• Characterization of aquifer heterogeneity using transient hydraulic tomography

      Zhu, Junfeng; Yeh, Tian-Chyi J.; Department of Hydrology & Water Resources, The University of Arizona (Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ), 2004-11)
      Hydraulic tomography is a cost -effective technique for characterizing the heterogeneity of hydraulic parameters in the subsurface. During hydraulic tomography surveys, a large number of hydraulic heads (i.e., aquifer responses) are collected from a series of pumping or injection tests in an aquifer. These responses are then used to interpret the spatial distribution of hydraulic parameters of the aquifer using inverse modeling. In this study, we developed an efficient sequential successive linear estimator (SSLE) for interpreting data from transient hydraulic tomography to estimate three-dimensional hydraulic conductivity and specific storage fields of aquifers. We first explored this estimator for transient hydraulic tomography in a hypothetical one-dimensional aquifer. Results show that during a pumping test, transient heads are highly correlated with specific storage at early time but with hydraulic conductivity at late time. Therefore, reliable estimates of both hydraulic conductivity and specific storage must exploit the head data at both early and late times. Our study also shows that the transient heads are highly correlated over time, implying only infrequent head measurements are needed during the estimation. Applying this sampling strategy to a well -posed problem, we show that our SSLE can produce accurate estimates of both hydraulic conductivity and specific storage fields. The benefit of hydraulic tomography for ill -posed problems is then demonstrated. Finally, to affirm the robustness of our SSLE approach, we apply the SSLE approach to transient hydraulic tomography in a hypothetical two- dimensional aquifer with nonstationary hydraulic properties, as well as a hypothetical three-dimensional heterogeneous aquifer.
    • Estimation of effective unsaturated hydraulic conductivity tensor using spatial moments of observed moisture plume

      Yeh, Tian-Chyi J.; Ye, Ming; Khaleel, Raziuddin; Department of Hydrology & Water Resources, The University of Arizona (Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ), 2004-10)
      Knowledge of unsaturated zone hydraulic properties is critical for many environmental and engineering applications. Various stochastic methods have been developed during the past two decades to estimate the effective unsaturated hydraulic properties. Independent of these stochastic methods, we develop in this paper a practical approach to estimate the three-dimensional (3 -D) effective unsaturated hydraulic conductivity tensor using spatial moments of 3-D snapshots of a moisture plume under transient flow conditions. approach hydraulic hydraulic Application of the new to a field site in southeastern Washington State yields an effective unsaturated conductivity tensor that exhibits moisture- dependent anisotropy. The effective conductivities compare well with laboratory- measured unsaturated hydraulic conductivity data from small core samples; they also reproduce the general behavior of the observed moisture plume at the site. We also define a moisture diffusivity length concept which we use in conjunction with estimated correlation scales of the geological media at the field site to explain deviations between the observed and simulated plumes based on the derived effective hydraulic properties.
    • Stochastic analysis of moisture plume dynamics of a field injection experiment

      Ye, Ming; Khaleel, Raziuddin; Yeh, Tian-Chyi J.; Department of Hydrology & Water Resources, The University of Arizona (Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ), 2004-10)
      A vadose zone field injection experiment was conducted in the summer of 2000 at theHanford Site, Washington. The unique moisture content database is used to identify the lithology at the field site and to interpret, visualize, and quantify the spatio- temporal evolution of the three -dimensional (3 -D) moisture plume created by the injection experiment. We conducted a hierarchical geostatistical analysis to examine the large -scale geologic structure for the entire field site, and then investigate small -scale features within different layers. Afterward, variogram analysis is applied to the O field measured for seven different days during the injection experiment. Temporal variations of sills and ranges are related to the observed moisture plume dynamics. A visualization of the 3 -D moisture plume evolution illustrates effects of media heterogeneity. Statistics of changes in moisture content as a function of distance reveals large variance near the wetting front and the coefficient of variation increases with decreasing mean.These findings support the gradient- and mean -dependent variability in the moisture content distribution as reported by existing stochastic theories. Spatial moment analysis is also conducted to quantify the rate and direction of movement of the plume mass center and its spatial spreading. The ratio of horizontal to vertical spreading at varying moisture contents suggests moisture- dependent anisotropy in effective unsaturated hydraulic conductivity, confirming existing stochastic theories. However, the principal directions of the spatial moments are found to vary as the moisture plume evolves through local heterogeneity, a feature that has not been recognized in the theories.
    • Traditional Aquifer Tests: Comparing Apples to Oranges?

      Wu, Cheng-Mau; Yeh, Tian-Chyi J.; Lee, Tim Hau; Hsu, Nein-Sheng; Chen, Chu-Hui; Sancho, Albert Folch; Department of Hydrology & Water Resources, The University of Arizona (Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ), 2004-10)
      Traditional analysis of aquifer tests uses the observed hydrograph at one well caused by pumping at another well for estimating transmissivity and storage coefficient of an aquifer. The analysis relies on Theis' or Jacob's approximate solution, which assumes aquifer homogeneity. Aquifers are inherently heterogeneous at different scales. If the observation well taps into a low permeability zone while the pumping well is located in a high permeable zone, the resulting situation contradicts the homogeneity assumption embedded in the traditional analysis. As a result, a practical but important question we ask: What do we derive from the traditional analysis? Using numerical experiments in synthetic aquifers, we answer this question. Results of the experiments indicate that the effective transmissivity, Teff , and storage coefficient, Seff , values vary with time, as well as the principal directions of the transmissivity, but both values approach their geometric means of the aquifer at large times. Analysis of the estimated transmissivity (T) and storage coefficient (S ) using well hydrographs from a single observation well shows that at early times, both the estimated T and S values vary with time. At late times, both estimates approach local averages near the observation well. The T value approaches but does not equal Teff , representing an average value over a broad area in the vicinity of the observation well while the S value converges to the value dominated by the storage coefficient near the observation wells (i.e., its average area is much smaller than that of the t value).