Page 69 - Dynamics and Control of Nuclear Reactors

6.2 Dynamics of xenon-135 61

Therefore

k eff 1 f f
0
¼ (6.14)
k eff f 0
Define the following:
X
aO
z ¼ X
af

X
ap
P ¼ X
af
Therefore
k eff 1 P
ρ ¼ ¼ (6.15)
k eff 1+ z
where ρ¼reactivity decrease due to fission product absorptions.
Since z « 1 in a reactor, a rough approximation (good enough to illustrate the
approximate magnitude of fission product poisons on reactivity) is.
Σ ap
ρ ¼ P ¼ (6.16)
Σ af
Note that the reactivity loss is given by

σ
0 aX
ρ ¼ X (6.17)
σ af
0
0
and X (recall X ¼X/N f ) is the solution variable in Eq. (6.6). The ratio of X-135
6
absorption cross section to U-235 absorption cross section is (3.5 10 )/650 or
5380. Therefore
0
ρ ¼ 5380 XðÞ (6.18)
At steady state, the Xenon value is given by
ð γ + γ Þσ f Φ
0 X I
X ¼ 5380 (6.19)
ss
ð λ X + σ aX ΦÞ
Using the cross sections for a moderator temperature of 300°C(σ f ¼348 barns
6
σ aX ¼2.22 10 barns) gives
ð 0:066Þ 348 10 24 Φ
0
ss 5 18
X ¼ 5380 (6.20)
2:09 10 +2:22 10 Φ
Fig. 6.2 shows the Xe-135 steady state poisoning as a function of neutron flux. Note
that the maximum steady state reactivity loss is around eight dollars at high flux
levels for this example.