  One dimensional analytical porosity-weighted solutions of the dual-porosity
model are derived, providing insights on how to relate exchange and storage
coefficients to the volumetric density of the high-permeability medium. It is
shown that porosity-weighted storage and exchange coefficients are needed when
handling highly heterogeneous systems - such as karstic aquifers - using
equivalent dual-porosity models. The sensitivity of these coefficients is
illustrated by means of numerical experiments with theoretical karst systems.
The presented 1-D dual-porosity analytical model is used to reproduce the
hydraulic responses of reference 3-D karst aquifers, modelled by a discrete
single-continuum approach. Under various stress conditions, simulation results
show the relations between the dual-porosity model coefficients and the
structural features of the discrete single-continuum model. The calibration of
the equivalent 1-D analytical dual-porosity model on reference hydraulic
responses confirms the dependence of the exchange coefficient with the karstic
network density. The use of the analytical model could also point out some
fundamental structural properties of the karstic network that rule the shape of
the hydraulic responses, such as density and connectivity.
