Semi-analytical modeling of transient flow to a partially penetrating variable-discharge well in a complex aquifer-aquitard system

Abstract

Accurate prediction of transient flow and vertical leakage in multilayer aquifer systems is critical for sustainable groundwater management and contaminant risk assessment. Conventional groundwater models often simplify subsurface conditions by assuming homogeneous aquitards, isotropic aquifers, constant pumping rates, and idealized boundary conditions, limiting their applicability in realistic field settings. This study develops semi-analytical solutions for three-dimensional transient flow toward a partially penetrating well under variable discharge in a complex aquifer-aquitard system. The model incorporates aquifer anisotropy and vertical heterogeneity in aquitard hydraulic conductivity (K) and specific storage (S_s). It considers representative upper boundary conditions: constant head, water table with delayed drainage, and no-flux. Solutions are derived in the Laplace-Hankel domain and numerically inverted to quantify drawdown and leakage response. Results show that stronger aquitard S_s decay enhances early- and mid-time drawdowns, while greater aquitard K decay limits vertical leakage and decreases aquitard and upper aquifer drawdowns. Compared with a homogeneous aquitard K, increasing dimensionless decay exponent of K from 1.5 to 2.5 reduces stable-stage leakage rates by 45% to 86%. Aquifer anisotropy intensifies vertical hydraulic gradient contrasts and promotes drawdown accumulation. Variable pumping induces nonlinear leakage responses and transient flow reversals. Boundary conditions significantly influence stable-stage leakage rates: compared to the constant-head boundary, the leakage rate at the aquifer-aquitard interface is 3% lower under the water table boundary and 10% lower under the no-flux boundary. The model offers a robust tool for evaluating leakage-driven risks to groundwater quality in complex, vertically heterogeneous hydrogeologic systems such as glacial and alluvial basins.