Xe-135 Effects in Reactor Operation B. Rouben McMaster University EP 4P03/6P03 2008 Jan-Apr
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)
Equilibrium Xenon Load [from Nuclear Reactor Kinetics, by D. Rozon, Polytechnic International Press, 1998]
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.
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 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 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 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.
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).
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 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 [from D. Rozon, Nuclear Reactor Kinetics, loc.cit.]
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.
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)!
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
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:
Steady State • In steady state the derivatives are zero:
Steady State (label results with ss) • Solve the 1st equation for I: • Substitute this in the 2nd equation • Now solve this for X (ss):
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,
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
Values at Steady State • If we substitute the numbers in the formulas, we get at full power: • I (ss, full power) = 3.06*1014 n.cm-3 • X (ss, full power) = 3.78*1013 n.cm-3 • [Note that II = 8.93*109» Xf = 3.44*108, so at full power the Xe-135 comes very predominantly from I-135 decay rather than directly from fission!] • In the limit where goes to infinity, X (ss, very high flux) = 4.14*1013 n.cm-3 X (ss, full power) = 0.914* X (ss, very high flux)
Xe-135 Load • By comparing the neutron absorption in Xe-135, XX, to the neutron production at full power, we can determine that Xe-135 load at full power = -28 mk. • In a transient, if we know the flux vs. time and the initial values of I and X, we can solve for X by (numerically) integrating the differential equations: e.g., X(t+t) = X(t) + (dX/dt)* t [e.g.,Use EXCEL] • Then, if we know X at any moment in a transient, we can determine the Xe-135 load by comparison to full-power values:
“Additional” Xe-135 Load • You will sometimes see the “additional” or “excess” xenon load quoted – this is the difference of the xenon load from its reference steady-state value (-28 mk), i.e., using the last equation in the previous slide: