Traditional analysis of aquifer tests: Comparing apples to oranges?

Abstract

Traditional analysis of aquifer tests uses the observed drawdown at one well, induced by pumping at another well, for estimating the transmissivity ( T ) and storage coefficient ( S ) of an aquifer. The analysis relies on Theis' solution or Jacob's approximate solution, which assumes aquifer homogeneity. Aquifers are inherently heterogeneous at different scales. If the observation well is screened in a low‐permeability zone while the pumping well is located in a high‐permeability zone, the resulting situation contradicts the homogeneity assumption in the traditional analysis. As a result, what does the traditional interpretation of the aquifer test tell us? Using numerical experiments and a first‐order correlation analysis, we investigate this question. Results of the investigation suggest that the effective T and S for an equivalent homogeneous aquifer of Gaussian random T and S fields vary with time as well as the principal directions of the effective T . The effective T and S converge to the geometric and arithmetic means, respectively, at large times. Analysis of the estimated T and S , using drawdown from a single observation well, shows that at early time both estimates vary with time. The estimated S stabilizes rapidly to the value dominated by the storage coefficient heterogeneity in between the pumping and the observation wells. At late time the estimated T approaches but does not equal the effective T . It represents an average value over the cone of depression but influenced by the location, size, and degree of heterogeneity as the cone of depression evolves.