MCCI pool temperature and viscosity: a discussion of the impact of scale

Transcription

1 MCCI pool temperature and viscosity: a discussion of the impact of scale A. FARGETTE 1 1 AREVA NP GmbH, Paul-Gossen Strasse Erlangen - Germany ABSTRACT A number of small-scale 2D MCCI tests have recently been performed in the frame of various international R&D projects. One of the goals of such tests was to obtain the temperature history of a corium pool under 2D MCCI conditions in order to estimate the temperature history of such a pool at reactor scale. This raises the problem of scaling, which is the focus of this paper. By examining a widely-used MCCI heat transfer correlation, the paper deduces that, among the numerous thermo-hydraulic properties that influence the temperature history of an ongoing MCCI, only two can account for a significant variation of the temperature: the viscosity η and, to a lesser extent, the heat flux density φ. As shown in the paper, it appears that these two controlling parameters evolve very differently at the beginning of an MCCI, depending on whether a small-scale or a largescale MCCI is considered. At a small scale, the corium mixture rapidly becomes less refractory and the heat flux density drops significantly. On the contrary, the pool only gradually becomes less refractory at a large scale and the heat flux density decreases slowly. The combination of both effects can be used to explain why small-scale 2D MCCIs exhibit an initial fast drop in temperature followed by a temperature plateau. At a larger scale, on the contrary, a gradual decline of the temperature is expected. More generally speaking, a decrease in the physical scale of the MCCI acts a temporal accelerator i.e. small MCCIs travel through the same (η, φ, T) states as large MCCIs, but at a much faster pace. On the basis of these considerations, the paper argues that the extrapolation of the temperature history to reactor scale should, in the short and medium term, rely on large 1D MCCI tests such as MACE rather than on small 2D tests. This is particularly relevant for the EPR, where only a short MCCI will take place in the reactor pit. Small 2D tests become relevant in the long term, as is the case during basemat ablation of a generation II plant. Another consequence of the predominance of the viscosity term in the temperaturebehavior of the pool is that no precise temperature predictions from codes should be expected as long as large uncertainties remain in the viscosity models, as is currently the case. 1/18 pages

2 1. INTRODUCTION: STRUCTURE OF THE PAPER The purpose of this paper is to assess the impact of the MCCI scale on the temperature history. To this end, a well-established hydraulic heat transfer correlation is analyzed in section 2 and a simplified temperature law is derived. On the basis of this temperature law, the governing hydraulic parameters of an MCCI pool are established. The impact of the pool scale on these parameters is then discussed in section 3 on the basis of a simple example, and general trends are deduced. In section 4, these trends are then verified against various MCCI tests involving different crucible dimensions and corium masses. Finally, section 5 discusses the extrapolation of these results to generation II plants and to the EPR. 2. DERIVATION OF A SIMPLIFIED MCCI TEMPERATURE LAW AND GOVERNING THERMO-HYDRAULIC POOL PROPERTIES 2.1 Derivation of a simplified temperature law Heat transport from a corium pool to concrete has traditionally been modeled with a convective heat transfer coefficient from the pool bulk to an interface temperature T int. Depending on the MCCI code considered, this interface temperature is either provided by the user or internally calculated by the code on the basis of assumptions on the character of the interface (e.g. deposition of a refractory crust at the surface of the concrete) 1. In any case, the heat flux density from the corium to the concrete can be expressed as: h conv ( Tbulk Tint ) (1) Note that φ only represents the heat flux density necessary to decompose the concrete (i.e. heat it up from room temperature to decomposition temperature): the heat-up of the concrete slag from decomposition temperature to pool temperature takes place in the pool bulk i.e. no heat transport to the concrete interface is required. Several correlations are available in the literature to estimate the convective heat transfer coefficient h conv. A widely-used correlation is the BALI correlation (Ref. [1]) developed by CEA: 1 Note: as the reader will probably notice, no in-depth discussion on the interface temperature will be provided here. The modeling of this term is subject to a great number of uncertainties: -Does a refractory crust deposit at the concrete surface or is the solid fraction dispersed in the pool? -If a crust does exist, what is its composition and which temperature boundary condition does it impose? -Does the orientation of the concrete surface (horizontal or vertical) have an impact on the crust s stability / existence? This means that any assumption made on the interface temperature is highly speculative. The purpose of this paper is to leave this discussion aside and to show that simple considerations on the pool thermo-hydraulics are sufficient to explain a number of trends observed during MCCIs. This being said, the behavior of the interface temperature may well have an additional impact on the temperature history. 2/18 pages

3 Nu M g 3 G j Pr 0.22 (2) where Nu is the Nusselt number (Nu = hl/λ) and Pr is the Prandtl number (Pr = ηc p /λ). Replacing (2) into (1) leads to the following expression for the pool temperature: T L g c p pool T int (3) jg The superficial gas velocity j G is the volume flow rate of concrete decomposition gases per unit surface: j G (4) h dec where ξ is the mass fraction of gaseous concrete decomposition products, Δh dec is the energy required to heat a unit mass of concrete from room temperature to decomposition temperature, ρ G is the density of the decomposition gases and φ is the heat flux density from the corium to the concrete (as defined in equation 1). The characteristic length L is the Laplace constant: G L c g (5) where σ is the surface tension and ρ c is the density of the corium. Replacing (4) and (5) in (3) leads to the following expression for the pool temperature: T c p hdec G pool T int (6) c g Let us now consider the various terms in equation (6): we are interested in those which could induce a significant variation of the pool temperature throughout the MCCI. The thermal conductivity of the pool is only a very weak function of composition (core oxides and concrete have a similar thermal conductivity): it therefore remains approximately constant when concrete is added to the pool. The specific heat of the corium changes more significantly during the MCCI, but, given that it is raised to a small power, variations do not have much of an impact on T pool. Similarly, the surface tension does not vary significantly and can be considered as roughly constant. The energy required to heat a unit mass of concrete from room temperature to decomposition temperature is only concrete-dependant i.e. for a given concrete, it is fixed. The density of the gases travelling through the MCCI are also only temperature-dependant i.e. variations in ρ G cannot cause a temperature variation. 3/18 pages

4 Since all the previously-mentioned terms are more or less constant for a given pool temperature, let us lump them into a constant a(t pool ) term. Equation (6) simplifies to: T pool a( Tpool) c Tint (7) 2.2 Estimation of the governing thermo-hydraulic properties of an MCCI pool Now that a simplified pool-temperature law is available, we can compare the fluctuations of the remaining thermo-hydraulic terms to establish which govern the temperature history. This is best done by means of a simple example. Note that, as explained in the footnote of section 2.1, no attempt is made here to assess changes in the interface temperature T int since any assumptions on this term are highly speculative: the analysis focuses on the hydraulic properties of the pool alone. However, the author acknowledges that changes in T int may have an additional impact on the temperature history. Returning to our simple example, let us first consider a corium pool containing a large fraction of refractory core oxides (e.g. 90 wt%) plus a small fraction of concrete (10 wt%). This pool is at a high temperature (e.g C). Note that these conditions (referred to as state 1 ) are typical of those at the beginning of an MCCI test. We then consider that a lump of concrete is dissolved in the pool to bring the concrete fraction to 30wt% ( state 2 ) and we assess the evolution of the thermo-hydraulic properties at 2200 C. The composition of the core oxides and the concrete used in the example are given in Table I. Table I: simplified corium and concrete composition Core oxides composition UO 2 ZrO 2 Simplified Concrete composition SiO 2 CaO 75 wt% 25 wt% 80 wt% 20 wt% Evolution of the heat flux density Aside from temporary transient effects, the heat flux density tends to drop during an MCCI because the wetted concrete surface area increases (in quasi-steady state, the heat flux density is inversely proportional to the wetted concrete surface area). Therefore, the heat flux density in state 2 will be smaller than in state 1 i.e.: Replacing this in (7), it can therefore be stated that the drop in the heat flux density between 1 and 2 will lead, to some extent, to a reduction in the pool temperature. 1 4/18 pages

5 Evolution of the density Simple density mixing rules show that in state 1, the density of the mixture is around 6490 kg/m³ at 2200 C. Similar calculations show that in state 2, the density of the mixture is around 4450 kg/m³ at 2200 C. Reporting this ratio in equation (7), we see that: This means that the drop in density would lead to a slight temperature increase in the pool if all other properties were kept constant. This is easily understandable: if the density of a hot fluid decreases, its ability to transfer heat to its environment is reduced and it takes a higher fluid temperature to transfer the same heat flux as before. Evolution of the viscosity Let us now turn to the viscosity term of equation (7). The computation of viscosity is significantly more complex and less accurate than other hydraulic properties. However, we can obtain an order of magnitude of the variation of viscosity between state 1 and 2 by employing corium-devoted models such as Urbain (for the liquid phase) and Ramaciotti (for the impact of the solid volume fraction) (Ref. [2]). By using standard parameters suggested by these authors, we obtain a viscosity of 1.5 Pa.s for state 1 at 2200 C and 0.02 Pa.s for state 2 at 2200 C. This large reduction in viscosity is due to the fact that concrete addition reduces the liquidus (and hence the solid fraction) in the pool. This effect easily outweighs the viscosity increase of the liquid phase induced by the addition of SiO 2. Reporting this ratio in equation (7), we see that: This means that the reduction in viscosity induced by the addition of concrete will lead to a very significant drop in the MCCI pool temperature. Physically, this is understandable since a fluid with low viscosity can more easily convect heat from its bulk to its environment i.e. a smaller driving temperature difference is sufficient to ensure the removal of a given heat flux density. Overall temperature evolution From the previous considerations, it is plain that the impact of this viscosity drop significantly outweighs the impact of the density reduction (0.22*1.27=0.28 <<1) i.e. overall, a significant drop in the pool temperature is expected. This is consistent with experimental results which indicate a declining temperature throughout the MCCI. From this analysis, it appears that the thermo-hydraulic property that governs the temperature drop during an MCCI is the viscosity and, to some extent, the drop in the heat flux density. The impact of other thermo-hydraulic properties is second-order. We may therefore re-write equation (7) as: 5/18 pages

6 T pool a ( Tpool) Tint The viscosity η of a melt depends on two factors: its composition and its temperature. Multi-component fluids like corium tend to exhibit a specific η T dependency. At high temperature, when they are fully liquid, a reduction in temperature does not increase the viscosity significantly. However, as soon as the temperature drops below the liquidus of the melt, the viscosity starts increasing much faster since the growing solid volume fraction strongly affects the apparent viscosity. When a threshold solid volume fraction is reached, the viscosity increases very abruptly and the corium looses its ability to flow (the corium has reached its so-called immobilization temperature ). This threshold solid volume fraction depends on the composition of the corium and its thermal history (hysteresis effects) but is typically around 0.5. The resulting η(t) curve is depicted in Figure 1 for two different coriums: one is refractory (small concrete fraction, dashed line) while the other is far less refractory (large concrete fraction, full line). We note T immobilization the temperature at which the viscosity starts increasing sharply. η refractory corium less refractory corium T immobilization T immobilization T Figure 1: Viscosity - Temperature curve for two different coriums With this in mind, we may re-write equation (7) as: T a( T ) ( T, x ) T pool pool pool conc int (7*) where x conc is the concrete fraction in the pool. Let us now apply this relation to two MCCIs of very different scales. 6/18 pages

7 3. THE IMPACT OF SCALE ON THE TEMPERATURE HISTORY Let us first consider a small-scale 2D MCCI heated by means of a fixed decay power Φ. We are interested in the thermo-hydraulic properties of this pool at several times during the MCCI: t 0 (start of concrete ablation), t 1 = t 0 +Δt, t 2 = t 0 +2Δt, t 3 = t 0 +3Δt, where Δt is the selected time-step, for example 30 min for typical MCCI tests. The corresponding cavity profile of the small-scale MCCI pool is given on the left-hand side of Figure 2. At the beginning of concrete ablation (t 0 ), the mixture does not contain any concrete (or is poor in concrete if concrete was included in the initial mixture) i.e. it is highly refractory and the pool temperature T 0 is high. Referring to Figure 2, we see that between t 0 and t 1 = t 0 + Δt, the amount of ablated concrete is significant (relative to the small initial amount of corium) i.e. the corium mixture has become significantly less refractory. The corresponding η(t) curve at t 1 is given on the left-hand side of Figure 3 (blue curve): it is significantly below the curve at t 0 (in black). Still referring to Figure 2, we see that the wetted concrete surface has also significantly increased between t 0 and t 1 (relatively speaking). This means that the heat flux density φ 1 at t 1 is lower than φ 0 at t 0 (transient effects set aside). The combination of both elements (large shift in the η(t) curve and smaller φ) means that the new temperature T 1 for which equation (7*) is satisfied will be much lower than T 0 : a large temperature-drop is therefore expected. Applying a similar reasoning between t 1 and t 2, we predict a further significant drop in the temperature. However, since the concrete fraction has, relatively speaking, less increased than between t 0 and t 1, the shift of the η(t) curve is less pronounced. Similarly, the relative increase in the concrete surface area (i.e. decrease in the heat flux density) is smaller than between t 0 and t 1. Both effects mean that the temperature drop is smaller than during the first time-step. From these considerations, a trend becomes apparent: the temperature decreases more slowly as time goes by (i.e. the absolute value of the derivative of T(t) decreases). In the late phases of the MCCI, the concrete fraction in the corium pool is high i.e. the addition of a further amount of concrete Δm during Δt does not significantly change the hydraulic properties of the pool. The η(t) curve remains therefore nearly unchanged: the hydraulic properties of the corium are dominated by that of concrete. The corium has by this stage reached a temperature for which a significant drop in the temperature is no longer possible by addition of more concrete. Indeed, the temperature of the mixture is at this stage close to its immobilization temperature : a significant temperature drop would mean an increase of viscosity of several orders of magnitude, and the pool would no longer be able to convect the generated heat to the pool boundaries. The temperature therefore reaches a plateau near (but above) T immobilization and remains there. This is depicted between during t 2 and t 3 in Figure 3. The shape of the corresponding T(t) curve is presented in Figure 4 (red line). 7/18 pages

8 Small-scale 2D MCCI Large-scale 2D MCCI t 0 t 1 = t 0 + Δt t 2 = t 0 + 2Δt t 3 = t 0 + 3Δt Figure 2: Cavity profile at various times after the start of the MCCI small-scale MCCI large-scale MCCI η 3 η 2 η 1 η 0 T 3 T 2 T 1 T 0 η 3* 2* 1* η 0* T 3* T 2* T 1* T 0* t 0 t 0 + Δt t 0 + 2Δt t 0 + 3Δt Figure 3: Pool viscosity at various times after the start of the MCCI 8/18 pages

9 Temperature T 0 T 1* T 2* T 3* large-scale MCCI small-scale MCCI T 1 T 2 T 3 t 0 t 1 t 2 t 3 time Figure 4: Temperature history of a large-scale (blue line) and small scale MCCI (red-line) with identical initial composition and heat flux density Let us now turn to a large-scale MCCI heated by means of a fixed decay power Φ *. Let us further assume that this pool has (i) the same initial corium composition as the small-scale MCCI and (ii) the selected Φ* leads to the same steady state heat flux density as in the small-scale MCCI (see Figure 2, right-hand side). Unlike the small-scale MCCI, the relative amount of concrete ablated during a time-step Δt is very small in comparison to the initial pool volume. Consequently, the concrete fraction only increases very slowly and the η(t) curve does not change significantly. Similarly, the wetted concrete surface does not increase significantly (relatively speaking) during a time step i.e. no drop of the heat flux density will be induced by surface effects. Referring to equation (7*), this means that the new temperature T 1 * at t 1 will be close to T 0. The same reasoning holds for the time intervals t 1 - t 2 and t 2 - t 3. Therefore, for a large-scale pool, only a slow gradual temperature drop results from the ongoing MCCI. The corresponding temperature history is depicted in Figure 4 (blue curve). Looking more closely at both above-mentioned MCCIs, it appears that the small pool travels through the same (η, φ, T) states as the large pool, but at a much faster pace. The preservation of the (η, φ, T) states stems from the fact that there is a fixed (i.e. scaleindependent) relative increase in surface area (which determines φ in steady-state) with the increase in pool volume (which determines the concrete content and hence the viscosity). For example, a doubling of the pool volume due to concrete ablation will lead to the same relative increase in the wetted concrete surface, regardless of the MCCI scale, provided the test geometries are identical (same aspect ratio at both scales i.e. same initial pool depth / initial radius). 9/18 pages

10 Consequently, by sufficiently shrinking the time scale in Figure 4, the blue curve could be made identical to the red curve. This means that both blue and red curves will tend towards the same temperature-asymptote. More generally speaking, decreasing the geometrical scale translates into a temporal acceleration. The results obtained in small MCCIs provide information on the long-term behavior of a large MCCI but are ill-suited for short-term information retrieval (the small MCCI passes through the corresponding (η, φ, T) states in a very short time period). 4. APPLICATION TO SMALL 2D MCCI TESTS, LARGE 2D MCCI TESTS, LARGE 1D MCCI TESTS On the basis of the previously-explained phenomenology, qualitative predictions can be made for various MCCI tests featuring different crucible sizes and corium masses. To ensure a consistent comparison, it must be checked that the initial conditions are comparable in all tests i.e. that the temperatures at ablation onset and the initial concrete fractions are comparable. These conditions are summarized in Table II and the discrepancies will be discussed in the corresponding paragraphs. Table II: Summary of initial conditions Test Temperature at ablation onset ( C) Initial concrete mass fraction (-) VBU C 7.8% CCI C 8% CCI C 14.1% MACE M-3b 1830 C 8.5% MACE M C 8.5% 2.1 Small 2D MCCI tests In small-scale 2D MCCIs, the wetted concrete surface sharply increases due to the small 2D configuration (i.e. a pronounced drop of the heat flux density is induced by surface effects) and the concrete fraction increases rapidly due to the small initial mass of corium. We therefore expect a large temperature drop in the initial phase of the MCCI. The VBU tests are representative of this test class: they combine both a 2D semicylindrical geometry (radius = 15cm) and a small initial corium mass (a few dozen kg). As an illustration, the temperature history in VBU-7 (Ref. [3]) is provided in Figure 5. Due to a coupling of the thermocouples with the inductor, the temperature readings are only valid when the inductor is turned off, for example at t 0 and at t 0 +75min. As can be seen, the temperature drops from 2250 C to 1550 C in 75 min (~9 K/min). Referring to Table II, you may note that the temperature at ablation onset is somewhat higher than that of other MCCI tests. This high initial overheat of the melt (due to the melt generation 10/18 pages

11 technique) might lead to an overestimation of the rate of temperature decrease. Considering a smaller value of 2000 C (more in line with other tests), we nevertheless obtain a high temperature decrease rate of 6 K/min. Another interesting feature of this test is that the pool temperature does not change between t min and the end of the test, when the generator is turned off: the temperature remains around 1550 C. As argued in section 3, this can be explained by the fact that the pool temperature has dropped to a value close to (but above) its immobilization temperature and that no further temperature drop can be induced by concrete addition. Figure 5: Temperature history during VBU Large 2D MCCI tests In large 2D MCCI tests, the wetted concrete surface increases rather fast (though not as fast as in a small test) due to the 2D geometry i.e. a gradual drop in the heat flux density is expected. The increase in the concrete fraction is relatively slow (due to the large initial corium mass). We therefore expect a temperature drop which is less pronounced than for small 2D MCCI tests. The CCI tests, which combine a 50cm*50cm square crucible with melt masses of several hundred kg, are representative of this category. As an illustration, the temperature histories recorded during CCI-2 (Ref. [4]) and CCI-3 (Ref. [5]) are given in Figure 6 and Figure 7, respectively. In order to compare the temperature decrease rate with the previous test, let us once again consider the first 75min. We obtain a decrease rate of about ( )/75~3.3 K/min for CCI-2 and ( )/75~3.3 K/min for CCI-3. These values are obviously not very accurate given the 11/18 pages

12 temperature spread between the various thermocouples but they are still significantly smaller than the 9 K/min (or 6K/min) obtained for the small 2D MCCI scale i.e. this trend is in line with our predictions. Note that in CCI-3, the initial concrete fraction is higher than in other MCCI tests (see Table II) i.e. the rate of temperature decrease might be slightly reduced (the temperature decrease is faster when the pool is still poor in concrete). Figure 6: temperature history during CCI-2 12/18 pages

13 Figure 7: temperature history during CCI Large 1D MCCI tests In a 1D configuration, the wetted surface area of concrete remains constant i.e. the heat flux density to the concrete cannot drop due to surface effects. Since the initial amount of corium is large, the increase of the concrete fraction is slow. Both effects mean that the temperature decline is expected to be slower and more gradual than in the other previously-analyzed tests. The MACE tests, which combine large 1D crucibles (up to 120cm*120cm) and melt masses of up to nearly 2 tons, are representative of this test class. As an illustration, the average temperature recorded during MACE test M-3b (Ref. [6]) is presented in Figure 8. Water addition took place 74 min after the start of the test i.e. 52 min after the start of basemat ablation (t=52 on Figure 8). As can be seen, despite the ongoing concrete ablation, the average temperature only drops by about 100 K (~2200K to ~2100K) before water addition, which corresponds to a decrease rate of 100/75~1.3 K/min. After water addition, the corium temperature drops more significantly, probably due to bulk cooling effects (inclusion and re-melting of quenched corium fragments in the pool bulk). 13/18 pages

14 Figure 8: Temperature history during the M-3b test In MACE test M4 (Ref. [7]), flooding took place 34 min after the beginning of the test i.e. 23 min after the start of basemat ablation (t=23 min on Figure 9 and Figure 10). This means that for our purpose we can unfortunately only use the first 23 min. Both array readings do not indicate any significant temperature decline trend during the considered period, despite the ongoing concrete ablation. This is in line with our predictions. 14/18 pages

15 Figure 9: Temperature history during the M-4 test (array BH-1) Figure 10: Temperature history during the M-4 test (array BH-3) 15/18 pages

16 5. EXTRAPOLATION TO REACTOR SCALE An MCCI at reactor scale (as in the EPR reactor pit) is characterized by a very large mass of corium (several dozens to more than one hundred tons of native corium) and a very large scale (pool diameter of several meters). This means that (i) the concrete fraction in the pool will remain low during the first few hours of MCCI and (ii) the wetted concrete surface will not increase significantly (relatively speaking) during the first few hours. From a thermo-hydraulic perspective, this means that large 1D MCCI tests are best adapted to the prediction of the temperature history at reactor scale during the first few hours of the MCCI. This applies to the MCCI in the EPR reactor pit. The EPR core catcher concept is only based on a short MCCI phase with a 50cm-thick concrete layer. Even though the MCCI at reactor scale is 2D, relying on temperatures recorded in small 2D tests for the estimation of viscosity and temperature at the reactor scale is misleading because both governing parameters (viscosity and heat flux density) evolve very differently at different scales. For generation II power plants with large (quasi-infinite) basemats, the concrete fraction will reach high levels in the long term and the wetted concrete surface will increase very significantly. Under these conditions, the results gained from small-scale 2D MCCIs are relevant and should be used. 16/18 pages

17 6. CONCLUSION In the short and medium term, small-scale 2D MCCIs are expected to behave very differently from large-scale 2D MCCIs. Although changes in the pool-concrete interface temperature may have an additional influence (not analyzed here), this difference in behavior can be explained by an examination of the pool thermo-hydraulics alone. The above-presented analysis has shown that 2 main factors, viscosity and, to a lesser extent, heat flux density, account for this difference: The concrete fraction increases quickly in a small-scale 2D MCCI due to the small pool volume. The pool becomes rapidly less refractory, which has a very large impact on the η(t) relation. This is not the case for a large-scale 2D MCCI since the initial amount of refractory corium is very large The heat flux density to the concrete tends to drop during a small-scale 2D MCCI due to the rapid increase of the wetted concrete surface. This is not the case for a large-scale 2D MCCI. The interplay between both factors explains why the temperature measured in small 2D MCCIs (e.g. VB-U tests) typically exhibit a fast initial temperature drop followed by a temperature plateau, whereas larger 1D MCCIs (e.g. MACE) exhibit a slow gradual temperature drop throughout the MCCI (at least before melt flooding). More generally speaking, a decrease in the physical scale of the MCCI acts a temporal accelerator i.e. small MCCIs travel through the same (η, φ, T) states as large MCCIs, but at a much faster pace. The temperature plateau observed towards the end of a small-scale MCCI would therefore also be observed at a larger scale if the test duration was sufficiently extended. The analysis therefore suggests that extrapolations to reactor scale in the short and medium term, as in the EPR reactor pit, should be based on large 1D MCCI tests rather than small 2D tests even if the reactor cavity is 2D. Small 2D tests become relevant in the long term, as is the case during basemat ablation of a generation II plant. From a modeling point of view, the high impact of the viscosity on the temperature history has rather unfortunate consequences. As stressed in Ref. [2], the results obtained with the Urbain model together with the Ramacciotti correlation become very inaccurate when the fraction of modifiers is high (i.e. fraction of glass formers is low). This is very much the case in the early stages of an MCCI when the amount of dissolved SiO 2 is low. Therefore, although the models are sufficient to capture general trends, no precise predictions of the corium temperature should be expected from MCCI codes as long as the viscosity models are not improved. 17/18 pages

18 7. AKNOWLEDGMENTS I would like to express my gratitude to M. Fischer, W. Schmidt, M. Cranga and C. Mun for their comments and remarks, which, no doubt, contributed to improving the quality and pertinence of this article. REFERENCES [1] Seiler, Froment, Material effects on multiphase phenomena in late phases of severe accidents in nuclear reactors Multiphase Science and Technology Vol 12, N 2, pp , 2000 [2] M Ramacciotti, Etude du comportement rhéologique de mélanges issus de l interaction corium/béton, Thèse, 24 Septembre 1999, Université de Provence (Aix- Marseille I) [3] L. Ferry et al, Interaction corium-béton en bain tout oxide sur l installation VULCANO: essai VB-U7 Béton FeSiCo (EPR), Document technique DEN, DEN/DTN/STRI/LMA/2010/002/0 [4] M.T Farmer et al, OECD MCCI Project, 2-D Core Concrete Interaction (CCI) Tests: CCI- 2 Test data report Thermalhydraulic Results, Rev. 0 October15, 2004, OECD/MCCI TR05 [5] M.T Farmer et al, OECD MCCI Project, 2-D Core Concrete Interaction (CCI) Tests: CCI- 3 Test data report Thermalhydraulic Results, Rev. 0 October15, 2004, OECD/MCCI TR04 [6] M. T Farmer et al, MACE Test M3b, Data Report, Volume I, MACE-TR-D13, EPRI TR , November 1997 [7] M. T Farmer et al, MACE Test M4 Data Report, MACE-TR-D-16, August /18 pages