Three-dimensional numerical analysis of steady state pumping tests in heterogeneous confined aquifers

We study three-dimensional steady state flow field generated by a fully penetrating well extracting a constant water discharge from a confined aquifer of constant thickness. The hydraulic conductivity K is modeled as an axisymmetric, stationary random space function, and the flow equation is solved by using the seven-node finite volume numerical scheme. In view of application in aquifer characterization we analyze how the equivalent conductivity Keq varies as a function of the distance from the extraction well. The numerical simulations showed that the boundary condition at the well exerts a large impact on Keq and that the first-order solution in (sigma)^2y obtained by Indelman et al. (1996) is valid up to (sigma)^2y = 0.5. For higher values of (sigma)^2y the first-order solution overestimates Keq with differences that for a given cry, reduce progressively as the formation becomes more anisotropic. A simple inverse procedure based on Keq, obtained through cross-well interference, is finally proposed and tested with the objective of estimating the parameters of the geostatistical model of variability of the hydraulic conductivity. A few parametric examples showed that a suitable interpretation of pumping tests can be used to safely estimate parameters such as the geometric mean of the hydraulic conductivity, its variance, and, although with larger uncertainty, the horizontal integral scale, while the inference of the anisotropy ratio is highly uncertain and error prone.