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Estimation of radionuclide transport to reactor containment building under unprotected severe accident scenario in SFR
Progress in Nuclear Energy 74 (2014) 120e128
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Progress in Nuclear Energy journal homepage: www.elsevier.com/locate/pnucene
Estimation of radionuclide transport to reactor containment building under unprotected severe accident scenario in SFR Arjun Pradeep, P. Mangarjuna Rao*, B.K. Nashine, P. Selvaraj, P. Chellapandi Computational Simulation Section, Safety Engineering Division, Reactor Analysis Group, Indira Gandhi Centre for Atomic Research, Kalpakkam 603 102, India
a r t i c l e i n f o
a b s t r a c t
Article history: Received 28 June 2013 Received in revised form 22 January 2014 Accepted 18 February 2014
In the design of Sodium cooled Fast Reactor (SFR), Defense in Depth (DiD) approach is followed with multiple barriers to limit the release of radionuclides to the environment under accidental conditions. Under severe accident scenario, the multiple barriers provided as part of DiD, can fail one by one and finally the radionuclides may be released to Reactor Containment Building (RCB). Under severe accident scenario, the extent of radionuclides release into the environment has to be limited based on the permissible dose to the public at the site exclusion zone boundary. The radionuclides of concern for SFR under accidental release are noble gases and volatile fission products (Cs, I, Te). A lumped analytical methodology has been developed to estimate the source term in the core and transport of radionuclides to cover gas region/RCB under severe accident scenario in SFR. The methodology estimates the fission product inventory in the core based on saturation analysis method. In the event of severe accident, the core melts and fission products are released into the sodium pool. The transport of fission products (volatile and non-volatile) from pool to cover gas region/RCB takes place mainly by the short term phenomenon (noble gas bubble transport) and sodium spray fire release. The transport of Volatile Fission Products (VFPs) to cover gas region/RCB also takes place via the long term phenomenon (by evaporation). The evaporative transport of VFPs from hot pool to cover gas region is evaluated based on equilibrium partition coefficient (KD). The methodology is verified with the results for radionuclide inventory in SFR core, available in literature and their fractional release to the RCB. This methodology is useful for the evaluation of public dose at the site exclusion zone boundary of a typical SFR under severe accident scenario. Ó 2014 Elsevier Ltd. All rights reserved.
Keywords: Radionuclide transport Fission product inventory Sodium cooled fast reactor Hypothetical core disruptive accident Reactor containment building
1. Introduction In the design of Sodium cooled Fast Reactor (SFR), Defense in Depth (DiD) approach is followed with multiple barriers to limit the release of radionuclides to the environment. The multiple barriers to radionuclide release are fuel pellet, fuel cladding, primary coolant, primary system boundary, reactor containment building (secondary containment) and site exclusion zone boundary. The SFR is provided with engineered safety features such as two independent, fast acting and reliable shutdown systems to prevent the progression of a Potential Initiating Event (PIE) to an accident. In case the shut down systems fail (unprotected), progression of accident can continue, resulting the failure of multiple barriers and
* Corresponding author. Tel.: þ91 44 27480500x23469; fax: þ91 44 27480195. E-mail addresses: [email protected], [email protected] (P. Mangarjuna Rao). http://dx.doi.org/10.1016/j.pnucene.2014.02.018 0149-1970/Ó 2014 Elsevier Ltd. All rights reserved.
release of radionuclides from the core to the Reactor Containment Building (RCB). In SFR the core is not in its most reactive configuration, hence disintegration of the core in SFR (e.g. fuel slumping) due to an initiating event may lead to power excursion, resulting an accident. The accidents that cause highest damage are labeled as Beyond Design Basis Accidents (BDBA) and the BDBA which causes degradation/melting of whole core is termed as Hypothetical Core Disruptive Accident (HCDA)/Severe accident. Severe accident can take place due to mismatch between heat generation and heat removal in the core. The PIE for severe accident in which the heat removal is less than heat generated and shutdown systems have failed is termed as Unprotected Loss of Flow Accident (ULOFA). The various stages that follow the PIE are the pre-disassembly phase, transition phase and disassembly phase. During the predisassembly phase, over heating occurs leading to melting of the core. The heating due to power excursion generates vapor (i.e., core bubble) in the subsequent stage which has the potential to cause
A. Pradeep et al. / Progress in Nuclear Energy 74 (2014) 120e128
Nomenclature A D f F g k L m p P Q t T v Y Greek
l m r
area of cross section (m2) diameter (m) friction factor fraction acceleration due to gravity (m/s2) pressure loss coefficient length (m) mass (kg) thermal power (Watt thermal (Wt)) pressure (Pa) activity (Bq, Ci) time (s) temperature (K) velocity (m/s) fission product cumulative yield decay constant (s1) dynamic viscosity (Pa.s) density (kg/m3)
mechanical loading on the primary system boundary due to high temperature and pressure. The mechanical energy release is due to expansion of vapor phase from initial pressure to ambient pressure (Walter et al., 2012). This energy release takes place in two consequent phases, direct impact pressure resulting in seal failure and escape of fission products/fuel in the cover gas region to RCB (early phase) and sodium slug impact at the top shield bottom causing spray release of sodium along with Fission Products (FPs)/ fuel through top shield Rotatable Plug (RP) penetrations (spray fire phase). During the early phase which takes place instantly (0e10 s), the FPs (volatile and non-volatile) and fuel escaping from the cover gas region to the RCB comes from the bubble transported fraction of radionuclides of the degraded core. During the spray fire phase (w1 s) the FPs and fuel escaping from the burned sodium to the RCB comes from the radionuclides uniformly distributed in the ejected portion of sodium pool. In vessel sodium pool fire is not considered as the top shield breach area is small. The mechanical energy release phases are followed by natural convective release of Volatile Fission Products (VFPs) along with sodium by evaporative mode from the hot cover gas region to the cold RCB which is considered for a period of 24 h from off-site dose evaluation point of view. Evaluation of radionuclide transport from the SFR core to RCB under HCDA scenario is important for quantifying the radioactivity in the RCB, which is essential for the estimation of the dose to the public at the site exclusion zone boundary. Codes like RCS (Umbel et al., 2011) evaluates the release and transport of radionuclides from the core to containment based on inputs from ORIGEN-2 (Croff, 1980). Advanced code system of ORIGEN-2 along with DIF3D/REBUS-3 (Derstine, 1984; Toppel, 1983) estimates the isotope inventory in the core. A lumped analytical methodology has been developed to evaluate the generation, release and transport of FPs from the reactor core to the cover gas region/containment under severe accident scenario in SFR. The present methodology estimates the radioactivity in the RCB due to FPs and actinides under HCDA scenario. 2. Methodology The methodology estimates the FP inventory in the core based on saturation analysis method (Li, 1998). Under HCDA scenario, radionuclide release takes place in many time dependent phases.
Subscript b bubble Cs RCB evap f H i Na pool 1 2
121
blanket bubble transport cesium Reactor Containment Building evaporative transport fuel hydraulic nuclide sodium sodium pool reactor containment building cover gas region
Non dimensional number KD equilibrium partition coefficient of fission product between liquid and gas phase RF Release Fraction from pool Re Reynolds number RT ReTention factor
Theoretical evaluation of the realistic release rate/fraction values for severe accident scenario (i.e., Hypothetical Core Disruptive Accident) is very intricate and depends on various parameters, such as the extent to which the core melts/degrades under severe accident, distribution of fission products and fuel within the sodium pool and in vessel components of reactor, reaction between fission products, fuel and sodium and also on the mechanical energy release phases of HCDA. Validated release rate/fraction values for various radionuclides under HCDA scenario based on the experiments are scarce in literature. Most of the published literature uses conservative values for HCDA release rate/fraction, and hence as an initial endeavor, in the present methodology we followed the same approach to evaluate the transport of various radionuclides under HCDA scenario. The transport of FPs/fuel to RCB is considered in two phases (early phase, spray fire phase) followed by evaporative release of VFPs by natural convection. The transport of FPs/fuel to cover gas region by bubble transport mode (early HCDA phase) is evaluated based on Release Fractions (RFs) available in literature. The transport of FPs to RCB during spray fire phase is evaluated based on ReTention Factor (RT) values available in literature. The evaporative transport of VFPs (i.e., Cs, I, Te) to cover gas region is evaluated based on equilibrium partition coefficient (KD). Fuel (i.e., U, Pu) radioactivity in RCB is evaluated based on HCDA RF values and End Of Equilibrium cycle Core (EOEC) inventories taken from literature. The various methods used in this methodology for evaluating various processes are described in the following subsections. The physical domain considered for the analysis using this methodology is shown in Fig.1. 2.1. Core inventory of radionuclides At the Beginning Of Life (BOL), SFR core consists of actinides in the form of fuel (PuO2 þ UO2) and blankets (depleted UO2), neutron source, coolant sodium and structural material in the form of reflectors, shielding and safety rods. After reactor startup and during normal operation, fission and capture reactions take place and radionuclides, namely FPs (Xe, Kr, Cs, Rb, Te, Se, I, Br) and activation products (Fe, Co, Mn, Cr, Ta) are generated in the core with time. For estimating the SFR core fission product inventory, the continuous operation of the reactor at its maximum power level for the
122
A. Pradeep et al. / Progress in Nuclear Energy 74 (2014) 120e128 Table 1 Cumulative fission product yield data of important fission products (JENDL 4.0). Fission product
Cumulative fission yield for fast fission of Pu-239
Cumulative fission yield for fast fission of U-235
54-Xe-133 36-Kr-85m 53-I-131 55-Cs-137 52-Te-129
0.0697 0.00594 0.0388 0.0658 0.0136
0.0671 0.0136 0.03217 0.06206 0.00809
and U) it is 0.005% (Umbel et al., 2011). In case of alkali metals and halogens, it is considered that 25% of core inventory gets released via bubble transport mode and the remaining 75% mixes with sodium pool. In case of Tellurium group (Te, Se) only 2.5% of the inventory is released by bubble transport mode, 75% mixes with sodium pool and remaining gets portioned with the clad constituents. In the bubble transport mode of these nuclides (during HCDA early phase), around 50% gets transmitted to the cover gas region due to pool scrubbing. RFs of these nuclides are estimated by using the following equation:
For volatile and non volatile nuclides; RFi;bubble ¼ Fi;bubble 0:5 (3) Fig. 1. Release of sodium and radionuclides to RCB during severe accident.
maximum possible operating time with one core was considered, which gives the highest fission product inventory value. The radioactivity (in Curie (Ci)) for each FP has been estimated analytically based on saturation activity method (Li, 1998) which considers FP generation from fission and parent decay and removal by radionuclide decay. The Activity (Qi) of radionuclide, i (having the half life of t1/2,i) at time, t inside the SFR core operating at thermal power p (Wt) is given by
Qi ¼ 0:8446 pYi ð1 expðli tÞÞ
(1)
where, li is the decay constant,
li ¼
0:693 t1=2; i
(2)
where, Yi is the cumulative fission yield of radionuclide, i and the cumulative fission yield data is taken from Japan Evaluated Nuclear Data Library e 4.0 (JENDL-4.0) (Shibata et al., 2011). For typical SFR fuel composition in the fast neutron spectrum, about 80% of the fission takes place in fissile nuclides of Pu-239, Pu-241 and U-235 (Glaser and Ramana, 2007). Hence the FP inventory is obtained from the cumulative FP yield of Pu-239 for the fuel region and U-235 for the blanket region. Equation (1) is used for estimating the activity of all radioactive FPs. The capacity factor for reactor operation is taken as unity for conservativeness in source term evaluation. The typical cumulative fission yields of important nuclides are given in Table 1 for fast fission of Pu-239 in fuel and U-235 in blanket. The total activity in the core is the sum of individual activities of each nuclide in the core. In this analysis, the methodology considered 571 radioisotopes and 76 stable isotopes of FPs like Xe, Kr, I, Br, Cs, Rb, Te, Se, Sb, Ba, Sr, Rh, Tc, Mo, Ru, Pd, Co, La, Nb, Nd, Pr, Zr, Y, Pm, Sm, Eu and Ce. 2.2. Radionuclide release from core to cover gas region/RCB during HCDA early phase In this analysis it is assumed that only the active core fuel region melts during HCDA. Based on the literature, the RF of Non-Volatile Fission Products, NVFPs (La, Zr, Nb, Ba, Sr) to cover gas region is considered as 1% (Umbel et al., 2011; Fies, 1971) and for the fuel (Pu
where, RFi,bubble is the RF of nuclide from the pool by bubble transport mode and Fi,bubble is the RF of nuclide from the core along with noble gas bubbles. 2.3. Radionuclide release from spray fire to RCB during spray fire phase of HCDA The release fractions of FPs/fuel during spray fire have been estimated based on the RT values obtained from PAVE and FANAL experimental tests (Middleton et al., 2011; Lee et al., 1999). The retention factor, RT was defined as the ratio of concentration of radionuclide in sodium pool to that in the burning sodium aerosol. The RF of the radionuclide was thus evaluated based on the fraction of the burned sodium and the RT of corresponding nuclide. The RT values of various radionuclides have been shown in Table 2.
Forvolatile and nonvolatile nuclides; RFi; spray ¼ RFNa; spray =RTi;Na (4) where, RFi,spray is the RF of nuclide from the sodium spray fire, RFNa,burned is the fraction of sodium sprayed from hot pool and RTi,Na is the RT of nuclide in sodium. In the present methodology it is assumed that all the sodium released gets burned. 2.4. Radionuclide release from cover gas region to RCB by natural convection Through the leak paths formed in the top shield, natural convection takes place between the hot cover gas region (which consists of argon, sodium vapor and radionuclides) and relatively cold Table 2 Retention factors of radionuclides for spray fire phase. Radionuclide
Retention factor (Middleton et al., 2011; Lee et al., 1999)
Halogen (I) Alkali metal (Cs) Tellurium group (Te) Alkaline earth metals (Ba,Sr) Noble metals (Ru) Non-volatile fission products (La) Fuel (U, Pu)
0.52 0.25 98.97 250.91 98.97 494.85 494.85
A. Pradeep et al. / Progress in Nuclear Energy 74 (2014) 120e128
RCB air, resulting in the transport of FPs from the cover gas region to RCB as shown in Fig. 1. The established leak paths in typical SFR, consists of horizontal and vertical paths to minimize the sodium release to RCB. In the present analysis to simplify the pressure drop calculations across the top shield, two vertical annular leak paths similar to Large Rotatable Plug (LRP) e Roof Slab (RS) and Small Rotatable Plug (SRP) e LRP gaps, have been considered. It has also been assumed that the air convective loop enters the reactor cover gas region through larger path (LRP-RS gap) and leaves the cover gas region through smaller path (SRP-LRP gap). By using the Bernoulli’s equation for upward and downward flow along with respective frictional pressure drops through the annular gaps, Eq. (5) and Eq. (6) are obtained. For downward flow of air through larger path
P2 ¼ P1
k1 r1 v21 f1 L1 r1 v21 þ r1 gL1 2 DH1 2
(5)
For upward flow of air through smaller path
P1 ¼ P2
k2 r2 v22 f2 L2 r2 v22 r2 gL2 2 DH2 2
(6)
P2 ¼ P1 þ
k2 r2 v22 f2 L2 r2 v22 þ þ r2 gL2 2 DH2 2
(7)
where, subscript 1 refers to RCB (through larger path, downward flow) and subscript 2 refers to cover gas region (through smaller path, upward flow). The thermo physical properties (density: r, dynamic viscosity: m) of air are taken at the pool temperature for cover gas region and at containment temperature for RCB. P is the pressure, k is the pressure loss coefficient, v is the velocity, L is the length and DH is the hydraulic diameter of the annular leak path. The Darcy friction factor, f for laminar flow through the annular gap is taken as
64 f ¼ Re Re ¼
(8)
rvDH m
(9)
The Continuity Equation is
A1 r1 v1 ¼ A2 r2 v2
(10)
where, A is the area of cross section of annular gap leak path. Equating Eqs. (5) and (7) along with Eq. (8), Eq. (9) and Eq. (10).
P1
k1 r1 A2 r2 v2 2 32m1 L1 A2 r2 v2 þ r1 gL1 2 A1 r1 A1 r1 D2H1
¼ P1 þ
k2 r2 v22 32m2 L2 þ v2 þ r2 gL2 2 D2H2
! ! m L A r m L k1 A2 r2 2 þ k2 r2 v22 þ 32 12 1 2 2 þ 22 2 v2 r1 A1 DH1 A1 r1 DH2
through leak paths is estimated. This sodium vapor mass flux is used to estimate the Release Fraction (RFi,evap) of VFPs from cover gas region to RCB. The evaporative transport due to natural convection has been estimated based on the equilibrium partition coefficient (KD) method and the equilibrium partition coefficient values used are taken from the literature (Haga et al., 1990). In the present analysis, evaporative mode release of the VFPs has been estimated for a period of 24 h.
For VFPs; RFi; evap ¼ KD; i RFNa; evap Fi; pool
(13)
RFi,evap is the RF of VFP from the pool by evaporative transport mode and Fi,pool is the RF of VFP from the core into the pool. RFNa,evap is the RF of sodium from the pool by evaporation. KD,i is the equilibrium partition coefficient of VFP i between sodium pool and the gas above. The release fraction values of FPs and fuel evaluated using the present methodology has been compared with release fraction data available for fast reactors under HCDA early phase release scenario as shown in Table 3. From this table, it is clear that the RFs estimated using the present methodology is conservative compared to the RFs used earlier for SFRs, which is good for radiological safety evaluation.
2.5. Inventory of radionuclides in the RCB The FP inventory in the RCB can be obtained from the product of core inventory and its corresponding release fractions. The release fraction corresponds to the total of RFs due to bubble transport, spray fire phase and evaporative transport. The activity (Qi,RCB in Ci) inside RCB at time t due to the radionuclide can be estimated from the following equation:
Qi;RCB ¼ Qi RFi;bubble þ RFi;spray þ RFi;evap ð1 expðli tÞÞ (14) where, Qi is the activity of radionuclide in the core before accident, RFi,bubble is the RF of FP/fuel during HCDA early phase, RFi,spray is the RF of FP/fuel during HCDA spray fire phase and RFi,evap is the RF of VFP during the evaporative phase due to natural convection. The radionuclide activity in the RCB has been evaluated by considering the decay of FPs and fuel for a period of 24 h.
3. Verification of the methodology The verification of the present methodology has been carried out with ORIGEN-2 and RIBD code results for the FP inventory in Table 3 HCDA release fractions for fission products and fuel in SFR during early phase.
(11)
Assuming pressure loss coefficient for expansion and contraction, k ¼ k1 ¼ k2 ¼ 1.5, and canceling the pressure terms, the resulting equation is
0:5
123
(12)
þ gðr2 L2 r1 L1 Þ ¼ 0 By solving the Eq. (12), the upward air flow velocity (v2) from the cover gas region to RCB is obtained. From this upward flow velocity, the mass flux of sodium vapor from the cover gas region to the RCB
Radionuclide released to RCB under HCDA
Release fraction during early phase (0e10 s) Present methodology
FFTF (Fies, 1971)
KALIMER (Lee et al., 1999)
ABR (Umbel et al., 2011)
Noble gas (Xe, Kr) Halogens (I, Br) Alkali metals (Cs, Rb) Tellurium group (Te, Se, Sb) Alkaline earth metals (Ba,Sr) Noble metals (Rh, Ru) Lanthanides (La, Zr) Cerium (Ce) Fuel (U, Pu)
1 0.125 0.125 0.0125
1 0.02 0.01 0.01
1 1 103 1 103 1 103
0.64 0.079 0.079 7.9 103
0.01
0.01
1 104
3.1 105
0.01 0.01 0.01 5 105
0.01 0.01 0.01 1 104
1 1 1 1
104 104 104 104
3.1 3.1 3.1 3.1
105 105 105 105
124
A. Pradeep et al. / Progress in Nuclear Energy 74 (2014) 120e128
Table 4 Predictions of Radionuclide core inventory by present methodology and ORIGEN-2 code for 2000 MWt SFR. Radionuclide Present study
ORIGEN-2
Deviation (%)
Core mass Activity Core mass Activity inventory (MCi) inventory (MCi) (kg) (kg) 54-Xe-133 36-Kr-85m 53-I-131 55-Cs-137 52-Te-129
0.628 0.0012 0.527 85.53 0.0011
117.7 10.03 65.51 7.42 23.03
0.577 0.0011 0.501 71.5 0.00104
Table 7 Release fraction for nuclides of typical SFR during bubble transport, spray fire and evaporative route under severe accident scenario. Radionuclide
Core mass Activity inventory
108 8.95 9.144 10.78 62.11 5.26 6.225 19.63 21.79 5.74
Noble gases (Xe, Kr) Halogens (I, Br) Volatile solids (Cs, Se, Te) All remaining fission products
Present study
RIBD
Activity (Ci)
Activity (Ci)
1.37 1.43 1.66 1.4
108 108 108 109
1.4 1.4 1.5 1.1
9.01 9.69 5.47 19.3 5.71
Noble gas Halogen (I) Alkali metal (Cs) Tellurium group (Te) Alkaline earth metals Noble metals Non-volatile fission products Fuel (U, Pu)
Deviation (%)
108 108 108 109
Evaporation (24 h) (Long term)
Total release fraction
2.23 105
6.1 104
1 0.125 0.125 0.0125
5.9 104 (Baskaran et al., 2004) 0 0.001126 0.002351 5.96 106
0 5.7 106 7.7 104 2.01 1010
1 0.126 0.128 0.0125
0.01
2.35 106
0.01
0.01 0.01
6
5.96 10 1.19 106
0.01 0.01
5 105
1.19 106
5.1 105
Sodium
Table 5 Predictions of radionuclide core inventory by present methodology and RBID code for 400 MWt SFR. Radionuclide
Spray
Bubble transport (Short term)
2.39 2.41 10.9 27.6
core and also with the results available in literature for released inventory to the RCB under HCDA.
that is in the order of 106 Ci. Hence the FPs are the dominant radionuclides that contribute to core source term in SFR and from Tables 4 and 5, it is clear that the present methodology is predicting the FP inventory in the core conservatively. 3.2. RCB fission product inventory
3.1. Core fission product inventory The inventory of FPs in the core predicted by the methodology used has been verified with the ORIGEN e 2 code predicted values for 2000 MWt SFR at EOEC (Kim and Yang, 2008). The SFR core was designed to achieve one year cycle length with 3 batch fuel management scheme. The verification details for mass inventories of Xe, Kr, I, Te and Cs are given in Table 4. The total radioactivity estimated by the method for 571 FP radionuclides and 76 stable FP nuclides is w9.37 109 Ci, which is comparable with the ORIGEN-2 predicted value of 9.105 109 Ci for SFR-2000 (Kim and Yang, 2008). The corresponding total FP mass inventory in the core estimated by this methodology is 2461.1 kg, which is comparable with the 2049.8 kg mass inventory estimated for SFR, by ORIGEN-2. The present analytical method estimates the SFR core FP inventory conservatively within 20% of the ORIGEN-2 prediction, which is adequate for safety evaluation of SFRs under HCDA. The radiological source term due to activation products is not considered in the present methodology due its very low value compared to FPs (Kim and Yang, 2008). This methodology has also been verified with the results obtained from Radio-Isotope Build up and Decay (RIBD) code for SFR core FP inventory which was operated for 200 days at full power of 400 MWt (Fies, 1971). The verification details for activities of Xe, Kr, I, Br, Cs, Te and Se are given in Table 5. The total activity due to noble gases (Xe, Kr), halogens (I, Br) and volatile solids (Cs, Te, Se) have been estimated by adding the activities of individual nuclides. The total activity due to FPs as predicted by the present methodology and RIBD code for SFR plutonium fuel irradiated for 200 days is of the order of 109 Ci, which is much higher than the fuel radioactivity
The predictions of this methodology has been verified for the released mass inventory of the FPs/fuel in the RCB of SFR of 1253 MWt under HCDA scenario (Baskaran et al., 2004) after 24 h and the results are given in Table 6. Under HCDA resultant spray fire of 350 kg sodium in the RCB, the aerosol mass concentration of sodium and VFPs (Cs, I) in the RCB is estimated to be 5.158 g/m3 by the present methodology compared to the published value of 5.15 g/m3 (Baskaran et al., 2004). The aerosol mass concentration of FPs, Sr and Te estimated by the present methodology is 1.97 mg/m3 compared to the value of 23.3 mg/m3 from Baskaran et al. (2004). The estimated total amount of tellurium and strontium in the RCB is lower than the value given in Baskaran et al. (2004) and this is due to the partition of Te with clad constituents which has been considered in the present methodology. The estimated aerosol mass concentration of fuel (U, Pu) in the RCB is 6.03 mg/m3 (where the core inventory was estimated based on Pandikumar et al. (2011)), which is in the same order of the value given in Baskaran et al. (2004) (i.e., 10.9 mg/m3) for an initial plutonium inventory of 2020 kg (at BOL). 4. Results and discussion The present methodology has been used to estimate the maximum achievable radioactive FP inventory generated in the fuel and blanket regions of a typical SFR producing 1253 MWt. A refueling time of 185 days in 3 batches for fuel and 8 batches for radial blanket was assumed for the present calculations. Hence a total fuel irradiation time of 555 days for fuel and 1480 days for blanket was assumed for this analysis. It is also assumed that 90% of the thermal
Table 6 Verification of RCB fission product inventory for SFR (1253 MWt) for 24 h of HCDA. Nuclide Ref (Baskaran et al., 2004) Model
Containment Containment Fuel region
Cs (kg)
I (kg)
Te þ Sr (kg)
Pu (kg)
U (kg)
9.22 10.18 79.49
0.858 0.914 7.25
1.63 0.138 13.36
0.143 0.114 2235.42 (Pandikumar et al., 2011)
0.583 0.308 6023.29 (Pandikumar et al., 2011)
A. Pradeep et al. / Progress in Nuclear Energy 74 (2014) 120e128 Table 8 Core (fuel þ blanket) maximum achievable fission product inventory in a typical breeder type SFR (1253 MWt). Radionuclide
Saturation activity method Core mass inventory (kg)
Noble gas (Xe, Kr) Halogens (I, Br) Alkali metals (Cs, Rb) Tellurium group (Te, Sb, Se) Alkaline earth metals (Ba, Sr) Noble metals (Rh, Tc, Mo, Ru, Pd, Co) Lanthanides (La, Nb, Nd, Pr, Zr, Y, Pm, Sm, Eu) Cerium group (Ce) Radioactive fission product total activity
Activity (MCi)
Unstable
Stable
Total
0.93 6.4 72 0.78 10.48 42.11
91.2 2.3 35.8 1.02 110.4 206.76
92.1 8.7 107.8 3.89 120.92 248.87
445.22 456.77 386.25 423.03 605.88 1322.25
99.01
208.22
307.2
2000.8
24.75
27.88
52.63 942.24
238.6 5878.86
Table 9 Fuel region actinide inventory in a typical breeder type SFR (1253 MWt) after 10 cycles. Actinide
Active core wt (%)
Mass (kg)
Activity (Ci)
U-232 U-233 U-234 U-235 U-236 U-238 Pu-238 Pu-239 Pu-240 Pu-241 Pu-242 Am-241 Total
5.47 107 5.77 107 0.007 0.056 0.103 72.768 0.05 16.642 8.623 1.151 0.584 0.018 1
4.52 105 4.77 105 0.578 4.62 8.51 6009.58 4.12 1374.38 712.13 95.05 48.23 1.49 8258.72
1.01 0.00045 3.6 0.01 0.55 2.02 7.08 104 8.53 104 1.62 105 9.88 106 190.91 5101.55 1.02 107
125
Cs to the cover gas region/RCB by the present methodology are given in Appendix A and B respectively. The typical RF values evaluated for various radionuclides are given in Table 7. From this table, it is clear that the RCB source term contribution is mainly from the bubble transport for VFPs than the spray fire release or evaporative route under HCDA release scenario. The methodology considers the mass of radioactive FPs and stable FPs. The maximum achievable FP inventory in the core (fuel þ blanket) for typical breeder type 1253 MWt SFR is given in Table 8. The method estimated FP contribution to the core radioactivity is 5.87109 Ci. For the typical 1253 MWt fast reactor core the activity due to actinides in the fuel region after 10 cycles of operation will be w1 107 Ci for the core fuel composition given in Table 9 (Pandikumar et al., 2011), in which the BOL core mass of Pu is 2.02 ton. The contribution of activity due to radionuclides (FPs þ actinides) in the fuel region of core which produces 90% of the total SFR thermal power is shown in Fig. 2. From Tables 8 and 9, it is clear that the main radioactivity contributor to the core is FPs compared to actinides. In the event of HCDA, the FPs and actinides gets released to the RCB. Based on the RFs already discussed (in Table 7), the activity of FPs released to RCB has been estimated and given in Table 10. The 24 h evaporative release for VFPs has been estimated only for Halogen (I), Alkali metal (Cs) and Tellurium group (Te). From Table 10 it is clear that under HCDA scenario, out of the total FP and actinide inventory in the active core fuel region about, 1.07% of mass inventory and 1.67% of radioactivity is present in the RCB after 24 h. The value of radioactivity due to fuel (U, Pu) is much lesser compared to the radioactivity of FPs in the RCB, hence almost the total radioactivity in the RCB of about 8.8107 Ci can be considered to be mainly from FPs. The contribution of various radionuclides (FPs and actinides) to total radioactivity in the RCB as evaluated by the methodology is shown in Fig. 3.
5. Conclusion power is generated in the fuel region with actinide mass of 8258.72 kg and the remaining 10% in the blankets (Roychowdhury et al., 2000). The typical estimations of the mass of FP Cs and its radio activity in the core of a breeder type SFR and the transport of
A lumped analytical methodology has been developed to evaluate the radioactivity in the RCB under energetic core disruptive accident scenario by considering radioactive fission product
Fig. 2. Percentage contribution of various radionuclides to total radioactivity in active core of typical 1253 MWt SFR.
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A. Pradeep et al. / Progress in Nuclear Energy 74 (2014) 120e128
Table 10 RCB source term due to fission products in a typical breeder type SFR (1253 MWt) under HCDA in 24 h. Radionuclide
Total activity due to fission products in RCB (MCi)
Total mass (kg)
Noble gas Halogen Alkali metal Tellurium group Alkaline earth metals Noble metals Lanthanides Cerium Pu U Total
72.18 8.61 0.42 0.67 0.69 1.75 2.72 0.99 5.1 104 3.68 1010 88.04
71.29 0.92 10.68 0.041 0.902 2.09 2.05 0.307 0.085 0.308 88.7
inventory in the core along with the radionuclide transport to RCB. The methodology uses the conservative saturation activity method to estimate the core inventory of fission products. Under HCDA release scenario to RCB, the release fraction of fission products via bubble transport mode are considered for early phase of release (0e10 s), the release fraction of fission products from the sodium spray fire are considered during spray fire phase (w1 s) and volatile fission products (Cs, I, Te) release by natural convection based evaporative transport is considered for a period of 24 h. The methodology predicted core inventory of fission products have been verified with ORIGEN-2 and RIBD code results available in literature for SFRs and have been found adequately conservative. The methodology predicted inventory of fission products in the RCB under HCDA scenario have been verified with results available in literature for typical SFR and have been found reasonable. The present methodology predictions show that in the event of severe accident scenario, the volatile fission product release is mainly due to the short term bubble transport compared to the long term evaporative transport and spray fire release phase. The methodology also shown that the main contributors to radiological evaluation of HCDA in SFR are the fission products compared to actinides, hence the RCB fission product inventory predicted by the present methodology can be effectively used for the evaluation of dose at site exclusion boundary. For a typical SFR of 1253 MWt, the
evaluated total source term in 86,146 m3 volume RCB, due to fission products under severe accident scenario is 3.78 1013 Bq/m3 and in the core is 2.18 1020 Bq. The public dose at the site exclusion zone boundary can be evaluated confidently based on the present methodology estimated RCB source term under HCDA scenario. Appendix A Estimation of maximum achievable radioactivity and mass of Cesium in the core. Activity of Cs-137 in fuel region:
3:12 1010 QCs137;f ¼ 1253 106 0:9 0:0658 3:7 1010 0:693 185 86400 3 1 exp 30:07 8760 3600 QCs137;f ¼ 2:15 106 Ci (A.1) Mass of Cs-137 in fuel region:
mCs137;f ¼
QCs137;f 0:69310006:0231023 30:07876036001373:71010
¼ 24:86 kg
(A.2)
Activity of Cs-137 in blanket region :
3:12 1010 1253 106 0:1 0:06206 3:7 1010 0:693 185 86400 8 1 exp 30:07 8760 3600
QCs137;b ¼
QCs137;b ¼ 0:585 106 Ci (A.3) Mass of Cs-137 in blanket region:
mCs137;b ¼
QCs137;b 0:69310006:0231023 30:07876036001373:71010
¼ 6:74 kg
Fig. 3. Percentage contribution of various radionuclides to total radioactivity in RCB of typical 1253 MWt SFR within 24 h after CDA initiation.
(A.4)
A. Pradeep et al. / Progress in Nuclear Energy 74 (2014) 120e128
The masses of radioisotope of Cs-137 are estimated using the above Eq. (A.2) and Eq. (A.4) and the mass of stable isotope, Cs-133 in the fuel and blanket region are estimated as follows. Mass of Cs-133 in fuel region:
mCs133;f ¼ 3:12 1010 1253 106 0:9 0:0697 3 185 8760 3600 ¼ 26 kg (A.5) Mass of Cs-133 in blanket region:
mCs133;b ¼ 3:12 1010 1253 106 0:1 0:0671 8 185 8760 3600 ¼ 7:42 kg
RFCs;spray ¼
By considering the remaining isotopes of Cs, the maximum achievable mass inventory of Cs in the core predicted by this method is 101 kg that have an activity of 2.41 108 Ci. Fig. A.1 shows the variation of core mass inventory of fission product Cs137 and I-133 with irradiation time at full power.
5:9 104 =0:25 ¼ 0:00235
127
(B.2)
To estimate the amount of Cs released by evaporative mode for 24 h, it is required to calculate the amount of Cs present in the pool and the release fraction of sodium vapor to RCB under rotatable plug seal leak failure condition. Out of the total Cs in the active core region, 75% gets mixed in the pool along with the pool scrubbed Cs, which failed to escape by the bubble transport mode. The Release fraction (RFNa,evap) of sodium by evaporation mode is estimated by solving the Eq. (B.3).
0:5 (A.6)
! ! m L A r m L k1 A2 r2 2 þ k2 r2 v22 þ 32 12 1 2 2 þ 22 2 v2 r1 A1 DH1 A1 r1 DH2
(B.3)
þ gðr2 L2 r1 L1 Þ ¼ 0 Conditions of RCB (1) used in the analysis: Temperature of RCB (T1) ¼ 313 K Pressure of RCB (P1) ¼ 101325 Pa Density of air (r1) ¼ 1.13 kg/m3 Viscosity of air (m1) ¼ 1.91 105 Pa.s Area of cross section of LRP-RS leak path (A1) ¼ 0.1 m2 Hydraulic diameter of LRP-RS leak path (DH1) ¼ 0.01 m Length of leak path (L1) ¼ 2.5 m Cover gas (2) conditions used in the analysis Temperature of hot pool (T2) ¼ 820 K Pressure of cover gas region (P2) ¼ 101325 Pa Density of air (r2) ¼ 0.43 kg/m3 Vapor pressure of sodium vapor ¼ 1300 Pa Density of sodium vapor ¼ 4.39 103 kg/m3 Viscosity of air (m2) ¼ 3.95 105 Pa.s Area of cross section of SRP-LRP leak path (A2) ¼ 0.0667 m2 Hydraulic diameter of SRP-LRP leak path (DH2) ¼ 0.01 m Length of leak path (L2) ¼ 2.5 m Pressure loss coefficient, k1 ¼ k2 ¼ 1.5
Fig. A.1. Mass inventory of radioactive fission products Cs-137 and I-131 as a function of time.
Appendix B Estimation of total release fraction of cesium. The present methodology assumes that under HCDA only the fuel region melts, and hence the amount of Cs that gets released from the active core region under HCDA is 79.49 kg. From this, 25% Cs gets released by bubble transport mode, out of which only 50% reaches the cover gas region due to pool scrubbing. Generally the bubble rise time is less than 10 s (Umbel et al., 2011) for the transmitted fraction of 50%. Release fraction of Cs from pool during initial release phase of HCDA by bubble transport mode is
RFCs;bubble ¼ ð0:25 0:5Þ ¼ 0:125
(B.1)
During the spray fire phase, w350 kg (Baskaran et al., 2004) of sodium is ejected from the reactor hot pool resulting sodium spray combustion in the RCB. The release fraction of Cs to the RCB during spray fire phase is evaluated using Eq. (4). For a given sodium spray release fraction of 5.9 104 (from the hot pool) and with the retention factor for Cs in completely burned sodium spray fire of 0.25, the Cs release fraction can be estimated as given below:
The estimated downward flow velocity of air (v1) from Eq. (B.3) is 0.132 m/s and the upward flow velocity of air, v2 is 0.523 m/s. Based on the upward flow velocity, the mass flow rate of sodium vapor estimated is 0.153 g/s under seal leak condition from an annular cross section area of 0.0667 m2. Based on the evaluated sodium vapor flow rate, the estimated evaporative release fraction of sodium (from the hot pool sodium of 5,93,095 kg) for a period of 24 h is 2.23 105. The evaporative release of Cs is estimated based on the equilibrium partition coefficient method. The equilibrium partition coefficient value of Cs at a pool temperature of 820 K is taken as 39.9. The mass of Cs released by evaporation is estimated for a period of 24 h as given below: Release fraction of Cs from pool by evaporative transport:
RFCs;evap ¼ KD;Cs RFNa;evap ð0:75 þ 0:25 0:5Þ ¼ 7:7 104
(B.4)
References Baskaran, R., et al., 2004. Aerosol test facility for fast reactor safety studies. Indian J. Pure Appl. Phys. 42, 873e878. Croff, A.G., 1980. ORIGEN-2 e a Revised and Updated Version of the Oak Ridge Isotope Generation and Depletion Code. Oak-Ridge National Laboratory. ORNL5621. Derstine, K.L., 1984. DIF3D: a Code to Solve One-, Two-, and Three-dimensional Finite Difference Diffusion Theory Problems. Argonne National Laboratory. ANL-82-64.
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Fies, C.L., 1971. Radiological Evaluation of a Hypothetical Core Disruptive Accident. Hanford Engineering Development Laboratory, United States Atomic Energy Commission. Glaser, Alexander, Ramana, M.V., 2007. Weapon-grade Plutonium Production Potential in the Indian Prototype Fast Breeder Reactor, Science and Global Security. Taylor & Francis, pp. 85e105. Haga, K., Nishizawa, Y., Watanabe, T., Miyahara, S., Himeno, Y., 1990. Experimental Study on Equilibrium Partition Coefficient of Volatile Fission Products between Liquid Sodium and the Gas Phase. International Fast Reactor Safety Meeting. Kim, T.K., Yang, W.S., 2008. Preliminary Estimation of Isotopic Inventories of 2000 MWt ABR (Revision 1). ANL-AFCI-207. Lee, Seong-Wook, et al., 1999. Preliminary containment performance analysis for the conceptual design of KALIMER. In: Korea Atomic Energy Research Institute, 7th International Conference on Nuclear Engineering, Tokyo, Japan, ICONE7347. Li, Q., 1998. Estimate of Radiation Release for MIT Research Reactor during Design Basis Accident. Nuclear Engineering Department, MIT. S.M. Thesis.
Middleton, Bobby D., Parma, Edward J., Olivier, Tara J., Phillips, Jesse, LaChance, Jeffrey L., 2011. The Development of a Realistic Source Term for Sodium-cooled Fast Reactors: Assessment of Current Status and Future Needs. SAND2011e3404. Pandikumar, G., et al., 2011. Improved analysis on multiple recycling of fuel in prototype fast breeder reactor in a closed fuel cycle. Pramana-J. Phys. 77 (2), 315e333. Roychowdhury, D.G., et al., 2000. Thermal hydraulic design of PFBR core. In: LMFR Core Thermohydraulics: Status and Prospects. International Atomic Energy Agency, Vienna, pp. 41e55. IAEA-TECDOC-1157. Shibata, K., et al., 2011. JENDL-4.0: a new library for nuclear science and engineering. J. Nucl. Sci. Technol. 48 (1), 1e30. Toppel, B.J., 1983. A User’s Guide to the REBUS-3 Fuel Cycle Analysis Capability. Argonne National Laboratory. ANL-83-2. Umbel, M., Denning, R., Brunett, A., 2011. Containment source terms in SFR accidents. In: PSA 2011 Conference, U.K. Walter, A., Todd, D., Tsvetkov, P. (Eds.), 2012. Fast Spectrum Reactors. Springer, US.
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Progress in Nuclear Energy journal homepage: www.elsevier.com/locate/pnucene
Estimation of radionuclide transport to reactor containment building under unprotected severe accident scenario in SFR Arjun Pradeep, P. Mangarjuna Rao*, B.K. Nashine, P. Selvaraj, P. Chellapandi Computational Simulation Section, Safety Engineering Division, Reactor Analysis Group, Indira Gandhi Centre for Atomic Research, Kalpakkam 603 102, India
a r t i c l e i n f o
a b s t r a c t
Article history: Received 28 June 2013 Received in revised form 22 January 2014 Accepted 18 February 2014
In the design of Sodium cooled Fast Reactor (SFR), Defense in Depth (DiD) approach is followed with multiple barriers to limit the release of radionuclides to the environment under accidental conditions. Under severe accident scenario, the multiple barriers provided as part of DiD, can fail one by one and finally the radionuclides may be released to Reactor Containment Building (RCB). Under severe accident scenario, the extent of radionuclides release into the environment has to be limited based on the permissible dose to the public at the site exclusion zone boundary. The radionuclides of concern for SFR under accidental release are noble gases and volatile fission products (Cs, I, Te). A lumped analytical methodology has been developed to estimate the source term in the core and transport of radionuclides to cover gas region/RCB under severe accident scenario in SFR. The methodology estimates the fission product inventory in the core based on saturation analysis method. In the event of severe accident, the core melts and fission products are released into the sodium pool. The transport of fission products (volatile and non-volatile) from pool to cover gas region/RCB takes place mainly by the short term phenomenon (noble gas bubble transport) and sodium spray fire release. The transport of Volatile Fission Products (VFPs) to cover gas region/RCB also takes place via the long term phenomenon (by evaporation). The evaporative transport of VFPs from hot pool to cover gas region is evaluated based on equilibrium partition coefficient (KD). The methodology is verified with the results for radionuclide inventory in SFR core, available in literature and their fractional release to the RCB. This methodology is useful for the evaluation of public dose at the site exclusion zone boundary of a typical SFR under severe accident scenario. Ó 2014 Elsevier Ltd. All rights reserved.
Keywords: Radionuclide transport Fission product inventory Sodium cooled fast reactor Hypothetical core disruptive accident Reactor containment building
1. Introduction In the design of Sodium cooled Fast Reactor (SFR), Defense in Depth (DiD) approach is followed with multiple barriers to limit the release of radionuclides to the environment. The multiple barriers to radionuclide release are fuel pellet, fuel cladding, primary coolant, primary system boundary, reactor containment building (secondary containment) and site exclusion zone boundary. The SFR is provided with engineered safety features such as two independent, fast acting and reliable shutdown systems to prevent the progression of a Potential Initiating Event (PIE) to an accident. In case the shut down systems fail (unprotected), progression of accident can continue, resulting the failure of multiple barriers and
* Corresponding author. Tel.: þ91 44 27480500x23469; fax: þ91 44 27480195. E-mail addresses: [email protected], [email protected] (P. Mangarjuna Rao). http://dx.doi.org/10.1016/j.pnucene.2014.02.018 0149-1970/Ó 2014 Elsevier Ltd. All rights reserved.
release of radionuclides from the core to the Reactor Containment Building (RCB). In SFR the core is not in its most reactive configuration, hence disintegration of the core in SFR (e.g. fuel slumping) due to an initiating event may lead to power excursion, resulting an accident. The accidents that cause highest damage are labeled as Beyond Design Basis Accidents (BDBA) and the BDBA which causes degradation/melting of whole core is termed as Hypothetical Core Disruptive Accident (HCDA)/Severe accident. Severe accident can take place due to mismatch between heat generation and heat removal in the core. The PIE for severe accident in which the heat removal is less than heat generated and shutdown systems have failed is termed as Unprotected Loss of Flow Accident (ULOFA). The various stages that follow the PIE are the pre-disassembly phase, transition phase and disassembly phase. During the predisassembly phase, over heating occurs leading to melting of the core. The heating due to power excursion generates vapor (i.e., core bubble) in the subsequent stage which has the potential to cause
A. Pradeep et al. / Progress in Nuclear Energy 74 (2014) 120e128
Nomenclature A D f F g k L m p P Q t T v Y Greek
l m r
area of cross section (m2) diameter (m) friction factor fraction acceleration due to gravity (m/s2) pressure loss coefficient length (m) mass (kg) thermal power (Watt thermal (Wt)) pressure (Pa) activity (Bq, Ci) time (s) temperature (K) velocity (m/s) fission product cumulative yield decay constant (s1) dynamic viscosity (Pa.s) density (kg/m3)
mechanical loading on the primary system boundary due to high temperature and pressure. The mechanical energy release is due to expansion of vapor phase from initial pressure to ambient pressure (Walter et al., 2012). This energy release takes place in two consequent phases, direct impact pressure resulting in seal failure and escape of fission products/fuel in the cover gas region to RCB (early phase) and sodium slug impact at the top shield bottom causing spray release of sodium along with Fission Products (FPs)/ fuel through top shield Rotatable Plug (RP) penetrations (spray fire phase). During the early phase which takes place instantly (0e10 s), the FPs (volatile and non-volatile) and fuel escaping from the cover gas region to the RCB comes from the bubble transported fraction of radionuclides of the degraded core. During the spray fire phase (w1 s) the FPs and fuel escaping from the burned sodium to the RCB comes from the radionuclides uniformly distributed in the ejected portion of sodium pool. In vessel sodium pool fire is not considered as the top shield breach area is small. The mechanical energy release phases are followed by natural convective release of Volatile Fission Products (VFPs) along with sodium by evaporative mode from the hot cover gas region to the cold RCB which is considered for a period of 24 h from off-site dose evaluation point of view. Evaluation of radionuclide transport from the SFR core to RCB under HCDA scenario is important for quantifying the radioactivity in the RCB, which is essential for the estimation of the dose to the public at the site exclusion zone boundary. Codes like RCS (Umbel et al., 2011) evaluates the release and transport of radionuclides from the core to containment based on inputs from ORIGEN-2 (Croff, 1980). Advanced code system of ORIGEN-2 along with DIF3D/REBUS-3 (Derstine, 1984; Toppel, 1983) estimates the isotope inventory in the core. A lumped analytical methodology has been developed to evaluate the generation, release and transport of FPs from the reactor core to the cover gas region/containment under severe accident scenario in SFR. The present methodology estimates the radioactivity in the RCB due to FPs and actinides under HCDA scenario. 2. Methodology The methodology estimates the FP inventory in the core based on saturation analysis method (Li, 1998). Under HCDA scenario, radionuclide release takes place in many time dependent phases.
Subscript b bubble Cs RCB evap f H i Na pool 1 2
121
blanket bubble transport cesium Reactor Containment Building evaporative transport fuel hydraulic nuclide sodium sodium pool reactor containment building cover gas region
Non dimensional number KD equilibrium partition coefficient of fission product between liquid and gas phase RF Release Fraction from pool Re Reynolds number RT ReTention factor
Theoretical evaluation of the realistic release rate/fraction values for severe accident scenario (i.e., Hypothetical Core Disruptive Accident) is very intricate and depends on various parameters, such as the extent to which the core melts/degrades under severe accident, distribution of fission products and fuel within the sodium pool and in vessel components of reactor, reaction between fission products, fuel and sodium and also on the mechanical energy release phases of HCDA. Validated release rate/fraction values for various radionuclides under HCDA scenario based on the experiments are scarce in literature. Most of the published literature uses conservative values for HCDA release rate/fraction, and hence as an initial endeavor, in the present methodology we followed the same approach to evaluate the transport of various radionuclides under HCDA scenario. The transport of FPs/fuel to RCB is considered in two phases (early phase, spray fire phase) followed by evaporative release of VFPs by natural convection. The transport of FPs/fuel to cover gas region by bubble transport mode (early HCDA phase) is evaluated based on Release Fractions (RFs) available in literature. The transport of FPs to RCB during spray fire phase is evaluated based on ReTention Factor (RT) values available in literature. The evaporative transport of VFPs (i.e., Cs, I, Te) to cover gas region is evaluated based on equilibrium partition coefficient (KD). Fuel (i.e., U, Pu) radioactivity in RCB is evaluated based on HCDA RF values and End Of Equilibrium cycle Core (EOEC) inventories taken from literature. The various methods used in this methodology for evaluating various processes are described in the following subsections. The physical domain considered for the analysis using this methodology is shown in Fig.1. 2.1. Core inventory of radionuclides At the Beginning Of Life (BOL), SFR core consists of actinides in the form of fuel (PuO2 þ UO2) and blankets (depleted UO2), neutron source, coolant sodium and structural material in the form of reflectors, shielding and safety rods. After reactor startup and during normal operation, fission and capture reactions take place and radionuclides, namely FPs (Xe, Kr, Cs, Rb, Te, Se, I, Br) and activation products (Fe, Co, Mn, Cr, Ta) are generated in the core with time. For estimating the SFR core fission product inventory, the continuous operation of the reactor at its maximum power level for the
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A. Pradeep et al. / Progress in Nuclear Energy 74 (2014) 120e128 Table 1 Cumulative fission product yield data of important fission products (JENDL 4.0). Fission product
Cumulative fission yield for fast fission of Pu-239
Cumulative fission yield for fast fission of U-235
54-Xe-133 36-Kr-85m 53-I-131 55-Cs-137 52-Te-129
0.0697 0.00594 0.0388 0.0658 0.0136
0.0671 0.0136 0.03217 0.06206 0.00809
and U) it is 0.005% (Umbel et al., 2011). In case of alkali metals and halogens, it is considered that 25% of core inventory gets released via bubble transport mode and the remaining 75% mixes with sodium pool. In case of Tellurium group (Te, Se) only 2.5% of the inventory is released by bubble transport mode, 75% mixes with sodium pool and remaining gets portioned with the clad constituents. In the bubble transport mode of these nuclides (during HCDA early phase), around 50% gets transmitted to the cover gas region due to pool scrubbing. RFs of these nuclides are estimated by using the following equation:
For volatile and non volatile nuclides; RFi;bubble ¼ Fi;bubble 0:5 (3) Fig. 1. Release of sodium and radionuclides to RCB during severe accident.
maximum possible operating time with one core was considered, which gives the highest fission product inventory value. The radioactivity (in Curie (Ci)) for each FP has been estimated analytically based on saturation activity method (Li, 1998) which considers FP generation from fission and parent decay and removal by radionuclide decay. The Activity (Qi) of radionuclide, i (having the half life of t1/2,i) at time, t inside the SFR core operating at thermal power p (Wt) is given by
Qi ¼ 0:8446 pYi ð1 expðli tÞÞ
(1)
where, li is the decay constant,
li ¼
0:693 t1=2; i
(2)
where, Yi is the cumulative fission yield of radionuclide, i and the cumulative fission yield data is taken from Japan Evaluated Nuclear Data Library e 4.0 (JENDL-4.0) (Shibata et al., 2011). For typical SFR fuel composition in the fast neutron spectrum, about 80% of the fission takes place in fissile nuclides of Pu-239, Pu-241 and U-235 (Glaser and Ramana, 2007). Hence the FP inventory is obtained from the cumulative FP yield of Pu-239 for the fuel region and U-235 for the blanket region. Equation (1) is used for estimating the activity of all radioactive FPs. The capacity factor for reactor operation is taken as unity for conservativeness in source term evaluation. The typical cumulative fission yields of important nuclides are given in Table 1 for fast fission of Pu-239 in fuel and U-235 in blanket. The total activity in the core is the sum of individual activities of each nuclide in the core. In this analysis, the methodology considered 571 radioisotopes and 76 stable isotopes of FPs like Xe, Kr, I, Br, Cs, Rb, Te, Se, Sb, Ba, Sr, Rh, Tc, Mo, Ru, Pd, Co, La, Nb, Nd, Pr, Zr, Y, Pm, Sm, Eu and Ce. 2.2. Radionuclide release from core to cover gas region/RCB during HCDA early phase In this analysis it is assumed that only the active core fuel region melts during HCDA. Based on the literature, the RF of Non-Volatile Fission Products, NVFPs (La, Zr, Nb, Ba, Sr) to cover gas region is considered as 1% (Umbel et al., 2011; Fies, 1971) and for the fuel (Pu
where, RFi,bubble is the RF of nuclide from the pool by bubble transport mode and Fi,bubble is the RF of nuclide from the core along with noble gas bubbles. 2.3. Radionuclide release from spray fire to RCB during spray fire phase of HCDA The release fractions of FPs/fuel during spray fire have been estimated based on the RT values obtained from PAVE and FANAL experimental tests (Middleton et al., 2011; Lee et al., 1999). The retention factor, RT was defined as the ratio of concentration of radionuclide in sodium pool to that in the burning sodium aerosol. The RF of the radionuclide was thus evaluated based on the fraction of the burned sodium and the RT of corresponding nuclide. The RT values of various radionuclides have been shown in Table 2.
Forvolatile and nonvolatile nuclides; RFi; spray ¼ RFNa; spray =RTi;Na (4) where, RFi,spray is the RF of nuclide from the sodium spray fire, RFNa,burned is the fraction of sodium sprayed from hot pool and RTi,Na is the RT of nuclide in sodium. In the present methodology it is assumed that all the sodium released gets burned. 2.4. Radionuclide release from cover gas region to RCB by natural convection Through the leak paths formed in the top shield, natural convection takes place between the hot cover gas region (which consists of argon, sodium vapor and radionuclides) and relatively cold Table 2 Retention factors of radionuclides for spray fire phase. Radionuclide
Retention factor (Middleton et al., 2011; Lee et al., 1999)
Halogen (I) Alkali metal (Cs) Tellurium group (Te) Alkaline earth metals (Ba,Sr) Noble metals (Ru) Non-volatile fission products (La) Fuel (U, Pu)
0.52 0.25 98.97 250.91 98.97 494.85 494.85
A. Pradeep et al. / Progress in Nuclear Energy 74 (2014) 120e128
RCB air, resulting in the transport of FPs from the cover gas region to RCB as shown in Fig. 1. The established leak paths in typical SFR, consists of horizontal and vertical paths to minimize the sodium release to RCB. In the present analysis to simplify the pressure drop calculations across the top shield, two vertical annular leak paths similar to Large Rotatable Plug (LRP) e Roof Slab (RS) and Small Rotatable Plug (SRP) e LRP gaps, have been considered. It has also been assumed that the air convective loop enters the reactor cover gas region through larger path (LRP-RS gap) and leaves the cover gas region through smaller path (SRP-LRP gap). By using the Bernoulli’s equation for upward and downward flow along with respective frictional pressure drops through the annular gaps, Eq. (5) and Eq. (6) are obtained. For downward flow of air through larger path
P2 ¼ P1
k1 r1 v21 f1 L1 r1 v21 þ r1 gL1 2 DH1 2
(5)
For upward flow of air through smaller path
P1 ¼ P2
k2 r2 v22 f2 L2 r2 v22 r2 gL2 2 DH2 2
(6)
P2 ¼ P1 þ
k2 r2 v22 f2 L2 r2 v22 þ þ r2 gL2 2 DH2 2
(7)
where, subscript 1 refers to RCB (through larger path, downward flow) and subscript 2 refers to cover gas region (through smaller path, upward flow). The thermo physical properties (density: r, dynamic viscosity: m) of air are taken at the pool temperature for cover gas region and at containment temperature for RCB. P is the pressure, k is the pressure loss coefficient, v is the velocity, L is the length and DH is the hydraulic diameter of the annular leak path. The Darcy friction factor, f for laminar flow through the annular gap is taken as
64 f ¼ Re Re ¼
(8)
rvDH m
(9)
The Continuity Equation is
A1 r1 v1 ¼ A2 r2 v2
(10)
where, A is the area of cross section of annular gap leak path. Equating Eqs. (5) and (7) along with Eq. (8), Eq. (9) and Eq. (10).
P1
k1 r1 A2 r2 v2 2 32m1 L1 A2 r2 v2 þ r1 gL1 2 A1 r1 A1 r1 D2H1
¼ P1 þ
k2 r2 v22 32m2 L2 þ v2 þ r2 gL2 2 D2H2
! ! m L A r m L k1 A2 r2 2 þ k2 r2 v22 þ 32 12 1 2 2 þ 22 2 v2 r1 A1 DH1 A1 r1 DH2
through leak paths is estimated. This sodium vapor mass flux is used to estimate the Release Fraction (RFi,evap) of VFPs from cover gas region to RCB. The evaporative transport due to natural convection has been estimated based on the equilibrium partition coefficient (KD) method and the equilibrium partition coefficient values used are taken from the literature (Haga et al., 1990). In the present analysis, evaporative mode release of the VFPs has been estimated for a period of 24 h.
For VFPs; RFi; evap ¼ KD; i RFNa; evap Fi; pool
(13)
RFi,evap is the RF of VFP from the pool by evaporative transport mode and Fi,pool is the RF of VFP from the core into the pool. RFNa,evap is the RF of sodium from the pool by evaporation. KD,i is the equilibrium partition coefficient of VFP i between sodium pool and the gas above. The release fraction values of FPs and fuel evaluated using the present methodology has been compared with release fraction data available for fast reactors under HCDA early phase release scenario as shown in Table 3. From this table, it is clear that the RFs estimated using the present methodology is conservative compared to the RFs used earlier for SFRs, which is good for radiological safety evaluation.
2.5. Inventory of radionuclides in the RCB The FP inventory in the RCB can be obtained from the product of core inventory and its corresponding release fractions. The release fraction corresponds to the total of RFs due to bubble transport, spray fire phase and evaporative transport. The activity (Qi,RCB in Ci) inside RCB at time t due to the radionuclide can be estimated from the following equation:
Qi;RCB ¼ Qi RFi;bubble þ RFi;spray þ RFi;evap ð1 expðli tÞÞ (14) where, Qi is the activity of radionuclide in the core before accident, RFi,bubble is the RF of FP/fuel during HCDA early phase, RFi,spray is the RF of FP/fuel during HCDA spray fire phase and RFi,evap is the RF of VFP during the evaporative phase due to natural convection. The radionuclide activity in the RCB has been evaluated by considering the decay of FPs and fuel for a period of 24 h.
3. Verification of the methodology The verification of the present methodology has been carried out with ORIGEN-2 and RIBD code results for the FP inventory in Table 3 HCDA release fractions for fission products and fuel in SFR during early phase.
(11)
Assuming pressure loss coefficient for expansion and contraction, k ¼ k1 ¼ k2 ¼ 1.5, and canceling the pressure terms, the resulting equation is
0:5
123
(12)
þ gðr2 L2 r1 L1 Þ ¼ 0 By solving the Eq. (12), the upward air flow velocity (v2) from the cover gas region to RCB is obtained. From this upward flow velocity, the mass flux of sodium vapor from the cover gas region to the RCB
Radionuclide released to RCB under HCDA
Release fraction during early phase (0e10 s) Present methodology
FFTF (Fies, 1971)
KALIMER (Lee et al., 1999)
ABR (Umbel et al., 2011)
Noble gas (Xe, Kr) Halogens (I, Br) Alkali metals (Cs, Rb) Tellurium group (Te, Se, Sb) Alkaline earth metals (Ba,Sr) Noble metals (Rh, Ru) Lanthanides (La, Zr) Cerium (Ce) Fuel (U, Pu)
1 0.125 0.125 0.0125
1 0.02 0.01 0.01
1 1 103 1 103 1 103
0.64 0.079 0.079 7.9 103
0.01
0.01
1 104
3.1 105
0.01 0.01 0.01 5 105
0.01 0.01 0.01 1 104
1 1 1 1
104 104 104 104
3.1 3.1 3.1 3.1
105 105 105 105
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A. Pradeep et al. / Progress in Nuclear Energy 74 (2014) 120e128
Table 4 Predictions of Radionuclide core inventory by present methodology and ORIGEN-2 code for 2000 MWt SFR. Radionuclide Present study
ORIGEN-2
Deviation (%)
Core mass Activity Core mass Activity inventory (MCi) inventory (MCi) (kg) (kg) 54-Xe-133 36-Kr-85m 53-I-131 55-Cs-137 52-Te-129
0.628 0.0012 0.527 85.53 0.0011
117.7 10.03 65.51 7.42 23.03
0.577 0.0011 0.501 71.5 0.00104
Table 7 Release fraction for nuclides of typical SFR during bubble transport, spray fire and evaporative route under severe accident scenario. Radionuclide
Core mass Activity inventory
108 8.95 9.144 10.78 62.11 5.26 6.225 19.63 21.79 5.74
Noble gases (Xe, Kr) Halogens (I, Br) Volatile solids (Cs, Se, Te) All remaining fission products
Present study
RIBD
Activity (Ci)
Activity (Ci)
1.37 1.43 1.66 1.4
108 108 108 109
1.4 1.4 1.5 1.1
9.01 9.69 5.47 19.3 5.71
Noble gas Halogen (I) Alkali metal (Cs) Tellurium group (Te) Alkaline earth metals Noble metals Non-volatile fission products Fuel (U, Pu)
Deviation (%)
108 108 108 109
Evaporation (24 h) (Long term)
Total release fraction
2.23 105
6.1 104
1 0.125 0.125 0.0125
5.9 104 (Baskaran et al., 2004) 0 0.001126 0.002351 5.96 106
0 5.7 106 7.7 104 2.01 1010
1 0.126 0.128 0.0125
0.01
2.35 106
0.01
0.01 0.01
6
5.96 10 1.19 106
0.01 0.01
5 105
1.19 106
5.1 105
Sodium
Table 5 Predictions of radionuclide core inventory by present methodology and RBID code for 400 MWt SFR. Radionuclide
Spray
Bubble transport (Short term)
2.39 2.41 10.9 27.6
core and also with the results available in literature for released inventory to the RCB under HCDA.
that is in the order of 106 Ci. Hence the FPs are the dominant radionuclides that contribute to core source term in SFR and from Tables 4 and 5, it is clear that the present methodology is predicting the FP inventory in the core conservatively. 3.2. RCB fission product inventory
3.1. Core fission product inventory The inventory of FPs in the core predicted by the methodology used has been verified with the ORIGEN e 2 code predicted values for 2000 MWt SFR at EOEC (Kim and Yang, 2008). The SFR core was designed to achieve one year cycle length with 3 batch fuel management scheme. The verification details for mass inventories of Xe, Kr, I, Te and Cs are given in Table 4. The total radioactivity estimated by the method for 571 FP radionuclides and 76 stable FP nuclides is w9.37 109 Ci, which is comparable with the ORIGEN-2 predicted value of 9.105 109 Ci for SFR-2000 (Kim and Yang, 2008). The corresponding total FP mass inventory in the core estimated by this methodology is 2461.1 kg, which is comparable with the 2049.8 kg mass inventory estimated for SFR, by ORIGEN-2. The present analytical method estimates the SFR core FP inventory conservatively within 20% of the ORIGEN-2 prediction, which is adequate for safety evaluation of SFRs under HCDA. The radiological source term due to activation products is not considered in the present methodology due its very low value compared to FPs (Kim and Yang, 2008). This methodology has also been verified with the results obtained from Radio-Isotope Build up and Decay (RIBD) code for SFR core FP inventory which was operated for 200 days at full power of 400 MWt (Fies, 1971). The verification details for activities of Xe, Kr, I, Br, Cs, Te and Se are given in Table 5. The total activity due to noble gases (Xe, Kr), halogens (I, Br) and volatile solids (Cs, Te, Se) have been estimated by adding the activities of individual nuclides. The total activity due to FPs as predicted by the present methodology and RIBD code for SFR plutonium fuel irradiated for 200 days is of the order of 109 Ci, which is much higher than the fuel radioactivity
The predictions of this methodology has been verified for the released mass inventory of the FPs/fuel in the RCB of SFR of 1253 MWt under HCDA scenario (Baskaran et al., 2004) after 24 h and the results are given in Table 6. Under HCDA resultant spray fire of 350 kg sodium in the RCB, the aerosol mass concentration of sodium and VFPs (Cs, I) in the RCB is estimated to be 5.158 g/m3 by the present methodology compared to the published value of 5.15 g/m3 (Baskaran et al., 2004). The aerosol mass concentration of FPs, Sr and Te estimated by the present methodology is 1.97 mg/m3 compared to the value of 23.3 mg/m3 from Baskaran et al. (2004). The estimated total amount of tellurium and strontium in the RCB is lower than the value given in Baskaran et al. (2004) and this is due to the partition of Te with clad constituents which has been considered in the present methodology. The estimated aerosol mass concentration of fuel (U, Pu) in the RCB is 6.03 mg/m3 (where the core inventory was estimated based on Pandikumar et al. (2011)), which is in the same order of the value given in Baskaran et al. (2004) (i.e., 10.9 mg/m3) for an initial plutonium inventory of 2020 kg (at BOL). 4. Results and discussion The present methodology has been used to estimate the maximum achievable radioactive FP inventory generated in the fuel and blanket regions of a typical SFR producing 1253 MWt. A refueling time of 185 days in 3 batches for fuel and 8 batches for radial blanket was assumed for the present calculations. Hence a total fuel irradiation time of 555 days for fuel and 1480 days for blanket was assumed for this analysis. It is also assumed that 90% of the thermal
Table 6 Verification of RCB fission product inventory for SFR (1253 MWt) for 24 h of HCDA. Nuclide Ref (Baskaran et al., 2004) Model
Containment Containment Fuel region
Cs (kg)
I (kg)
Te þ Sr (kg)
Pu (kg)
U (kg)
9.22 10.18 79.49
0.858 0.914 7.25
1.63 0.138 13.36
0.143 0.114 2235.42 (Pandikumar et al., 2011)
0.583 0.308 6023.29 (Pandikumar et al., 2011)
A. Pradeep et al. / Progress in Nuclear Energy 74 (2014) 120e128 Table 8 Core (fuel þ blanket) maximum achievable fission product inventory in a typical breeder type SFR (1253 MWt). Radionuclide
Saturation activity method Core mass inventory (kg)
Noble gas (Xe, Kr) Halogens (I, Br) Alkali metals (Cs, Rb) Tellurium group (Te, Sb, Se) Alkaline earth metals (Ba, Sr) Noble metals (Rh, Tc, Mo, Ru, Pd, Co) Lanthanides (La, Nb, Nd, Pr, Zr, Y, Pm, Sm, Eu) Cerium group (Ce) Radioactive fission product total activity
Activity (MCi)
Unstable
Stable
Total
0.93 6.4 72 0.78 10.48 42.11
91.2 2.3 35.8 1.02 110.4 206.76
92.1 8.7 107.8 3.89 120.92 248.87
445.22 456.77 386.25 423.03 605.88 1322.25
99.01
208.22
307.2
2000.8
24.75
27.88
52.63 942.24
238.6 5878.86
Table 9 Fuel region actinide inventory in a typical breeder type SFR (1253 MWt) after 10 cycles. Actinide
Active core wt (%)
Mass (kg)
Activity (Ci)
U-232 U-233 U-234 U-235 U-236 U-238 Pu-238 Pu-239 Pu-240 Pu-241 Pu-242 Am-241 Total
5.47 107 5.77 107 0.007 0.056 0.103 72.768 0.05 16.642 8.623 1.151 0.584 0.018 1
4.52 105 4.77 105 0.578 4.62 8.51 6009.58 4.12 1374.38 712.13 95.05 48.23 1.49 8258.72
1.01 0.00045 3.6 0.01 0.55 2.02 7.08 104 8.53 104 1.62 105 9.88 106 190.91 5101.55 1.02 107
125
Cs to the cover gas region/RCB by the present methodology are given in Appendix A and B respectively. The typical RF values evaluated for various radionuclides are given in Table 7. From this table, it is clear that the RCB source term contribution is mainly from the bubble transport for VFPs than the spray fire release or evaporative route under HCDA release scenario. The methodology considers the mass of radioactive FPs and stable FPs. The maximum achievable FP inventory in the core (fuel þ blanket) for typical breeder type 1253 MWt SFR is given in Table 8. The method estimated FP contribution to the core radioactivity is 5.87109 Ci. For the typical 1253 MWt fast reactor core the activity due to actinides in the fuel region after 10 cycles of operation will be w1 107 Ci for the core fuel composition given in Table 9 (Pandikumar et al., 2011), in which the BOL core mass of Pu is 2.02 ton. The contribution of activity due to radionuclides (FPs þ actinides) in the fuel region of core which produces 90% of the total SFR thermal power is shown in Fig. 2. From Tables 8 and 9, it is clear that the main radioactivity contributor to the core is FPs compared to actinides. In the event of HCDA, the FPs and actinides gets released to the RCB. Based on the RFs already discussed (in Table 7), the activity of FPs released to RCB has been estimated and given in Table 10. The 24 h evaporative release for VFPs has been estimated only for Halogen (I), Alkali metal (Cs) and Tellurium group (Te). From Table 10 it is clear that under HCDA scenario, out of the total FP and actinide inventory in the active core fuel region about, 1.07% of mass inventory and 1.67% of radioactivity is present in the RCB after 24 h. The value of radioactivity due to fuel (U, Pu) is much lesser compared to the radioactivity of FPs in the RCB, hence almost the total radioactivity in the RCB of about 8.8107 Ci can be considered to be mainly from FPs. The contribution of various radionuclides (FPs and actinides) to total radioactivity in the RCB as evaluated by the methodology is shown in Fig. 3.
5. Conclusion power is generated in the fuel region with actinide mass of 8258.72 kg and the remaining 10% in the blankets (Roychowdhury et al., 2000). The typical estimations of the mass of FP Cs and its radio activity in the core of a breeder type SFR and the transport of
A lumped analytical methodology has been developed to evaluate the radioactivity in the RCB under energetic core disruptive accident scenario by considering radioactive fission product
Fig. 2. Percentage contribution of various radionuclides to total radioactivity in active core of typical 1253 MWt SFR.
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A. Pradeep et al. / Progress in Nuclear Energy 74 (2014) 120e128
Table 10 RCB source term due to fission products in a typical breeder type SFR (1253 MWt) under HCDA in 24 h. Radionuclide
Total activity due to fission products in RCB (MCi)
Total mass (kg)
Noble gas Halogen Alkali metal Tellurium group Alkaline earth metals Noble metals Lanthanides Cerium Pu U Total
72.18 8.61 0.42 0.67 0.69 1.75 2.72 0.99 5.1 104 3.68 1010 88.04
71.29 0.92 10.68 0.041 0.902 2.09 2.05 0.307 0.085 0.308 88.7
inventory in the core along with the radionuclide transport to RCB. The methodology uses the conservative saturation activity method to estimate the core inventory of fission products. Under HCDA release scenario to RCB, the release fraction of fission products via bubble transport mode are considered for early phase of release (0e10 s), the release fraction of fission products from the sodium spray fire are considered during spray fire phase (w1 s) and volatile fission products (Cs, I, Te) release by natural convection based evaporative transport is considered for a period of 24 h. The methodology predicted core inventory of fission products have been verified with ORIGEN-2 and RIBD code results available in literature for SFRs and have been found adequately conservative. The methodology predicted inventory of fission products in the RCB under HCDA scenario have been verified with results available in literature for typical SFR and have been found reasonable. The present methodology predictions show that in the event of severe accident scenario, the volatile fission product release is mainly due to the short term bubble transport compared to the long term evaporative transport and spray fire release phase. The methodology also shown that the main contributors to radiological evaluation of HCDA in SFR are the fission products compared to actinides, hence the RCB fission product inventory predicted by the present methodology can be effectively used for the evaluation of dose at site exclusion boundary. For a typical SFR of 1253 MWt, the
evaluated total source term in 86,146 m3 volume RCB, due to fission products under severe accident scenario is 3.78 1013 Bq/m3 and in the core is 2.18 1020 Bq. The public dose at the site exclusion zone boundary can be evaluated confidently based on the present methodology estimated RCB source term under HCDA scenario. Appendix A Estimation of maximum achievable radioactivity and mass of Cesium in the core. Activity of Cs-137 in fuel region:
3:12 1010 QCs137;f ¼ 1253 106 0:9 0:0658 3:7 1010 0:693 185 86400 3 1 exp 30:07 8760 3600 QCs137;f ¼ 2:15 106 Ci (A.1) Mass of Cs-137 in fuel region:
mCs137;f ¼
QCs137;f 0:69310006:0231023 30:07876036001373:71010
¼ 24:86 kg
(A.2)
Activity of Cs-137 in blanket region :
3:12 1010 1253 106 0:1 0:06206 3:7 1010 0:693 185 86400 8 1 exp 30:07 8760 3600
QCs137;b ¼
QCs137;b ¼ 0:585 106 Ci (A.3) Mass of Cs-137 in blanket region:
mCs137;b ¼
QCs137;b 0:69310006:0231023 30:07876036001373:71010
¼ 6:74 kg
Fig. 3. Percentage contribution of various radionuclides to total radioactivity in RCB of typical 1253 MWt SFR within 24 h after CDA initiation.
(A.4)
A. Pradeep et al. / Progress in Nuclear Energy 74 (2014) 120e128
The masses of radioisotope of Cs-137 are estimated using the above Eq. (A.2) and Eq. (A.4) and the mass of stable isotope, Cs-133 in the fuel and blanket region are estimated as follows. Mass of Cs-133 in fuel region:
mCs133;f ¼ 3:12 1010 1253 106 0:9 0:0697 3 185 8760 3600 ¼ 26 kg (A.5) Mass of Cs-133 in blanket region:
mCs133;b ¼ 3:12 1010 1253 106 0:1 0:0671 8 185 8760 3600 ¼ 7:42 kg
RFCs;spray ¼
By considering the remaining isotopes of Cs, the maximum achievable mass inventory of Cs in the core predicted by this method is 101 kg that have an activity of 2.41 108 Ci. Fig. A.1 shows the variation of core mass inventory of fission product Cs137 and I-133 with irradiation time at full power.
5:9 104 =0:25 ¼ 0:00235
127
(B.2)
To estimate the amount of Cs released by evaporative mode for 24 h, it is required to calculate the amount of Cs present in the pool and the release fraction of sodium vapor to RCB under rotatable plug seal leak failure condition. Out of the total Cs in the active core region, 75% gets mixed in the pool along with the pool scrubbed Cs, which failed to escape by the bubble transport mode. The Release fraction (RFNa,evap) of sodium by evaporation mode is estimated by solving the Eq. (B.3).
0:5 (A.6)
! ! m L A r m L k1 A2 r2 2 þ k2 r2 v22 þ 32 12 1 2 2 þ 22 2 v2 r1 A1 DH1 A1 r1 DH2
(B.3)
þ gðr2 L2 r1 L1 Þ ¼ 0 Conditions of RCB (1) used in the analysis: Temperature of RCB (T1) ¼ 313 K Pressure of RCB (P1) ¼ 101325 Pa Density of air (r1) ¼ 1.13 kg/m3 Viscosity of air (m1) ¼ 1.91 105 Pa.s Area of cross section of LRP-RS leak path (A1) ¼ 0.1 m2 Hydraulic diameter of LRP-RS leak path (DH1) ¼ 0.01 m Length of leak path (L1) ¼ 2.5 m Cover gas (2) conditions used in the analysis Temperature of hot pool (T2) ¼ 820 K Pressure of cover gas region (P2) ¼ 101325 Pa Density of air (r2) ¼ 0.43 kg/m3 Vapor pressure of sodium vapor ¼ 1300 Pa Density of sodium vapor ¼ 4.39 103 kg/m3 Viscosity of air (m2) ¼ 3.95 105 Pa.s Area of cross section of SRP-LRP leak path (A2) ¼ 0.0667 m2 Hydraulic diameter of SRP-LRP leak path (DH2) ¼ 0.01 m Length of leak path (L2) ¼ 2.5 m Pressure loss coefficient, k1 ¼ k2 ¼ 1.5
Fig. A.1. Mass inventory of radioactive fission products Cs-137 and I-131 as a function of time.
Appendix B Estimation of total release fraction of cesium. The present methodology assumes that under HCDA only the fuel region melts, and hence the amount of Cs that gets released from the active core region under HCDA is 79.49 kg. From this, 25% Cs gets released by bubble transport mode, out of which only 50% reaches the cover gas region due to pool scrubbing. Generally the bubble rise time is less than 10 s (Umbel et al., 2011) for the transmitted fraction of 50%. Release fraction of Cs from pool during initial release phase of HCDA by bubble transport mode is
RFCs;bubble ¼ ð0:25 0:5Þ ¼ 0:125
(B.1)
During the spray fire phase, w350 kg (Baskaran et al., 2004) of sodium is ejected from the reactor hot pool resulting sodium spray combustion in the RCB. The release fraction of Cs to the RCB during spray fire phase is evaluated using Eq. (4). For a given sodium spray release fraction of 5.9 104 (from the hot pool) and with the retention factor for Cs in completely burned sodium spray fire of 0.25, the Cs release fraction can be estimated as given below:
The estimated downward flow velocity of air (v1) from Eq. (B.3) is 0.132 m/s and the upward flow velocity of air, v2 is 0.523 m/s. Based on the upward flow velocity, the mass flow rate of sodium vapor estimated is 0.153 g/s under seal leak condition from an annular cross section area of 0.0667 m2. Based on the evaluated sodium vapor flow rate, the estimated evaporative release fraction of sodium (from the hot pool sodium of 5,93,095 kg) for a period of 24 h is 2.23 105. The evaporative release of Cs is estimated based on the equilibrium partition coefficient method. The equilibrium partition coefficient value of Cs at a pool temperature of 820 K is taken as 39.9. The mass of Cs released by evaporation is estimated for a period of 24 h as given below: Release fraction of Cs from pool by evaporative transport:
RFCs;evap ¼ KD;Cs RFNa;evap ð0:75 þ 0:25 0:5Þ ¼ 7:7 104
(B.4)
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Fies, C.L., 1971. Radiological Evaluation of a Hypothetical Core Disruptive Accident. Hanford Engineering Development Laboratory, United States Atomic Energy Commission. Glaser, Alexander, Ramana, M.V., 2007. Weapon-grade Plutonium Production Potential in the Indian Prototype Fast Breeder Reactor, Science and Global Security. Taylor & Francis, pp. 85e105. Haga, K., Nishizawa, Y., Watanabe, T., Miyahara, S., Himeno, Y., 1990. Experimental Study on Equilibrium Partition Coefficient of Volatile Fission Products between Liquid Sodium and the Gas Phase. International Fast Reactor Safety Meeting. Kim, T.K., Yang, W.S., 2008. Preliminary Estimation of Isotopic Inventories of 2000 MWt ABR (Revision 1). ANL-AFCI-207. Lee, Seong-Wook, et al., 1999. Preliminary containment performance analysis for the conceptual design of KALIMER. In: Korea Atomic Energy Research Institute, 7th International Conference on Nuclear Engineering, Tokyo, Japan, ICONE7347. Li, Q., 1998. Estimate of Radiation Release for MIT Research Reactor during Design Basis Accident. Nuclear Engineering Department, MIT. S.M. Thesis.
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