On the theory of tracer experiments in fissured rocks with a porous matrix

Abstract A model of parallel fractures, having equal spacing and width, has been applied to tracer movement in fissured rocks with a porous matrix. The exact solution has been obtained for instantaneous injection. Graphical presentations demonstrate the applicability and the limitations of particular approximations. In short-term experiments the single fracture approximation works well because the tracer has not penetrated the matrix deeply enough to be influenced by the adjacent fractures. In high matrix porosity, diffusion into the matrix is dominant and the model may be simplified by neglecting the influence of dispersivity. In low matrix porosity, a dispersion model with no diffusion into the matrix may often yield approximately the mean transit time of water. By contrast, in long-term tracer experiments, the tracer appears to exploit the whole water volume, i.e. both the mobile fissure volume and the stagnant micropore volume. The tracer curve yields the mean transit time of tracer, which is related to the mean transit time of water by the retardation factor. This factor is expressed approximately by the ratio of total porosity to fissure porosity, provided the tracer is non-adsorbable. For adsorbable tracers the microporosity acts as a strong sink due to the large adsorption surface. This fact is most probably the cause of the discrepancies observed between 14C ages in carbonate aquifers and the stable isotope shift expected from the climate change at the end of the last glaciation. It is also shown that the 14C exchange in carbonate rocks may yield 14C ages orders of magnitude too high in comparison with conventional flow data. Examples of the interpretation of artificial tracer experiments demonstrate that the model developed works surprisingly well.