Forward and back diffusion through argillaceous formations

Abstract

AbstractThe exchange of solutes between aquifers and lower‐permeability argillaceous formations is of considerable interest for solute and contaminant fate and transport. We present a synthesis of analytical solutions for solute diffusion between aquifers and single aquitard systems, validated in well‐controlled experiments, and applied to several data sets from laboratory and field‐scale problems with diffusion time and length scales ranging from 10−2 to 108 years and 10−2 to 102 m. One‐dimensional diffusion models were applied using the method of images to consider the general cases of a finite aquitard bounded by two aquifers at the top and bottom, or a semiinfinite aquitard bounded by an aquifer. The simpler semiinfinite equations are appropriate for all domains with dimensionless relative diffusion length, ZD < 0.7. At dimensionless length scales above this threshold, application of semiinfinite equations to aquitards of finite thickness leads to increasing errors and solutions based on the method of images are required. Measured resident solute concentration profiles in aquitards and flux‐averaged solute concentrations in surrounding aquifers were accurately modeled by appropriately accounting for generalized dynamic aquifer‐aquitard boundary conditions, including concentration gradient reversals. Dimensionless diffusion length scales were used to illustrate the transferability of these relatively simple models to physical systems with dimensions that spanned 10 orders of magnitude. The results of this study offer guidance on the application of a simplified analytical approach to environmentally important layered problems with one or two diffusion interfaces.