2014 january1 xe-135 effects in reactor operation b. rouben mcmaster university ep 4p03/6p03 2014...

2014 January 1

Xe-135 Effects in Reactor Operation

B. Rouben

McMaster University

EP 4P03/6P03

2014 Jan-Apr

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.

2014 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 reach high concentration.

If, on the other hand, the fission-product half-life is long, the fission product will accumulate.

As many fission products absorb neutrons, their accumulation will affect the chain reaction – it will introduce negative reactivity and will contribute to the need to refuel.

2014 January 3

2014 January 4

Saturating fission products are fission products whose concentration does not accumulate without limit in a steady flux (i.e., at steady power), instead it: 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 to increase to infinity. 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 another fission product.

Saturating Fission Products

2014 January 5

135Xe is the most important saturating fission product because it has the largest reactivity effect: its neutron absorption represents about 30 mk (3%) off fission- neutron production – this is huge for a single fission product!

The effects of 135Xe are felt in steady-state operation but even more so in power manoeuvres.

There is no power manoeuvre which does not involve a xenon transient.

Xe-135

2014 January 6

135Xe 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.

135Xe and 135I

2014 January 7

I-135/Xe-135 Kinetics

Fissions

135Te 135I-(1/2=18 s)

135Xe-(1/2=6.585 h)

Burnout by neutron absorption

-(1/2=9.169 h)

Production of 135Xe by beta decay of 135I dominates over its direct production in fission.

2014 January 8

135Xe 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.

135Xe and 135I

2014 January 9

The large absorption cross section of 135Xe plays a significant role in the overall neutron balance and directly affects system reactivity, both in steady state and in transients.

It also influences the spatial power distribution in the reactor.

The limiting absorption rate at extremely high flux maximum steady-state reactivity load ~ ‑30 mk.

In CANDU, the equilibrium load at full power ~ ‑28 mk (see Figure)

135Xe and 135I (cont’d)

2014 January 10

[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

Equilibrium Xenon Load

2014 January 11

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!

Effects of 135Xe on Power Distribution

2014 January 12

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.

Effect of Power Changes on 135Xe Concentration

2014 January 13

Xenon Reactivity Transients Following Setback to

Various Power Levels

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!

2014 January 14



2014 January 15



2014 January 16

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.

2014 January 17

Xenon Reactivity Transients Following

a Shutdown from Full Power

2014 January 18


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.

2014 January 19


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.

2014 January 20

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).

Effect of Power Changes on 135Xe Concentration

2014 January 21

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 days than immediately later – the effect may range up to ~10% on bundle power, and ~5% on channel power.

Saturating-Fission-Product-Free Fuel

2014 January 22 [from D. Rozon, Nuclear Reactor Kinetics, loc.cit.]

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

2014 January 23

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

Xenon Oscillations

2014 January 24

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

Xenon Oscillations (cont’d)

2014 January 25

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


2014 January 26

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)!


2014 January 27

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

2014 January 28

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:

Idt

dIIfI

XXIdt

dXXXfXI

2014 January 29

Steady State

In steady state the derivatives are zero:

0 IIfI

0 XXI XXfXI

2014 January 30

Steady State (label results with ss)

Solve the 1st equation for I:

Substitute this in the 2nd equation

Now solve this for X (ss):

I

fIssI

)(

fXfIXX XX

XX

fXIssX

)(

2014 January 31

Steady State – Final Equations

We see that the steady-state I-135 concentration is directly proportional to the flux value

Whereas

X is not proportional to the flux. In the limit where goes to infinity,

I

fIssI

)(

XX

fXIssX

)(

X

fXIfluxhighveryssX

),(

2014 January 32

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

2014 January 33

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

Therefore at steady-state full power the Xe-135 comes very predominantly (96%) from I-135 decay rather than directly from fission!

13812131,

13931415,

.10*44.310*0.7*002.0*00246.0

.10*93.810*06.3*10*92.2

scmscmcm

scmcmsI

fpssfX

fpssI

2014 January 34

Values at Steady State

Also at steady-state full power

Therefore, at steady-state full power, the Xe-135 disappears very predominantly (91%) from burnout (by neutron absorption) rather than from decay!

139

1213313218,,

13831315,

.10*48.8

.10*0.7*10*79.3*10*2.3

.10*95.710*78.3*10*1.2

scm

scmcmcmX

scmcmsX

fpssfpssX

fpssX

2014 January 35

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

powerfullatsaturatedisXetheei

XX

findwepowerfullatvaluestatesteadythewiththisComparing

cmnuclides

X

ssfpss

X

fXIss

%92135,.

*92.0

,

.10*11.410*2.3

002.0*00246.00638.0

,,

31318

,

2014 January 36

Xe-135 Load = Xe-135 Reactivity Effect

.28

.

3003.01

1,03.01*004.0

10*79.3*10*2.3

,1

:

**

,

.2

'.

135.,sec135

,

2

,,

1318

,

,

2

,2,

2

,2

211

212

2

,2,

2,2

211

21

2

,2

2

mkisvalueaccuratemoreA

estimateanisThis

mkk

k

kandk

XandkreactorcriticalafromStarting

kkformsimilarahavewouldkinchangeThe

kk

tochangetheapplyweIf

kforformulagroup

therecallingbyeffectreactivitysxenontheofestimateangetcanWeXis

oncontributiXeThetioncrossabsorptionthermalthemostlyaffectsXe

fpX

eff

Xeff

efffpXXeff

fpsseff

effa

XaXeffeff

a

Xa

af

a

XaX

aXa

aa

f

XXa

a

2014 January 37

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:

The instantaneous Xe-135 concentration X would of course have to be determined, say by solving the differential Xe-135/I-135 kinetics equations.

313,

,, 10*79.3

*28*28* cm

Xmk

X

Xmk

X

X

fpssfpX

fpssX

2014 January 38

“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:

mkX

LoadXeAdditionalorExcess

fpXX

110*79.3

*28

135""

13,

2014 January 39

END

2014 january1 xe-135 effects in reactor operation b. rouben mcmaster university ep 4p03/6p03 2014...

Documents