Modeling the Effect of Sorption Kinetics on Radionuclide Migration in Crystalline Rock
Authors: Wörman Anders , Xu Shulan , Dverstorp Björn 
Published: April 2011

The preferred methods for nuclear waste disposal in Sweden are based on isolation in deep repositories in crystalline rock. As part of its research programme on the safety of final disposal, the Swedish Nuclear Power Inspectorate (SKI) initiated a project to examine how spatial variability in rock chemistry in combination with spatial variability in matrix diffusion affects the radionuclide migration along single fractures in crystalline rock.

A mathematical framework describing migration was developed with a numerical simulation package. In order to determine statistical patterns in geochemistry, in-diffusion, through-diffusion, and batch experiments will be performed. The purpose is to use the knowledge of statistical patterns in geochemistry as a basis for stochastic predictions which will be validated against the results of several laboratory migration experiments.

A medium grained granite and a diorite were selected at Äspö hard rock laboratory in southeastern Sweden. Four drill cores with a diameter of 20 [cm] have been collected from each of two rock types. One of the four drill cores in each series was sliced into cubes in order to evaluate sorption characteristics, porosity and effective diffusivity by in-diffusion and through-diffusion experiments on the individual pieces. The other three drill cores are to be used in three migration experiments. Experiments with the two rock types are run in two parallel series. Currently, all the laboratory experiments are underway.

The present paper describes the mathematical framework used for planning and interpreting experimental results. In particular, the formulations for sorption kinetics and matrix diffusion are crucial for distinguishing between the effects of various hydrodynamic and geochemical effects. Neretnieks [I] proposed a one-dimensional formulation for radionuclide migration that includes the effect of matrix diffusion and instantaneous matrix sorption. This concept has been further developed into two dimensional formulations [2], [3]. The model framework developed in this project [4] includes additional first order sorption kinetics in the rock matrix. Preliminary analyses indicate that sorption kinetics (non-equilibrium sorption) are often sufficiently pronounced so as to significantly affect interpretation of other phenomena affecting the migration process. Acknowledgement of sorption kinetics is, therefore, deemed important for reliable generalisations of the retardation of radionuclide migration.

Several investigations of Cs sorption onto minerals indicate that equilibration time varies from weeks in laboratory tests with illite and montmorillonite [5] to up to several years under special conditions for Chernobyl Cs in lake sediments [6]. Comans et al., [7], Nyffeler et al., [8] and Smith and Comans [9] discussed the different equilibrium times associated with the readily available binding sites on grain surfaces and less available sites such as frayed edges or in the grain interior. Skagius [10] conducted experiments with adsorption and desorption of Cs on crushed granite in different size fractions, the major constituents of which were quartz, feldspar and microcline. In some experiments the ratio between dissolved and particulate phases of Cs was still changing even after more than a years time.

In order to quantify kinetics of Cs adsorption on granite batch tests were conducted on crushed rock. Relationships between surface area available to sorption and transfer rate coefficients, as well as the ratio of dissolved to adsorbed mass phase species at equilibrium are established from the experiments. The specific surface area for the parent, intact rock, as well as coefficients of sorption kinetics, can be evaluated by combining the results with the crushed rock with those of the parent intact rock. Hence the effect of sorption kinetics on the solute pulse propagation along a single fracture can be numerically simulated. The maximum concentration of the breakthrough from a Dirac mass spike is higher than that obtained with equilibrium sorption. The kinetics of the adsorption process during the uptake phase can be interpreted as a decrease in the effective partition coefficient (adsorbed/dissolved ratio). In contrast, sorption kinetics during the release phase, can be interpreted as the results of an increase in the partition coefficient. This, in turn, causes a prolonged tail in the breakthrough curve. If a Heaviside step function is used as a boundary condition, simulation indicates an earlier arrival of the breakthrough curve front than that obtained with equilibrium sorption.

The impact of sorption kinetics on breakthrough curves is of the same order as the effect of shear dispersion. This is of great importance in the interpretation of the migration tests and to future generalisations to a field scale.