温度が上昇すると、被覆管外周部では水蒸気酸化（水蒸気/Zr反応）により酸化物の二重層構造（ZrO2外層とα-Zr（O）内層）が形成され、約1200℃を超えると、水蒸気/Zry反応が急速に進み、温度の急上昇が起こる（毎秒8℃以上）<ref name="Hurumai" />。被覆管の中央にはβ相が残留する。UO2燃料t/Zry界面では、酸素とウランがペレットからジルカロイ側に、Zrが燃料側に拡散を開始する。しかしながら、比較的低い温度（約1800℃以下）では酸素の拡散が支配的と考えられ、UとZrの拡散は界面近傍に限定される<ref name="Hofmann">P. Hofmann, D.K. Peck, "UO<sub>2</sub>/Zircaloy-4 chemical interactions from 1000 to 1700ﾟC under isothermal and transient temperature conditions", ''J. Nucl. Mat.'' 124, 80-105 (1984). https://doi.org/10.1016/0022-3115(84)90013-8</ref>。 酸素ポテンシャルが低下したUO2/Zry界面の非常に狭い領域（おそらくα-Zr（O）領域側）において、UO2とZrの間の酸化還元相互作用によって少量の液体が形成される可能性がある。その先に燃料からZryへの酸素拡散によるα-Zr(O)相が形成される。
温度が上昇すると、被覆管外周部では水蒸気酸化（水蒸気/Zr反応）により酸化物の二重層構造（ZrO<sub>2</sub>外層とα-Zr（O）内層）が形成され、約1200℃を超えると、水蒸気/Zry反応が急速に進み、温度の急上昇が起こる（毎秒8℃以上）<ref name="Hurumai" />。被覆管の中央にはβ相が残留する。UO<sub>2</sub>燃料t/Zry界面では、酸素とウランがペレットからジルカロイ側に、Zrが燃料側に拡散を開始する。しかしながら、比較的低い温度（約1800℃以下）では酸素の拡散が支配的と考えられ、UとZrの拡散は界面近傍に限定される<ref name="Hofmann">P. Hofmann, D.K. Peck, "UO<sub>2</sub>/Zircaloy-4 chemical interactions from 1000 to 1700ﾟC under isothermal and transient temperature conditions", ''J. Nucl. Mat.'' 124, 80-105 (1984). https://doi.org/10.1016/0022-3115(84)90013-8</ref>。 酸素ポテンシャルが低下したUO<sub>2</sub>/Zry界面の非常に狭い領域（おそらくα-Zr（O）領域側）において、UO<sub>2</sub>とZrの間の酸化還元相互作用によって少量の液体が形成される可能性がある。その先に燃料からZryへの酸素拡散によるα-Zr(O)相が形成される。
Phebus-FPT試験<ref name="Phebus">B. Clément, N.H. Girault, G. Repetto, D. Jacquemain, A.V. Jones, M.P. Kissane, P. von der Hardt, "LWR severe accident simulation: synthesis of the results and interpretation of the first Phebus FP experiment FPT0", ''Nucl. Eng. Des.'' 226, 5-82 (2003). https://doi.org/10.1016/S0029-5493(03)00157-2</ref>等の模擬試験での観測結果に基づき、約2200℃でU-Zr-Oメルトが燃料棒の外周から噴出し、炉心下方向にリロケーション開始すると考えられている<ref name="ANFC_kurata" />。シビアアクシデント解析コード（MAAP、MELCOR、ASTEC、SAMPSONなど）では、この温度が燃料溶融温度としてモデル化されている。また、ASTECコード等では、溶融物がZrO<sub>2</sub>膜を破って下方にリロケーションするか、あるいは、ZrO<sub>2</sub>膜の内側に維持されたまま、機械的に崩落するかについて、閾条件があるとされている。約2200℃に到達した際の外周のZrO<sub>2</sub>膜が約200～250μmより厚い場合、U-Zr-Oメルトはこれを破ることができず、燃料棒内部で保持され、なんらかの衝撃により、機械的に崩落すると考えられている。
Phebus-FPT試験<ref name="Phebus">B. Clément, N.H. Girault, G. Repetto, D. Jacquemain, A.V. Jones, M.P. Kissane, P. von der Hardt, "LWR severe accident simulation: synthesis of the results and interpretation of the first Phebus FP experiment FPT0", ''Nucl. Eng. Des.'' 226, 5-82 (2003). https://doi.org/10.1016/S0029-5493(03)00157-2</ref>等の模擬試験での観測結果に基づき、約2200℃でU-Zr-Oメルトが燃料棒の外周から噴出し、炉心下方向にリロケーション開始すると考えられている<ref name="ANFC_kurata" />。シビアアクシデント解析コード（MAAP、MELCOR、ASTEC、SAMPSONなど）では、この温度が燃料溶融温度としてモデル化されている。また、ASTECコード等では、溶融物がZrO<sub>2</sub>膜を破って下方にリロケーションするか、あるいは、ZrO<sub>2</sub>膜の内側に維持されたまま、機械的に崩落するかについて、閾条件があるとされている。約2200℃に到達した際の外周のZrO<sub>2</sub>膜が約200～250μmより厚い場合、U-Zr-Oメルトはこれを破ることができず、燃料棒内部で保持され、なんらかの衝撃により、機械的に崩落すると考えられている。
<span style="color: red;">参考文献：Phebusの論文。これ？PFT 0 - 5全部ある or 持ってる人いる？</span>
======燃料溶融進展にともなう溶融物の平均組成の変化======
======燃料溶融進展にともなう溶融物の平均組成の変化======
[[ファイル:Variation in the local composition of the fuel rod with increasing temperature.png|サムネイル|315x315ピクセル|'''Figure 2: Variation in the local composition of the fuel rod with increasing temperature. A’ represents the initial internal oxidation (a-Zry formation) at the initial temperature excursion and A represents the onset of major oxidation/liquefaction reactions.''']]
[[ファイル:Variation in the local composition of the fuel rod with increasing temperature.png|サムネイル|315x315ピクセル|図 2: Variation in the local composition of the fuel rod with increasing temperature. A’ represents the initial internal oxidation (a-Zry formation) at the initial temperature excursion and A represents the onset of major oxidation/liquefaction reactions.]]
[[ファイル:Figure 18(a) Schematic image of a horizontal cross section of a prototypic BWR Fuel assembly. The red square shows the section illustrated in Fig. 18(b)..png|サムネイル|304x304ピクセル|Figure 3(a) Schematic image of a horizontal cross section of a prototypic BWR Fuel assembly. The red square shows the section illustrated in Fig. 3(b).]]
[[ファイル:Figure 18(a) Schematic image of a horizontal cross section of a prototypic BWR Fuel assembly. The red square shows the section illustrated in Fig. 18(b)..png|サムネイル|304x304ピクセル|図3(a) Schematic image of a horizontal cross section of a prototypic BWR Fuel assembly. The red square shows the section illustrated in Fig. 3(b).]]
(d) B4C-SS-Zrメルトと残留B4Cの水蒸気酸化反応[[ファイル:Schematic image of liquefaction progression at the interface between the control blade and the channel box.png|サムネイル|472x472ピクセル|Figure 3(b) Schematic image of liquefaction progression at the interface between the control blade and the channel box.]]
(d) B4C-SS-Zrメルトと残留B4Cの水蒸気酸化反応
<u>Reaction (a) (B4C-SS system):</u>
So-called ‘eutectic’ melting between B4C and SS could occur at approximately 1200 °C. The Fe-B-C ternary phase diagram indicates that the most of SS cladding (major component: Fe) and a small amount of B4C are liquefied by the ‘eutectic’ formation. Hence, a significant amount of B4C is able to remain in the B4C-SS melt [10]. For more detailed understanding of the ‘eutectic’ melting, one needs to evaluate selective Fe-C reactions as opposed Fe-B reactions in the Fe-B-C melt and the local precipitation of Cr-boride [11, 12].
Table 16 shows the current assessed status of the ternary sub-systems of the B4C-SS systems. (‘⭕’ means the full assessment and ‘-’ means that its system has not been assessed yet.) The most important sub-system for this particular interaction is clearly Fe-B-C, because Fe is a dominant component of SS, which is already stored in both of TAF-ID and NUCLEA. Also, Fe-Ni-Cr system is already stored in the both databases. By using these databases, the ‘simplified’ evaluation of the ‘eutectic’ melting between B4C and SS could be carried out. However, the databases are still insufficient for the other subsystems especially including Cr, B and C. Cr could selectively react with B and C during solidification of the melt. This reaction appears to be important for the characterization of metallic debris [13].
Table 16: Current assessed status of ternary sub-systems regarding the liquefaction of the BWR control rod, which stored in TAF-ID and NUCLEA
<u>Reaction (b) (Zr-O system):</u>
As for the thermodynamic understanding of the oxidation of the channel box, one needs the Zr-O binary database which is already stored in the both databases.
[[ファイル:Schematic image of liquefaction progression at the interface between the control blade and the channel box.png|サムネイル|472x472ピクセル|図 3(b) Schematic image of liquefaction progression at the interface between the control blade and the channel box.|代替文=]]
<u>Reaction (c) (B4C-SS-Zr-O system):</u>
After the control blade melt (SS-B4C melt) makes contact with the Zry channel box, there is an interaction between the SS-B4C melt and the partially oxidized Zr. Several chemical reactions could simultaneously progress and hence the overall phenomena are very complicated. A kinetic model is definitely necessary for the detailed understanding. Thermodynamic database could identify the tendency (driving force) or threshold condition for the reaction.
The interaction’s progress depends on the thickness of the Zry surface oxide of the channel box. If the oxide film is not sufficiently protective in a non-oxidizing atmosphere, the interaction between SS-B4C melt and Zr can occur upon contact. As a result, B and C are transported to the Zry via liquid and could cause a sudden change of the system toward its equilibrium state, in which Zr-boride or Zr-carbide could precipitate in the melt. This is predicted to be an exothermic reaction.
Table 17 shows the ternary subsystems regarding the liquefaction between the non-oxidized Zircaloy channel box and the SS-B4C melt (in addition to Table 16). The dominant subsystem for this particular interaction could be Fe-Zr-X (X: Ni,Cr,B,C). The database is still insufficient for developing the mechanistic model. Also, considering the solidification path of the metallic debris, one needs to improve Zr-B-X and Zr-C-X databases.
Table 17: Current assessed status of ternary subsystems regarding the interaction between SS-B4C and non-oxidizing Zr (in addition to Table 16)
On the other hand, in the case of a thick oxide film on the Zry channel box. This interaction (SS-B4C and Zr) does not significantly occur and only SS-B4C melt relocates to the lower part (the channel box could maintain its original configuration during the absorber rod melting). Then, after melting of the Zr-channel box interior at higher temperatures, one needs to evaluate the dissolution of ZrO2 in the metallic melt which could be extremely important to the metallic debris characteristics.
Table 18 shows the ternary sub-systems with oxygen. Both databases can roughly evaluate the effects of oxidation. However, the formation of ternary compounds could not be sufficiently evaluated using these databases. Also, TAF-ID does not store any databases on the stable compounds of B-oxide in the melt.
Reaction (d) (B4C-SS-Zr-O system):
The steam oxidation of the SS-B4C-Zr melt is extremely important for the characteristics of the metallic debris. Also, the formation of B2O3 could accelerate the liquefaction of the fuel rod, because the melting temperature range of B2O3 is ~ 450-465 °C and it could allow the easy contact/wetting with the fuel rod. Moreover, volatilization of B is extremely accelerated by the steam oxidation and gaseous boron oxides could influence the chemical stability of volatile FP, such as Cs and I [10, 14-15]. The improvement of B-related database is highly recommended.
On the other hand, in the case of a thick oxide film on the Zry channel box. This interaction (SS-B<sub>4</sub>C and Zr) does not significantly occur and only SS-B<sub>4</sub>C melt relocates to the lower part (the channel box could maintain its original configuration during the absorber rod melting). Then, after melting of the Zr-channel box interior at higher temperatures, one needs to evaluate the dissolution of ZrO2 in the metallic melt which could be extremely important to the metallic debris characteristics.
'''Table 18''' shows the ternary sub-systems with oxygen. Both databases can roughly evaluate the effects of oxidation. However, the formation of ternary compounds could not be sufficiently evaluated using these databases. Also, TAF-ID does not store any databases on the stable compounds of B-oxide in the melt.
The steam oxidation of the SS-B<sub>4</sub>C-Zr melt is extremely important for the characteristics of the metallic debris. Also, the formation of B<sub>2</sub>O<sub>3</sub> could accelerate the liquefaction of the fuel rod, because the melting temperature range of B<sub>2</sub>O<sub>3</sub> is ~ 450-465 °C and it could allow the easy contact/wetting with the fuel rod. Moreover, volatilization of B is extremely accelerated by the steam oxidation and gaseous boron oxides could influence the chemical stability of volatile FP, such as Cs and I [10, 14-15]. The improvement of B-related database is highly recommended.
==== b. Transient and late phases ====
[[ファイル:Schematic image of the five stages (b1-b5) in the transient and late phases of in-vessel phenomena.png|サムネイル|857x857ピクセル|Figure 4 Schematic image of the five stages (b1-b5) in the transient and late phases of in-vessel phenomena.]]
'''Figures 4 (b1)-(b5)''' indicate the schematic image of the prototypic five stages for the transient and late phases:
(b1) Start significant relocation of the fuel melt,
(b2) Blockage of steam flow at lower part of the core by the relocated debris,
(b3) Formation of corium pool,
(b4) Secondary relocation of corium melt to the lower plenum,
(b5) Liquefaction and stratification of oxidic and metallic melt in the lower plenum.
==== b. Transient and late phases ====
[[ファイル:Schematic image of the five stages (b1-b5) in the transient and late phases of in-vessel phenomena.png|サムネイル|857x857ピクセル|図４ Schematic image of the five stages (b1-b5) in the transient and late phases of in-vessel phenomena.]]
図4(b1)-(b5)に、 transient and late phasesの典型的な5段階の概略図を示しています。
(b1) Start significant relocation of the fuel melt:
(b3) コリウムプールの形成:
The leading relocation mainly of the metal components (such as the control rod blades and channel box) begins and then the partial blockage of the coolant flow path occurs by the relocated melt. After that, the relocation to the lower head of the U-Zr-O melt occurs. It is not sufficient to understand precisely these complicated reactions only by the thermodynamic approach because each reaction is accompanied by the rapid temperature changes. However, the reaction trends according to the accident scenarios could be evaluated by the thermodynamic databases. In the FDNPS accident, the different progression from the typical accident scenarios could occur (see chapter 4.6). The improvement/enlargement of the thermodynamic databases is expected to show some of the reasons of these deviations. Especially, it is important to improve the accuracy of the high temperature database of U-Zr-O system because the initial U-Zr-O melt is generally oxidized but the composition of the melt becomes more complex during the relocation stage.
(b2) Blockage of steam flow at lower part of the core by the relocated debris:
(b4)溶融物の下部プレナムへの二次リロケーション:
The blockage of the lower part of the core occurs by the collapsed oxide and metal debris. However, the BWR drainage scenario could occur in case of the insufficient blockage [16]. It is necessary to enhance accuracy of the U-Zr-Fe-O system data because the degree of blockage depends on the degree of oxidation of debris and the dissolution of the oxidized structural materials by the oxidic melt. As shown in chapter 4.5, the reaction between the U-Zr-O melt and Fe-oxide could proceed rapidly with local heat generation according to the thermodynamic analysis. This process could enhance the drainage scenario.
The melted and collapsed fuel is once cooled and re-solidified by the inhibition of the steam oxidation of Zr. After that, the temperature rises again by the decay heat, and this leads to the corium pool formation with a crust. The main components of corium are UO<sub>2</sub>-ZrO<sub>2</sub> due to the oxidation progression of Zr. (However, in the case of the unit-2 of FDNPS, in which fuel melt could progress under the steam-served condition, the phase separation of oxidic and metallic melts could occur.) Therefore, the important system in this stage is also the U-Zr-O system.
The corium pool is insulated by the surrounding crust layer and then it gradually expands. When the crust cannot support the corium weight with the corium extenuation, then the liquid corium can have secondary relocations to the lower plenum in a short period, either as rivulets or larger masses. The important database for this particular stage is U-Zr-Fe-O. However, the Fe-related databases are insufficient. The improvement is necessary. Besides, if the blockage by the crust layer is incomplete, it could lead to, not the corium pool growth, but the drainage scenario [16].
i)U-Zr-O系デブリの凝固パス解析
(b5) liquefaction and stratification of oxidic and metallic melt in the lower plenum:
図５にU-Zr-Oシステムにおける２つの凝固パスパターン図を示す。
In a typical accident scenario, the debris, which has fallen into the lower plenum and has cooled and solidified again on the lower plenum. Subsequent reheating and melting, could cause a stratification of the oxide and metal layers. In this scenario, the oxide melt is composed mainly of UO<sub>2</sub>-ZrO<sub>2</sub>-FeO, and mixed with the easily oxidized FP and presumably boron oxide. Metallic melts are mainly composed of SS-Zr-U, and mixed with metallic FP and B compounds. In some cases, the metal layer might be separated into heavy metal (U-Zr-rich) and light metal (Fe-rich) layers, according to MASCA results [17].
１）亜量論U-Zr-Oメルトからの凝固
[[ファイル:U-Zr-Oシステムの凝固パス.png|サムネイル|653x653ピクセル|図5 Solidification path pattern diagrams under hypo- and hyper- conditions on U-Zr-O system]]
急冷：HT-Fluorite相が検出される可能性
In such a multi-component system, it is difficult to evaluate its properties only by experiments, and conversely, it is effective to roughly evaluate the chemical state by the thermodynamic database [18]. Therefore, the accumulation of the experimental data and the improvement of thermodynamic databases and their joint evaluation for the multi-component system is continuously necessary.
徐冷：LT-Fluorite相とα-Zr(O)相とMonoclinic相が検出される可能性
Consequently, the base thermodynamic system for investigating these sequential reactions is U-Zr-SS-B<sub>4</sub>C-O. By considering the metallic corium and the oxidic corium separately, metallic corium can be evaluated by mainly Fe-Zr-X (X means U, Cr, Ni, B or C), and basically, it is important to enlarge the thermodynamic data already shown in the early phase section. On the other hand, the oxidic corium consists of mainly U-O-X and Zr-O-X (X means Fe, Cr, Ni, B or C). '''Table 19''' shows the currently assessed status of U-O-X (see Table 18 as for the Zr-O-Fe system). The important systems are U-O-Zr, U-O-Fe and Zr-O-Fe. In the future, the enlargement of the U-Zr-Fe-O system will be an important issue for performing FDNPS debris analysis.
図 2: Variation in the local composition of the fuel rod with increasing temperature. A’ represents the initial internal oxidation (a-Zry formation) at the initial temperature excursion and A represents the onset of major oxidation/liquefaction reactions.
↑P. Hofmann, D.K. Peck, "UO2/Zircaloy-4 chemical interactions from 1000 to 1700ﾟC under isothermal and transient temperature conditions", J. Nucl. Mat. 124, 80-105 (1984). https://doi.org/10.1016/0022-3115(84)90013-8
↑ 3.03.13.2M.H.A. Piro, Advances in Nuclear Fuel Chemistry, Woodhead Publishing, 555-625, ISBN 9780081025710 (20202).
↑B. Clément, N.H. Girault, G. Repetto, D. Jacquemain, A.V. Jones, M.P. Kissane, P. von der Hardt, "LWR severe accident simulation: synthesis of the results and interpretation of the first Phebus FP experiment FPT0", Nucl. Eng. Des. 226, 5-82 (2003). https://doi.org/10.1016/S0029-5493(03)00157-2
_Schematic_image_of_a_horizontal_cross_section_of_a_prototypic_BWR_Fuel_assembly._The_red_square_shows_the_section_illustrated_in_Fig._18(b)..png)
_in_the_transient_and_late_phases_of_in-vessel_phenomena.png)
