0 p 0,5 f % 0,0 1,0-0,5 0,9 0,8 0,7 0,6 0,5 0,4 0,3 0, eta eps Kinf -1,0-1,5 g/cm3 Figure 10: Inter-assembly gap higher than 15 cm: k-inf and 4 factors variations The previous picture shows that: K-inf variation is essentially determined by f variation; t high water densities, k-inf decreases due to p and f decrease; f factor (and the k-inf) decreases until about 0.8 g/cm 3,after the tendency inverts; ε contribution is always positive and growing, but is compensated at low density by p decrease; η contribution is negligible. Only the main term f is analyzed in the following. Figures 11 and 1 illustrate this f factor and its components (fuel thermal absorption, F and total thermal absorption ) behavior with the water density decrease. Figure 11: Inter-assembly gap higher than 15 cm: f factor and its components PHYSOR 014 The Role of Reactor Physics Towarda Sustainable Future Kyoto, Japan, September 8 October 3, 014 9 / 13

G. CPLIN &. SRGENI Figure 1: Inter-assembly gap higher than 15 cm: variations of f factor and its components f factor variation is explained (see above pictures) as the sum of the negative variation of the fuel total thermal absorption (thermal neutron number decreases with the decreasing of the water density) and of the total thermal absorption, firstly negative and after positive. To better understand this last point, given its importance on f variation, the total thermal absorption variation has been split up into a sum of the absorption variations of fuel (, ), clad ( F, ), in-assembly C water ( ) and inter-assembly water (, SB _ W ):, INTER _ W δ δ, F δ, C δ, SB _ W δ, INTER _ W = + + + These variations are presented in the Figure 13. Figure 13: Inter-assembly gap higher than 15 cm: variations of total thermal absorption components The above picture shows how the total thermal absorption is essentially driven by the inter-assembly water absorption. Moreover, two zones can be distinguished: a first one, where the inter-assembly thermal absorption increases with the water density decreasing and a second one (stating around 0.7 g/cm 3 ), where the thermal reaction rate constantly decreases. In turn, the in- 10 / 13 PHYSOR 014 The Role of Reactor Physics Toward a Sustainable Future Kyoto, Japan, September 8 October 3, 014

Why a criticality excursion was possible in the Fukushima Spent Fuel Pools ter-assembly water thermal absorption rate ( ) can be decomposed as the product of a, INTER _ W mean macroscopic cross section (Σ ) and an integrated thermal flux (ϕ ): Σ ϕ, INTER _ W = Σ ϕ = ϕ = Σ ϕ, whose relative first-order variation is: ϕ δ, INTER _ W, INTER _ W δσ Σ δϕ +, that are represented in Figure 14. ϕ Figure 14: Inter-assembly gap higher than 15 cm: variations of inter-assembly water thermal components The mean cross-section (see above pictures) always decreases but the thermal flux begins to increase and then, afterwards, decreases. The sum of these two terms produces the thermal absorption variation trend. The thermal flux (Figure 15) increases due to the increase of the fast flux (in turn, due to the fast fissions and to the decreasing of the water moderation) and, globally, the spectrum becomes harder. Figure 15: Inter-assembly gap higher than 15 cm: Inter-assembly water thermal and fast flux PHYSOR 014 The Role of Reactor Physics Towarda Sustainable Future Kyoto, Japan, September 8 October 3, 014 11 / 13

G. CPLIN &. SRGENI The main conclusions of this analysis are: total thermal assembly absorption increases between 1 and 0.7 g/cm 3 and, afterwards, decreases,, F as a consequence, f = increases below 0.7 g/cm 3 because fuel thermal absorption remains, practically, constant, total thermal absorption is driven, essentially, by the inter-assembly water absorption which, in turn, follows the thermal flux variation, the thermal flux increase is due to the fast flux increase: as long as the water moderation is sufficient, the thermal flux increase brings about an increase of thermal absorption hence a reactivity decrease. When the water density begins to become really small, the thermal flux decrease induces a decrease of the thermal absorption, hence the k-inf growth. 4.4 ssembly with Not Zero Burn-Up and Leakage The method used to take into account depletion effects was to deplete at nominal condition (i.e., reference water gap, critical buckling) up to 18 GWd/t and 36 GWd/t and, starting with the isotopic concentrations corresponding to these burn-up, water density and inter-assembly distance have been modified exactly as shown in the previous paragraph. From a qualitative point of view, the curves obtained are exactly the same. The only BU effect is to shift the k-inf towards smaller values, but the curves shapes are preserved. In order to take into account leakage effects, an approximate Buckling value of 10-4 cm - (actual buckling varies with the water density) has been computed using MORET5, by modeling a realistic 3D storage pool. Leakage does not perturb the k-inf curves (at least for B values of this magnitude order) and shapes are still preserved. Moreover, k-eff behaves like the k-inf. 5. CONCLUSIONS In this paper we have tried to highlight the physical reasons of the behavior of a spent fuel pool k-inf in case of a water density lower than 1 g/cm 3. s shown by a sequence of MORET5 (pointwise Monte-Carlo) computations, k-inf may increase with the water density decrease and its behavior is also depending on the inter-assembly distance. To explain where this behavior comes from, all the computations have been repeated with the deterministic transport code DRGON: k-inf relative variations with water density, for a number of inter-assembly gaps, have been split using the 4-factors formula and results demonstrate how such behaviors are possible if the adapted conditions are brought together. Indeed, for a given inter-assembly distance, k-inf may increase or decrease because: fast fissions increase when water density decrease, hence reactivity increases; resonances escape probability always decreases with the water density decrease, hence reactivity decreases; water thermal absorption depends, at the same time, of the water density and of the inter-assembly gap. Water thermal absorption follows the thermal flux that can increase or decrease if there is enough water to moderate the fast neutrons produced by the fast fissions; hence reactivity can increase or decrease if the water thermal absorption decreases or increases. 1 / 13 PHYSOR 014 The Role of Reactor Physics Toward a Sustainable Future Kyoto, Japan, September 8 October 3, 014

Why a criticality excursion was possible in the Fukushima Spent Fuel Pools When the k-inf increases, the maximal value is obtained for a water density range between 0.1 and 0.3 g/cm 3 (i.e. a water-air mixture with a void fraction between 70% and 90%). Conditions of such low water densities within a spent fuel pool may be reached in case of: a long term loss of coolant (water heating due the residual spent fuel power); in case of refilling operations following a dry-out of the pool (injection of water by spraying devices). IRSN is studying these two scenarios as the increase of the k-eff may reach criticality. In particular, the designs of spent fuel pools that may become critical with realistic conditions are under investigation. Even if the main issue regarding loss of coolant of a spent fuel pool is the release of radioactive materials, the occurrence of a criticality accident would induce consequences (more heating power due to induced fissions, more radiations, etc.) that should be accounted for the prediction of the evolution of such a situation and to define adequate emergency actions. REFERENCES [1] J.-M. Gomit et al., CRISTL V1: Criticality package for burn up credit calculations, Proc. Int. Conf. International Conference on Nuclear Criticality Safety(ICNC003), Tokai-Mura, Japan, Oct. 0-4 (003). [] G. Caplin et al., Criticality accident in case of a spent fuel pool dry-out, EUROSFE FORUM 011, Paris, France, Nov. 7-8 (011), http://www.eurosafe-forum.org/011-posters [3] L. Heulers et al., MORET 5 Overview of the new capabilities implemented in the multigroup/continuous-energy version, Proc. Int. Conf. International Conference on Nuclear Criticality Safety(ICNC011), Edinburgh, Scotland, Sep. 19- (011). [4] G. Marleau,. Hébert, R. Roy, New Computational Methods Used in the Lattice Code DRGON, Proc. Int. Topical. Mtg. on dvances in Reactor Physics, merican Nuclear Society, Charleston, US, March 8-11, 199 [5] P. Reuss, Neutron Physics, EDP Sciences, Les Ulis, France, (008) [6] N. Hafaiedh,. Santamarina, Determination of the Optimized SHEM Mesh for Neutron Transport Calculations, Proc. Topical. Mtg. in Mathematics and Computations, Reactor Physics and Nuclear and Biological pplications, September 9-15, vignon, France, 005 [7] T. Reysset, Development and Qualification of dvanced Computational Schemes for PWR and Creation of Specific Interfaces towards GRS Full-Core Tools, EcolePolytechnique de Montréal, Canada, URL http://www.polymtl.ca/merlin/downloads/reysset_these.pdf PHYSOR 014 The Role of Reactor Physics Towarda Sustainable Future Kyoto, Japan, September 8 October 3, 014 13 / 13