Theoretical Basis for experimental design of radial diffusion tests

Evaluation of the directional diffusivities and adsorptive properties of natural barrier materials is of fundamental importance in the design and assessment of the geological disposal of hazardous contaminants including radioactive nuclear wastes. In order to facilitate evaluation of the directional diffusivities of anisotropic media, a single-reservoir radial diffusion test for cylindrical specimens is proposed and an analytical solution corresponding to the experimental configuration of the proposed test is derived in this study. The feasibility of the diffusion test depends on whether the experiment can be performed within a reasonable period and whether reliable parameter estimation is ensured. In order to examine these factors for the proposed test, a feasibility study based on theoretical and numerical examinations was performed. A series of examinations showed that the use of a sorptive tracer is advantageous for both obtaining measurement data within a short period of time and for increasing parameter sensitivity; however these also depend on selected experimental conditions, such as the dimensions of the specimen and the reservoir. The effects of the tracer properties and the other experimental conditions can be represented by the dimensionless reservoir volume defined as the ratio of reservoir volume over the adsorptive capacity of the specimen. Therefore, in designing experiments, it is important to evaluate the value of the dimensionless reservoir volume based on the information available for the testing material and the tracer. When the effective diffusion coefficient of the testing material is very small, the duration of the experiment becomes very long. In such a case, a practical way of determining the values of the parameters is inverse analysis of the transient data. In order to clarify the applicability and limitations of inverse analysis for the proposed test, typical inverse methods are briefly summarized and some considerations are made, especially as regards characterization and conditioning of the weighted Jacobian matrix for the inverse analyses. Characterization of the weighted Jacobian matrix for the proposed test revealed that the weighted Jacobian matrix is not necessarily well-conditioned, owing to differences in the orders of magnitude between the values of the effective diffusion coefficient and the capacity factor. A promising way of conditioning the weighted Jacobian matrix is also introduced. (authors)