Development of computation schemes for small-sized boron-free PWR

Commercial pressurized water reactors (PWR) typically rely on high electrical output power, greater than or around 1 GWe. With the emergence of newly identified uses such as power supply in remote area or heat production, small modular reactors (SMR) concepts have been designed with an electrical output power below 300 MWe. Although soluble boron is commonly used in PWR to control the reactivity, some SMR are designed without soluble boron in the primary circuit. The reactivity control in soluble boron-free (SBF) reactors relies mainly on the insertion or withdrawal of control rods. The introduction of burnable absorbers also contributes by design to the reactivity control. Soluble boron-free SMR can be justified regarding safety, economic and environmental advantages.Two-level deterministic computational schemes are generally used for PWR modelling. The first step consists in 2D detailed assembly calculations where refined energy and spatial meshes are considered to solve the neutron transport equation. In the standard computational scheme, a first depletion calculation is performed over a full range of burnup steps in an All-Rods-Out (ARO) configuration to compute isotopic concentrations. Branch calculations are then carried out at each burnup step by varying different parameters: moderator density, fuel temperature and rod insertion. The fine energy mesh cross sections are then collapsed to two-group cross sections and homogenized over the pin cell. This cross section library is then used at the core level to compute the 3D power distribution by solving the two-group diffusion equations. With SBF cores, the assumption of an ARO configuration for computing the fuel depletion can be questioned since the depletion history includes the presence of inserted control rods that modifies the neutron spectrum.The first objective of this thesis is to quantify the numerical biases introduced by the standard neutronic computational scheme in the modelling of SBF fuel assemblies, cluster and SMR core including a large quantity of burnable absorber (in the form of gadolinium oxide). The second and main objective is to develop a method able to simulate spectrum history effects over the entire core at reasonable computing cost.This work is carried out using the APOLLO3-R deterministic code. The developed method called COHLISEE is inspired from previous work found in the scientific literature about spectrum history effects. COHLISEE is a hybrid method that consists in using both microscopic depletion and spectrum history indicator in 3D diffusion core calculation. The multigroup cross section libraries are generated by merging All Rods Out (ARO) and All Rods In (ARI) depleted libraries. The method has been verified and validated on fuel assemblies and 2x2 cluster 2D calculations. Reference results have been obtained with 2D transport calculations performed with controls rods inserted following specific sequences. COHLISEE results (reactivity, power, material balance) are compared to standard schemes using either macroscopic or microscopic depletion. The V and V process shows that macroscopic standard calculations are leading to massive numerical biases on reactivity for all control rods sequences studied. With the microscopic standard scheme, numerical biases are relatively small for UO₂ fuel assembly without burnable absorbers but can be comparable to macroscopic standard scheme for poisoned fuel assemblies. Core calculations performed with the COHLISEE method show a reduction of the numerical biases, especially on pin-by-pin power distributions, at a computing cost comparable to standard microscopic scheme.In order to compare the COHLISEE method to standard schemes, 3D whole-core calculations are performed for a SBF-SMR benchmark. This study evaluates the magnitude of numerical differences between COHLISEE and standard schemes. (author)