GPU-accelerated volumetric lattice Boltzmann method for pore-scale diffusion-advection in geopolymer porous structures for nuclear waste treatment

Porous materials serve as advantageous media for immobilizing radioactive ions in nuclear waste streams. To enhance absorption efficiency in nuclear waste treatment, a profound understanding of the diffusion-advection process within porous structures is imperative for designing such materials. In this study, we present the development of the volumetric lattice Boltzmann method (VLBM) to solve pore-scale diffusion-advection in geopolymer porous structures, which are generated using the phase field method (PFM) with specific pore structures. Mass transport is driven by diffusion, convection, and interface reaction. The concentration field's lattice Boltzmann equation is constructed in a manner similar to that of the velocity field. To tackle the computationally intensive nature of the coupled lattice Boltzmann equations for velocity and concentration fields, we implement GPU (Graphics Processing Unit) parallelization. We first examine the solution of pure diffusion with a point source, and favorable agreements between VLBM and PFM are observed for both velocity and concentration fields. Then, we investigate the influence of porosity, mass diffusivity, and flow rate on the diffusion by varying the pore volume fraction, diffusion coefficient, and background flow velocity. Notably, both porous material properties and fluid characteristics significantly impact this multi-physics process. Through this comprehensive parametric study, we gain insights into the kinetics of ion uptake in porous structures, facilitating the advancement of porous materials for nuclear waste treatment applications.