↑burnup ⇒ ↓keff = ↓η .ε.p. ↓f . ↑↓Pf. ↑↓Pt
It is hard to describe the effects of fuel burnup on the six factor formula. It must be noted, the criticality must be maintained for long period and therefore all the negative effects must be compensated by the increase in the thermal utilization factor (boron dilution or compensating rods withdrawal).
Thermal Utilization Factor
The thermal utilization factor slightly changes with the fuel burnup. The fresh fuel at the beginning of the cycle comprises only the absorption by the 235U. As the amount of 239Pu and other higher transuranic elements increases because of the radiative capture of neutron by the 238U in the core, it is necessary to consider the change of fuel composition in determining the value of f at different times of the fuel cycle.
In general, the thermal utilization factor decreases in time as the total content of fissile isotopes decreases and the total content of neutron poisons (fission products with high absorption cross-sections) increases. But in the power reactors, in which the criticality must be maintained for long period (e.g. 12-month or up to 24-month) without refueling, the thermal utilization factor may not decrease. Such the decrease would imply inevitable reactor shutdown. The continuous decrease in ΣaU must be offset by the continuous decrease in ΣaB, which means the concentration of boric acid (in case of PWRs) must be continuously decreased as the fuel loses its reactivity (kinf). For reactors, in which the chemical shim can not be used, the excess of reactivity is compensated by compensating rods.
There is essentially small change in η over the lifetime of the reactor core (decreases).This is due to the fact there is a continuous decrease in ΣfU, but on the other hand this decrease is partially offset by the increase in ΣfPu. As the fuel burnup increases, the 239Pu begins to contribute to the neutron economy of the core.
See also: Nuclear Breeding
In power reactors, the total non-leakage probability also significantly changes with fuel burnup. This dependency is not associated with any of the parameters like the diffusion coefficient or the geometrical buckling. In power reactors, the total non-leakage probability strongly depends on the certain fuel loading pattern and also on the reload strategy. The neutron leakage is one of key parameters in the neutron and fuel economy.
In order to enhance the neutron and fuel economy, core designers designs the low leakage loading patterns, in which fresh fuel assemblies are not situated in the peripheral positions of the reactor core. The peripheral positions are loaded with the fuel with highest fuel burnup. These “high” burnup assemblies have inherently lower relative power (due to the lower kinf and due to the fact they feel the presence of non-multiplying environment) in comparison with the average assemblies. In short, this parameter is significantly dependent on the certain loading pattern. During fuel burnup, the neutron leakage usually increases, especially in low leakage loading patterns. This process is caused by reducing the differences in kinf between fresh fuel assemblies and peripheral high-burnup assemblies.