Modeling Slug Tests in Unconfined Aquifers Taking into Account Water Table Kinematics, Wellbore Skin and Inertial Effects

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Two models for slug tests conducted in unconfined aquifers are developed by (a) extending the unconfined KGS solution to oscillatory responses, yielding a model referred to herein as the unified model, and (b) replacing the constant head condition with the linearized kinematic condition at the water table. The models can be used to analyze the full range of responses from highly oscillatory to overdamped. The second model, refered to as the moving water table (MWT) model, is only applicable when effects of well bore skin are negligible. The models are validated by comparison with published solutions, and by application to a published case study of field tests conducted in wells without skin in an unconfined aquifer at the MSEA site in Nebraska. In this regard (a) the MWT model essentially yields the same results as the confined KGS model, except very close to the water table, and (b) the unified model yields slightly smaller aquifer K-values relative to the MWT model at all positions in the well. All model solutions yield comparable results when fitted to published field data obtained in an unconfined fluvial aquifer at the MSEA site in Nebraska. The unified model is fitted to field data collected in wells known to exhibit positive skin effects at the Boise Hydrogeophysical Research Site (BHRS) in Boise, Idaho. It is shown to yield hydraulic conductivity estimates of comparable magnitude to those obtained with the KGS model for overdamped responses, and the Springer–Gelhar model for oscillatory responses. Sensitivity of the MWT model to specific yield, Sy, and hydraulic anisotropy, κ is evaluated and the results, when plotted in log–log space and with consideration of log-scale time derivatives of the response, indicate that these two parameters should be estimable from slug test data, though challenges still remain.