enon Effects B. Rouben McMaster University Course EP 4D03/6D03 Nuclear Reactor Analysis (Reactor Physics) 2015 Sept.-Dec. 2015 September 1
Contents We study the importance of e-135 in the operation of nuclear reactors. 2015 September 2
Effects of enon 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 135 e, but other examples are 103 Rh, 149 Sm and 151 Sm. n each case the nuclide is a direct fission product, but is also produced by the -decay of another fission product. 2015 September 3
135 e and 135 135 e is produced directly in fission, but mostly from the beta decay of its precursor 135 (half-life 6.585 hours). t is destroyed in two ways: By its own radioactive decay (half-life 9.169 hours), and By neutron absorption to 136 e. See Figure 135 e/ 135 Kinetics in next slide. 2015 September 4
-135/e-135 Kinetics We will see that production of 135 e by beta decay of 135 dominates over its direct production in fission. Fissions -( 1/2 =18 s) 135 Te 135 -( 1/2 =6.585 h) -( 1/2 =9.169 h) 135 e Burnout by neutron absorption 2015 September 5
135 e and 135 135 e has a very important role in the reactor t has a very large thermal-neutron absorption cross section t is a considerable load on the chain reaction ts 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. 2015 September 6
135 e and 135 (cont d) The large absorption cross section of 135 e plays a significant role in the overall neutron balance and directly affects system reactivity, both in steady state and in transients. t also influences the spatial power distribution in the reactor. The limiting absorption rate at extremely high flux maximum steady-state reactivity load ~ -30 mk. n CANDU, the equilibrium load at full power ~ -28 mk (see Figure) 2015 September 7
The Equations for -135/e-135 Kinetics First, define symbols: Let and be the -135 and e-135 concentrations in the fuel. Let and be the -135 and e-135 decay constants, and Let and be their direct yields in fission Let be the e-135 microscopic absorption cross section Let be the neutron flux in the fuel, and Let f be the fuel fission cross section 2015 September 8
Differential Equations for Production and Removal -135 has 1 way to be produced, and 1 way to disappear, whereas e-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: d dt f (1) d dt f (2) 2015 September 9
Steady State Use Subscript ss n steady state the derivatives are zero: f ss ss 0 (3) ss f ss ss ss ss 0 (4) 2015 September 10
Steady State Solve Eq. (3) for steady-state -135 concentration ss : ss fss Substitute this in Eq. (4): (5) ss ss ss f ss f ss Now solve this for steady-state e-135 concentration ss : ss f ss ss 2015 September 11
nteractive Discussion/Exercise What is the difference in character between the equations for the e and steady-state concentrations? 2015 September 12
ss fss Steady State Final Equations The steady-state -135 concentration is directly proportional to the flux value Whereas fss ss (6) ss ss is not proportional to the flux, in fact it saturates in high flux: n the limit where goes to infinity: (5) ss ( steady state, very high flux ) f (7) 2015 September 13
Typical Values Typical values of the parameters: -135 half-life = 6.585 h = 2.92*10-5 s -1 e-135 half-life = 9.169 h = 2.10*10-5 s -1 = 0.0638 = 0.00246 ( depends on the fuel burnup, because the e-135 yields from U-235 and Pu-239 fission are quite different) = 3.20*10-18 cm 2 [that s 3.2 million barns!] [ depends on temperature] f = 0.002 cm -1, and For full power in CANDU, ss,fp = 7.00*10 13 n.cm -2 s -1 2015 September 14
Values at Steady State f we substitute these numbers into Eqs. (5) and (6), we find that at steady-state full power: ss,fp = 3.06*10 14 nuclides.cm -3 (8) ss,fp = 3.79*10 13 nuclides.cm -3 (9) With these values we note that at steady-state full power ss, fp f ss, fp 2.92*10 5 s 1 *3.06*10 0.00246*0.002cm 1 14 cm 3 *7.0*10 8.93*10 13 cm 2 s 9 1 cm 3. s 1 3.44*10 8 cm 3. s 1 Therefore at steady-state full power the e-135 comes very predominantly (96%) from -135 decay rather than directly from fission! 2015 September 15
Values at Steady State Also at steady-state full power ss, fp ss, fp 2.1*10 ss, fp 5 s 8.48*10 1 3.2*10 9 *3.78*10 18 cm cm 3. s 2 1 Therefore, at steady-state full power, the e-135 disappears very predominantly (91%) from burnout (by neutron absorption) rather than from decay! 13 cm 3 *3.79*10 13 7.95*10 cm 3 8 cm 3 *7.0*10. s 13 1 cm 2. s 1 2015 September 16
Values at Steady State with Very High Flux n the limit where ss is very large (goes to infinity), we find from Eq.(7) i. e, ss, the e 0.0638 0.00246 18 3.2*10 Comparing Eq.(8) with ss, fp 0.92* 135 is f ss, 92% *0.002 this value, saturated 4.11*10 we at find full 13 nuclides. cm power 3 (10) (11) 2015 September 17
2015 September 18 e-135 Load = e-135 Reactivity Effect. 28. 30 0.03 1 1 0.03, *1 0.004 *3.79*10 3.2*10 1, : * *,. 2 '. 135., sec 135, 2,, 13 18,, 2 2,, 2 2, 2 1 1 2 1 2 2 2,, 2 2, 2 1 1 2 1 2 2, 2 mk is value accurate A more estimate an is This mk k k k and k and k reactor critical from a Starting k k form a similar would have k in change The k k to change the apply we f k for formula group the recalling by effect reactivity s xenon the of estimate an get can We is contribution e The tion cross absorption thermal the mostly affects e fp eff eff eff fp eff fp ss eff eff a a eff eff a a a f a a a a a a f a a
e-135 Load in Various Conditions The most accurate value for the steady-state e-135 load in CANDU at full power is,fp = -28 mk (12) n any other condition, when the e-135 concentration is different from the steady-state full-power value (e.g., in a transient), we can determine the e-135 load by using the ratio of the instantaneous value of to ss,fp: *, fp 28 mk * 28 mk * 13 3 3.79*10 cm ss, fp ss, fp (13) The instantaneous e-135 concentration would of course have to be determined, say by solving the differential e-135/-135 kinetics equations (1)-(2). 2015 September 19
Excess e-135 Load We may sometimes like to quote not the absolute e-135 load, but instead the excess xenon load, i.e., the difference from its reference steady-state value (-28 mk), Using Eq.(13) in the previous slide: Excess or " Additional " e 135 Load, fp 28* 1 mk 13 3.79*10 (14) 2015 September 20
Equilibrium enon Load Figure Credit: Nuclear Reactor Kinetics, by D. Rozon, Polytechnic nternational Press, 1998 2015 September 21
Effects of 135 e on Power Distribution High-power bundles have a higher e-135 concentration, i.e., a higher xenon load, therefore a lower local reactivity xenon flattens the power distribution n steady state, 135 e reduces maximum bundle and channel powers by ~ 5% and 3% respectively. 2015 September 22
Saturating-Fission-Product-Free Fuel n fresh bundles entering the reactor, 135 e 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. 2015 September 23
Build-up of 135 e in Fresh Fuel Figure Credit: Nuclear Reactor Kinetics, by D. Rozon, Polytechnic nternational Press, 1998 2015 September 24
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. 2015 September 25
Effect of Power Decrease on 135 e Concentration The e-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 135 e is decreased in the reduced flux, but 135 e is still produced by the decay of 135 the 135 e concentration increases at first But the 135 production rate is decreased in the lower flux, therefore the 135 inventory starts to decrease The 135 decay rate decreases correspondingly the 135 e 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. 2015 September 26
enon Reactivity Transients Following Setback to -27.0 Various Power Levels e Reactivity (mk) vs. Time (h): Step Change from FP to 80% FP 0 10 20 30 40 50 60 70 80 90 100 110 120 130-28.0-29.0-30.0-31.0-32.0-33.0 2015 September 27
enon Reactivity Transients Following Setback to Various Power Levels -2.600E+01 e Reactivity (mk) vs. Time (h): Step Change from FP to 60% FP 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140-2.800E+01-3.000E+01-3.200E+01-3.400E+01-3.600E+01-3.800E+01-4.000E+01 2015 September 28
enon Reactivity Transients Following Setback to Various Power Levels e Reactivity (mk) vs. Time (h): Step Change from FP to 40% FP 0 10 20 30 40 50 60 70 80 90 100 110 120 130-22.0-27.0-32.0-37.0-42.0-47.0-52.0 2015 September 29
enon Transient Following a Shutdown A reactor shutdown presents the same scenario in an extreme version: there is a very large initial increase in 135 e concentration and decrease in core reactivity. f 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 e growth and decay following a shutdown in a typical CANDU is shown in the next Figure. 2015 September 30
enon Transient Following Reactor Shutdown 2015 September 31
enon Transient Following a Shutdown t can be seen that, at about 10 hours after shutdown, the (negative) reactivity worth of 135 e has increased to several times its equilibrium full-power value. At ~35-40 hours the 135 e has decayed back to its pre-shutdown level. f 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. 2015 September 32
enon 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. t 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. 2015 September 33
Case of Power ncrease Conversely to the situation in a power reduction, when power is increased the 135 e 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 higher value). However, one point to remember is that e-135 changes following power changes provide positive feedback. Large reactors may be unstable with respect to xenon changes above a certain power level. 2015 September 34
Solution of e- Kinetics After a Shutdown The differential equations for e-135/-135 kinetics are: d f (15) dt d f (16) dt n a transient (non-steady-state) situation, these equations can be numerically integrated to find the evolution of and, starting from known initial conditions 0 and 0. 2015 September 35
Case of an nstantaneous Shutdown f the reactor is subjected to an instantaneous shutdown, we can solve Eqs. (15) and (16) analytically. f the flux 0 at t = 0, the terms containing disappear, and the equations simplify to: d dt d dt (17) (18) The solution of Eq. (17) is immediate: decays according to the exponential-decay law: 0 e t (19) 2015 September 36
2015 September 37 nstantaneous Shutdown Solving for Eq.(18) for becomes., (21).(19) int 10 (20). exp (19) 0 0 separately out balance must e and e in terms the t all for equality a n be to this for order n Be Ae e e B e A yields Eq o form the Substituting Be Ae try So e and form e the of onentials contain may for solution the that suggest and e in terms The e dt d t t t t t t t t t t t
2015 September 38 nstantaneous Shutdown Solving for (18)!].(17) [ (11) (5) : (10) 0 :.(7), min det. inf, (9), 0 0 0 0 0 0 0 0 0 0 Eqs satisfy indeed these that to verify you to it leave e e e solution full the have we Therefore A B B A t condition initial the and Eq to resort we B e er To B on ormation no balance already e in terms The A A A get we e the Balancing t t t t t
nstantaneous Shutdown - Numerics t will be left as an exercise to evaluate and, and the corresponding reactivity effect, for a time period following a reactor shutdown, using the initial conditions of a steady state at various powers. 2015 September 39
enon Oscillations enon oscillations are an extremely important scenario to guard against in reactor design and operation. magine 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 e concentration, but in different directions, in the two reactor halves. cont d 2015 September 40
enon Oscillations (cont d) The 135 e concentration will increase in the reactor half where the power is decreasing. t will decrease in the half where the power is increasing. These changes will induce positive-feedback reactivity changes (why?). Thus, the e and power changes will be amplified (at first) by this positive feedback! cont d 2015 September 41
enon Oscillations (cont d) f not controlled, the effects will reverse after many hours (just as we have seen in the xenon transients in the earlier slides). enon 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 2015 September 42
enon Oscillations (cont d) Large reactors, at high power (where 135 e reactivity is important) are unstable with respect to xenon! This is exacerbated in cores which are more decoupled (as in CANDU). t s the zone controllers which dampen/remove these oscillations that s one of their big jobs (spatial control)! 2015 September 43
END 2015 September 44