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Evaluation of spent fuel pool temperature and water level during SBO
Annals of Nuclear Energy 109 (2017) 548–556
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Annals of Nuclear Energy journal homepage: www.elsevier.com/locate/anucene
Evaluation of spent fuel pool temperature and water level during SBO Hiroyasu Mochizuki Laboratory for Advanced Nuclear Energy, Institute of Innovative Research, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8550, Japan
a r t i c l e
i n f o
Article history: Received 13 August 2016 Received in revised form 8 April 2017 Accepted 2 June 2017
Keywords: Spent fuel pool SBO Boil-off Dryout RELAP5-3D Hand calculation
a b s t r a c t The objective of the present study is to evaluate water level of a spent fuel pool during a station blackout (SBO) event which was really caused in the Fukushima-Daiichi (Fukushima-I) accident. The water level during the event can be calculated using a computer code based on the inventory of water in the spent fuel pool and decay heat of spent fuel assemblies. However, a calculation model should be prepared and a longer CPU time is required to obtain the result. If the water level change can be calculated by a hand calculation, it is fast and convenient to obtain the result. Therefore, the calculation results in terms of timings of saturated condition and boil-off are compared to the hand calculation results. It has been shown that the hand calculation results about the saturated and boil-off timings have good agreement with the calculated results using the RELAP5-3D code. The calculation model using the RELAP5-3D is verified using the water level data measured during the Fukushima-I accident. The spent fuel has a dryout phenomenon after the collapsed water level decreases below the top of the active fuel. The calculation model is verified using the measured data under an atmospheric pressure. The code can trace the collapsed water level to cause dryout at the top of the fuel assembly. Ó 2017 Elsevier Ltd. All rights reserved.
1. Introduction During the Fukushima Daiichi (Fukushima-I) Accident on 11th March 2011, many people were anxious about the cooling of spent fuel pools (SFPs) implemented in the reactor buildings from Unit 1 to 4. Especially at the SFP of the Unit-4, all fuel assemblies of the reactor core were withdrawn and stored in the SFP in order to have a special maintenance of the reactor. They did not have alternative current (AC) power for 10 days. In a certain period of time in the Unit-1 and 2, they also lost direct current (DC) power due to flooding of seawater by the huge tsunami. Then after, the Unit 4 had caused hydrogen explosion inside the reactor building. The hydrogen was generated by the core melt of the Unit 3 and reversed into the Unit 4 through an exhaust pipe connected to a common stuck. Operators did not have any measures to cool down spent fuels and to keep the water level in the SFPs at the initial stage of the accident. Helicopters of the Self-Defense Forces poured seawater on the pool using a special bucket hanged beneath the helicopter in order to keep the water level above the top of the active fuel (TAF). The water level was observed visually during the flight. But we learned afterward that this action was not effective, and a most effective measure to keep the water level was seawater supply by a concrete pumping machine. Water in the pool was evaporated and water level was lowered gradually. However,
E-mail address: [email protected] http://dx.doi.org/10.1016/j.anucene.2017.06.006 0306-4549/Ó 2017 Elsevier Ltd. All rights reserved.
nobody knew the correct water level and condition of the spent fuels for a long period of time. In some case, the Tokyo Electric Power Company (TEPCO) might think that they had to use a computer code to predict the timing of water evaporation when the fuel uncovery might occur. After this accident, the importance of the cooling of the SFP is recognized and the International Panel on Fissile Materials made a report (Feiveson et al., 2011) to discuss the relevant issues about the management of the spent fuel. Before this accident, Collins and Hubbard (2001) pointed out potential risks of the SFP at a decommissioning nuclear power plant (NPP) because the SFP is not implemented in the containment vessel but in the reactor building which cannot endure an overpressure condition. The Nuclear Energy Agency Committee on the Safety of Nuclear Installations prepared a status report on SFPs under loss of cooling accident conditions (NEA, 2015). Studies relating passive cooling of the SFPs using heat pipes have also been conducted by several researchers (Miller, 2012), (Ye et al., 2013). Temperature and water level of the SFP at the Fukushima-I nuclear power station have been studied by Yanagi (2013) using a computer code developed by himself. Good agreement was obtained in water level between the calculated and measured results after the Fukushima accident was temporary calmed down. There is a precedent study to predict the water level behavior of a PWR spent fuel pit (Yanagi et al., 2012). Yanagi (2013) investigated thermal-hydraulics of the SFP taking into account the decay heat
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Nomenclature A B C Cp hfg Qd Q0 Ti Ts t
constant constant constant specific heat capacity (J/kg K) latent heat of evaporation (J/kg) decay power (kW) nominal reactor power (kW) initial water temperature (K) saturation water temperature (K) elapsed time from the time of reactor shutdown (s)
and water evaporation rate under high temperature conditions. He also used a computational fluid dynamics (CFD) code to investigate temperature distribution in the pool during the accident. Park et al. (2013) also calculated temperature distribution in a SFP using a CFD code when a SFP cooling is lost in Korean NPP. However, the CFD calculation is usually a laborious work to obtain the long term temperature distribution and water level in the pool. Therefore, thermal-hydraulic calculation using a 1-D system code is realistic one. Franiewski et al. (2013) evaluated the consequences of fuel damage in a SPF after a loss-of-coolant event using the TRACE code. Kaliatka et al. (2013) evaluated the consequences of fuel melt in the pool during the similar event for the SFP of the Ignalina RBMK NPP using mainly the ATHLET-CD code. They used the ASTEK and RELAP5/SCDAPSIM codes in order to benchmark the same accident. Wu et al. (2014) also evaluated an accident of loss-of-pool-cooling of a PWR using the MAAP5 code. Kocar and Dagli (2015) calculated the thermal-hydraulics of the SFP of the Fukushima-I Unit 4 using the RELAP5/SCDAP code system to observe the water level reduction and fuel uncovery under an assumption that the boil off continues. Unfortunately, both timings of saturation and boil-off were too fast because total water inventory might not be correct. They concluded that natural circulation flow is stopped when the coolant level decreases below the top of fuel assemblies and the fuel cladding temperature starts to increase. However, it was confirmed that fuel uncovery occurs when the collapsed water level is below the TAF according to the experiment using a mock-up (Mochizuki, 2014). This behavior is discussed in the present study through the calculation with the RELAP5-3D code. Lee et al. (1994) calculated thermal-hydraulics of a SFP with rather simple method. Nonboiling water level is evaluated using their specific method which is a simplified flow network model like electrical circuits. The thermal-hydraulics till the fuel is uncovered is seemed to be simple according to the results conducted by the above mentioned researchers, and the timings of reaching saturation temperature and the water level lowering due to evaporation may be estimated by the hand calculations. Therefore, one of the objectives of the present study is to compare the hand calculation results to the calculated results by RELAP5-3D. The other objective is to verify the calculation model with a measured result at the Unit 4 of the Fukushima-I.
2. Estimation of decay heat Water level of the SFP is dependent on the decay heat of the spent fuels and water inventory in the pool during a loss of cooling accident. Therefore, the correlation to predict the decay heat is investigated in the present study. The aim of this investigation is to use the correlation which predict highest decay power. Way and Wigner (1948) proposed an equation relating the decay power as follows.
ts toff
ss
V VT
q qs
timing of saturated condition (s) timing of boil-off (s) time period of reactor operation (s) total water inventory above top of fuel (m3) total water inventory in the pool (m3) density of subcooled water (kg/m3) density of saturated water (kg/m3)
n o Qd ¼ C t 0:2 ðt þ ss Þ0:2 ; Qo
ð1Þ
where Qd is the decay power, Q0 is the nominal reactor power, ss is the time of reactor shutdown measured from the time of startup and t is the elapsed time from the time of reactor shutdown. C is a constant which is specific value for a fuel assembly. Todreas and Kazimi (1990) give the following approximate decay power correlation based on Glasstone and Sesonske (1981) for beta heating as and the approximate decay power for gamma heating,
n o Qd ¼ 0:066 t 0:2 ðt þ ss Þ0:2 : Qo
ð2Þ
Their correlation has the 0.2th power of time as well as the correlation of Way and Wigner. Todreas and Kazimi also proposed the following less simple expression in their textbook.
o 0:2 Qd n ¼ 0:1ðt þ 10Þ0:2 0:087ðt þ 2 107 Þ Qo n o 0:2 0:1ðt þ ss þ 10Þ0:2 0:087ðt þ ss þ 2 107 Þ
ð3Þ
The American Nuclear Society proposed the following correlation in ANS (1973):
Qd ¼ 0:005At b ; Qo
ð4Þ
where constants A and b are defined as a function of the elapsed time as listed in Table 1. These correlations are compared in Fig. 1. Since the decay heat power is large when the operating period of a reactor is short, onemonth operation is assumed in the comparison. The correlation of Way and Wigner is highest among three correlations. The committee in the Atomic Energy Society in Japan proposed a correlation to predict decay heat using a complex way (Research Advisory Committee for Reactor Decay Heat Standard, 1989). However, the correlation has a trend slightly lower than the ANS correlation. 3. Calculation model The calculation model of an SFP of the Advanced Boiling Water Reactor (ABWR) at Hamaoka NPP is illustrated in Fig. 2. The components in the model consist of two time-dependent volumes
Table 1 Constants of the ANS decay heat curve. t (s)
0 < t 10
10 < t 150
150 < t 8 108
A b
12.05 0.0639
15.31 0.1807
27.43 0.2962
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Fig. 1. Correlations to predict decay heat.
300 and 720, a pool bottom 310, five kinds of spent fuels from 410 to 450, lower pool-sides in four directions from 460 to 490, a region above the spent fuel 500, an upper part of the pool 610 and upper pool-sides from 660 to 690, an air region in the pool 700, an air region inside the building 710 and other junction components. The time-dependent volumes are used to set a boundary conditions regarding pressure and temperature of coolant using tables of the RELAP5 code input deck. The lower pool-sides are provided outside region of the spent fuel racks in east, north, west and south directions, i.e., components 460, 470, 480 and 490 in Fig. 2, which are water space in the real spent fuel pool. Although two
components are not shown in Fig. 2, there are two other poolsides in front and behind, i.e., components 470 and 490. Since there is no precise drawing of the spent fuel pool which is available to make the calculation model, widths between the racks and walls for these components are assumed as 1.0 m and 1.5 m, respectively. The pipe model is applied to the lower pool sides and spent fuel racks which are divided into 22 nodes. In the case of the component 460, the divided nodes are described from 460,001 to 460,022 as illustrated in the figure although the number of meshes do not match this number. Volume lengths from 1 to 21 and 22 are 0.1855 and 0.195, respectively. The pipe model is also applied to the upper part of the pool 610 and upper pool-sides 660, 670, 680 and 690 which are divided into 10 nodes. Uniform volume length of 0.7 m is applied to these components. The singlevolume model is applied to the other volumes. In regard to the components above the spent fuel rack, components and nodes are connected by horizontal junctions in order to allow free convection between the components. Since the method to determine flow rate in the junctions is described in the RELAP5-3D manual volume I (The RELAP5-3DÓ Code Development Team, 2012) over 100 pages, you can understand the theory. There is no horizontal junction in the fuel rack region because the rack inside has no horizontal connection between the neighboring channels. Although the components 500, 560, 570, 580 and 590 can be included in the above components 610, 660, 670, 680 and 690 respectively, these components are provided in order to adjust height. The size of the SFP where water is filled is approximately 14 m in length, 18 m in width and 12 m in height and number of spent fuels in the pool is 2527 according to the information on the web-side of the Chubu Electric Company (Chuden, 2016). These dimensions can be obtained through internet. Although the precise size of the fuel bundle is not known, it is assumed that the fuel bundle is inserted in the rack as shown in Fig. 3. Elevation of the bottom of spent fuels is assumed as 0.3 m. Length of the effective fuel length is assumed as 3.71 m. Elevation of top of the fuel assembly is 4.4 m. Decay power is assumed in order to have a temperature distribution in the SFP under a hypothetical situation. It is roughly
Fig. 2. Calculation model of an SFP of the Hamaoka ABWR using the RELAP5-3D code.
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4. Calculation results
Fig. 3. Fuel bundle configuration and its assumed height in a spent fuel rack.
assumed that there are 100 highest power fuels, 100 intermediate power fuels, 200 low power fuels, 100 empty channels and 2127 average power fuels. Total water volume and water volume above the components 500, 560, 570, 580 and 590 are approximately 3075m3 and 1790 m3, respectively. Decay powers of one assembly for various kinds of fuels are listed in Table 2. Total decay power is assumed as approximately 4800 kW which is larger than the actual decay power of the SFP at the Hamaoka NPP in Japan. There is no flow connection between fuels in the rack. Water supplied from a time-dependent volume 300 is drained from a time-dependent volume 320 via a valve component 619. The pool is cooled by 295 K and 139 kg/s feed water at the initial. One air region is assumed above the water region and the other one volume is for the air in the building. Outside air is assumed using a timedependent volume. The inside of the building has a connection to the outside via a 1m2 flow pass. Heat loss from the pool through building wall and the heat capacity of the concrete are neglected in the present calculation because the decay power itself is assumed and the ratios of these effects are very small compared to the decay power. Therefore, it is assumed that the pool is surrounded with the adiabatic walls.
A velocity distribution in the pool under the steady state condition is illustrated in Fig. 4 using three kinds of vectors with different thicknesses ranging 104–102 m/s. The vectors are different each other by an order of magnitude and each kind of vector length outside the frame of the SFP shows the unit length. Velocities inside the racks where fuel assemblies are inserted are in the range from 2.5 105 to 5.7 103 m/s. Velocity in the high power channel is fastest and there is almost no flow in the empty channel. Velocity in the SFP above the rack is asymmetry because water is drained from the top node of the component 660 which is one of the pool sides. Supplied water at the bottom of the SFP raises upward and makes a very weak swirl on the left side of the SFP. However, supplied water on the right side of the SFP flows in the direction of the drainage. The temperature distribution in the pool under the steady state conditions is illustrated in Fig. 5. Temperatures at the outlet of the racks are almost same because the higher power channels have larger inlet velocities, and warmed water is mixed in the upper region of the pool. The temperature distribution in this region is uniform at approximately 303 K because of mixing. Since there is a heat source at the bottom of the SFP, it was presumed that a thermal stratification might occur. However, the temperature distribution is unexpectedly uniform. When the station blackout (SBO) occurs water supply and drainage are suspended, and temperature in the SFP starts to increase. Velocity in the SFP also increases compared to the velocity at the initial steady state condition by an order of magnitude as shown in Fig. 6. A large swirl in the upper part of the SFP and the other swirl through the spent fuel racks via the pool sides are observed when the water reaches to the saturated condition at approximately 2 105 s (2.3 days) after the SBO. The velocity of the natural circulation is faster than that in forced circulation during the steady state conditions. The flow pattern and the velocity calculated by the RELAP5-3D are similar to the calculated results using a CFD code by Yanagi (2013). Fig. 7 illustrates the temperature distribution in the SFP at the same period of time. Temperature in the SFP is almost uniform at 375.4 K. Since it is assumed that a connection between inside the SFP building and the outside air is only 1 m2, pressure inside the building is slightly pressurized by evaporated steam. The temperature distribution in the SFP calculated by the RELAP5-3D code also shows a similar pattern calculated by Yanagi (2013) using the CFD code. Fig. 8 illustrates the evolution of the collapsed water level after the SBO event. Since the calculation is slightly unstable when the collapsed water level is below 5 m from the pool bottom, the calculation is terminated when water level reached 4.5 m on the 9.22th day. The water level from the pool bottom increases after
Table 2 Decay power of individual channel. Channel
Number of assemblies
Decay power of one assembly kW
Comment
410
100
13.59
420 430
100 200
3.627 0.06
440 450
100 2127
0.0 1.445
1 day after reactor shutdown 10 days Average of 1 and 2 years Empty channels 1 month
Fig. 4. Velocity distribution in the pool under the steady state condition.
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Fig. 8. Evolution of collapsed water level in the SFP for ABWR under SBO conditions.
Fig. 5. Temperature distribution in the pool under the steady state condition.
Fig. 6. Velocity distribution in the pool when water reaches at the saturated condition.
the SBO till the water surface reaches to the saturated condition without any water supply. Since the initial temperature of the SFP is approximately 303 K, temperature increases to the saturation temperature by 72 K. The volume of water expands due to temperature increase until the water reaches the saturated condition. During this period, although a part of the water is lost due to evaporation, the volume expansion is larger than the loss of water. After that the collapsed water level decreases gradually due to evaporation with much higher speed. Finally, the collapsed water level reaches the elevation of 5 m from the bottom on approximately the 9th day after the SBO. During the water evaporation process, the decreasing curve is not smooth. Although this zigzag characteristic is seemed to have a relationship with meshes provided in the pool model, the cause is not clear. Two timings of saturated condition and boil-off are compared to the results of the hand calculation which are conducted using the following simple equations. Heat capacity of the rack and the spent fuels are neglected because water volume is enormous compared to these volumes. Physical properties are fixed at the representative temperature, i.e., lumped parameters are used. This is the major difference between the hand calculation and the calculation using RELAP5-3D which calculates time-dependent spatial physical properties for every volume using the pressure and temperature in the volume.
ts ¼ tb ¼
qV T CpðT s T i Þ Qd
qs Vhfg Qd
toff ¼ t b ¼ ts þ tb
;
ð5Þ
:
ð6Þ for
Case 1
for
Case 2
ð7Þ
Density and specific heat capacity during heating-up to the saturated condition in the hand calculation are evaluated by steam table values at 340 K which is average temperature between the initial and the saturated condition as listed in Table 3. Meanwhile for the boil-off calculation, it is assumed that density and latent heat are calculated at the saturated condition, and evaporation is assumed as constant from the beginning of the SBO in Case-1. No
Table 3 Physical properties for hand calculation.
Fig. 7. Temperature distribution in the pool when water reaches at the saturated condition.
Item
Value
Density to calculate saturated condition q Specific heat capacity Cp Density to calculate boil-off qs Latent heat of evaporation hfg
980.0 kg/m3 4.186 kJ/kg 955.9 kg/m3 2248.9 kJ/kg
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evaporation is assumed in Case-2 until the water reaches the saturated condition. Therefore, the boil-off timing for the Case-2 is simply calculated as a summation of the saturation timing and the timing of boil-off in the Case-1. The boil-off timings are compared when the initial water level decreases to 5 m in height from the pool bottom. Comparison is shown in Table 4. As shown in this table, the timing of the saturation is slightly underestimated by the hand calculation. This is because of neglecting the inventory of the spent fuels in the hand calculation. However, the simple hand calculation about the saturation timing coincides with the calculation result of RELAP5 within approximately 3% error. Regarding the boil-off timing by the hand calculation, the Case-1 gives almost the same result as the calculation by the RELAP5 code, and the Case-2 overestimated by approximately 25%. Since the pool water evaporates before it reaches saturated condition, the boil-off timing can be estimated by the hand calculation under the concept of the Case-1. Namely, we can assume the same amount of evaporation from the beginning of the SBO to estimate the water level. The reason of the accurate hand calculation is almost uniform water temperature in the pool due to free convection as illustrated in Fig. 7. Since temperature is uniform, the calculation using representative physical properties provides the equivalent result as the calculated result which takes into account the time-dependent spatial physical properties. Evolution of void fraction in the rack is illustrated in Fig. 9. When the pool water temperature reaches to the saturated condition, there are no voids in the spent fuel rack. Voids appear in the highest power channel when the collapsed water level is lowered to 11 m from the bottom of the pool (6.6 m above the top of the rack), and the void fraction is very low. Therefore, the pool water circulates naturally as if it is a single-phase flow. Void fraction at the top of the fuel assembly becomes more than 1% when collapsed water level is less than 1 m from the top of the fuel.
5. Discussion 5.1. Verification of calculation model for SFP water level It is shown in the previous section that the hand calculations give good estimations for the saturation and boil-off timings of the SFP. The calculation model using the RELAP5-3D code should be verified using the data measured during the Fukushima-I accident in March 2011 in order to convince the accuracy of the hand calculation. A similar calculation model shown in Fig. 2 is adopted in the verification. However, there are small differences in dimensions of the pool size and the number of spent fuels. The pool size is 12.2 m by 9.9 m, and water depth is 11.5 m. Total water inventory in the SFP was reported as approximately 1390 m3. However, the water volume above the fuel assembly is important compared with the total volume. Water volume above the component 500, 560, 570, 580 and 590 is approximately 540 m3. Since there is no precise description on the size of the SFP in TEPCO Report (2012) or Atomic Energy Society of Japan (AESJ) report (2013), the dimension described in Yanagi (2013) is adopted in the present calculation. The number of spent fuels in the pool and total decay heat power are described in the Report by TEPCO (2012) as listed in Table 5.
Fig. 9. Evolution of void fraction at the top of the spent fuel channel from 410 to 450.
Table 5 Spent fuels in the SFP of the Unit 4 in the Fukushima-I. Spent fuel assemblies
Number of assemblies
Channel classification in RELAP5
Decay heat assumed in the calculation (kW)
Fresh fuel 8 8 BJ Older 8 8 and 7 7 STEP2 STEP3-B Total spent fuel
204 30 5 560 736 1331
410 420 430 450 450
1.0 360.6 45.2 800.8 1052.4 Total power: 2260.0
Under the above conditions, the water evaporation of the SFP is calculated by the RELAP5-3D code. The evolution of the water level during the accident without no water supply is illustrated in Fig. 10 together with the measured data. Good agreement is obtained in the calculation. However, we have to remind that the measurement was conducted visually from a helicopter. Therefore, the measured value contains a large error which is indicated in the TEPCO Report (2012) and AESJ Report (2014). Since the roof was blown away by the hydrogen explosion, pilots could see the water surface from the helicopter 5 and a half days after the SBO. If operators in the Fukushina-I nuclear power station verified the photograph or video of the SFP, they possibly evaluated the correct water level. Therefore, the water level evaluated as 2.3 m below the full capacity level is reliable. The timing to reach the saturated condition is calculated as 2.31 days which is underestimated as 2.1 days by the hand calculation. In terms of temperature of the SFP, the report describes it was approximately 363 K at the surface of the pool. However, it is 373.5 K during the evaporation process in the calculation. In the same figure, a calculated result by Yanagi (2013) is illustrated. The calculated result by him shows practically the similar result calculated in the present verification. In his original thesis, since the initial water level is measured as 6.8 m from the top of the rack, water level is shifted to 11.6 m from the bottom of the pool. His result gives higher collapsed water level than the result of the RELAP5, and the discrepancy becomes large as time. Since water inventory of the pool above 5 m is approximately 785 m3, all water will be evaporated within 7.47 105 s (8.65 days) if the
Table 4 Timings of pool water saturation and boil-off. Timing of saturation RELAP5-3D
1.94 105 s
Timing of boil-off Hand calculation
1.89 105 s
RELAP5-3D
7.92 105 s
Hand calculation Case-1
Case-2
8.00 105 s
9.89 105 s
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Fig. 10. Evolution of SFP water level during SBO of the Unit 4 in the Fukushima-I.
Fig. 11. Safety Experiment Facility (SEL) to conduct boil-off experiment.
same hand calculation is applied to this case. Therefore, the evaporation rate by Yanagi is possibly underestimated compared to the reality. 5.2. Water level to cause dryout of a spent fuel assembly In general, dryout of a fuel assembly does not occur when the collapsed water level decreases under the TAF. This is because of the low power of the fuel assembly and voiding in the rack. When the decay heat power of the spent fuel is very low, top of the fuel
immediately causes dryout if the collapsed water level is lowered under the top. However, the spent fuel is covered with voided water when the power is high in the category of the decay heat. It is important to know the actual dryout water level of a spent fuel assembly in order to evaluate the critical condition of the spent fuels. The author conducted dryout experiment using a large facility called Safety Experiment Loop (SEL) illustrated in Fig. 11 with a fuel bundle consisting of 36 pins which had 3.6 m in active heated length. Temperatures in various locations are measured by a thermocouple at the inlet of the test section and cladding surface on different levels as shown in Fig. 12. The water level on the downcomer side was lowered by discharging water slowly from the bottom of the downcomer and the collapsed water level in the test section at which dryout occurred was measured. Although each experiment was conducted with constant power and saturated conditions, a slightly subcooled inlet temperature condition was attained due to time required for the water level to set. The experiment was conducted for different system pressures: 0.1, 1, 5 and 7 MPa. Average subcooling was 15 K, 9 K, 42 K, and 5 K for 0.1, 1, 5 and 7 MPa system pressure conditions, respectively. Among them, dryout under 0.1 MPa is calculated and compared in the present study. Since the density of the coolant in the channel containing the fuel bundle was lower than that of single phase water due to voiding, the collapsed water level at which dryout occurs is lower than the top of the active fuel (TAF). Especially the collapsed water level becomes very low under the atmospheric pressure. This situation is calculated using the model illustrated in Fig. 13. The test section indicated as a pipe component 100 is basically the same model as used for the spent fuel in the rack of the SFP analysis which is shown in Fig. 2. The calculated results for collapsed water level which causes dryout is illustrated in Fig. 14 as a function of the decay heat power. The RELAP5-3D code underestimates the collapsed water level for all power levels by approximately 0.5 m. However, the trend is followed by the code. This difference may be caused by voids behavior in a channel. If void rising velocity is calculated faster than this result, the calculated result possibly approaches to the measured result. Heat transfer coefficients when dryout occurs are evaluated using the thermal equilibrium evaporation rate and measured cladding surface temperature. The comparison between calculation and measurement is shown in Fig. 15. The heat transfer coefficient under dryout condition is properly calculated. However, the heat transfer coefficients in nucleate boiling region are overestimated by RELAP5. Therefore, void behavior and heat transfer coefficient of the RELAP5-3D code under atmospheric conditions should be improved further.
Fig. 12. Heater bundle used in the experiment and thermocouple locations.
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6. Conclusions Water evaporation of a spent fuel pool (SFP) implemented in an advanced boiling water reactor (ABWR) during a station blackout event is calculated using the RELAP5-3D code and by a hand calculation. As a result of the calculations, the following conclusions are obtained.
Fig. 13. Calculation model of RELAP5-3D for boil-off experiment.
(1) Temperature distribution above the rack in the SFP calculated by the RELAP5-3D code is almost uniform under the steady state conditions. The whole pool temperature is almost uniform under transient conditions without heat removal. These are the similar results calculated by a CFD code. (2) Hand calculation results of timings to reach a saturated condition and boil-off coincide with the calculation results with the RELAP5-3D within a practical accuracy. (3) The model to calculate collapsed water level decrease of the spent fuel pool is verified using the measured data at the Unit 4 of the Fukushima-Daiichi. As a result, it has been confirmed that the hand calculation is practical to evaluate the boil-off timing. (4) The spent fuel assembly causes dryout at the top when collapsed water level decreases far below the top of the active fuel. The RELAP5 code underestimate the collapsed water level compared to the measured result. This suggest that the void model under atmospheric pressure should be modified in order to have much faster bubble rising velocity.
Acknowledgements The author would like to express his sincere thanks to Idaho National Laboratory which gives the author one license to use the RELAP5-3D code. The present work could not be done without this code. The author also thanks to Mr. T. Yano who was student in my laboratory and Dr. T. Kaliatka in the Lithuania Energy Institute. They made a basic model to calculate the dryout phenomenon measured in the blowdown facility SEL. References Fig. 14. Collapsed water level to cause dryout.
Fig. 15. Evaluated heat transfer coefficient along the fuel bundle when dryout occurs at the top.
Atomic Energy Society of Japan (AESJ) Investigation Committee, 2014. The Fukushima Nuclear Accident–Final Report of the AESJ Investigation Committee, Maruzen Publishing Co., Ltd., ISBN 978-4-431-55159-1. ANS, 1973. ANS-5.1 1973 Decay Energy Release Rates Following Shutdown of Uranium-Fueled Thermal Reactors, Draft ANS-5.1/N18.6, October 1973. Chuden, 2016. http://hamaoka.chuden.jp/spentfuel/qa02.html, (in Japanese). Collins, T.E., Hubbard, G., 2001. Technical study of spent fuel pool accident at decommissioning nuclear power plants, U.S. Nuclear Regulatory Commission, NUREG-1738. Feiveson, H., Mian, Z., Ramana, M.V., von Hippel, F., 2011. Spent fuel from nuclear power reactors – an overview of a new study, The International Panel on Fissile Materials. Franiewski, Z.I., Geleskie, D.M., Grove, B.E., Maguire, K.G., 2013. Spent fuel pool analysis of a BWR-4 fuel bundle under loss of coolant conditions using TRACE, NucE431W S2013. The Pennsylvania State University. Glasstone, S., Sesonske, A., 1981. Nuclear Reactor Engineering. Krieger Publishing Company, Malabar, Florida 32950. ISBN 0-89464-567-6. Kaliatka, A., Ognerubov, V., Vileiniškis, V., Ušpuras, E., 2013. Analysis of the processes in spent fuel pools in case of loss of heat removal due to water leakage. Sci. Technol. Nucl. Installations 2013, 1–11. http://dx.doi.org/10.1155/ 2013/598975. Article ID 598975. Kocar, C., Dagli, C.P., 2015. Analysis of LOFA in BWR spent fuel storage pool. In: Proc. of the 24th International Conference Nuclear Energy for New Europe, Portorozˇ, Slovenia, pp. 508.1–508.7. Lee, K.B., Nam, K.I., Park, J.R., Lee, S.K., 1994. Thermal-hydraulic analysis and parametric study on the spent fuel pool storage. J. Korean Nucl. Soc. 26 (1), 19– 31. Miller, Ian J., 2012. A System for Cooling Nuclear Spent Fuel using Fluidized Bed Technology, University of Tennessee Honors Thesis Projects, http://trace. tennessee.edu/utk_chanhonoproj/1507.
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Mochizuki, H., 2014. Dryout phenomena under low water level. In: Proc. of Int. Workshop on Nuclear Safety and Severe Accident (NUSSA-2014), Chiba, Japan. NEA Committee on the safety of nuclear installations, 2015. Status report on spent fuel pools under loss-of-cooling and loss-of-coolant accident conditions (Final report), OECD/NEA, NEA/CSNI/R(2015) 2. Park, C.H., Lee, A., Lee, J.M., Moon, J.H., 2013. Estimation of the spent fuel pool water temperature at a Loss-of-Pool-Cooling accident. Int. J. Math. Comput. Phys. Electr. Comput. Eng. 7 (7), 1183–1186. Research Advisory Committee for Reactor Decay Heat Standard, 1989. Nuclear Reactor Decay Heat and Its Recommendation Value. Atomic Energy Society of Japan (AESJ). The RELAP5-3DÓ Code Development Team, 2012. RELAP5-3DÓ Code Manual Volume I: Code Structure, System Models and Solution Methods, INEEL-EXT-9800834 Revision 4.0, http://www4vip.inl.gov/relap5/r5manuals/ver_4_0/vol-1. pdf. Todreas, N.E., Kazimi, M.S., 1990. Nuclear Systems I, Thermal Hydraulic Fundamentals. Hemisphere Publishing Corporation. 0-89116-935-0 (v. 1). Tokyo Electric Power Company (TEPCO), 2012. Fukushima-I Nuclear Power Station –Impact of the earthquake in Tohoku region of the Pacific Ocean on nuclear
facilities, Press report, (in Japanese), http://www.tepco.co.jp/cc/press/betu12_j/ images/120509j0101.pdf. Way, K., Wigner, E.P., 1948. The rate of decay of fission products. Phys. Rev. 73, 1318–1330. Wu, X., Li, W., Zhang, Y., Qiu, S.Z., 2014. Analysis of the loss of pool cooling accident in a PWR spent fuel pool with MAAP5. Ann. Nucl. Energy 72, 198–213. http://dx. doi.org/10.1016/j.anucene.2014.05.030. Ye, C., Zheng, M.G., Wang, M.L., Zhnag, R.H., Xiong, Z.Q., 2013. The design and simulation of a new spent fuel pool passive cooling system. Ann. Nucl. Energy 58, 124–131. http://dx.doi.org/10.1016/j.anucene.2013.03.007. Yanagi, C., Murase, M., Yoshitda, Y., Kusunoki, T., 2012. Prediction of temperature and water level in a spent fuel pit during loss of all AC powers. J. At. Energy Soc. Japan 11 (3), 193–202. http://dx.doi.org/10.3327/taesj.J11.050 (in Japanese). Yanagi, C., 2013. Study on prediction of temperature and water level in a spent fuel pit during loss of all AC powers (Ph.D. thesis). University of Fukui (in Japanese) http://repo.flib.u-fukui.ac.jp/dspace/bitstream/10098/7580/1/%E5%8D%9A%E5% A3%AB%E8%AB%96%E6%96%87%EF%BC%88%E6%9F%B3%E5%8D%83%E8%A3%95% EF%BC%89.pdf.
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Annals of Nuclear Energy journal homepage: www.elsevier.com/locate/anucene
Evaluation of spent fuel pool temperature and water level during SBO Hiroyasu Mochizuki Laboratory for Advanced Nuclear Energy, Institute of Innovative Research, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8550, Japan
a r t i c l e
i n f o
Article history: Received 13 August 2016 Received in revised form 8 April 2017 Accepted 2 June 2017
Keywords: Spent fuel pool SBO Boil-off Dryout RELAP5-3D Hand calculation
a b s t r a c t The objective of the present study is to evaluate water level of a spent fuel pool during a station blackout (SBO) event which was really caused in the Fukushima-Daiichi (Fukushima-I) accident. The water level during the event can be calculated using a computer code based on the inventory of water in the spent fuel pool and decay heat of spent fuel assemblies. However, a calculation model should be prepared and a longer CPU time is required to obtain the result. If the water level change can be calculated by a hand calculation, it is fast and convenient to obtain the result. Therefore, the calculation results in terms of timings of saturated condition and boil-off are compared to the hand calculation results. It has been shown that the hand calculation results about the saturated and boil-off timings have good agreement with the calculated results using the RELAP5-3D code. The calculation model using the RELAP5-3D is verified using the water level data measured during the Fukushima-I accident. The spent fuel has a dryout phenomenon after the collapsed water level decreases below the top of the active fuel. The calculation model is verified using the measured data under an atmospheric pressure. The code can trace the collapsed water level to cause dryout at the top of the fuel assembly. Ó 2017 Elsevier Ltd. All rights reserved.
1. Introduction During the Fukushima Daiichi (Fukushima-I) Accident on 11th March 2011, many people were anxious about the cooling of spent fuel pools (SFPs) implemented in the reactor buildings from Unit 1 to 4. Especially at the SFP of the Unit-4, all fuel assemblies of the reactor core were withdrawn and stored in the SFP in order to have a special maintenance of the reactor. They did not have alternative current (AC) power for 10 days. In a certain period of time in the Unit-1 and 2, they also lost direct current (DC) power due to flooding of seawater by the huge tsunami. Then after, the Unit 4 had caused hydrogen explosion inside the reactor building. The hydrogen was generated by the core melt of the Unit 3 and reversed into the Unit 4 through an exhaust pipe connected to a common stuck. Operators did not have any measures to cool down spent fuels and to keep the water level in the SFPs at the initial stage of the accident. Helicopters of the Self-Defense Forces poured seawater on the pool using a special bucket hanged beneath the helicopter in order to keep the water level above the top of the active fuel (TAF). The water level was observed visually during the flight. But we learned afterward that this action was not effective, and a most effective measure to keep the water level was seawater supply by a concrete pumping machine. Water in the pool was evaporated and water level was lowered gradually. However,
E-mail address: [email protected] http://dx.doi.org/10.1016/j.anucene.2017.06.006 0306-4549/Ó 2017 Elsevier Ltd. All rights reserved.
nobody knew the correct water level and condition of the spent fuels for a long period of time. In some case, the Tokyo Electric Power Company (TEPCO) might think that they had to use a computer code to predict the timing of water evaporation when the fuel uncovery might occur. After this accident, the importance of the cooling of the SFP is recognized and the International Panel on Fissile Materials made a report (Feiveson et al., 2011) to discuss the relevant issues about the management of the spent fuel. Before this accident, Collins and Hubbard (2001) pointed out potential risks of the SFP at a decommissioning nuclear power plant (NPP) because the SFP is not implemented in the containment vessel but in the reactor building which cannot endure an overpressure condition. The Nuclear Energy Agency Committee on the Safety of Nuclear Installations prepared a status report on SFPs under loss of cooling accident conditions (NEA, 2015). Studies relating passive cooling of the SFPs using heat pipes have also been conducted by several researchers (Miller, 2012), (Ye et al., 2013). Temperature and water level of the SFP at the Fukushima-I nuclear power station have been studied by Yanagi (2013) using a computer code developed by himself. Good agreement was obtained in water level between the calculated and measured results after the Fukushima accident was temporary calmed down. There is a precedent study to predict the water level behavior of a PWR spent fuel pit (Yanagi et al., 2012). Yanagi (2013) investigated thermal-hydraulics of the SFP taking into account the decay heat
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Nomenclature A B C Cp hfg Qd Q0 Ti Ts t
constant constant constant specific heat capacity (J/kg K) latent heat of evaporation (J/kg) decay power (kW) nominal reactor power (kW) initial water temperature (K) saturation water temperature (K) elapsed time from the time of reactor shutdown (s)
and water evaporation rate under high temperature conditions. He also used a computational fluid dynamics (CFD) code to investigate temperature distribution in the pool during the accident. Park et al. (2013) also calculated temperature distribution in a SFP using a CFD code when a SFP cooling is lost in Korean NPP. However, the CFD calculation is usually a laborious work to obtain the long term temperature distribution and water level in the pool. Therefore, thermal-hydraulic calculation using a 1-D system code is realistic one. Franiewski et al. (2013) evaluated the consequences of fuel damage in a SPF after a loss-of-coolant event using the TRACE code. Kaliatka et al. (2013) evaluated the consequences of fuel melt in the pool during the similar event for the SFP of the Ignalina RBMK NPP using mainly the ATHLET-CD code. They used the ASTEK and RELAP5/SCDAPSIM codes in order to benchmark the same accident. Wu et al. (2014) also evaluated an accident of loss-of-pool-cooling of a PWR using the MAAP5 code. Kocar and Dagli (2015) calculated the thermal-hydraulics of the SFP of the Fukushima-I Unit 4 using the RELAP5/SCDAP code system to observe the water level reduction and fuel uncovery under an assumption that the boil off continues. Unfortunately, both timings of saturation and boil-off were too fast because total water inventory might not be correct. They concluded that natural circulation flow is stopped when the coolant level decreases below the top of fuel assemblies and the fuel cladding temperature starts to increase. However, it was confirmed that fuel uncovery occurs when the collapsed water level is below the TAF according to the experiment using a mock-up (Mochizuki, 2014). This behavior is discussed in the present study through the calculation with the RELAP5-3D code. Lee et al. (1994) calculated thermal-hydraulics of a SFP with rather simple method. Nonboiling water level is evaluated using their specific method which is a simplified flow network model like electrical circuits. The thermal-hydraulics till the fuel is uncovered is seemed to be simple according to the results conducted by the above mentioned researchers, and the timings of reaching saturation temperature and the water level lowering due to evaporation may be estimated by the hand calculations. Therefore, one of the objectives of the present study is to compare the hand calculation results to the calculated results by RELAP5-3D. The other objective is to verify the calculation model with a measured result at the Unit 4 of the Fukushima-I.
2. Estimation of decay heat Water level of the SFP is dependent on the decay heat of the spent fuels and water inventory in the pool during a loss of cooling accident. Therefore, the correlation to predict the decay heat is investigated in the present study. The aim of this investigation is to use the correlation which predict highest decay power. Way and Wigner (1948) proposed an equation relating the decay power as follows.
ts toff
ss
V VT
q qs
timing of saturated condition (s) timing of boil-off (s) time period of reactor operation (s) total water inventory above top of fuel (m3) total water inventory in the pool (m3) density of subcooled water (kg/m3) density of saturated water (kg/m3)
n o Qd ¼ C t 0:2 ðt þ ss Þ0:2 ; Qo
ð1Þ
where Qd is the decay power, Q0 is the nominal reactor power, ss is the time of reactor shutdown measured from the time of startup and t is the elapsed time from the time of reactor shutdown. C is a constant which is specific value for a fuel assembly. Todreas and Kazimi (1990) give the following approximate decay power correlation based on Glasstone and Sesonske (1981) for beta heating as and the approximate decay power for gamma heating,
n o Qd ¼ 0:066 t 0:2 ðt þ ss Þ0:2 : Qo
ð2Þ
Their correlation has the 0.2th power of time as well as the correlation of Way and Wigner. Todreas and Kazimi also proposed the following less simple expression in their textbook.
o 0:2 Qd n ¼ 0:1ðt þ 10Þ0:2 0:087ðt þ 2 107 Þ Qo n o 0:2 0:1ðt þ ss þ 10Þ0:2 0:087ðt þ ss þ 2 107 Þ
ð3Þ
The American Nuclear Society proposed the following correlation in ANS (1973):
Qd ¼ 0:005At b ; Qo
ð4Þ
where constants A and b are defined as a function of the elapsed time as listed in Table 1. These correlations are compared in Fig. 1. Since the decay heat power is large when the operating period of a reactor is short, onemonth operation is assumed in the comparison. The correlation of Way and Wigner is highest among three correlations. The committee in the Atomic Energy Society in Japan proposed a correlation to predict decay heat using a complex way (Research Advisory Committee for Reactor Decay Heat Standard, 1989). However, the correlation has a trend slightly lower than the ANS correlation. 3. Calculation model The calculation model of an SFP of the Advanced Boiling Water Reactor (ABWR) at Hamaoka NPP is illustrated in Fig. 2. The components in the model consist of two time-dependent volumes
Table 1 Constants of the ANS decay heat curve. t (s)
0 < t 10
10 < t 150
150 < t 8 108
A b
12.05 0.0639
15.31 0.1807
27.43 0.2962
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Fig. 1. Correlations to predict decay heat.
300 and 720, a pool bottom 310, five kinds of spent fuels from 410 to 450, lower pool-sides in four directions from 460 to 490, a region above the spent fuel 500, an upper part of the pool 610 and upper pool-sides from 660 to 690, an air region in the pool 700, an air region inside the building 710 and other junction components. The time-dependent volumes are used to set a boundary conditions regarding pressure and temperature of coolant using tables of the RELAP5 code input deck. The lower pool-sides are provided outside region of the spent fuel racks in east, north, west and south directions, i.e., components 460, 470, 480 and 490 in Fig. 2, which are water space in the real spent fuel pool. Although two
components are not shown in Fig. 2, there are two other poolsides in front and behind, i.e., components 470 and 490. Since there is no precise drawing of the spent fuel pool which is available to make the calculation model, widths between the racks and walls for these components are assumed as 1.0 m and 1.5 m, respectively. The pipe model is applied to the lower pool sides and spent fuel racks which are divided into 22 nodes. In the case of the component 460, the divided nodes are described from 460,001 to 460,022 as illustrated in the figure although the number of meshes do not match this number. Volume lengths from 1 to 21 and 22 are 0.1855 and 0.195, respectively. The pipe model is also applied to the upper part of the pool 610 and upper pool-sides 660, 670, 680 and 690 which are divided into 10 nodes. Uniform volume length of 0.7 m is applied to these components. The singlevolume model is applied to the other volumes. In regard to the components above the spent fuel rack, components and nodes are connected by horizontal junctions in order to allow free convection between the components. Since the method to determine flow rate in the junctions is described in the RELAP5-3D manual volume I (The RELAP5-3DÓ Code Development Team, 2012) over 100 pages, you can understand the theory. There is no horizontal junction in the fuel rack region because the rack inside has no horizontal connection between the neighboring channels. Although the components 500, 560, 570, 580 and 590 can be included in the above components 610, 660, 670, 680 and 690 respectively, these components are provided in order to adjust height. The size of the SFP where water is filled is approximately 14 m in length, 18 m in width and 12 m in height and number of spent fuels in the pool is 2527 according to the information on the web-side of the Chubu Electric Company (Chuden, 2016). These dimensions can be obtained through internet. Although the precise size of the fuel bundle is not known, it is assumed that the fuel bundle is inserted in the rack as shown in Fig. 3. Elevation of the bottom of spent fuels is assumed as 0.3 m. Length of the effective fuel length is assumed as 3.71 m. Elevation of top of the fuel assembly is 4.4 m. Decay power is assumed in order to have a temperature distribution in the SFP under a hypothetical situation. It is roughly
Fig. 2. Calculation model of an SFP of the Hamaoka ABWR using the RELAP5-3D code.
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4. Calculation results
Fig. 3. Fuel bundle configuration and its assumed height in a spent fuel rack.
assumed that there are 100 highest power fuels, 100 intermediate power fuels, 200 low power fuels, 100 empty channels and 2127 average power fuels. Total water volume and water volume above the components 500, 560, 570, 580 and 590 are approximately 3075m3 and 1790 m3, respectively. Decay powers of one assembly for various kinds of fuels are listed in Table 2. Total decay power is assumed as approximately 4800 kW which is larger than the actual decay power of the SFP at the Hamaoka NPP in Japan. There is no flow connection between fuels in the rack. Water supplied from a time-dependent volume 300 is drained from a time-dependent volume 320 via a valve component 619. The pool is cooled by 295 K and 139 kg/s feed water at the initial. One air region is assumed above the water region and the other one volume is for the air in the building. Outside air is assumed using a timedependent volume. The inside of the building has a connection to the outside via a 1m2 flow pass. Heat loss from the pool through building wall and the heat capacity of the concrete are neglected in the present calculation because the decay power itself is assumed and the ratios of these effects are very small compared to the decay power. Therefore, it is assumed that the pool is surrounded with the adiabatic walls.
A velocity distribution in the pool under the steady state condition is illustrated in Fig. 4 using three kinds of vectors with different thicknesses ranging 104–102 m/s. The vectors are different each other by an order of magnitude and each kind of vector length outside the frame of the SFP shows the unit length. Velocities inside the racks where fuel assemblies are inserted are in the range from 2.5 105 to 5.7 103 m/s. Velocity in the high power channel is fastest and there is almost no flow in the empty channel. Velocity in the SFP above the rack is asymmetry because water is drained from the top node of the component 660 which is one of the pool sides. Supplied water at the bottom of the SFP raises upward and makes a very weak swirl on the left side of the SFP. However, supplied water on the right side of the SFP flows in the direction of the drainage. The temperature distribution in the pool under the steady state conditions is illustrated in Fig. 5. Temperatures at the outlet of the racks are almost same because the higher power channels have larger inlet velocities, and warmed water is mixed in the upper region of the pool. The temperature distribution in this region is uniform at approximately 303 K because of mixing. Since there is a heat source at the bottom of the SFP, it was presumed that a thermal stratification might occur. However, the temperature distribution is unexpectedly uniform. When the station blackout (SBO) occurs water supply and drainage are suspended, and temperature in the SFP starts to increase. Velocity in the SFP also increases compared to the velocity at the initial steady state condition by an order of magnitude as shown in Fig. 6. A large swirl in the upper part of the SFP and the other swirl through the spent fuel racks via the pool sides are observed when the water reaches to the saturated condition at approximately 2 105 s (2.3 days) after the SBO. The velocity of the natural circulation is faster than that in forced circulation during the steady state conditions. The flow pattern and the velocity calculated by the RELAP5-3D are similar to the calculated results using a CFD code by Yanagi (2013). Fig. 7 illustrates the temperature distribution in the SFP at the same period of time. Temperature in the SFP is almost uniform at 375.4 K. Since it is assumed that a connection between inside the SFP building and the outside air is only 1 m2, pressure inside the building is slightly pressurized by evaporated steam. The temperature distribution in the SFP calculated by the RELAP5-3D code also shows a similar pattern calculated by Yanagi (2013) using the CFD code. Fig. 8 illustrates the evolution of the collapsed water level after the SBO event. Since the calculation is slightly unstable when the collapsed water level is below 5 m from the pool bottom, the calculation is terminated when water level reached 4.5 m on the 9.22th day. The water level from the pool bottom increases after
Table 2 Decay power of individual channel. Channel
Number of assemblies
Decay power of one assembly kW
Comment
410
100
13.59
420 430
100 200
3.627 0.06
440 450
100 2127
0.0 1.445
1 day after reactor shutdown 10 days Average of 1 and 2 years Empty channels 1 month
Fig. 4. Velocity distribution in the pool under the steady state condition.
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Fig. 8. Evolution of collapsed water level in the SFP for ABWR under SBO conditions.
Fig. 5. Temperature distribution in the pool under the steady state condition.
Fig. 6. Velocity distribution in the pool when water reaches at the saturated condition.
the SBO till the water surface reaches to the saturated condition without any water supply. Since the initial temperature of the SFP is approximately 303 K, temperature increases to the saturation temperature by 72 K. The volume of water expands due to temperature increase until the water reaches the saturated condition. During this period, although a part of the water is lost due to evaporation, the volume expansion is larger than the loss of water. After that the collapsed water level decreases gradually due to evaporation with much higher speed. Finally, the collapsed water level reaches the elevation of 5 m from the bottom on approximately the 9th day after the SBO. During the water evaporation process, the decreasing curve is not smooth. Although this zigzag characteristic is seemed to have a relationship with meshes provided in the pool model, the cause is not clear. Two timings of saturated condition and boil-off are compared to the results of the hand calculation which are conducted using the following simple equations. Heat capacity of the rack and the spent fuels are neglected because water volume is enormous compared to these volumes. Physical properties are fixed at the representative temperature, i.e., lumped parameters are used. This is the major difference between the hand calculation and the calculation using RELAP5-3D which calculates time-dependent spatial physical properties for every volume using the pressure and temperature in the volume.
ts ¼ tb ¼
qV T CpðT s T i Þ Qd
qs Vhfg Qd
toff ¼ t b ¼ ts þ tb
;
ð5Þ
:
ð6Þ for
Case 1
for
Case 2
ð7Þ
Density and specific heat capacity during heating-up to the saturated condition in the hand calculation are evaluated by steam table values at 340 K which is average temperature between the initial and the saturated condition as listed in Table 3. Meanwhile for the boil-off calculation, it is assumed that density and latent heat are calculated at the saturated condition, and evaporation is assumed as constant from the beginning of the SBO in Case-1. No
Table 3 Physical properties for hand calculation.
Fig. 7. Temperature distribution in the pool when water reaches at the saturated condition.
Item
Value
Density to calculate saturated condition q Specific heat capacity Cp Density to calculate boil-off qs Latent heat of evaporation hfg
980.0 kg/m3 4.186 kJ/kg 955.9 kg/m3 2248.9 kJ/kg
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evaporation is assumed in Case-2 until the water reaches the saturated condition. Therefore, the boil-off timing for the Case-2 is simply calculated as a summation of the saturation timing and the timing of boil-off in the Case-1. The boil-off timings are compared when the initial water level decreases to 5 m in height from the pool bottom. Comparison is shown in Table 4. As shown in this table, the timing of the saturation is slightly underestimated by the hand calculation. This is because of neglecting the inventory of the spent fuels in the hand calculation. However, the simple hand calculation about the saturation timing coincides with the calculation result of RELAP5 within approximately 3% error. Regarding the boil-off timing by the hand calculation, the Case-1 gives almost the same result as the calculation by the RELAP5 code, and the Case-2 overestimated by approximately 25%. Since the pool water evaporates before it reaches saturated condition, the boil-off timing can be estimated by the hand calculation under the concept of the Case-1. Namely, we can assume the same amount of evaporation from the beginning of the SBO to estimate the water level. The reason of the accurate hand calculation is almost uniform water temperature in the pool due to free convection as illustrated in Fig. 7. Since temperature is uniform, the calculation using representative physical properties provides the equivalent result as the calculated result which takes into account the time-dependent spatial physical properties. Evolution of void fraction in the rack is illustrated in Fig. 9. When the pool water temperature reaches to the saturated condition, there are no voids in the spent fuel rack. Voids appear in the highest power channel when the collapsed water level is lowered to 11 m from the bottom of the pool (6.6 m above the top of the rack), and the void fraction is very low. Therefore, the pool water circulates naturally as if it is a single-phase flow. Void fraction at the top of the fuel assembly becomes more than 1% when collapsed water level is less than 1 m from the top of the fuel.
5. Discussion 5.1. Verification of calculation model for SFP water level It is shown in the previous section that the hand calculations give good estimations for the saturation and boil-off timings of the SFP. The calculation model using the RELAP5-3D code should be verified using the data measured during the Fukushima-I accident in March 2011 in order to convince the accuracy of the hand calculation. A similar calculation model shown in Fig. 2 is adopted in the verification. However, there are small differences in dimensions of the pool size and the number of spent fuels. The pool size is 12.2 m by 9.9 m, and water depth is 11.5 m. Total water inventory in the SFP was reported as approximately 1390 m3. However, the water volume above the fuel assembly is important compared with the total volume. Water volume above the component 500, 560, 570, 580 and 590 is approximately 540 m3. Since there is no precise description on the size of the SFP in TEPCO Report (2012) or Atomic Energy Society of Japan (AESJ) report (2013), the dimension described in Yanagi (2013) is adopted in the present calculation. The number of spent fuels in the pool and total decay heat power are described in the Report by TEPCO (2012) as listed in Table 5.
Fig. 9. Evolution of void fraction at the top of the spent fuel channel from 410 to 450.
Table 5 Spent fuels in the SFP of the Unit 4 in the Fukushima-I. Spent fuel assemblies
Number of assemblies
Channel classification in RELAP5
Decay heat assumed in the calculation (kW)
Fresh fuel 8 8 BJ Older 8 8 and 7 7 STEP2 STEP3-B Total spent fuel
204 30 5 560 736 1331
410 420 430 450 450
1.0 360.6 45.2 800.8 1052.4 Total power: 2260.0
Under the above conditions, the water evaporation of the SFP is calculated by the RELAP5-3D code. The evolution of the water level during the accident without no water supply is illustrated in Fig. 10 together with the measured data. Good agreement is obtained in the calculation. However, we have to remind that the measurement was conducted visually from a helicopter. Therefore, the measured value contains a large error which is indicated in the TEPCO Report (2012) and AESJ Report (2014). Since the roof was blown away by the hydrogen explosion, pilots could see the water surface from the helicopter 5 and a half days after the SBO. If operators in the Fukushina-I nuclear power station verified the photograph or video of the SFP, they possibly evaluated the correct water level. Therefore, the water level evaluated as 2.3 m below the full capacity level is reliable. The timing to reach the saturated condition is calculated as 2.31 days which is underestimated as 2.1 days by the hand calculation. In terms of temperature of the SFP, the report describes it was approximately 363 K at the surface of the pool. However, it is 373.5 K during the evaporation process in the calculation. In the same figure, a calculated result by Yanagi (2013) is illustrated. The calculated result by him shows practically the similar result calculated in the present verification. In his original thesis, since the initial water level is measured as 6.8 m from the top of the rack, water level is shifted to 11.6 m from the bottom of the pool. His result gives higher collapsed water level than the result of the RELAP5, and the discrepancy becomes large as time. Since water inventory of the pool above 5 m is approximately 785 m3, all water will be evaporated within 7.47 105 s (8.65 days) if the
Table 4 Timings of pool water saturation and boil-off. Timing of saturation RELAP5-3D
1.94 105 s
Timing of boil-off Hand calculation
1.89 105 s
RELAP5-3D
7.92 105 s
Hand calculation Case-1
Case-2
8.00 105 s
9.89 105 s
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Fig. 10. Evolution of SFP water level during SBO of the Unit 4 in the Fukushima-I.
Fig. 11. Safety Experiment Facility (SEL) to conduct boil-off experiment.
same hand calculation is applied to this case. Therefore, the evaporation rate by Yanagi is possibly underestimated compared to the reality. 5.2. Water level to cause dryout of a spent fuel assembly In general, dryout of a fuel assembly does not occur when the collapsed water level decreases under the TAF. This is because of the low power of the fuel assembly and voiding in the rack. When the decay heat power of the spent fuel is very low, top of the fuel
immediately causes dryout if the collapsed water level is lowered under the top. However, the spent fuel is covered with voided water when the power is high in the category of the decay heat. It is important to know the actual dryout water level of a spent fuel assembly in order to evaluate the critical condition of the spent fuels. The author conducted dryout experiment using a large facility called Safety Experiment Loop (SEL) illustrated in Fig. 11 with a fuel bundle consisting of 36 pins which had 3.6 m in active heated length. Temperatures in various locations are measured by a thermocouple at the inlet of the test section and cladding surface on different levels as shown in Fig. 12. The water level on the downcomer side was lowered by discharging water slowly from the bottom of the downcomer and the collapsed water level in the test section at which dryout occurred was measured. Although each experiment was conducted with constant power and saturated conditions, a slightly subcooled inlet temperature condition was attained due to time required for the water level to set. The experiment was conducted for different system pressures: 0.1, 1, 5 and 7 MPa. Average subcooling was 15 K, 9 K, 42 K, and 5 K for 0.1, 1, 5 and 7 MPa system pressure conditions, respectively. Among them, dryout under 0.1 MPa is calculated and compared in the present study. Since the density of the coolant in the channel containing the fuel bundle was lower than that of single phase water due to voiding, the collapsed water level at which dryout occurs is lower than the top of the active fuel (TAF). Especially the collapsed water level becomes very low under the atmospheric pressure. This situation is calculated using the model illustrated in Fig. 13. The test section indicated as a pipe component 100 is basically the same model as used for the spent fuel in the rack of the SFP analysis which is shown in Fig. 2. The calculated results for collapsed water level which causes dryout is illustrated in Fig. 14 as a function of the decay heat power. The RELAP5-3D code underestimates the collapsed water level for all power levels by approximately 0.5 m. However, the trend is followed by the code. This difference may be caused by voids behavior in a channel. If void rising velocity is calculated faster than this result, the calculated result possibly approaches to the measured result. Heat transfer coefficients when dryout occurs are evaluated using the thermal equilibrium evaporation rate and measured cladding surface temperature. The comparison between calculation and measurement is shown in Fig. 15. The heat transfer coefficient under dryout condition is properly calculated. However, the heat transfer coefficients in nucleate boiling region are overestimated by RELAP5. Therefore, void behavior and heat transfer coefficient of the RELAP5-3D code under atmospheric conditions should be improved further.
Fig. 12. Heater bundle used in the experiment and thermocouple locations.
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6. Conclusions Water evaporation of a spent fuel pool (SFP) implemented in an advanced boiling water reactor (ABWR) during a station blackout event is calculated using the RELAP5-3D code and by a hand calculation. As a result of the calculations, the following conclusions are obtained.
Fig. 13. Calculation model of RELAP5-3D for boil-off experiment.
(1) Temperature distribution above the rack in the SFP calculated by the RELAP5-3D code is almost uniform under the steady state conditions. The whole pool temperature is almost uniform under transient conditions without heat removal. These are the similar results calculated by a CFD code. (2) Hand calculation results of timings to reach a saturated condition and boil-off coincide with the calculation results with the RELAP5-3D within a practical accuracy. (3) The model to calculate collapsed water level decrease of the spent fuel pool is verified using the measured data at the Unit 4 of the Fukushima-Daiichi. As a result, it has been confirmed that the hand calculation is practical to evaluate the boil-off timing. (4) The spent fuel assembly causes dryout at the top when collapsed water level decreases far below the top of the active fuel. The RELAP5 code underestimate the collapsed water level compared to the measured result. This suggest that the void model under atmospheric pressure should be modified in order to have much faster bubble rising velocity.
Acknowledgements The author would like to express his sincere thanks to Idaho National Laboratory which gives the author one license to use the RELAP5-3D code. The present work could not be done without this code. The author also thanks to Mr. T. Yano who was student in my laboratory and Dr. T. Kaliatka in the Lithuania Energy Institute. They made a basic model to calculate the dryout phenomenon measured in the blowdown facility SEL. References Fig. 14. Collapsed water level to cause dryout.
Fig. 15. Evaluated heat transfer coefficient along the fuel bundle when dryout occurs at the top.
Atomic Energy Society of Japan (AESJ) Investigation Committee, 2014. The Fukushima Nuclear Accident–Final Report of the AESJ Investigation Committee, Maruzen Publishing Co., Ltd., ISBN 978-4-431-55159-1. ANS, 1973. ANS-5.1 1973 Decay Energy Release Rates Following Shutdown of Uranium-Fueled Thermal Reactors, Draft ANS-5.1/N18.6, October 1973. Chuden, 2016. http://hamaoka.chuden.jp/spentfuel/qa02.html, (in Japanese). Collins, T.E., Hubbard, G., 2001. Technical study of spent fuel pool accident at decommissioning nuclear power plants, U.S. Nuclear Regulatory Commission, NUREG-1738. Feiveson, H., Mian, Z., Ramana, M.V., von Hippel, F., 2011. Spent fuel from nuclear power reactors – an overview of a new study, The International Panel on Fissile Materials. Franiewski, Z.I., Geleskie, D.M., Grove, B.E., Maguire, K.G., 2013. Spent fuel pool analysis of a BWR-4 fuel bundle under loss of coolant conditions using TRACE, NucE431W S2013. The Pennsylvania State University. Glasstone, S., Sesonske, A., 1981. Nuclear Reactor Engineering. Krieger Publishing Company, Malabar, Florida 32950. ISBN 0-89464-567-6. Kaliatka, A., Ognerubov, V., Vileiniškis, V., Ušpuras, E., 2013. Analysis of the processes in spent fuel pools in case of loss of heat removal due to water leakage. Sci. Technol. Nucl. Installations 2013, 1–11. http://dx.doi.org/10.1155/ 2013/598975. Article ID 598975. Kocar, C., Dagli, C.P., 2015. Analysis of LOFA in BWR spent fuel storage pool. In: Proc. of the 24th International Conference Nuclear Energy for New Europe, Portorozˇ, Slovenia, pp. 508.1–508.7. Lee, K.B., Nam, K.I., Park, J.R., Lee, S.K., 1994. Thermal-hydraulic analysis and parametric study on the spent fuel pool storage. J. Korean Nucl. Soc. 26 (1), 19– 31. Miller, Ian J., 2012. A System for Cooling Nuclear Spent Fuel using Fluidized Bed Technology, University of Tennessee Honors Thesis Projects, http://trace. tennessee.edu/utk_chanhonoproj/1507.
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H. Mochizuki / Annals of Nuclear Energy 109 (2017) 548–556
Mochizuki, H., 2014. Dryout phenomena under low water level. In: Proc. of Int. Workshop on Nuclear Safety and Severe Accident (NUSSA-2014), Chiba, Japan. NEA Committee on the safety of nuclear installations, 2015. Status report on spent fuel pools under loss-of-cooling and loss-of-coolant accident conditions (Final report), OECD/NEA, NEA/CSNI/R(2015) 2. Park, C.H., Lee, A., Lee, J.M., Moon, J.H., 2013. Estimation of the spent fuel pool water temperature at a Loss-of-Pool-Cooling accident. Int. J. Math. Comput. Phys. Electr. Comput. Eng. 7 (7), 1183–1186. Research Advisory Committee for Reactor Decay Heat Standard, 1989. Nuclear Reactor Decay Heat and Its Recommendation Value. Atomic Energy Society of Japan (AESJ). The RELAP5-3DÓ Code Development Team, 2012. RELAP5-3DÓ Code Manual Volume I: Code Structure, System Models and Solution Methods, INEEL-EXT-9800834 Revision 4.0, http://www4vip.inl.gov/relap5/r5manuals/ver_4_0/vol-1. pdf. Todreas, N.E., Kazimi, M.S., 1990. Nuclear Systems I, Thermal Hydraulic Fundamentals. Hemisphere Publishing Corporation. 0-89116-935-0 (v. 1). Tokyo Electric Power Company (TEPCO), 2012. Fukushima-I Nuclear Power Station –Impact of the earthquake in Tohoku region of the Pacific Ocean on nuclear
facilities, Press report, (in Japanese), http://www.tepco.co.jp/cc/press/betu12_j/ images/120509j0101.pdf. Way, K., Wigner, E.P., 1948. The rate of decay of fission products. Phys. Rev. 73, 1318–1330. Wu, X., Li, W., Zhang, Y., Qiu, S.Z., 2014. Analysis of the loss of pool cooling accident in a PWR spent fuel pool with MAAP5. Ann. Nucl. Energy 72, 198–213. http://dx. doi.org/10.1016/j.anucene.2014.05.030. Ye, C., Zheng, M.G., Wang, M.L., Zhnag, R.H., Xiong, Z.Q., 2013. The design and simulation of a new spent fuel pool passive cooling system. Ann. Nucl. Energy 58, 124–131. http://dx.doi.org/10.1016/j.anucene.2013.03.007. Yanagi, C., Murase, M., Yoshitda, Y., Kusunoki, T., 2012. Prediction of temperature and water level in a spent fuel pit during loss of all AC powers. J. At. Energy Soc. Japan 11 (3), 193–202. http://dx.doi.org/10.3327/taesj.J11.050 (in Japanese). Yanagi, C., 2013. Study on prediction of temperature and water level in a spent fuel pit during loss of all AC powers (Ph.D. thesis). University of Fukui (in Japanese) http://repo.flib.u-fukui.ac.jp/dspace/bitstream/10098/7580/1/%E5%8D%9A%E5% A3%AB%E8%AB%96%E6%96%87%EF%BC%88%E6%9F%B3%E5%8D%83%E8%A3%95% EF%BC%89.pdf.