核化学与放射化学2025，Vol.47Issue(3)：267-275,9.DOI:10.7538/hhx.2025.47.03.0267
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
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 coefficientβThe 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 andβ 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 Dme of I-without electric field is(2.25±0.35)×10-14 m2/s,and the Dme 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.关键词
动力学吸附-对流-弥散模型/非线性吸附/阻滞/数学模型/放射性核素迁移Key words
dynamic adsorption-advection-dispersion model/nonlinear adsorption/retardation/mathem-atical model/radionuclide migration分类
核科学引用本文复制引用
李小杰,谭凯旋,刘龙成,李咏梅,李春光,邹智,柳琪..花岗岩中放射性核素电迁移实验的多重耦合数学模型[J].核化学与放射化学,2025,47(3):267-275,9.基金项目
国家自然科学基金结余经费后续研究项目(230XJZ129) （230XJZ129）
国家自然科学基金资助项目(U1703123) （U1703123）
湖南省自然科学基金资助项目(2020JJ40522) （2020JJ40522）
湖南省研究生科研创新项目(QL20230233) （QL20230233）
