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Atomic Energy, Vol. 107, No. 6, 2009 XENON STABILITY OF VVER-1200 S. P. Aver’yanova and P. E. Filimonov UDC 621.039.50 It is known that VVER stability with respect to xenon oscillations of the power decreases with increasing specific power, core dimensions and fuel enrichment and weakening of negative feedbacks on temperature and power [1–5]. So, xenon processes engender in VVER-440 only integral power oscillations [4], while integral as well as spatial xenon oscillations are characteristic for VVER-1000 [5]. VVER-1200 (AES-2000 design) possesses higher power, greater core height, and higher fuel enrichment (nominal uranium–gadolinium fuel loads are considered) than VVER-1000 [6]. By analogy with the transition from VVER-440 to VVER-1000, it can be suggested that VVER-1200 should be even less stable with respect to xenon processes. However, computational analysis performed with the IR program [7] in the course of design work showed that VVER-1200 is on the whole more stable than VVER-1000. Figure 1 shows the computed characteristics of stationary poisoning. Xenon poisoning is weaker in VVER-1200 than in VVER-1000. Figure 2 shows the free integral-spatial xenon oscillations of the power in the core, which are due to the initial change of power from 100 to 95% with the reactor subsequently operating in the absence of any controlling actions. The oscillations of the integral power W and of the axial offset AO in VVER-1200 have smaller amplitude and die out in contrast to VVER-1000. Only offset oscillations are observed during the operation of the reactor, since the power is automatically maintained at a prescribed level. Figure 3 shows the change of the offset in the course of free oscillations of the axial xenon oscillations with the reactor operating at 100% power. The oscillations in VVER-1200 die out much more rapidly than in VVER-1000. The stability of the reactor with respect to axial xenon oscillations is conventionally characterized by the stability index α, which corresponds to representation of the oscillations in the form AO = AO* + Aexp(αt)cos(2πt/TXe), where AO* is the equilibrium offset, A is the amplitude of the oscillations, t is the time, and TXe is the period of the oscillations. Figure 4 shows the variation change of the stability index as a function of the run time T. With the exception of the initial stage, in the course of a run VVER-1200 possesses smaller stability index than VVER-1000 and is therefore more stable. Likewise, the stability index of VVER-1200 is lower during an entire stationary run and the reactor retains absolute stability (α < 0), while VVER-1000 becomes unstable during the second half of the run (α > 0). It can be assumed that on the whole VVER-1200 is more stable with respect to axial xenon oscillations. So, there is a discrepancy between the expected decrease of xenon stability of VVER-1200 and the computational results, according to which VVER-1200 is more stable than VVER-1000. The reliability of the calculations is not in doubt, since the experiments of [5] confirm it. Consequently, for eliminate the discrepancy it is necessary to perform a qualitative analysis of the changes of the xenon stability of the reactor under the influence of changes of power, average enrichment of the fuel, core height, and feedbacks on temperature and power. An increase of the core height is seen unequivocally as a factor that makes VVER-1200 less stable. On switching from VVER-1000 to VVER-1200 the increase of power combined with an increase of the core volume leaves the specific power unchanged, and therefore in this case it has no direct effect on the stability. However, the fact that the specific power is conserved itself has a substantial effect on the subsequent analysis. Russian Science Center Kurchatov Institute, Moscow, Russia. Translated from Atomnaya Énergiya, Vol. 107, No. 6, pp. 348–351, December, 2009. Original article submitted July 24, 2009. 424 1063-4258/09/10706-0424 ©2009 Springer Science+Business Media, Inc. 3.0 âˆ†ρ, % 2.9 2.8 2.7 2.6 0 100 200 300 T, eff. days Fig. 1. Total xenon effect of reactivity at nominal power during the first run of VVER-1000 (1) and VVER-1200 (2) and a stationary run (3, 4, respectively). AO, % W, % 125 75 100 50 75 25 50 0 25 –25 0 0 10 20 30 0 10 20 30 t, h Fig. 2. Free xenon oscillations of the power and offset during the first run of 160 eff. days VVER-1000 (1) and VVER-1200 (2). Ordinarily, xenon effects are evaluated using the ratio of the rate of absorption of thermal neutrons by xenon (135Xe) and the fuel (mixture of 235U and 238U ions) [2, 3]: Q = N Xeσ aXe /( N 5σ 5a + N 8σ 8a ) , where N Xe, N 5, and N 8 are, respectively, the 135Xe, 235U, and 238U concentrations, and σaXe, σa5, and σa8 are, respectively, the absorption cross sections of 135Xe, 235U, and 238U (the following values are used below for the cross sections: 2.65·106, 680.9, and 0.482 b). Setting N 5 = εN and N 8 = (1 – ε)N, where ε is the enrichment, and N is the concentration of uranium nuclei, the expression for evaluating the xenon effects can be written in the form 425 AO, % 0 –2 –4 –6 –8 0 24 48 72 96 t, h Fig. 3. Free absolute xenon oscillations in a stationary run of 180 eff. days VVER-1000 (1) and VVER-1200 (2). Q = N Xeσ aXe /[ N ( ε (σ 5a − σ 8a ) + σ 8a ]. (1) N Xe = ω σ 5f N 5Φ /(λ Xe + σ Xe a Φ) , (2) For stationary poisoning where ω is the total yield of 135Xe (0.063), σƒ5 is the fission cross section of 235U (583.5 b), λXe is the decay constant of 135 Xe (2.1·10–5 sec–1), and Φ is the neutron flux density. For Φ ~ 1014 sec–1·cm–2, the stationary concentration of xenon is almost independent of the neutron flux density, so that expression (2) can be written as N Xe ~ εN and therefore expression (1) assumes the form Q( ε ) ~ ε /[ ε (σ 5a − σ 8a ) + σ 8a ]. (3) The function Q(ε) increases monotonically for ε > 0. It is concluded on this basis that the effect of xenon on the neutron-physical processes in the reactor core increases with increasing enrichment [3]. Therefore, an increase of fuel enrichment decreases the xenon stability of the reactor. The derivation of relation (3) implicitly assumed that the fission rate σƒ5N 5Φ is not constant, so that the assertion that the influence of xenon processes increases with increasing fission rate concerns the case of increasing fission rate, i.e., the specific power of the reactor. But if it is assumed that the specific power is conserved, as required when comparing VVER-1200 and VVER-1000, i.e., σƒ5N 5Φ = K, where K = const, then expression (1) becomes Q( ε ) = Aε /[( ε + B)( ε + C )], (4) where 5 8 A = ω σ Xe a K /[(σ a − σ a ) N λ Xe ]; B = σ 8a /(σ 5a − σ 8a ) ; C = σ aXe K /(σ 5f λ Xe N ). Figure 5 shows the qualitative behavior of the function Q(ε) in the form of (4). Equating the derivative to zero, it is possible to find the fuel enrichment ε* at which the function reaches its maximum value for positive ε: ε * = BC . 426 α, 1/h 0.08 0.04 0 –0.04 0 90 180 270 360 T, eff. days Fig. 4. Stability index of a reactor with respect to the axial xenon oscillations in the first run of VVER-100 (1) and VVER-1200 (2) and stationary run (3, 4, respectively). Fig. 5. Fraction of neutron absorption by xenon as a function of the fuel enrichment. For ε > ε*, the function Q(ε) decreases. If the ratio K/N is determined taking account of the thermal power 3200 MW(t) and uranium dioxide mass 87 tons adopted for VVER-1200 and using the neutron-physical constants presented, then ε* = 0.88·10–2 or ε* = 0.88% (a value close to this is also obtained by using the power and fuel mass of VVER-1000). For VVER, the average enrichment is >1%, and therefore ε > ε* for such reactors, i.e., the enrichment lies in the region of decreasing values of the function Q(ε). Thus, under the condition that the specific power remains constant the effect of xenon on the neutron-physical process in the VVER core decreases with increasing fuel enrichment. The enrichment of VVER-1200 fuel is higher than that of VVER-1000 fuel, and therefore xenon processes play a smaller role in VVER-1200, which makes this reactor more stable. As noted above, feedbacks also influence the xenon stability of a reactor. The negative feedbacks in a reactor are characterized by negative coefficients of reactivity on power and temperature, which are essentially identical for VVER-1200 and VVER-1000. The temperature coefficient of reactivity µ, taken with an opposite sign, is higher for VVER-1200, as shown in Fig. 6; therefore negative feedback is stronger this reactor, which makes it more stable. 427 µ, 10–5 1/°C 80 60 40 20 0 100 200 300 T, eff. days Fig. 6. Coefficient of reactivity on coolant temperature in the first run of VVER-1000 (1) and VVER-1000 (2) and in a stationary run (3, 4, respectively). In summary, with respect to xenon processes VVER-1200 is more stable than VVER-1000. 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