Forward and back diffusion through aquitards in linearly depleting sources

When an aquitard layer is present at contaminated sites, forward and back diffusion through the aquitard layer can result from changes in the concentration gradient between the aquifer and aquitard. The source depletion through the in situ remediation shows various patterns due to properties of contaminants and geological structures. The source depletion patterns were classified into step-change, linear source depletion (LSD), and exponential source depletion (ESD). This study aims to propose a modified analytical solution applying the method of images based on the LSD model and to understand the semi-infinite and finite analytical solutions through the contaminant concentrations of the aquifer and aquitard. A conceptual model was designed with 15 m length, 10 m width, and 5m thickness of an aquifer underlain by 0.5 m thickness of an aquitard. A diffusion scenario assumed a model in which the concentration of trichloroethylene (TCE) in the aquifer decreased linearly from 1100 to 0 mg/L over 11 years. While the TCE concentrations in the aquifer were reduced linearly, the relative concentrations of the aquifer-aquitard interface were continuously decreased. The goodness of fit (E) comparing the results of semi-infinite and finite solutions decreased from 1 to -2.3. This discrepancy results from the application of semi-infinite solutions to the finite thickness of the aquifer. The simulated TCE flux at the interface resulted in the initial negative concentration gradient (forward diffusion) reversing and becoming increasingly positive (back diffusion) starting at 5.5 years. At the end of the LSD, the TCE flux of the semi-infinite and finite solutions continued to back diffusion with 12.8 g/m²/year and 15.8 g/m²/year. After the source was exhausted (11 years), the TCE concentrations simulated the semi-infinite and finite solutions at the aquifer exceeded the maximum contaminant level (MCL, TCE = 5 μg/L) for 18 and 20 years. The difference between the results of analytical solutions at the plume persistence was small at two years, but it seems that this gap will be widened if the contamination persists for a long time.