Matthew Anderson Jessee

Sensitivity and Uncertainty Analysis Capabilities and Data in SCALE

Abstract In SCALE 6, the Tools for Sensitivity and UNcertainty Analysis Methodology Implementation (TSUNAMI) modules calculate the sensitivity of keff or reactivity differences to the neutron cross-section data on an energy-dependent, nuclide-reaction-specific basis. These sensitivity data are useful for uncertainty quantification, using the comprehensive neutron cross-section-covariance data in SCALE 6. Additional modules in SCALE 6 use the sensitivity and uncertainty data to produce correlation coefficients and other relational parameters that quantify the similarity of benchmark experiments to application systems for code validation purposes. Bias and bias uncertainties are quantified using parametric trending analysis or data adjustment techniques, providing detailed assessments of sources of biases and their uncertainties and quantifying gaps in experimental data available for validation. An example application of these methods is presented for a generic burnup credit cask model.

A Statistical Sampling Method for Uncertainty Analysis with SCALE and XSUSA

A new statistical sampling sequence called Sampler has been developed for the SCALE code system. Random values for the input multigroup cross sections are determined by using the XSUSA program to sample uncertainty data provided in the SCALE covariance library. Using these samples, Sampler computes perturbed self-shielded cross sections and propagates the perturbed nuclear data through any specified SCALE analysis sequence, including those for criticality safety, lattice physics with depletion, and shielding calculations. Statistical analysis of the output distributions provides uncertainties and correlations in the desired responses, due to nuclear data uncertainties. The Sampler/XSUSA methodology is described, and example applications are shown for criticality safety and spent-fuel analysis.

Efficient Subspace Methods-Based Algorithms for Performing Sensitivity, Uncertainty, and Adaptive Simulation of Large-Scale Computational Models

Abstract This paper introduces the concepts and derives the mathematical theory of efficient subspace methods (ESMs) applied to the simulation of large-scale complex models, of which nuclear reactor simulation will serve as a test basis. ESMs are intended to advance the capabilities of predictive simulation to meet the functional requirements of future energy system simulation and overcome the inadequacies of current design methods. Some of the inadequacies addressed by ESM include lack of rigorous approach to perform comprehensive validation of the multitudes of models and input data used in the design calculations and lack of robust mathematical approaches to enhance fidelity of existing and advanced computational codes. To accomplish these tasks, the computational tools must be capable of performing the following three applications with both accuracy and efficiency: (a) sensitivity analysis of key system attributes with respect to various input data; (b) uncertainty quantification for key system attributes; and (c) adaptive simulation, also known as data assimilation, for adapting existing models based on the assimilated body of experimental information to achieve the best possible prediction accuracy. These three applications, involving large-scale computational models, are now considered computationally infeasible if both the input data and key system attributes or experimental information fields are large. This paper will develop the mathematical theory of ESM-based algorithms for these three applications. The treatment in this paper is based on linearized approximation of the associated computational models. Extension to higher-order approximations represents the focus of our ongoing research.

Many-Group Cross-Section Adjustment Techniques for Boiling Water Reactor Adaptive Simulation

Abstract Computational capability has been developed to adjust multigroup neutron cross sections, including self-shielding correction factors, to improve the fidelity of boiling water reactor (BWR) core modeling and simulation. The method involves propagating multigroup neutron cross-section uncertainties through various BWR computational models to evaluate uncertainties in key core attributes such as core keff, nodal power distributions, thermal margins, and in-core detector readings. Uncertainty-based inverse theory methods are then employed to adjust multigroup cross sections to minimize the disagreement between BWR core modeling predictions and observed (i.e., measured) plant data. For this paper, observed plant data are virtually simulated in the form of perturbed three-dimensional nodal power distributions with the perturbations sized to represent actual discrepancies between predictions and real plant data. The major focus of this work is to efficiently propagate multigroup neutron cross-section uncertainty through BWR lattice physics and core simulator calculations. The data adjustment equations are developed using a subspace approach that exploits the ill-conditioning of the multigroup cross-section covariance matrix to minimize computation and storage burden. Tikhonov regularization is also employed to improve the conditioning of the data adjustment equations. Expressions are also provided for posterior covariance matrices of both the multigroup cross-section and core attributes uncertainties.

A Two-Step Approach to Uncertainty Quantification of Core Simulators

For the multiple sources of error introduced into the standard computational regime for simulating reactor cores, rigorous uncertainty analysis methods are available primarily to quantify the effects of cross section uncertainties. Two methods for propagating cross section uncertainties through core simulators are the XSUSA statistical approach and the “two-step” method. The XSUSA approach, which is based on the SUSA code package, is fundamentally a stochastic sampling method. Alternatively, the two-step method utilizes generalized perturbation theory in the first step and stochastic sampling in the second step. The consistency of these two methods in quantifying uncertainties in the multiplication factor and in the core power distribution was examined in the framework of phase I-3 of the OECD Uncertainty Analysis in Modeling benchmark. With the Three Mile Island Unit 1 core as a base model for analysis, the XSUSA and two-step methods were applied with certain limitations, and the results were compared to those produced by other stochastic sampling-based codes. Based on the uncertainty analysis results, conclusions were drawn as to the method that is currently more viable for computing uncertainties in burnup and transient calculations.

SCALE Code System

The Criticality Safety Analysis Sequences with KENO V.a (CSAS5) provides reliable and efficient means of performing keff calculations for systems that are routinely encountered in engineering practice. In the multigroup calculation mode, CSAS5 uses XSProc to process the cross sections for temperature corrections and problem-dependent resonance self-shielding and calculates the keff of a three-dimensional (3-D) system model. If the continuous energy calculation mode is selected no resonance processing is needed and the continuous energy cross sections are used directly in KENO V.a, with temperature corrections provided as the cross sections are loaded. The geometric modeling capabilities available in KENO V.a coupled with the automated cross-section processing within the control sequences allow complex, 3-D systems to be easily analyzed. A search capability is achieved by repeatedly activating the control module MODIFY, to alter either the system dimensions or densities, and the functional module KENO V.a to calculate the keff for the modified dimensions or densities. Formerly with Oak Ridge National Laboratory. 2-5 TABLE OF CONTENTS