The production process of 135Xe is presented in Fig. 1.5. In the decay chain of mass number 135 related to 135Xe production, 135Sb, 135Te, 135I, and 135Xe are the main FPs. Because 135Sb and 135Te are short-lived nuclides, they can be assumed to decay very rapidly to 135I.

The time-dependent nuclide concentrations of 135I and 135Xe are represented by /(t) and X(t), respectively, the fission yields (FP yields per fission shown in Table 1.1) are represented by у: and yXe, and the decay constants are represented by 2/ and 2Xe. Assuming the thermal absorption cross section of 135Xe is WXе and time-independent neutron flux is ф, the production-destruction equations of /(t) and X(t) can be represented as follows.

(1.23)

(1.24)

[1] Solution at initial startup

When the reactor is started up from a clean condition in which /(0) = X(0) = 0, the 135I and 135Xe concentrations can be obtained as shown in Eqs. (1.25) and

(1.26) .

Table 1.1 Fission yields by thermal fission [8] Fission yield (number of a fission product Fission produced per fission) product Decay constant [2] 1) 233 U 235 U 239 Pu 135 I 2.93 x 10-5 0.0491 0.0629 0.0645 135 Xe 2.11 x 10-5 0.0128 0.0024 0.0115 149 Nd 1.11 x 10~4 0.0078 0.0107 0.0124 The fission yields of 135I and 149Nd are the cumulative fission yields including nuclides in the upper part of each decay chain. The fission yield of 135Xe is the independent fission yield representing the direct production by fission

(1.25)

(1.26)

Within enough time after the reactor startup, the concentrations approach equilibrium values, Ieq and Xeq, which can be found at t ! 1 in Eqs. (1.25) and

(1.26) as follows.

(1.27)

(1.28)

These equations can be directly obtained by placing the time derivatives in Eqs. (1.23) and (1.24) equal to zero.

Upon inserting Eq. (1.28) into Eq. (1.22), the reactivity change due to equilibrium 135Xe is found to be

ofeXeq _ Гі + ухе Ф vlfpe vpe ЛХе/CFа Є+Ф

If, ф ^ XXe jo X the negative reactivity increases linearly with ф. On the other hand, if ф ^ XXe joX, the negative reactivity takes its maximum value

To estimate the magnitude of the maximum value, suppose that a thermal reactor is fueled with 235U and contains no resonance absorbers and fast fission materials. In this case, p = є = 1, and the negative reactivity gives

by using the fission yield from 235U in Table 1.1 and v = 2.42. This is a considerably large reactivity which is about —4.2 dollars for the delayed neutron fraction of 0.0064 in thermal fission of 235U.

[2] Solution after shutdown

Although the production of 135I and 135Xe by fission and the transmutation of 135Xe by thermal neutron absorption cease when the reactor is shut down, 135Xe continues to be produced as the result of the decay of 135I present in the system. It eventually disappears by its own decay.

After shutdown, the production-destruction equations of 135I and 135Xe are given by the next expressions.

(1.30)

(1.31)

If the concentrations at shutdown are 10 and X0, the concentrations at a later time t can be written as follows.

(1.32)

If 135I and 135Xe had reached equilibrium prior to shutdown, then 10 and X0 would be given by Eqs. (1.27) and (1.28), and the concentration of 135Xe becomes

The resulting reactivity change due to 135Xe at a later time t after shutdown is given by Eq. (1.35).

(1.35)

Figure 1.6 shows the reactivity change due to 135Xe buildup in a 235U-fueled thermal reactor after shutdown as calculated by Eq. (1.35). The buildup of 135Xe rises to a maximum, which occurs at about 10 h after shutdown, and then decreases to zero. It should be particularly noted that the buildup of 135Xe is greatest in reactors which have been operating at the highest flux before shutdown. This gives rise to a reactor dead time in the operation of high-flux reactors, during which time the reactor cannot be restarted. This situation is indicated in Fig. 1.6 during the time interval from ta to tb, where the horizontal line represents a hypothetical reactivity margin of 0.2 Ak/k by withdrawal of all

Fig. 1.6 Negative reactivity due to 135Xe buildup after shutdown [7]

control rods. As a countermeasure to reduce the reactor dead time, a gradual reduction in reactor power and the shutdown at a low neutron flux can suppress the buildup of 135Xe.

Figure 1.7 shows the negative reactivity change due to 135Xe in a reactor that is returned to full power just at the end of the dead time. If a reactor is restarted while a large amount of 135Xe is present in the system, it should be noted that the subsequent burnout of this poison substantially increases the reactivity of the reactor.