Note: Descriptions are shown in the official language in which they were submitted.
BACKGROUN~ OF T~ INVEN ION
The present invention relates to the detection
and determination of the characterlstics of breakages
which can occur to cans in nuclear reactors. It more
specifically applies to heavy or light water reactors, but
also has lnteresting ~pplications in the field o~ liquid
metal-cooled reactors.
In the remainder of the text an~ in order not
to make the description unduly long reference wlll almost
exclusively be made to light water-cooled, moderated
reactors, but it is obvious that this is not to be con-
sidered as a limitation to the scope of t~le prese~t invent-
ion.
In the hitherto kno~ PWR or BWR light water
moderated reactors~ the fuel is generally uranium oxide
U02, jacketed by zircaloy sheaths, the fueI being distri-
buted into a certain number of autonomous assemblies, each
having a large number of fuel rods. As an example and
to give an idea of the orders of magnitude a PWR reactor
with an electric power of 900 MW has approximately 40,000
fuel rods of length ~.60 m, subdivided into 15~ assemblies,
,j
each of 264 rods.
These fuel elements, which co~stitute the core
of the reactorJ are directly immersed in the moderating
water~ which also constitutes the primary coolant of the
reactor. In the case where one or more fuel rod cans
sufrers from cracking or breakage, the radioactive rission
3~
products, which are normally trapped wlthin the can are
spread outside the latter into the primary coolant and
from there carl contamina~e the reactor vessel and a cer-
tain number o~ components, such as pumps and primary
exchangers. It is thererore very lmportant to monitor,
during the operation of such a nuclear reactor, the appear
ance and the possible spread o~ cracks or breaks in the
cans constituting the ~uel element rods.
Hitherto no completel~ satis~actory method has
been developed to meet this requirement and it has been
necessary to make do with more or lèss empirical methods
of monitoring the overall activity o~ the pr~nary coollng
water ~or ~ission products.
BRIEF SUMMARY_OF_THE_INVENTION
The present invention relates to a method for
detecting and determining the characteristics ofbreaks or
~ractures o~ cans ~or nuclear reactor ~uel elements which
makes i~ possible, a~ter carrying out the detection o~ any
can fracture occurring in one of the rod assemblies of the
core, to determine the a~erage number thereof~ the extent
of the fracture and possibly the position thereo~ by
employing simple means. -
In ~eneral terms it is only possible to monitor
any ~ractures or breaks ko cans by using as the i~ormation
source the relative ackivities either of gaseous ~lssion
products or of solid ~ission products, whlch are ~oluble
in the primary ~luid of the operating reactor. The most
common and most intere~ting o~ the nuclides which can be
used are in the case o.t` gaseous products,rare gases,
kryptons and xenons and in the case of solid products
iodines and cesiums. The ro:Llowing Table lis~s the
various nuclides accompanied by their period, which can
vary very widely from a ~ew mlnutes to several years.
NUCLID~ PERXOD
85m Kr 4.48 hours
87 Kr 76.3 minutes
88 Kr 2.8 hours
89 Kr 3.18 minutes
134 Cs 2.06 years
1~7 Cs 30.1 years
138 Cs 32.2 m~nutes
133 Xe 5.29 days
133m Xe 2.2 days
135 Xe 9.17 hours
137 Xe 3.83 minutes
138 Xe 14.1 minutes
131 I 8.o4 days
132 T 2.38 hours
133 I ~0.8 hours
1~4 I 52 minutes
135 I 6.59 hours
N.B.: In the Table m means metastable.
As a ~irst approximation the fission product
. activity o~ the primary water of a pressurised water-cooled
3Lls3~t;()
~5~
nuclear reactor is only dependent on three parame~ers,
namely:
the number n o~ breaks in the cans;
the temperature ~ of the ~uel rod or rods~
which has been rractured;
the slze o~ the break or breaks, which can be
translated by the leakage ~actor ~g~
As the in~ormation coll.ected on the a¢kivity o~
the water or the primary circuit is overall in~ormation and
there is no possibility o~ "sectorizing" the inrormation
source the temperature de~ined can only be the mean temper-
ature o~ the temperatures o~ the dif~erent points o~ ~uel
rods which have become cracked, so that the number n o~
~ractures exceeds 1. In the same way the concept o~
the size Or the ~racture can only represent the mean value
for existing raulty surfaces~ These observations are
important ~or the remainder o~ the description in which
: re~erence must always be made to this reature whenever it
is a questlon of the temperature of the cracks or the siz
Or the fractures. For this latter ractor a more pre-
cise definition can be given to it ln the case o~ a single
break, as ~ollows: :
~g = D/~ x s/V
In this rormula:
D is the coe~ricient of dl~fusion o~ the fission
product determined in cm /s;
e is the path in centimetres taken by the ~ission
~ ~ .
~..
~1~34~
product, l.e. with minor di~erences the thick-
ness o~ the can;
s is the fault sur~ace or crack in cm ;
V is in practice the volume o~ the expansion
chamber between the ~uel and i~s can, expressed
in cm3.
Xt is therefore readily apparent that the
coef~icient ~g characterlses the proportion o~ the total
activity present in the expa~sion chamber3 which passes
through the cracked can in each second. It thererore
characterises ~he gravity of a break and is eæpressed by a
number havlng the dimensions of the inverse o~ a time.
The standard values for the coefficient ~g are between
10 2/s and.10 6/s on average ~or a reac~or o~ the type
indicated hereinbefore,
The acti~ity o~ a nuclide fission produck in the
primary circuit Or a pressurized water reactor can there-
~ore be represented by an expression of the formo
Ai = F(n, T, ~g)
For a can fracture or fractures having identical
: characteriskics the ratio of the acti~ikies o~ two nuclldes~
4i and Aj is independent o~ the number o~ fractures5 gi~-
ing;
R - Ai/Aj = F'~T~ ~g)
The dekermination o~ the temperature and size o~
the can frackure or fractures in a reactor core can there-
~ore easily be carried out by studying the nuclide activi~y
., :
. ... . . .
--7--
ratios on knowing both the functions F' (T3 ~g) and the
value of one o* the parameters T or ~g. In the general
case this is not so, but the Applicant has ~ound, this
constituting an unexpected and interestin~ result, that by
especially choosing the pairs of nuclides used for ~orming
the activity ratios it was possible to determine in this
way pairs, whose ac~ivity ratlos (which can easily be
measured) are more particularly dependent on ~g or the
temperature.
As the functions F' (T, ~g) can now be cal- ~;
culated by computer using special known programmes it is
merely a question o~ solving equations with a single
unknownJ making it posslble to successively calculate the
parameters T, ~g and n.
This novel and ~ery important finding has made
it possible to develop a method ~or the determination o~
the characteristics of the breaks or fractures of cans for
- fuel elements of nuclear reactors, which is characterised
by the following succession of operations:
by calculating for given characteristics o~ the
reactor core and for the burn-up o~ its fuel elements lt
is possible to determine:
a) a series of first nomograms ~iving~ ~or a
certain ~umber of nuclides, their total activity in the prim-
ary coolant as a function o~ the average temperature of
the cracked fuel element for a ~racture state of the cans
. ~
. arbitrarily defined by a single ~racture~ each nomogram of
' '
360
said series bein~ es~ablished ~or a particular value o*
the coe~ficient ~g;
b) a second nomogram giving, for dif~er~nt
values Or the coe~icient ~g and as a ~unction Or the
average temperature o~ khe cracked fuel element~ the act-
ivity ratios o~ the differen~ nuclides taken in pairs in
such a way as to show two groups of ratios, namely ratio.s
of a ~irst group whichJ ln a ~irst approximation, are
independent o~ the temperature and ratios o~ a second group,
which vary in an increasing manner as a ~unction o~ khe
temperature;
c) a third nomogram, derived ~rom activity
ratios Or the first group, giving for said sarae ratios of
the first group the variations o~ the coer~lcient ~ g as a
~unction o~ khe actual activity ratio;
from the values o~ the activity ratios o~
nuclides o~ the first ~roup measured in ~he primary coolant
o~ the reactor and tr2nsrerred to the third nomo~ram i'c ls
possible to determine a mean value of the ¢oefficient ~g,
from the values of the activity ratios o~ nuclides
o~ the second group measured in the primary coolant o~ the
reactor and transferred at the same time as the previously
found value of coef~icient ~ g to the second nomogram it
is possible to determine a mean value o~ the cracked ~uel
element temperature;
~ rom the measured activities for a certain number
of nuclides present in the primar~ coolant and trans~erred
.
~ ' ' ,, 'I
. - . - . - . . . . . . .
~3~
_g_
at the same time as the above mentioned temperature to
the nomogram of the first series corresponding to ~he
coe~icient ~g obtained it is possible to determine the
true number of cracks.
The Applicant has been able to demonstrate that
certain activity ratios of nuclicle rission products con-
tained in the primary cooling water o~ a nuclear reactor
essentially onl~ depend on one parameter, namely the value
of ~g representing the average gravity o~ the cracks. As
it is now standard practice to be able to determine by cal-
culation using existing programmes the nomograms represent-
ing the ~unctions R = F'(T, ~g)~ when said ~unction is
dependent on more than only a single yariablQ it is readily
apparent that it is possible to determine this variable by
moving the values read on the theoretically established
nomograms closer to the values ef~ectively determined by
spectrometric measurement on the reactor coolant. Such
programmes make it possible to simulate b~ a co.~puter the
appearance in the reactor coolant fluid of a ~ission prod-
uct activity ~ollowin~ a can fracture and are more partic-
ularly known under the name PROFIP ~ and have been covered
by the ~ollowing publication : Third cycle thesis,
University o~ Parls, Faculty o~ Sciences~ Orsay (Paris XI),
June 1978 "Study o~ the contamination o~ the primary circuit
o~ pressurized water reactors" by J. M. GOMIT.
It is there~ore apparent that the realisation of
the method according to the invention calls ~or the prior
,'~
!~
3~3~ iO
10 -
calculation o~ three dir~erent nomograms by means o~ a
programme simulating the migration phenomena of fissio~
products resulting ~rom the fracture of cans in the coolant
o~ the nuclear reactor, as well E~S the experimental measure-
ment by per se known gamma spectrometric methods o~ acertain number o~ activtty ratios o~ nuclides present in
the primary coolan~ as a result of can fractureJ
Thus, ~he realisatlon of the me~hod according to
the invention leads to the step by step determinatlon of
the average value of coe~ficient ~g~ the average value T
of the temperature of the rods at the location of the cracks
and of the probable number n of actual cracks. At this
stage it is pointed out that the di~erent values deter-
mined are only in actual fact mean values, because the
measurements are made on khe primary coolant ~rom all the
rods of the reactor core and it is necessary to interpret
the signl~icance in t'ne manner indicated hereinafter.
The mean value o~ the coefficient ~g is charact-
eristic of the average gravityof cracks in cans throughou~
the presently considered reackor core. This coefficlent
approximately represents the total surface area of cracks
existing in the core divided by the numher thereo~. The
means temperature o~ the cracks must be considered as the ~-
mean value of the true temperatures in the axis of each of
the different rods which have suffered from cracking.
The average number of cracks n which is finally obtained
is derived from the mean value o~ a certain number o~
'
:.. . .
'
~.34~;0
activity ratlos compared with a nomogram calculated in
the hypothesis of one crack. The number n obtained in
this way represents the probable number Or true cracks,
taking account of the hypothesis of the identity Or gravity
of the various cracks, said hypothesis leading to a part-
icular value of the coe~icient ~ g.
The final determination o~ the three character-
istics ~)g, T and n can be carried out, hS desired, either
manually, or ~ithin the scope o~ the complete automation o~
the method, using computers and thus permitting the oontin-
uous monitoring of the reactor,
According to the invention two di~ferent categor-
ies of nuclide pairs are used ~or carrying out the measure-
ments. The first group of nuclide pairs gives activity
ratios which are substantially independent o~ the temper-
ature o~ the cracks and is obtained by associating the
nuclides in pairs in a ~raction, whose first term cor-
responds to a nuclide, whose period is below ten hours and
whose second term corresponds to a nuclide, whose period
is between three minutes and the period o~ the nuclide o~
the first term. Preferably the best results are
obtained when the two nuclides o~ the ~irst group have a
maximum period variation. On referring ~o the above-
mentioned Table of the main ~ission products and their
periods it can he seen that a large number o~ nuclide
pairs can be used ~or constituting pairs o~ the first
group. However, it is advantageous to use in the
, :
:,
-12-
denominator o~ the ~raction 135 xenon, whose period is
9.17 hours, associated with in the numerakor one o~ ~he
nuclides chosen from among 138 xenon (14.1 minutes), 87
krypton (76.3 minutes) and 138 cesium (~2.2 minutes). It
is also possible to use 89 krypton (3.18 minutes) or 137
xenon (3.83 minutes) ~or the numerator o~ the frackion,
which would be in accordance with the definition. For
a chosen pair of nuclides it is obviously possible to use
inverses of the above ratios, by lnverting the numerator
and the denominator.
For the purpose of determining the nuclides
which can be associated in pairs for constituting activity
ratios o~ the second groupJ i.e. incPeasing the temperature,
it is necessary to associate the nuclides in pairs in a
fraction, whose ~irst term corresponds to a nuclide having
a period below 10 hours and whose second term corresponds
to a nuclide havin~ a period above 24 hours. As an
example 1~5 xenon (9.17 hours) is frequently used in the
denominator o~ the fraction o~ the activity ratio and 133
xenon (5.29 days) or for example 1~3 m ~enon (2.2 days) or
131 iodine (8.o4 days) in the numerator. Obviously
these combinations are given in an in~ormative and in no
wa~ limitative manner~ the optimum conditions being defined
in the manner described hereinbe~ore. As previously
stated with regard to the first group it is possible to use
inverses o~ the above ratios~ by inverting the numerator
and the denominator.
.~ " .
3 ~
-13-
Finally the present lnvention relates to a
method for the determinatlon o~ characteristics Or fract-
ures o~ cans ~or fuel elements o~ nuclear reactors by
means of values o~ the ratio R/B for a certain number o~
nuclides present in the cooling ~luid and in which:
R is the number o~ atoms Or such a nuclide
released every second into the primary ~luid by
the operating reactor core;
B is the calculated number o~ atoms o~ the same
nuclide which are theoretically produced every
second,
wherein ~or detecting the appearance o~ a crack the differ-
ent values of the ra~io R/B determined in this way are
placed on a ~raph in cartesian coordinates as a function
of the decay constant ~ o~ each nuclide represented in
the abscissa and wherein the satisfactory alignment on a
single horizontal line of the different points obtained in
this way is monitored, any discontinuance o~ said alignment
being characteristic of the appearance o~ at least one
crack.
Th`e method is particularly simple because it is
merely necessary to take into consideration a small number
o~ nuclides, for e~ample ten, in order to be able to
obtain a graphically satis~actory result and to determine
the true ack~vit~ released every second into the prlmary
cooling ~luid.
By forming the ratio R/B of said number o~ atoms
.
.
. . , ,
.' ' ''' . ' ' " ~ ' ' ' ' ,' ~,~.. ' '
. ' . : ~' ~ '. ' '
` ~34~t;0
released per second with the number o~ atoms produced per
second and theoretically calculated for the same nuclide,
obviously taking account of the reactor operating power,
a certain number of points theoretically shown to be
located on the same horizontal l:lne when there is no can
fracture is obtained on a graph as a function o~ ~ . It
is therefore merely necessary to periodically trace this
graph and check the alignment of the various points,
allowing for measuring errors, whereby the discontinuance
o~ this alignment is characteristic of the appearance of a
~ault. I~ this first part of the diagnosis proves
positive and such a fault is in fact detected, the method
according to the invention then makes it possible to check
the ~raature revealed in the ~ollowing manner.
BRIEF DESCRIPTION OF THE DRAWINGS -
The invention will be better understood from
the ~ollowing description of a number of examples o~ the
detection and determinatlon of characteris~ics o~ fractures
in cans for fuel elements of a PWR-type nuclear reactor,
said description being provided in an illustrative and
non-limitative manner, with reference to the attached
drawings:
Fig. 1 which illustrates the method ~or the detection
of can ~racturesJ shows for a certain number o~
nuclides the activity ratio R/B as a function of
the decay constant ~ o~ each of these expressed
in seconds~l.
- ~34~60
--15 -
Fig. 2 shows an example Or the calculation o~ the
rir~t nomogram giving, for. a gi.ve~ coefficient
~g and as a ~unction o~ the temperature, the
total activity in curies/konne o~ primary cooling
water o~ a reactor ~or dif~erent radioactive
~isq~on products resulting ~rom a single can
~racture.
Fig. 3 shows an example of a second nomogram on which
the ratio of the ac~ivities o~ nuclides o~ the
~irst and second groups is plotted as a ~unckion
o~ the temperature in C ~or di~erent values o~
coer~icient ~g.
Fig. 4 shows an example o~ a third nomogram plotted for
three particular activity ratios o~ the ~irs~
group of Fig. ~ and giving values of Vg as a
~unction o~ the activity ratio.
DETAILED DESCRIPTION OF THE_P~EFE M ED EMBODIMEMTS
. Fig.- 1 relates to the Fes~enheim reactor 1, which
at the tlme when the ourve was plotted was operating at a
20 power of 2650 MW thermal. The ratio R/B, defined as .
hereinbe~ore by the ratio of the number Or atoms of each
fission nuclide released per second i~to the liquid, rel-
ative to the calculated number o~ akoms of the same
nuclide theore~ically produced per second, is plotted in
logarithmic scale on the ordina~e as a ~unction o~ the
radioactive decay constant ~ expressed in second 1 and
~ . plotted in logarithmic s¢ale on the abscissa. Twelve .
: ~ .
, ' ~ ' ' ' .,
r ~ ~ :
~L~3~
radioactive ~ission nuclldes were examined and were used
~or determining the twelve corresponding points on the
curve. In the order o~ rising abscissas it ls possible
to see iodine 131, xenon 1~3, 135 m xenon, iodine 133,
xenon 1~5~ iodine 135~ 85 m kr~ptonJ 88 krypton, iodine 132
87 krypton, iodine 1~4 and xenon 138. As can be seen
from the ~raph the dif~erent points, naturally allowing
~or measuring errors~ are distributed over two curves 1
and 2 which are separate and therefore dir~er ~rom a single
horiæontal line. This simple ~indin~ gives the cextainty
that at this time there is already at least one crack in
the rods constituting the reactor core. For the purpose
o~ additional explanakion the portion of the horizontal line
correspondlng to the contamination level prior to can
~racture is plotted in dotted lines under the re~erence 2a.
With reference to Figs. 2 to 4 we will now des-
cribe in a complete manner a study o~ the can ~ractures, in
- the manner in which it was carried out in practice on the
pressurized water reactor o~ the Tihan~e nuclear power
station in 197g.
Fig. 2 shows a first nomogram (with the meaning
given to this term in the present text) calculated on the
computer by means o~ the PROFIP ~ programme on the basis
of the following hypotheses: the leakage factor ~ g o~
the cracked cans was fixed at 10 2/s in the case o~ a
sin~le can ~racture. Moreover the calculation was made
on the basis Or a fuel element specific burn-up o~
.
, ~
' . ` " . ~ ' . . , ,,~' ' . ;. '.' ' ' , . ' ,, ,,, ', , ' :
' ';
~ 3 ~3
12,000 M~IJ/T .
Thus, the activity in curie/konne of water was
calculated in the prlmary water of the reactor ror seven
fission product nuclldes, namely the three xenons 133, 135
and 138, three kryptons 85 m, 87 and 88 and cesium 138, as
a ~unction of the de~ec~i~e rod temperature in C. The
ordinates are in logarithmic scale and ~he abscissas ln
linear scale.
Fig. 3 shows a second nomogram also calculated
for a speci~ic burn-up of 12,000 MWJ/T. It shows the
evolution of the activlky ratios of fission product nuclides
plotted on the ordinate in logarithmic scale, as a ~unction
o~ khe average temperature o~ the cracked rods plokted in
linear scale on the abscissa. These ratios were made
for a certain number of values o~ coe~icien~ ~g varying
from 10 2/s ko 10 6/s. The value of Fi~. ~ is that ik
clearly shows the two groups o~ nuclide pairs, namely in
the lowe~ part of Fig. 3 the ratios of the rirst g-roup
~Jhich are substantially independent of the temperature and
in the upper part t~e activity ratios o~ the second group
(in solid lines), which signi~icantly and rapidly rise as
a function o~ the same temperature. In the example o~
Fig. 3 the rakios o~ the nuclides o~ the ~irst group are
three in allg namely 87 ~rypton/135 xenon, 138 xenon/135
xenon and 138 cesium/1~5 xenon. Only one pair was
studied in the second group, namely the ratio o~ 13~ xenon/
1~5 xenon.
t
~''"" .
34~60
-18 -
Fig. 4 g~ves khe results o~ pairs of nuclldes
o~ the first group o~ Fig. 3, in the form of a di~erenk
presentation~ corresponding to a nomogram o~ the third
type described hereinbe~ore. The value o~ the coe~fici-
ent ~g in second 1 is plotted in logarithmic scale on theordina~e and the ratio of the activities o~ each pair of
nuclides is plotted in logarikhmic scale on khe abscissa.
In Fig. 4 the temperature is absent, because by de~inition
it has no action on the activi~g rakios of nuclides of the
~ st group.
In practice ~or monitorlng ~ractures o~ cans the
third nomogram is used ~irst and ~he activity ratios o~
nuclides belonging to khe rirst group are measured. It
is then easy to deduce the average value ~g characteristlc
o~ the state o~ ~ractures Or cans in the core at the given
time, i.e. in practice khe ratio of the kotal sur~ace area
o~ the cracks to the number of cracks.
In the particular case of the calculation car-
ried ouk on the Tihange reactor a ~g oP the order of
10 2/s was found as the mean value through using this third
nomogram.
By then trans~erring this mean ~alue ~g to
ratios o~ ac~ivities o~ nuclides o~ the second group on
the second nomogram (Fig. 3) and by approximaking it to
the activity ratio measured by spectrometry in the primary
. .
water o~ the core for ~he ratio o~ nuclides 13~ xenon/135
xenon it is possible to determine the mean temperature o~
-
: ~
:
.,
i, .' . '. ', i : , ' ' ' ' ~ '
113~0
~-19- '
the cracked cans. ~his mean temperature was found to
be 1560 C in the case o~ the Tihange reackor.
By transferring the latter temperature value to
the ~irst nomogram of Fig. 2~ corresponding to a coe~ici-
ent Yg of 10 2/s and a single can fracture and a specificburn-up o~ 12~000 ~J/T it is possible to determine the
real number of can fractures by comparison wi~h the
measured value of the tokal activity in primary water for
each o~ the seven fission products on the first nomo~ram.
After taking account o~ the dif~erent possible errors
this determination led to an average number of cracks
n = 2.7 + 0.5.
The accura~e resul~s measured for the activity
of each nuclide appear in the att~ched Table corresponding
to measurements carried out during January 1978 in the
Tihange nuclear power station.
~ = 10-2 T = 1550
Nuclides Measured activiky PROF~P calc~lat- Galculated
(Ci/t3 lon for a single number of
can fracture fractures
133 Xe(7.52 + 2.04) 10 ~2.50 10~1 7.0 + o.8
173mXe(1.87 + 0.38j 10~16.78 10-3 2.8 + o.6
135 Xe(1.61 + O.l9j 10 15.77 1o~2 2.8 + 0.3
85mKr(3.o8 + 0.4~j 10-21.18 10-2 2.6 + 0.4
2587 Kr~.12 + 0.40j 10 21.87 10 2 2.2 + 0.2
88 Kr(6.04 + 0.76) 10-21.85 10 2 3.3 ~ o.4
At the end of the test cycle the reactor was
shutdown and the core was discharged and examined. It
~ ' '
~1~3~
-20-
was round that three fuel rods were damaged and one hand
in ~act lost its plug. The three rods were operating
at temperatures of about 1560 C, i.e. above the average
core temperature, taken in the axls of the rods~ where it
was about 1300 C.
., , . "
:
