Imparting realism to criticality evaluations

4 March 2011

The most reactive configuration for the fuel assembly contents of a BWR package must take into consideration parameters that may not be known with a high degree of certainty, such as burnable absorber rod distribution and packaging material composition during a fire. By Peter Vescovi and Tanya Sloma

Transport regulations define normal and accident transport conditions that enable package evaluation to be limited to identification of potential criticality [1]. The criticality evaluation is a demonstration of the most reactive configuration of the individual package in isolation, arrays of undamaged packages,

and arrays of damaged packages. The identification of potential criticality is based on the results of transport condition tests that are performed on a package, or simulated with computational modeling software. Nuclear analysis considers the package configurations, adequate optimization, and other estimations that are consistent with the consequences of transport conditions known from testing or simulation.

Transportation safety for fissile material packages is best served when identification of potential criticality is based upon realistic assumptions for criticality parameters and credible nuclear analysis.

A criticality evaluation of a fissile material package should demonstrate a maximum neutron multiplication by using realistic values for parameters and taking into consideration credible transport conditions including any credible intermediate conditions. The packaging and contents are controlled by the design specifications, and this known configuration should be represented in the nuclear analysis. Values for parameters used in the criticality evaluation should be assigned in a manner consistent with constraints imposed by the fuel assembly design and performance of the package during the prescribed sequence of mechanical, thermal and water immersion tests.

The BWR packaging used in this review consists of inner and outer containers that retain the contents within a fixed geometry relative to other such packages in an array. The radioactive contents consist of a fuel assembly with structure that retains the fuel rods within a fixed geometry. Individual fuel rods retain the fuel pellets within a fixed geometry of a fuel rod tube. Therefore, the confinement system is known to consist of the inner and outer containers, fuel assembly structure, and the fuel rod tube.

Neutron absorption is provided by packaging materials and burnable neutron absorbers present in the fissile fuel mixture. The packaging may not have specific design features that provide neutron moderation and absorption for criticality control. However, neutron absorbers in the structural components and contents provide significant neutron absorption that is considered in the criticality safety evaluation.

Internal moderation is provided by packaging materials such as paper honeycomb, wood, and polyethylene, but none of these materials are present in a configuration to provide the sufficient neutron moderation required for effective neutron absorption or multiplication, with exception of accident conditions for air transport. Hence, neutron moderation from external sources is required to have significant neutron multiplication. Because the water immersion test is not performed, assumptions are made about leakage of water into and out of the package void spaces that are subject to engineering judgment. Adequate assumptions are made for optimizing neutron moderation from internal and external sources that are consistent with the known transport conditions and laws of nature.

Possible configurations of the radioactive contents and packaging (single package, arrays of undamaged packages, and arrays of damaged packages) that are consistent with each condition of transport are evaluated. The most reactive contents are evaluated with the packaging to identify the optimum combination of packaging materials, internal moderation and interspersed moderation. The most reactive configuration for each type of fuel assembly contents takes into consideration partial-length fuel rods in fuel bundle, neutron-absorbing BA rods in the fuel bundle, and rearrangement of the fuel bundle in the form of lattice expansion during accident transport conditions. Fuel rearrangement is limited by the fuel bundle structure, fuel assembly structure, or inner wall of the inner container. First, the fuel bundle structure (tie plates, spacer grids) confines fuel rods to a nominal pitch during normal transport conditions. Second, rearrangement of the bundle lattice resulting from an impact consistent with accident transport conditions is confined by the fuel channel for fuel assembly contents. Third, the inner wall of the inner container provides confinement for fuel bundle contents or fuel rods without the rod container.

Arrangement of radioactive contents and packaging material composition are important to consider in the optimization of reactivity. Since there is no guarantee of a particular sequence of impacts or the complete progression of a fire during a transport accident, intermediate conditions that may result in the maximum neutron multiplication are considered.

Burnable absorber (BA) rods that are used to extend the life of the fuel bundle during the power generation cycle also provide neutron absorption for transport conditions where moderation of the fuel occurs. Internal sources of moderation from polyethylene packaging materials such as foam, protective spacers, cluster separators, and sheathing, or water from external sources are credible sources of moderation for the fuel bundle. The effectiveness of the BA rods as a neutron absorber is significant in a moderated fuel bundle, but the relative efficacy as a neutron absorber varies sensitively with the location of the BA rod within the fuel bundle lattice. In order to evaluate the relative efficacy of BA rods, neutron absorption in the gadolinium is assessed at each location within a fuel bundle lattice.

A sensitivity analysis based on analytical perturbation methods is used to select the BA rod locations. Constraints that are consistent with the design objectives for a BWR fuel assembly are as follows:

1) Rule of symmetry: BA rods shall be in positions that are symmetric across the geometric major diagonal

2) No BA rod shall be located in the outermost edge or corner location of the fuel rod lattice

3) Partial length fuel rods shall not be BA rods

4) At least one BA rod shall be located in three of the four fuel lattice quadrants

5) There shall be at least 8 BA rods in the fuel bundle

Applying these rules in the selection process results in a pattern of burnable absorber rods that is not the most reactive conceivable arrangement nor an actual rod pattern expected in the fuel design, but rather represents a pattern that provides adequate neutron absorption and acknowledges realistic constraints imposed by the fuel bundle design.


Intermediate conditions result from the transition of packaging materials’ composition or phase changes that occur during a fire. The combustion or redistribution of packaging material during the fire are considered in the evaluation, because the neutron multiplication may be larger for the intermediate condition as compared to the final state.

Water or void is commonly assumed to fill the void space left by the complete combustion of impact absorber material. However, thermal testing and analysis demonstrate that impact absorber material (paper honeycomb, balsa wood) may undergo only partial combustion during a fire. The chemical composition of impact absorber material is carbon (C), hydrogen (H), and oxygen (O). Char is produced in the absence of oxygen by the slow pyrolysis of the impact absorber material. By the action of heat, charring removes hydrogen and oxygen from the solid so that the remaining char is composed primarily of carbon. Carbon at the original density is assumed to evaluate the effect that incomplete combustion has on neutron multiplication.

The moderating ratio—a measure of the effectiveness of neutron scattering in the packaging materials and contents to slow down neutrons to thermal energies–increases when char displaces water in the package or char instead of void is assumed to remain in the package. Chromium in the stainless steel package structure and fissile uranium in the contents compete for absorption of neutrons during the slowing down process. An increase in moderating ratio for the individual package configuration results in preferential absorption in the fissile uranium contents due to the limited quantity of stainless steel, and the neutron multiplication increases as compared to a reference configuration with water instead of char. An increase in moderating ratio for the package array results in preferential absorption in the stainless steel due to the large amount of neutron interaction between packages as neutrons slow down. The multiplication factor for the package array decreases as compared to a reference configuration with void instead of char. An intermediate material condition due the incomplete combustion of impact absorber material can result in a maximum neutron multiplication that may otherwise have been overlooked if complete combustion is assumed.

During a fire, redistribution of moderating materials such as polyethylene packing materials may also provide moderation of the contents resulting in an increase, decrease or no significant change in neutron multiplication. Packaging materials normally present and contiguous with the contents such as polyethylene cluster separators, spacers, and wrap are considered for all transport conditions. The effect on moderation by these packing materials is evaluated by assuming that these materials are uniformly distributed on the fuel rod outer surface regardless of the condition of transport. The effect of a polyethylene foam cushion that may melt during accident conditions and provide additional moderation within the fuel bundle is also considered in the evaluation. An intermediate condition such as the accident transport condition prior a fire or the absence of a fire, results in a credible configuration where foam material remains rather than becoming a space filled with water during immersion. This configuration with the foam intact results in more neutron interaction for the accident package array than if the foam were assumed to melt and be replaced by water. Therefore, this intermediate accident condition for foam cannot be ignored as it is a credible accident condition that results in the maximum neutron multiplication.

Lattice expansion

Tests demonstrate that virtually all fuel rod deformations induced from an axial impact are due to interactions between the end of the fuel rod and the deformed nozzles. BWR fuels are designed to be under-moderated, hence an impact event which increases the pin pitch results in an increase in reactivity.

It has been observed that for BWR fuel subjected to end impacts, the lattice may contract near the impacted end but expand slightly in the adjacent intra-grid length. Relying only on the fuel bundle structure for confinement, a mean lattice pitch change of less than 5 mm is predicted by static analysis methods between the second and third spacer grids from the bottom of the fuel assembly [2]. Nominal dimension between the second and third grid is less than 50 cm for BWR fuel assemblies. Analyzed performance of the lower tie plate and cladding during an end impact predicts responses similar to that observed in mechanical tests. The analysis concludes that the lower tie plate will not fail during an end drop and the cladding will not rupture due to the rod bowing. The testing and analytical results justify the assumptions that the individual fuel pellets are contained in the cladding and no water can leak into the void space between fuel pellet and cladding during accident transport conditions.

The criticality analysis ignores lattice contraction near the end, but does consider the uniform lattice expansion above the first grid. A BWR fuel assembly is evaluated to determine the maximum reactivity due to an increase in lattice pitch that is confined to a length of 50 cm near the end of the fuel bundle. This assessment is done for a range of fuel rod pitches that includes the dimensions that are associated with each confinement boundary (nominal fuel bundle, fuel channel, inner container). Lattice expansion for a fuel bundle shipped with the fuel channel installed, referred to as the fuel assembly, is confined to the fuel channel. A fuel bundle not confined by the fuel channel can expand to the inside dimension of the inner container. The nuclear analysis demonstrates that an allowed package array size is dependent on the extent of the lattice expansion. By recognizing this realistic difference in the confinement boundary for a fuel bundle as compared to the fuel assembly, a smaller criticality safety index (CSI) is possible when the fuel channel is present.

Author Info:

This article is an excerpt of a paper presented at PATRAM 2010, the 16th international symposium on the packaging and transport of radioactive materials, 3-8 October in London. Peter Vescovi and Tanya Sloma, Westinghouse Electric Company, 5801 Bluff Road, Columbia, South Carolina 29209 USA


[1] ORNL/M-5003, “The Radioactive Materials Packaging Handbook,” 1998
[2] Peter C Purcell, “Method To Evaluate Limits Of Lattice Expansion In Light Water Reactor Fuel From An Axial Impact Accident During Transport,” Proceedings of the 15th International Symposium on the Packaging and Transportation of Radioactive Materials
PATRAM 2007, Miami, Florida USA (October 2007)

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