An analytical model for the interpretation of pulse injection experiments performed for testing the spatial variability of clay formations

Abstract

This paper presents an analytical model to describe pulse injection experiments. This model solves the advection–diffusion equation while taking into account back diffusion from the clay core to the inlet and from the outlet to the clay core. In most analytical models, back diffusion is neglected. For sufficiently high Péclet numbers, this is a good approximation. However, in experiments where the Péclet number is low, back diffusion is important and must be taken into account. An additional advantage of the present model is that both concentration and flux are conserved at the inlet and at the outlet of the clay core.

This model is used to fit pulse injection experiments with iodide and tritiated water (HTO) in clay cores. The (new) model is required for fitting the experimental results since in clay layers advection is very slow leading to a low Péclet number. The experiments are performed on clay cores taken from different depths from the Boom Clay and the Ypres Clay layer under the site of the nuclear power plant of Doel (Belgium). The quality of all fits is excellent and the obtained parameter values are coherent. For HTO, the fitted value for the diffusion accessible porosity is consistent with measurements of the water content in Ypres Clay cores. In both types of clays, the apparent diffusion coefficient at zero flow is between 10⁻¹⁰ and 2×10⁻¹⁰ m²/s for iodide and between 2×10⁻¹⁰ and 3×10⁻¹⁰ m²/s for HTO. The dispersion length is in the order of 10⁻³ m. The average value for the diffusion accessible porosity is between 0.35 and 0.4 for HTO and between 0.2 and 0.25 for iodide.

Introduction

The disposal of hazardous (nuclear) waste in a safe manner is an important environmental problem. A possible solution is to encapsulate the waste in an appropriate ‘package’ and dispose this package in a suitable geological formation. In Belgium, Boom Clay and Ypres Clay are being considered as potential host formations. Due to the low hydraulic gradient (approximately 0.02 m/m) and the very low hydraulic conductivity (in the order of 10⁻¹¹ to 10⁻¹² m/s), diffusion is the dominant process in radionuclide transport in these clay layers.

For the estimation of the diffusion rate of radionuclides in the clay, it is necessary to know the value of (a) the product ηR where η is the diffusion accessible porosity and R the retardation coefficient, and (b) the apparent hydrodynamic dispersion coefficient D. Values for these parameters are obtained here by fitting the experimental data of a pulse injection experiment. First, such an experiment is briefly described. Then follows the introduction of an analytical model allowing to calculate as a function of time the concentration of the injected tracer at the outlet. Finally, presented are the values of the fitted parameters for two radionuclides (iodide and tritiated water (HTO)) in the Boom Clay and Ypres Clay below the site of the nuclear power plant of Doel. The purpose of the present study is to examine the spatial variability of the migration parameters and the hydraulic conductivity. Therefore, clay cores are taken over the entire thickness of the clay formations.