Study of gas bubble behavior for high burnup nuclear fuels using the phase field methodology

Abstract

To reduce the emission of greenhouse gases, nuclear power stations are widely built around the world. A lot of research work has been done in the study of advanced nuclear reactors and advanced nuclear fuels. Among all the issues encountered during the operation of nuclear power stations, fission products in nuclear fuels have the most profound effects on the safe operation of nuclear reactors. The fission gases xenon (Xe) and krypton (Kr) are unceasingly generated in nuclear fuels during the irradiation process, which has great impact on granular uranium dioxide nuclear fuel (UO2) in the current commercial Light Water Reactors (LWRs). Due to their extremely low solubility in the UO2 nuclear fuel, the fission gases tend either to precipitate into gas bubbles or to be released to the free volume in the nuclear fuel rods. Fission gas release and gas bubbles swelling are critical issues for the fuel performance in the LWRs. Released fission gas can reduce the thermal conductivity of the fuel-cladding gap and cause temperature and pressure increases in the fuel pellets, and gas bubbles swelling can increase the contact pressure between the fuel pellets and cladding, and finally leads to cladding failure. The current nuclear fuel performance codes are mainly based on empirical formulas of gas bubble behavior and its effects on the thermo-mechanical properties of the fuels that are derived from important assumptions that significantly limit their predictive capability, especially for the development of advanced reactors and nuclear fuels. Therefore, understanding and predicting the behavior and evolution kinetics of fission gas are essential for enhancing the fuel performance codes and the development of high burn-up reactor technologies. In recent years, with the rapid development of computer power, computational methods, and the accumulated knowledge on radiation damage mechanisms, it is possible for theoretical predictions of the microstructure evolution of materials undergo irradiation. Atomistic simulations, such as Monte Carlo methods, first principles, and molecular dynamics, enable the accurate calculation of thermodynamic and kinetic properties of defects such as the generation, resolution, and clustering of defects in irradiated materials. The mesoscale phase-field method (PFM) has shown great capability in predicting phase stability and microstructure evolution kinetics in chemically and microstructurally complicated systems, not only for systems close to the equilibrium state but also for systems far from equilibrium state. One of the advantages of this method lies in the natural and straightforward way in which multiple material processes, such as multiple species diffusion, the evolution of gas bubbles, and elastic interaction, are accounted for. In the present work, an atomistically informed and microstructurally resolved phase-field (PF) model is developed for predicting the fission gas bubbles behavior in UO2 nuclear fuels and providing accurate thermodynamic and kinetic data to enhance the prediction capability of nuclear fuel performance codes. Due to the large formation energy of vacancies and noble gas atoms at interstitial and/or substitutional sites in the UO2 nuclear fuel, the thermodynamic equilibrium concentrations of these species are extremely low in the UO2 nuclear fuel matrix even at very high temperature (close to the melting temperature), which imposes difficulties upon the quantitative study of the gas bubble evolution via the PFM. In this study, a quantitative PF model is proposed to deal with this issue. The free energy density of the system is derived according to the principles of thermodynamics, with consideration of the elastic interaction and internal pressure of each gas bubble, and with the use of material parameters from experiments and atomistic simulations. The model enables one to study the kinetics of gas bubble growth with very dilute concentrations of vacancy and gas atoms in the matrix. With this model, the growth of a single gas bubble and multiple gas bubbles were simulated under different concentrations of vacancy and gas atoms and at different temperatures. The effect of elastic interaction energy and the generation rate of vacancies and gas atoms on gas bubble growth are analyzed. In this simulation, both Van der Waals equation of state (EOS) and Ronchi's EOS were used to study the gas bubbles behavior in the UO2 nuclear fuels, and the results were compared. The effect of temperatures and generation rates of vacancies and gas atoms on gas bubbles swelling were also studied by using Ronchi's EOS. PF models are developed to study the gas bubble migration in uranium dioxide nuclear fuel in which a large temperature gradient exists during the operation. In this work, the thermal diffusion mechanism for nanosized gas bubbles and the vapor transport process for micron-sized gas bubbles are considered, respectively. In both cases, gas bubbles migrate to the high-temperature area. Due to the velocity difference between leading and trailing edges of the gas bubbles, nanosized gas bubbles are elongated along the temperature gradient direction when thermal diffusion is dominated. Micron-sized gas bubbles are either compressed along temperature gradient direction to form lenticular shape bubbles or elongated along temperature gradient direction, depending on the location of the gas bubbles within the fuel pellet. The initial gas bubble radius has no significant effect on the gas bubble migration velocity for both thermal diffusion and vapor transport mechanisms. The shape change of the gas bubble due to vapor transport mechanism has no significant effect on the migration velocity. Furthermore, the center cavity formation is also captured by our model which is due to the migration and accumulation of lenticular gas bubbles at the center of the fuel pellet. The modeling results compare well with experimental observations and theoretical analysis in the literature.