Comprehensive modeling of hydrogen transport and accumulation in titanium and zirconium

We developed kinetic models of hydrogen absorption in Ti and Zr. The models comprise series connections of the hydrogen-transport processes of surface dissociative adsorption and recombinative desorption; subsurface transport; and bulk diffusion. Numerical calculations using the models quantitatively reproduce the results of experimental series of time-transient absorption curves at various temperatures, demonstrating the validity of our models. Experimental desorption curves at various temperatures are also reproduced by the same model equations and kinetic parameters, particularly for Zr, demonstrating the dual functionality of our single model for hydrogen-transport directions. We use an effectiveness factor defined as the ratio between the real absorption rate and the virtual rate neglecting bulk diffusion. The transitions of the rate-determining steps of hydrogen transport in Ti and Zr under various conditions - such as temperature, pressure, and metal object size and shape - are systematically analyzed. As a case study to test the applicability of our model, hydrogen accumulation in the fuel claddings of light-water nuclear reactors was simulated to determine the cladding thickness required to prevent hydrogen embrittlement during the practical operation period. Our versatile kinetic models could be a useful tool that can aid the structural design and optimization of nuclear materials and facilities.