1. 2014 January1 Xe-135 Effects in Reactor Operation B. Rouben McMaster University EP 4P03/6P03 2014 Jan-Apr

2. 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 January2

3. 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 January3

4. 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 135 Xe, but other examples are 103 Rh, 149 Sm and 151 Sm. In each case the nuclide is a direct fission product, but is also produced by the  -decay of another fission product. Saturating Fission Products

5. 2014 January5 135 Xe 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 135 Xe 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

6. 2014 January6 135 Xe is produced directly in fission, but mostly from the beta decay of its precursor 135 I (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 136 Xe. See Figure “ 135 Xe/ 135 I Kinetics” in next slide. 135 Xe and 135 I

7. 2014 January7 I-135/Xe-135 Kinetics Fissions 135 Te 135 I  - (  1/2 =18 s) 135 Xe  - (  1/2 =6.585 h) Burnout by neutron absorption  - (  1/2 =9.169 h) Production of 135 Xe by beta decay of 135 I dominates over its direct production in fission.

8. 2014 January8 135 Xe 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. 135 Xe and 135 I

9. 2014 January9 The large absorption cross section of 135 Xe 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) 135 Xe and 135 I (cont’d)

10. 2014 January10 [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

11. 2014 January11 High-power bundles have a higher xenon load, therefore a lower local reactivity  xenon flattens the power distribution In steady state, 135 Xe reduces maximum bundle and channel powers by ~ 5% and 3% respectively. This “natural” flattening by 135 Xe helps to comply with maximum licensed channel and bundle powers! Effects of 135 Xe on Power Distribution

12. 2014 January12 When power is reduced from a steady level: The burnout rate of 135 Xe is decreased in the reduced flux, but 135 Xe is still produced by the decay of the 135 I inventory  the 135 Xe concentration increases at first But the 135 I production rate is decreased in the lower flux, therefore the 135 I inventory starts to decrease The 135 I decay rate decreases correspondingly  the 135 Xe 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 135 Xe Concentration

13. 2014 January13 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!

14. 2014 January14 Xenon Reactivity Transients Following Setback to Various Power Levels

15. 2014 January15 Xenon Reactivity Transients Following Setback to Various Power Levels

16. 2014 January16 Xenon Transient Following a Shutdown A reactor shutdown presents the same scenario in an extreme version: there is a very large initial increase in 135 Xe 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 135 Xe growth and decay following a shutdown in a typical CANDU is shown in the next Figure.

17. 2014 January17 Xenon Reactivity Transients Following a Shutdown from Full Power

18. 2014 January18 Xenon Transient Following a Shutdown It can be seen that, at about 10 hours after shutdown, the (negative) reactivity worth of 135 Xe has increased to several times its equilibrium full-power value. At ~35-40 hours the 135 Xe 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.

19. 2014 January19 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.

20. 2014 January20 Conversely to the situation in a power reduction, when power is increased the 135 Xe 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 135 Xe Concentration

21. 2014 January21 In fresh bundles entering reactor, 135 Xe 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

22. 2014 January22 [from D. Rozon, Nuclear Reactor Kinetics, loc.cit.] Build-up of 135 Xe 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

23. 2014 January23 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 135 Xe concentration, but in different directions, in the two reactor halves. cont’d Xenon Oscillations

24. 2014 January24 The 135 Xe 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)

25. 2014 January25 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 Xenon Oscillations (cont’d)

26. 2014 January26 Large reactors, at high power (where 135 Xe 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)! Xenon Oscillations (cont’d)

27. 2014 January27 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

28. 2014 January28 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:

29. 2014 January29 Steady State In steady state the derivatives are zero:

30. 2014 January30 Steady State (label results with ss) Solve the 1st equation for I: Substitute this in the 2nd equation Now solve this for X (ss):

31. 2014 January31 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,

32. 2014 January32 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 cm 2 [that’s 3.2 million barns!]  f = 0.002 cm -1, and For full-power,  = 7.00*10 13 n.cm -2 s -1

33. 2014 January33 Values at Steady State If we substitute these numbers into the equations, we find that at steady-state full power: I ss,fp = 3.06*10 14 nuclides.cm -3 X ss,fp = 3.79*10 13 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!

34. 2014 January34 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!

35. 2014 January35 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

36. 2014 January36 Xe-135 Load = Xe-135 Reactivity Effect

37. 2014 January37 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 X ss,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.

38. 2014 January38 “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:

39. 2014 January39 END