Xe-135 Effects in Reactor Operation

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## Xe-135 Effects in Reactor Operation

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**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 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 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: