Forward and back diffusion through argillaceous formations

Abstract

The 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.

Unraveling the Fate and Transport of DNAPLs in Heterogeneous Aquifer Systems—A Critical Review and Bibliometric Analysis

“…Analytical solutions were derived to analyze the diffusive flux exchange between aquifer and a single aquitard layer with the thickness varying from centimeters to hundreds of meters [85]. One-dimensional analytical solutions were derived to analyze the impacts of an exponential depleting source and back diffusion from LPPM on long tailings of BTCs [11].…”

“…One-dimensional analytical solutions were derived to analyze the impacts of an exponential depleting source and back diffusion from LPPM on long tailings of BTCs [11]. However, the abovementioned analytical and semi-analytical solutions could only be applied to 1D saturated porous systems [11,48,84,85]. In addition, several semianalytical/analytical models were coupled to numerical transport simulators to eliminate the limitations of analytical approaches.…”

“…It is observed that information related to site-specific processes and values of parameters from ICET 3 would enhance the efficiency of a mathematical model, support the risk assessment framework, and promote cost-effective remediation and management procedures [91]. In most studies [11,48,84,85], only diffusion was assumed for contaminant transport in the aquitard or LPPM region. Therefore, it can be stated that a hybrid analytical-numerical modeling approach should be implemented whenever simulating DNAPLs under field-scale conditions.…”

Effects of Dispersion Parameters and Low Permeability Porous Media on the Contaminant Transport Behavior in the Aquifer System: A Numerical Study

“…Studies indicated that low permeability porous media (LPPM) or aquitard region behave as a sink during contaminant loading period and as a source when the contaminant source is removed or isolated (Chapman and Parker 2005;Chapman et al, 2012;Guo and Brusseau 2017a;Yang et al 2017a;b). LPPM caused long plume tailing for a longer duration due to de-sorption (Brown et al 2012).…”