Transient Flow Behavior Induced by Variable-Rate Pumping in a Two-Layer Confined Aquifer with Formation Interface Flow

A novel analytical model is developed for describing transient flow to a partially penetrated well pumped at variable discharge in an anisotropic two-layer confined aquifer with interface flow, allowing the well screen to cross the layer interface—a common but previously unaddressed scenario. Using Laplace and Weber transforms, semianalytical solutions for drawdown in each layer are derived, along with the respective contributions of each layer to the total pumping discharge; time-domain results are obtained via numerical inversion. For identical layer properties, equal well screen segments in each layer, and constant pumping rate, each layer contributes half of the total discharge, and the drawdown results agree well with existing and numerical solutions, thereby validating the model. Drawdown responses and discharge contributions for each aquifer are analyzed under exponentially decaying pumping rates. Results indicate that the discharge contribution of from the lower aquifer with higher groundwater flow capacity decreases over time but stabilizes at a constant value during intermediate to late stages of pumping, consistently exceeding that of the upper layer with lower groundwater flow capacity during the pumping duration. A longer well screen segment in the lower layer increases its discharge contribution, amplifying the disparity between the two layers over time. Additionally, the conventional equivalent homogeneous aquifer approach generally underestimates the actual drawdown, leading to significant errors. Sensitivity analysis reveals that discharge contributions from both layers are sensitive to well screen placement and length, as well as to the horizontal hydraulic conductivity and specific storage of each layer, particularly during the stabilized discharge phase. In contrast, discharge contribution is insensitive to the vertical hydraulic conductivity of both layers and the well radius throughout the entire pumping duration. Notably, the late-time drawdown near the pumping well in both layers shows strong sensitivity to the horizontal hydraulic conductivity of each layer but remains insensitive to well radius.