REACTOR CRITICALITY

The radionuclide release rates predicted by the corrosion model took no account of any change in corrosion rates or fission product inventories due to possible criticality. However, since very little of the fuel had been used in the cores, it was decided to investigate the possibility of criticality being achieved as corrosion progressed. If a reactor core could achieve criticality, this could potentially have affected the predicted radionuclide release rates in two ways  

Three scenarios were reviewed to investigate the possibility of any of the reactor cores achieving a critical state  

As a very rough estimate, a marine PWR core will reach the end of its useful life once about 40% of the fuel has been used, after which point it must be refuelled. For a core with a fuel load of SO kg of this equates to 30 kg remaining. This end of life fuel load gives an indication of how much fuel is required for a critical assembly of a lattice of fuel pins in water. Hence, for all core types, in the following analysis a mass of fuel of less than 30 kg will be considered to be unable to achieve criticality, while a mass of more than that may achieve it. 

Analysis of the core bum-ups, assuming 1.25 g per GW d bum-up rate, showed that none of the submarine PWRs with SNF had used more than about 3.5 kg of hence a typical dumped SGI fuelled PWR core could be assumed to contain about 47 kg of fissile material, or 94% of the original (start of life) fuel load. The right board LMR in submarine factory number 601 was undamaged and so could be assumed to contain around 89 kg of the left board core lost 20% of its load as a result of the accident, so was assumed to contain 71 kg. 

All the corrosion models studied by the lASAP use the control rod channel as one of the primary ingress routes for sea water to the core Aus the control rods are subject to corrosion by water as soon 

---

The boundary conditions at the wall, on the other hand, influence the performance of the reactor critically, and should be determined as accurately as possible. For the equations of concentration (or conversion) the condition at the wall is that the flux of material normal to the wall is zero, which requires that the directional derivative of concentration normal to the wall be zero. For the tubular reactor, with cylindrical symmetry, the condition is expressed by the equation... 

To keep the reactor critical during long-term changes in fuel composition and reactivity... 

Fermi and co-workers build the first nuclear reactor (critical on December 2). 

The Usachev Gandini derivation of GPT is based on physical considerations. Their formulation is applicable to alterations that leave the reactor critical. Stacey (40) derived GPT from variational principles. His GPT formulations are also applicable to perturbations that change the static eigenvalue of the Boltzmann equation that is, that do not preserve criticality. The approach used in this work for deriving GPT expressions is neither that of the variational, nor of the physical consideration. It uses conventional perturbation techniques combined with the flux-difference and adjoint-difference methods (see Section III,B). A third version of GPT is presented in this work. Like Stacey s this new version is applicable to perturbations that do not preserve criticality. It pertains, however, to integral parameters that are related to the prompt-mode rather than to the static eigenfunctions. At the end of this section we discuss the relation between... 

SCALE-4 Analysis of Pressurized Water Reactor Critical Configurations Volume 1 — Summary... 

SCALE-4 ANALYSIS OF PRESSURIZED WATER REACTOR CRITICAL CONFIGURATIONS VOLUME 1 — SUMMARY... 

KENO V.a calculated results for reactor critical configurations.19... 

Incremental worth of fission products and parasitic absorbers in reactor criticals.24... 

The requirements of ANSI/ANS 8.1 specify that calculational methods for away-from-reactor criticality safety analyses be validated against experimental measurements. If credit is to be taken for the reduced reactivity of burned or spent fuel relative to its original fresh composition, it is necessary to benchmark computational methods used in determining such reactivity worth against spent fuel reactivity measurements. This report summarizes a portion of the ongoing effort to benchmark away-from-reactor criticality analysis methods using critical configurations from commercial pressurized- water reactors (PWR). 

This report describes the data and procedures used to predict the multiplication factor for several measured critical core configurations using a select set of APR analysis codes. The analyses were performed for precise state points at beginning of cycle (BOC) (mixture of fresh and burned fuel) and at measured state points throughout the cycle depletion (all burned fuel). Self-consistency among the reactor criticals in the prediction of k will allow the determination of the bias of the approach taken in representing the effect of those materials not present in fi esh fuel. 

The following section (1) discusses the differences between the reactor critical configurations and the results computed for each configuration and (2) provides possible explanations for these differences. 

Each of the seven reactor critical scenarios represents a unique set of operating conditions, including factors such as bumup, power, xenon worth, soluble boron concentration, fraction of spent fuel, downtime prior to critical, and temperature conditions. These quantities are summarized in Tables 5 and 6 and demonstrate the range of conditions spanned by these calculations. 

Table 5, Significant aspects of reactor critical configurations...

As has been discussed earlier, notable differences exist between the four reactor designs. These differences may introduce biases in criticality calculations due to modeling approximations or assumptions. Insufficient data exist to allow a statistical determination of any trends and biases in the various reactor critical results. However, it is important to recognize those conditions that might result in such differences because these items should be considered in additional reactor critical calculations, as well as in future uncertainty analyses. The remainder of this section discusses possible causes for differences between the reactor criticals. 

Each of the reactor criticals contains some fraction of burned fuel, ranging from about 50% to 100% of all assemblies. Because of the neutron absorption in U followed by P decay, u is present in all burned fuel assemblies the fractional content will depend on the initial enrichment and assembly bumup. An energy-dependent bias in is known to exist in the 27BURNUPLIB cross-section library for systems containing plutonium.This bias is discussed further in the following section. The net effect of this bias will be an increased value of k jf for lower-energy (more thermalized) systems. Note that this plutonium bias is not limited to the 27BURNUPLIB instead, it appears to be inherent in current plutonium cross-section data. " ... 

---