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Xenon Effects. B. Rouben McMaster University EP 4D03/6D03 Nuclear Reactor Analysis 2008 Sept-Dec. Contents. We study the importance of Xe-135 in the operation of nuclear reactors. Effects of Xenon Poison.
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Xenon Effects B. Rouben McMaster University EP 4D03/6D03 Nuclear Reactor Analysis 2008 Sept-Dec
Contents • We study the importance of Xe-135 in the operation of nuclear reactors.
Effects of Xenon Poison • Saturating fission products are fission products whose concentration in fuel operating in a steady flux (i.e., at steady power): • 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.
135Xe and 135I • 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.
I-135/Xe-135 Kinetics Production of 135Xe by beta decay of 135I dominates over its direct production in fission. -(1/2=18 s) -(1/2=9.169 h) 135Te 135I -(1/2=6.585 h) 135Xe Fissions Burnout by neutron absorption
135Xe and 135I • 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 (cont’d) • 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)
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 Iand Xbe the I-135 and Xe-135 decay constants, and • Let Iand Xbe their direct yields in fission • Let X be the Xe-135 microscopic absorption cross section • Let be the neutron flux in the fuel, and • Let f be the fuel fission cross section
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 ways to disappear • The differential equations for the production and removal vs. time t can then be written as follows:
Interactive Discussion/Exercise • Write the Xe and I equations for steady state, and solve them. • Do not turn the page until you have attempted/done this discussion/exercise.
Steady State – Use Subscript ss • In steady state the derivatives are zero:
Steady State • Solve Eq. (3) for steady-state I-135 concentration Iss: • Substitute this in Eq. (4): • Now solve this for steady-state Xe-135 concentration Xss:
Interactive Discussion/Exercise • What is the difference in character between the equations for the Xe and I steady-state concentrations? • Do not turn the page until you have attempted/done this discussion/exercise.
Steady State – Final Equations • The steady-state I-135 concentration is directly proportional to the flux value • Whereas • Xss is not proportional to the flux, in fact it saturates in high flux: • In the limit where goes to infinity:
Typical Values Typical values of the parameters: • 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 (X depends on the fuel burnup, because the Xe-135 yields from U-235 and Pu-239 fission are quite different) • X = 3.20*10-18 cm2 [that’s 3.2 million barns!] [X depends on temperature] • f = 0.002 cm-1, and • For full power in CANDU, ss,fp = 7.00*1013 n.cm-2s-1
Interactive Discussion/Exercise • Calculate the steady-state Xe and I concentrations at full power • Work out the relative rates of production of Xe from fission and I decay, and • the relative rates of Xe disappearance by decay and burnout. • Do not turn the page until you have attempted/done this discussion/exercise.
Values at Steady State • If we substitute these numbers into Eqs. (5) and (6), we find that at steady-state full power: • Iss,fp = 3.06*1014 nuclides.cm-3 (8) • Xss,fp= 3.79*1013 nuclides.cm-3 (9) • 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!
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!
Values at Steady State with Very High Flux • In the limit where ss is very large (goes to infinity), we find from Eq.(7)
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 (12) • 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 (1)-(2).
“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 Eq.(13) in the previous slide:
Equilibrium Xenon Load Figure Credit: “Nuclear Reactor Kinetics”, by D. Rozon, Polytechnic International Press, 1998
Effects of 135Xe on Power Distribution • High-power bundles have a higher Xe-135 concentration, i.e., 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.
Saturating-Fission-Product-Free Fuel • In fresh bundles entering the reactor, 135Xe and other saturating fission products will build up (see Figure). • The reactivity of fresh bundlesdrops in the first few days,assaturating fission products build in. • “Saturating-fission-product-free fuel” will have higher power for the first hours and days than immediately later – the effectmay range up to ~10% on bundle power, and ~5% on channel power.
Build-up of 135Xe in Fresh Fuel Figure Credit: “Nuclear Reactor Kinetics”, by D. Rozon, Polytechnic International Press, 1998
Saturating-Fission-Product-Free Fuel • For an accurate assessment of powers after refuelling, calculations of the nuclear properties need to be performed at close intervals (a few hours) to capture the build-up of saturaring fission products, or else a “phenomenological” correction of the properties offresh bundles needs to be made.
Effect of Power Decrease on 135Xe Concentration • The Xe-135 concentration changes significantly in power changes, and this has very strong effects on the system reactivity. • 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 135I the 135Xeconcentration 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.
Xenon Reactivity Transients Following Setback to Various Power Levels
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.
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.
Xenon Override • 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.
Case of Power Increase • 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). • However, one point to remember is that Xe-135 changes following power changes provide positive feedback. • Large reactors may be unstable with respect to xenon changes above a certain power level.
Solution of Xe-I Kinetics After a Shutdown • The differential equations for Xe-135/I-135 kinetics are: • In a transient (non-steady-state) situation, these equations can be numerically integrated to find the evolution of I and X, starting from known initial conditions I0 and X0.
Case of an Instantaneous Shutdown • If the reactor is subjected to an “instantaneous” shutdown, we can solve Eqs. (15) and (16) analytically. • If the flux 0 at t = 0, the terms containing disappear, and the equations simplify to: • The solution of Eq. (17) is immediate: I decays according to the exponential-decay law:
Instantaneous Shutdown – Solving for X • Eq.(18) for X becomes
Instantaneous Shutdown - Numerics • It will be left as an exercise to evaluate I and X, and the corresponding reactivity effect, for a time period following a reactor shutdown, using the initial conditions of a steady state at various powers.
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
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
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! • [Are xenon oscillations completely hypothetical, or can they really happen? What daily perturbation can set off such transients?] cont’d
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)!
