Analytical 1D dual-porosity equivalent solutions to 3D discrete single-continuum models. Application to karstic spring hydrograph modelling

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 1D dual-porosity analytical model is used to reproduce the hydraulic responses of reference 3D 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 1D 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.