The extended generalized radial flow model and effective conductivity for truncated power law variograms

Sebastian Mueller, Falk Hesse, Sabine Attinger, Alraune Zech

Research output: Contribution to journalArticleAcademicpeer-review


Pumping tests are established for characterizing spatial average properties of aquifers. At the same time, they are promising tools to identify heterogeneity characteristics such as log-conductivity variance and correlation scales. We present the extended Generalized Radial Flow Model (eGRF) which combines the characterization of well flow in fractal geometry with an upscaled conductivity for pumping tests in heterogeneous media. We show that the eGRF is a generalization of previously solutions, such as that of Barker, Butler and Neuman. We derive effective conductivities for uniform and well flow conditions in heterogeneous log-normal media with a truncated power law correlation structure through the upscaling procedure Coarse Graining. The radial-dependent effective conductivity for well flow reflects the gradual change of heterogeneity impact on average pumping test drawdowns. We then combine upscaled conductivities with the eGRF model to determine the effective pumping test solution. We provide a proof of concept by comparing theoretical upscaling results with Monte Carlo well flow simulations in heterogeneous fractal fields. The eGRF and upscaling results are implemented and made freely available as python code for transport simulation as well as pumping test analysis.
Original languageEnglish
Article number104027
JournalAdvances in Water Resources
Publication statusPublished - Oct 2021


  • eGRF
  • Groundwater
  • Heterogeneity
  • Groundwater flow equation
  • Pumping test


Dive into the research topics of 'The extended generalized radial flow model and effective conductivity for truncated power law variograms'. Together they form a unique fingerprint.

Cite this