Importance of Xe-135 in Reactor Operation B. Rouben McMaster University EP 4P03/6P03 2016 Jan-Apr 2016 January

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. 2016 January

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 half-life 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. 2016 January

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. 2016 January

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. 2016 January

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. 2016 January

I-135/Xe-135 Kinetics 135Te 135I 135Xe Fissions -(1/2=9.169 h) 135Te 135I -(1/2=6.585 h) 135Xe Fissions Burnout by neutron absorption In steady state these processes equilibrate to steady values for the 135Xe and 135I concentrations. 2016 January

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. 2016 January

Xe-I “Double-Bathtub” Analogy Fissions Legend Neutron Flux I X X and Neutron Flux I X At Full Power, I ~ 8 X - this is a “reserve” of xenon. X production is ~96% from I decay, 4% from fission. X loss is ~9% from decay, ~91% from burnout. 2016 January

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. 2016 January

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 2016 January

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! 2016 January

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. 2016 January

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 [from D. Rozon, Nuclear Reactor Kinetics, loc.cit.] 2016 January

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. 2016 January

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! 2016 January

Xenon Reactivity Transients Following Setback to Various Power Levels 2016 January

Xenon Reactivity Transients Following Setback to Various Power Levels 2016 January

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. 2016 January

Xenon Reactivity Transients Following a Shutdown from Full Power 2016 January

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. 2016 January

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. 2016 January

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). 2016 January

 Reactors at high power are unstable with respect to xenon! Positive Feedback In all cases of power changes from high power, xenon provides positive feedback reactivity  Reactors at high power are unstable with respect to xenon! It’s the liquid-zone controllers that combat the instability! 2016 January

The bulk-control function of the RRS will bring the total power back. 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), creating a power tilt. The bulk-control function of the RRS will bring the total power back. But if the spatial control does not act, the tilt will remain. cont’d 2016 January

Xenon-Oscillation Scenario 1 1 1.04 1 1.02 0.98 Initial Perturbation Bulk Control (e.g.) If there is no (or no adequate) spatial control, a xenon oscillation can ensue 2016 January

Xenon Oscillations (cont’d)   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. The 135Xe concentration will increase in the reactor half where the power is decreasing. It will decrease where the power is increasing. These changes will induce positive-feedback reactivity changes. Thus, the Xe and power changes will be amplified (at first) by this positive feedback! cont’d 2016 January

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). These are the xenon oscillations They may grow – 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. Xenon oscillations have been observed in some instances, with a period of 20-30 hours. cont’d 2016 January

Xenon Oscillations - Summary   Large reactors, at high power (where 135Xe reactivity is important) are unstable with respect to xenon! It’s the zone controllers which dampen/remove these oscillations – that’s one of their big jobs (spatial control)! 2016 January

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 2016 January

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: 2016 January

In steady state the derivatives are zero: 2016 January

Steady State (label results with ss) Solve the 1st equation for I: Substitute this in the 2nd equation Now solve this for X (ss): 2016 January

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, 2016 January

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 2016 January

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! 2016 January

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! 2016 January

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 2016 January

Xe-135 Load  Xe-135 Reactivity 135Xe acts mostly through its thermal absorption cross section Knowing that thermal absorption in the CANDU cell represents about -850 mk (fast and resonance absorption + leakage  15%) We can obtain a good estimate of the xenon reactivity at full power steady state by multiplying this by the ratio A more accurate analysis gives 2016 January

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. 2016 January

“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: 2016 January

END 2016 January