Low-permeability aquitards may serve as secondary sources of slow-releasing contaminants into the adjacent aquifer system, creating considerable obstacles to groundwater cleanup. Accurately capturing the exchange of contaminant mass between aquitards and aquifers can facilitate site management and remediation. Previous simulation studies were mainly limited to one-dimensional (1D) back diffusion from aquitards during the remediation of the source zone. In this study, a novel two-dimensional (2D) back-diffusion model is developed to investigate the storage and release of contaminants in aquitards after source isolation. This model coupled the dynamical decay of isolated sources and the diffusion-sorption process of contaminants in the layered aquitards. Exact analytical solutions for the present 2D multilayer model were derived using the finite cosine transform, Duhamel Theorem, separation of variables, and transfer matrix method. Results indicated that the previous 1D model would overestimate the contaminant concentration in the aquitard and the back-diffusion risk when the source zone was isolated. The proposed 2D back-diffusion model enables quantitative prediction of how source zone width, source concentration, and aquitard heterogeneity impact plume trailing time, thus aiding in understanding the mechanisms of aquifer contamination beyond barrier-controlled source zones.
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