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62 CHAPTER 6 Fission product poisoning

Reactivity loss due to Xe-135 ($) 10 8 6 4 2

0
10 12 10 13 10 14 10 15
–2
Neutron flux (#/ cm s)
FIG. 6.2
Xenon steady-state poisoning reactivity loss as a function of neutron flux.

6.2.6 Behavior of Xe-135 after Startup
Eqs. (6.5) and (6.6) apply for reactor startup (with initial conditions, I ¼0 and
0
0
X ¼0).
For a hypothetical step change to full power (in actual operation, power would be
increased gradually), the equations can be solved readily by analytical or numerical
methods.
A reference reactor is defined here. It is also the basis for illustrations appearing
later in this chapter. The pertinent characteristics of the reference reactor are as
follows:

9
Reactor power¼3000MW (3 10 W)
8
Fuel loading¼100 metric tons (10 g of enriched fuel)
Fuel enrichment¼3% U-235
6
Loading of U-235¼3 10 g
Moderator temperature¼300°C
Effective microscopic fission cross section for U-235 at 300°C¼
2
348 10 24 cm .
2
Neutron flux at full power¼3.47 10 13 #neutron/cm -sec (See Appendix I for
calculation of the flux.)
23
The number of fissile atoms in the reactor is given by (6.023 10 )x
6
3 10 ¼1.8069 10 29
The effective absorption cross section for Xe-135 at 300°C is given by
18 r ffiffiffiffiffiffiffiffi
3:5x10 293 18 2
σ aX ¼ ¼ 2:22 10 cm
1:128 573
Therefore, the terms, σ f Φ and σ aX Φ, in the equations become
24 13 8
σ f Φ ¼ 348 10 3:47 10 ¼ 1:208 10
and
18 13 5
σ aX Φ ¼ 2:22 10 3:47 10 ¼ 7:70 10