Adjoint-Based Uncertainty Quantification and Sensitivity Analysis for Reactor Depletion Calculations

Abstract

Depletion calculations for nuclear reactors model the dynamic coupling between the material composition and neutron flux and help predict reactor performance and safety characteristics. In order to be trusted as reliable predictive tools and inputs to licensing and operational decisions, the simulations must include an accurate and holistic quantification of errors and uncertainties in its outputs. Uncertainty quantification is a formidable challenge in large, realistic reactor models because of the large number of unknowns and myriad sources of uncertainty and error.

We present a framework for performing efficient uncertainty quantification in depletion problems using an adjoint approach, with emphasis on high-fidelity calculations using advanced massively parallel computing architectures. This approach calls for a solution to two systems of equations: (a) the forward, engineering system that models the reactor, and (b) the adjoint system, which is mathematically related to but different from the forward system. We use the solutions of these systems to produce sensitivity and error estimates at a cost that does not grow rapidly with the number of uncertain inputs. We present the framework in a general fashion and apply it to both the source-driven and k-eigenvalue forms of the depletion equations. We describe the implementation and verification of solvers for the forward and ad- joint equations in the PDT code, and we test the algorithms on realistic reactor analysis problems. We demonstrate a new approach for reducing the memory and I/O demands on the host machine, which can be overwhelming for typical adjoint algorithms. Our conclusion is that adjoint depletion calculations using full transport solutions are not only computationally tractable, they are the most attractive option for performing uncertainty quantification on high-fidelity reactor analysis problems.