Three-dimensional response to a partially penetration well pumping in a general anisotropic three-layer aquifer system

Three-dimensional response to well pumping in a multilayer aquifer system with rigorous treatment of interfacial flow attracts great attention among the subsurface hydrologists because of its theoretical importance and practical merits. In this study, a general theory of three-dimensional groundwater flow to a well of infinitesimal radius in an anisotropic three-layer aquifer system is developed with a constant-rate pumping in the lower layer, and associated semi-analytical solutions of drawdowns in individual layers are obtained. This theory discards many previous assumptions for studying a multilayer aquifer system such as simplified flow configuration in the aquitard, treatment of cross-formation flow as a volumetric averaged term adding to the governing equations of aquifer flows, and sometimes negligence of vertical flow components in the aquifers. Additionally, this theory considers three types of commonly used top boundary conditions: A water table with delayed gravity drainage boundary condition (Case 1), a constant-head top boundary condition (Case 2), and a no-flow top boundary condition (Case 3). The dimensionless drawdown solutions in Laplace domain are obtained and inverted numerically to calculate the time-domain solutions. The solution encompasses existing solutions for a two-layer or a single-layer (e.g. unconfined or confined) aquifer system as subsets. The developed solutions are tested extensively with a finite-element numerical solution using COMSOL and other existing solutions, and a sensitivity analysis is performed to prioritize the influences of different parameter groups. The results of this study can be used to predict the pumping induced drawdown at any position with an observation well, and to estimate the hydraulic parameters of the lower pumped layer and upper layer, as well as the middle layer. The developed theory provides a basis for other potential applications such as geotechnical engineering and groundwater management.