[1] 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.

[1] Hydraulic tomography is a method that images the hydraulic heterogeneity of the subsurface through the inversion of multiple pumping or cross-hole hydraulic test data. Transient hydraulic tomography is different from steady state hydraulic tomography in that it utilizes transient hydraulic head records to yield the distribution of hydraulic conductivity (K) as well as specific storage (S s ) of an aquifer. In this paper we demonstrate the robustness of transient hydraulic tomography through the use of hydraulic head data obtained from multiple cross-hole pumping tests conducted in a laboratory sandbox with deterministic heterogeneity. We utilize the algorithm developed by Zhu and Yeh (2005) to conduct the transient inversions and validate the K and S s tomograms using a multimethod and multiscale validation approach previously proposed by Illman et al. (2006). Validation data consist of cross-hole tests not used in the inversion as well as other hydraulic tests that provided local (core, single-hole tests) as well as large-scale (unidirectional flow-through tests) estimates of hydraulic parameters. Results show that the algorithm is able to yield consistent estimates that agree with independently collected local as well as large-scale hydraulic parameter data. In addition, we find that the transient hydraulic tomography requires a fewer number of pumping tests to estimate a similar quality K tomogram when compared with steady state hydraulic tomography, as the former approach utilizes more data from each pumping test. Overall, we find that transient hydraulic tomography is a robust subsurface characterization technique that can delineate the subsurface heterogeneity in both K and S s from multiple pumping or crosshole hydraulic tests.

[1] This paper investigates our ability to characterize an aquifer using a sequential aquifer test in a well field that consists of six wells. During the test, we pumped water out from the aquifer at one well and monitored the water level changes at the rest of the wells to obtain a set of five well hydrographs. By pumping at another of the six wells, we obtained another set of five hydrographs. This procedure was repeated until each of the six wells was pumped. We then analyzed the six sets of hydrographs using the classical drawdown-time, the drawdown-distance, and the drawdown-distance/time methods. Results of the analysis confirm recent findings that the transmissivity estimates vary significantly at early time and stabilize at late time. At late time, the estimated values from all hydrographs are similar overall but vary slightly according to the locations of the pumping and observation wells. In contrast, storage coefficient estimates stabilized rapidly to distinct values associated with the well locations. We subsequently used a hydraulic tomography approach to include all hydrographs from the sequential aquifer test to estimate the spatially varying transmissivity and storage coefficient fields. The estimated fields appear to be realistic: They reflect the geologic setting and the behaviors of the well hydrographs, although more definitive confirmation is needed.