As the fuel burn-up proceeds, the fuel composition and the control effectiveness changes and thus the reactivity balance of the system alters. These changes are also feedback effects, although the time scale is very large. Because these changes are long-term, they have no immediate effect on stability and so they are generally omitted from transient calculations. They are, however, accounted for by performing safety evaluations at several times during the burn-up cycle, particularly at start-of-life, during the equilibrium cycle, and at end-of-life.

We can separate out effects due to fuel and control changes:

Fuel, (a) The reactivity effect of the core fissile concentration decrease can be expressed as

дк _ 1 6M _ IB-10-» l + a

~k T Ж ~ ~~T ~ T+~<5 — bi)

If the internal breeding ratio bt of the core is 0.9 and the fractional enrich­ment є in the core is 0.16, then at a burn-up В of 50,000 MWD/tonne this reactivity change is —0.015 or about $ 3 to $4 negative. (Here the ratio of fissile captures to fissions a is taken to be 0.15 and the ratio of fertile to fissile fissions <5 is assumed to be 0.2.)

(b) Fission product build-up can be expressed as

dk 2 В-10-6 1 + a a4v

к ~ 5 є 1 + <5 cr

which includes the competition of absorption cross sections in the fission products a4p and in the plutonium cra239 . This reactivity change is usually about $ 2-І 3 negative.

(c) In 233^232^ cycle systems, the reactivity effect is a swing due to the hold-up of the intermediate 233Pa. There is a delay of about 30 days before a 232Th capture results in the production of an atom of 233U. This leads to a decrease in reactivity at the start of irradiation, with a consequent increase of reactivity after shut-down due to the decay of the 233Pa. It is similar to a reverse xenon poisoning effect (see Section 1.4.2.3). The re­activity swing is given by

J_ Ф_ <*<=,„

к 2 Є ^233

where the protactinium decay constant Д2зз *s taken as 2.9-10-7 per sec and the 232Th capture cross section aCai is about 0.4 b. Thus, for a fast flux of 2-1015 n/cm2-sec, the reactivity swing is 0.008 or $2.5.

Control assembly, (a) The 10B absorber burns out at an appreciable rate of approximately one percent per month for an in-core rod. Therefore the rods must be replaced every year or two.

(b) The 10B absorber captures by a (n, a) reaction and the helium gas inside a boron carbide rod leads to a pressure build-up inside the control assembly cladding, which also leads to a need to replace the rods.

(c) Fuel management compensation leads to possible multizone refueling

schemes to reduce the reactivity swing by a factor of approximately 2. Such multizone refueling schemes of course lead to additional shut-down time.