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Fluence is the time-accumulated neutron or gamma flux through a given surface for a given period of time. In simpler terms, it’s the amount of radiation a component has received over time. Many factors go into determining the rate of fluence accumulations, also known as flux, including reactor power, fuel bundle designs, and operating strategies. Fluence is further broken into two categories, fast fluence (neutrons with energy > 1.0 MeV), and thermal fluence (neutrons with energy of about 0.025 eV). The distinction between the two categories is important because the two types of fluence have vastly different effects on materials and require different approaches in their calculation.

Fast neutrons displace atoms in a material’s structure, weakening the lattice and causing it to become more brittle. Embrittled material is more susceptible to cracking, and existing cracks will grow faster. Core shrouds and former plates are the most susceptible to cracking due to their proximity to the core. Fast fluence also causes structural lattices to expand, lengthening materials over time, which is a contributing factor to such industry issues as channel bow. More recently, concerns regarding the effect of fluence on the elongation of the core support plate rim bolts in BWR’s have been raised.

Thermal neutrons tend to be absorbed by impurities in the material lattice, such as boron. The resulting heavy elements are often unstable, emitting alpha particles as they decay. These alpha particles, or helium atoms, get trapped in the material, which can affect its weldability for performing repairs, thus necessitating the replacement of failed components. 

All material changes must be considered when it’s time to repair a weld, develop your in-service inspection plans to monitor shroud weld crack growth, or update P-T curves.

When do you know if a component is approaching or has exceeded its durable lifetime? 

Inspections and calculations. With the aging of the current nuclear fleet, radiation effects on all material structures inside and outside the vessel, including reinforced concrete structures housing the pressure vessel, are being reviewed with all possible means. The most cost-effective means are calculations.

There are many tools for calculating fluence, the first of which were developed more than 50 years ago. Today, there are several categories of fluence codes, the broadest of which include Monte Carlo methods and deterministic methods. Monte Carlo codes function by brute force simulation of neutron particles and statistical analysis. With enough particle simulations, or histories, the method approaches an asymptotic solution along with a corresponding uncertainty. The process is time consuming, but it can produce very good results. Besides computational time, these methods are further limited by requiring the user to specify the specific tally regions in which to obtain a solution. As the number of tally regions increase, so does the solution time and statistical error.

To address these inherent limitations, another class of codes was developed that solve the Boltzmann transport equation analytically by making certain approximations. These methods are collectively referred to as deterministic methods. Since the equations are solved analytically for the entire problem geometry, a deterministic code allows the user to get detailed results for the entire reactor in a relatively short period of time.

Regardless of the type of code used, the overall accuracy is limited by the quality of the input data. Since fluence is cumulative, data spanning the entire history of the plant must be obtained. This data includes plant mechanical drawings, core configurations, and operating parameters. In the absence of recorded data, approximations may be made, with a corresponding impact on the overall uncertainty of the evaluation.

TransWare Enterprises Inc. utilizes the RAMA Fluence Methodology, a deterministic fluence code developed by TransWare under a research program funded by EPRI. RAMA has been approved for use by the NRC for determining neutron fluence in accordance with U. S. Regulatory Guide 1.190 with a zero bias. RAMA utilizes a 3-D arbitrary geometry model builder, method-of-characteristics particle solver, and a series of pre- and post-processing tools to generate detailed and highly accurate fluence profiles for any component or region inside and outside of the pressure vessel.

The RAMA fluence code has been tested against a series of industry benchmarks and real-world comparisons against BWR and PWR dosimetry samples. While pressure vessel calculations are required by U. S. Regulatory Guide 1.190 to have an uncertainty of less than 20%, RAMA performs much better. After performing comparisons to more than 1,000 data points, TransWare has achieved an overall unadjusted calculated-to-measured comparison ratio of 1.02 with a standard deviation of less than 10%.