Improving dual-porosity-medium approaches to account for karstic flow in a fractured limestone: Application to the automatic inversion of hydraulic interference tests (Hydrogeological Experimental Site, HES – Poitiers – France)

SummaryA reassessment-improvement of a previous work by the authors is proposed on the inversion of hydraulic interference testing by means of dual-porosity-medium approaches. The tests have been performed over a fractured limestone aquifer (Poitiers, France) showing a preferential and rapid flow path along open karstic drains. All drawdown curves are merged together both in amplitude and time irrespective of their location relative to the single pumped well and classical dual-porosity-medium approaches are unable to mimic this behavior. A pressure wave propagation by advection is added to the classical diffusion equations of dual-porosity-medium in order to stress the medium almost evenly whatever the distance from the pumped well. The problem is set up to keep the continuous dual-porosity-medium framework with only two state variables, i.e. the heads in fractures and matrix. Even though the wave velocity is not well-conditioned because the ratio of the volume of drains to the total volume of the medium is unknown, automatic inversion remains feasible. The dual-porosity-medium (without the drains) can be homogeneous or fractal, having in the latter case hydraulic parameters ruled by scaling power laws. In both cases, it is shown that adding an advection term allows to invert accurately all experimental drawdown curves. Statistical fluctuations of the sought hydraulic parameters are quite small and do not show any trend with respect to the distance. Thus, modifying a dual-porosity-medium approach by adding an advection term allows for the homogenization of a reservoir that combines the general drainage of a fracture-matrix system and a rapid drainage through karstic conduits.