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Nuclear Engineering and Design 248 (2012) 156– 168
Contents lists available at SciVerse ScienceDirect
Nuclear Engineering and Design
jo u r n al hom epage : www.elsev ier .com/ locate /nucengdes
elation between a fuel rod failure cause and a reactor coolant radioactivityariation
yu-Tae Kim ∗
ongguk University, College of Energy & Environment, 707 Seokjang-Dong, Gyeongju, Gyeongbuk 780-714, Republic of Korea
r t i c l e i n f o
rticle history:eceived 18 July 2011ccepted 30 March 2012
a b s t r a c t
The reactor coolant radioactivity in the coolant caused by unstable fission products released into thecoolant depends usually on fuel burnup, fuel rod power, cladding defect size and its axial location, andcoolant letdown flow rate. In this study, taken into account are three main fuel rod failure causes for PWRsin Korea that include debris-induced fuel failure, grid-to-rod fretting wear-induced one and excessivecladding oxide-induced one. Characteristics of reactor coolant radioactivity variations of xenon and iodinespecific to each fuel rod failure cause have been analyzed by considering fuel burnups at the fuel failureoutset, cladding through-hole sizes and their axial locations, letdown flow rate, and steam-induced UO2
pellet oxidation along with interlinked fraction of fission gas bubbles. It was found that there existsan outstanding relation between a fuel failure cause and its relevant coolant radioactivity variation ofxenon and iodine. The relation found in this study may be utilized proactively to predict a certain fuelrod failure cause during the reactor operation, which can provide utilities with an extra time enough toprovide a countermeasure(s) against the predicted fuel failure cause and consequently eliminate suchthe fuel failure for the upcoming next cycle.
. Introduction
Considering the harmful nature of long-lived radioactive fissionroducts, a major safety issue in operating nuclear power plantsuring the normal reactor operation is the release of radioactivession products from the fuel rod gap into the reactor coolant,hile the major safety issue for severe reactor accidents is the pos-
ibility of radioactive fission products released to the environment.hen a fuel rod has been perforated by a certain failure mechanism,
he coolant may enter the fuel rod gap and subsequently volatilession gases start to be released into the coolant instantly but sol-ble fission products adsorbed on the pellet and cladding surfacesay be released into the coolant only with the water pushed out
f the gap that usually occurs during power changes (Lewis et al.,997; Bishop, 1986). The reactor operation with defective fuel rodsill cause a reduced heat transfer in the pellet-to-cladding gap and
nhance the steam-induced pellet oxidation, which will decreaseellet thermal conductivity and consequently increase fuel tem-erature and fission product diffusivity. In general, therefore, the
ssion product radioactivity in the coolant depends strongly on theumber of failed fuel rods, their fuel burnups, their defect sizes andxial locations, and coolant letdown flow rate, etc.∗ Tel.: +82 11 9805 1447; fax: +82 54 770 2282.E-mail address: [email protected]
029-5493/$ – see front matter © 2012 Elsevier B.V. All rights reserved.ttp://dx.doi.org/10.1016/j.nucengdes.2012.03.051
© 2012 Elsevier B.V. All rights reserved.
Fuel vendors have been employing various fission productradioactivity analysis codes (Correal-Pulver, 1993; CE, 1991) to esti-mate the number of failed fuel rods with the use of the activityratios of Xe-133 to Xe-135 or I-131 to I-133 and to calculate bur-nups of such failed fuel rods with the use of the activity ratio ofCs-134 to Cs-137. To predict the number of failed fuel rods, the twostages of radioactive fission product release models from defectivefuel to the reactor coolant are needed: the first stage is the releaseof radioactive fission products to the furl rod gap and the secondstage is the release of such fission products from the gap into thecoolant through the defects. The CEA in France has performed seriesof analytical experiments to investigate the phenomena of unsta-ble fission products release in PWR fuel rods (Bruet et al., 1980;Charles et al., 1982, 1985), which have been used to develop fissionproduct release models. Koo et al. (1994) has proposed a modelfor the release of unstable fission products from the defective fuelrods into the PWR coolants with the use of the White and Tucker’smodel (White and Tucker, 1983) and the Monte Carlo technique.Ivanov has also proposed a model for the release of fission gasesout of porous fuel (Ivanov, 1998). Andrew has employed an arti-ficial neural network-based model for estimating fission productrelease during severe accident conditions (Andrew et al., 1999).
Lewis proposed a model for predicting coolant activity behaviorfor fuel failure monitoring analysis (Lewis et al., 2007).It should be noted, however, that the aforementioned fissionproduct radioactivity analysis codes and fission product release
K.-T. Kim / Nuclear Engineering and Design 248 (2012) 156– 168 157
Table 1Isotopic data for unstable xenon gases and iodine fission products (Lewis et al., 1990; Iqbal et al., 2008).
Isotope Decay constant (� s−1) Fission yield (Y) Precursor correction factor (H) Neutron absorption cross-section (barn)
Xe-133 1.53 × 10−6 0.0670 1.205 24.4−5 3.3
1.01.1
mbuaufipiftmaaufdwofiraoateta
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wei
Xe-135 2.12 × 10 0.0654
I-131 1.00 × 10−6 0.0238
I-133 9.26 × 10−6 0.0670
odels can predict only the number of failed fuel rods and theirurnups rather than predicting a failure root cause(s). A fuel fail-re root cause is usually found out through poolside examinationsnd/or hot cell examinations for failed fuel rods, which may requiretilities to take usually at least one year. Based on time-dependentssion product radioactivity variations in the coolant, therefore, therediction of a fuel failure root cause during the reactor operation
s far more important than the prediction of the number of faileduel rods and their burnups, resulting in the drastic reduction ofime for finding out a failure root cause(s). Naturally the former
ay provide utilities with an extra time enough to come up with countermeasure(s) against predicted fuel failure root cause(s)nd consequently eliminate such the fuel failure cause(s) for thepcoming next cycle. Therefore, three main fuel rod failure causesound in PWRs in Korea are considered in this study, which includeebris-induced fuel rod failure at low burnup, grid-to-rod frettingere-induced fuel rod failure at low burnup and excessive cladding
xide-induced fuel rod failure at high burnup. For these three fuelailure causes, time-dependent reactor coolant radioactivity behav-ors of xenon and iodine will be analyzed in detail, based on the fuelod burnup at the fuel failure outset, the fuel rod defect size and itsxial location, letdown flow rate and the steam-induced UO2 pelletxidation with the development of release paths in the pellet thatre specific to each failure cause. Then, characteristics of the reac-or coolant activity variations of xenon gases and iodine specific toach failure cause are provided, which may be utilized by utilitieso predict a certain fuel rod failure during the reactor operation, ifny.
. Equations simulating fission product radioactivityariations
It is generally accepted that unstable fission products areeleased from the fuel matrix to the gap via two routes: the firstne is free and cracked surfaces created by thermal stresses, and theecond one is tunnel networks formed by the growth and coales-ence of stable fission gas bubbles located at the grain boundariesTurnbull and Friskney, 1978). Then, the release rate of unstablession products from the pellet to the gap can be written as follows:
igap = Ri
crack + Rigb (1)
here Rigap, release rate of an unstable fission product i from the
ellet to the gap, Ricrack
, release rate of an unstable fission product from the pellet to the gap through pellet cracks, Ri
gb, release rate
f an unstable fission product i from the pellet to the gap throughrain boundary tunnel networks in the pellet.
With use of the White and Tucker model (White and Tucker,983) and the Monte Carlo technique generating the interlinkedraction of fission gas bubbles to open surfaces employed by Koo etl. (1994), the release rate of unstable fission product i (Ri
gap) maye given as:
igap = Lq′YiHi εi (2)
Ef
here L = total active length of the fuel rod, q′ = linear heat gen-ration rate, Yi = fission yield (atoms/fission) of a fission product, Hi = precursor correction factor of a fission product i, Ef = energy
53 244,50000 ∼0.300 ∼0.0
produced per fission, εi = an escape rate coefficient from the pelletto the gap = ((S/V)c + f(S/V)gb)(Di/�i)1/2. (S/V)c = ratio of surface areato volume for a cracked pellet, f = fraction of interlinked grain cornerbubbles to the pellet exterior, (S/V)gb = ratio of surface area coveredby grain corner bubbles to grain volume, Di = gas atom diffusioncoefficient of a fission product i, �i = decay constant of a fissionproduct i.
Table 1 summarizes decay constants (�), fission yields (Y), pre-cursor correction factors (H) and neutron absorption cross-sections(�) for unstable noble gases (Xe-133 and Xe-135) and unstableiodine fission products (I-131 and I-133) that are considered in thisstudy.
For an intact fuel rod, the mass balance in the gap for unstablefission product i (Ni
gap) can be written as:
dNigap
dt= Ri
gap − �iNigap − �i�Ni
gap (3)
where �i = microscopic cross-section of fission product i,� = neutron flux.
Assuming a quasi-steady-state operating conditions (i.e.,dNi
gap/dt = 0), the activity of unstable fission product i in the gapcan be written as:
Activity in the gap = �iNigap =
[�i
�iq
]Ri
gap =[
�i
�iq
]Lq′YiHi
Efεi (4)
where �iq = �i + �i�.It is noteworthy that �iq given in Eq. (4) represents �i + �i�.
However, �iq is reduced to �i for Xe-133, I-131 and I-133 sincetheir �i� values are far less than �i, considering �i, �i and � givenin Tables 1 and 2. Naturally, Xe-135 will disappear much fasterbecause of a quite large �i than the other fission products.
For a leak fuel rod, on the other hand, the release rate of unstablefission product i from the gap to the coolant is proportional to thetotal number of unstable fission product i in the gap (Beraha et al.,1980; Lewis et al., 1986; Lewis, 1988). Then, the mass balance forunstable fission product i in the gap can be written as:
dNigap
dt= Ri
gap − �iNigap − �iN
igap − �i�Ni
gap (5)
where �i = an escape rate coefficient of fission product i from thegap to the coolant.
Assuming quasi-steady-state operating conditions (i.e.,dNi
gap/dt = 0), the release rate of an unstable fission productfrom the gap to the coolant (Ri
coolant) can be obtained from Eq. (5)
as follows:
Ricoolant = �iN
igap =
[�i
�iq + �i
]Ri
gap =[
�i
�iq + �i
]Lq′YiHi
Efεi (6)
By the way, a schematic diagram of release of unstable fission prod-uct i from the pellet to the gap and from the gap to the coolant is
shown in Fig. 1 to illustrate the stepwise release of unstable fissionproduct i. In this figure, the fuel is divided into eight cracked pelletssince the PWR pellet is reported to be cracked into between eightand ten (Evans and Davidge, 1969; Radford, 1979).
158 K.-T. Kim / Nuclear Engineering and Design 248 (2012) 156– 168
Table 2Fuel and reactor core data for three kinds of failed fuel rods in PWRs.
Characteristics Fuel rod failure causes
Debris GTRFa Oxidation
Reactor core conditionsReactor coolant pressure (bar) 155 155 155Coolant inlet temperature (◦C) 282.3 285.4 285.8Total coolant volume of reactor (l) 154,000 234,000 222,000Coolant volume of reactor core (l) 10,352 14,124 14,118Letdown flow rate at failure outset (l/min) 240 440 240Letdown flow rate during failure Constant Constant VariedAverage neutron flux in coolant (n/cm2/s) ∼7 × 1013 ∼5 × 1013 ∼5 × 1013
Fuel rod failure descriptionFailure onset time (days) 50 330 270Perforated location from rod bottom (mm) ∼70 ∼105 ∼2300
(below bottom grid) (at bottom grid) (around middle)Number of operation cycles First First ThirdBurnup at failure outset (MWD/kgU) 2.0 13 40Rod internal pressure at failure outset (bar) ∼50 ∼60 ∼95Average neutron flux in the gap (n/cm2/s) ∼6 × 1013 ∼5 × 1013 ∼5 × 1013
Secondary hydride location from rod bottom (mm) ∼2400 ∼2100 No hydrideLinear heat generation rate (kW/m)
Rod averaged 20.0 18.2 17.8Local (at perforation position) 8.0 7.2 21.4
Pellet descriptionPellet-clad diametral gap (mm) 0.178 0.165 0.165Pellet outer diameter (mm) 8.75 8.19 8.19Pellet length (mm) 10.50 9.83 9.83
Cladding descriptionCladding materials Zry-4 Zry-4 Zry-4Cladding OD/ID (mm) 10.16/8.93 9.50/8.36 9.50/8.36
c
wpl
oo
A
w
Cladding thickness (mm) 0.62
a GTRF stands for grid-to-rod fretting wear.
Finally, the rate change of unstable fission product i in theoolant can be written as:
dNicoolant
dt= Ri
coolant − �iNicoolant − Q
WNi
coolant − ��i�Nicoolant (7)
here Q = letdown flow rate, W = total coolant volume, � = ratio ofrimary coolant residence time in the core to total primary circu-
ation time.Assuming a quasi-steady-state operating conditions, the activity
f unstable fission product i in the coolant (�iNicoolant
) can be easilybtained from Eqs. (6) and (7) as follows:[ ] [ ] ′
ctivity in the coolant = �i�iqq + Q/W
�i
�iq + �i
Lq YiHi
Efεi (8)
here �iqq = �i + ��i�.
Cladding wi th
a th rou gh-hole
Cracked
pelle t
Nigap
Ricoolan t = Nigap
RigbRicrack
Gap
Fig. 1. A schematic diagram of fission product releases from a failed fuel rod.
0.57 0.57
It is obvious from Eq. (8) that the radioactivity in the coolantmay increase with the increase of �i, εi and q′, while it decreasewith the increase of �i, �i� and Q.
By the way, a time-dependent escape rate coefficient (�(t)) isassumed to be composed of two terms. The first term may repre-sent initial burst and subsequent exponential fall-down of fissionproducts through the perforated hole for an initial period, whilethe second term may represent a linear increase of through-holesize and its effect on the release of fission products. Then, the time-dependent escape rate coefficient that is valid only for t is equal toand greater than to can be written as:
�(t) = �oe−�(t−to) + �o[ω(t − to)] (9)
where �o = an escape rate coefficient from the gap to the coolantat the cladding perforation outset time (t = to), � = a constant rep-resenting initial burst and subsequent exponential fall-down, ω = aconstant representing a linear increase of through-hole size.
One can find easily which term in Eq. (9) is more effective tothree fuel failure causes considered in this study with the use ofcorresponding time-dependent coolant radioactivity variations.
On the other hand, it is known that a perforated cladding willgenerate UO2 pellet oxidation by steam coming into the gap. Toaccount for the effect of steam-induced UO2 oxidation on theenhancement of fission products release from the pellet to thegap for the perforated cladding, its oxidation kinetics must betaken into account as a function of the failed fuel rod itself andthe reactor core (Olander, 1986; Olander et al., 1999; Lewis et al.,2004; Matzke, 1980). According to Olander et al. (1999), oxidationof a pellet of UO2 to UO2.01 during the normal operation wouldrequire nearly eight months for LWR defective fuel rods. Further-
more, hydrogen gas released by steam-induced cladding oxidationwould strongly retard UO2 pellet oxidation rate, resulting in ahyper-stoichiometry of UO2 pellets below 2.01. However, the effectof the hyper-stoichiometry of UO2 pellets on the fission product
K.-T. Kim / Nuclear Engineering and Design 248 (2012) 156– 168 159
Table 3Fuel rod failure criteria.
Nuclides employed Failure criteria Remarks
Ratio of I-131 to I-133 Greater than 0.25 Small perforated hole if I-131/I-133 > 1.0
de
E
3
rfmeatl
gapufuloarufEficIbr
F
Ratio of Xe-133 to Xe-135 Greater than 1.0
iffusivity is provided in Fig. 2 (Shiba, 1975). The diffusivitynhancement factors given in this figure is defined as:
nhancement factor =[
D(x, T)tD(0, T)t
]1/2
(10)
. Key parameters affecting reactor coolant activity
As indicated in Eq. (9), for a reactor core having leaking fuelod(s), the level of reactor coolant activity may be governed by theollowing key parameters: (a) the amount of fission products accu-
ulated in the gap that can be released into the coolant, (b) thenhanced release rate of fission products from the pellet to the gapfter the fuel failure, (c) the extent of fission product release fromhe gap to the coolant through a cladding through-hole(s) and (d)etdown flow rate.
First of all, the amount of fission products accumulated in theap is dependent on an elapsed time from the beginning of cycle to
failure outset that will determine the amount of unstable fissionroducts accumulated in the gap. Assuming that a fission prod-ct release rate from the pellet to the gap is constant when theuel rod maintains the same power, the accumulated amount ofnstable fission products in the gap will reach about 95% of equi-
ibrium vales when a reactor operation time is as long as three timesf unstable fission products’ half lives. Therefore, the accumulatedmount of unstable fission products in the gap may be assumed toeach equilibrium values before the failed fuel rod starts to releasenstable fission only if the reactor operation time prior to the fuelailure exceeds three times of unstable fission products’ half lives.q. (2) represents the equilibrium values in the gap for unstablession products before the fuel failure. For the three failure cases
onsidered in this study, the amount of Xe-133, Xe-135, I-131 and-133 accumulated in the gap may reach equilibrium values longefore the fuel starts to release xenon and iodine since the timesequired for the cladding perforation for such three kinds of fuelig. 2. UO2 pellet oxidation-induced enhancement factor for fission gas release.
Large perforated hole if I-131/I-133 < 0.4Small perforated hole if I-131/I-133 > 3.0Large perforated hole if I-131/I-133 < 1.8
failures are much larger than three times of their half lives, as seenin Tables 1 and 2.
The release rates of fission products from the pellet to the gapafter the fuel failure are dependent on the steam-induced pelletoxidation along with the interlinked fraction of fission gas bub-bles open to the pellet free surfaces. However, the effect of theinterlinked fraction of fission gas bubbles on the fission productrelease may be negligible for a quite long time from the failureoutset for lower burnup fuel since the amount of fission productsaccumulated in the pellet matrix at the low burnup is relativelysmall.
The extent of fission product release from the gap into thecoolant is dependent on the through-hole size, its axial locationand the fuel rod burnup. The fission product release may show aburst behavior at the outset of fuel failure and then fall-down foran initial period, as shown in Eq. (9). In addition, the fission productrelease increase steadily due to the through-hole size increase withtime. In other words, the larger size of through-hole will naturallygenerate the larger release of fission products, especially for solu-ble iodine and cesium adsorbed in the cladding and pellet surfaces.In detail, the larger through-hole size will increase the probabilitythat the water coming into the gap exists as water not convertedinto steam around the through-hole and then soluble iodine andcesium adsorbed on the surfaces may have a chance to be washedout into the coolant. The fuel rod burnup will determine the fuel rodgap size. The gap size will be decreased with burnup, resulting inthe pellet-clad hard contact, and consequently the steam in the gapcannot pass through that hard contact region, resulting in the retar-dation of the secondary hydride formation and the steam-inducedpellet oxidation.
4. Results and discussion
Only one fuel rod for the three failure cases considered has beenfailed for PWRs in Korea. Fig. 3 shows a debris-induced frettingwear mark and a secondary hydride-induced ballooning and tear-ing. Fig. 4 shows a GTRF-induced through hole with a fretting-wearmark and the secondary hydride-induced ballooning. Fig. 5 showsexcessive cladding oxide-induced spalling and tearing marks andaxial cracks around the middle of the fuel rod. Table 2 summarizesreactor core operation data, fuel dimensions, fuel failure infor-mation on failure outset times, fuel burnups, through-hole axiallocations, etc.
For each fuel failure cause, reactor power and letdown flow his-tories, xenon activity variations and the activity ratio of Xe-133 toXe-135, and iodine activity variations and the activity ratio of I-131to I-133 are plotted in Figs. 6 through 14
4.1. Debris-induced fuel failure
Optical micrographs for the failed fuel rod shown in Fig. 3indicate that the debris-induced wear mark is located just belowthe bottom spacer grid (∼70 mm from the fuel rod bottom) and
the debris may be considered a kind of wire, based on the wearmarks. The length of the through-hole is about 3 mm. The secondaryhydride-induced ballooning and tearing are also found in the mid-dle of the fuel rod (∼2400 mm from the fuel rod bottom), which
160 K.-T. Kim / Nuclear Engineering and Design 248 (2012) 156– 168
wAboFuidi
Fig. 3. Optical micrographs of a fuel rod having debris-induced fuel failure.
ere produced later after the debris-induced cladding perforation.s shown in Fig. 7, the coolant activities of Xe-133 and Xe-135 gasesegan to increase at about 50 days. Likewise the coolant activitiesf I-131 and I-133 started to increase at about 50 days, as shown inig. 8, which indicates that a fuel rod starts to release fission prod-
cts at around 50 days. In addition, the fuel rod failure criteria givenn Table 3 also indicate that the fuel rod failure occurred at about 50ays since the ratios of Xe-133 to Xe-135 and I-131 to I-133 shown
n Figs. 7 and 8 are greater than 1.0 and 0.25, respectively. It is noted
Fig. 4. Optical micrographs of a fuel rod having grid-to-rod fretting wear-inducedfuel failure.
that the letdown flow rate is increased from 120 to 240 l/min fromthe fuel failure outset and remains unchanged afterward, as seenin Fig. 6. It may be said that considering Eq. (8), the coolant activ-ity variations after the fuel failure was not affected by the letdownflow rate since it remains constant after the fuel failure.
From Fig. 7, it can be seen that the activities of Xe-133 and Xe-135 in the coolant increase steadily from the outset of the fuelfailure. After remaining at a peak value from about 100 to 150 days,they decrease very slightly up to 250 days and then remain nearlyconstant. As seen in Tables 1 and 2, Xe-135 has �� about 104 largerand � ten times larger than Xe-133, resulting in that the amountof Xe-135 gas accumulated in the gap before the fuel leak is muchsmaller than the amount of Xe-133, which can be easily seen fromEq. (2). Therefore, the amount of Xe-133 gas released through thedebris-made through-hole is much larger than that of Xe-135 allthe way up to the end of cycle. The activities of Xe-133 and Xe-135 gases increase steadily from 50 days and then reach a peakat about 100 days. This indicates that the debris-induced through-hole enlargement with time is more effective to the coolant activityvariations than the initial burst and subsequent fall-down (see Eq.(9)). From about 150 to 250 days, however, the release rates ofxenon gases decrease very slightly since the release rates of xenongases from the pellet to the gap is not enough to compensate therelease rates of xenon gases from the gap into the coolant. From250 days, the release rates of xenon gases start to increase barely.This can be explained by the steam-induced pellet oxidation andthe interlinked fraction of fission gas bubbles during a later period
after the fuel failure (e.g., after 250 days). The release rates of xenongases from the pellet to the gap can be enhanced by a factor of1.5 due to the steam-induced pellet oxidation, assuming that theUO2 pellets are oxidized below to UO2.01, according to Olander et
K.-T. Kim / Nuclear Engineering and Design 248 (2012) 156– 168 161
e oxid
aitffadgfgiOpettcoaf
impitdsdtIstnt1alTge1atsb
Fig. 5. Optical micrographs of a fuel rod having excessiv
l. (1999). They can also be enhanced by the increased number ofnterlinked fraction of fission gas bubbles that is represented by εierm, as seen in Eq. (2). It is noteworthy that the debris-induceduel failure occurred at very low burnup (∼2 MWD/kgU) and theuel burnup is increased to 9 MWD/kgU at 250 days, indicating thatbout seven months after the fuel failure may be enough to oxi-ize the UO2 pellets and enhance the interlinked fraction of fissionas bubbles. Therefore, it may be said that the xenon gases releasedrom the pellet to the gap after 250 days may compensate the xenonases in the gap exhausted by its release into the coolant, resultingn slight increase in the release rates of xenon gases from 250 days.n the other hand, the effect of the secondary hydride-inducedhenomena appeared in the middle of the fuel rod is not appar-nt for the changes in the xenon activities in the coolant. However,he secondary hydride-induced phenomena may have an effect onhe enhanced release rate of xenon gases from the gap into theoolant in the range of between 100 and 150 days since the sec-ndary hydride-induced phenomena are known to be generated in
few months after the cladding perforation at some axial positionsar from such the perforation.
From Fig. 8, it can be seen that the activities of I-131 and I-133n the coolant show a spike at the outset of the fuel failure, which
ay represent the burst and subsequent fall-down behaviors, asredicted in Eq. (9). After this spike, the activities of I-131 and I-133
ncrease noticeably for a while, which may represent the effect ofhe through-hole size enlargement on the fission gas release, as pre-icted in Eq. (9). From 70 to 120 days, the iodine activities decreaseomewhat significantly and then they remain constant up to 170ays. Up to about 250 days from 170 days, the I-131 activity startso decreases quite a lot, whereas the I-133 activity decreases barely.t should be noted that the I-133 activity after 170 days is nearly theame as the tramp uranium-induced radioactivity prevailed prioro the fuel failure outset. It means that the release of I-133 may beegligible after 170 days. After 250 days, the I-131 activity changeso an increasing mode. The ratio of I-131 to I-133 is always below.0 and furthermore decreases to below 0.25 after 180 days. Theforementioned iodine activity behaviors may be explained as fol-ows. First of all, I-133 has larger value of YH than I-131, as given inable 1, resulting in that the amount of I-133 gas released from theap into the coolant is larger than the amount of I-131, which can beasily seen from Eq. (6) or Eq. (8). In other words, the amount of I-33 adsorbed on the cladding and pellet surfaces are larger than the
mount of I-131 before the fuel failure. Secondly, the reason thathe release rates of I-131 and I-133 after the fuel failure decreaseignificantly from 70 days to about 120 days is because the solu-le iodine products adsorbed on the cladding and pellet surfaces areation-induced fuel failure in the middle of the fuel rod.
washed out into the coolant by the water in the gap but the amountof the soluble iodine products released into the coolant becomesmaller with time since the iodine products adsorbed on the sur-faces near the through-hole are exhausted with time. From 120and 170 days, however, the release rates of I-131 and I-133 prod-ucts from the gap into the coolant remains nearly constant since thesecondary hydride-induced tearing sites and axial cracks may gen-erate another source of the soluble iodine products released fromthe gap into the coolant. Similarly, the iodine products adsorbedon the surfaces near the secondary hydride-induced through-holesmay be exhausted with time, causing the release rates of I-131 todecrease up to 250 days but the I-133 activity remains constantsince it cannot be lower than the tramp uranium-induced radioac-tivity prevailed prior to the fuel failure. After 250 days, the I-131release rate from the pellet becomes larger, which may be causedby the fact that the I-131 release rate is enhanced by the increasedfission product diffusivity caused by the steam-induced pellet oxi-dation as well as the increased numbers of cracks and interlinkedgrain boundary bubbles to the pellet surfaces as explained above.This is valid for the I-133 release rate from the pellet but its half lifeis much less than the I-131’s half life, which may make the releaserate of I-133 from the pellet much smaller, compared to that ofI-131.
.
4.2. Grid-to-rod fretting wear-induced fuel failure
Optical micrographs for the failed fuel rod shown in Fig. 4 indi-cate that the GTRF-induced wear mark is located just at the bottomspacer grid (∼105 mm from the fuel rod bottom). The through-hole size made by the GTRF appears to be much smaller than thatby the debris (see Figs. 3 and 4). The secondary hydride-inducedphenomena are also found in the middle of the fuel rod, whichwas produced later after the GTRF-induced cladding perforation.As shown in Fig. 8, the coolant activities of Xe-133 and Xe-135gases began to increase at about 330 days without the burst andsubsequent fall-down behaviors. It means that the through-holeenlargement in Eq. (9) is more effective than the initial burst andsubsequent fall-down. Likewise the coolant activities of I-131 and I-133 started to increase at about 340 days, as shown in Fig. 11, whichindicates that there exists a time lag of 10 days for the fuel failureinitiation predicted by the xenon and iodine activity variations. This
time lag can occur since the xenon gas may release instantly whenthe through-hole is formed but the release of the iodine productsadsorbed on the surfaces requires some time for water to comeinto the gap and to dissolve the iodine products and then to be
162 K.-T. Kim / Nuclear Engineering and Design 248 (2012) 156– 168
100
Rea
ctor
Pow
er (
%)
50
0
Let
dow
n F
low
Rate
(L/m
in)
400
800
0
Letdown Flow Ra te
600
200
0 50 100 150 200 250 300 350 400 450
Ti m
500
Reactor Po wer
tories
finafft2bdIts
Xo
Operation
Fig. 6. Reactor power and letdown flow rate his
nally pushed out of the gap with dissolved iodine products. It isoteworthy that the ratio of Xe-133 to Xe-135 shown in Fig. 10 isround 1.0 for the clean core and increases to 2 and 3 after the fuelailure. The ratio of I-131 to I-133 shown in Fig. 11 is 2 at the fuelailure outset and then slowly decreases to 1.0 except at the reac-or trip. As shown in Fig. 9, the letdown flow rate is increased from40 to 440 l/min during the second reactor trip and then decreasedetween 240 and 440 l/min. After the fuel failure outset, the let-own flow rate is increased to 440 l/min and remains unchanged.
t may be said that considering Eq. (8), the coolant activity varia-ions after the fuel failure was not affected by the letdown flow rate
ince it remains constant after the fuel failure.From Fig. 10, it can be seen that the activities of Xe-133 ande-135 in the coolant increase significantly from the fuel failureutset to about 345 days and then increased steadily until the
1.0E-04
1.0E-03
1.0E-02
1.0E-01
1.0E+00
1.0E+01
Xen
on
Act
ivit
y (
Ci/
cc)
0 50 100 150 200
Xe-133
Operation
Xe-135
0.01
0.10
1.00
10.0
Xe
-13
3/X
e-1
35
0 50 100 150 200
Operation
Fig. 7. Xenon gas activity history in the coolant for
e (d ays)
for the cycle having debris-induced fuel failure.
reactor trip at 410 days. After this reactor trip, the activities of Xe-133 and Xe-135 remain at a little higher values up to 450 daysthan those before this trip. After 450 days, the activities of Xe-133and Xe-135 increase somewhat noticeably. These activity behav-iors may be explained as follows. First of all, the Xe-135 has about105 larger value of �� and ten times larger value of � than Xe-133, resulting in that the amount of Xe-135 gas accumulated inthe gap before the fuel leak is much smaller than the amount ofXe-133, as explained above. Therefore, the amount of Xe-133 gasreleased through the through-hole is larger than that of Xe-135 allthe way up to the end of cycle. However, it should be noted that
the xenon activity levels for the GTRF-induced failure are one orderlower than those for the debris-induced fuel failure, as shown inFigs. 7 and 10. This is because the tramp unranium-induced activi-ties for the GTRF-induced failure shown in Fig. 10 are about one or250 300 350 400 450
Ti me (d ays)
500
250 300 350 400 450
Ti me (d ays)
500
the cycle having debris-induced fuel failure.
K.-T. Kim / Nuclear Engineering and Design 248 (2012) 156– 168 163
1.0E-04
1.0E-03
1.0E-02
1.0E-01
1.0E+00
1.0E+01
Iod
ine
Act
ivit
y (
Ci/
cc)
0 50 100 150 200 250 300 350 400 450
I-131
Operation Ti me (d ays)
500
I-133
0.01
0.10
1.00
10.0
I -1
31
/I-1
33
0 50 100 150 200 250 300 350 400 450
ation
500
t for th
tifftmtcsfdComt
Oper
Fig. 8. Iodine activity history in the coolan
wo order lower than those for the debris-induced failure shownn Fig. 7 and because the letdown flow rate for the GTRF-inducedailure is about two times larger than that for the debris-inducedailure. In addition, the springs or dimples of the spacer grids duringhe GTRF-induced wear can block the through-hole in a periodic
anner, according to fluid-induced grid-to-rod vibration charac-eristics, whereas the debris may be worn out usually after theladding perforation, possibly not blocking the through-hole for theubsequent period. Therefore, it may be said that the GTRF-induceduel failure tends to retard fission product release more than theebris-induced fuel failure with the same size of through-holes.
onsequently, for the GTRF-induced fuel failure case, the amountf the xenon gases released from the gap into the coolant can beore than compensated by the xenon gases released from the pelleto the gap since the relatively smaller amount of the xenon gases is
100
Rea
ctor
Pow
er (
%)
50
0
Reactor Po wer
0 50 100 150 200 250 Operation Ti m
Letdown Flow Ra te
Fig. 9. Reactor power and letdown flow rate histories for the cy
Ti me (d ays)
e cycle having debris-induced fuel failure.
released into the coolant. Then, the release rates of the xenon gasesinto the coolant increase steadily up to 410 days with enlarging thethrough-hole caused by the continuing grid-to-rod fretting wear,as predicted by Eq. (9). After 410 days, however, the xenon gasesaccumulated in the gap far from the through-hole, which could notmove to the perforation site located at the bottom grid because ofthe pellet-clad hard around the middle of the fuel rod, may startto come to the through-hole site since the reactor trip reopenedthe pellet-to-clad hard contact region. As expected, the activities ofXe-133 and Xe-135 after the trip remain at a little higher value upto 450 days than those prior to the trip. From 450 days to the end of
cycle, the activities of Xe-133 and Xe-135 increase somewhat con-siderably since the release rates of xenon gases from the pellet tothe gap may be enhanced by the steam-induced pellet oxidation aswell as the increased interlinked fraction fission gas bubbles withLet
dow
n F
low
Rate
(L/m
in)
400
800
0
600
200
300 350 400 450
e (d ays)
500
cle having grid-to-rod fretting wear-induced fuel failure.
164 K.-T. Kim / Nuclear Engineering and Design 248 (2012) 156– 168
1.0E-04
1.0E-03
1.0E-02
1.0E-01
1.0E+00
1.0E+01
Xen
on
Act
ivit
y (
Ci/
cc)
0 50 100 150 200 250 300 350 400 450
Xe-133
Operation Ti me (d ays)
500
Xe-135
0.01
0.10
1.00
10.0
Xe
-13
3/X
e-1
35
0 50 100 150 200 250 300 350 400 450
Operation Ti me (d ays)
500
e cycle
tp3attbs
Fig. 10. Xenon gas activity history in the coolant for th
he increase of fuel burnup, as explained above. This can be sup-orted by the fact that the GTRF-induced fuel failure occurred at30 days (13 MWD/kgU) and then the fuel burnup is increased tobout 18 MWD/kgU at 450 days. On the other hand, it is noteworthyhat the ratio of Xe-133 to Xe-135 may not represent a variation of
he through-hole size since the ratio is about 2 from 350 to 410 daysut 3.0 from 410 to 480 days. This indicates that the through-holeize becomes smaller with time, which is contrary to the course of1.0E-04
1.0E-03
1.0E-02
1.0E-01
1.0E+00
1.0E+01
Iod
ine
Act
ivit
y (
Ci/
cc)
0 50 100 150 200
Operation
0.01
0.10
1.00
10.0
I -1
31/I
-133
0 50 100 150 200
Operation
I-
Fig. 11. Iodine activity history in the coolant for the cycle h
having grid-to-rod fretting wear-induced fuel failure.
nature. Therefore, the ratio of Xe-133 to Xe-135 is to be interpretedby the combined effects of a variation of through-hole size (fromthe gap to coolant) and changes in the release rate from the pelletto the gap with the increase of fuel burnup.
From Fig. 11, it can be seen that the activities of I-131 and I-133
in the coolant show no spike at the outset of the fuel failure andincreases steadily up to about 450 days and then decreases after-ward. Obviously there exist two spikes for I-131 and I-133 at the250 300 350 400 450
Ti me (d ays)
500
250 300 350 400 450
Ti me (d ays)
500
I-131133
aving grid-to-rod fretting wear-induced fuel failure.
K.-T. Kim / Nuclear Engineering and Design 248 (2012) 156– 168 165
100
Rea
ctor
Pow
er (
%)
50
0
Let
dow
n F
low
Rate
(L/m
in)
400
800
0
Reactor Po wer
600
200
0 50 100 150 200 250 300 350 400 450
on Ti 500
Letdown Flow Ra te
for th
rhf1tiilFtrqso
Operati
Fig. 12. Reactor power and letdown flow rate histories
eactor trip and at the end of cycle. This indicates that the through-ole size enlargement is more effective than the initial burst and
all-down without the reactor trips, as seen in Eq. (9). The ratio of I-31 to I-133 decreases from 2.0 to 1.0 with time, indicating that thehrough-hole is increasing with time but still remains small, as seenn Fig. 4. For the same reason explained above, the activity of theodine products for the GTRF-induced fuel failure are two ordersower than those for the debris-induced fuel failure, as shown inigs. 8 and 11. By the way, the release rates of I-131 and I-133 afterhe fuel failure increase steadily up to 450 days since the release
ates of the soluble iodine products adsorbed on the surfaces areuite small due to a small through-hole and consequently theretill exists a sufficient amount of soluble I-131 and I-133 adsorbedn the surfaces. Finally, the soluble I-131 and I-133 adsorbed on1.0E-04
1.0E-03
1.0E-02
1.0E-01
1.0E+00
1.0E+01
Xen
on
Act
ivit
y (
Ci/
cc)
0 50 100 150 200
Operation
0.10
1.00
10.0
100
Xe
-13
3/X
e-1
35
0 50 100 150 200
Operation
Fig. 13. Xenon gas activity history in the coolant for the cy
me (d ays)
e cycle having excessive oxidation-induced fuel failure.
the surfaces are exhausted around 450 days and subsequently therelease rates of the iodine products change to a decreasing mode.In the meantime, the release rates of the iodine products from thepellet to the gap may be enhanced by the steam-induced pelletoxidation as well as the increased interlinked fraction of fissiongas bubbles open to the pellet free surfaces with the increase offuel burnup, as explained above. Through such the release from thepellet to the gap, however, the amount of iodine products addi-tionally adsorbed on the surfaces around the through-hole maynot be sufficient to compensate the exhaustion of iodine around
the through-hole because it is located at the bottom grid region farfrom highly burned pellets located around the middle of the fuelrod, resulting in the decrease mode even after 450 days, not likethe increase mode of the xenon activity after 450 days.250 300 350 400 450
Xe-133
Ti me (d ays)
500
Xe-135
250 300 350 400 450
Ti me (d ays)
500
cle having excessive oxidation-induced fuel failure.
166 K.-T. Kim / Nuclear Engineering and Design 248 (2012) 156– 168
1.0E-04
1.0E-03
1.0E-02
1.0E-01
1.0E+00
1.0E+01
Iod
ine
Act
ivit
y (
Ci/
cc)
0 50 100 150 200 250 300 350 400 450
Operation Ti me (d ays)
500
0.01
0.10
1.00
10.0
I -1
31
/I-1
33
0 50 100 150 200 250 300 350 400 450
Operation Ti me (d ays)
500
I-131
I-133
e cycl
4
aontIihtocoLaebfdipbfltrtlblatd4tts
Fig. 14. Iodine activity history in the coolant for th
.3. Excessive oxide-induced fuel failure
Optical micrographs for the failed fuel rod shown in Fig. 5 show lot of oxide spalling/tearing and long axial cracks in the middlef the fuel rod. The secondary hydride-induced phenomena wereot observed because of the difficulty in the steam movement inhe axial direction through the pellet-to-clad hard contact areas.t is noteworthy that the excessive oxide-induced failure occurredn the middle of the fuel rod of 40 MWD/kgU and its cladding gapad already been tightly closed by the pellet-clad hard contact inhe middle of the fuel rod, which will prevent a free movementf steam in upper or lower axial directions through the pellet-to-lad hard contact areas. As shown in Fig. 13, the coolant activitiesf Xe-133 and Xe-135 gases began to increase at about 270 days.ikewise the coolant activities of I-131 and I-133 started to increaset about 320 days, as shown in Fig. 14, which indicates that therexists a time lag of 50 days for indicating the fuel failure initiationy the xenon and iodine activity variations. The time lag of 50 daysor this oxide-induced failure is much larger than the time of 10ays for the GTRF-induced failure. This is because much more time
s needed for water to come into the gap and subsequently to beushed out of the gap with the dissolved iodine products for a highurnup fuel, considering that there is some difficulty in the coolantow through the through-hole into the gap with high-pressure forhe high burnup fuel. It is noteworthy that after the fuel failure theatio of Xe-133 to Xe-135 shown in Fig. 13 is about 1 initially andhen increases to 10 and finally decreases to 5, which is explainedater with the use of the increased interlinked fraction of fission gasubbles. The ratio of I-131 to I-133 shown in Fig. 14 is also explained
ater. As shown in Fig. 12, the letdown flow rate is about 240 l/mint the failure outset (270 days) and increases to 440 l/min duringhe second trip and then decreases to 240 l/min. From 350 to 440ays, the letdown flow rate increases to about 320 l/min and then
40 l/min near the end of cycle. It can be seen in Figs. 13 and 14 thathe coolant activity near the end of cycle may become lower dueo the direct impact of letdown flow rate increase, which is easilyeen from Eq. (8).e having excessive oxidation-induced fuel failure.
From Fig. 13, it can be seen that the activities of Xe-133 and Xe-135 in the coolant increase significantly from the fuel failure outset(270 days) to 430 days and then decrease slightly up to the end ofcycle. The Xe-135 has about 105 larger value of �� and ten timeslarger value of � than Xe-133, resulting in that the amount of Xe-133 gas accumulated in the gap before the fuel leak is larger thanthe amount of Xe-135, as explained above. Therefore, the releaserate of Xe-135 gas is much smaller than that of Xe-133 all the wayup to the end of cycle. These activity behaviors showing nearly ever-increasing modes up to 430 days can be explained as follows. Firstof all, the accumulated amount of fission products in the pelletsaround the oxide-induced cladding perforation site may be consid-erably larger than those in the pellets around the debris-inducedand the GTRF-induced cladding perforation sites since the local rodpower for the oxide-induced fuel failure is 21.4 kW/m, whereasthose for the debris-induced and the GTRF-induced fuel failuresare 8.0 and 7.2 kW/m, respectively, as given in Table 2. In addition,for this oxide-induced fuel failure, the release paths of fission prod-ucts along the interlinked grain boundaries and cracks are surelywell developed due to the high burn fuel (40 MWd/kgU) on the onehand and fission product diffusivity may be enhanced due to thesteam-induced pellet oxidation on the other hand. Therefore, it isnatural that xenon gases released from the pellet to the gap shouldfill up the gap more than xenon gases released from the gap into thecoolant, resulting in the increasing rate of xenon gases with time.
From Fig. 14, it can be seen that the activities of I-131 and I-133 inthe coolant increase steadily except near the end of cycle, while theI-131 activity increases with a higher gradient than the I-133 activ-ity. The relatively lower activities of I-131 and I-133 near the endof cycle can be easily explained by the letdown flow rate increasenear the end of cycle, as predicted by Eq. (8). By the way, the releasepaths of fission products along the interlinked grain boundariesand cracks are surely well developed for the highly burned pellets
located in the middle of fuel rod on the one hand and fission productdiffusivity may be enhanced due to the pellet oxidation. Further-more, the amount of iodine products released from the pellet to thegap is much more than that from the gap into the coolant. Therefore,
g and
tfm
ratf
–
–
–
–
–
–
5
pnacieapfua
1
2
K.-T. Kim / Nuclear Engineerin
he high burnup fuel with through-holes around the middle of theuel rod can release the iodine products through the through-holes
ore and more with time, just like the xenon gases.Based on the relations between the xenon and iodine coolant
adioactivity variations in the coolant and the fuel failure causesnalyzed in this study, the characteristics of the coolant radioac-ivity variations for such three failure cases may be described asollows:
◦ Debris-induced fuel failure at low burnup activities of xenon gases increase steadily, level off, decreaseslightly, and finally level off again, activities of iodine increasenoticeably for an initial short period, reach a peak, decreasesteadily for quite a long period and then reach to a bottom, andfinally change to a steadily increasing mode, no failure outsettime lag exists when predicted by xenon and iodine activity vari-ations.
initial burst and subsequent fall-down phenomena are observedonly for iodine.
◦ Grid-to-rod fretting wear (GTRF)-induced fuel failure at low bur-nup
activities of xenon gases increase continuously with a relativelylower slope, activities of iodine increase with a relatively lowerslope for quite a long period and finally change to a steadilydecreasing mode, a relatively short failure outset time lag existswhen predicted by xenon and iodine activity variations.
initial burst and subsequent fall-down phenomena are notobserved for both iodine and xenon when no reactor trip occurs.
◦ Excessive oxide-induced fuel failure at high burnup activities of xenon gases increase continuously with a relativelyhigher gradient, compared to those of iodine, activities of iodineincrease continuously with a relatively lower gradient, comparedto those of xenon, a relatively long failure outset time lag existswhen predicted by xenon and iodine activity variations.
initial burst and subsequent fall-down phenomena are notobserved for both iodine and xenon when no reactor trip occurs.
. Conclusions
For the typical fuel failure causes found in commercial PWRlants in Korea that include debris-induced fuel failure at low bur-up, grid-to-rod fretting wear-induced fuel failure at low burnupnd excessive cladding oxide-induced fuel failure at high burnup,haracteristics of reactor coolant activity variations of xenon andodine specific to each fuel failure are analyzed in detail by consid-ring fuel rod burnups at the fuel failure outset, fuel rod defect sizend its axial location, steam-induced pellet oxidation and fissionroduct release paths in the pellet for the defective fuel rods. It wasound that there exists an outstanding relation between a fuel fail-re cause and its relevant coolant radioactivity variation of xenonnd iodine. The results may be summarized as follows:
. For the debris-induced fuel failure at low burnup, the xenon andiodine activities increase noticeably for an initial period, whilethey decrease somewhat significantly for quite a long time afterreaching a peak. There exists little effect of the steam-inducedpellet oxidation and the fission product release enhancementalong the grain boundaries and pellet cracks on the fission prod-uct release rates. In addition, there was no failure outset time lagwhen predicted by xenon and iodine activity variations.
. For the grid-to-rod fretting wear-induced fuel failure at low bur-
nup, the xenon and iodine activities increase noticeably for aninitial period and then increase steadily with a relatively lowergradient. There exists some effect of the steam-induced pelletoxidation and the fission product release enhancement along theDesign 248 (2012) 156– 168 167
grain boundaries and pellet cracks on the fission product releaserates. In addition, there was a failure outset time lag of about 10days when predicted by xenon and iodine activity variations.
3. For the excessive cladding oxide-induced fuel failure at high bur-nup, the xenon activities increase significantly all the way up tothe end of cycle. The iodine activities increase with a relativelyhigher gradient than those for the grid-to-rod fretting wear-induced fuel failure. There exists a considerable effect of thesteam-induced pellet oxidation and the fission product releaseenhancement along the grain boundaries and pellet cracks onthe fission product release rates. In addition, there was a failureoutset time lag of about 50 days when predicted by xenon andiodine activity variations.
4. The ratios of Xe-133 to Xe-135 and I-131 to I-133 do notrepresent the actual sizes of through-holes specific to each fail-ure cause. They may be explained by combined effects of thethrough-hole size and the enhanced release rates of fissionproducts caused by the steam-induced pellet oxidation and theinterlinked fraction of fission gas bubbles along the grain bound-aries and pellet cracks.
5. The through-hole size enlargement with time is more effectiveto reactor coolant radioactivity variations than the initial burstand fall-down when no reactor trip occurs.
Acknowledgements
This research was supported by both Basic Atomic EnergyResearch Institute Program (No. 2011-0006316) and YoungResearcher Supporting Program (No. 2011-0005785) through theNational Research Foundation of Korea (NRF) and funded by theMinistry of Education, Science and Technology.
References
Andrew, W., Lewis, B., Cox, D., 1999. Artificial neural network models for volatilefission product release during severe accident conditions. J. Nucl. Mater. 270,74–86.
Beraha, R., Beuken, G., Frejaville, G., Leuthrot, C., Musante, Y., 1980. Fuel survey in thelight water reactors based on the activity of the fission products. Nucl. Technol.49, 426–434.
Bishop, W., 1986. Iodine spiking, EPRI NP-4595. Electric Power Research Institute.Bruet, M., Pointud, M., Dodelier, J., Melin, Ph., 1980. CONTACT 1 and 2 experiments.
In: IAEA Specialists’ Meeting on Water Reactor Fuel Performance ComputerModelling, Blackpool, UK, March 17–21.
CE, 1991, PWR fuel follow from coolant activity analysis (training manual), CE NPSE-308-P (Rev. 1-P).
Charles, M., Abassin, J., Bruet, M., Baron, D., Melin, Ph., 1982. Utilization of CON-TACT experiments to improve the fission gas release knowledge in PWR fuelrod. In: IAEA Specialists’ Meeting on Water Reactor Fuel Performance ComputerModelling, Preston, UK, March 15–19.
Charles, M., Chenebault, P., Melin, Ph., 1985. Mechanisms of fission gas releasefrom different types of fuel rods, during normal operation: results and analysisof CONTACT experiments. In: Light Water Reactor Fuel Performance, Orlando,Florida, April 21–24.
Correal-Pulver, O., 1993. Coolant Activity Data Evaluation Personal Computer Pro-gram, (User’s Manual). Westinghouse Electric Company.
Evans, A., Davidge, R., 1969. The strength and fracture of stochiometric polycrys-talline UO2 fuel pellets. J. Nucl. Mater. 33, 249–260.
Iqbal, M., Mirza, N., Mirza, S., 2008. Stochastic simulation of fission product activity inprimary coolant due to fuel rod failures in typical PWRs under power transients.J. Nucl. Mater. 372, 132–140.
Ivanov, A., 1998. The model of the fission gas release out of porous fuel. Ann. Nucl.Energy 25 (15), 1275.
Koo, Y., Sohn, D., Yoon, Y., 1994. Release of unstable fission products from defectivefuel rods to the coolant of a PWR. J. Nucl. Mater. 209, 248–258.
Lewis, B., 1988. Fundamental aspects of defective nuclear fuel behavior and fissionproduct release. J. Nucl. Mater. 160, 201–217.
Lewis, B., El-Jaby, A., Higgs, J., Thompson, W., Iglesias, F., Laidler, R., Armstrong, J.,Stone, R., Oduntan, R., 2007. J. Nucl. Mater. 366, 37–51.
Lewis, B., Hunt, C., Iglesias, F., 1990. Source term of iodine and noble gas fissionproducts in the fuel-to-sheath gap of intact operating nuclear fuel elements. J.Nucl. Mater. 172, 197–205.
Lewis, B., Iglesias, F., Postma, A., Steininger, S., 1997. Iodine spiking model for pres-surized water reactors. J. Nucl. Mater. 244, 153–167.
1 g and
L
L
M
OO
Turnbull, J., Friskney, C., 1978. The relation between microstructure and the release
68 K.-T. Kim / Nuclear Engineerin
ewis, B., Phillips, C., Notley, M., 1986. Model for the release of radioactive krypton,xenon, and iodine from defective UO2 fuel elements. Nucl. Technol. 73, 72–83.
ewis, B., Thompson, W., Akbari, F., Thompson, D., Thurgood, C., Higgs, J., 2004. Ther-modynamics and kinetic modelling of the fuel oxidation behavior in operatingdefective fuel. J. Nucl. Mater. 328, 180–196.
atzke, H.J., 1980. Gas release mechanisms in UO2 – a critical review. Radiat. Eff. 53,219.
lander, D., 1986. Oxidation of UO2 by high-pressure steam. Nucl. Technol. 74, 215.lander, D., Kim, Y., Wang, W., Yagnik, S., 1999. Steam oxidation of fuel in defective
LWR rods. J. Nucl. Mater. 270, 11.
Design 248 (2012) 156– 168
Radford, K., 1979. Effect of fabrication parameters and microstructure on themechanical strength of UO2 fuel pellets. J. Nucl. Mater. 84, 222–236.
Shiba, K., 1975. Fission iodine and xenon release from the UO2–U3O8 system withemphasis on radiation damage. J. Nucl. Mater. 57, 271–279.
of unstable fission products during high temperature irradiation of uraniumdioxide. J. Nucl. Mater. 71, 238–248.
White, R., Tucker, M., 1983. A new fission-gas release model. J. Nucl. Mater. 118,1–38.
