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Hydrology and Earth System Sciences An interactive open-access journal of the European Geosciences Union
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Volume 20, issue 5
Hydrol. Earth Syst. Sci., 20, 1655–1667, 2016
https://doi.org/10.5194/hess-20-1655-2016
© Author(s) 2016. This work is distributed under
the Creative Commons Attribution 3.0 License.
Hydrol. Earth Syst. Sci., 20, 1655–1667, 2016
https://doi.org/10.5194/hess-20-1655-2016
© Author(s) 2016. This work is distributed under
the Creative Commons Attribution 3.0 License.

Technical note 03 May 2016

Technical note | 03 May 2016

Technical note: Analytical drawdown solution for steady-state pumping tests in two-dimensional isotropic heterogeneous aquifers

Alraune Zech1 and Sabine Attinger1,2 Alraune Zech and Sabine Attinger
  • 1Department of Computational Hydrosystems, UFZ Helmholtz Centre for Environmental Research, Leipzig, Germany
  • 2Institute for Geosciences, Friedrich Schiller University, Jena, Germany

Abstract. A new method is presented which allows interpreting steady-state pumping tests in heterogeneous isotropic transmissivity fields. In contrast to mean uniform flow, pumping test drawdowns in heterogeneous media cannot be described by a single effective or equivalent value of hydraulic transmissivity. An effective description of transmissivity is required, being a function of the radial distance to the well and including the parameters of log-transmissivity: 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 this approach, an analytical solution for a steady-state pumping test drawdown is deduced. The so-called effective well flow solution is derived for two cases: the ensemble mean of pumping tests and the drawdown within an individual heterogeneous transmissivity field. The analytical form of the solution allows inversely estimating the parameters of aquifer heterogeneity. For comparison with the effective well flow solution, virtual pumping tests are performed and analysed for both cases, the ensemble mean drawdown and pumping tests at individual transmissivity fields. Interpretation of ensemble mean drawdowns showed proof of the upscaling method. The effective well flow solution reproduces the drawdown for two-dimensional pumping tests in heterogeneous media in contrast to Thiem's solution for homogeneous media. Multiple pumping tests conducted at different locations within an individual transmissivity field are analysed, making use of the effective well flow solution to show that all statistical parameters of aquifer heterogeneity can be inferred under field conditions. Thus, the presented method is a promising tool with which to estimate parameters of aquifer heterogeneity, in particular variance and horizontal correlation length of log-transmissivity fields from steady-state pumping test measurements.

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A new method is presented which allows interpreting pumping test in heterogeneous transmissivity fields. Based on radially dependent transmissivity, the 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 inversely estimating the parameters of aquifer heterogeneity (mean, variance, and correlation length) from steady-state pumping test data.
A new method is presented which allows interpreting pumping test in heterogeneous transmissivity...
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