The trailing effect caused by the back diffusion (BD) of contaminants in low-permeability zones (LPZs), which prolongs remediation time and increases remediation costs, has caused widespread concern. In this study, the BD of trichloroethylene (TCE) from the LPZ to the high-permeability zone (HPZ) was determined using flow cell experiments. The anomalous variance in the BD flux of the TCE-spanning 2-4 times the deviation under identical experimental conditions, attracted our attention. To determine the cause of this aberrant behavior, a micro computed tomography (micro-CT) characterization of the flow cell was conducted, which revealed significant microstructural disparities in the LPZ. The study found that the pore connectivity of LPZs determines the efficiency of BD and that LPZs with different porosities have different sensitivities to connectivity. The pore shape complexity indicates the possibility of BD retardation, and remediation is more difficult for these types of LPZs. Changing the structure of LPZs to improve their remediation efficiency may be a new research topic. Notably, correcting the model parameters through microstructural characterization significantly refined the prediction accuracy.

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.

Cadmium (Cd) has impacted groundwater resources and can pose a serious threat to human health and the environment. Its fate in groundwater is complex and challenging to predict, as it is affected by adsorption to sediments, complexation with aqueous phase ligands, and variations in hydraulic conductivity. In this study, a 2D reactive transport model based on MODFLOW and RT3D is used to simulate published experimental results of cadmium migration without and with EDTA present in a flow cell containing high- and low-permeability zones (i.e., HPZs and LPZs). The model is then extended to conceptual flow cells with more complex LPZ configurations. Simulation results generally match the experimental data well, and analysis of experimental and simulated Cd effluent concentration profiles shows that EDTA enhances Cd removal from LPZs relative to water alone. Simulation results indicate that faster Cd removal is due to EDTA complexation with adsorbed Cd in LPZs, which enhances its solubilization and subsequent back diffusion. Lastly, simulation results show that with increasing LPZ heterogeneity more Cd is retained in flow cells, and EDTA is more effective in enhancing Cd removal relative to water alone; these results are attributed to more LPZ-HPZ interfaces that enhance Cd mass transfer into LPZs during contamination, and enhance EDTA mass transfer into LPZs to promote cleanup. Overall, the results highlight the promise of using EDTA to remove Cd from heterogeneous sites, but caution is advised due to model simplicity and lack of consideration of changes in solution pH, redox potential, or competing cations.

Recalcitrant groundwater contamination is a common problem at hazardous waste sites worldwide. Groundwater contamination persists despite decades of remediation efforts at many sites because contaminants sorbed or dissolved within low-conductivity zones can back diffuse into high-conductivity zones, and therefore act as a continuing source of contamination to flowing groundwater. A review of the available literature on remediation of plume persistence due to back diffusion was conducted, and four sites were selected as case studies. Remediation at the sites included pump and treat, enhanced bioremediation, and thermal treatment. Our review highlights that a relatively small number of sites have been studied in sufficient detail to fully evaluate remediation of back diffusion; however, three general conclusions can be made based on the review. First, it is difficult to assess the significance of back diffusion without sufficient data to distinguish between multiple factors contributing to contaminant rebound and plume persistence. Second, high-resolution vertical samples are decidedly valuable for back diffusion assessment but are generally lacking in post-treatment assessments. Third, complete contaminant mass removal from back diffusion sources may not always be possible. Partial contaminant mass removal may nonetheless have potential benefits, similar to partial mass removal from primary DNAPL source zones.

Perfluorooctane sulfonic acid (PFOS) is one of the most common per- and polyfluoroalkyl substances (PFAS) and is a significant risk driver for these emerging contaminants of concern. A series of two-dimensional flow cell experiments was conducted to investigate the impact of flow field heterogeneity on the transport, attenuation, and mass removal of PFOS. A simplified model heterogeneous system was employed consisting of a lower-permeability fine sand lens placed within a higher-permeability coarse sand matrix. Three nonreactive tracers with different aqueous diffusion coefficients, sodium chloride, pentafluorobenzoic acid, and β-cyclodextrin, were used to characterize the influence of diffusive mass transfer on transport and for comparison to PFOS results. The results confirm that the attenuation and subsequent mass removal of the nonreactive tracers and PFOS were influenced by mass transfer between the hydraulically less accessible zone and the coarser matrix (i.e., back diffusion). A mathematical model was used to simulate flow and transport, with the values for all input parameters determined independently. The model predictions provided good matches to the measured breakthrough curves, as well as to plots of reductions in mass flux as a function of mass removed. These results reveal the importance of molecular diffusion and pore water velocity variability even for systems with relatively minor hydraulic conductivity heterogeneity. The impacts of the diffusive mass transfer limitation were quantified using an empirical function relating reductions in contaminant mass flux (MFR) to mass removal (MR). Multi-step regression was used to quantify the nonlinear, multi-stage MFR/MR behavior observed for the heterogeneous experiments. The MFR/MR function adequately reproduced the measured data, which suggests that the MFR/MR approach can be used to evaluate PFOS removal from heterogeneous media.

Contaminants stored in the low permeability sediments will continue to threaten the adjacent shallow groundwater system after the aquifer is remediated. Understanding the storage and discharge behavior of contaminants in the aquitards is essential for the efficient remediation of contaminated sites, but most of the previous analytical studies focused on nonreactive solutes in a single homogenous aquitard. This study presents novel analytical solutions for the forward and back diffusion of contaminants through multi-layer low permeability sediments considering abiotic and biotic environmental degradation. Three representative source depletion patterns (i.e., instantaneous, linear, and exponential patterns) were selected to describe the dissolution of dense non-aqueous phase liquids (DNAPL) in the aquifer more realistically. At the forward diffusion stage, the mass storage of contaminants in the aquitards with the instantaneous pattern is the largest, nearly twice that with the exponential pattern. A simple equivalent homogeneous model is generally adopted in the risk assessment. However, relative to the proposed multi-layer model, it will significantly underestimate the onset of the back-diffusion of heterogeneous aquitards and overestimate the persistence of aquifer plumes. The previously-reported semi-infinite boundary assumption is also not applicable, with a maximum error of over 200% in the long-term prediction of back diffusion behavior of a thin aquitard. Moreover, when the degradation half-life is less than 16 years, less than 10% of the contaminants stored in the aquitards will diffuse into the overlying aquifer, suggesting that biostimulation or bioaugmentation can effectively mitigate back-diffusion risk. Overall, the proposed diffusion-reaction coupled model with multi-layer media is of great value and high demand in predicting the back-diffusion behavior of heterogeneous aquitards and guiding the soil bioremediation.

Aquitards contaminated by chlorinated solvents may act as a secondary source slowly releasing contaminants into adjacent aquifers, thus severely hampering the remediation of groundwater systems. Accurate predicting the long-term exchange of solvents between aquifers and aquitards can more effectively guide site management and remediation. This study presented a general analytical model for the back-diffusion of chlorinated solvents through multilayer aquitards. This model considers the slow advection and local degradation of dissolved constituents in natural aquitards and the dynamic depletion of dense nonaqueous phase liquid (DNAPL) source zone in aquifers. Transient solutions for the proposed multilayer model were derived using Duhamel\'s Theorem, the separation of variables method, and the transfer matrix method, verified against experimental and numerical concentration data. Results reveal that advection in aquitards can significantly shorten the trailing time of chlorinated solvent plumes, and highly adsorptive soils may reduce this effect in layered aquitards. The previous no-degradation model is no longer applicable to predict the back-diffusion behavior of chlorinated solvents when the extent and rate of solvent degradation are large, giving a \"strong-effect zone\". Based on numerous example simulations and data fitting, the forecast functions for the back-diffusion onset time and plume trailing time were proposed, greatly facilitating remediation decisions and risk assessment of chlorinated-solvent contaminated sites.

Back diffusion of groundwater contaminants from low permeability (K) zones can be a major factor controlling the time to reach cleanup goals in downgradient monitor wells. We identify the aquifer and contaminant characteristics that have the greatest influence on the time (TOoM) after complete source removal for contaminant concentrations to decline by 1, 2 and 3 Orders-of-Magnitude (T1, T2 and T3). Two aquifer configurations are evaluated: (a) layered geometry (LG) with finite thickness low K layers; and (b) boundary geometry (BG) with thick semi-infinite low K boundaries. A semi-analytical modeling approach (Muskus and Falta, 2018) is used to simulate the concentration decline following source removal for a range of conditions and generate ≈21,000 independent values of T1, T2 and T3. Linear regression is applied to interpret this large dataset and develop simple relationships to estimate TOoM from three characteristic parameters - the mass residence time (TM), diffusion time (TD), and ratio of low K to high K mass storage (γ). TM is most important predictor of T1, T2 and T3 for both geometries and is equal to the combined high and low K contaminant mass divided by the mass flux, at the end of the loading period (TL). For LG, T3 is strongly influenced by TD = RLLD2/(4D*), where RL is the low K retardation factor, LD is the half-thickness of the embedded low K layers, and D* is the effective diffusion coefficient. For BG, T3 is strongly influenced by γ. Contaminant decay in low K zones can significantly reduce cleanup times when λLTD > 0.01, where λL is the effective first order decay rate in the low K zone. The 1st Damköhler (Da), equal to TM/TD, provides a useful indicator of the relative importance of back diffusion on TOoM. Back diffusion impacts are greatest on T3 when 0.01 > Da > 0.1, then decrease with increasing Da. Back diffusion has less impacts on T2, with limited influence on T1. The results are summarized in a simple conceptual model to aid in evaluating the impact of back diffusion on the time for concentrations to decline by 1-3 OoM.

Low permeability zones (LPZs) are major sources of groundwater contamination after active remediation to remove pollutants in adjacent high permeability zones (HPZs). Slow back diffusion from LPZs to HPZs can extend management of polluted sites by decades. Numerical models are often used to simulate back diffusion, estimate cleanup times, and develop site management strategies. Sharp concentration gradients of pollutants are present at the interface between HPZs and LPZs, and hence accurate simulation requires fine grid sizes resulting in high computational burden. Since the MODFLOW family of codes is widely used in practice, we develop a new approach for modeling pollutant back diffusion using MODFLOW/RT3D that eliminates the need for fine discretization of the LPZ. Instead, the LPZ is treated as an impermeable region in MODFLOW, while in RT3D the LPZ is conceptualized as a series of immobile zones coupled with a mobile zone at the HPZ/LPZ interface. Finite volume discretization of diffusion and reaction within the LPZ is then modeled as mass transfer and reaction among several immobile species. This results in a simulation domain with significantly fewer grid cells compared to that required if all LPZs are discretized, providing potential for improved computational efficiency. Cases, including a layer of HPZ over an LPZ, a thin/thick lens of LPZ embedded in HPZ, and multiple lens of LPZs embedded in HPZ are tested by the new approach for tracer and reactive scenarios.

Low-permeability aquitards can significantly affect the transport, distribution, and persistence of contaminant plumes in subsurface systems. Although such low-permeability materials are often charged, the key role of charge-induced electrostatic processes during contaminant transport has not been extensively studied. This work presents a detailed investigation exploring the coupled effects of heterogeneous distribution of physical, chemical and electrostatic properties on reactive contaminant transport in field-scale groundwater systems including spatially distributed clay zones. We performed an extensive series of numerical experiments in three distinct heterogeneous sandy-clayey domains with different levels of complexity. The flow and reactive transport simulations were performed by explicitly resolving the complex velocity fields, the small-scale electrostatic processes, the compound-specific diffusive/dispersive fluxes and the chemical processes utilizing a multi-continua based reactive transport code (MMIT-Clay). In each particular domain, numerical experiments were performed focusing on both the forward and back diffusion through the sandy-clayey interfaces. The results illuminate the control of microscopic electrostatic mechanisms on macroscopic mass transfer. Coulombic interactions in the clay\'s diffuse layer can significantly accelerate or retard a particular species depending on its charge. Furthermore, the chemical heterogeneity plays a major role in mass storage and release during reactive transport. Neglecting such processes can lead to substantial over- or underestimation of the overall transport behavior, which underlines the need for integrated physical, chemical and electrostatic approaches to accurately describe mass transfer processes in systems including low-permeability inclusions.