[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.

Abstract:This study presents a novel hysteresis model based on van Genuchten's soil-moisture relationships. The proposed model yields a series of closed-form relationships in which two shape factors˛and Á are determined from the main drying and wetting curves. Experimental and literature-cited data were used to assess model accuracy. The proposed model was also compared with the Scott and KP models. Analytical results indicate that the present model is simple, accurate and effective in constructing the series of wetting and drying scanning curves. Notably, the proposed model outperforms the Scott and KP models in terms of model accuracy. Moreover, the novel model eliminates the pumping effect and has perfect closure at scanning curve reversal points.

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Abstract:This paper is a continuation of previous research, which obtained a convenient solution for arbitrary surface fluxes before ponding. By means of Fourier Transformation this has been extended to derive analytical solutions of a linearized Richards' equation for arbitrary input fluxes after surface saturation.

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