Perturbation and sensitivity theory for burnup analysis

Thesis/Dissertation · Mon Jan 01 04:00:00 EST 1979

OSTI ID:5459362

Williams, M L

Perturbation theory is developed for the nonlinear burnup equations describing the time-dependent behavior of the neutron and nuclide fields in a reactor core. General aspects of adjoint equations for nonliner systems are first discussed and then various approximations to the burnup equations are rigorously derived and their areas for application presented. In particular, the concept of coupled neutron/nuclide fields (in which perturbations in either the neutron or nuclide field are allowed to influence the behavior of the other field) is contrasted to the uncoupled approximation (in which the fields may be perturbed independently). Solution algorithms are given for numerically solving the adjoint burnup equations, and the implementation of these procedures into existing computer codes is discussed. Perturbation theory is used to define sensitivity coefficients for burnup-dependent responses. Uncoupled depletion sensitivity theory is applied to the analysis of an irradiation experiment being used to evaluate new actinide cross-section data. The computed sensitivity coefficients are used to determine the sensitivity of various nuclide concentrations in the irradiated sample to actinide cross sections. Uncertainty analysis is used to calculate the standard deviation in the computed values for the plutonium isotopics. Coupled depletion sensitivity theory is used to analyze a 3000 MW/sub th/ denatured LMFBR model (2 region, sphere). The changes in the final inventories of /sup 232/U, /sup 233/U, and /sup 239/Pu due to changes in concentrations of several nuclides at the beginning of cycle are predicted using depletion perturbation theory and are compared with direct calculation. In all cases the perturbation results show excellent agreement with the direct changes.

• Research Organization: Tennessee Univ., Memphis (USA)
• OSTI ID: 5459362
• Country of Publication: United States
• Language: English

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