Title: Evaluating Quantities of Interest Other Than Nuclide Densities in the Bateman Equations

Abstract

Traditionally, analysts solve the Bateman depletion equations to calculate the nuclide number density (NND) of each nuclide since these densities impact other reactor parameters, such as reactivity, as they change. Many quantities of interest, such as radiation damage, are calculated using simple integration methods, assuming that the NNDs are constant over a given depletion interval. However, the NNDs are time dependent, which can be accurately represented only by the Bateman depletion equations. We propose that these quantities can be calculated simultaneously with the NNDs within the Bateman depletion equations, preserving the coupled nature of these quantities to the time-dependent NNDs. We implemented this functionality in Griffin, demonstrating that only minor code modifications were necessary in order to accommodate an evaluation of these quantities in the Bateman depletion equations. The Chebyshev Rational Approximation Method was used to successfully solve for these additional quantities in the Bateman depletion equations. For radiation damage, the results calculated by Griffin were very accurate, differing by less than 2.5% from an analytical benchmark. For other quantities, the discrepancy between quantities calculated by the Bateman depletion equations versus those calculated by the Forward Euler method exceeded 10% for decay energy and 2% for fissions per initial heavymore » metal atom and kinetic energy released per unit mass when few depletion intervals were used. As the number of depletion intervals increased, both methods began to converge as expected.« less

Authors:

Calvin, Olin W.  ^[1];

• Search DOE PAGES for author "Calvin, Olin W."
• Search DOE PAGES for ORCID "0000-0001-9560-0356"

Gale, Micah D. ^[2]; Schunert, Sebastian ^[2]

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+ Show Author Affiliations

1. Idaho National Laboratory, Reactor System Design and Analysis Division, 1955 North Fremont Avenue, MS 1347, Idaho Falls, Idaho 83415, University of Idaho, Idaho Falls, Center for Advanced Energy Studies, 995 MK Simpson Boulevard, Idaho Falls, Idaho 83401
2. Idaho National Laboratory, Reactor System Design and Analysis Division, 1955 North Fremont Avenue, MS 1347, Idaho Falls, Idaho 83415

Publication Date:

Mon Feb 13 00:00:00 EST 2023

Research Org.:

Idaho National Laboratory (INL), Idaho Falls, ID (United States)

Sponsoring Org.:

USDOE Office of Nuclear Energy (NE); USDOE Laboratory Directed Research and Development (LDRD) Program

OSTI Identifier:

1924357

Alternate Identifier(s):

OSTI ID: 1957753

Report Number(s):

INL/JOU-22-68732-Rev000
Journal ID: ISSN 0029-5639; 44

Grant/Contract Number:  

AC07-05ID14517

Resource Type:

Published Article

Journal Name:

Nuclear Science and Engineering

Additional Journal Information:

Journal Name: Nuclear Science and Engineering Journal Volume: 197 Journal Issue: 8; Journal ID: ISSN 0029-5639

Publisher:

Informa UK Limited

Country of Publication:

United States

Language:

English

Subject:

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS; 97 MATHEMATICS AND COMPUTING; 36 MATERIALS SCIENCE; Bateman equations; transmutation; depletion; Chebyshev Rational Approximation Method; displacement radiation damage