Diffusion of solutes from depleting sources into and out of finite low-permeability zones

Two important factors that affect groundwater contaminant persistence are the temporal pattern of contaminant source depletion and solute diffusion into and out of aquitards. This study provides a framework to evaluate the relative importance of these effects on contaminant persistence, with emphasis on the importance of thin aquitards. We developed one-dimensional (1D) analytical solutions for forward and back diffusion in a finite domain with a no flux boundary using the method of images and demonstrated their applicability to measured data from three well-controlled laboratory diffusion experiments with exponentially depleting sources. We used both in situ aquitard solute concentrations and aquifer breakthrough curves for sorbing and non-sorbing solutes. The finite-domain no flux boundary solutions showed better agreement with measured data than was available with semi-infinite approaches, with increasing discrepancy for dimensionless relative diffusion length scale beyond a critical threshold value (Z_d > 0.7). We also used a mass balance to demonstrate that the temporal pattern of contaminant source depletion controls the duration of solute mass accumulation in the aquitard, as well as the total solute mass release back into the aquifer. Lower rates of source depletion result in a longer period of mass accumulation in the aquitard and later back diffusion initiation time. The amount of solute mass stored in the aquitard increases with longer loading duration, thereby contributing to overall longer contaminant persistence in aquifers. This study entails widespread implications for anthropogenic waste and contamination sites, which are all dependent on efficient and cost-effective contaminant management strategies.