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Breakthrough of attenuating contaminant plumes in pumping wells: Analytical model and implications for integral pumping tests

Monitoring of contaminant plumes and predicting their future fate are essential for effective management of groundwater contaminants. Solute breakthrough curves from operating pumping wells can provide information on the water quality in relatively large aquifer regions, which may be unavailable to instrumentation and direct measurement for practical and/or economical reasons. Relations between spatially varying aquifer concentrations C0(x, y) initially surrounding a well and temporally varying concentrations of subsequently extracted well water, Cp(t), then need to be quantified. However, limited applicability of analytical expressions and numerical inaccuracies related to solving transport equations for converging flow fields hamper such quantifications even in homogeneous aquifers. We use a stream‐tube approach and provide a general problem formulation that accounts for first‐order degradation and linear, instantaneous, sorption/retardation in heterogeneous aquifers. An analytical expression is obtained for homogeneous aquifer conditions (in the well vicinity), relating any given initial C0(x, y) function and the subsequent contaminant breakthrough Cp(t) in the well. Results for wide plumes subject to first‐order degradation show that concentrations at the extraction well will increase as a function of pumping time. This increase is despite the fact that late‐time data reflect longer transport paths (to the well), along which mass is removed through degradation. We also derive unique solutions for the inverse problem, in particular considering how the average contaminant concentration Cav (averaged along a control plane through the well within its capture zone, perpendicular to the mean groundwater flow direction) depends on the measurable Cp(t). The solutions demonstrate that the longer the pumping time, the more sensitive the solutions for Cav become to degradation rate constants, which if needed can be determined in situ using multiple control planes.