How High-Fidelity Modeling is Improving Radionuclide Uptake Process
Zirui Mao

Nuclear power is expected to play a crucial role in America's clean energy future as it provides a reliable and low-carbon source of electricity. However, the generation of nuclear energy produces radioactive waste products that require proper management, processing, and disposal to prevent potential harm to human health and the environment. This highlights the importance of developing advanced technologies and science to ensure the safe and efficient treatment of nuclear waste products.

Treatment of nuclear waste stream

To render radioactive waste safe, scientists contain it within special materials called nuclear wasteforms [1]. Wasteform materials can have a porous or hierarchical structure that can absorb harmful Sr2+ ions as the radioactive solution flows through it, as shown in Fig. 1. The treated solution becomes safe to discharge, while the now radioactive wasteform materials can be safely buried deep.

Figure SEQ \* ARABIC 1 Illustration of radionuclide uptake process from stream to wasteform materials

This method of radionuclide uptake is a complicated transport process that occurs in a complex multi-phase system at the mesoscale, which includes (i) ions moving at highly variable rates in liquid solution and solid phases, (ii) the development of electrochemical potential from the movement of these ions, (iii) the transfer of ions between the solution and the solid at the solid–solution interface, and (iv) dynamic flow through the 3D multiple length scale porous structure of the wasteform material.

The Center for Hierarchical Waste Form Materials (CHWM) conducts a wide range of experimental and modeling studies to develop the chemistry and structural motifs needed to create hierarchical materials that effectively immobilize nuclear waste. A team of researchers at the Pacific Northwest National Laboratory (PNNL) led by Dr. Shenyang Hu and Dr. Zirui Mao are currently developing a high-fidelity numerical model for simulating the uptake process of radionuclides from waste streams to solid wasteform materials. This work enables investigations leading to enhanced understanding of how the wasteform microstructure affects radionuclide-uptake, facilitating the design of higher-performance radionuclide-treatment procedures and nuclear wasteform materials.

High-fidelity modeling of waste stream treatment

Researchers in the CHWM have developed a mesoscale microstructural model of the porous structure to predict the uptake kinetics of electrically charged species in hierarchical waste form materials [2-3]. In particular, the team has successfully coupled a phase-field model with a computational fluid dynamics (CFD) model to describe phase stability, flow through porous materials, ion diffusion and convection, and interface reactions. Each separate model requires an appropriate calibration based on the corresponding experimental or measurement data. Moreover, high-fidelity modeling of such multi-physics processes require extensive computational time and processor power, especially when considering the strong inhomogeneity of the kinetic properties. A short “time marching” (refers to the process of advancing the simulation forward in time) is required to capture the ‘fast’ diffusion/transport within the liquid solution.

To mitigate the computational demand, the CHWM team used two approaches. One is to approximate that the radionuclide-uptake takes place during ‘steady’ flow of the waste stream through the wasteform material, which decouples the dynamic flow calculation (velocity field) from the species transport calculations. The second is superposing the long-time diffusing results of each spatial point obtained from the short-time marching solver to form a long-time marching solver, which eventually overcomes massive computational load challenges.

The high-fidelity mesoscale microstructural model proposed by the CHWM team incorporates the key physics involved in the radionuclide uptake process. As a result, it has the capability to accurately represented the breadth of ion exchange kinetics and interactions, facilitating further exploration of the radionuclide uptake performance under various environmental and operational conditions. The robustness of this modeling approach has significant potential in supporting the development of optimized wasteform materials for efficient and safe immobilization of radioactive waste.

More Information

[1] zur Loye, H.-C., Besmann, T. M., Amoroso, J., Brinkman, K. S., Grandjean, A., Henager Jr., C. H., Hu, S., Misture, S. T., Phillpot, S. R., Shustova, N. B., Wang, H., Koch, R. J., Morrison, G., Dolgopolova, E. A., “Hierarchical Materials as Tailored Nuclear Waste Forms: A Perspective”, DOI:10.1021/acs.chemmater.8b00766.  Chem. Mater., 2018, 30, 4475-4488.

[2] Y.L. Li, B.D. Zeidman, S.Y. Hu, C.H. Henager, T.M. Besmann, A. Grandjean, A physics-based mesoscale phase-field model for predicting the uptake kinetics of radionuclides in hierarchical nuclear wasteform materials, Comput. Mater. Sci. 159 (2019) 103–109. DOI: 10.1016/j.commatsci.2018.11.041

[3] Y.L. Li, S. Hu, R. Montgomery, A. Grandjean, T. Besmann, H. zur Loye, Effect of charge and anisotropic diffusivity on ion exchange kinetics in nuclear waste form materials, Journal of Nuclear Materials, Volume 572, 2022, 154077. DOI: 10.1016/j.jnucmat.2022.154077


The work described in this article was performed by Pacific Northwest National Laboratory, which is operated by Battelle for the U.S. Department of Energy under Contract DE-AC05-76RL01830. This work was supported as part of the Center for Hierarchical Waste Form Materials, an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Basic Energy Sciences under Award No. DE-SC0016574.

About the author(s):

Zirui Mao is a Research Associate at Pacific Northwest National Laboratory working in the Center for Hierarchical Waste Form Materials (CHWM) EFRC. His research focuses on the area of computational mechanics, using knowledge of mechanics, mathematics, and emerging ML algorithms to solve numerically realistic engineering problems via computer programming and HPC. He has experience in solving large deformation problems of granular materials, simulating multiphase flow through porous structures, multi-physics modeling of CFD problems, and optimal controlling of microstructure evolution with the numerical approaches including meshfree methods, phase-field method, Finite Difference method, FFT, reinforcement learning algorithm etc.  ORCID ID # 0000-0003-3223-8921.