The development, implementation, and verification of multicycle depletion perturbation theory

A generalized depletion perturbation formulation based on the "quasi-static" method for solving realistic multicycle reactor depletion problems is developed and implemented within the VENTURE/BURNER modular code system. The present development extends the original formulation derived by M. L. Williams to include nuclide discontinuities such as fuel shuffling and discharge. This theory is first described in detail with particular emphasis given to the similarity of the forward and adjoint quasi-static burnup equations. The specific algorithm and computational methods utilized to solve the adjoint problem within the newly developed DEPTH (Depletion Perturbation Theory) module are then briefly discussed. Finally, the main features and computational accuracy of this new method are illustrated through its application to several representative reactor depletion problems.

The examples utilized in the study cover the range from one-group one-dimensional reactor models to more complex multigroup two-dimensional calculational representations. A set of multicycle calculations are also presented as a test of the adjoint formulation for problems involving discontinuous nuclide fields. Final-time nuclide inventories, eff and the microscopic 238 U capture to 239 Pu fission ratio were utilized as representative responses of interest. Perturbations to the reference system included variations in the fissile, fertile, structural and coolant material concentrations within the fast reactor models utilized. Material concentrations were perturbed locally and globally so as to change the distribution as well as magnitudes of the nuclide and neutron fields within the system. The question of nonlinear behavior for certain perturbation/response pairs was also investigated by varying the magnitude of the material perturbations.

The comparison of predicted responses with direct computation for this large calculational data base clearly demonstrates the remarkable predictive capability of the adjoint depletion formulation implemented within the DEPTH module. This new method can accurately account for variations in the time-dependent neutron and nuclide fields arising from variations in the time-step initial conditions. Thus, multicycle depletion perturbation theory represents an attractive alternate computational method for certain types of burnup analyses, with the greatest cost benefits being associated with repetitive-type scoping calculations.