BEAVRS: An integral full core multi-physics PWR benchmark with measurements and uncertainties

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Highlights

  • Uncertainty in BEAVRS radial fission reaction rates is quantified.

  • Traditional UQ methods and methods based on simulation model fitting agree closely.

  • Uncertainty in using tilt-corrected BEAVRS data is assessed.

Abstract

The BEAVRS benchmark was proposed in 2013 to serve as a non-proprietary benchmark based on measured reactor data to validate high-fidelity reactor simulation methods. In its third version release, the benchmark now includes an open source repository to provide users all source files related to BEAVRS. This version will also contain complete documentation of the uncertainty quantification work conducted. As part of this process, this paper elaborates on a systematic approach to quantifying the uncertainty that arises from using radial tilt-corrected data to compare BEAVRS data to simulated data. These uncertainty metrics are combined with model fitting uncertainties from fitting simulation model trends to BEAVRS data in order to compute overall time-dependent uncertainty of fission reaction rates. It is found that axially-integrated fission chamber time-dependent 95% uncertainty values are 1.8% and 1.9% for Cycle 1 and Cycle 2 respectively, which match well with results using traditional methods for uncertainty quantification.

Introduction

BEAVRS (Benchmark for Evaluation and Validation of Reactor Simulations) is a full-core LWR depletion benchmark created to validate the development of new reactor simulation tools that incorporate sophisticated high-fidelity models. Based on two cycles of operational data from a commercial nuclear power plant, BEAVRS represents a four-loop Westinghouse plant in as much details as available in the open literature. These specifications and all data packages are all publicly available at http://crpg.mit.edu. Recent releases to the benchmark have focused primarily on improvements to the BEAVRS model as well as inclusion of newly available data.

As part of the BEAVRS v3.0 release, the benchmark now features an open source repository (Liang et al., 2018) where users will be given access to all the benchmark-related materials including the documentation, measurement data, scripts for data processing, and inputs of simulation codes. With these source files, it should be much easier to create models, parse data, or make comparisons using this benchmark.

Another significant portion of this release is to outline the uncertainty quantification work conducted for BEAVRS in its entirety. This includes work on Hot Zero Power (HZP) measurement uncertainty, Hot Full Power (HFP) boron letdown uncertainties, reaction rate map uncertainties, and time series analysis. Previous work on the BEAVRS benchmark related to uncertainty quantification has focused on determining the uncertainty in fission reaction rate maps using traditional methods of analyzing axial uncertainties as well as using time series analysis methods to fit burnup trends from simulation tools to BEAVRS data (Liang et al., 2017; Kumar et al., 2016). This paper serves to expound on these subjects and provide final uncertainty results for the benchmark as a whole. Furthermore, previous findings show that radial reaction rate maps computed from measured data exhibit a noticeable tilt in in the northwest-southeast direction despite an eighth-core symmetric core loading pattern (Liang et al., 2017). Thus, a key effort for this uncertainty quantification process is to outline a possible cause for this tilt, correct for this tilt to compare operational data with simulated data, and finally evaluate the additional uncertainty incurred from the tilt-correction process. For reference, the enrichment loading plan for Cycle 1 is shown in Fig. 1, while the loading pattern for Cycle 2 can be found in the full BEAVRS specifications document (Liang et al., 2018).

Section 2 summarizes key results and methodologies for determining reaction rate map uncertainties, while Section 3 devises a methodology to compute uncertainty from tilt-correcting the data. This tilt-corrected data is used when conducting time series analysis on the BEAVRS benchmark, so Section 4 discusses final steps in quantifying time-dependent uncertainty and focuses on combining this tilt-correction uncertainty with the uncertainty that arises from employing a linear regression on time-dependent fission reaction rate data. Finally, Section 5 summarizes benchmark uncertainty values based on the different methods employed.

Section snippets

Reaction rate map uncertainties

All work related to generating BEAVRS fission reaction rate maps and determining uncertainties of these maps has already been published in the conference proceedings for M&C 2013 (Horelik et al., 2013) and M&C 2017 (Liang et al., 2017) but will be summarized here for completeness in order to compare with methods presented in Section 3 and Section 4. The process of generating radial fission reaction rates involves extracting the normalized axial signal and integrating over all axial points to

Uncertainty in using tilt-corrected BEAVRS data

In conjunction with analyzing radial map uncertainties using traditional methods discussed in Section 2 (“Theoretical Analysis of Axial Uncertainties” and “Multiple Measurements” methods), a novel approach that utilizes time series methods is also introduced as part of the BEAVRS uncertainty quantification work (Kumar et al., 2016; Liang et al., 2017). The motivation for such analysis can be understood by trying to fit trends from predictive models over short time intervals. Any deviation from

Time series analysis

The motivation for computing time-dependent uncertainty can be understood by noting the changes in operational data over time. Assuming that at each burnup point, there is a constant but independent uncertainty associated with each axially-integrated reaction rate for a particular assembly, the goal for this section is to figure out whether time-varying data from simulation tools follow similar trends to those from reactor data. Any deviation between the model and reactor data can thus be

Conclusion

The 95% confidence estimates of the UQ methods based on the CASMO/SIMULATE model are presented in Table 9. Similarly, traditional methods for uncertainty quantification are also presented in Table 8 for comparison. Theoretical analysis of axial uncertainties computes uncertainty using all measurements based on variations of signal strengths by groups. This approach determines uncertainties at each axial point using lookup tables and also sums each axial point and associated uncertainty to

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This research was performed using funding received from the DOE Office of Nuclear Energy's Nuclear Energy University Program. This research was also partly supported by the Consortium for Advanced Simulation of Light Water Reactors (CASL), an Energy Innovation Hub for Modeling and Simulation of Nuclear Reactors under U.S. Department of Energy Contract No. DE-AC05-00OR22725. The authors would like to thank Studsvik Scandpower for providing access to CASMO/SIMULATE data, as well as Benjamin

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