Roles of diffusive boundary layer and initial contamination in back diffusion from heterogeneous low permeability sediments: A source-history-inversion-independent model and field application

Persistent groundwater contamination due to back diffusion from low-permeability sediments (aquifers) poses a challenge to remediation efforts, yet existing models tend to oversimplify key controls, such as the diffusive boundary layer (DBL) and initial contamination, while relying on uncertain source depletion histories. This study introduces a novel analytical framework that eliminates the dependence on source history to predict back diffusion dynamics, explicitly incorporating the DBL effects, sediment heterogeneity, and spatially variable initial contaminant distribution. The model was validated against controlled flow chamber experiments and numerical simulations. Applied to a tetrachloroethylene (PCE)-contaminated site in Jacksonville, Florida, this work successfully predicts forward and back diffusion behaviors using field-derived concentration profiles, demonstrating plume persistence risks under various remediation scenarios. Results reveal that neglecting DBL underestimates the tailing time by up to 40 years, and when the DBL mass transfer coefficient (k_DBL) is small (i.e., when the DBL is thick or the contaminant diffusivity is strong), its inclusion in back-diffusion models is recommended to ensure accurate predictions. Exceptionally low k_DBL corresponds to shorter plume tailing time, implying that suppressing mass transfer across DBL is a promising strategy to mitigate back-diffusion risks in low-permeability sediments. Furthermore, Initial concentration distribution variance (σ) and peak position (μ) significantly affect back diffusion, with tailing times varying exponentially and parabolically, respectively, while aquitard heterogeneity in retardation and diffusivity would amplify plume persistence by orders of magnitude compared to homogeneous assumptions. This source-history-inversion-independent back diffusion model, combined with the DBL, enhances predictive accuracy and efficiency, offering critical insights into managing long-term aquifer contamination risks.