An Application of Inverse Problem and Universal Solutions for Pumping Wells in Unconfined Aquifers

Abstract

As far as we know, universal solutions (or type-curves) for scenarios of flow through anisotropic unconfined aquifers due to pumping wells cannot be found in the literature. On the contrary, those theoretical solutions in hydrogeological manuals are commonly based on Dupuit solutions for isotropic soils or simplifying other characteristics of the chosen medium. In this study, the application of the discriminated nondimensionalization technique allowed for the inclusion of vertical and radial hydraulic conductivities in the data set, with which the monomials ruling unknown variables of the problem, pumping flow and seepage surface in their dimensionless form are obtained. One of the main findings of this research is depicting these relationships as type-curves from a large number of precise numerical simulations based on the Network Simulation Method. The other main finding is an easy-to-apply methodology to estimate vertical and radial hydraulic conductivities employing these type-curves. This methodology can be considered as an inverse problem. In addition, an example of the problem is presented, in which the influence that measure deviations may have on the estimated values of the hydraulic conductivities in anisotropic soils is also studied and discussed.