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

Abstract

One-dimensional analytical porosity-weighted solutions of the dual-porosity model are derived, providing insights on how to relate exchange and storage coef®cients to the volumetric density of the high-permeability medium. It is shown that porosityweighted storage and exchange coef®cients are needed when handling highly heterogeneous systemsÐsuch as karstic aquifersÐusing equivalent dual-porosity models. The sensitivity of these coef®cients 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 coef®cients and the structural features of the discrete single-continuum model. The calibration of the equivalent 1D analytical dual-porosity model on reference hydraulic responses con®rms the dependence of the exchange coef®cient 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.

Simplified Conceptual Structures and Analytical Solutions for Groundwater Discharge Using Reservoir Equations

“…Methods that consider the exchange between fissure matrix and conduits can be found in Cornaton & Perrochet (2002) and Sauter (1992). In Fig.…”

Representation of water abstraction from a karst conduit with numerical discrete-continuum models

“…Storage directly associated with discrete conduits was not considered. However, the existence of water storage within highly permeable karst structures is known from karst hydraulics (e.g., Cornaton and Perrochet, 2002;Geyer et al, 2008;Maréchal et al, 2008). Worthington et al (2000) and Worthington (2007) presented field studies that clearly emphasize the necessity to describe karst aquifers as triple porosity systems.…”

Complexity selection of a neural network model for karst flood forecasting: The case of the Lez Basin (southern France)

“…More specific models have thus been developed for karsts. Double-permeability models featuring fracture permeability and conduit permeability have been introduced, for example, by Mohrlok and Teutsch (1997), Cornaton and Perrochet (2002) and Long (2009). These models consider an average distribution for both the matrix and conduits.…”