Final Report for the NERI Project

Abstract

a manuscript summarizing the fuel cycle optimization algorithms for the sodium-cooled fast reactor (SFR) developed under the grant. These three latest papers are attached to the report. Summary of research accomplishments Task Optimization of fast rector transmuterWith the objective to perform systematic optimization of SFR transmuters, we developed a general fuel cycle optimization methodology that could be applied to the optimization of fuel cycles both for SFRs and pressurized water reactors (PWRs). The key features of the optimization algorithms include:(1) The optimization algorithms are based on the calculus of variations that allows for a systematic augmentation of desired objective function typically expressed in terms of end-of-cycle (EOC) fuel cycle attributes, (2)The Lagrange multipliers introduced in the augmentation process allows for direct representation of system constraints, e.g., the power peaking factor constraint, (3) A first-order variation of the augmented objective function yields the necessary condition for optimality together with Euler-Lagrange equations for the Lagrange multipliers cast in the form of adjoint system equations, (4) The adjoint flux and depletion equations are solved backward from EOC to beginning-of-cycle (BOC), with discontinuities introduced in the adjoint neutron flux at the constraint boundaries, (5) The adjoint flux, combined with the forward flux, provides the search directions for the control variables, e.g., transuranics (TRU) enrichment or burnable absorber (BA) placement, and (6) The combination of forward diffusion-depletion calculations and backward adjoint flux-depletion calculations is repeated until the objective function is minimized. The deterministic algorithms may be initiated from arbitrary core configurations and typically converge in a few iterations to yield optimal configurations desired. This is to be contrasted with many of the popular stochastic optimization algorithms that require 2 10 4~1 0 5 iterations before an optimal configuration is attained. Furthermore, through a separate backward diffusion theory algorithm, the power peaking constraints are rigorously satisfied. The optimization algorithm for SFR transmuter cases systematically yields an optimized core configuration with a reduced power peaking factor and lower reactivity swing over a fuel cycle. Similarly, the PWR optimization algorithm applied to the AP600 design yields a lower radial peaking factor than that presented in the Standard Safety Analysis Report, together with a reduced number of BA rods required. This implies that the improved design allows for (a) a higher power density, (b) an increased cycle length due to a reduction in the residual BA penalty at EOC, and (c) savings in the BA cost. Two doctoral dissertations were completed under Task 1.Publications resulting from Task 1 are listed below:1. R. T. Sorensen, J. C. Davis, and J. C. Lee, "Systematic Method for Optimizing Plutonium Transmutation in LWRs," Trans. Am. Nucl. Soc., 95, 217 (2006). Task 2. Development of equ...