- Email: [email protected]
VVER vessel steel corrosion at interaction with molten corium in oxidizing atmosphere
Nuclear Engineering and Design 239 (2009) 1103–1112
Contents lists available at ScienceDirect
Nuclear Engineering and Design journal homepage: www.elsevier.com/locate/nucengdes
VVER vessel steel corrosion at interaction with molten corium in oxidizing atmosphere S.V. Bechta a,∗ , V.S. Granovsky a , V.B. Khabensky a , E.V. Krushinov a , S.A. Vitol a , A.A. Sulatsky a , V.V. Gusarov b , V.I. Almiashev b , D.B. Lopukh c , D. Bottomley d , M. Fischer e , P. Piluso f , A. Miassoedov g , W. Tromm g , E. Altstadt h , F. Fichot i , O. Kymalainen j a
Alexandrov Research Institute of Technologies (NITI), Sosnovy Bor, Russia Institute of Silicate Chemistry, Russian Academy of Sciences (ISCh RAS), St. Petersburg, Russia c SPb State Electrotechnical University (SPbGETU), St. Petersburg, Russia d EUROPÄISCHE KOMMISSION, Joint Research Centre Institut für Transurane (ITU), Karlsruhe, Germany e AREVA NP GmbH, Erlangen, Germany f CEA/DEN/DSNI, Saclay, France g Forschungszentrum Karlsruhe, Karlsruhe, Germany h Forschungszentrum Rossendorf (FZR), Dresden, Germany i IRSN/DPAM/SEMCA, St. Paul lez Durance, France j FORTUM Nuclear Services Ltd., Espoo, Finland b
a r t i c l e
i n f o
Article history: Received 23 October 2008 Received in revised form 3 December 2008 Accepted 5 December 2008
a b s t r a c t The long-term in-vessel corium retention (IVR) in the lower head bears a risk of the vessel wall deterioration caused by steel corrosion. The ISTC METCOR Project has studied physicochemical impact of prototypic coria having different compositions in air and steam and has generated valuable experimental data on vessel steel corrosion. It is found that the corrosion rate is sensitive to corium composition, but the composition of oxidizing above-melt atmosphere (air, steam) has practically no influence on it. A model of the corrosion process that integrates the experimental data, is proposed and used for development of correlations. Crown Copyright © 2008 Published by Elsevier B.V. All rights reserved.
1. Introduction In a general case of IVR the vessel integrity depends both on its temperature condition and the wall thickness. The original thickness can be reduced due to a partial steel melting caused by the thermal impact of molten corium. The steel wall can also become thinner due to a physicochemical interaction with the melt. In Theofanous et al. (1996) and Froment et al. (1998), the results of experimental and numerical analyses were used to get the temperature values on the inner surface of the steel wall; the values are critical for the wall thickness during an interaction with the metallic part of the suboxidized corium melt. In the publications Bechta et al. (2004, 2006a) experimental studies of interaction between the melt of suboxidized corium and VVER vessel steel are presented which were carried out within the ISTC METCOR project. It was established that steel corrosion resulted from the partitioning of elements such as Fe, U, and Zr
∗ Corresponding author at: NITI, Sosnovy Bor, Leningrad Oblast 188540, Russia. Tel.: +7 81369 60 675; fax: +7 81369 23 672. E-mail address: [email protected] (S.V. Bechta).
between molten corium and steel, formation and liquefaction of surface Fe–U–Zr–O layer. The minimum steel temperature, at which corrosion stops, was determined; the correlations describing steel corrosion kinetics during the interaction with oxidic and metallic parts of the melt were developed. But we cannot exclude a complete oxidation of corium relocated to the lower head for the whole range of reactors, in which IVR is foreseen, and for different scenarios of severe accident progression, in particular, during the implementation of specific severe accident management strategies. This is confirmed by the TMI-2 post-accident studies of corium (Wolf and Rempe, 1993). The mentioned circumstances stipulate the relevance of studies examining steel corrosion at its interaction with oxidized corium, particularly, in presence of the oxidizing above-melt atmosphere. These studies were also carried out within the METCOR project. In the publications Bechta et al. (2006b,c, 2008) the experimental data for UO2+x –ZrO2 –FeOy corium are presented, and the main result from this data is that vessel corrosion is caused by steel oxidation. Along with UO2+x –ZrO2 –FeOy studies, the METCOR project included experiments with UO2+x –ZrO2 corium in oxidizing atmosphere. This article gives and analyses the available data together
0029-5493/$ – see front matter. Crown Copyright © 2008 Published by Elsevier B.V. All rights reserved. doi:10.1016/j.nucengdes.2008.12.009
1104
S.V. Bechta et al. / Nuclear Engineering and Design 239 (2009) 1103–1112
with the results of all METCOR tests on the mentioned interactions in the oxidizing atmosphere. 2. Experimental facility and methodology Two experiments with UO2+x –ZrO2 corium were conducted at the facilities of the RASPLAV platform, which are based on the technology of induction melting in a cold crucible (IMCC) (Petrov, 1983). Test MC10 was performed at the RASPLAV-2 facility, and MCP-2 – at RASPLAV-3; they operate at different inductor current frequencies. A full description of the setups and methodologies of experimental apparatus and the post-test analyses, which were nevertheless similar in MC10 and MCP-2, is presented in Bechta et al. (2006a,b, 2008). Fig. 1 shows the diagram of the induction furnace. To minimize, to the greatest extent possible, the influence of the electromagnetic (EM) field on the corrosion process, the specimen (12) and the volume above the specimen pool are shielded from the field in all METCOR experiments. The shielding is achieved by welding the gaps between the cold crucible sections (7) at the specimen elevation, by the positioning of a movable water-cooled EM screen (17) around the steel specimen and melt. The overlying melt (9) would also contribute to shielding the steel surface. A minor difference of MC10 furnace (steam atmosphere) in comparison with MCP-2 (air) is in the lid design, which in MC10 provided steam supply and minimized its condensation on water-cooled surfaces. For the same purpose pyrometer shaft was water-cooled. The shaft in MC10 was shortly inserted into the furnace for measuring the melt surface temperature, while blowing the pyrometer spot with high-purity nitrogen to avoid any aerosols affecting the result. A 1700 g of 71% UO2+x –29% ZrO2 furnace charge (mass%) was used in the both experiments. The VVER vessel steel specimens (Fig. 2, mass%: C: 0.17; Si: 0.24; Mn: 0.5; Cr: 1.93; Ni: 1.28; Mo: 0.52; V: 0.08; and Fe: the rest) in the design and thermocouple (TC) location scheme were identical to those tested in Bechta et al. (2006a, 2008). Calorimeters (14, 15, Fig. 1) were used for specimen cooling. In the experiments the corrosion depth was continuously measured in the central zone of the specimen surface (approximately 15-mm diameter) using the ultra-sonic sensor (USS, 16 in Fig. 1).
Fig. 2. Vessel steel specimen.
The on-line measurements of corrosion depth, temperature profile of the specimen and melt surface temperature, which was in the range of 2700–2800 ◦ C, were accompanied by the measurements of cooling water temperature and flow-rate as well as the electrical parameters of induction system. Each experiment included several ‘quasi-stationary’ regimes of gradually increasing specimen surface temperature. After reaching a certain temperature the specimen-corium system was held at these conditions for a predetermined period of time. After that the melt-specimen heat flux was increased either by a higher power deposition in the melt (rise in melt temperature) or by moving either the crucible (7, Fig. 1) or the EM screen (17) versus the inductor (8). At each quasi-stationary regime efforts were taken to keep the interaction interface temperature (and heat flux into the specimen) stable by adjusting the inductor voltage. Upon completion of the experiment, the electromagnetic heating was disconnected and the melt was allowed to crystallize. The ingot was then cooled in steam or air. The post-test analysis included a series of physicochemical studies of the specimen and corium ingot, as well as the numerical modeling of molten pool thermohydrodynamics and specimen temperature conditions. 3. Experimental results
Fig. 1. Diagram of the induction furnace. 1: Gas and aerosol out; 2: steam in; 3: pyrometer shaft; 4: lid; 5: quartz tubes; 6: EM screen hanger tube; 7: crucible sections; 8: inductor; 9: melt; 10: acoustic defect; 11: ZrO2 insulation; 12: vessel steel specimen; 13: K-type TCs; 14: top calorimeter of the specimen; 15: bottom calorimeter of the specimen; 16: ultra-sonic sensor (USS) and 17: EM screen.
Three regimes were reached in MC10. Fig. 3 shows TC readings. A small increase of power supply after the third regime caused sharp temperature growth on the specimen surface, which was accompanied by the steel melting. This was due to the temperature instability caused by corium/steel interaction at elevated temperatures/heat fluxes; the applied inductor voltage adjustment failed to keep the temperature stable. Then the temperature was lowered by a significant inductor power drop, and the experiment was completed after a short exposure time. Fig. 4 shows the specimen corrosion depth measured by the USS. As the temperature on the interaction interface grows, the corrosion rate accelerates. During the above-mentioned brief period of steel melting its rate was substantially higher than the maximum corrosion rate. The final ablation depth (corrosion and melting) in the USS sighting spot, which was measured after the test, was 5.15 mm, which agrees with the on-line measurements. 9 regimes were reached in МCР-2. Figs. 5 and 6 show thermocouple readings and measured specimen corrosion depth. The on-line measurements of the corrosion depth in the 1st regime were unreliable due to technical problems, for this reason the corrosion depth in the beginning of the 2nd regime was used for corrosion rate estimation in the 1st regime (thin line in Fig. 6). As
S.V. Bechta et al. / Nuclear Engineering and Design 239 (2009) 1103–1112
Fig. 3. Thermocouple readings in MC10. 1–3: regime number; - - -: regime time periods, r: radial distance from the specimen axis to the hot junction and z: distance of thermocouple junction from the surface.
1105
Fig. 4. Specimen corrosion depth in MC10. 䊉: post-test measurement; 1–3: regime numbers; - - -: regime time frames.
Fig. 5. Thermocouple readings in MCP-2. 1–9: regime number; - - -: regime time periods, r: radial distance from the specimen axis to the hot junction and z: distance of thermocouple junction from the surface.
Fig. 6. Specimen corrosion depth in MCP-2. 1–9: regime numbers; –– on-line measurements; measurement.
linearization of the 1st regime - - - -: regime timeframes;
: post-test
1106
S.V. Bechta et al. / Nuclear Engineering and Design 239 (2009) 1103–1112
Table 1 Matrix of experiments with UO2+x –ZrO2 corium in the oxidizing atmosphere. Test
Atmosphere
Regime no.
Temperature of the specimen surface (◦ C)
Heat flux (MW/m2 )
Corrosion rate (mm/h)
MC10
Steam
1 2 3
1035 1185 1235
0.95 1.05 1.1
0.55 1.07 2.07
MCP-2
Air
1 2 3 4 5 6 7 8 9
870 950 1080 1165 1210 1230 1325 1350 1370
0.74 0.81 0.92 1.0 1.04 1.06 1.15 1.17 1.19
0.085 0.13 0.7 1.77 2.38 3.46 4.25 4.75 5.8
the corrosion rate increased following the temperature growth on the interaction interface, the duration of regimes shortened. Posttest measurements of corrosion depth also practically coincide with the on-line data. Similar to tests with corium UO2+x –ZrO2 –FeOy , in MC10, the corrosion rate for MCP-2 at constant interface temperature and corium-specimen heat flux practically does not change in time.
4. Post-test analysis A numerical modeling of specimen temperature conditions was performed in order to estimate the temperature and heat flux on the interaction interface in the USS sighting spot for each of the regimes. The examples of methodology and calculation details are given in Bechta et al. (2004, 2006a, 2008). Table 1 shows the measured corrosion rate, along with the calculated temperature and heat flux for all stationary regimes of the MC10 and MCP-2 tests.
Chemical analyses of melt and ingot samples confirmed a high oxygen potential of the corium: e.g. in MC10 U6+ had approximately 8 mass% of the total U6+ and U4+ , and in MCP-2 it was 13–20 mass%. As the steel specimen corrosion was in progress, the corium melt became enriched with iron oxides. X-ray fluorescence (XRF) and chemical analyses of the average ingot samples determined the concentration of iron oxides, which by the end of MC10 was approximately 2 mass%, and in MCP-2–5 mass%. These values agree with the mass losses of steel specimens by the end of the tests. The MCP-2 steel–corium interaction zone was studied by scanning electron microscopy with microprobe analysis (SEM/EDX). Figs. 7–9 show the characteristic microstructures of the interaction zone. It should be noted that the maximum temperature of the MCP-2 interaction interface in the central part of the specimen was 1370 ◦ C. A multi-phase ∼250 m layer on the interface periphery should be mentioned. The boundary with steel has rounded oxidic Fe[CrFe]O4 spinel-based inclusions (Fig. 7), their shape and presence in metal testify to their liquid-phase origin. Next is a
Fig. 7. Interface microstructure in the specimen periphery zone.
S.V. Bechta et al. / Nuclear Engineering and Design 239 (2009) 1103–1112
1107
Fig. 8. Interface microstructure at a distance of a quarter of diameter from the specimen edge.
∼50–100-m thick Wüstite corrosion layer, which consists mostly of the FeO-based (Wüstite) phase. Beside this phase the layer includes at least two more phases: one with a high content of uranium, and another based on the ␥-(Fe, Ni) solid solution. The uranium-bearing phase is observed as far as the boundary with the phase containing rounded spinel inclusions. Eutectically crystallized zones are other interesting formations in this layer: the rounded contours of the phases and the presence of zones having the eutectic crystallization character indicate the liquid-phase condition at the time of the layer formation. Above this multiphase layer is another having a ∼200-m thickness and with large, rounded pores. This layer includes the same phases as the previous layer, but it has more eutectics and ␥-(Fe, Ni) and a smaller content of the FeO-based phase. The overlying layer is enriched with refractory oxidic components and contains eutectically crystallized regions in the iron oxide-based phase. These are oxidic eutectics, which have a different uranium–zirconium ratio in comparison with metallic eutectics observed in the underlying layer. Therefore, a liquid phase is clearly present in the whole interaction zone. The following changes can be seen from the specimen surface periphery to its centre. The layer, in which FeO-based phase prevails, disappears. The presence of metallic eutectics and ␥-(Fe,Ni) solid solution increases, and rounded inclusions of ␥-(Fe, Ni)-based solid solution having a characteristic size of 50–100 m appear in the top part of the zone (Fig. 8). The finely dispersed character and grain boundary alignment of steel spinel-based grains should be also mentioned (Fig. 8).
The presence of tree-like branching cracks typical of the stress corrosion cracking regime is observed closer to the central part (Fig. 9). The layer containing much FeO and metallic eutectics disappears in the center. There, the steel is in direct contact with the ␥-(Fe, Ni) solid solution-based layer. This layer has a few drop-like inclusions of the FeO-based phase. The studied crust was found to have phases of (Zr, U)O2 and (U, Zr)O2 , but there are no indications of the liquid phase presence in the crust at the interaction zone (Fig. 9). Therefore, we can conclude that under these conditions the corrosion layer contained a completely or mainly liquid phase, while most of the corium crust adjacent to the corrosion layer was in the solid state. 5. Model of the process and generalization of experimental data The Tamman equation-based model (Tamman, 1920) of steel corrosion at the interaction with molten corium in the oxidizing above-melt atmosphere was put forward in Bechta et al. (2008).
E 1 a , RT ı
W = A exp −
(1)
where A is pre-exponential factor; Ea is activation energy, J/mol; R = 8.314 J/(mol K) is the universal gas constant; T is temperature, K; ı is total thickness of corrosion layer and corium crust on the steel surface, m. Value ı is determined from the equation of
1108
S.V. Bechta et al. / Nuclear Engineering and Design 239 (2009) 1103–1112
Fig. 9. Interface microstructure in the specimen central zone.
thermal conductivity ı
(Tsol − TS ) = , q
(2)
where is thermal conductivity, W/(m K); Tsol is temperature of corium crust adjacent to the melt, which is equal to solidus temperature of crust average composition, K; TS is temperature of the steel surface, K; q is heat flux, W/m2 . The generalization of experimental data of Bechta et al. (2006b, 2008) was made for the UO2+x –ZrO2 –FeOy corium in accordance with this model in Bechta et al. (2008) and is shown in Fig. 10. The observed corrosion intensification at a temperature on the interaction interface, which is slightly higher than 1050 ◦ C, is explained in Bechta et al. (2008) by the formation of a liquid phase in the corrosion layer and corium crust, which reduces diffusion resistance, as Fe2+ ions move from the steel surface to corium melt. This phenomenon was reflected in the structure of the following correlation:
Ea,1 W (Tsol − TS ) = A1 exp − q RTS
E a,2
+ A2 exp −
RTS
,
correlation in the Arrhenius plot. From this it follows that the contribution of corrosion layer to the total diffusion resistance is negligibly small, even if it is completely solid-phase, especially since its thickness is smaller than corium crust thickness almost by one order. For this reason the observed corrosion intensification at
(3)
where indices 1 and 2 refer to the parameters characterizing the solid-phase and liquid-phase diffusion respectively. Fig. 10 also shows the experimental data for UO2+x –ZrO2 corium, which were provided by MC10, MCP-2 tests. It can be seen that in spite of the liquid phase prevalence in the corrosion layer in the last regimes of MCP-2 (TS > 1300 ◦ C), which was determined by the SEM/EDX analysis, and its complete absence in tests with TS < 1000 ◦ C, all experimental points are described by the linear
Fig. 10. Generalization of experimental data using TS .
S.V. Bechta et al. / Nuclear Engineering and Design 239 (2009) 1103–1112
TS > 1050 ◦ C for UO2+x –ZrO2 –FeOy corium, which has a low solidus temperature (i.e. is a fusible corium), can be primarily explained by the liquid phase formation in the corium crust, but not in the corrosion layer. The liquid phase is formed within the corrosion layer as soon as it reaches the eutectic temperature of the FeO–SiO2 –Cr2 O3 –. . . system. Rapid diffusion processes in the liquid provide the transport of its components to the corium crust zone that has a higher temperature. The transport of oxidized steel components to the fusible corium crust having a high concentration of iron oxides results in the appearance of a liquid phase, the volume of which is sufficient for the formation of channels that percolate through the crust, reduce the crust diffusion resistance, and thus corrosion is intensified (Bechta et al., 2008). In the UO2+x –ZrO2 corium having a high solidus temperature (i.e. a refractory corium) a rather thick crust is formed, which has a small content of iron oxides; the liquid phase generated in the corrosion layer is likely to be insufficient for the penetrating channel formation. Therefore, the formation of liquid phase in the corrosion layer is a necessary, but not a sufficient condition for corrosion intensification. However, if the corrosion layer is neglected and, consequently, its diffusion resistance is disregarded, no modification of the previous corrosion model (Bechta et al., 2008) is required. But an assumption that TS on the right-hand side of Eq. (3) is the critical temperature for corrosion rate (diffusion rate) requires the model to be updated, because, in principle, this assumption does not allow one to take into account a significant temperature change and, correspondingly, diffusion rates through corium crust ıcr . Let us introduce the term of effective temperature, the magnitude of which is in the range between TS and Tsol . It is determined from the following conditions. Time of Fe2+ transport through the corrosion layer and corium crust
ı˙ t1 =
dz , W
(4)
0
T = TS +
The right parts in Eqs. (7) and (8) give the equation, from which Tef can be determined. Tsol − TS = A exp(−Ea /RTef )
z (Tsol − TS ), ı˙
(5)
ı˙ Tsol − TS
Tsol
dT . W
(6)
TS
After expressing W from Eq. (1) and substituting into Eq. (6) we get 2
ıcr t1 = (Tsol − TS )
Tsol
dT . A exp(−Ea /RT )
(7)
TS
In this equation, the thickness of corrosion layer was neglected (which was expressed by the substitution of ı by ıcr ). The effective temperature Tef is taken as the temperature, at which the rate determined by expression (Eq. (1)) at T = Tef ensures the Fe2+ transport time through the corium crust, which is equal to the time evaluated in accordance with expression (Eq. (7)) ıcr t1 = . (1/ıcr ) A exp(−Ea /RTef )
(8)
Tsol
dT . A exp(−Ea /RT )
(9)
TS
Similarly for UO2+x –ZrO2 –FeOy corium Tsol − TS /RT ) + A exp(−E /RT ) A1 exp(−Ea,1 ef ef 2 a,2
Tsol
TS
we can transform expression (Eq. (4)) as t=
Fig. 11. Generalization of experimental data using Tef .
=
where z is surface normal coordinate, m. Taking into account the linear dependence of T from z
1109
dT /RT ) + A exp(−E /RT ) . A1 exp(−Ea,1 2 a,2
(10)
Tsol values can be determined using the following reasoning. The composition of corium in MC10, MCP-2 is close to eutectic of the UO2 –ZrO2 system, i.e. Tsol = Teut = 2550 ◦ C (Grebenschikov, 1991). The phase diagram has not been determined for the superstoichiometric composition, but it is known (Toropov et al., 1970) that as the oxygen content increases, the melting temperature of UO2+x drops from 2750 ◦ C for UO2.05 to 2400 ◦ C for UO2.2 . In accordance with this for UO2+x –ZrO2 the Tsol value was decreased in comparison with Teut of the UO2 –ZrO2 system and was taken as approximately equal to 2450 ◦ C. For UO2+x –ZrO2 –FeOy corium it was assumed that value Tsol is close to Teut = 1340 ◦ C, which was determined in air for eutectic composition, mass%: 61.04% UO2+x –1.74% ZrO2 –37.22% FeOy (Aniskevich et al., 2004). Fig. 11 shows the results of experimental data generalization. Values A and Ea were produced by iteration. The error of experimental points corresponds to the measurement errors—W: 20%, calculated q: 20% and TS : 30 K. The q and TS errors were determined from the comparison of the measured and the calculated values. This resulted in the following correlations, which generalize the experimental data for UO2+x –ZrO2 corium W (2723 − TS ) = 11.6 exp q
1.46 × 105 − RTef
,
(11)
1110
S.V. Bechta et al. / Nuclear Engineering and Design 239 (2009) 1103–1112
for UO2+x –ZrO2 –FeOy corium, W (1613 − TS ) = 0.28 exp q
14
+ 2 × 10
−
5
1.12 × 10 RTef
exp
5.24 × 105 − RTef
(12)
The approximate dependence of Tef from TS using the available A and Ea values is as follows:for UO2+x –ZrO2 corium in Eq. (11) Tef = TS + [0.2 + 2.5 × 10−4 (TS − 1000)] × (2723 − TS ),
(13)
for UO2+x –ZrO2 –FeOy corium in Eq. (12) Tef = TS + [0.31 + 4 × 10−4 (TS − 800)] × (1613 − TS )
(14)
Taking into account a simple single-valued relations between Tef and TS in Eqs. (13) and (14) within certain intervals, in practical application, not Tef , but TS can be used in the correlations for corrosion rate presenting approximations of experimental data. In this case the activation energy is a formal value, which differs from the actual one, and the correlations are simplified without losing accuracy. The corresponding generalization of experimental data is shown in Fig. 10, and the correlations are expressed as follows:for UO2+x –ZrO2 corium W (2723 − TS ) = 4.98 exp q
1.1 × 105 − RTS
for UO2+x –ZrO2 –FeOy corium W (1613 − TS ) = 0.1 exp q
5
0.91 × 10 − RTS
+ 3.4 × 1014 exp
,
(15)
released in the reaction layer, have shown that it can strongly influence both the interaction kinetics and the heat flux across the vessel wall, i.e. the oxidation will affect DNB margins. Therefore, more detailed experimental studies of the effect and its role under the IVR conditions are highly relevant. It is clear that the reported quantitative characteristics are not fully applicable to other reactor vessel steels. But the qualitative effects (like constant corrosion rate vs. time, applicability of the Tamman equation, minor differences in the atmosphere change from air to steam) are expected to be general. The temperature of corrosion activation due to the liquefaction of fusible corium crust is sensitive to steel composition, particularly the content of fusible impurities. For example VVER and 16MNDS steels have a similar content of silicon, which greatly influences the liquefaction of the crust and so the activation temperatures could be also similar. The completed study enables to establish the relation between quantitative characteristics of vessel steel corrosion kinetics at its interaction with molten corium and the phenomena leading to steel oxidation. We should remember that phenomena, which influence steel corrosion at its interaction with suboxidized molten corium, are not related to oxidation (Bechta et al., 2004, 2006a). The first question to be answered is: to what extent diffusion processes in oxidized corium conditions are similar or different from diffusion in air (without interaction with corium). The correlation obtained by using the experimental data (Bechta et al., 2006b,c) on steel oxidation in air is
1 W= 3.32 × 10−7 exp 2
4.99 × 105 − RTS
1.2 × 105 − RTS
1/2 t −1/2 ,
(17)
and for the interaction with UO2 –ZrO2 –FeO in the neutral atmosphere is
(16)
In Eqs. (11)–(16) the following dimensions were used—W: m/s, q: MW/m2 , T: K. The application of correlations (Eqs. (11), (12), (15) and (16)) is limited by the ranges, within which the critical parameters were varied in experiments, specifically: – UO2+x –ZrO2 corium: mass concentration FeOy = 0· · ·5%, atomic ratio U/Zr ≈ 1.1, TS = 870· · ·1370 ◦ C, q = 0.74· · ·1.19 MW/m2 . – UO2+x –ZrO2 –FeOy corium: mass concentration FeOy = 20· · ·30%, atomic ratio U/Zr = 0.11· · ·1.05, TS = 720· · ·1200 ◦ C, 2 q = 0.3· · ·1.3 MW/m . The validity of the resulting correlations can be checked by evaluation of the mean-square deviations of the experimental points, which are 25% for the UO2+x –ZrO2 corium, and 35% for UO2+x –ZrO2 –FeOy . 6. Discussion It should be mentioned that only a limited inventory of parameters for the physicochemical interaction has been studied in the presented work, in particular the steel surface temperature range has been limited. Nevertheless we can clearly observe the corrosion acceleration for fusible corium, when the mentioned temperature reaches the vessel steel liquidus, which is possible under IVR conditions. For example a heat flux of 0.4 MW/m2 estimated for a fully oxidized molten pool in the lower head of a VVER-1000 will inevitably cause partial vessel wall melting. Moreover, the power deposition in the interaction zone is likely to be substantially increased due to chemical reactions. Estimations made in Khabensky et al. (2006), as to the contribution of oxidation energy
1 W= 3.4 × 10−7 exp 2
1.26 × 105 − RTS
1/2 t −1/2 ,
(18)
where W is corrosion rate (m/s), t is time (s), TS is temperature (K). These show that the value of a basic parameter, which characterizes the corrosion process, the activation energy, is practically stable; it stays within the range of (1.0· · ·1.5) × 105 J/mol as determined in Kofstad (1972) and Frost and Ashby (1982) for Fe2+ diffusion in Fe1−x O. The parabolic law of oxidation, which follows from Eqs. (17) and (18), confirms that in both cases the main diffusion resistance for Fe2+ is provided by the growing corrosion layer, which fully or mainly consists of iron monoxide. Similarity to the linear corrosion law, which was demonstrated by the experiments with corium in the oxidizing atmosphere, means that the thickness of the solid corrosion layer (at relatively small values of TS ) practically does not change in time. This phenomenon can be explained by the following processes (Fig. 12). The mass flow of Fe2+ ions from the steel surface through corrosion layer is accompanied by the mass transfer of Fe2+ ions from the surface of corrosion layer through the corium crust into the melt, and with the counter-flow of oxygen ions. Note that the charge compensation during the diffusion, which provides the electric neutrality of each layer, in this case is likely to be performed by the matched transfer of electrons (holes), as it is typical, for example, for the diffusion in Fe1−x O (Kofstad, 1972). The stability of corrosion layer thickness in time meets the condition of a balance between the mentioned mass flows of Fe ions, which is reached when this thickness has a certain concrete “equilibrium value”. At its lower value the mass flow of Fe2+ through the corrosion layer would exceed the mass flow of Fe2+ from the corrosion layer surface, and vice versa, i.e. the corrosion layer thickness would change in time.
S.V. Bechta et al. / Nuclear Engineering and Design 239 (2009) 1103–1112
1111
The experimental data for UO2+x –ZrO2 –FeOy corium in the following correlation:
Ea,1 W = A1 exp − q RTS
Fig. 12. Schematics of diffusion processes in the steel-adjacent layers.
In the thermal gradient conditions of the tests the corrosion layer thickness was determined by the expression ı=
(Tı − TS ) , q
(19)
where is thermal conductivity, W/(m K); Tı , TS are temperature on the external surface of corrosion layer and on the steel surface, respectively, K; q is heat flux from melt to steel through the corrosion layer, W/m2 . Let us make a rough assumption that if TS changes, it causes the change of Fe2+ flow through the corrosion layer, which is “compensated” by a similar change of Fe2+ flow from the external boundary of corrosion layer through the corium crust caused by the changed Tı equal to the changed TS , i.e. at Tı − TS = const. In this case at a certain value, which is not temperature-dependent, corrosion layer thickness ı depends only on q, that is ı∼
1 . q
(20)
The validity of the assumptions can be checked by the posttest measurements of the average corrosion layer thickness. In Regime 4 of MC2 with TS,1 = 720 ◦ C and q1 = 0.3 MW/m2 , ı1 = 0.7 mm (Bechta et al., 2006b), and in Regime 6 of MC12 with TS,2 = 1125 ◦ C and q2 = 1.09 MW/m2 , ı2 = 0.24 mm (Bechta et al., 2008). At this, in accordance with Eq. (20), value (q·ı) should stay constant, i.e. (q2 ·ı2 )/(q1 ·ı1 ) = 1. For the given values of q and ı this ratio is 1.25, which means a 25% difference from 1, which can be regarded as acceptable taking into account the measurement error of typical ı value and a wide parameter range in the considered regimes. Considering Fe2+ diffusion only within the corrosion layer and substituting Eq. (20) in Eq. (1), where ı is replaced by ı, we get
Ea W = A exp − q RT
,
(21)
and due to an insignificant temperature change within the corrosion layer T = TS ,
W Ea = A exp − q RTS
.
(22)
After using the experimental data for UO2+x –ZrO2 corium in Eq. (22), an average value of Ea equal to 1.22 × 105 J/mol was estimated.
E a,2
+ A2 exp −
RTS
,
(23)
was used and the average Ea,1 value for the low-temperature region with a solid corrosion layer was equal to 1.15 × 105 J/mol. These activation energy values are close to each other and to the values typical of the steel oxidation in air (without corium) – 1.2 × 105 J/mol in Eq. (17); and for the interaction with molten corium in case of oxygen deficit −1.26 × 105 J/mol in Eq. (18), which confirms the applicability of Tamman equation for corrosion modeling in various conditions. The activation energy value, which characterizes the process of Fe2+ diffusion in the solid crust (not in the corrosion layer), for UO2+x –ZrO2 –FeOy corium is provided by correlation (Eq. (12)), in accordance with which the activation energy (Ea,1 value) is 1.12 × 105 J/mol. For UO2+x –ZrO2 corium the activation energy value in accordance with Eq. (11) is noticeably higher and equals to 1.46 × 105 J/mol. But we should keep in mind that only some experimental points, which were generalized by correlation (Eq. (11)), correspond to the composition of UO2+x –ZrO2 corium, for which the solidus temperature is taken as equal to 2450 ◦ C. These are the points of Regime 1 in MC10 and Regimes 1 and 2 of MCP-2. During the subsequent regimes of these tests the FeOy concentration grew in corium and in the crust (in MCP-2—up to 5 mass%). An addition of relatively fusible compounds, iron oxides, which form solid solutions with UO2+x and ZrO2 (Grebenschikov, 1991; Toropov et al., 1970; Bechta et al., 2006d, 2007), to UO2+x –ZrO2 leads to the reduction of both liquidus and solidus temperatures of the system. As a result of this the angle of line connecting the experimental points for UO2+x –ZrO2 corium (Fig. 11) is to be smaller, that is, the value of Ea should decrease in comparison with 1.46 × 105 J/mol and, probably get closer to the value obtained for UO2+x –ZrO2 –FeOy corium in the TS temperature range below 1050 ◦ C. In this way, the value of activation energy in the Fe2+ diffusion process, which influences the vessel steel oxidation in all the conditions considered, changes within a rather narrow range close to 1.2 × 105 J/mol. Let us compare the experimental data for refractory and fusible corium in the low-temperature range, where, even in the case of a fusible corium the steel surface crust does not contain a liquid phase (see Eqs. (11) and (12) and Fig. 11). It can be noted that the normalized corrosion rate W(Tsol − TS )/q for refractory corium is 2· · ·3 times higher than for a fusible one. Assuming that in the studied conditions the oxygen concentration in the melt is rather high and the O2− diffusion does not limit the process, the mentioned difference in the corrosion rate can be explained by a considerably smaller Fe concentration in the refractory corium melt than in the fusible one. This explains a larger mass flow of Fe from the inner corium crust boundary into the melt and an accordingly higher corrosion rate for refractory corium than for the fusible one. In terms of mathematics it means only the difference of the pre-exponential factor in the Tamman expression (Eq. (1)). 7. Conclusions The results of studies confirm the general pattern of steel oxidation in air and in its interaction with corium melt in the oxidizing atmosphere, which is influenced by the peculiarities of the Fe2+ ion diffusion. However during the corium–steel interaction in the oxidizing atmosphere the main resistance to diffusion is provided not by the Wüstite corrosion layer, but by the corium crust on its surface.
1112
S.V. Bechta et al. / Nuclear Engineering and Design 239 (2009) 1103–1112
In case of a fusible corium with a high content of iron oxides there is a possibility of corrosion intensification due to the presence of liquid-phase, which form percolation channels through the corium crust. This phenomenon has been proved for the studied vessel steel at temperatures above 1330 K. The available experimental data confirm that in the studied conditions the corrosion rate is practically un-influenced by the change of oxidizing atmosphere (steam, air) but, by contrast, it is sensitive to the corium composition. The resulting correlations given in Eqs. (11), (12), (15), (16) can be used for estimating the vessel steel corrosion factor in future IVR analyses. Acknowledgements This work has been supported by the ISTC (Project # 833 METCOR). Authors express their gratitude to the ISTC staff, in particular to Prof. L. Tocheny, and members of the Contact Expert Group on Severe Accident Management, in particular, to its heads Dr. A. Zurita, and later Dr. M. Hugon and the scientific secretary Dr. P. Hofmann for their valuable recommendations for the work concept, its organization and discussion of results. Authors are grateful to researchers and engineers of NITI, VNIPIET, LSK “RADON”, SPbGETU and ISCh RAS for their creative contribution to the experimental program and physicochemical analysis. Special mention should be given to engineer A. Lysenko (pyrometry), Dr. S. Kotova and engineer V. Blizniuk (chemical analysis), Dr. M. Tolkachev and engineer V. Martynov (SEM/EDX), Dr. I. Kulaghin and engineer A. Chertkov (ultrasonic measurements), engineer V. Bulighin and engineer A. Martynov (electrotechnology of corium melting). References Aniskevich, Yu. A., et al., 2004. Phase diagrams for multicomponent systems containing corium and products of its interaction with NPP materials (CORPHAD).
Investigation of Ternary Oxidic Systems: System UO2+x –ZrO2 –FeOy . Annual Technical Report, Project #1950.2-2003, ISTC. Bechta, S.V., Khabensky, V.B., Granovsky, V.S., et al., 2004. New experimental results on the interaction of molten corium with reactor vessel steel. In: Proceedings of the ICAPP 04, Pittsburgh, USA. Bechta, S.V., Khabensky, V.B., Granovsky, V.S., et al., 2006a. Experimental study of interaction between suboxidized corium and reactor vessel steel. In: Proceedings of the ICAPP 06, Reno, USA. Bechta, S.V., Khabensky, V.B., et al., 2006b. Corrosion of vessel steel during its interaction with molten corium. Part 1. Experimental. NED 236, 1810–1829. Bechta, S.V., Khabensky, V.B., et al., 2006c. Corrosion of vessel steel during its interaction with molten corium. Part 2. Model development. NED 236 (2006), 1362–1370. Bechta, S.V., et al., 2006d. Phase diagram of the ZrO2 –FeO system. J. Nucl. Mater. 348, 114–121. Bechta, S.V., et al., 2007. Phase diagram of the UO2 –FeO1+x system. J. Nucl. Mater. 362, 46–52. Bechta, S.V., et al., 2008. Interactions of UO2+x –ZrO2 –FeOy corium melt with vessel steel of VVER reactor. In: Proceedings of the ICAPP 08, Anaheim, USA. Froment, K., Seiler, J.M., Gueniau, C., et al., 1998. Physico-chemistry and corium properties for in-vessel retention. In: In-vessel Core Debris Retention and Coolability, Workshop Proceedings, 3–6 March 1998, Garching near Munich, Germany. Frost, H.J., Ashby, M.F., 1982. Deformation-mechanism Maps. Pergamon Press, Oxford, New York, Toronto, Sydney, Paris, Frankfurt. Grebenschikov, R.G., 1991. Phase Diagrams of Refractory Oxide Systems. Reference Book, L. Nauka, vol. 5, p. 5, (in Russian). Khabensky, V.B. et al., 2006. Investigation of corium melt interaction with NPP reactor vessel steel (METCOR). Final Technical Report, Project # 833.2-2003, ISTC, A2, 111–113. Kofstad, P., 1972. Nonstoichiometry. In: Diffusion and Electrical Conductivity in Binary Metal Oxides. Wiley-Interscience, New York. Petrov, Yu B., 1983. Induction Melting of Oxides. L.: Energoatomizdat, (in Russian). Tamman, G., 1920. Uber Anlauffarben von Metallen, Z. Anorg. Allg., Chem., B III. H 1.5. 78–89. Theofanous, T.G., et al., 1996. In-vessel coolability and retention of a core melt. DOE/ID-10460. Toropov, N.A., Barzakovsky, V.P., Bondar’, I.A., Udalov, Yu.P., 1970. Phase Diagrams of Silicate Systems. Reference Book, L. Nauka, vol. 1, 2, (in Russian). Wolf, J.R., Rempe, J.L., 1993. TMI-2 vessel investigation project integrated report. INL, TMI V(93)EG10, 5–21.
Contents lists available at ScienceDirect
Nuclear Engineering and Design journal homepage: www.elsevier.com/locate/nucengdes
VVER vessel steel corrosion at interaction with molten corium in oxidizing atmosphere S.V. Bechta a,∗ , V.S. Granovsky a , V.B. Khabensky a , E.V. Krushinov a , S.A. Vitol a , A.A. Sulatsky a , V.V. Gusarov b , V.I. Almiashev b , D.B. Lopukh c , D. Bottomley d , M. Fischer e , P. Piluso f , A. Miassoedov g , W. Tromm g , E. Altstadt h , F. Fichot i , O. Kymalainen j a
Alexandrov Research Institute of Technologies (NITI), Sosnovy Bor, Russia Institute of Silicate Chemistry, Russian Academy of Sciences (ISCh RAS), St. Petersburg, Russia c SPb State Electrotechnical University (SPbGETU), St. Petersburg, Russia d EUROPÄISCHE KOMMISSION, Joint Research Centre Institut für Transurane (ITU), Karlsruhe, Germany e AREVA NP GmbH, Erlangen, Germany f CEA/DEN/DSNI, Saclay, France g Forschungszentrum Karlsruhe, Karlsruhe, Germany h Forschungszentrum Rossendorf (FZR), Dresden, Germany i IRSN/DPAM/SEMCA, St. Paul lez Durance, France j FORTUM Nuclear Services Ltd., Espoo, Finland b
a r t i c l e
i n f o
Article history: Received 23 October 2008 Received in revised form 3 December 2008 Accepted 5 December 2008
a b s t r a c t The long-term in-vessel corium retention (IVR) in the lower head bears a risk of the vessel wall deterioration caused by steel corrosion. The ISTC METCOR Project has studied physicochemical impact of prototypic coria having different compositions in air and steam and has generated valuable experimental data on vessel steel corrosion. It is found that the corrosion rate is sensitive to corium composition, but the composition of oxidizing above-melt atmosphere (air, steam) has practically no influence on it. A model of the corrosion process that integrates the experimental data, is proposed and used for development of correlations. Crown Copyright © 2008 Published by Elsevier B.V. All rights reserved.
1. Introduction In a general case of IVR the vessel integrity depends both on its temperature condition and the wall thickness. The original thickness can be reduced due to a partial steel melting caused by the thermal impact of molten corium. The steel wall can also become thinner due to a physicochemical interaction with the melt. In Theofanous et al. (1996) and Froment et al. (1998), the results of experimental and numerical analyses were used to get the temperature values on the inner surface of the steel wall; the values are critical for the wall thickness during an interaction with the metallic part of the suboxidized corium melt. In the publications Bechta et al. (2004, 2006a) experimental studies of interaction between the melt of suboxidized corium and VVER vessel steel are presented which were carried out within the ISTC METCOR project. It was established that steel corrosion resulted from the partitioning of elements such as Fe, U, and Zr
∗ Corresponding author at: NITI, Sosnovy Bor, Leningrad Oblast 188540, Russia. Tel.: +7 81369 60 675; fax: +7 81369 23 672. E-mail address: [email protected] (S.V. Bechta).
between molten corium and steel, formation and liquefaction of surface Fe–U–Zr–O layer. The minimum steel temperature, at which corrosion stops, was determined; the correlations describing steel corrosion kinetics during the interaction with oxidic and metallic parts of the melt were developed. But we cannot exclude a complete oxidation of corium relocated to the lower head for the whole range of reactors, in which IVR is foreseen, and for different scenarios of severe accident progression, in particular, during the implementation of specific severe accident management strategies. This is confirmed by the TMI-2 post-accident studies of corium (Wolf and Rempe, 1993). The mentioned circumstances stipulate the relevance of studies examining steel corrosion at its interaction with oxidized corium, particularly, in presence of the oxidizing above-melt atmosphere. These studies were also carried out within the METCOR project. In the publications Bechta et al. (2006b,c, 2008) the experimental data for UO2+x –ZrO2 –FeOy corium are presented, and the main result from this data is that vessel corrosion is caused by steel oxidation. Along with UO2+x –ZrO2 –FeOy studies, the METCOR project included experiments with UO2+x –ZrO2 corium in oxidizing atmosphere. This article gives and analyses the available data together
0029-5493/$ – see front matter. Crown Copyright © 2008 Published by Elsevier B.V. All rights reserved. doi:10.1016/j.nucengdes.2008.12.009
1104
S.V. Bechta et al. / Nuclear Engineering and Design 239 (2009) 1103–1112
with the results of all METCOR tests on the mentioned interactions in the oxidizing atmosphere. 2. Experimental facility and methodology Two experiments with UO2+x –ZrO2 corium were conducted at the facilities of the RASPLAV platform, which are based on the technology of induction melting in a cold crucible (IMCC) (Petrov, 1983). Test MC10 was performed at the RASPLAV-2 facility, and MCP-2 – at RASPLAV-3; they operate at different inductor current frequencies. A full description of the setups and methodologies of experimental apparatus and the post-test analyses, which were nevertheless similar in MC10 and MCP-2, is presented in Bechta et al. (2006a,b, 2008). Fig. 1 shows the diagram of the induction furnace. To minimize, to the greatest extent possible, the influence of the electromagnetic (EM) field on the corrosion process, the specimen (12) and the volume above the specimen pool are shielded from the field in all METCOR experiments. The shielding is achieved by welding the gaps between the cold crucible sections (7) at the specimen elevation, by the positioning of a movable water-cooled EM screen (17) around the steel specimen and melt. The overlying melt (9) would also contribute to shielding the steel surface. A minor difference of MC10 furnace (steam atmosphere) in comparison with MCP-2 (air) is in the lid design, which in MC10 provided steam supply and minimized its condensation on water-cooled surfaces. For the same purpose pyrometer shaft was water-cooled. The shaft in MC10 was shortly inserted into the furnace for measuring the melt surface temperature, while blowing the pyrometer spot with high-purity nitrogen to avoid any aerosols affecting the result. A 1700 g of 71% UO2+x –29% ZrO2 furnace charge (mass%) was used in the both experiments. The VVER vessel steel specimens (Fig. 2, mass%: C: 0.17; Si: 0.24; Mn: 0.5; Cr: 1.93; Ni: 1.28; Mo: 0.52; V: 0.08; and Fe: the rest) in the design and thermocouple (TC) location scheme were identical to those tested in Bechta et al. (2006a, 2008). Calorimeters (14, 15, Fig. 1) were used for specimen cooling. In the experiments the corrosion depth was continuously measured in the central zone of the specimen surface (approximately 15-mm diameter) using the ultra-sonic sensor (USS, 16 in Fig. 1).
Fig. 2. Vessel steel specimen.
The on-line measurements of corrosion depth, temperature profile of the specimen and melt surface temperature, which was in the range of 2700–2800 ◦ C, were accompanied by the measurements of cooling water temperature and flow-rate as well as the electrical parameters of induction system. Each experiment included several ‘quasi-stationary’ regimes of gradually increasing specimen surface temperature. After reaching a certain temperature the specimen-corium system was held at these conditions for a predetermined period of time. After that the melt-specimen heat flux was increased either by a higher power deposition in the melt (rise in melt temperature) or by moving either the crucible (7, Fig. 1) or the EM screen (17) versus the inductor (8). At each quasi-stationary regime efforts were taken to keep the interaction interface temperature (and heat flux into the specimen) stable by adjusting the inductor voltage. Upon completion of the experiment, the electromagnetic heating was disconnected and the melt was allowed to crystallize. The ingot was then cooled in steam or air. The post-test analysis included a series of physicochemical studies of the specimen and corium ingot, as well as the numerical modeling of molten pool thermohydrodynamics and specimen temperature conditions. 3. Experimental results
Fig. 1. Diagram of the induction furnace. 1: Gas and aerosol out; 2: steam in; 3: pyrometer shaft; 4: lid; 5: quartz tubes; 6: EM screen hanger tube; 7: crucible sections; 8: inductor; 9: melt; 10: acoustic defect; 11: ZrO2 insulation; 12: vessel steel specimen; 13: K-type TCs; 14: top calorimeter of the specimen; 15: bottom calorimeter of the specimen; 16: ultra-sonic sensor (USS) and 17: EM screen.
Three regimes were reached in MC10. Fig. 3 shows TC readings. A small increase of power supply after the third regime caused sharp temperature growth on the specimen surface, which was accompanied by the steel melting. This was due to the temperature instability caused by corium/steel interaction at elevated temperatures/heat fluxes; the applied inductor voltage adjustment failed to keep the temperature stable. Then the temperature was lowered by a significant inductor power drop, and the experiment was completed after a short exposure time. Fig. 4 shows the specimen corrosion depth measured by the USS. As the temperature on the interaction interface grows, the corrosion rate accelerates. During the above-mentioned brief period of steel melting its rate was substantially higher than the maximum corrosion rate. The final ablation depth (corrosion and melting) in the USS sighting spot, which was measured after the test, was 5.15 mm, which agrees with the on-line measurements. 9 regimes were reached in МCР-2. Figs. 5 and 6 show thermocouple readings and measured specimen corrosion depth. The on-line measurements of the corrosion depth in the 1st regime were unreliable due to technical problems, for this reason the corrosion depth in the beginning of the 2nd regime was used for corrosion rate estimation in the 1st regime (thin line in Fig. 6). As
S.V. Bechta et al. / Nuclear Engineering and Design 239 (2009) 1103–1112
Fig. 3. Thermocouple readings in MC10. 1–3: regime number; - - -: regime time periods, r: radial distance from the specimen axis to the hot junction and z: distance of thermocouple junction from the surface.
1105
Fig. 4. Specimen corrosion depth in MC10. 䊉: post-test measurement; 1–3: regime numbers; - - -: regime time frames.
Fig. 5. Thermocouple readings in MCP-2. 1–9: regime number; - - -: regime time periods, r: radial distance from the specimen axis to the hot junction and z: distance of thermocouple junction from the surface.
Fig. 6. Specimen corrosion depth in MCP-2. 1–9: regime numbers; –– on-line measurements; measurement.
linearization of the 1st regime - - - -: regime timeframes;
: post-test
1106
S.V. Bechta et al. / Nuclear Engineering and Design 239 (2009) 1103–1112
Table 1 Matrix of experiments with UO2+x –ZrO2 corium in the oxidizing atmosphere. Test
Atmosphere
Regime no.
Temperature of the specimen surface (◦ C)
Heat flux (MW/m2 )
Corrosion rate (mm/h)
MC10
Steam
1 2 3
1035 1185 1235
0.95 1.05 1.1
0.55 1.07 2.07
MCP-2
Air
1 2 3 4 5 6 7 8 9
870 950 1080 1165 1210 1230 1325 1350 1370
0.74 0.81 0.92 1.0 1.04 1.06 1.15 1.17 1.19
0.085 0.13 0.7 1.77 2.38 3.46 4.25 4.75 5.8
the corrosion rate increased following the temperature growth on the interaction interface, the duration of regimes shortened. Posttest measurements of corrosion depth also practically coincide with the on-line data. Similar to tests with corium UO2+x –ZrO2 –FeOy , in MC10, the corrosion rate for MCP-2 at constant interface temperature and corium-specimen heat flux practically does not change in time.
4. Post-test analysis A numerical modeling of specimen temperature conditions was performed in order to estimate the temperature and heat flux on the interaction interface in the USS sighting spot for each of the regimes. The examples of methodology and calculation details are given in Bechta et al. (2004, 2006a, 2008). Table 1 shows the measured corrosion rate, along with the calculated temperature and heat flux for all stationary regimes of the MC10 and MCP-2 tests.
Chemical analyses of melt and ingot samples confirmed a high oxygen potential of the corium: e.g. in MC10 U6+ had approximately 8 mass% of the total U6+ and U4+ , and in MCP-2 it was 13–20 mass%. As the steel specimen corrosion was in progress, the corium melt became enriched with iron oxides. X-ray fluorescence (XRF) and chemical analyses of the average ingot samples determined the concentration of iron oxides, which by the end of MC10 was approximately 2 mass%, and in MCP-2–5 mass%. These values agree with the mass losses of steel specimens by the end of the tests. The MCP-2 steel–corium interaction zone was studied by scanning electron microscopy with microprobe analysis (SEM/EDX). Figs. 7–9 show the characteristic microstructures of the interaction zone. It should be noted that the maximum temperature of the MCP-2 interaction interface in the central part of the specimen was 1370 ◦ C. A multi-phase ∼250 m layer on the interface periphery should be mentioned. The boundary with steel has rounded oxidic Fe[CrFe]O4 spinel-based inclusions (Fig. 7), their shape and presence in metal testify to their liquid-phase origin. Next is a
Fig. 7. Interface microstructure in the specimen periphery zone.
S.V. Bechta et al. / Nuclear Engineering and Design 239 (2009) 1103–1112
1107
Fig. 8. Interface microstructure at a distance of a quarter of diameter from the specimen edge.
∼50–100-m thick Wüstite corrosion layer, which consists mostly of the FeO-based (Wüstite) phase. Beside this phase the layer includes at least two more phases: one with a high content of uranium, and another based on the ␥-(Fe, Ni) solid solution. The uranium-bearing phase is observed as far as the boundary with the phase containing rounded spinel inclusions. Eutectically crystallized zones are other interesting formations in this layer: the rounded contours of the phases and the presence of zones having the eutectic crystallization character indicate the liquid-phase condition at the time of the layer formation. Above this multiphase layer is another having a ∼200-m thickness and with large, rounded pores. This layer includes the same phases as the previous layer, but it has more eutectics and ␥-(Fe, Ni) and a smaller content of the FeO-based phase. The overlying layer is enriched with refractory oxidic components and contains eutectically crystallized regions in the iron oxide-based phase. These are oxidic eutectics, which have a different uranium–zirconium ratio in comparison with metallic eutectics observed in the underlying layer. Therefore, a liquid phase is clearly present in the whole interaction zone. The following changes can be seen from the specimen surface periphery to its centre. The layer, in which FeO-based phase prevails, disappears. The presence of metallic eutectics and ␥-(Fe,Ni) solid solution increases, and rounded inclusions of ␥-(Fe, Ni)-based solid solution having a characteristic size of 50–100 m appear in the top part of the zone (Fig. 8). The finely dispersed character and grain boundary alignment of steel spinel-based grains should be also mentioned (Fig. 8).
The presence of tree-like branching cracks typical of the stress corrosion cracking regime is observed closer to the central part (Fig. 9). The layer containing much FeO and metallic eutectics disappears in the center. There, the steel is in direct contact with the ␥-(Fe, Ni) solid solution-based layer. This layer has a few drop-like inclusions of the FeO-based phase. The studied crust was found to have phases of (Zr, U)O2 and (U, Zr)O2 , but there are no indications of the liquid phase presence in the crust at the interaction zone (Fig. 9). Therefore, we can conclude that under these conditions the corrosion layer contained a completely or mainly liquid phase, while most of the corium crust adjacent to the corrosion layer was in the solid state. 5. Model of the process and generalization of experimental data The Tamman equation-based model (Tamman, 1920) of steel corrosion at the interaction with molten corium in the oxidizing above-melt atmosphere was put forward in Bechta et al. (2008).
E 1 a , RT ı
W = A exp −
(1)
where A is pre-exponential factor; Ea is activation energy, J/mol; R = 8.314 J/(mol K) is the universal gas constant; T is temperature, K; ı is total thickness of corrosion layer and corium crust on the steel surface, m. Value ı is determined from the equation of
1108
S.V. Bechta et al. / Nuclear Engineering and Design 239 (2009) 1103–1112
Fig. 9. Interface microstructure in the specimen central zone.
thermal conductivity ı
(Tsol − TS ) = , q
(2)
where is thermal conductivity, W/(m K); Tsol is temperature of corium crust adjacent to the melt, which is equal to solidus temperature of crust average composition, K; TS is temperature of the steel surface, K; q is heat flux, W/m2 . The generalization of experimental data of Bechta et al. (2006b, 2008) was made for the UO2+x –ZrO2 –FeOy corium in accordance with this model in Bechta et al. (2008) and is shown in Fig. 10. The observed corrosion intensification at a temperature on the interaction interface, which is slightly higher than 1050 ◦ C, is explained in Bechta et al. (2008) by the formation of a liquid phase in the corrosion layer and corium crust, which reduces diffusion resistance, as Fe2+ ions move from the steel surface to corium melt. This phenomenon was reflected in the structure of the following correlation:
Ea,1 W (Tsol − TS ) = A1 exp − q RTS
E a,2
+ A2 exp −
RTS
,
correlation in the Arrhenius plot. From this it follows that the contribution of corrosion layer to the total diffusion resistance is negligibly small, even if it is completely solid-phase, especially since its thickness is smaller than corium crust thickness almost by one order. For this reason the observed corrosion intensification at
(3)
where indices 1 and 2 refer to the parameters characterizing the solid-phase and liquid-phase diffusion respectively. Fig. 10 also shows the experimental data for UO2+x –ZrO2 corium, which were provided by MC10, MCP-2 tests. It can be seen that in spite of the liquid phase prevalence in the corrosion layer in the last regimes of MCP-2 (TS > 1300 ◦ C), which was determined by the SEM/EDX analysis, and its complete absence in tests with TS < 1000 ◦ C, all experimental points are described by the linear
Fig. 10. Generalization of experimental data using TS .
S.V. Bechta et al. / Nuclear Engineering and Design 239 (2009) 1103–1112
TS > 1050 ◦ C for UO2+x –ZrO2 –FeOy corium, which has a low solidus temperature (i.e. is a fusible corium), can be primarily explained by the liquid phase formation in the corium crust, but not in the corrosion layer. The liquid phase is formed within the corrosion layer as soon as it reaches the eutectic temperature of the FeO–SiO2 –Cr2 O3 –. . . system. Rapid diffusion processes in the liquid provide the transport of its components to the corium crust zone that has a higher temperature. The transport of oxidized steel components to the fusible corium crust having a high concentration of iron oxides results in the appearance of a liquid phase, the volume of which is sufficient for the formation of channels that percolate through the crust, reduce the crust diffusion resistance, and thus corrosion is intensified (Bechta et al., 2008). In the UO2+x –ZrO2 corium having a high solidus temperature (i.e. a refractory corium) a rather thick crust is formed, which has a small content of iron oxides; the liquid phase generated in the corrosion layer is likely to be insufficient for the penetrating channel formation. Therefore, the formation of liquid phase in the corrosion layer is a necessary, but not a sufficient condition for corrosion intensification. However, if the corrosion layer is neglected and, consequently, its diffusion resistance is disregarded, no modification of the previous corrosion model (Bechta et al., 2008) is required. But an assumption that TS on the right-hand side of Eq. (3) is the critical temperature for corrosion rate (diffusion rate) requires the model to be updated, because, in principle, this assumption does not allow one to take into account a significant temperature change and, correspondingly, diffusion rates through corium crust ıcr . Let us introduce the term of effective temperature, the magnitude of which is in the range between TS and Tsol . It is determined from the following conditions. Time of Fe2+ transport through the corrosion layer and corium crust
ı˙ t1 =
dz , W
(4)
0
T = TS +
The right parts in Eqs. (7) and (8) give the equation, from which Tef can be determined. Tsol − TS = A exp(−Ea /RTef )
z (Tsol − TS ), ı˙
(5)
ı˙ Tsol − TS
Tsol
dT . W
(6)
TS
After expressing W from Eq. (1) and substituting into Eq. (6) we get 2
ıcr t1 = (Tsol − TS )
Tsol
dT . A exp(−Ea /RT )
(7)
TS
In this equation, the thickness of corrosion layer was neglected (which was expressed by the substitution of ı by ıcr ). The effective temperature Tef is taken as the temperature, at which the rate determined by expression (Eq. (1)) at T = Tef ensures the Fe2+ transport time through the corium crust, which is equal to the time evaluated in accordance with expression (Eq. (7)) ıcr t1 = . (1/ıcr ) A exp(−Ea /RTef )
(8)
Tsol
dT . A exp(−Ea /RT )
(9)
TS
Similarly for UO2+x –ZrO2 –FeOy corium Tsol − TS /RT ) + A exp(−E /RT ) A1 exp(−Ea,1 ef ef 2 a,2
Tsol
TS
we can transform expression (Eq. (4)) as t=
Fig. 11. Generalization of experimental data using Tef .
=
where z is surface normal coordinate, m. Taking into account the linear dependence of T from z
1109
dT /RT ) + A exp(−E /RT ) . A1 exp(−Ea,1 2 a,2
(10)
Tsol values can be determined using the following reasoning. The composition of corium in MC10, MCP-2 is close to eutectic of the UO2 –ZrO2 system, i.e. Tsol = Teut = 2550 ◦ C (Grebenschikov, 1991). The phase diagram has not been determined for the superstoichiometric composition, but it is known (Toropov et al., 1970) that as the oxygen content increases, the melting temperature of UO2+x drops from 2750 ◦ C for UO2.05 to 2400 ◦ C for UO2.2 . In accordance with this for UO2+x –ZrO2 the Tsol value was decreased in comparison with Teut of the UO2 –ZrO2 system and was taken as approximately equal to 2450 ◦ C. For UO2+x –ZrO2 –FeOy corium it was assumed that value Tsol is close to Teut = 1340 ◦ C, which was determined in air for eutectic composition, mass%: 61.04% UO2+x –1.74% ZrO2 –37.22% FeOy (Aniskevich et al., 2004). Fig. 11 shows the results of experimental data generalization. Values A and Ea were produced by iteration. The error of experimental points corresponds to the measurement errors—W: 20%, calculated q: 20% and TS : 30 K. The q and TS errors were determined from the comparison of the measured and the calculated values. This resulted in the following correlations, which generalize the experimental data for UO2+x –ZrO2 corium W (2723 − TS ) = 11.6 exp q
1.46 × 105 − RTef
,
(11)
1110
S.V. Bechta et al. / Nuclear Engineering and Design 239 (2009) 1103–1112
for UO2+x –ZrO2 –FeOy corium, W (1613 − TS ) = 0.28 exp q
14
+ 2 × 10
−
5
1.12 × 10 RTef
exp
5.24 × 105 − RTef
(12)
The approximate dependence of Tef from TS using the available A and Ea values is as follows:for UO2+x –ZrO2 corium in Eq. (11) Tef = TS + [0.2 + 2.5 × 10−4 (TS − 1000)] × (2723 − TS ),
(13)
for UO2+x –ZrO2 –FeOy corium in Eq. (12) Tef = TS + [0.31 + 4 × 10−4 (TS − 800)] × (1613 − TS )
(14)
Taking into account a simple single-valued relations between Tef and TS in Eqs. (13) and (14) within certain intervals, in practical application, not Tef , but TS can be used in the correlations for corrosion rate presenting approximations of experimental data. In this case the activation energy is a formal value, which differs from the actual one, and the correlations are simplified without losing accuracy. The corresponding generalization of experimental data is shown in Fig. 10, and the correlations are expressed as follows:for UO2+x –ZrO2 corium W (2723 − TS ) = 4.98 exp q
1.1 × 105 − RTS
for UO2+x –ZrO2 –FeOy corium W (1613 − TS ) = 0.1 exp q
5
0.91 × 10 − RTS
+ 3.4 × 1014 exp
,
(15)
released in the reaction layer, have shown that it can strongly influence both the interaction kinetics and the heat flux across the vessel wall, i.e. the oxidation will affect DNB margins. Therefore, more detailed experimental studies of the effect and its role under the IVR conditions are highly relevant. It is clear that the reported quantitative characteristics are not fully applicable to other reactor vessel steels. But the qualitative effects (like constant corrosion rate vs. time, applicability of the Tamman equation, minor differences in the atmosphere change from air to steam) are expected to be general. The temperature of corrosion activation due to the liquefaction of fusible corium crust is sensitive to steel composition, particularly the content of fusible impurities. For example VVER and 16MNDS steels have a similar content of silicon, which greatly influences the liquefaction of the crust and so the activation temperatures could be also similar. The completed study enables to establish the relation between quantitative characteristics of vessel steel corrosion kinetics at its interaction with molten corium and the phenomena leading to steel oxidation. We should remember that phenomena, which influence steel corrosion at its interaction with suboxidized molten corium, are not related to oxidation (Bechta et al., 2004, 2006a). The first question to be answered is: to what extent diffusion processes in oxidized corium conditions are similar or different from diffusion in air (without interaction with corium). The correlation obtained by using the experimental data (Bechta et al., 2006b,c) on steel oxidation in air is
1 W= 3.32 × 10−7 exp 2
4.99 × 105 − RTS
1.2 × 105 − RTS
1/2 t −1/2 ,
(17)
and for the interaction with UO2 –ZrO2 –FeO in the neutral atmosphere is
(16)
In Eqs. (11)–(16) the following dimensions were used—W: m/s, q: MW/m2 , T: K. The application of correlations (Eqs. (11), (12), (15) and (16)) is limited by the ranges, within which the critical parameters were varied in experiments, specifically: – UO2+x –ZrO2 corium: mass concentration FeOy = 0· · ·5%, atomic ratio U/Zr ≈ 1.1, TS = 870· · ·1370 ◦ C, q = 0.74· · ·1.19 MW/m2 . – UO2+x –ZrO2 –FeOy corium: mass concentration FeOy = 20· · ·30%, atomic ratio U/Zr = 0.11· · ·1.05, TS = 720· · ·1200 ◦ C, 2 q = 0.3· · ·1.3 MW/m . The validity of the resulting correlations can be checked by evaluation of the mean-square deviations of the experimental points, which are 25% for the UO2+x –ZrO2 corium, and 35% for UO2+x –ZrO2 –FeOy . 6. Discussion It should be mentioned that only a limited inventory of parameters for the physicochemical interaction has been studied in the presented work, in particular the steel surface temperature range has been limited. Nevertheless we can clearly observe the corrosion acceleration for fusible corium, when the mentioned temperature reaches the vessel steel liquidus, which is possible under IVR conditions. For example a heat flux of 0.4 MW/m2 estimated for a fully oxidized molten pool in the lower head of a VVER-1000 will inevitably cause partial vessel wall melting. Moreover, the power deposition in the interaction zone is likely to be substantially increased due to chemical reactions. Estimations made in Khabensky et al. (2006), as to the contribution of oxidation energy
1 W= 3.4 × 10−7 exp 2
1.26 × 105 − RTS
1/2 t −1/2 ,
(18)
where W is corrosion rate (m/s), t is time (s), TS is temperature (K). These show that the value of a basic parameter, which characterizes the corrosion process, the activation energy, is practically stable; it stays within the range of (1.0· · ·1.5) × 105 J/mol as determined in Kofstad (1972) and Frost and Ashby (1982) for Fe2+ diffusion in Fe1−x O. The parabolic law of oxidation, which follows from Eqs. (17) and (18), confirms that in both cases the main diffusion resistance for Fe2+ is provided by the growing corrosion layer, which fully or mainly consists of iron monoxide. Similarity to the linear corrosion law, which was demonstrated by the experiments with corium in the oxidizing atmosphere, means that the thickness of the solid corrosion layer (at relatively small values of TS ) practically does not change in time. This phenomenon can be explained by the following processes (Fig. 12). The mass flow of Fe2+ ions from the steel surface through corrosion layer is accompanied by the mass transfer of Fe2+ ions from the surface of corrosion layer through the corium crust into the melt, and with the counter-flow of oxygen ions. Note that the charge compensation during the diffusion, which provides the electric neutrality of each layer, in this case is likely to be performed by the matched transfer of electrons (holes), as it is typical, for example, for the diffusion in Fe1−x O (Kofstad, 1972). The stability of corrosion layer thickness in time meets the condition of a balance between the mentioned mass flows of Fe ions, which is reached when this thickness has a certain concrete “equilibrium value”. At its lower value the mass flow of Fe2+ through the corrosion layer would exceed the mass flow of Fe2+ from the corrosion layer surface, and vice versa, i.e. the corrosion layer thickness would change in time.
S.V. Bechta et al. / Nuclear Engineering and Design 239 (2009) 1103–1112
1111
The experimental data for UO2+x –ZrO2 –FeOy corium in the following correlation:
Ea,1 W = A1 exp − q RTS
Fig. 12. Schematics of diffusion processes in the steel-adjacent layers.
In the thermal gradient conditions of the tests the corrosion layer thickness was determined by the expression ı=
(Tı − TS ) , q
(19)
where is thermal conductivity, W/(m K); Tı , TS are temperature on the external surface of corrosion layer and on the steel surface, respectively, K; q is heat flux from melt to steel through the corrosion layer, W/m2 . Let us make a rough assumption that if TS changes, it causes the change of Fe2+ flow through the corrosion layer, which is “compensated” by a similar change of Fe2+ flow from the external boundary of corrosion layer through the corium crust caused by the changed Tı equal to the changed TS , i.e. at Tı − TS = const. In this case at a certain value, which is not temperature-dependent, corrosion layer thickness ı depends only on q, that is ı∼
1 . q
(20)
The validity of the assumptions can be checked by the posttest measurements of the average corrosion layer thickness. In Regime 4 of MC2 with TS,1 = 720 ◦ C and q1 = 0.3 MW/m2 , ı1 = 0.7 mm (Bechta et al., 2006b), and in Regime 6 of MC12 with TS,2 = 1125 ◦ C and q2 = 1.09 MW/m2 , ı2 = 0.24 mm (Bechta et al., 2008). At this, in accordance with Eq. (20), value (q·ı) should stay constant, i.e. (q2 ·ı2 )/(q1 ·ı1 ) = 1. For the given values of q and ı this ratio is 1.25, which means a 25% difference from 1, which can be regarded as acceptable taking into account the measurement error of typical ı value and a wide parameter range in the considered regimes. Considering Fe2+ diffusion only within the corrosion layer and substituting Eq. (20) in Eq. (1), where ı is replaced by ı, we get
Ea W = A exp − q RT
,
(21)
and due to an insignificant temperature change within the corrosion layer T = TS ,
W Ea = A exp − q RTS
.
(22)
After using the experimental data for UO2+x –ZrO2 corium in Eq. (22), an average value of Ea equal to 1.22 × 105 J/mol was estimated.
E a,2
+ A2 exp −
RTS
,
(23)
was used and the average Ea,1 value for the low-temperature region with a solid corrosion layer was equal to 1.15 × 105 J/mol. These activation energy values are close to each other and to the values typical of the steel oxidation in air (without corium) – 1.2 × 105 J/mol in Eq. (17); and for the interaction with molten corium in case of oxygen deficit −1.26 × 105 J/mol in Eq. (18), which confirms the applicability of Tamman equation for corrosion modeling in various conditions. The activation energy value, which characterizes the process of Fe2+ diffusion in the solid crust (not in the corrosion layer), for UO2+x –ZrO2 –FeOy corium is provided by correlation (Eq. (12)), in accordance with which the activation energy (Ea,1 value) is 1.12 × 105 J/mol. For UO2+x –ZrO2 corium the activation energy value in accordance with Eq. (11) is noticeably higher and equals to 1.46 × 105 J/mol. But we should keep in mind that only some experimental points, which were generalized by correlation (Eq. (11)), correspond to the composition of UO2+x –ZrO2 corium, for which the solidus temperature is taken as equal to 2450 ◦ C. These are the points of Regime 1 in MC10 and Regimes 1 and 2 of MCP-2. During the subsequent regimes of these tests the FeOy concentration grew in corium and in the crust (in MCP-2—up to 5 mass%). An addition of relatively fusible compounds, iron oxides, which form solid solutions with UO2+x and ZrO2 (Grebenschikov, 1991; Toropov et al., 1970; Bechta et al., 2006d, 2007), to UO2+x –ZrO2 leads to the reduction of both liquidus and solidus temperatures of the system. As a result of this the angle of line connecting the experimental points for UO2+x –ZrO2 corium (Fig. 11) is to be smaller, that is, the value of Ea should decrease in comparison with 1.46 × 105 J/mol and, probably get closer to the value obtained for UO2+x –ZrO2 –FeOy corium in the TS temperature range below 1050 ◦ C. In this way, the value of activation energy in the Fe2+ diffusion process, which influences the vessel steel oxidation in all the conditions considered, changes within a rather narrow range close to 1.2 × 105 J/mol. Let us compare the experimental data for refractory and fusible corium in the low-temperature range, where, even in the case of a fusible corium the steel surface crust does not contain a liquid phase (see Eqs. (11) and (12) and Fig. 11). It can be noted that the normalized corrosion rate W(Tsol − TS )/q for refractory corium is 2· · ·3 times higher than for a fusible one. Assuming that in the studied conditions the oxygen concentration in the melt is rather high and the O2− diffusion does not limit the process, the mentioned difference in the corrosion rate can be explained by a considerably smaller Fe concentration in the refractory corium melt than in the fusible one. This explains a larger mass flow of Fe from the inner corium crust boundary into the melt and an accordingly higher corrosion rate for refractory corium than for the fusible one. In terms of mathematics it means only the difference of the pre-exponential factor in the Tamman expression (Eq. (1)). 7. Conclusions The results of studies confirm the general pattern of steel oxidation in air and in its interaction with corium melt in the oxidizing atmosphere, which is influenced by the peculiarities of the Fe2+ ion diffusion. However during the corium–steel interaction in the oxidizing atmosphere the main resistance to diffusion is provided not by the Wüstite corrosion layer, but by the corium crust on its surface.
1112
S.V. Bechta et al. / Nuclear Engineering and Design 239 (2009) 1103–1112
In case of a fusible corium with a high content of iron oxides there is a possibility of corrosion intensification due to the presence of liquid-phase, which form percolation channels through the corium crust. This phenomenon has been proved for the studied vessel steel at temperatures above 1330 K. The available experimental data confirm that in the studied conditions the corrosion rate is practically un-influenced by the change of oxidizing atmosphere (steam, air) but, by contrast, it is sensitive to the corium composition. The resulting correlations given in Eqs. (11), (12), (15), (16) can be used for estimating the vessel steel corrosion factor in future IVR analyses. Acknowledgements This work has been supported by the ISTC (Project # 833 METCOR). Authors express their gratitude to the ISTC staff, in particular to Prof. L. Tocheny, and members of the Contact Expert Group on Severe Accident Management, in particular, to its heads Dr. A. Zurita, and later Dr. M. Hugon and the scientific secretary Dr. P. Hofmann for their valuable recommendations for the work concept, its organization and discussion of results. Authors are grateful to researchers and engineers of NITI, VNIPIET, LSK “RADON”, SPbGETU and ISCh RAS for their creative contribution to the experimental program and physicochemical analysis. Special mention should be given to engineer A. Lysenko (pyrometry), Dr. S. Kotova and engineer V. Blizniuk (chemical analysis), Dr. M. Tolkachev and engineer V. Martynov (SEM/EDX), Dr. I. Kulaghin and engineer A. Chertkov (ultrasonic measurements), engineer V. Bulighin and engineer A. Martynov (electrotechnology of corium melting). References Aniskevich, Yu. A., et al., 2004. Phase diagrams for multicomponent systems containing corium and products of its interaction with NPP materials (CORPHAD).
Investigation of Ternary Oxidic Systems: System UO2+x –ZrO2 –FeOy . Annual Technical Report, Project #1950.2-2003, ISTC. Bechta, S.V., Khabensky, V.B., Granovsky, V.S., et al., 2004. New experimental results on the interaction of molten corium with reactor vessel steel. In: Proceedings of the ICAPP 04, Pittsburgh, USA. Bechta, S.V., Khabensky, V.B., Granovsky, V.S., et al., 2006a. Experimental study of interaction between suboxidized corium and reactor vessel steel. In: Proceedings of the ICAPP 06, Reno, USA. Bechta, S.V., Khabensky, V.B., et al., 2006b. Corrosion of vessel steel during its interaction with molten corium. Part 1. Experimental. NED 236, 1810–1829. Bechta, S.V., Khabensky, V.B., et al., 2006c. Corrosion of vessel steel during its interaction with molten corium. Part 2. Model development. NED 236 (2006), 1362–1370. Bechta, S.V., et al., 2006d. Phase diagram of the ZrO2 –FeO system. J. Nucl. Mater. 348, 114–121. Bechta, S.V., et al., 2007. Phase diagram of the UO2 –FeO1+x system. J. Nucl. Mater. 362, 46–52. Bechta, S.V., et al., 2008. Interactions of UO2+x –ZrO2 –FeOy corium melt with vessel steel of VVER reactor. In: Proceedings of the ICAPP 08, Anaheim, USA. Froment, K., Seiler, J.M., Gueniau, C., et al., 1998. Physico-chemistry and corium properties for in-vessel retention. In: In-vessel Core Debris Retention and Coolability, Workshop Proceedings, 3–6 March 1998, Garching near Munich, Germany. Frost, H.J., Ashby, M.F., 1982. Deformation-mechanism Maps. Pergamon Press, Oxford, New York, Toronto, Sydney, Paris, Frankfurt. Grebenschikov, R.G., 1991. Phase Diagrams of Refractory Oxide Systems. Reference Book, L. Nauka, vol. 5, p. 5, (in Russian). Khabensky, V.B. et al., 2006. Investigation of corium melt interaction with NPP reactor vessel steel (METCOR). Final Technical Report, Project # 833.2-2003, ISTC, A2, 111–113. Kofstad, P., 1972. Nonstoichiometry. In: Diffusion and Electrical Conductivity in Binary Metal Oxides. Wiley-Interscience, New York. Petrov, Yu B., 1983. Induction Melting of Oxides. L.: Energoatomizdat, (in Russian). Tamman, G., 1920. Uber Anlauffarben von Metallen, Z. Anorg. Allg., Chem., B III. H 1.5. 78–89. Theofanous, T.G., et al., 1996. In-vessel coolability and retention of a core melt. DOE/ID-10460. Toropov, N.A., Barzakovsky, V.P., Bondar’, I.A., Udalov, Yu.P., 1970. Phase Diagrams of Silicate Systems. Reference Book, L. Nauka, vol. 1, 2, (in Russian). Wolf, J.R., Rempe, J.L., 1993. TMI-2 vessel investigation project integrated report. INL, TMI V(93)EG10, 5–21.