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WATER RESOURCES RESEARCH, VOL. 43, W03414, doi:10.1029/2006WR005241, 2007

Ergodicity of pumping tests

Xavier Sanchez-Vila

Department of Geotechnical Engineering and Geosciences, Technical University of Catalonia, Barcelona, Spain


Daniel M. Tartakovsky

Department of Mechanical and Aerospace Engineering, University of California, San Diego, La Jolla, California, USA
Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico, USA


Abstract

Standard interpretations of pumping tests in heterogeneous formations rely on effective representations of porous media, which replace spatially varying hydraulic properties with their constant counterparts averaged over the support volume of a test. Rigorous approaches for deriving representative (effective, apparent, upscaled, etc.) parameters employ either ensemble or spatial averaging. We derive a set of conditions under which these two paradigms yield identical results. We refer to them as conditions for the ergodicity of pumping tests. This allows one to use stochastic approaches to estimate the statistics of the spatial variability of hydraulic parameters on scales smaller than the support volume of a pumping test.

Received 19 June 2006; accepted 30 October 2006; published 10 March 2007.

Keywords: heterogeneity; ergodicity; pumping tests.

Index Terms: 1829 Hydrology: Groundwater hydrology; 1869 Hydrology: Stochastic hydrology.

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Citation: Sanchez-Vila, X., and D. M. Tartakovsky (2007), Ergodicity of pumping tests, Water Resour. Res., 43, W03414, doi:10.1029/2006WR005241.