Ergodicity of pumping tests

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.

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