Pumping-induced Well Hydraulics and Groundwater Budget in a Leaky Aquifer System with Vertical Heterogeneity in Aquitard Hydraulic Properties

In groundwater hydrology, aquitard heterogeneity is often less considered compared to aquifers, despite its significant impact on groundwater hydraulics and groundwater resources evaluation. A semi-analytical solution is derived for pumping-induced well hydraulics and groundwater budget with consideration of vertical heterogeneity in aquitard hydraulic conductivity (K) and specific storage (Ss). The proposed new solution is innovative in its partitioning of the aquitard into multiple homogeneous sub-layers to enable consideration of various forms of vertically heterogeneous K or Ss. Two scenarios of analytical investigations are explored: one is the presence of aquitard interlayers with distinct K or Ss values, a common field-scale occurrence; another is an exponentially depth-decaying aquitard Ss, a regional-scale phenomenon supported by statistical analysis. Analytical investigations reveal that a low-K interlayer can significantly increase aquifer drawdown and enhance aquifer/aquitard depletion; a high-Ss interlayer can noticeably reduce aquifer drawdown and increase aquitard depletion. Locations of low-K or high-Ss interlayers also significantly impact well hydraulics and groundwater budget. In the context of an exponentially depth-decaying aquitard Ss, a larger decay exponent can enhance aquifer drawdown. When using current models with a vertically homogeneous aquitard, half the sum of the geometric and harmonic means of exponentially depth-decaying aquitard Ss should be used to calculate aquitard depletion and unconfined aquifer leakage.