Transport Of Radionuclides In Porous Media Research Articles

An Adjoint Sensitivity Model for Transient Sequentially Coupled Radionuclide Transport in Porous Media

AbstractWe present an efficient mathematical/numerical adjoint sensitivity analysis model for transient radionuclide transport through heterogeneous porous media. This work extends our previous research on radionuclide transport in a steady‐state regime. Both continuous and discrete adjoint approaches have been developed in this current research. The mathematical equations associated with the adjoint system and required for the continuous approach have been derived. The methodology for deriving the discrete adjoint solution is also presented.For the homogeneous case, the adjoint system for radionuclide decay chain is solved analytically. The four‐member decay chain (238Pu → 234U → 230Th → 226Ra) is considered for validation. The validity of the analytical adjoint sensitivity model has been shown using two illustrative examples associated with two performance measures. The analytical adjoint states are compared with calculated numerical results and show excellent agreements. The sensitivity coefficients are also computed numerically using the perturbation method. The numerical sensitivity coefficients successfully reproduce the analytically derived sensitivities based on adjoint states. The adjoint model has been coupled with a derivative‐based global sensitivity method and applied to a real field case involving the performance assessment of a site currently being considered for underground nuclear storage in northern Switzerland, Zürich Nordost. An illustrative case study of spent fuel and high‐level waste (SF/HLW) repository involving 6 radionuclides and 48 parameters has been considered for identifying the most important parameters with respect to the maximum radionuclide dose at the interface geosphere/biosphere. Based on the results of sensitivity analysis, the uncertainty of the maximum radionuclide dose has been performed using Monte Carlo simulations.

An Adjoint Sensitivity Model for Steady‐State Sequentially Coupled Radionuclide Transport in Porous Media

AbstractThis work presents an efficient mathematical/numerical model to compute the sensitivity coefficients of a predefined performance measure to model parameters for one‐dimensional steady‐state sequentially coupled radionuclide transport in a finite heterogeneous porous medium. The model is based on the adjoint sensitivity approach that offers an elegant and computationally efficient alternative way to compute the sensitivity coefficients. The transport parameters include the radionuclide retardation factors due to sorption, the Darcy velocity, and the effective diffusion/dispersion coefficients. Both continuous and discrete adjoint approaches are considered. The partial differential equations associated with the adjoint system are derived based on the adjoint state theory for coupled problems. Physical interpretations of the adjoint states are given in analogy to results obtained in the theory of groundwater flow. For the homogeneous case, analytical solutions for primary and adjoint systems are derived and presented in closed forms. Numerically calculated solutions are compared to the analytical results and show excellent agreements. Insights from sensitivity analysis are discussed to get a better understanding of the values of sensitivity coefficients. The sensitivity coefficients are also computed numerically by finite differences. The numerical sensitivity coefficients successfully reproduce the analytically derived sensitivities based on adjoint states. A derivative‐based global sensitivity method coupled with the adjoint state method is presented and applied to a real field case represented by a site currently being considered for underground nuclear storage in Northern Switzerland, “Zürich Nordost”, to demonstrate the proposed method. The results show the advantage of the adjoint state method compared to other methods in term of computational effort.

3D simulation of radionuclide transport in porous media

AbstractWe present an efficient and easily implementable finite volume method simulating radionuclide transport through highly heterogeneous grounds in three space dimensions. The numerical concentration of the transported chemicals are proved to remain nonnegative and stable.Then, we run a realistic test case in which some radioactive iodine I129 particles are released from a leak in an underground nuclear waste disposal site. The question of whether the radionuclide invades the underground and reach the ground surface is investigated.Because of the 3D nature of the problem, a particular emphasis is made on the control of CPU time. Copyright © 2009 John Wiley & Sons, Ltd.

The effect of bacterial generation on the transport of radionuclide in porous media

The purpose of this paper is to provide a methodology to develop a predictive model based on a conceptual three-phase system and to investigate the influence of bacteria and their generation on the radionuclide transport in porous media. The mass balance equations for bacteria, substrate and radionuclide were formulated. To illustrate the model simply, an equilibrium condition was assumed to partition the substrate, bacteria and radionuclide concentrations between the solid soil matrix, aqueous phase and bacterial surface. From the numerical calculation of radionuclide transport in the presence of bacteria, it was found that the growth of bacteria and supplied primary substrate as a limiting or stimulating growth factor of bacteria are the most important factors of the radionuclide transport. It was also found that, depending on the transport of bacteria, the temporal and spatial distribution of the radionuclide concentration was significantly affected. The model proposed in this study will improve the evaluation of the role of the bacteria to the transport of radionuclide in groundwater systems. Furthermore, this model can be usefully utilized in analyzing the important role of colloidal particulate on the overall performance of radioactive waste safety.

Assessment of the effect of kinetics on colloid facilitated radionuclide transport in porous media

Binding of radionuclides to natural colloids can significantly alter their transport behaviour in porous media. Dependent on the interaction between radionuclides, colloids and the solid matrix, radionuclide transport may be enhanced or retarded as a result of the presence of colloids. Often, equilibrium models are used to describe interactions between radionuclides, colloids and the solid matrix. However, experimental results indicate that kinetic processes may be important. In this paper, a model for coupled colloid and radionuclide transport in porous media is presented. Kinetic relationships are incorporated for the interaction between radionuclides, colloids and solid matrix. With this transport model, column experiments have been simulated, and modelling results are compared with experimental data reported in literature. It appears that kinetic interaction relationships are required to adequately model the experimental data.

Derivation of an Equation for Radionuclide Transport in Porous Media

To analytically predict the transport of radionuclides in porous media, it is necessary to develop a complete mathematical model. This means that the mechanisms must be described and the governing equations derived, along with their general solutions for the transport processes. The four major mechanisms---advection, dispersion, adsorption-desorption and ion exchange, and degradation---are physically described and mathematically modeled. Based on the classic principle of mass conservation in a control volume, the governing equation for the transport of radionuclides in porous media is derived, which may be called the advection-dispersion equation. Some general solutions of the governing equation are obtained by using constant dispersion coefficients. In addition, some ambiguities of the advective-dispersion equation are solved, and this equation is extended to fractured media.