Abstract. A new method is presented which allows to interpret steady state pumping test in heterogeneous isotropic transmissivity fields. In contrast to mean uniform flow, the pumping test drawdowns in heterogeneous media cannot be described by a single effective or equivalent value of hydraulic transmissivity. A radially depending description of transmissivity is required, including the parameters of aquifer heterogeneity: mean, variance and correlation length. Such a model is provided by the upscaling procedure Radial Coarse Graining, which describes the transition of near well to far field transmissivity effectively. Based on the Radial Coarse Graining Transmissivity, an analytical solution for a steady state pumping test drawdown is derived. The so-called effective well flow solution is derived for two cases: the ensemble mean of pumping tests and the drawdown at an individual heterogeneous transmissivity field. The analytical form of the solution allows to inversely estimate the parameters of aquifer heterogeneity from pumping test data. This is shown making use of virtual pumping test data, for both cases the ensemble mean drawdown and pumping tests at individual transmissivity fields. The effective well flow solution reproduces the drawdown for two-dimensional pumping tests in heterogeneous media and is a promising tool to estimate parameters of aquifer heterogeneity, in particular for the horizontal correlation length.
Coarse-graining two-dimensional turbulence via dynamical optimization
