Importance of Xe-135 in Reactor Operation
B. Rouben
McMaster University
EP 4P03/6P03
2015 Jan-Apr
2015 January
1
Fission Products



Fission products are the large nuclides (about
half the size of uranium) which are created in
fission.
There are hundreds of different fission products.
Most of them are radioactive and decay by
various modes (mostly , , , etc.) and with
various half-lives.
2015 January
2
Fission Products (cont’d)



If the fission-product half-life is very short
(much shorter than the residence time of the fuel
in the reactor), the fission product decays
quickly and it does not accumulate a lot.
If, on the other hand, the fission-product halflife is long, the fission product will accumulate.
Many fission products absorb neutrons, so their
accumulation will be a growing negative
reactivity effect. This is one of the contributing
factors to the eventual need to refuel.
2015 January
3
Saturating Fission Products

Saturating fission products are fission products whose
concentration does not accumulate without limit in a
steady flux (i.e., at steady power). Instead, their
concentration:
 comes to an equilibrium, steady value which depends
on the flux level, and
 comes to an asymptotic, finite limit even as the value
of the steady flux is assumed greater and greater.

The most important saturating fission product is 135Xe,
but other examples are 103Rh, 149Sm and 151Sm. In each
case the nuclide is a direct fission product, but is also
produced by the -decay of a “partner” fission product.
2015 January
4
Xe-135


135Xe
is the most important saturating fission
product because it has a high neutron-absorption
cross section.
At full CANDU power its
reactivity effect is about -28 mk: a huge negative
effect for a single fission product!
This is the value at normal power. But the 135Xe
effect can be magnified significantly in power
manoeuvres, because there is no power
manoeuvre which does not involve a xenon
transient.
2015 January
5
135Xe
and 135I
 135

Xe is produced directly in fission, but mostly
from the beta decay of its precursor 135I (half-life
6.585 hours).
It is destroyed in two ways:



By its own radioactive decay (half-life 9.169 hours),
and
By neutron absorption to 136Xe.
See Figure “135Xe/135I Kinetics” in next slide.
2015 January
6
I-135/Xe-135 Kinetics
135Te
-(1/2=18 s)
135I
-(1/2=9.169 h)
-(1/2=6.585 h)
Fissions
135Xe
Burnout by neutron
absorption
In steady state these processes equilibrate to steady values for
the 135Xe and 135I concentrations.
2015 January
7
135Xe
and 135I
 135



Xe has a very important role in the reactor
It has a very large thermal-neutron absorption
cross section
It is a considerable load on the chain reaction
Its concentration has an impact on power
distribution, but in turn is affected by the power
distribution, by movement of reactivity devices,
and significantly by changes in power.
2015 January
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135Xe



and 135I (cont’d)
The limiting 135Xe concentration rate at extremely
high flux  maximum steady-state reactivity
load ~ -30 mk.
In CANDU, the equilibrium load at full power
~ -28 mk (see Figure).
At steady-state full power, production of 135Xe by
beta decay of 135I dominates over its direct
production in fission.
2015 January
9
Equilibrium Xenon Load
[from Nuclear Reactor Kinetics, by D. Rozon, Polytechnic International Press, 1998]
The numbers on the horizontal axis can also be taken as relative rather than absolute numbers,
i.e., higher-power regions or fuel bundles on the right, lower-power on the left
2015 January
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Effects of 135Xe on Power Distribution



High-power bundles have a higher xenon load,
therefore a lower local reactivity  xenon
flattens the power distribution
In steady state, 135Xe reduces maximum bundle
and channel powers by ~ 5% and 3% respectively.
This “natural” flattening by 135Xe helps to comply
with maximum licensed channel and bundle
powers!
2015 January
11
Effect of Power Changes on 135Xe Concentration

When power is reduced from a steady level:




The burnout rate of 135Xe is decreased in the reduced flux, but
135Xe is still produced by the decay of the 135I inventory
 the 135Xe concentration increases at first
But the 135I production rate is decreased in the lower
flux, therefore the 135I inventory starts to decrease
The 135I decay rate decreases correspondingly
 the 135Xe concentration reaches a peak, then starts to
decrease - see Figure.
The net result is that there is an initial decrease in core
reactivity; the reactivity starts to turn around after the
xenon reaches its peak.
2015 January
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Xenon Reactivity Transients Following Setback to
Various Power Levels
Xe Reactivity (mk) vs. Time (h):
Step Change from FP to 80% FP
0
10
20
30
40
50
60
70
80
90
100
110
120
130
-27.0
-28.0
-29.0
-30.0
-31.0
-32.0
-33.0
Note: In this & following graphs, power is assumed to be maintained at the new
level, i.e., the overall system reactivity must be maintained at 0 following the
power reduction!
2015 January
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Xenon Reactivity Transients Following Setback to
Various Power Levels
Xe Reactivity (mk) vs. Time (h):
Step Change from FP to 60% FP
0
10
20
30
40
50
60
70
80
90
100
110
120
130
140
-2.600E+01
-2.800E+01
-3.000E+01
-3.200E+01
-3.400E+01
-3.600E+01
-3.800E+01
-4.000E+01
2015 January
14
Xenon Reactivity Transients Following Setback to
Various Power Levels
Xe Reactivity (mk) vs. Time (h):
Step Change from FP to 40% FP
0
10
20
30
40
50
60
70
80
90
100
110
120
130
-22.0
-27.0
-32.0
-37.0
-42.0
-47.0
-52.0
2015 January
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Xenon Transient Following a Shutdown



A reactor shutdown presents the same scenario in an
extreme version: there is a very large initial increase
in 135Xe concentration and decrease in core
reactivity.
If the reactor is required to be started up shortly after
shutdown, extra positive reactivity must be supplied,
if possible, by the Reactor Regulating System.
The 135Xe growth and decay following a shutdown in
a typical CANDU is shown in the next Figure.
2015 January
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Xenon Reactivity Transients Following
a Shutdown from Full Power
2015 January
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Xenon Transient Following a Shutdown



It can be seen that, at about 10 hours after shutdown,
the (negative) reactivity worth of 135Xe has increased
to several times its equilibrium full-power value.
At ~35-40 hours the 135Xe has decayed back to its
pre-shutdown level.
If it were not possible to add positive reactivity
during this period, every shutdown would necessarily
last some 40 hours, when the reactor would again
reach criticality.
2015 January
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Xenon Transient Following a Shutdown



To achieve xenon “override” and permit power
recovery following a shutdown (or reduction in reactor
power), positive reactivity must be supplied to
“override” xenon growth; e.g., the adjuster rods can be
withdrawn to provide positive reactivity.
It is not possible to provide “complete” xenon
override capability; this would require > 100 mk of
positive reactivity!
The CANDU-6 adjuster rods provide approximately
15 milli-k of reactivity, which is sufficient for about
30 minutes of xenon override following a shutdown.
2015 January
19
Effect of Power Changes on 135Xe Concentration


Conversely to the situation in a power reduction,
when power is increased the 135Xe concentration
will first decrease, and then go through a
minimum.
Then it will rise again to a new saturated level (if
power is held constant at the reduced value).
2015 January
20
Saturating-Fission-Product-Free Fuel



In fresh bundles entering reactor, 135Xe and other
saturating fission products will build up (see
Figure).
The reactivity of fresh bundles drops in the first
few days, as saturating fission products build in.
“Saturating-fission-product-free fuel” will have
higher power for the first hours and couple of
days than afterwards – the effect may range up to
~10% on bundle power, and ~5% on channel
power.
2015 January
21
Build-up of 135Xe in Fresh Fuel
When fresh fuel is inserted in the reactor, it takes 1-2 days
for the xenon level to reach its equilibrium value
2015 January
[from D. Rozon, Nuclear Reactor Kinetics, loc.cit.]
22
Xenon Oscillations




Xenon oscillations are an extremely important scenario
to guard against in reactor design and operation.
Imagine that power rises in part of the reactor (say one
half), but the regulating system keeps the total power
constant (as its mandate normally requires).
Therefore the power must decrease in the other half of
the reactor.
The changes in power in different directions in the two
halves of the reactor will set off changes in 135Xe
concentration, but in different directions, in the two
reactor halves.
cont’d
2015 January
23
Xenon Oscillations (cont’d)




The 135Xe concentration will increase in the
reactor half where the power is decreasing.
It will decrease in the half where the power is
increasing.
These changes will induce positive-feedback
reactivity changes (why?).
Thus, the Xe and power changes will be
amplified (at first) by this positive feedback!
cont’d
2015 January
24
Xenon Oscillations (cont’d)




If not controlled, the effects will reverse after many
hours (just as we have seen in the xenon transients in the
earlier slides).
Xenon oscillations may ensue, with a period
of ~20-30 h.
These may be growing oscillations – the amplitude will
increase!
Xenon oscillations are not hypothetical, they can be set
off by regional perturbations, for example in CANDU
the routine refuelling of a channel – such perturbations
occur every day in CANDU reactors.
cont’d
2015 January
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Xenon Oscillations (cont’d)



Large reactors, at high power (where 135Xe
reactivity is important) are unstable with respect
to xenon!
This is exacerbated in cores which are more
decoupled (as in CANDU).
It’s the zone controllers which dampen/remove
these oscillations – that’s one of their big jobs
(spatial control)!
2015 January
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The Equations for I-135/Xe-135 Kinetics






First, define symbols:
Let I and X be the I-135 and Xe-135
concentrations in the fuel.
Let I and X be the I-135 and Xe-135
decay constants, and
Let I and X be their direct yields in fission
Let X be the Xe-135 miscroscopic
absorption cross section
Let  be the neutron flux in the fuel, and
Let f be the fuel fission cross section
2015 January
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Differential Equations for Production and Removal


I-135 has 1 way to be produced, and 1 way to
disappear, whereas Xe-135 has 2 ways to be
produced, and 2 way to disappear
The differential equations for the production and
removal vs. time t can then be written as follows:
dI
  I  f   I I
dt
dX
  I I   X  f    X X   X X
dt
2015 January
28
Steady State

In steady state the derivatives are zero:
 I  f   I I  0
I I   X  f   X X  X X  0
2015 January
29
Steady State (label results with ss)

Solve the 1st equation for I:
 I f
I ( ss ) 
I

Substitute this in the 2nd equation
X X  X X  I  f    X  f 

Now solve this for X (ss):
X ( ss ) 
2015 January
 I   X  f 
X   X 
30
Steady State – Final Equations
 I f
I ( ss ) 
I


We see that the steady-state I-135 concentration is directly
proportional to the flux value
Whereas
X ( ss ) 

 I   X  f 
X   X 
X is not proportional to the flux. In the limit where  goes
to infinity,
X ( ss, very high flux) 
2015 January
 I   X  f
X
31
Typical Values






Typical values of the parameters, which could
be used in the equations (values depend on fuel
burnup):
I-135 half-life = 6.585 h  I = 2.92*10-5 s-1
Xe-135 half-life = 9.169 h  X = 2.10*10-5 s-1
I = 0.0638 , X = 0.00246 (these depend on the
fuel burnup, because the yields from U-235 and
Pu-239 fission are quite different)
X = 3.20*10-18 cm2 [that’s 3.2 million barns!]
f = 0.002 cm-1, and
For full-power,  = 7.00*1013 n.cm-2s-1
2015 January
32
Values at Steady State




If we substitute these numbers into the equations, we
find that at steady-state full power:
Iss,fp = 3.06*1014 nuclides.cm-3
Xss,fp = 3.79*1013 nuclides.cm-3
With these values we note that at steady-state full power
I I ss , fp  2.92 *105 s 1 * 3.06 *1014 cm3  8.93*109 cm3.s 1
 X  f ss , fp  0.00246* 0.002cm1 * 7.0 *1013 cm2 s 1  3.44 *108 cm3.s 1

Therefore at steady-state full power the Xe-135 comes
very predominantly (96%) from I-135 decay rather than
directly from fission!
2015 January
33
Values at Steady State

Also at steady-state full power
X X ss , fp  2.1 *105 s 1 * 3.78*1013 cm3  7.95*108 cm3.s 1
 X X ss , fpss , fp  3.2 *1018 cm2 * 3.79 *1013 cm3 * 7.0 *1013 cm2 .s 1
 8.48*109 cm3.s 1

Therefore, at steady-state full power, the Xe-135
disappears very predominantly (91%) from burnout
(by neutron absorption) rather than from  decay!
2015 January
34
Values at Steady State with Very High Flux

In the limit where ss is very large (goes to infinity), we
find from the equation for the steady-state
X ss ,  

 I   X  f
X
0.0638 0.00246* 0.002  4.11*1013 nuclides.cm3
3.2 *1018
Com paringthis with the steady  state value at full power, we find
X ss , fp  0.92* X ss , 
i.e, the Xe  135 is 92% saturated at full power
2015 January
35
Xe-135 Load = Xe-135 Reactivity Effect
Xe  135 affects m ostly the therm alabsorptioncross sec tion,  a 2 . The Xe  135 contribution
is a 2, X   X X . We can get an estim ate of the xenon' s reactivity effect by recalling the
2  group form ula for k 
 f
a2
12
.
 a1  12
If we apply the changea 2, X to  a 2 ,
k , X  
a 2, X
 a 2 2
a 2, X
12
* f

* k
 a1 12
a2
The changein keff would have a sim ilar form : keff , X  
Starting from a critical reactor keff  1, and X ss , fp 
a 2, X
a2
keff

3.2 *1018 * 3.79*1013
1
keff , X  
*1  0.03, and  X , fp  1 
 k
0.004
eff

This is an estim ate.
A m ore accurate value is  X , fp  28 m k.
2015 January
 keff , X

 0.03  30 m k
2

k
eff

36
Xe-135 Load in Various Conditions


The most accurate value for the steady-state Xe-135 load
in CANDU at full power is X,fp = -28 mk
In any other condition, when the Xe-135 concentration
is different from the steady-state full-power value (e.g.,
in a transient), we can determine the Xe-135 load by
using the ratio of the instantaneous value of X to Xss,fp:
X 

X
X ss , fp
*  X , fp  28 m k *
X
X ss , fp
 28 m k *
X
3.79*1013 cm3
The instantaneous Xe-135 concentration X would of
course have to be determined, say by solving the
differential Xe-135/I-135 kinetics equations.
2015 January
37
“Excess” Xe-135 Load

We may sometimes like to quote not the absolute
Xe-135 load, but instead the “excess” xenon load,
i.e., the difference from its reference steady-state
value (-28 mk),
Using the last equation in the previous slide:
Excess or "Additional" Xe  135 Load
  X   X , fp
2015 January
X


  28* 

1
 mk
13
 3.79*10

38
END
2015 January
39