A New Approach to Analyze Pumping Test in Unconfined Aquifers

Existing analytical models for the analysis of pumping tests in unconfined aquifers rely on either a depth- averaged, two-dimensional groundwater flow equation with delayed yield source function, or a three- dimensional groundwater flow model with a free surface boundary condition, neglecting the unsaturated zone (i.e., gravity drainage model). Furthermore, these models assume aquifer homogeneity. Recent advances in computer technology and numerical analysis make it possible to investigate usefulness of the estimated hydraulic properties derived from these analytical models and compel us to develop more realistic models. In this study, we first use a 3-D variably saturated flow model that considers interactions between the vadose zone and the saturated aquifer to simulate pumping tests in unconfined aquifers with homogeneous hydraulic properties and in aquifers with heterogeneous hydraulic properties. We then apply the popular analytical models to the simulated drawdown-time data in the homogeneous aquifers to verify their abilities to obtain true hydraulic properties. Subsequently, these models are applied to those simulated data in heterogeneous aquifers to obtain effective hydraulic properties. In addition, we develop an inverse model based on the 3-D variably saturated flow numerical model to estimate both saturated and unsaturated hydraulic properties of homogeneous unconfined aquifers. The inverse method utilizes the maximum likelihood approach and employs Levenberg-Marquardt algorithm. Moreover, a cross-correlation analysis is developed to investigate the relationship between the hydraulic head at different locations and each hydraulic parameter in the aquifer since the cross correlation is a weighted sensitivity that considers contributions from other parameters. Our study shows that moisture retention characteristics have more profound impacts on the "delayed yield" phenomenon of the well hydrograph than the unsaturated hydraulic conductivity characteristics. The early time drawdown data is highly correlated with the specific storage while the later time drawdown is strongly corrected with the saturated hydraulic conductivity. Similarly, unsaturated parameters are found to correlate highly with late time data. These findings serve as a guide to estimate the hydraulic parameters of the aquifer and the vadose zone during the interpretation of pumping tests. Subsequently, we investigate the usefulness of the effective parameters for predicting independent pumping tests at different locations. We show that phenomenological nature of the effective parameters depends on the degree of heterogeneity. Finally, applications of the inverse model to some field experiments are discussed.