MELCOR modeling and sensitivity analysis of Fukushima Daiichi unit 2 accident considering the latest TEPCO investigations

Annals of Nuclear Energy 112 (2018) 364–373

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Annals of Nuclear Energy journal homepage: www.elsevier.com/locate/anucene

MELCOR modeling and sensitivity analysis of Fukushima Daiichi unit 2 accident considering the latest TEPCO investigations Gen Li, Jun Zhang, Binbin Qiu, Ming Liu ⇑, Junjie Yan State Key Laboratory of Multiphase Flow in Power Engineering, Xi’an Jiaotong University, Xi’an 710049, China

a r t i c l e

i n f o

Article history: Received 26 June 2017 Received in revised form 11 October 2017 Accepted 13 October 2017 Available online 20 October 2017 Keywords: Fukushima Severe accident Sensitivity analysis MELCOR

a b s t r a c t Fukushima Daiichi accident occurred on 11 March 2011 due to the Great East Japan Earthquake and the following tsunami. Recently, Tokyo Electric Power Company (TEPCO) published investigation reports pertaining to the status of unit 2 and other issues that were confirmed. The present study modeled unit 2 accident with MELCOR 2.1 code and performed sensitivity analysis, in order to provide information towards understanding severe accident. The two-phase flow rate and its void fraction in the steam line connecting to the turbine of reactor core isolation cooling (RCIC) system were calculated using the developed RCIC operation model, and the pump injection rate was obtained as well. The suppression chamber (S/C) was divided into three layers with flow path connection to model thermal stratification and the mixing flow at SRV discharge, thereby enabling to capture the measured dry well (D/W) pressure. Through sensitivity analysis of seawater injection, it indicates that the likely seawater injection rate was about 1–2% of the total flow rate through fire engines, and the corresponding reactor pressure vessel (RPV) lower head failure time was located in 92.84 h– 96.17 h. As a result, about 74% of total fuel debris discharged into the reactor pedestal, and the release fractions of noble gas, iodine and cesium to the environment were about 0.741, 0.0167 and 0.00331, respectively. Even though the plausible accident progression was tentatively given, there are still many uncertainties concerning models, boundary conditions and the accident progression. Ó 2017 Elsevier Ltd. All rights reserved.

1. Introduction Fukushima Daiichi accident occurred on 11 March 2011 due to the Great East Japan Earthquake and the following tsunami. Reactor scram initiated at the occurrence of earthquake, and AC and some DC electrical power supplies lost following the arrival of tsunami. It is widely acknowledged that the reactor cores of units 1–3 have experienced some degradation. Tokyo Electric Power Company (TEPCO) and international research institutes have made great efforts to investigate accident progression and to decommission nuclear power plant. From the preceding investigations, it seems that the core damage of unit 2 is less serious than units 1 and 3 (Kim et al., 2016). Despite many efforts to understand accident progressions, the investigation results still have many uncertainties due to complicated site environment and lack of monitored data. A retrospection of unit 2 accident progression is presented in Fig. 1. The RCIC system started operation following the occurrence of earthquake, but it automatically tripped several times due to ⇑ Corresponding author. E-mail address: [email protected] (M. Liu). https://doi.org/10.1016/j.anucene.2017.10.029 0306-4549/Ó 2017 Elsevier Ltd. All rights reserved.

high reactor water level. The water source of RCIC was switched from condensate storage tank (CST) to suppression chamber (S/C) at about 5:00 on 12nd March due to water consumption. The RCIC was confirmed stopping operation until RPV water level was found trending downward at 13:18 on 14th March, but the reason was not clear. As the loss of reactor cooling and the consequent water boiling in RPV, the SRV started to operate at about 70 h. In order to enable water being injected into RPV, the RPV was depressurized at approximate 75 h through manually opening SRV. Seawater injection though fire engine initiated following RPV depressurization, but unfortunately one hour later the workers discovered that an engine had run out of fuel and no seawater was being injected into the reactor. With the operators’ onsite treatment, the second water injection commenced at 19:54 on 14th March, and another fire engine was put into operation as well. The operators have attempted many times to vent the containment including W/W and D/W to reduce pressure but all attempts were unsuccessful. Later, however, the containment pressure decreased from 0.73 MPa at 7:20 on 15th March to 0.155 MPa at 11:25 without specific indication. The detailed information and event timeline could be found in Refs. (Institute of Nuclear Power Operations, 2011;

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Fig. 1. Event progress of unit 2 accident (Li, 2014).

Examination Committee on Accident at Fukushima Daiichi Nuclear Power Station, 2011). The unit 2 accident has been studied by TEPCO (Tokyo Electric Power Company, 2015a) with MAAP, Gauntt et al. with MELCOR (Phillips et al., 2012), Sevon with MELCOR (Sevón et al., 2013), Kim et al. with MELCOR (Kim et al., 2016) and Bonneville et al. with ASTEC (Bonneville and Lucian, 2014). The researchers developed models for analyzing unit 2 accident with the integral codes, and gave their understandings on the accident progression. However, these studies are not able to well reproduce the measured pressure in RPV and D/W, especially the RPV pressure in period of 78–83 h after reactor scram and D/W pressure at SRV forced open. The operation performances of turbine and pump in RCIC system were neglected in modeling, by assuming a constant injection rate or a function related to void fraction in steam line. The MELCOR modeling by Kim et al. considered the impact of turbine efficiency, but the pump operation which correlates injection rate to turbine output work was not taken into account. S/C thermal stratification as well as mixing flow at SRV discharge which probably happened in accident has significant influence on D/W pressure. In the preceding research, only Sevon’s modeling attempted to divide the S/C into two layers to produce thermal stratification, but the mixing flow at SRV discharge was difficult to be modeled using MELCOR code. Thus, the pressure decreasing trend at SRV operation and sustaining stable at SRV forced was not predicted. The seawater injection though fire engines is another big uncertainty affecting RPV pressure, D/W pressure and core degradation. The injection rate to reactor is not only determined by pump pressure head, RPV pressure, gravitational head, but also affected by neighboring reactor because the fire engine was injecting water to units 2 and 3 simultaneously. Some of water seemed to flow to the outside parts of reactor, such as CST and main condenser, due to complex pipe connections. Sensitivity study on the exact seawater injection amount into the reactor has not been performed. The researchers have performed many analyses with the integral severe accident codes and provided valuable information towards understanding severe accident, but there are still some uncertainties and unclear matters that need to be confirmed, e.g. the operation performance of RCIC, thermal stratification in S/C and seawater injection amount through fire engines. Moreover,

TEPCO has published its new investigation results on unit 2 PCV condition, which points out that some parts of pedestal structures were destroyed and some molten materials were found in the pedestal (Tokyo Electric Power Company Holdings, 2017). Even though the specific causes have not been clarified, the possibility of RPV failure such as penetration tube failure or localized break cannot be ruled out. Some issues were confirmed as well in TEPCO 4th progress report (Tokyo Electric Power Company, 2015b), such as SRV operations after reactor core damage and S/C thermal stratification. Therefore, it is necessary to model accident in detail considering TEPCO’s investigations, and perform sensitivity analysis on uncertainties. The purpose of the present study is to model Fukushima Daiichi unit 2 accident and do sensitivity analysis by considering the RCIC operation condition, S/C thermal stratification and mixing flow, and the seawater injection through fire engines. These models were developed on the basis of Sevon’s modeling for unit 2 accident (Sevón et al., 2013). The seawater flow rate that was injected into the reactor through fire engines was determined, and the plausible accident progression was proposed. The RPV lower head failure time, debris discharge amount and components and fission products (FPs) release were evaluated. 2. MELCOR 2.1 modeling of unit 2 2.1. Plant system Nodalization scheme of plant system is presented in Fig. 2. The reactor building was divided into volumes of floors 1–4, floor 5, shield volume and torus room. Within containment the volumes of pedestal, drywell, sump, venting line and wetwell (W/W) were included. The volumes of control volumes are listed in Table 1. Flow paths were set between volumes allowing fluid circulation according to the plant actual configuration. Furthermore, considering the specific accident progression of unit 2, some flow paths were modeled as well, such as the SRV flange gasket leakage path, PCV leakage path and torus room flooding (seawater inundating torus room) path. The RCIC system, driven by a steam turbine and pumping water for RPV injection, was modeled as well. The exhaust of RCIC turbine was discharged to S/C. The suction side

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Unit 2 has eight SRVs discharging from steam lines to wetwell. They work at relief function in normal operation and at safety function when the power supply is not available. The relief valve function initiates at 7.44–7.58 MPa (gauge pressure), and the valves are closed at 7.15–7.28 MPa. In the safety valve function, the valves open at 7.64–7.78 MPa and close at 7.11–7.24 MPa. In addition, there are three safety valves that discharge to the drywell. These valves open at 8.55 MPa and close at 7.70 MPa (Sevón et al., 2013). The safety valves discharging to the drywell were not included in the MELCOR model. The specific operation records could be found in TEPCO report attachment 2–12 (Tokyo Electric Power Company, 2015d). In some cases, the measured reactor pressure changed with the operation of SRV, but in some cases the reactor pressure had no response to SRV operation. In the present modeling, the SRV worked at relief function before tsunami arrival, and at safety function after tsunami flooding. Other SRV manual operations are listed in Table 2.

Reactor building floor 5

SRV

Environment

Shield volume

Reactor building floors 1-4

RCIC turbine

Pump

Pedestal Drywell Ve

nti

ng

line

Wetwell

Sump

Sea water Torus room

Condensate storage tank

2.2. Reactor nodalization

Fig. 2. Nodalization of plant system.

Table 1 Volumes of control volumes (Sevón et al., 2013). Control volume

Volume (m3)

Reactor building floors 1–4 Reactor building floor 5 Shield volume Pedestal Drywell Venting line Wetwell gas space Wetwell water volume Torus room

37,000 25,000 380 287 3483 470 3160 2980 8900

of RCIC pump was alternatively changed between CST and S/C. The detailed operation conditions of RCIC system during the accident will be illustrated in the following section. Referring to TEPCO report attachment 2–10 (Tokyo Electric Power Company, 2015c), a rapid increase of radiation dose was recognized at 23:42 on March 14th, but the ascending gradient in D/W was larger than in W/W, and the D/W reading continued increasing while the W/W reading sustained constant for a while and then tended to decrease. The TEPCO inferred that a breach might present at the RPV boundary, enabling a direct release of radionuclides from RPV to D/W. In order to model this leakage, a flow path with an opening of 1.2E-3 m2 was assumed at SRV flange gasket at about 80 h. The containment overpressure leakage was considered in MELCOR modeling, and the leakage position was placed at D/W head flange. According to unit 2 modeling by Sevon (Sevón et al., 2013), the leakage area was assumed increasing linearly with containment pressure, which increased from 0.0 cm2 at 0.1 MPa to 0.023 cm2 at 0.71 MPa, and continued increasing to 15.0 cm2 at 0.8 MPa. Furthermore, the measured D/W pressure was 0.73 MPa at 7:20 on March 15 th, but it dropped to 0.155 MPa at 11:25 after a while of absence (Sevón et al., 2013). Even though the cause is not clearly known, it was modeled by a leakage area of 30.0 cm2 at D/W head flange. The possibility of torus room flooding was considered as well, which was modeled by a flow path connecting control volumes of seawater and torus room. The seawater temperature was sustained at 10 °C, but the flooding rate was artificially adjusted to enable the D/W pressure to match with the measured data.

Thermal hydraulic control volumes of the reactor are shown in Fig. 3. The core region was divided into 5 concentric control volumes, including one for bypass channel. Each of the internal three rings contains 144 fuel assemblies, while the peripheral ring has 116 fuel assemblies. The control volumes were connected by flow paths at upper and bottom parts to allow circulation flow in the core. The lower plenum, steam separator, steam dryer, RPV dome, downcomer and jet pump were modeled as individual thermalhydraulic volume. Four steam lines were modeled as two control volumes, one for single steam line which connected to RCIC turbine, and another one corresponding to other three steam lines. Recirculation loops were modeled by being divided into the parts of RPV-pumps and pump-RPVs. Lower plenum was divided into levels 1–4, and a fifth radial ring was included to model the peripheral region of lower plenum, which extends beyond the radial perimeter of the core. The core region was divided into another 11 axial levels continuing the lower plenum, which are level 5 corresponding to lower core plate, levels 6–14 corresponding to active fuel region, and level 15 corresponding to the top guide and upper tie plates. Fuel canisters and control blades were modeled as nonsupporting structures, while the core plate and control rod guide tubes were modeled as supporting structures. The component mass and surface areas were calculated from their concrete dimensions. Initial temperature of the components in lower plenum was set at 528 K, while the temperatures of the structures and fuel claddings in fuel region were 551 K and 552 K, respectively. The initial fuel temperature was set at 623 K (Sevón et al., 2013). These initial temperatures are approximately the reactor normal operation temperatures. The failure temperature of control blades was set at the default value, 1520 K (Humphries et al., 2015), while the failure of supporting structures was evaluated by stress calculation.

Table 2 Manual operation of SRV (Tokyo Electric Power Company, 2015d). Time (hours)

Operation

75.23 75.35 77.77 78.53 81.32 82.33

Open (fraction 0.6) Open Close Open Close Open

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line. As the water level was assumed to be stable in the modeling, the flow rate that was extracted from steam line was equal to the injection rate.

RPV dome

Gp ¼ Gw þ Gstm Steam dryer

Downcomer

Single steam line PumpA-RPV

RPV-PumpA

Jet pump

Core4

Gstm Dp ¼ Gw þ Gstm Dhstm qgt gm gp

The RCIC system started operation at reactor scram, but after a while the RCIC system operated in uncontrolled manner due to the occurrence of station black out caused by tsunami flooding. Referring to TEPCO report attachment 2–4 (Tokyo Electric Power Company, 2015e), the RCIC turbine was probably operating under two-phase flow condition, but the two-phase flow rate as well as the void fraction is not clear. In the modeling of RCIC behavior, the turbine and pump operations and RPV thermal-hydraulics were assumed as quasi-static states. The turbine driving power was assumed as being from steam enthalpy drop only, while the water enthalpy drop was assumed to discharge into S/C. The relationship of pump shaft power and flow rate is written as follows.

Gp Dp

qgp

Gp hinject þ Q decay þ Pp  Gw hw;sat  Gstm hs;sat ¼ 0

Q decay ðhw;sat  hinject Þ þ ðhs;sat  hw;sat Þx  Dhgt gm x

ð1Þ

ð2Þ

where Gstm is turbine steam flow rate, Dhstm is steam enthalpy drop,

gt is turbine efficiency, and gm is mechanical efficiency. Combining Eqs. (1) and (2), the following equation can be deduced.

ð3Þ

The measured PRV water level indicates that it surpasses the limitation of water level indicator. Water level was probably maintained as high as steam line, resulting in two-phase flow in steam

ð7Þ

Since the turbine and pump worked at off-design conditions under two-phase flow, the efficiencies gt, gm, gp were calculated by multiplying two-phase flow void fraction to their rated values. With the developed RCIC operation model, the flow rates of steam and water to RCIC turbine and pump injection rate were calculated, as shown in Fig. 4. Referring to the operation records in the first 55 min, the normal RCIC steam flow rate was 5.42 kg/s, and the corresponding injection rate was 24 kg/s (Investigation Committee on the Accident at Fukushima Nuclear Power Stations of Tokyo Electric Power Company, 2012). At the loss of power supply for valve control, the steam flow rate increased to 7.0 kg/s, and the injection rate burst up to 31 kg/s (Investigation Committee on the Accident at Fukushima Nuclear Power Stations of Tokyo Electric Power Company, 2012). The RCIC turbine started operating under two-phase flow from 1.65 h when the water level rose to the measurement limit of indicator. Pump injection rate sharply dropped down due to the deterioration of turbine operation once water flooded into. Finally, the RCIC system stopped at around 66.23 h due to unknown malfunction. However, the steam release continued as the RPV pressure didn’t increase immediately. During the whole two-phase operation process, the void fraction in steam line was about 0.72.

where Pp is pump shaft power, Gp is pump flow rate, Dp is pressure increase at pump outlet, q is water density, and gp is pump efficiency. Since the RCIC turbine and pump are coaxial transmission, the pump shaft power can also be expressed as

Pp ¼ Gstm Dhstm gt gm

ð6Þ

where hinject is the enthalpy of water in tank or suppression chamber, Qdecay is decay heat, hw,sat is enthalpy of the saturated water extracted from steam line, hs,sat is enthalpy of the saturated steam extracted from steam line, the pump shaft power Pp included here is due to its contribution to water enthalpy. Substituting Eqs. (2), (4) and (5) into Eq. (6), we could obtain the Gp as follows.

Gp ¼

2.3. Modeling of RCIC operation

Gstm Dp ¼ Gp Dhstm qgt gm gp

ð5Þ

Considering the energy conservation within RPV, the following equation was written.

Bypass

Core2

Core1 Jet pump RPV-PumpB

PumpB-RPV

Core3

Downcomer

Triple steam line

x¼

Fig. 3. Reactor nodalization (Sevón et al., 2013).

Pp ¼

ð4Þ

where Gw is turbine water flow rate. The void fraction of the flow extracted to RCIC turbine could be calculated as

Shroud dome & steam separator

Lower plume

367

Fig. 4. RCIC system flow rates and void fraction in steam line.

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2.4. Thermal stratification and mixing flow in S/C The drywell pressure decreased when SRV started operation from 12:00 on March 14th, which is an abnormal behavior. Besides that, no change of drywell pressure can be observed although a lot of steam (energy) flowed into S/C when SRV was manually opened. According to TEPCO’s conjecture, it is likely that at SRV operation the water in main steam lines was discharged into S/C where thermal stratification had occurred, and the discharged water moved upward accompanied by lower temperature water at the low part as a result of forced convection. This mixing flow resulted in a decrease of temperature at S/C water surface, and thus the PCV pressure decreased (Tokyo Electric Power Company, 2015f). In order to confirm the validity of this conjecture, we attempted to model S/C thermal stratification and the mixing flow at SRV discharge. Thermal stratification is caused by natural convection, enabling hot fluid to flow upward. Mixing flow is caused by forced convection as a result of SRV discharge. MELCOR is an integral code, which is not able to model natural and forced convection physically. However, we could create thermal stratification and mixing phenomena by dividing the S/C into layers with flow path connections and applying flow rate to every flow path. This MELCOR modeling approach is derived from physical understanding of thermal stratification and mixing flow, but not the physical models. Fig. 5 shows the nodalization of S/C, which was divided into three layers. The layers were separated by thin stainless-steel slices. Flow paths were set up for the flow from top to middle layer and from middle to bottom layer. An artificial flow path was also set up to connect bottom layer to top layer, and its flow rate was set to be proportional to SRV discharge rate. In this way, the separated layers could create thermal stratification with lower temperature water at S/C lower position, while the flow path from bottom to top layer could model mixing flow caused by SRV discharge. According to TEPCO’s investigation, seawater has probably flooded torus room and cooled S/C outside wall. Since the flooding rate is not available, it was artificially adjusted to reproduce drywell pressure. In this modeling, it was assumed as 0.038 m3/s from 10 h to 20 h, and then was 0.0043 m3/s from 20 h to 68 h. The maximum water level in torus room reached to about 0.6 m.

3. Sensitivity analysis of accident progression 3.1. Effect of S/C thermal stratification and mixing flow

Fig. 6. Effect of S/C thermal stratification and mixing flow on D/W pressure.

the D/W pressure calculated by Kim and Sevon significantly deviated from the measured data. At SRV forced open, the increase of D/W pressure was the largest in the case of modeling S/C as one layer, while it was the least in the present modeling. Nevertheless, the pressure increase was not suppressed completely, which may be because the present three-layer modeling was not sufficient to simulate mixing flow at SRV discharge. Fig. 7 shows the W/W temperature, where the temperature stratification was well produced. In the period from 25 h to 70 h, the temperature at top layer was close to the saturate temperature of W/W pressure, indicating that the W/W pressure was determined by S/C surface water temperature. At SRV starting operation, as the flow path pumped lower temperature water from bottom layer to top layer and high temperature water moved downward, the W/W saturate temperature and top layer water temperature decreased, and the temperatures of water at middle and bottom layers increased. At SRV forced open, the temperatures of all S/C layers increased, because a large amount of steam flowed into S/C instantaneously, resulting in that the lower temperature water moving to top layer was not sufficient to balance the energy of steam. Moreover, the temperature increase at around 80 h is attributed to steam inrush into S/C at debris relocation stage (as depicted in Fig. 12) as well as the leakage of gaseous phase to D/W due to SRV flange gasket failure.

Fig. 6 presents the D/W pressure behavior at SRV starting operation and forced open. The calculated results by modeling S/C as one layer by Kim (Kim et al., 2016) and as two layers by Sevon (Sevón et al., 2013) were plotted as well. It could be observed that

SRV discharge

RCIC exhaust

1.6 0.3

Artificial flow path

-2.55

Fig. 5. S/C nodalization.

-0.5 RCIC pump suction Fig. 7. Wetwell temperature.

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3.2. Effect of injection rate by fire engines TEPCO’s investigation has confirmed that some areas of pedestal grate have significantly deformed (Tokyo Electric Power Company Holdings, 2017), and the thermal attack from the discharged fuel debris is a possible cause. In addition, the containment atmospheric monitoring system (CAMS) indicates that the radiation dose in D/W increased rapidly, reaching to 138 Sv/h by 16:10 on March 15th from the previous value 47.7 Sv/h at 13:00, while the does in S/C increased slightly (Tokyo Electric Power Company, 2015g). If the RPV has failed, it probably occurred during this period, about 94.2 h to 97.4 h since reactor scram. The seawater injection to RPV by fire engines started at around 77.1 h (19:52, March 11st), after reactor depressurization. However, there are some paths which may have generated bypass flows to the main condenser and condensate storage tank, and the TEPCO’s investigation confirmed that some water has accumulated in the main condenser (Tokyo Electric Power Company, 2014). In addition, the fire engines were supplying seawater for units 2 and 3 simultaneously. It is very difficult to know the exact amount of water that was injected into the pressure vessel of unit 2. However, the daily average flow rate through the fire engines can be calculated, as shown in Fig. 8. Therefore, it is necessary to make sensitivity calculation on seawater injection flow rate, with the presupposition of RPV failure. Fig. 8 presents several injection flow rates to unit 2 RPV, hypothesized as 1%, 2% and 5% of daily average flow rate through fire engines. The injection rate used in MAAP analysis by TEPCO was also plotted, which is close to 5% of daily flow rate through fire engines. As the shutoff head of the fire engine pump is 0.85 MPa, in the modeling the injection was interrupted when the required pump head for seawater injection, equal to reactor pressure plus gravitational head minus atmospheric pressure, surpasses 0.85 MPa. Fig. 9 shows the RPV pressure after seawater injection. The case of no seawater injection into RPV was also included in the calculation. There are two SRV close-open operations after SRV was forced open for RPV depressurization. The first close and open was at 77.77 h and 78.53 h, and the second close and open was at 81.32 h and 82.33 h. These operations were consistent with RPV pressure increase and decrease at those time points. The pressure peak in the period from 80 h to 80.9 h, in the cases of no injection, 1% and 2% of flow rate through fire engines, was caused by debris relocation, as depicted in Fig. 12. The third pressure increase after RPV depressurization was overestimated in the case of 1% of flow rate

through fire engines, which may be caused by fuel debris relocation. Fig. 10 shows the D/W pressure behavior after seawater injection. As the injection of seawater, the generated hydrogen and steam entered S/C through SRV discharge, and then went to D/W through vacuum breaker. The D/W pressure from injection starting time to 80 h was overestimated in the cases of injection rates equal to 2% and 5% of the flow rate through fire engines. It is because a lot of hydrogen and steam has generated due to large injection rates. The D/W pressure from 80 h to 90 h was underestimated in all cases due to the neglect of direct RPV leakage to D/W. The effect of this leakage will be discussed in the next section. The rapid decrease of D/W pressure at around 90 h is due to the containment leakage that was modeled in calculation, although the specific break position was not known. Thereafter, the transient increase in the cases of no injection, 1% and 2% of flow rate through fire engines indicates that the RPV lower head failed. The case of injection rate equal to 5% of flow rate through fire engines didn’t experience RPV lower head failure. Fig. 11 presents the RPV water levels under different seawater injection rates. We can see the discrepancies between calculation and the measured data are very large. In fact, the measured water level cannot serve as an evidence characterizing accident progression, because at the RCIC operation stage the water level exceeds

Fig. 8. Seawater injection flow rate.

Fig. 10. Drywell pressure behavior after seawater injection.

Fig. 9. RPV pressure behavior after seawater injection.

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exact water level in the calculation, which is a defect of MELCOR data post processing. Fig. 13 shows the cumulative hydrogen in RPV from all oxidation processes. The hydrogen generation started from 76.5 h, and was accelerated by seawater injection. The generation rate was faster at large injection flow rate. By 80 h the accumulated hydrogen was the most in the case of injection rate equal to 5% of the flow rate through fire engines, about 650 kg. In the case of 2% of flow rate through fire engines, the hydrogen generation reached to a plateau at 80 h and sustained for about 15 h, and then started increasing again. The second increase occurred at RPV failure time, as the hydrogen released from the reactor pedestal due to the interaction of discharged fuel debris with the water in pedestal. The hydrogen amount in the cases of no injection and 1% of total flow rate has no large difference, which also experienced second increase when fuel debris discharged into pedestal, but the increment was not significant. It might be because little water leaked to pedestal through the breach at RPV lower head, thus slowing down the fuel debris and water reaction. It is one of the uncertainties of this study, which need further research.

Fig. 11. Water level.

the measurement range of instrument, and the instrument cannot correctly measure the water level under two-phase mixture condition during the accident. The water level presented here is to show the effect of water injection rates on water levels. In the cases of no injection, 1% and 2% of the flow rate through fire engines, the water level finally dropped to the bottom of lower plenum. As compared to those cases, the water level in the case of injection rate equal to 5% of flow rate through fire engines rose up at around 105 h. Table 3 lists event timelines under different injection flow rates. The event time points have no large difference before debris relocation into lower plenum. The events that were dramatically affected were the lower plenum dryout and lower head failure. The lower head failure didn’t occur in the case of injection at 5% of total flow rate. As discussed at the beginning of this section, the RPV lower head probably has failed during the period of 94.2 h–97.4 h. Therefore, we may infer that the seawater flow that was exactly injected into unit 2 RPV was about 1–2% of total flow rate through fire engines. However, many uncertainties still existed with the present results, for example some of RPV and D/W pressure boundaries (SRV flange gasket opening size and artificial D/W opening size at 90 h) were assumed without definite evidences, and the RCIC model and S/C thermal stratification and mixing model were not physically established. Fig. 12 depicts core degradation evolution. In the case of water injection at 2% of total flow rate, core damage occurred at the center region, and the fuel debris relocated into the lower plenum and then discharged out at the failure of RPV lower head. The intact fuel at peripheral region was sustained after lower head failure due to the cooling by water injection. In the case of water injection at 5%, core degradation only occurred at the top part of center region, and the remaining fuel was intact. The water depicted in the images cannot reflect the

4. Plausible accident progression The above analysis indicates that the modeling of S/C thermal stratification and mixing flow could reproduce the D/W pressure at SRV discharge, and the injection rate at 1–2% of total amount through fire engines could enable RPV lower head failure time to match with the time of rapid increase of D/W radiation dose. Observing the D/W pressure shown above, however, we could find that the pressure was underestimated during the period of 80 h–90 h. This is another issue that need to be considered, to well simulate accident progression. The CAMS reading indicates that the D/W radiation dose monotonously increased for 6 h since 80 h, while the dose in S/C tended to decrease (Tokyo Electric Power Company, 2015g). This may imply a possibility that the FPs directly transferred to D/W from RPV due to the leak at RPV boundary. In simulation, a breach of 1.2E-3 m2 was assumed to occur at SRV flange gasket. Figs. 14 and 15 illustrate RPV pressure and D/W pressure. The calculated RPV pressure agreed well with the measured data, indicating that the present RCIC operation model could predict the flow rates of pump injection and the steam-water flow that was extracted to RCIC turbine. After RPV depressurization, three peaks in the measured RPV pressure were reproduced. The D/W pressure was determined by the energy accumulated in the PCV, and this accumulated energy changed with the energy transfer from the RPV and the energy release to the seawater. The high plateau of D/W pressure from 80 h to 90 h was reproduced by modeling a direct leak of gaseous phase from RPV to D/W. The good agreement of D/W pressure demonstrates the validity of RCIC operation model, S/C thermal stratification and mixing flow model, and the RPV

Table 3 Event timelines. Event

No injection

1% of total flow rate

2% of total flow rate

5% of total flow rate

Earthquake/Reactor scram TAF uncover Gap release BAF uncover First channel box failure First fuel rod failure Core plate failure Start of debris relocation Lower plenum dryout RPV lower head failure

0.0 74.26 76.60 75.63 78.14 80.09 80.09 80.29 83.88 91.19

0.0 74.26 76.60 75.63 77.81 80.09 80.09 80.09 82.83 92.84

0.0 74.26 76.61 75.63 77.56 79.97 80.24 80.24 87.40 96.17

0.0 74.26 76.60 75.63 77.56 79.51 – – – –

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Intact fuel

2% flow rate

Structure Water Particulate debris Oxide molten pool Metallic molten pool

5% flow rate

void

80.28h

80.42h

93.67h

93.98h

Fig. 12. Core degradation evolution.

Fig. 13. Hydrogen generation.

and PCV pressure boundaries, even though some uncertainties still existed with these models. The discharge amount and the distribution of fuel debris are the major concerns of TEPCO investigation. They have impacts on the decommissioning work of Fukushima Daiichi nuclear power plant. Fig. 16 shows the core materials that existed within RPV in the case of seawater injection at 1% of total flow rate. The ZrO2 and SSOx (stainless steel oxide) generated as the oxidation progressed. The fuel debris discharged out at about 92.9 h when RPV lower head failed from thru-wall yielding, but a part of fuel debris still remained in RPV. About 74% of total debris discharged out, and the discharged mass of each component is presented in Table 4.

Fig. 14. RPV pressure.

Fig. 17 shows the noble gas, cesium and iodine release to the environment. In the modeling, leak area at PCV pressure boundary was related to pressure. The first increase of radionuclides is due to D/ W overpressure which resulted in a maximum leak area of 1.5E3 m2 at D/W head flange. The second increase is because a leak area of 3.0E3 m2 was assumed to capture the rapid decrease of D/W pressure. By 120 h the cumulative release fractions of noble gas, iodine and cesium to the environment were about 0.741, 0.0167 and 0.00331, respectively. The release fractions of iodine and cesium were about one order of magnitude smaller than Kim’s results (Kim et al., 2016), but about one order of magnitude larger than Sevon’s results (Sevón et al., 2013), which highlights large uncertainties in the modeling.

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Fig. 15. D/W pressure.

Fig. 16. Core materials in RPV.

Table 4 Discharged fuel debris. Material

Discharged mass (kg)

UO2 ZrO2 Zr SS SSOx B4C Total

82,491 7573 29,528 25,420 2303 579 147,894

5. Conclusions and uncertainties The Fukushima Daiichi unit 2 accident was modeled and analyzed with MELCOR 2.1 code. The following conclusions were drawn for accident progression, where some uncertainties and limitations were discussed as well.  The flow rates of steam and water that were extracted into RCIC turbine and the pump injection rate were calculated. The analysis indicates that the void fraction of two-phase flow to RCIC turbine was about 0.72. A good agreement between RPV pressure and the measured data was achieved. The major uncertainties in the present RCIC modeling are the turbine

Fig. 17. Noble gas, cesium and iodine release to the environment.

and pump operation performances and the assumed quasistatic thermal equilibrium in RPV. The turbine efficiency was assumed and the characteristic curve of pump was not known.  Thermal stratification in S/C was produced by dividing it into three layers, and the mixing flow at SRV discharge was realized by a flow path connecting from bottom layer to top layer. The mixing flow could effectively suppress pressure increase when SRV was in operation and forced open. Even if the impact of S/C thermal stratification and mixing flow on D/W pressure behavior was proved, and the D/W pressure seemed to agree well with the measured data, the uncertainties remain concerning the layer partitioning and flow rates used between layers.  The effect of seawater injection by fire engines on reactor thermal-hydraulic behavior and accident progression was analyzed. Through sensitivity analysis of seawater injection, the likely injection rate was 1–2% of total flow rate through fire engines, and the corresponding RPV lower head failure time was located in 92.84 h–96.17 h, which matched with the time of rapid increase of monitored D/W radiation dose. As a result, about 147,894 kg, 74% of total debris, discharged into the reactor pedestal, and the release fractions of noble gas, iodine and cesium to the environment were about 0.741, 0.0167 and 0.00331, respectively. However, the vessel failure mode and debris discharge amount have large uncertainties, because the gross-failure model in MELCOR code version 2.1 cannot predict the gradual melt-thru process of vessel penetrations. Further improvements on MELCOR models for lower head failure analysis are needed to provide higher-fidelity simulations on breach size and debris discharge amount. The uncertainties also exist in the nodalization sensitivity and assumed boundary conditions. In summary, the RCIC system, S/C thermal stratification and mixing flow and seawater injection were modeled and sensitively analyzed. Good agreement between the calculated RPV and D/W pressure and the measured data was achieved, and plausible accident progression was tentatively given. Even so, some uncertainties still remain in models, assumptions and boundary conditions, and there are some limitations of MELCOR capacity in modeling debris relocation, vessel failure and debris discharge. Further research on understanding severe accident phenomena and MELCOR model improvement are necessary. Acknowledgements This work was supported by the National Natural Science Foundation of China (Grant Number 11605129) and China Postdoctoral

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Science Foundation (Grant Number 2015M582670), and the ‘‘Fundamental Research Funds for the Central Universities”. We would like to extend our thanks to Tuomo Sevón for providing the basic MELCOR input of Fukushima unit 2.

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