Cumulative Drawdown as a Primary State Variable: The Absement Method for Leaky-Aquifer Pumping-Test Analysis

Abstract

Abstract

This study extends the Absement Method to leaky-aquifer pumping-test analysis by time integrating the Hantush–Jacob governing equation and deriving four complementary operators. Time integrating the Hantush–Jacob equation yields S·s = T∇2A − C·A, with storativity S, drawdown s, transmissivity T, the time (t)-integrated drawdown A(t) (absement), and leakance C. The four operators, A(t), time-averaged A(t)/t, windowed ΔA/Δt, and the normalized absement derivative (NAD), are applied jointly across all available observation wells. In a homogeneous aquifer, the fitted operators and NAD diagnostic provide mutually consistent parameter and flow-regime signatures. In a heterogeneous aquifer, systematic differences between operators become part of the interpretation: T-related variation appears as changes in the ΔA/Δt sliding profile across wells, whereas the leakage factor B = √(T/C)-related variation is identified by divergent A(t)/t asymptotes and NAD type-curve crossing. Monte Carlo assessment under composite noise (N = 50) confirms near-zero parameter bias, with T and S standard deviations approximately 3–4 times smaller for A(t)/t and ΔA/Δt than for A(t). The three field cases are identified: a 14% outward T decline with spatially uniform B (sandstone aquifer); approximately homogeneous T with outward-declining B flagged by NAD type-curve crossing before fitting (sandy aquifer); and T–B coupling resolution through the windowed ΔA/Δt profile (medium-grained sandstone aquifer). The outputs supported sustainable-yield assessment directly from routine pumping-test records.