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 m 2/s for iodide and between 2×10 −10 and 3×10 −10 m 2/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.