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Part4_1: Xenon Effects on Reactor Operation B. Rouben Course UN 0802 2012 Mar-Apr 2012 March 1 Contents We study the reactor-physics effects of Xe-135 in the operation of nuclear reactors, and their importance. 2012 March 2 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 for values of the steady flux 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. 2012 March 3 135Xe and 135I 135Xe is produced directly in fission, and also 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 (which has no significant absorption cross section). It will be important and instructive to understand the relative importance of each production pathway and each destruction pathway. Figure “135Xe/135I Kinetics” in next slide. 4 See March 2012 I-135/Xe-135 Kinetics Production of 135Xe by beta decay of 135I dominates over its direct production in fission. -(1/2=18 s) 135Te 135I -(1/2=9.169 h) -(1/2=6.585 h) 135Xe Fissions Burnout by neutron absorption 2012 March 5 “Double-Bathtub” Analogy I Bathtub Xe Bathtub 2012 March 6 135Xe and 135I 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. 2012 March 7 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. Looking ahead, 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 (more on this later) 2012 March 8 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 microscopic absorption cross section Let be the neutron flux in the fuel, and Let f be the fuel fission cross section 2012 March 9 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: dI I f I I (1) dt dX I I X f X X X X ( 2) dt 2012 March 10 Let Us First Study the Steady State – Use Subscript ss In steady state the derivatives are zero: I f ss I I ss 0 (3) I I ss X f ss X X ss X X ssss 0 ( 4) 2012 March 11 Steady State Solve Eq. (3) for steady-state I-135 concentration Iss: I f ss I ss (5) I Substitute this in Eq. (4): X X ss X X ssss I f ss X f ss Now solve this for steady-state Xe-135 concentration Xss: I X f ss X ss X X ss 2012 March 12 Interactive Discussion/Exercise What is the difference in character between the equations for the Xe and I steady-state concentrations? 2012 March 13 Steady State – Final Equations I f ss I ss (5) I The steady-state I-135 concentration is directly proportional to the flux value Whereas I X f ss X ss ( 6) X X ss Xss is not proportional to the flux, in fact it saturates in high flux: In the limit where ss is infinitely large (i.e., very high power): I X f X ss ( steady state, very high flux ) (7) X 2012 March 14 Now Let’s Look at Typical ss 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 2012 March 15 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 I I ss , fp 2.92 * 10 5 s 1 * 3.06 * 1014 cm 3 8.93 * 10 9 cm 3.s 1 X f ss , fp 0.00246 * 0.002 cm 1 * 7.0 * 1013 cm 2 s 1 3.44 * 10 8 cm 3.s 1 Therefore at steady-state full power the Xe-135 comes very predominantly (96%) from I-135 decay rather than directly from fission! 2012 March 16 Values at Steady State Also at steady-state full power X X ss , fp 2.1 *105 s 1 * 3.78 *1013 cm 3 7.95 *108 cm 3.s 1 X X ss , fpss , fp 3.2 *1018 cm 2 * 3.79 *1013 cm 3 * 7.0 *1013 cm 2 .s 1 8.48 *109 cm 3.s 1 Therefore, at steady-state full power, the Xe-135 disappears very predominantly (91%) from burnout (by neutron absorption) rather than from its decay! 2012 March 17 Values at Steady State with Very High Flux In the limit where ss is very large (goes to infinity), we find from Eq.(7) I X f X ss , X 0.0638 0.00246* 0.002 cm 1 3.2 *1018 cm 2 4.11*1013 nuclides.cm 3 (10) Comparing Eq.(8) with this value, we find X ss , fp 0.92 * X ss , (11) i.e, we can say that the Xe 135 concentration is 92% saturated at full power. 2012 March 18 Xe-135 Load (Xe-135 Reactivity Effect) at Full Power Here we make an estimate of the Xe 135 reactivity at full power : Xe 135 affects mostly the thermal absorption cross sec tion, a 2 . The Xe 135 contribution is a 2, X X X . We can then get an estimate of the reactivity effect by f 12 recalling the 2 group formula for k . a2 a1 12 If we apply the change a 2, X to a 2 , a 2, X 12 k , X * f a 2, X * k a 2 2 a1 12 a2 a 2, X The change in keff would have a similar form : keff , X keff a2 Starting from a critical reactor keff 1, and X ss , fp 3.2 *1018 * 3.79 *1013 k keff , X *1 0.03, and X , fp 1 1 eff , X 0.03 30 mk 0.004 k 2 keff eff This is a first estimate. A more accurate treatment gives X , fp 28 mk. 2012 March 19 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), since the reactivity effect is proportional to the Xe-135 cross section, and therefore to X, we can determine the Xe-135 load by using the ratio of the instantaneous value of X to Xss,fp: X X X X * X , fp 28 mk * 28 mk * 13 3 (13) X ss , fp X ss , fp 3.79 * 10 cm The concentration X would of course have to be known, say, by solving the Xe/I kinetics equations (1)-(2). 2012 March 20 “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 full-power value (-28 mk), Using Eq.(13) in the previous slide: Excess or "Additional" Xe 135 Load X X X , fp 28* 1 mk (14) 3.79 *10 13 2012 March 21 Xenon Load at Various Power Levels Figure Credit: “Nuclear Reactor Kinetics”, by D. Rozon, Polytechnic International Press, 1998. 2012 March Note: The Xenon Load should really have a minus sign. 22 Effects of 135Xe on Power Distribution In the figure on the previous slide, the power on the horizontal axis can be taken as “relative” rather than as an absolute value, i.e., the figure can tell us the relative local xenon concentration as a function of the local power: 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. 2012 March 23 Saturating-Fission-Product-Free Fuel In fresh bundles entering the reactor, 135Xe and other saturating fission products will build up (see Figure on next slide). 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 in the first couple of days than later – the effect may range up to ~10% on bundle power, and ~5% on channel power. 2012 March 24 Build-up of 135Xe in Fresh Fuel Figure Credit: “Nuclear Reactor Kinetics”, by D. Rozon, Polytechnic International Press, 1998 2012 March 25 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 of fresh bundles needs to be made. 2012 March 26 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 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. 2012 March 27 Xenon Reactivity Transients Following Setback to Various Power Levels Xe Reactivity (mk) vs. Time (h): Step Change from FP to 80% FP 0 10 20 30 40 50 60 70 80 90 100 110 120 130 -27.0 -28.0 Note: this is just the Xe-135 -29.0 -30.0 reactivity. If the reactor is to continue operating at this power, -31.0 the change in Xe-135 reactivity must be compensated by some -32.0 other change in reactivity, i.e., by moving control rods (zone -33.0 controllers, adjusters) 2012 March 28 Xenon Reactivity Transients Following Setback to Various Power Levels Xe Reactivity (mk) vs. Time (h): Step Change from FP to 60% FP 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 -26 -28 -30 Note: the final Xe-135 -32 reactivity is less negative -34 than the starting value, as is to be expected on -36 account of the lower steady-state power. -38 -40 2012 March 29 Xenon Reactivity Transients Following Setback to Various Power Levels Xe Reactivity (mk) vs. Time (h): Step Change from FP to 40% FP 0 10 20 30 40 50 60 70 80 90 100 110 120 130 -22.0 -27.0 -32.0 Note: It is unlikely that a reduction from full power to -37.0 -42.0 50%FP or lower can be sustained, because the change -47.0 in Xe-135 reactivity is too large to be compensated by adjuster-rod withdrawal. -52.0 2012 March 30 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. 2012 March 31 Xenon Reactivity Transients Following a Shutdown from Full Power Xe Reactivity (mk) vs. Time (h): Shutdown from Full Power 0 10 20 30 40 50 60 70 80 90 100 110 120 130 0.0 -10.0 -20.0 -30.0 -40.0 -50.0 -60.0 -70.0 -80.0 -90.0 -100.0 -110.0 -120.0 2012 March 32 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. Beyond that time it will go to 0. If it were not possible to add positive reactivity during this period, the reactor would go into “poison-out” and the shutdown would necessarily last some 40 hours, when the reactor would again reach criticality. In “poison-out”, the reactor must be put into “guaranteed shutdown” (overpoisoned with B or Gd), to ensure that the reactor cannot go critical when the Xe-135 has decayed away, until a conscious decision is made to restart. 2012 March 33 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 30-35 minutes of xenon override following a shutdown. 2012 March 34 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. 2012 March 35 Solution of Xe-I Kinetics After a Shutdown The differential equations for Xe-135/I-135 kinetics are: dI I f I I (15) dt dX I I X f X X X X (16) dt 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. 2012 March 36 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: dI I I (17) dt dX I I X X (18) dt The solution of Eq. (17) is immediate: I decays according to the exponential-decay law: I I 0 e I t (19 ) 2012 March 37 Instantaneous Shutdown – Solving for X Eq.(18) for X becomes dX I I 0 e I t X X (19) dt The terms in e I t and X X suggest that the solution for X may contain exp onentials of the form e I I and e X X . So try X AeI t BeX t ( 20) Substituting the form 10 int o Eq.(19) yields AI e I t B X e X t I I 0e I t X AeI t Be X t ( 21) In order for this to be a n equality for all t , the terms in e I t and e X t must balance out separately. 2012 March 38 Instantaneous Shutdown – Solving for X Balancing the e I t , we get I I 0 AI I I 0 X A A ( 9) X I The terms in e X t already balance, no inf ormation on B. To det er min e B, we resort to Eq.(7) and the initial condition : X t 0 X 0 A B I I 0 B X0 A X0 (10) X I Therefore we have the full solution : I I 0 e I t (5) I I 0 t I I 0 X t X e X0 I e (11) X I X I [ I leave it to you to verify that these indeed satisfy Eqs.(17) (18)!] 2012 March 39 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. 2012 March 40 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 (i.e., the assumption is that bulk control is active, but spatial control is lost) 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 2012 March 41 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 2012 March 42 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 2012 March 43 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)! 2012 March 44 END 2012 March 45