Determining karst transmissivities with inverse modeling and an equivalent porous media

Flow simulation is difficult to implement in heterogeneous media such as karst aquifers, primarily because the structure of the rock is extremely complex and usually unknown. The aim of this study was to verify the possibility of using inverse modeling and an equivalent porous media to identify transmissivities in a slightly karstified aquifer, the La Rochefoucauld karst (Charente, France), Different simulation scenarios were tested: using two spatial discretizations with different finite-element cell sizes and using measured or interpolated heads. The inverse modeling was performed with the downscaling parameterization procedure, using a finite-element representation of bidimensional ground water flow. The inverse modeling converged satisfactorily with all scenarios: head residuals were small and spring flow rates and the river/aquifer exchanges were adequately stimulated. The scenario using small cells and measured heads generated a highly heterogeneous transmissivity field, indicating an overparameterization of the problem. The calibrated transmissivities and simulated heads of this scenario proved less reliable overall than those of the other scenarios. The use of interpolated heads generated more uniform transmissivities as a result of the head smoothing. A rotation of the initial parameter mesh showed that the scenarios using interpolated heads generate the most stable and reliable results. The scenarios with interpolated heads could therefore be used when head measurements are limited or are unevenly distributed over the aquifer. Overall, the calibrated transmissivities reproduced the entire range of transmissivities measured in the field using different methods. The results indicate that inverse modeling and an equivalent porous media can be used to determine transmissivities in a moderately karstified aquifer.