Upscaling Radionuclide Reactive Transport Parameters In Fractured Rocks

Deep geological disposal is widely accepted as a safe and feasible long-term strategy for managing high-level radioactive waste（HLW）globally.To evaluate the safety performance of the geological disposal repository,it is essential to conduct a safety assessment to numerically predict the reactive transport process of radionuclides through fractured rocks over millions of years.However,owing to the scale effect originating from the physical and chemical heterogeneity of natural fractured rocks,the effective values of solute transport parameters will change with the scale.Therefore,to obtain reliable simulation results,upscaling studies are necessary to estimate scale-justified reactive transport parameters at the site scale based on measured parameters at the laboratory scale.This study conducted experiments on radionuclide strontium（Sr）transport in single minerals and mineral assemblages.Through calibrating the breakthrough curves using inverse methods,sorption coefficients of single minerals and mineral assemblages were identified.A multi-scale conceptual model of fractured rocks was established,and the upscaling equation of the sorption coefficient was derived by combining geostatistical methods.The global sensitivity analysis of the upscaling equation was conducted to quantify the relative contribution of each input parameter to the calculation results.The spatial correlation structure of mineral phases and sorption coefficients was characterized using transfer probability models and covariance functions.The accuracy of the upscaling equation was verified using experimental data and numerical simulations.A numerical simulation method of solute transport in multi-scale fractured rocks was established by coupling the upscaling algorithm with the discrete fracture-matrix model.This method was used to explore the impact of different reactive transport parameters on solute transport in fractured rocks.The main findings of this study are as follows:（1）The reactive transport mechanism of Sr reactive transport in single minerals and mineral assemblages was revealed using mineral-packed column experiments and fracture radionuclide transport experiments.The results showed that the sorption properties and spatial distribution of minerals controlled the sorption capacity of mineral assemblages.The sorption capacity of different minerals for radionuclide Sr is positively correlated with the specific surface area of minerals.The sorption coefficients of granite constituent minerals for Sr are in the order of biotite>plagioclase>K-feldspar>quartz.Due to the difference in contact surface area with the solute,the sorption coefficients of single minerals were generally two to three orders of magnitude greater than those of mineral assemblages.（2）By combining the hierarchical structure and discrete fracture-matrix model,this study presented a multi-scale conceptual model of fracture rocks,which characterized the fractured rocks as single minerals,fractured mineral assemblages,and discrete fractured rocks from microform scale to macroform scale.Based on the conceptual framework,the spatial correlation structure of single minerals and sorption coefficients were respectively characterized by the transition probability model and the covariance function.The upscaling equation of the sorption coefficient was derived using volume averaging methods.The control mechanism of heterogeneous structure on the scale effect of the sorption coefficient was revealed.Various parameters influenced the scale effect of the sorption coefficient,including the volume proportion of constituent minerals,indicator correlation length,fracture length,mean and variance of logarithmic sorption coefficient,and integral scale.The global sensitivity analysis of the upscaling equation indicated that the volume ratio of constituent minerals and the logarithmic mean value of sorption coefficients of strongly sorptive minerals were the most sensitive parameters.（3）The accuracy of the upscaling equation for the sorption coefficient was verified through experimental results and Monte Carlo stochastic simulation.The relative errors of the two methods were 4.83%and 7.73%,respectively.The results showed that if the spatial distribution of minerals was not considered,the sorption coefficient calculated by geometric mean can only provide a constant estimate that does not vary with scale and can cause serious parameter underestimation.However,the upscaling equation can accurately capture the variation of the sorption coefficient with scale and provide more precise parameter calculations.（4）This study utilized the open-source finite element software Open Geo Sys to establish a simulation method for radionuclide transport in fractured rocks,which integrates the generation of a discrete fracture network,mesh generation,upscaling parameter assignment,and solute transport simulation.Using a granite site in northwestern China as the study area,a hypothetical HLW disposal scenario was designed,and the reactive transport behavior of radionuclide ⁷⁹Se in the natural barrier of the disposal system over a timescale of one million years.The simulation results indicated that the release rate of ⁷⁹Se in the biosphere reached a peak of about 52.44 Bq/a at around500,000 years,with a corresponding radiation dose of 4.698×10^-9 mSv/a.Compared with traditional simulation methods,which ignore the scale effect of transport parameters,the developed method can provide more reasonable parameter assignment and accurate prediction results,supporting the safety assessment of HLW geological disposal in China.（5）The influence of different reactive transport parameters on the simulation results of solute transport in fractured rocks was explored using the numerical simulation method.The results showed that in large spatiotemporal scale radionuclide transport prediction,neglecting the scale effect of the matrix diffusion coefficient and sorption coefficient would underestimate the retardation performance of fractured rocks.From the perspective of safety assessment,this is beneficial for researchers to provide conservative radionuclide transport predictions.However,under different dispersivity conditions,with the increase of dispersivity,radionuclides would be released from the fracture outlet prematurely,bringing great uncertainty to radionuclide transport predictions.This phenomenon should be particularly concerned in the safety assessment.