Multiple Coupled Mathematical Model for Radionuclide Electromigration Experiments in Granites
Granite is considered an ideal medium for geological disposal of nuclear waste due to its unique stability and wide distribution. When the repository media barrier fails, granite serves as the peripheral rock medium. The porous nature of intact granite in the deep subsurface provides a basis for gro...
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Editorial Office of Journal of Nuclear and Radiochemistry
2025-06-01
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| Series: | He huaxue yu fangshe huaxue |
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| Online Access: | https://jnrc.xml-journal.net/cn/article/doi/10.7538/hhx.2025.47.03.0267 |
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| author | Xiao-jie LI Kai-xuan TAN Long-cheng LIU Yong-mei LI Chun-guang LI Zhi ZOU Qi LIU |
| author_facet | Xiao-jie LI Kai-xuan TAN Long-cheng LIU Yong-mei LI Chun-guang LI Zhi ZOU Qi LIU |
| author_sort | Xiao-jie LI |
| collection | DOAJ |
| description | Granite is considered an ideal medium for geological disposal of nuclear waste due to its unique stability and wide distribution. When the repository media barrier fails, granite serves as the peripheral rock medium. The porous nature of intact granite in the deep subsurface provides a basis for groundwater storage and radionuclide migration, allowing radionuclides to migrate and diffuse to the biosphere along with groundwater flow, ultimately affecting the ecological environment. In this study, an advection-dispersion model for primary kinetic adsorption was developed, introducing a primary adsorption rate coefficient β to describe the kinetic adsorption phenomenon. The model also considered important mechanisms affecting the movement of nuclide ions, including electromigration, electroosmosis, and dispersion. Using the Laplace transform, combined with the nonlinear adsorption process of the nuclide ion tracer between solid-phase granite and liquid-phase water-saturated pores, the first-order reversible kinetic reaction equation was introduced into the total continuity equation to obtain an analytical solution for the standardized concentration of nuclides in the intact granite porous medium. The computational program was coded in MATLAB. The non-adsorbed nuclides I− and the moderately strongly adsorbed nuclides Sr2+ were selected as the analytical objects during the simulation process. The diffusion and adsorption in the matrix domains of the studied granite rock samples were analyzed in conjunction with basic parameters such as the porosity and the dry weight of the studied granite rock samples to obtain the relevant key migration parameters. The conclusions of this study are as follows: (1) The new model is based on the advection-dispersion model with linear adsorption and introduces a first-order adsorption rate coefficient β. The first-order adsorption kinetic advection-dispersion model has been successfully established. (2) The sensitivity analysis of the new model proves that the primary adsorption rate coefficient β affects the output of the model. When the partition coefficient Kd between the solution phase and the solid phase is fixed and β is large to a certain extent, the new model reaches a linear adsorption state. (3) Using this model to analyze the electromigration experimental data of I− and Sr2+, the \begin{document}$D_{\mathrm{m}}^{\mathrm{e}} $\end{document} of I− without electric field is （2.25±0.35）×10−14 m2/s, and the \begin{document}$D_{\mathrm{m}}^{\mathrm{e}} $\end{document} of Sr2+ without electric field is （4.80±0.31）×10−13 m2/s. Additionally, this model can estimate the first-order adsorption rate coefficient β, and explain the adsorption retardation mechanism of nuclide ions in intact granite. By analyzing the slope and curvature of the breakthrough curve, the migration mechanism of nonlinear adsorption can be deeply understood. |
| format | Article |
| id | doaj-art-009c7a90bdf64ac9b110d98b178b91c0 |
| institution | OA Journals |
| issn | 0253-9950 |
| language | zho |
| publishDate | 2025-06-01 |
| publisher | Editorial Office of Journal of Nuclear and Radiochemistry |
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| series | He huaxue yu fangshe huaxue |
| spelling | doaj-art-009c7a90bdf64ac9b110d98b178b91c02025-08-20T02:21:33ZzhoEditorial Office of Journal of Nuclear and RadiochemistryHe huaxue yu fangshe huaxue0253-99502025-06-0147326727510.7538/hhx.2025.47.03.02672024-028Multiple Coupled Mathematical Model for Radionuclide Electromigration Experiments in GranitesXiao-jie LI0Kai-xuan TAN1Long-cheng LIU2Yong-mei LI3Chun-guang LI4Zhi ZOU5Qi LIU6School of Resource Environment and Safety Engineering, University of South China, Hengyang 421001, ChinaSchool of Resource Environment and Safety Engineering, University of South China, Hengyang 421001, ChinaR & D and Modelling Center for Treatment and Disposal of Radioactive Waste, University of South China, Hengyang 421001, ChinaSchool of Resource Environment and Safety Engineering, University of South China, Hengyang 421001, ChinaSchool of Resource Environment and Safety Engineering, University of South China, Hengyang 421001, ChinaR & D and Modelling Center for Treatment and Disposal of Radioactive Waste, University of South China, Hengyang 421001, ChinaSchool of Resource Environment and Safety Engineering, University of South China, Hengyang 421001, ChinaGranite is considered an ideal medium for geological disposal of nuclear waste due to its unique stability and wide distribution. When the repository media barrier fails, granite serves as the peripheral rock medium. The porous nature of intact granite in the deep subsurface provides a basis for groundwater storage and radionuclide migration, allowing radionuclides to migrate and diffuse to the biosphere along with groundwater flow, ultimately affecting the ecological environment. In this study, an advection-dispersion model for primary kinetic adsorption was developed, introducing a primary adsorption rate coefficient β to describe the kinetic adsorption phenomenon. The model also considered important mechanisms affecting the movement of nuclide ions, including electromigration, electroosmosis, and dispersion. Using the Laplace transform, combined with the nonlinear adsorption process of the nuclide ion tracer between solid-phase granite and liquid-phase water-saturated pores, the first-order reversible kinetic reaction equation was introduced into the total continuity equation to obtain an analytical solution for the standardized concentration of nuclides in the intact granite porous medium. The computational program was coded in MATLAB. The non-adsorbed nuclides I− and the moderately strongly adsorbed nuclides Sr2+ were selected as the analytical objects during the simulation process. The diffusion and adsorption in the matrix domains of the studied granite rock samples were analyzed in conjunction with basic parameters such as the porosity and the dry weight of the studied granite rock samples to obtain the relevant key migration parameters. The conclusions of this study are as follows: (1) The new model is based on the advection-dispersion model with linear adsorption and introduces a first-order adsorption rate coefficient β. The first-order adsorption kinetic advection-dispersion model has been successfully established. (2) The sensitivity analysis of the new model proves that the primary adsorption rate coefficient β affects the output of the model. When the partition coefficient Kd between the solution phase and the solid phase is fixed and β is large to a certain extent, the new model reaches a linear adsorption state. (3) Using this model to analyze the electromigration experimental data of I− and Sr2+, the \begin{document}$D_{\mathrm{m}}^{\mathrm{e}} $\end{document} of I− without electric field is （2.25±0.35）×10−14 m2/s, and the \begin{document}$D_{\mathrm{m}}^{\mathrm{e}} $\end{document} of Sr2+ without electric field is （4.80±0.31）×10−13 m2/s. Additionally, this model can estimate the first-order adsorption rate coefficient β, and explain the adsorption retardation mechanism of nuclide ions in intact granite. By analyzing the slope and curvature of the breakthrough curve, the migration mechanism of nonlinear adsorption can be deeply understood.https://jnrc.xml-journal.net/cn/article/doi/10.7538/hhx.2025.47.03.0267dynamic adsorption-advection-dispersion modelnonlinear adsorptionretardationmathematical modelradionuclide migration |
| spellingShingle | Xiao-jie LI Kai-xuan TAN Long-cheng LIU Yong-mei LI Chun-guang LI Zhi ZOU Qi LIU Multiple Coupled Mathematical Model for Radionuclide Electromigration Experiments in Granites He huaxue yu fangshe huaxue dynamic adsorption-advection-dispersion model nonlinear adsorption retardation mathematical model radionuclide migration |
| title | Multiple Coupled Mathematical Model for Radionuclide Electromigration Experiments in Granites |
| title_full | Multiple Coupled Mathematical Model for Radionuclide Electromigration Experiments in Granites |
| title_fullStr | Multiple Coupled Mathematical Model for Radionuclide Electromigration Experiments in Granites |
| title_full_unstemmed | Multiple Coupled Mathematical Model for Radionuclide Electromigration Experiments in Granites |
| title_short | Multiple Coupled Mathematical Model for Radionuclide Electromigration Experiments in Granites |
| title_sort | multiple coupled mathematical model for radionuclide electromigration experiments in granites |
| topic | dynamic adsorption-advection-dispersion model nonlinear adsorption retardation mathematical model radionuclide migration |
| url | https://jnrc.xml-journal.net/cn/article/doi/10.7538/hhx.2025.47.03.0267 |
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