Evaluating the impact of back diffusion on groundwater cleanup time

Back diffusion of groundwater contaminants from low permeability (K) zones can be a major factor controlling the time to reach cleanup goals in downgradient monitor wells. We identify the aquifer and contaminant characteristics that have the greatest influence on the time (T_OoM) after complete source removal for contaminant concentrations to decline by 1, 2 and 3 Orders-of-Magnitude (T₁, T₂ and T₃). Two aquifer configurations are evaluated: (a) layered geometry (LG) with finite thickness low K layers; and (b) boundary geometry (BG) with thick semi-infinite low K boundaries. A semi-analytical modeling approach (Muskus and Falta, 2018) is used to simulate the concentration decline following source removal for a range of conditions and generate ≈21,000 independent values of T₁, T₂ and T₃. Linear regression is applied to interpret this large dataset and develop simple relationships to estimate T_OoM from three characteristic parameters - the mass residence time (T_M), diffusion time (T_D), and ratio of low K to high K mass storage (γ). T_M is most important predictor of T₁, T₂ and T₃ for both geometries and is equal to the combined high and low K contaminant mass divided by the mass flux, at the end of the loading period (T_L). For LG, T₃ is strongly influenced by T_D = R_LL_D²/(4D*), where R_L is the low K retardation factor, L_D is the half-thickness of the embedded low K layers, and D* is the effective diffusion coefficient. For BG, T₃ is strongly influenced by γ. Contaminant decay in low K zones can significantly reduce cleanup times when λ_LT_D > 0.01, where λ_L is the effective first order decay rate in the low K zone. The 1st Damköhler (Da), equal to T_M/T_D, provides a useful indicator of the relative importance of back diffusion on T_OoM. Back diffusion impacts are greatest on T₃ when 0.01 > Da > 0.1, then decrease with increasing Da. Back diffusion has less impacts on T₂, with limited influence on T₁. The results are summarized in a simple conceptual model to aid in evaluating the impact of back diffusion on the time for concentrations to decline by 1-3 OoM.