Volumetric lattice Boltzmann method for pore-scale mass diffusion-advection process in geopolymer porous structures

Porous materials present significant advantages for absorbing radioactive isotopes in nuclear waste streams. To improve absorption efficiency in nuclear waste treatment, a thorough understanding of the diffusion-advection process within porous structures is essential for material design. In this study, we present advancements in the volumetric lattice Boltzmann method (VLBM) for modeling and simulating pore-scale diffusion-advection of radioactive isotopes within geopolymer porous structures. These structures are created using the phase field method (PFM) to precisely control pore architectures. In our VLBM approach, we introduce a concentration field of an isotope seamlessly coupled with the velocity field and solve it by the time evolution of its particle population function. To address the computational intensity inherent in the coupled lattice Boltzmann equations for velocity and concentration fields, we implement graphics processing unit (GPU) parallelization. Validation of the developed model involves examining the flow and diffusion fields in porous structures. Remarkably, good agreement is observed for both the velocity field from VLBM and multiphysics object-oriented simulation environment (MOOSE), and the concentration field from VLBM and the finite difference method (FDM). Furthermore, we investigate the effects of background flow, species diffusivity, and porosity on the diffusion-advection behavior by varying the background flow velocity, diffusion coefficient, and pore volume fraction, respectively. Notably, all three parameters exert an influence on the diffusion-advection process. Increased background flow and diffusivity markedly accelerate the process due to increased advection intensity and enhanced diffusion capability, respectively. Conversely, increasing the porosity has a less significant effect, causing a slight slowdown of the diffusion-advection process due to the expanded pore volume. This comprehensive parametric study provides valuable insights into the kinetics of isotope uptake in porous structures, facilitating the development of porous materials for nuclear waste treatment applications.