PNNL

Abstract

The flow field within the mesopores of sorbent particles plays a crucial role in radionuclide diffusion and ion uptake kinetics, thus, impacts the overall performance of porous nuclear waste form materials. To fundamentally understand the influence of microstructures and material properties on radionuclide uptaking processes requires a multi-physics coupling model that considers the convection and diffusion within the flow field, the reaction at liquid-solid interfaces, and finally, the solid-state diffusion within a complex nanoporous medium. This study employs the volumetric lattice Boltzmann method (VLBM) to accurately and efficiently calculate the steady state velocity field inside the mesopores of sorbent particles. The obtained velocity field is then utilized to calculate the convection of ions in the steady flow. A phase field (PF) model of ion uptake is used to describe the reaction occurring at the solid-liquid interface and diffusion inside the porous medium. The integrated PF-VLBM model is validated in terms of the mass conservation and numerical efficiency. Then, it is applied to study the influence of thermodynamic and kinetic properties, as well as flow field conditions on the ion uptake kinetics. The numerical results demonstrate that the ion uptake kinetics in porous particles has three distinct stages, which is in agreement with the observations in continuous flow experiments. In the first stage, the kinetics is predominantly controlled by the flow field and ion diffusivity in the liquid phase. The kinetics in the second stage is primarily governed by ion diffusivity in the solid phase. In the third stage the system reaches a dynamic equilibrium without net uptake at the interface. It is also found that porous structures significantly affect the efficiency and capacity of ion uptake. The simulation results can help to understand the physics behind the observed ion uptake kinetics in experiments and to facilitate the development of constitutive equations that can account for heterogeneous microstructures in engineering performance codes.