# Main results of an in-vessel corium thermochemistry benchmark based on MASCA and CORDEB2 experimental data

Romain Le Tellier, Laure Carénini, Florian Fichot, Rositsa Gencheva, Pavlin

Groudev, Ivan Melnikov, Maksim Golubev, Aleksandr Filippov

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Romain Le Tellier, Laure Carénini, Florian Fichot, Rositsa Gencheva, Pavlin Groudev, et al. Main results of an in-vessel corium thermochemistry benchmark based on MASCA and CORDEB2 experimental data. ERMSAR 2024: Latest achievements in severe accidents research, May 2024, Stockholm, Sweden. pp.111514, 10.1016/j.anucene.2025.111514. cea-05183361v2

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# Main results of an in-vessel corium thermochemistry benchmark based on MASCA and CORDEB2 experimental data☆

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R. Le Tellier<sup>a, *</sup>, L. Carénini<sup>b</sup>, F. Fichot<sup>b</sup>, R. Gencheva<sup>c</sup>, P. Groudev<sup>c</sup>, I. Melnikov<sup>d</sup>, M. Golubev<sup>d</sup>, A. Filippov<sup>e</sup>

## ARTICLE INFO

Keywords:

Corium
Thermochemistry
Stratification
Benchmark

## ABSTRACT

This paper is dedicated to an international benchmark on in-vessel corium thermochemistry. Composed of three different steps, it was constructed in the frame of the IAEA Coordinated Research Project on In-Vessel Melt Retention and focuses on the stratification of corium in the lower plenum of a reactor vessel during a severe accident. The experimental data obtained from the MASCA and CORDEB2 programs is utilized to validate and calibrate the models of the various codes employed by the participants. The paper gives an overview of the different models, including their underlying assumptions. The results show that the models are generally in good agreement with the experimental data, but further experimental data is needed for model validation. Besides the need for further work, this paper highlights the fact that integral models (published in the open literature for most of them) are available to account for the first-order phenomena associated with in-vessel corium. Accordingly, this paper may be useful for code developers that would like to upgrade their models in order to take into account transient stratification kinetics, a prerequisite for a state-of-the-art analysis of in-vessel melt retention.

## 1. Introduction

In the framework of the IAEA Coordinated Research Project (CRP) on In-Vessel Melt Retention,<fnref n="1" /> a code-to-experiment benchmark devoted to in-vessel corium thermochemistry was proposed by CEA and IRSN with participation from INRNE-BAS, NRC “Kurchatov Institute” and IBRAE. Based on results of prototypic corium experiments from the open literature or made available in the scope of this CRP, it is devoted to oxide/metal pool thermochemistry phenomena of first-order importance when assessing in-vessel corium behavior (Fichot et al., 2020). Indeed, as clearly demonstrated by the H2020 IVMR European project, taking into account the transient multi-layer corium configuration in the vessel lower head is mandatory for assessing In-Vessel Retention (IVR) for high power reactors.

It is a three-step benchmark involving both severe accident codes (ASTEC, HEFEST-URAN, HEFEST, PROCOR) and thermodynamic equilibrium solvers (TSAR, OpenCalphad) with associated databases (NUCLEA).

The first step considers two-layer stationary (under chemical equilibrium conditions) pool configurations using oxide/metal phases' composition and relative position information taken from the MASCA MA tests series (Tsurikov et al., 2007). It is used for comparison and validation of the modelling of the liquid miscibility gap of the U-O-Zr-steel thermodynamic system and the liquid phase density laws. The second step is focused on the heavy metal layer formation kinetics considering the last phase of the MASCA RCW-100 experiment and associated post-mortem ingot information (Asmolov et al., 2003). Here, a semi-quantitative comparison with experimental results (in terms of

<footnote><sup>a</sup> CEA, DES, IRESNE, DTN, Cadarache, F-13108 Saint Paul-lez-Durance, France</footnote>

<footnote><sup>b</sup> IRSN, Cadarache, F-13108 Saint Paul-lez-Durance, France</footnote>

<footnote><sup>c</sup> Institute for Nuclear Research and Nuclear Energy – Bulgarian Academy of Sciences, INRNE-BAS, 72 Tsarigradsko shosse Blvd. BG-1784 Sofia, Bulgaria</footnote>

<footnote><sup>d</sup> NRC “Kurchatov Institute”, 1 Akademika Kurchatova Pl., RU-123182 Moscow, Russia</footnote>

<footnote><sup>e</sup> IBRAE, 52 B. Tulskaya St., RU-115191 Moscow, Russia</footnote>

<footnote>* This article is part of a special issue entitled: 'ERMSAR 2024' published in Annals of Nuclear Energy.</footnote>

<footnote>* Corresponding author.</footnote>

<footnote>E-mail addresses: romain.le-tellier@cea.fr (R.L. Tellier), laure.carenini@irsn.fr (L. Carénini), r.gencheva@inrne.bas.bg (R. Gencheva), pavlinpg@inrne.bas.bg (P. Groudev), Melnikov_IA@nrcki.ru (I. Melnikov), phil@ibrae.ac.ru (A. Filippov).</footnote>

<footnote n="1">¹ https://www.iaea.org/projects/crp/j46002.</footnote>
metal phase spatial distribution and composition) is performed in order to assess intra-layer mass transfer models that simulate corium stratification transients in severe accident codes. In this second step, the light metal layer and the oxide phase are not separated by a solid crust contrarily to the supposed state in the reactor case. In the third step, it is the transient evolution of a three-layer stratified corium pool in presence of a solid crust at the top oxide surface that is studied considering the results of CORDEB2 CP7-02 test on the stratification kinetics (Fichot et al., 2019). In this experiment, the thermal gradient expected in reactor configuration leading to crust formation between the oxide and the top metal layer is considered, albeit in a small geometry for which the crust is mechanically stable.

This paper presents the three different steps of this benchmark along with an analysis of the results obtained by the participants. For the sake of conciseness, the actual experimental results that have been used for the benchmark specifications are not provided in the main body of this paper but as "supplementary material" attached to it.

## 2. Step 1: MASCA MA

### 2.1. Brief summary of the experiments

The OECD-MASCA experimental program (see (Tsurikov et al., 2007)) has studied the thermochemical interactions between oxide and metallic liquid phases. Among other achievements, it has helped characterizing the (U, Zr) mass transfer to the metal phase that can lead to a significant increase in its density so that, in some conditions, the metal phase can be relocated at the bottom of the pool because of gravity.

In particular, some experiments of the MA series (MA-1 to MA-6), under inert atmosphere (Ar) in the RASPLAV-3 facility (NITI), have shown the possibility of two stratified configurations at steady-state.<fnref n="2" /> These experiments were conducted using the cold-crucible technique to melt about 2 kg of oxidic corium by inductive heating in a 7 cm-diameter crucible. Steady state was reached in any case in less that 30 min. Both direct observation of the free surface during the experiment and post-mortem analyses of the solidified ingots have been performed. Supplemented by the STFM-Fe experiments, the MA series give a rather complete picture of phase and species partitioning in a stratified pool associated with the U-O-Zr-steel system.

The MA series partial test matrix is given at Table 1. The associated parameters are the melt temperature $T^{exp}$, the exposure time, the sub-oxidized corium initial composition (defined by its U-over-Zr molar ratio $R_{U/Zr}$ and the Zr molar oxidation degree $C_{Zr}$) and the ratio between the steel mass and the initial corium mass (denoted $x_{steel}^{exp}$).

Note that Table 1 gives the specified test conditions; actual molten masses at play in the corium-steel interactions slightly differ.<fnref n="3" />

Fig. 1 depicts typical post-mortem ingots that have been analyzed in order to get information about the phases stratification. For the MA-1, MA-3, MA-4, MA-5, MA-5b tests, a clear stratification with a metal phase heavier than the oxide has been observed while the metal phase is lighter and on top of the oxide in the MA-6 test.

**Nota Bene** The MA-2 test is the only test that does not exhibits a clear phase stratification. It is also the only case with a highly oxidized corium ($C_{Zr}^{exp} = 74.5\%$). The metal phase is inhomogeneous and has a “diabolo” shape with a top (resp. bottom) part that is lighter (resp. heavier) with a density of 7930 kg/m<fnref n="3" /> (resp. 8890 kg/m<fnref n="3" />) than the oxide phase (8610 kg/m<fnref n="3" />). Obviously, an equilibrium calculation cannot reproduce or

<table><caption>**Table 1**
MA series partial test matrix.</caption><thead><tr><th>Test</th><th><i>T</i><sup>exp</sup>(°C)</th><th>Exposure time (min)</th><th><i>R</i><sub>U/Zr</sub><sup>exp</sup></th><th><i>C</i><sub>Zr</sub><sup>exp</sup> (%)</th><th><i>x</i><sub>steel</sub><sup>exp</sup><br><i>x</i><sub>steel</sub><sup>exp</sup> + 1 (%)</th></tr></thead><tbody><tr><td>MA-1</td><td></td><td></td><td>1.45</td><td>33.1</td><td>11.42</td></tr><tr><td>MA-2</td><td></td><td></td><td>1.28</td><td>74.5</td><td>10.80</td></tr><tr><td>MA-3</td><td></td><td>30</td><td>1.14</td><td>36.5</td><td>10.78</td></tr><tr><td>MA-4</td><td>2500</td><td></td><td>1.17</td><td>39.7</td><td>19.09</td></tr><tr><td>MA-5</td><td></td><td></td><td>0.89</td><td>31.5</td><td>9.89</td></tr><tr><td>MA-5b</td><td></td><td>120</td><td>0.90</td><td>30.5</td><td>7.05</td></tr><tr><td>MA-6</td><td>2600</td><td>30</td><td>1.14</td><td>29.1</td><td>29.71</td></tr></tbody></table>

explain such a configuration. Different supplementary explanations (magneto-hydrodynamic effects associated with the inductive heating, helicoidal shrinkage during solidification, complicated phase segregation during solidification – possibly largely impacted by oxygen redistribution) have been proposed in the literature; they are out of the scope of this benchmark.

### 2.2. Benchmark definition

The general goal is a comparison between the experimental results (associated with the post-mortem ingots analyses) and numerical results obtained by different models that predict the two-phase thermodynamic equilibria in the liquid miscibility gap of the U-O-Zr-steel system. These calculations are performed from the element inventories deciphered from the actual molten masses as evaluated from post-mortem test analyses in (Bechta et al., 2008).<fnref n="4" /> They are given in the “supplementary material” section.

For each experiment, two different calculations are performed:

C1. A first one at the composition corresponding to the actual experimental conditions that is used for direct comparison with the experimental results in terms of element phases partitioning;

C2. A second one where, the composition is varied in terms of steel amount near $x_{steel}^{exp}$ ($R_{U/Zr} = R_{U/Zr}^{exp}$ and $C_{Zr} = C_{Zr}^{exp}$ are kept); more precisely, five calculations with $x_{steel} \in \{0.75, 0.875, 1.0, 1.125, 1.25\} \times x_{steel}^{exp}$ are performed in order to characterize the evolution of the mass densities.

Regarding the temperature, while the different species phase partitioning models are or not temperature dependent, the mixture density laws are in any case temperature dependent. For calculation C1, the temperature is set to $T_{calc} = \max(T^{exp}, T_{liquidus})$, where $T_{liquidus}$ is the liquidus temperature (calculated by the model if available) at which the fluorite refractory phase ($U_y, Zr_{1-y}$) $O_{2-x}$ is formed when the melt is cooled down (assuming thermodynamic equilibrium). For calculations C2, a temperature of $T^{exp} + 100$ is used in order to ensure that the system remains completely liquid whatever the composition is when varying $x_{steel}$.<fnref n="5" />

### 2.3. Codes and models involved

The participants have used different thermodynamic equilibrium models for the liquid miscibility gap of the U-O-Zr-Steel system through different codes as described in Table 2. Such models provide the phase mass fractions along with their composition. From there, the phase

<footnote n="2">² Note that, in the frame of the MASCA program, the STFM-Fe experiment series has also investigated this stratification, albeit with smaller corium masses.</footnote>

<footnote n="3">³ Moreover, in MA-3 and MA-4 tests, the corium load contained fission products (FP) simulant elements with a mass fraction of about 3%. The goal was to characterize the FP partitioning between the metal and oxide phases. These elements are not considered in the first step of this benchmark.</footnote>

<footnote n="4">⁴ Inventories reported in (Bechta et al., 2008) differs from those in (Tsurikov et al., 2007) because of more accurate measurements of the oxygen content in the metallic layers.</footnote>

<footnote n="5">⁵ Then, one should keep in mind that the densities will be lower than in C1 calculations.</footnote>
<figure><img src="image_3.png" /><figcaption>**Fig. 1.** Different views associated with the post-mortem ingots of MA-3, MA-2 and MA-6 tests (adapted from (Tsurikov et al., 2007).</figcaption></figure>

<table><caption>**Table 2**
The different codes and models for the liquid miscibility gap of the U-O-Zr-Steel system involved in step-1.</caption><thead><tr><th>Institution</th><th>N°</th><th>Code / model</th><th>Description / comments</th><th>Ref.</th></tr></thead><tbody><tr><td>NRC “Kurchatov Institute”</td><td>1</td><td>TSAR / GIBBS</td><td>Thermodynamic approach based on Gibbs energy minimization using regular solution model (CALPHAD-like technique)</td><td>(Golubev et al., 2023)</td></tr><tr><td>IRSN</td><td>2</td><td>ASTEC / Salay-Fichot model</td><td>Analytical model calibrated on experimental results from MASCA MA-1, 2, 3, STFM-Fe-2, 3, 4, 5, 6, 7, 8, 9, 14, 15</td><td>(Salay and Fichot, 2005)</td></tr><tr><td>INRNE-BAS</td><td>3</td><td>HEFEST_URAN</td><td>Interpolation scheme based on MASCA MA and STFM-Fe test experimental results</td><td>(Ozrin et al., 2010)</td></tr><tr><td>IBRAE</td><td>4</td><td></td><td>CALPHAD method with a non-ideal associate model for the Gibbs energy of the liquid phase</td><td>(Sundman et al., 2016) (Bakardjieva et al., 2010)</td></tr><tr><td>CEA</td><td>5</td><td>PROCOR interface with OpenCalphad / Gibbs energy minimizer with NUCLEA'19 database</td><td>See ASTEC above</td><td>(Salay and Fichot, 2005)</td></tr><tr><td></td><td>6</td><td>PROCOR / Salay-Fichot model</td><td>Analytical model calibrated on OpenCalphad calculations with NUCLEA'19 database</td><td>(Nandan et al., Aug. 2020)</td></tr><tr><td></td><td>7</td><td>PROCOR / Nandan-Fichot model</td><td>Interpolation scheme based on OpenCalphad calculations with NUCLEA'19 database</td><td>(Mativet et al., 2024)</td></tr><tr><td></td><td>8</td><td>PROCOR / thermodynamic closures associated with the stratification kinetics model proposed in (Mativet et al., 2024)</td><td></td><td></td></tr></tbody></table>

densities are calculated from:

a non-ideal mixture law based on element density laws and an excess volume term function of the temperature (see (Asmolov et al., Aug. 2008)) in NRC “Kurchatov Institute” and IBRAE calculations; an ideal mixture law based on species density laws function of the temperature $ρ_i(T)$ (see (Barrachin and Defoort, 2004)) in case of IRSN, INRNE-BAS and CEA calculations.

The parameters of these density laws are code/model dependent and are based on different experimental results gathered in different databases. In the case of CEA calculations, the laws proposed in (Barrachin and Defoort, 2004) were used (even if there are not the default ones considered in PROCOR) considering, as suggested in (Barrachin and Defoort, 2004), two possible treatments when, for a given species i, the mixture temperature T is below the species liquidus temperature $T_i^{liquidus}$: either $ρ_i(T < T_i^{liquidus})$ is set to $ρ_i(T_i^{liquidus})$ (M1 hypothesis) or it is extrapolated (M2 hypothesis).

## 2.4. Results comparison and analysis

Table 3 gives the results for the C1 calculations in terms of their comparison against the experimental values. The quantities of interest selected for this comparison are: the oxide phase mass fraction ($w^{oxy}$), the uranium (resp. zirconium) mass fraction in the metal phase $w_U^{met}$ (resp. $w_{Zr}^{met}$). First of all, in most cases, the relative discrepancy associated with the phase partitioning (in terms of oxide phase mass fraction) is less than 10 %. For calculations based on the NUCLEA database (n°5 and, through fitting/interpolation, n°7 and 8), results are deteriorated in MA-

6 conditions i.e. with a higher $χ_{steel}^{exp}$ value. The same comment is valid for results n°6, 2 and 3$^6$ based on the Salay-Fichot model along with IBRAE result n°4. Then, the metal phase enrichment in Zr is underestimated in most calculations in MA-3, 4, 5, 5b, 6 conditions. This discrepancy is the highest for results n°2, 3, 6 and 7 because of the underlying hypothesis of the Salay-Fichot and Nandan-Fichot models that considers the $R_{U/Zr}$ ratio as uniform between the two phases. Indeed, actually, Zr is preferentially extracted in the metal phase in such a way that this ratio significantly decreases in the metal phase at equilibrium. Only result n°1 shows a limited Zr underestimation in these five tests. In MA-1 (higher $R_{U/Zr}$ w.r.t. MA-3) and MA-2 (higher $C_{Zr}$ w.r.t. MA-3) conditions, calculations 1 and 5, both based on thermodynamic databases, are consistent with a significant overestimation of the Zr content. In results n°2, 3, 6 and 7, a compensation effect can be observed for these two tests because of the previously mentioned hypothesis and the associated bias. Regarding result n°8, it gives consistent results w.r.t. result n°1 in terms of $w^{oxy}$ and $w_{Zr}^{met}$ and about 10 % difference in $w_U^{met}$ in all cases. This is expected as explained in more details in (Mativet et al., 2024) because of the way the interpolation scheme is constructed. One can also note that relative discrepancies in terms of $w^{oxy}$ and $w_U^{met}$ are higher for MA-6 test where $χ_{steel}^{exp}$ is the highest (and accordingly, $w^{oxy}$ and $w_U^{met}$ the lowest).

On the overall, considering the fact that these tests are not strictly at

<footnote>$^6$ Note that ASTEC results obtained independently by IRSN and INRNE-BAS are almost the same while, apparently, the Salay-Fichot model implemented in PROCOR differs significantly from the one in ASTEC code. This is attributed to the treatment of steel (as a pseudo-component) that differs between both codes.</footnote>
<caption>**Table 3**</caption>

Step-1, C1 calculations: experimental values for the oxide phase mass fraction $w^{oxy}$, the U (resp. Zr) mass fraction in the metal phase $w_{U}^{met}$ (resp. $w_{Zr}^{met}$) and relative difference (%) for the different codes and models. Cell colors correspond to the error range (green ≤ 5% ≤ yellow ≤ 10% ≤ orange ≤ 15% ≤ red).

<table><thead><tr><th></th><th></th><th>Exp. value</th><th>1<br>NRC KI -<br>TSAR</th><th>2<br>IRSN -<br>ASTEC</th><th>3<br>INRNE -<br>ASTEC</th><th>4<br>IBRAE -<br>HEFEST-<br>URAN</th><th>5<br>CEA -<br>PROCOR -<br>NUCLEA</th><th>6<br>CEA -<br>PROCOR -<br>S&F</th><th>7<br>CEA -<br>PROCOR -<br>N&F</th><th>8<br>CEA -<br>PROCOR -<br>closures</th></tr></thead><tbody><tr><td rowspan="3">MA-1</td><td>$w^{oxy}$</td><td>0.781</td><td>4.2%</td><td>1.0%</td><td>1.0%</td><td>-2.7%</td><td>-2.4%</td><td>-1.6%</td><td>-3.1%</td><td>-1.0%</td></tr><tr><td>$w_{U}^{met}$</td><td>0.425</td><td>-2.9%</td><td>-8.3%</td><td>-8.1%</td><td>-10.7%</td><td>-5.9%</td><td>1.9%</td><td>0.1%</td><td>-14.2%</td></tr><tr><td>$w_{Zr}^{met}$</td><td>0.103</td><td>36.3%</td><td>-0.5%</td><td>-0.3%</td><td>24.5%</td><td>34.0%</td><td>6.5%</td><td>8.7%</td><td>35.3%</td></tr><tr><td rowspan="3">MA-2</td><td>$w^{oxy}$</td><td>0.878</td><td>1.6%</td><td>-1.3%</td><td>-1.4%</td><td>-1.9%</td><td>-3.4%</td><td>-2.5%</td><td>-3.7%</td><td>-3.0%</td></tr><tr><td>$w_{U}^{met}$</td><td>0.201</td><td>-4.9%</td><td>-2.8%</td><td>-1.6%</td><td>-14.4%</td><td>16.2%</td><td>10.5%</td><td>17.0%</td><td>-6.5%</td></tr><tr><td>$w_{Zr}^{met}$</td><td>0.055</td><td>69.9%</td><td>6.4%</td><td>7.8%</td><td>-15.0%</td><td>66.2%</td><td>21.0%</td><td>28.1%</td><td>66.4%</td></tr><tr><td rowspan="3">MA-3</td><td>$w^{oxy}$</td><td>0.726</td><td>8.0%</td><td>5.3%</td><td>5.2%</td><td>4.5%</td><td>1.9%</td><td>3.1%</td><td>1.6%</td><td>4.0%</td></tr><tr><td>$w_{U}^{met}$</td><td>0.430</td><td>-5.5%</td><td>-3.7%</td><td>-3.6%</td><td>-10.1%</td><td>-3.5%</td><td>-0.0%</td><td>1.5%</td><td>-12.5%</td></tr><tr><td>$w_{Zr}^{met}$</td><td>0.173</td><td>4.0%</td><td>-19.9%</td><td>-19.9%</td><td>-21.8%</td><td>-1.5%</td><td>-16.9%</td><td>-15.6%</td><td>1.3%</td></tr><tr><td rowspan="3">MA-4</td><td>$w^{oxy}$</td><td>0.639</td><td>6.3%</td><td>-0.2%</td><td>-0.2%</td><td>-2.2%</td><td>-3.2%</td><td>-3.3%</td><td>-2.9%</td><td>-0.3%</td></tr><tr><td>$w_{U}^{met}$</td><td>0.322</td><td>5.9%</td><td>11.1%</td><td>11.1%</td><td>-0.7%</td><td>9.8%</td><td>15.9%</td><td>14.8%</td><td>0.3%</td></tr><tr><td>$w_{Zr}^{met}$</td><td>0.158</td><td>-3.1%</td><td>-26.2%</td><td>-26.1%</td><td>-10.7%</td><td>-9.9%</td><td>-23.0%</td><td>-23.7%</td><td>-9.0%</td></tr><tr><td rowspan="3">MA-5</td><td>$w^{oxy}$</td><td>0.754</td><td>-0.5%</td><td>-3.7%</td><td>-3.7%</td><td>-3.1%</td><td>-7.6%</td><td>-6.6%</td><td>-7.1%</td><td>-4.7%</td></tr><tr><td>$w_{U}^{met}$</td><td>0.374</td><td>16.4%</td><td>22.9%</td><td>23.0%</td><td>18.6%</td><td>21.9%</td><td>26.2%</td><td>26.0%</td><td>12.4%</td></tr><tr><td>$w_{Zr}^{met}$</td><td>0.256</td><td>-0.4%</td><td>-22.4%</td><td>-22.3%</td><td>-35.9%</td><td>-11.7%</td><td>-20.3%</td><td>-20.5%</td><td>-9.3%</td></tr><tr><td rowspan="3">MA-5b</td><td>$w^{oxy}$</td><td>0.799</td><td>-1.4%</td><td>-2.8%</td><td>-2.9%</td><td>-3.9%</td><td>-7.0%</td><td>-5.3%</td><td>-6.6%</td><td>-4.2%</td></tr><tr><td>$w_{U}^{met}$</td><td>0.428</td><td>10.4%</td><td>16.1%</td><td>16.2%</td><td>16.3%</td><td>15.3%</td><td>18.7%</td><td>19.3%</td><td>6.5%</td></tr><tr><td>$w_{Zr}^{met}$</td><td>0.274</td><td>-1.5%</td><td>-22.6%</td><td>-22.5%</td><td>-37.7%</td><td>-12.7%</td><td>-20.9%</td><td>-20.5%</td><td>-9.7%</td></tr><tr><td rowspan="3">MA-6</td><td>$w^{oxy}$</td><td>0.565</td><td>2.4%</td><td>-7.9%</td><td>-7.2%</td><td>-7.7%</td><td>-9.6%</td><td>-11.3%</td><td>-8.1%</td><td>-13.6%</td></tr><tr><td>$w_{U}^{met}$</td><td>0.215</td><td>21.0%</td><td>35.1%</td><td>35.2%</td><td>16.7%</td><td>30.7%</td><td>41.3%</td><td>35.0%</td><td>41.2%</td></tr><tr><td>$w_{Zr}^{met}$</td><td>0.142</td><td>-12.2%</td><td>-31.8%</td><td>-31.7%</td><td>-19.9%</td><td>-18.1%</td><td>-28.6%</td><td>-31.8%</td><td>-15.7%</td></tr></tbody></table>

<figure><img src="image_4.png" /><figcaption>**Fig. 2.** Step −1, C2 calculations: oxide phase density $\rho^{oxy}$ as a function of $x_{steel}$ in MA-1 (left) and MA-6 cases – circled numbers in the legend refer to the code/model numbering of Table 2.</figcaption></figure>

thermodynamic equilibrium and the underlying experimental uncertainty, it is worth noting that the results based on a thermodynamic database with a Gibbs energy minimizer (n°1 and 5) are in fairly good agreement.

Fig. 2 (resp. Fig. 3) depicts the oxide (resp. metal) phase density $\rho^{oxy}$ (resp. $\rho^{met}$) as a function of $x_{steel}$ for C2 calculations in the MA-1 (heavier metal) and MA-6 (lighter metal) cases. In addition, phase density differences $\rho^{met} - \rho^{oxy}$ [kg.m$^{-3}$] for $x_{steel} = \chi_{steel}^{exp}$ are given for all the cases in Table 4. In this second set of calculations, PROCOR results are only shown with the Salay-Fichot equilibrium model (n°6) with the two different hypotheses (denoted M1 and M2) regarding the density calculation introduced in §2.3. It can be observed that, as expected,

these hypotheses have only an impact on the oxide phase density. Moreover, using M1 (resp. M2), the oxide mass density calculated by PROCOR is rather consistent with result n°1 by NRC KI (resp. n°2 by IRSN). In all cases, result n°4 by IBRAE exhibits a significantly higher oxide density. In the case of INRNE-BAS result (n°3), they were performed at a lower temperature in such a way that, compared with result n°2 (that uses the same ASTEC code), a higher oxide density is obtained. Regarding the metal density, result n°4 gives lower density than results n°2 and 6 while calculation n°1 gives a higher (resp. lower) density for a low (resp. high) $x_{steel}$ value as in MA-1 (resp. MA-6) conditions. On the overall, when looking at the phase density differences, PROCOR results with M2 hypothesis, ASTEC results produced by IRSN and NRC-KI
<figure><img src="image_5.png" /><figcaption>Fig. 3. Step − 1, C2 calculations: metal phase density ρ met as a function of x steel in MA-1 (left) and MA-6 cases.</figcaption></figure>

results are rather close. The order of magnitude of the difference is comparable with the temperature effect that can be quantified when comparing ASTEC results between IRSN and INRNE-BAS. The calcula- tions that give the most significant differences are the ones produced by IBRAE with HEFEST_URAN.

These density differences would need further analysis going back to the density laws implemented in the different codes that may not be at the state-of-the-art (this comment applies to PROCOR based on TOLBIAC-ICB physical properties laws for instance) taking into account recent experimental data. This was out of the scope of this benchmark but is a clear perspective.

3. Step 2: MASCA RCW-100

3.1. *Brief summary of the experiment*

In the OECD-MASCA experimental program (Tsurikov et al., 2007), one prototypical experiment of larger scale than the previous MA tests has been conducted. As such, this MASCA RCW-100 test (Asmolov et al., 2003), carried out in a cold crucible of about 18 cm-diameter, is of in- terest for characterizing the stratification transient. In this experiment, 45.3 kg of suboxidized molten corium ($R_{U/Zr} = 1.2$, $C_{Zr} = 0.32$) has been put in interaction with about 4.6 kg of molten steel poured on top during 22 min under inert atmosphere (Ar). From the thermodynamic equilibrium point of view, $x_{steel}$ is well below the stratification inversion threshold. The analysis of the post-mortem ingot clearly shows that the system has not reached a stationary state with two stratified layers. The vertical cross-section of the ingot is shown in Fig. 4. The interpretation proposed in (Ratel et al., 2007) considers this post-mortem ingot as the solidified state of the system during the transient relocation of steel below the oxide; the metal phases are spatially distributed as follows:

- a continuous light metal phase (7) above the oxide pool (5);

- a dispersed metallic phase enriched in U and Zr that can be viewed as centimetric droplets (4) relocating downward through oxide (5);

- a continuous heavy metal phase (2) below the oxide (5).

From there, two mechanisms are at play, as discussed in (Ratel et al., 2007). First, U and Zr transfer from the oxide to the steel (associated with modification of the redox equilibrium $U+ZrO_2 \leftrightarrow UO_2+Zr$ at the interface) that induces local changes in mass density. Then, when the metal in the boundary region becomes “sufficiently” heavier than the oxide, the triggering and growth of Rayleigh-Taylor instabilities at the interface between the light metal layer and the oxide lead to the for- mation and detachment of heavy metal droplets. They sink through the oxide and form a continuous heavy metal phase at the bottom. These hydrodynamic phenomena appear to be periodic in nature and are much faster than the bulk transport of components within the light metal layer. Indeed, as shown in Fig. 5, the boundary region near the interface concentrates the U and Zr components of the light metal phase.

In particular, this interpretation of RCW-100 test is the basis of the legacy PROCOR stratification model (Le Tellier et al., 2015) (originating from the modelling hypotheses proposed in (Ratel et al., 2007) where the overall kinetics is supposed to be controlled by the interlayer mass transfer (the hydrodynamic phenomena are not modelled).

3.2. *Benchmark definition*

The general goal is a comparison between the experimental results (from the post-mortem ingots analyses) and numerical results. The different models aim at simulating the stratification transient where, from a two-layer pool with steel on the top, a heavy metal phase is formed. The initial state of the two-layer system is described in details in the “supplementary material” section. From there, the time-dependent spatial distribution of the phases is simulated until steady-state has been reached. This initial inventory was constructed back from the in- ventory of the different phases in the post-mortem that is used for comparison with simulation results at time $t = 22$ min.

This is a complex experiment and only indirect post-mortem data are available for characterizing the phases stratification.<fnref n="8" /> Accordingly, the considered simulation set-up is actually an idealized two-layer config- uration representative of the system state after the corium has been melted and the molten steel has been poured on top.

<footnote n="7">⁷ In the post-mortem state, internal porosities can be observed in these droplets. The SEM/EDX composition analysis reveals that they were probably filled by CO gas (traces of Zr($O_{0.14}C_{0.85}$) are found at the interface). Accord- ingly, as mentioned in (Asmolov et al., 2003), it is considered that this gas formation is associated with the decrease of the oxygen solubility in metal when solidification took place and CO was formed by the interaction between this oxygen and carbon coming from the steel. Accordingly, at liquid state, no gas is expected.</footnote>

<footnote n="8">⁸ In the CORDEB2 CP7-02 experiment used in the third step of this bench- mark, the experimental procedure included taking samples from the top metal layer during the transient. In this way, the post-mortem ingot is not the only source of information. In the MASCA program, such a procedure was not considered.</footnote>
<caption>**Table 4**</caption>

Step-1, C2 calculations: phase density difference $\rho^{met} - \rho^{oxy}$ [kg.m$^{-3}$] for $x_{steel} = x_{steel}^{exp}$.

<table><thead><tr><th></th><th>1<br>NRC KI - TSAR</th><th>2<br>IRSN - ASTEC</th><th>3<br>INRNE-BAS - ASTEC</th><th>4<br>IBRAE - HEFEST_URAN</th><th>6<br>CEA - PROCOR - S&amp;F, M1</th><th>6<br>CEA - PROCOR - S&amp;F, M2</th></tr></thead><tbody><tr><td>MA-1</td><td>305.6</td><td>-35.3</td><td>-91.4</td><td>-342.9</td><td>245.3</td><td>42.8</td></tr><tr><td>MA-2</td><td>-717.3</td><td>-771.1</td><td>-785.6</td><td>-1075.9</td><td>-559.3</td><td>-763.2</td></tr><tr><td>MA-3</td><td>543.6</td><td>315.4</td><td>316.1</td><td>-68.3</td><td>503.3</td><td>316.1</td></tr><tr><td>MA-4</td><td>64.8</td><td>-4.5</td><td>-50.5</td><td>-489.1</td><td>183.6</td><td>-7.6</td></tr><tr><td>MA-5</td><td>794.0</td><td>712.7</td><td>721.0</td><td>542.4</td><td>907.3</td><td>740.9</td></tr><tr><td>MA-5b</td><td>955.1</td><td>927.0</td><td>936.2</td><td>984.1</td><td>1100.8</td><td>937.7</td></tr><tr><td>MA-6</td><td>-454.4</td><td>-271.1</td><td>-296.8</td><td>-809.3</td><td>-207.4</td><td>-334.4</td></tr></tbody></table>

<figure><img src="image_6.png" /><figcaption>**Fig. 4.** Vertical cross-section of the MASCA-RCW post-mortem ingot (adapted from (Tsurikov et al., 2007)) – diameter ~ 18 cm and height ~ 26 cm – without (1).</figcaption></figure>

As such, only a semi-quantitative comparison between codes and experiment is possible. However, in view of the level of uncertainty associated with this stratification issue, it is the authors' point of view that such a comparison (and the associated code-to-code comparison) is still very valuable.

During these 22 min of interaction between molten steel and molten corium, the thermal power deposited into the melt was about 25 kW while the liquidus temperature of the overall system is about 2500 °C. It is worth noting that the steel was poured in liquid state on top of the two-layer pool at a temperature of about 1500 °C.

**Nota Bene** The first phase of the experiment (corium melting), while not the focus of this benchmark as discussed above, is also of partial interest for code validation as demonstrated by supplementary calculations performed by IBRAE with HEFEST_URAN in the frame of this collaborative work. A summary of these calculations is given in the "supplementary material" section associated with this paper.

### 3.3. Codes and models involved, main parameters selection

The different stratification kinetics models used by the participants through different codes are described in Table 5. Regarding these models, important remarks can be made:

- in most of these models, the detachment of U-/Zr- enriched metal from the upper metal phase under the form of droplets (that relocate downwards to form the heavy metal phase formation) is based on a

<figure><img src="image_7.png" /><figcaption>**Fig. 5.** Microscopic structure of the solidified light metal phase of the MASCA-RCW post-mortem ingot (adapted from (Tsurikov et al., 2007)) – dimensions ~ 9x4cm.</figcaption></figure>

1. The corium lower non-melted briquettes;

2. The lower metallic part;

3. Zone of a partially melted corium;

4. Roundish metallic parts in the central zone;

5. The ingot oxidic part;

6. Epoxy;

7. The upper metallic part;

8. The ingot surface;

simple density difference criterion between the interfacial enriched metal and the oxide;

- only the model associated with result n°5 explicitly takes into account the metal droplets and their relocation; in other models, the time for relocation is neglected.

In all these models, the main important parameters are related to the inter-layer mass transfer kinetics (either effective diffusion coefficients or mass transfer coefficients). In the frame of this benchmark, a calibration has been performed by the different participants so that the mass of the heavy metal phase at t = 22 min is in good agreement with the experiment. In addition, for result n°5, the model parameters were selected so that the first droplet detachment occurs slightly before t = 22 min in accordance with the measurements during the experiment that show a rapid increase in the temperature at the bottom of the crucible slightly before the power was shutdown, indicating a change in the melt phase topology. Fig. 6 illustrates such calibrations (through limited single mode parametric analyses) for the ASTEC (IRSN) and PROCOR (CEA) models in terms of the oxide and heavy metal masses evolutions. In both ASTEC (n°1) and PROCOR “legacy” (n°4) models, this parameter is an effective diffusion coefficient and, interestingly, in both cases, the optimal value is close to 5·10⁻⁹ m²s⁻¹. In the third model depicted, PROCOR “new” model (n°5), a different calibration was chosen with a diffusion coefficient (in this case, associated with the oxygen effective diffusion in the oxide phase) kept constant equal to 5·10⁻⁹ m²s⁻¹. Indeed, in this more complex model, the mass transfer coefficients are calculated at each time step by an heat and mass transfer analogy that requires the evaluation of the thermal balance of the different pool layers. For such an experimental process, the closure laws for this thermal balance are not trivial as the usual Nusselt correlations are not directly applicable. Indeed, the inductive heating creates additional eddy currents (Guo et al., 2024) and the cold crucible is much smaller than an actual reactor vessel. Accordingly, it was chosen to do the calibration under the form of multiplicative coefficients applied to the transfer coefficients evaluated by these usual correlations. In this same model, it is also worth noting that the density difference criterion for triggering Rayleigh-Taylor instability and the formation of metal
<table><caption>**Table 5**
The different codes and models for the stratification kinetics involved in step-2.</caption><thead><tr><th>Institution</th><th>N°</th><th>Code / model</th><th>Description / comments</th><th>Ref.</th></tr></thead><tbody><tr><td>IRSN<br>INRNE-<br>BAS</td><td>1<br>2</td><td>ASTEC / inter-layer<br>mass transfer model</td><td>Mass transfer<br>considered<br>simultaneously at the<br>two interfaces upper<br>metal/oxide, oxide/<br>lower metal; local<br>interface equilibrium<br>approximated by the<br>thermochemical<br>equilibrium (Salay-<br>Fichot model, see n°2/<br>3 in Table 2) of the<br>two phases at this<br>interface</td><td>(Carénini<br>and<br>Fichot,<br>2018)</td></tr><tr><td>IBRAE</td><td>3</td><td>HEFEST_URAN /<br>MultiMelt module</td><td>1D finite element<br>diffusion model for<br>uranium in the upper<br>metal phase</td><td>–</td></tr><tr><td>CEA</td><td>4</td><td>PROCOR / legacy<br>inter-layer mass<br>transfer model</td><td>Evolution equation for<br>the uranium mass<br>fraction in the oxide<br>phase considering the<br>exchange with the<br>upper metal phase;<br>degree of<br>advancement towards<br>global<br>thermochemical<br>equilibrium (Salay-<br>Fichot model, see n°6<br>in Table 2)</td><td>(Le Tellier<br>et al.,<br>2015)</td></tr><tr><td></td><td>5</td><td>PROCOR / “new”<br>integral mass transfer<br>model that takes into<br>account the dispersed<br>metal phase (mass<br>transfer and<br>dynamics)</td><td>Mass and element<br>mass conservation for<br>all phases; interface<br>jump conditions<br>associated with local<br>equilibrium simplified<br>under the hypothesis<br>that there is no oxygen<br>(resp. steel) in the<br>metal (resp oxide)<br>phases;<br>thermodynamic<br>closures: see n°8 in<br>Table 2; 1D droplet<br>momentum<br>conservation equation</td><td>(Le<br>Tellier,<br>2021)<br>(Le<br>Tellier,<br>2023)<br>(Mativet<br>et al.,<br>2024)</td></tr></tbody></table>

droplet was set to 200 kg.m⁻³. This value was estimated from the actual composition of the metal droplets (n°4 in Fig. 4) and the oxide phase (n°5 in Fig. 4) in the RCW-100 post-mortem ingot.

### 3.4. Results comparison and analysis

Fig. 7 presents the results obtained with the different codes in terms of the oxide ($m^{oxy}$) and heavy metal phase ($m^{metl}$) masses evolution. The U ($w_{U}^{metl}$) and Zr ($w_{Zr}^{metl}$) mass fractions in the heavy metal phase are also depicted as a function of time. Experimental values (from post-mortem analyses of the experiment ingot's metal phases) are also shown at t = 22 min for comparison purpose. More precisely, three values are depicted for $m^{metl}$, $w_{U}^{metl}$ and $w_{Zr}^{metl}$ considering:

- the actual heavy metal phase below the oxide (met↓);

- the actual heavy metal phase (met↓) plus the droplets inside the oxide (drop↓);

- the actual heavy metal phase (met↓) plus the droplets (drop↓) plus the U-, Zr-enriched boundary region of the light metal layer (met↑).

The following general trends can be observed on the phase masses

evolution. The heavy metal phase formation is described continuously in results n°1, 2, and 4 (as the underlying models do not intend to capture the discontinuous nature of the process associated with the Rayleigh-Taylor instabilities) and starts from t = 0 s. In result n°3, the heavy metal formation starts around 800 s and then steadily increases by further continuous relocation from the light metal layer. In result n°5, a first droplets' detachment occurs just around 1310 s to form the heavy metal layer. Afterwards, its mass slowly increases by mass transfer through its interface with the oxide phase until the next droplet detachment (not shown in Fig. 7, occurring around 2750 s). As expected from calibration, the different models' prediction of the heavy metal mass at 22 min is fairly good.

Further remarks can be made based on the evolution of the U and Zr mass fractions in the heavy metal layer in Fig. 7. First, the heavy metal phase composition is constant in time in the PROCOR legacy model. Indeed, because of the underlying modelling hypotheses, it is set to its value at global thermochemical equilibrium. With ASTEC model,<fnref n="9" /> this composition in U and Zr rapidly increases after 200 s and then slowly decreases towards its global equilibrium value. At the experiment exposure time, for both models, the U mass fraction is approximately reproduced while the Zr mass fraction is underestimated. This is consistent with the trends observed with the Salay-Fichot equilibrium model in both codes in Table 3 considering the MA-3 conditions that are close to the RCW-100 global inventory. Second, in PROCOR “new” model, looking at the heavy metal phase composition when it is formed around 1310 s, the opposite trend is observed consistently with the observations made in Table 3 in MA-3 conditions for result n°8. After its formation, the U and Zr content of the heavy metal phase increases by mass transfer through its interface with the oxide phase. Third, in IBRAE calculation, the heavy metal formed around 650 s exhibits a high U and Zr content that rapidly decreases (by further addition of metal relocated from the light metal layer); at the experiment exposure time, the U mass fraction is approximately reproduced while the Zr mass fraction is underestimated.

While this experiment offers a unique qualitative comparison for stratification kinetics and can be used for calibration purpose, it appears clearly that additional experimental results are needed to go further in the model validation as already stated in (Fichot et al., 2020).

### 4. Step 3: CORDEB2 CP7-02

#### 4.1. Brief summary of the experiment

In the H2020 IVMR European project, CORDEB2 CP7-02 prototypical experiment was performed in RASPLAV-3 facility at NITI. This program was proposed and co-funded by IRSN, CEA, EDF and Framatome. It studied the interaction between a two-layer pool (heavy metal layer below the oxide) with a crust at the oxide top surface, and molten steel added on top. The test facility uses a 7 cm -diameter cold crucible, as in the MASCA-MA tests. The results of this test were shared by French partners in the scope of this CRP.

The experimental procedure for establishing the three-layer molten pool was the following:

- a suboxidized corium pool ($R_{U/Zr} = 1.2, C_{Zr} = 0.30$) of about 2.15 kg was originally produced under argon atmosphere;

- 0.43 kg of stainless steel was then added, corresponding to a mass ratio $x_{steel}$ of about 20 % with respect to the mass of oxide;

- the resulting metallic melt was heavier than the oxide and fall at the bottom of the pool ($T_{pool} \approx 2590^{\circ}\text{C}$);

- the crust was then formed by freezing on top of the oxidic layer;

<footnote n="9">⁹ both IRSN and INRNE-BAS calculations are almost undistinguishable.</footnote>
<figure><img src="image_8.png" /><figcaption>**Fig. 6.** Step-2: illustration of model calibration: heavy metal phase (m<sup>metl</sup>) mass evolution when varying some models parameters and comparison with experimental values.</figcaption></figure>

- after that at 4200 s, 0.33 kg of stainless steel was poured onto the crust surface; its mass ratio x<sub>steel</sub> was about 15 % with respect to the mass of oxide.

The test was then conducted under inert atmosphere (Ar) and
maintaining a temperature of about 1900 °C at the surface of the pool
during 6 h. During the test, regular sampling of the top metal layer were
carried out. Post-mortem analyses of these samples offer interesting
information about the time evolution of the top metal layer composition.

The vertical cross-section of the post-mortem ingot is depicted in
Fig. 8 where a clear interaction through the crust can be observed. The
metal phases are spatially distributed as follows:

- a light metal phase (1) above the oxide crust (2);

- a light metal phase (3) below the crust (2) and above the oxide pool (6);

- two others heavy metal phases of smaller sizes (4) and (5), respec-
tively in the middle and below the oxide (6).

This test shows that the molten steel at the top interacts with the
oxide crust and the pool below leading to species partitioning between
the oxide and metal phases. At the end of the experiment, the heavy
metal layer has become lighter than the oxide and has relocated below
the oxide crust. A major part of the molten steel above the crust has
relocated through the crust and joined the metal layer below the crust.
The composition of the top metal layer shows a significant enrichment in
Zr and U. Compositions of the metal layers above and below the crust are
similar. Interactions between stainless steel and oxide crust are visible in
the microscopic structure of the interface illustrated in Fig. 9.

<figure><img src="image_9.png" /><figcaption>**Fig. 7.** Step-2: phase masses and heavy metal phase composition evolution for the different simulations and comparison with experimental values – circled numbers in the legend refer to the code/model numbering of Table 5.</figcaption></figure>
<figure><img src="image_10.png" /><figcaption>Fig. 8. Vertical cross-section of the CORDEB2 CP7-02 post-mortem ingot (adapted from (Almjashev et al., 2019)) – diameter ~ 7 cm.</figcaption></figure>

<figure><img src="image_11.png" /><figcaption>Fig. 9. Microscopic structure of the interface between oxide crust and light metal phase of the CORDEB2 CP7_02 post-mortem ingot (adapted from (Almjashev et al., 2019)).</figcaption></figure>

<figure><img src="image_12.png" /><figcaption>Fig. 10. Step-3: top metal layer content in Zr and U with time – Time corresponds to the absolute time form the beginning of the test: introduction of the 2nd part of the oxide at the top of the pool after oxide crust formation begins at 1.17 h, followed by about 6 h of exposure.</figcaption></figure>

## 4.2. Benchmark definition

The general goal is a comparison between the experimental results and numerical results obtained by different models that simulate such a

stratification transient. Experimental data are based on the post-mortem analyses of the ingot and top metal layer samples. Detailed results of the CP7-02 tests are given in the supplementary material associated with this paper. As in the previous steps of this benchmark, the focus is on the simulation of the inter-layer mass transfer and the associated stratification transients with prescribed temperature gradient and crust thickness. Accordingly, the benchmark participants did not simulate the complete thermalhydraulic behavior of the melt.

## 4.3. Codes and models involved

In this third step, the different stratification kinetics models used by the participants are a subset of the ones used in the previous step (described in Table 5). Namely, ASTEC with its inter-layer mass transfer model (n°1 and n°2 in Table 5), HEFEST_URAN with the MultiMelt module (n°3 in Table 5), and PROCOR with its “new” inter-layer mass transfer model (n°6 in Table 5) were used for this step 3 of the benchmark. In order to account for the specificity of the CORDEB2 CP7-02 test compared to MASCA RCW-100 test, i.e. the presence of the oxide crust between the oxide and the top metal layer, HEFEST_URAN and PROCOR model were updated: a mass transfer resistance was added in order to represent the crust.<fnref n="10" />

<footnote n="10">¹⁰ Regarding PROCOR, only the “new” model was considered by CEA in this step as its legacy model would not have been suitable to introduce such a mass transfer resistance to take into account the crust effect.</footnote>
<figure><img src="image_13.png" /><figcaption>**Fig. 11.** Step-3: influence of crust resistance modelling assumption in PROCOR code: mass fraction evolution in the light metal layer (the associated crust resistances' evolutions are depicted in Fig. 12).</figcaption></figure>

<figure><img src="image_14.png" /><figcaption>**Fig. 12.** Step-3: crust resistances' evolutions considered in PROCOR calculations.</figcaption></figure>

### 4.4. Results comparison and analysis

The overall trend observed during the experiment were captured in all simulations with a progressive top layer enrichment in Zr and U. As illustrated in Fig. 10, final values of the top metal layer composition are in overall good agreement with the experimental results. This was expected considering the results obtained for the phases composition at thermochemical equilibrium previously discussed with MASCA MA validation step. The main differences between participants lie in the kinetics of species transfer, especially during the first two hours of interaction.

Both INRNE-BAS and IRSN simulations with the ASTEC code exhibit a clear overestimation of the mass transfer kinetics. This is consistent with the fact that the resistance of the oxide crust is not taken into account in current ASTEC modelling. On the contrary, results of PROCOR and HEFEST codes, with consideration of crust resistance to species transfer show a better agreement with the experimental results. It indicates that, in lumped parameter models, such a simple approach is suitable.

In PROCOR code, different evolution assumptions of this crust resistance $R_c$ have been tested as illustrated in Fig. 11 and Fig. 12. In particular, it can be seen that a constant value of $R_c$ cannot adequately

capture the evolution of the light metal layer composition. Actually, this result is consistent with the fact that the complex crust dissolution process cannot be taken into account with a constant crust resistance. The best-estimate results (used in Fig. 10 for comparison with other codes) have been obtained by considering that $R_c$ follows an inverse-linear law after a 1 h-period during which the crust resistance is assumed to be constant (see $R_c^2$ in red in Fig. 12). The 1 h-phase with a constant crust resistance is an initial incubation period representing the time necessary for interaction between the oxide crust and the molten steel. Such modelling is in agreement with interpretation of experimental results proposed in (Fichot et al., 2019) and in (Fichot et al., 2022), with identification of channels formation through the crust, enriched with metallic species (cf. Fig. 9). In addition, the motivation for choosing an inverse-linear law for $R_c$ after this incubation period is the following. The crust resistance $R_c$ can be expressed as $\frac{e_c}{D_c^{eff}}$ where $e_c$ is the crust thickness (fairly constant during the experiment exposure time, equal to about 5 mm) and $D_c^{eff}$ is an effective diffusion coefficient. Based on the results of the CORMET<fnref n="11" /> experiments (Pivano et al., 2019); $D_c^{eff}$ is assumed to vary linearly in time. Indeed, in these dissolution experiments, it was found, through a series of experiments with different exposure times (ranging from 30 min to 3 h), that the penetration length of steel through the crust $L_{pen}$ varies almost linearly as a function of the exposure time $t_{exp}$ in such a way that the effective diffusion coefficient evaluated as $\frac{L_{pen}^2}{t_{exp}}$ varies almost linearly as a function of $t_{exp}$.

Further comparisons are proposed in Fig. 13 in terms of the phases mass evolution. In ASTEC simulation by INRNE-BAS, the 3-layer configuration was initialized with the first part of the steel introduced at the bottom of the crucible (in the heavy metal layer) and the 2nd part at the top (the light metal layer). Hence, material interaction begins at the same time at both interfaces of the oxide. This differs from the experiment where the bottom metal layer has already reached its equilibrium composition when the 2nd part of steel is introduced. This explains differences with ASTEC results from IRSN in terms of initial masses of oxide and heavy metal.

Considering the stratification inversion, as observed at the end of the simulation, ASTEC code predicts layers inversion whereas HEFEST and

<footnote n="11">¹¹ These experiments were carried out in the VITI facility at CEA Cadarache in order to specifically study the dissolution process (in supplement to CORDEB2 tests) by considering the interaction of steel droplet on top of suboxidized solid corium.</footnote>
<figure><img src="image_15.png" /><figcaption>Fig. 13. Step-3: evolution of masses of the metal and oxide layers with time in the different simulations and comparison of final values with experimental results. For HEFEST results, it should be noted that LM layer corresponds to the sum of the light metal above and below the oxide crust.</figcaption></figure>

PROCOR codes do not simulate it in this benchmark even when the heavy metal layer density is lower than the one of the oxide. In the case of PROCOR, it is because the actual density different criterion (set to the same value as in RCW-100 simulation) is not met. To further compare the kinetics of interaction between all simulations, taking into account the large uncertainty associated with this density difference criterion, phases densities have been compared for HEFEST_URAN and PROCOR simulations and it indicates that density inversion is reached about 1 h after the begins of the 3 layers interaction, consistently with the ASTEC result obtained by IRSN.

Kinetics of interaction obtained in the ASTEC simulation by INRNE-BAS is significantly slower and does well reproduce the heavy metal layer mass at the end of the experiment. However, in this test CP7-02 test, the small mass of heavy metal layer observed in the ingot after the experiment may not be interpreted as an indication of the kinetics of the stratification inversion, 6 h after the beginning of the 3-layer interaction. It seems probable that this mass is associated with the cooling at the bottom of the crucible, leading to a partial solidification of the heavy metal layer that does not participate anymore in the species interaction in the molten pool.

## 5. Conclusions and perspectives

In this paper, the three steps of a benchmark devoted to in-vessel corium thermochemistry have been presented both in terms of test specifications and results obtained by the participants involved in the frame of the IAEA CRP on In-Vessel Melt Retention. The first step, based on the MASCA MA experiment series, has highlighted the overall good capability of either simple models published in the open literature or thermodynamic equilibrium calculations (based on a thermodynamic database and a Gibbs energy minimizer) to evaluate the mass and species partitioning of the two-layer pool at steady-state. It has also shown discrepancies among codes regarding the phase density evaluation that would require further analysis and comparison with state-of-the-art experimental measurements of such mixture densities. Considering the MASCA RCW-100 experiment, the second step was devoted to the stratification transient associated with the heavy metal formation at the bottom of the pool. Four different models were approximately calibrated and compared based on the experimental post-mortem analyses

highlighting the needs for further work on the transient model validation. In the third step, three out of these four models were used in a case where the effect of a mechanically stable crust at the interface between the oxide and light metal layers is considered, based on the CORDEB CP7-02 experiment. It was shown that, in lumped parameter models, its effect can be captured by introducing a crust resistance (to mass transfer) and the modelling effort should now be put on the establishment of closure laws for this resistance. In terms of R&D to further improve stratification modelling in severe accident codes, dedicated new experiments adequately combined with focused mesoscopic scale simulations are needed. Sensitivity analyses carried with existing models (as used in this benchmark, keeping in mind their actual limitations) can be helpful to prioritize this work.

## Declaration of competing interest

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

## Acknowledgments

Authors would like to acknowledge the IAEA for the coordination of this CRP and in particular Mr. Miassoedov from the Division of Nuclear Power and Mr. Massara and Ms. Veneau from the Division of Nuclear Installation Safety.

## Appendix A. Supplementary data

Supplementary data to this article can be found online at https://doi.org/10.1016/j.anucene.2025.111514.

## Data availability

Data will be made available on request.

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