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.

The Oak Ridge Isotope Generation and Depletion – Automatic Rapid Proccessing (ORIGEN-ARP) deterministic code has been extensively utilized for determining nuclide concentrations at various specific burnup values for a variety of nuclear reactor designs. Given nuclide concentrations or ratios, such calculations can be used in nuclear forensics and nuclear non-proliferation applications to reverse-calculate the type of reactor and specific burnup of the fuel from which the nuclides originated. Recently, Los Alamos National Laboratory has released a version of its probabilistic radiation transport code, MCNPX 2.6.0, which incorporates a fuel burnup feature which can also determine, via the probabilistic Monte Carlo method, nuclide concentrations as a function of fuel burnup. This dissertation compares the concentrations of 46 nuclides significant to nuclear forensics analyses for different reactor types using results from the ORIGEN-ARP and the MCNPX 2.6.0 codes. Three reactor types were chosen: the Westinghouse 17x17 Pressurized Water Reactor (PWR), the GE 8x8-4 Boiling Water Reactor (BWR), and the Canadian Deuterium Uranium, CANDU-37, reactor. Additionally, a sensitivity study of the different reactor parameters within the MCNPX Westinghouse 17x17 PWR model was performed. This study analyzed the different nuclide concentrations resulting from minor perturbations of the following parameters: assembly rod pitch, initial moderator boron concentration, fuel pin cladding thickness, moderator density, and fuel temperature. / text

Depuis quelques années, les codes de calculs Monte Carlo évoluant qui couplent un code Monte Carlo, pour simuler le transport des neutrons, à un solveur déterministe, qui traite l'évolution des milieux dû à l'irradiation sous le flux neutronique, sont apparus. Ces codes permettent de résoudre les équations de Boltzmann et de Bateman dans des configurations complexes en trois dimensions et de s'affranchir des hypothèses multi-groupes utilisées par les solveurs déterministes. En contrepartie, l'utilisation du code Monte Carlo à chaque pas de temps requiert un temps de calcul prohibitif.Dans ce manuscrit, nous présentons une méthodologie originale évitant la répétition des simulations Monte Carlo coûteuses en temps et en les remplaçant par des perturbations. En effet, les différentes simulations Monte Carlo successives peuvent être vues comme des perturbations des concentrations isotopiques de la première simulation. Dans une première partie, nous présenterons donc cette méthode, ainsi que la méthode de perturbation utilisée: l'échantillonnage corrélé. Dans un second temps, nous mettrons en place un modèle théorique permettant d'étudier les caractéristiques de la méthode des échantillons corrélés afin de comprendre ses effets durant les calculs en évolution. Enfin, dans la troisième partie nous discuterons de l'implémentation de cette méthode dans TRIPOLI-4® en apportant quelques précisions sur le schéma de calcul qui apportera une accélération importante aux calculs en évolution. Nous commencerons par valider et optimiser le schéma de perturbation à travers l'étude de l'évolution d'une cellule de combustible de type REP. Puis cette technique sera utilisée sur un calcul d'un assemblage de type REP en début de cycle. Après avoir validé la méthode avec un calcul de référence, nous montrerons qu'elle peut accélérer les codes Monte Carlo évoluant standard de presque un ordre de grandeur. / For several years, Monte Carlo burnup/depletion codes have appeared, which couple Monte Carlo codes to simulate the neutron transport to deterministic methods, which handle the medium depletion due to the neutron flux. Solving Boltzmann and Bateman equations in such a way allows to track fine 3-dimensional effects and to get rid of multi-group hypotheses done by deterministic solvers. The counterpart is the prohibitive calculation time due to the Monte Carlo solver called at each time step.In this document we present an original methodology to avoid the repetitive and time-expensive Monte Carlo simulations, and to replace them by perturbation calculations: indeed the different burnup steps may be seen as perturbations of the isotopic concentration of an initial Monte Carlo simulation. In a first time we will present this method, and provide details on the perturbative technique used, namely the correlated sampling. In a second time we develop a theoretical model to study the features of the correlated sampling method to understand its effects on depletion calculations. In a third time the implementation of this method in the TRIPOLI-4® code will be discussed, as well as the precise calculation scheme a meme to bring important speed-up of the depletion calculation. We will begin to validate and optimize the perturbed depletion scheme with the calculation of a REP-like fuel cell depletion. Then this technique will be used to calculate the depletion of a REP-like assembly, studied at beginning of its cycle. After having validated the method with a reference calculation we will show that it can speed-up by nearly an order of magnitude standard Monte-Carlo depletion codes.