# Development of a generalized perturbation theory method for sensitivity analysis using continuous-energy Monte Carlo methods

## Abstract

The sensitivity and uncertainty analysis tools of the ORNL SCALE nuclear modeling and simulation code system that have been developed over the last decade have proven indispensable for numerous application and design studies for nuclear criticality safety and reactor physics. SCALE contains tools for analyzing the uncertainty in the eigenvalue of critical systems, but cannot quantify uncertainty in important neutronic parameters such as multigroup cross sections, fuel fission rates, activation rates, and neutron fluence rates with realistic three-dimensional Monte Carlo simulations. A more complete understanding of the sources of uncertainty in these design-limiting parameters could lead to improvements in process optimization, reactor safety, and help inform regulators when setting operational safety margins. A novel approach for calculating eigenvalue sensitivity coefficients, known as the CLUTCH method, was recently explored as academic research and has been found to accurately and rapidly calculate sensitivity coefficients in criticality safety applications. The work presented here describes a new method, known as the GEAR-MC method, which extends the CLUTCH theory for calculating eigenvalue sensitivity coefficients to enable sensitivity coefficient calculations and uncertainty analysis for a generalized set of neutronic responses using high-fidelity continuous-energy Monte Carlo calculations. Here, several criticality safety systems were examined to demonstrate proofmore »

- Authors:

- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

- Publication Date:

- Research Org.:
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA)

- OSTI Identifier:
- 1245346

- Grant/Contract Number:
- AC05-00OR22725

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Nuclear Science and Engineering

- Additional Journal Information:
- Journal Volume: 182; Journal Issue: 3; Journal ID: ISSN 0029-5639

- Publisher:
- American Nuclear Society

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 22 GENERAL STUDIES OF NUCLEAR REACTORS; 97 MATHEMATICS AND COMPUTING; generalized perturbation theory; sensitivity coefficients; Monte Carlo

### Citation Formats

```
Perfetti, Christopher M., and Rearden, Bradley T.
```*Development of a generalized perturbation theory method for sensitivity analysis using continuous-energy Monte Carlo methods*. United States: N. p., 2016.
Web. doi:10.13182/NSE15-13.

```
Perfetti, Christopher M., & Rearden, Bradley T.
```*Development of a generalized perturbation theory method for sensitivity analysis using continuous-energy Monte Carlo methods*. United States. doi:10.13182/NSE15-13.

```
Perfetti, Christopher M., and Rearden, Bradley T. Tue .
"Development of a generalized perturbation theory method for sensitivity analysis using continuous-energy Monte Carlo methods". United States. doi:10.13182/NSE15-13. https://www.osti.gov/servlets/purl/1245346.
```

```
@article{osti_1245346,
```

title = {Development of a generalized perturbation theory method for sensitivity analysis using continuous-energy Monte Carlo methods},

author = {Perfetti, Christopher M. and Rearden, Bradley T.},

abstractNote = {The sensitivity and uncertainty analysis tools of the ORNL SCALE nuclear modeling and simulation code system that have been developed over the last decade have proven indispensable for numerous application and design studies for nuclear criticality safety and reactor physics. SCALE contains tools for analyzing the uncertainty in the eigenvalue of critical systems, but cannot quantify uncertainty in important neutronic parameters such as multigroup cross sections, fuel fission rates, activation rates, and neutron fluence rates with realistic three-dimensional Monte Carlo simulations. A more complete understanding of the sources of uncertainty in these design-limiting parameters could lead to improvements in process optimization, reactor safety, and help inform regulators when setting operational safety margins. A novel approach for calculating eigenvalue sensitivity coefficients, known as the CLUTCH method, was recently explored as academic research and has been found to accurately and rapidly calculate sensitivity coefficients in criticality safety applications. The work presented here describes a new method, known as the GEAR-MC method, which extends the CLUTCH theory for calculating eigenvalue sensitivity coefficients to enable sensitivity coefficient calculations and uncertainty analysis for a generalized set of neutronic responses using high-fidelity continuous-energy Monte Carlo calculations. Here, several criticality safety systems were examined to demonstrate proof of principle for the GEAR-MC method, and GEAR-MC was seen to produce response sensitivity coefficients that agreed well with reference direct perturbation sensitivity coefficients.},

doi = {10.13182/NSE15-13},

journal = {Nuclear Science and Engineering},

issn = {0029-5639},

number = 3,

volume = 182,

place = {United States},

year = {2016},

month = {3}

}

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