Determination of Three-Dimensional Aquifer Anisotropy of an Unconfined Aquifer under Partially Penetrating Pumping Conditions
Field and theoretical investigations were made to study the three-dimensional hydraulic conductivity anisotropy of an unconfined aquifer. A well field, consisting of three multilevel samplers/piezometers (MLSP), ten fully screened observation wells, and two pumping wells, was developed in the Sevilleta Wildlife Refuge, north of New Mexico Tech. The MLSP can give depth-specific drawdown and groundwater samples for the three-dimensional analysis. The fully screened observation well can yield vertically-averaged drawdown and groundwater samples for the two-dimensional analysis. The three-dimensional aquifer anisotropy is characterized using the depth-specific drawdown data and a method based on the Laplace-Hankel domain solution of a pertinent three-dimensional unconfined well hydraulics theory. The Laplace-Hankel domain solution involves three mathematically simple terms representing the Theis solution, the water-table effect, and the partially penetrating effect, respectively. The fast Hankel transform (FHT) technique and the Stehfest Laplace inverse method are employed to calculate the drawdown of interest from the Laplace-Hankel domain counterpart. This Laplace-Hankel domain analysis provides an effective way to evaluate and understand complicated well hydraulics theories.
Also, a mapping function technique was developed to diagnose the drawdown data. The mapping function essentially represents any difference between the actual hydrogeological conditions embedded in the field data and the idealistic assumptions invoked in the Theis solution. A new analytical solution for well hydraulics involving the temporal mapping function was obtained. Based on this solution, a robust method was developed to find the mapping function from available field drawdown data.
A few case studies demonstrated that the mapping function indeed can yield diagnostic curve characteristics pertinent to important hydrogeological conditions. During the course of reviewing currently available well hydraulics, it was found that the method normally used in finding the asymptotic solutions from the Laplace domain can lead to incorrect results. To avoid this pitfall, it is suggested that the Tauberian Theorem be used to check the validity of the asymptotic solutions obtained using the normally accepted method.