Extension of the ERANOS capabilities in performing depletion sensitivity analyses for fast reactors

Sensitivity analysis is one of the fundamental components of nuclear reactor design, enabling the estimation of how input perturbations propagate to output quantities. This work extends the capabilities of the ERANOS code to perform sensitivity analyses in depletion problems for fast reactors. An important point concerns the number and quality of the indirect effects accounted for in the sensitivity coefficients. The present extension enables ERANOS to include the previously missing indirect effects associated with variations in the shape and intensity of the neutron flux, while improving the evaluation of those related to isotopic evolution. The new implementation relies on the quasi-static approximation with constant flux depletion and on the variational formulation of the Generalized Perturbation Theory (GPT), both already adopted in ERANOS. The GPT implementation was developed without modifying the ERANOS source code. This was achieved by exploiting formal similarities between quantities already available in the code and those required by the new formulation. An internal verification tool based on the direct perturbation (DP) method complements the GPT extension, allowing the computation of sensitivities also with separation of the direct and indirect components. The extended capabilities were verified on a set of test cases of increasing complexity, ranging from infinite homogeneous systems to finite heterogeneous ones. In the early phases, a MATLAB® symbolic solver was employed for analytical verification. Subsequently, within ERANOS, GPT sensitivities were compared under different sets of constraints. Then, sensitivities with full perturbative coupling were benchmarked against those obtained with the APOLLO3® code and ERANOS DP sensitivities. The results show the impact of the extension with respect to the previous implementation, as well as a strong consistency between ERANOS and APOLLO3®, with relative discrepancies consistently below 3%–4%. These findings provide a solid basis for applying the new implementation to analyses of fast nuclear reactors.