花岗岩中放射性核素电迁移实验的多重耦合数学模型

    Multiple Coupled Mathematical Model for Radionuclide Electromigration Experiments in Granites

    • 摘要: 花岗岩是高放射性废物处置库的首选介质屏障,获取花岗岩中核素迁移参数是处置库安全评价的基础。本工作旨在以电迁移实验获取的完整花岗岩中核素迁移的数据为基础,并以此建立动力学吸附-对流-弥散的多重耦合数学模型。以拉普拉斯变换求解得到核素在完整花岗岩多孔隙介质当中标准化浓度的解析解,并应用MATLAB中的最小二乘法汇编数据拟合程序,模型的敏感性分析表明,本模型相比其他模型更具普适性,不论是中强吸附核素还是弱吸附核素,都能更好地解释核素离子在完整花岗岩岩芯中的迁移机理。应用该模型分析I和Sr2+的电迁移实验数据,得到I在无电场条件下的D_\mathrmm^\mathrme 值为(2.25±0.35)×10−14 m2/s,Sr2+在无电场条件下的D_\mathrmm^\mathrme 值为(4.80±0.31)×10−13 m2/s。此外,该模型还可以估算一级吸附速率系数β,进而解释核素离子在完整花岗岩中的吸附阻滞机制。同时,通过分析突破曲线的斜率和弯曲度,能够深入理解非线性吸附的迁移机制。

       

      Abstract: 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 D_\mathrmm^\mathrme of I without electric field is (2.25±0.35)×10−14 m2/s, and the D_\mathrmm^\mathrme 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.

       

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