Approximate solutions for flows in unconfined double porosity aquifers

Abstract

Although flow in unconfined double porosity aquifers occurs in most part of the world such as in karst and crystalline aquifers, their hydrodynamic behavior is still poorly understood. Especially, analytical or semi-analytical solutions for flow in unconfined double porosity (DP) aquifers are scarce. In this paper analytical solutions are proposed for two configurations involving groundwater discharge to a stream adjacent to an unconfined aquifer, and flow induced by pumping with constant extraction rate, respectively. The analytical solutions are obtained based on an h2-linearization technique of the full mathematical model and using a Laplace transform. The above technique has not been used before to investigate the behavior in DP aquifers. The newly developed analytical solution is in agreement with numerical solutions of the full mathematical model, for small to moderate drawdowns which are as high as 25% of the initial water table (case of the well pumping problem). This confirms on one side the correctness of the analytical solution and on the other side the reliability of the developed h2-linearization technique. On the contrary the conventional confined aquifer equations approach can be used only if the drawdown does not exceed 5% of the initial head values. As potential application examples, the estimation of the flow-rate from an aquifer to an adjacent water body, and the interpretation of pumping tests in unconfined double porosity aquifers, allowing to estimate the values of the models parameters, are proposed.