Systematic Uncertainty Due to Statistics in Monte Carlo Burnup Codes: Application to a Simple Benchmark with TRIPOLI-4-D

A new burnup code, TRIPOLI-4-D, has been developed at CEA Saclay. It relies on the use of TRIPOLI-4 for the Monte Carlo neutron transport part, and on MENDEL nuclide depletion solver for the burnup calculation. Its main characteristics are pointwise energies, probability tables for the unresolved resonances range, potential fine multigroup calculation of reaction rates, the fourth order Runge-Kutta to solve Bateman's equations, predictor/corrector schemes, novice and expert levels (either launch the calculation with TRIPOLI-4 data set or potential C++ scripting to interact with the coupling macro, through the use of CINT, the ROOT C++ interpreter), post-processing with ROOT, possibility to perform parallel calculations, restart capability. This code owns a special parameter that allows the user to calculate the statistical uncertainty on any physics quantity using the Central Limit Theorem (this very classical Monte Carlo method is also often referred to as “brute force” or “independent replicas” since it consists in replicating a given simulation many times using different random sequences). This technique is particularly adapted to massive parallelism, but can also be set up sequentially on personal computers. In this paper we will apply it on a simple case study, a Pressurized Water Reactor (PWR) cell, and we will analyze different quantities with their associated statistical error bars. Comparing those results to reference simulations, we will try to highlight systematic errors, inherent to Monte Carlo burnup codes, and we will show that a particular systematic error, due to the number of simulated particles, has to be considered while performing Monte Carlo burnup simulations.