Knowledge of perfluorooctanoic acid (PFOA) and perfluorooctanesulfonic acid (PFOS) accumulation at the air−water interface is critical to understanding the fate and transport of these substances in subsurface environments. The surface tension of aqueous solutions containing PFOA and PFOS at concentrations ranging from 0.1 to >1000 mg/L and with dissolved solids (i.e., cations and anions) commonly found in groundwater was measured using the Wilhelmy plate method. The surface tensions of solutions containing dissolved solids were lower than those for ultrapure water, indicating an increase in the surface excess of PFOA and PFOS in the presence of dissolved solids. An equation for the surface excess of PFOA and PFOS with total dissolved solids was developed by fitting the measured surface tension values, which ranged from 72.0 to 16.7 mN/m, to the Szyszkowski equation. On the basis of mass distribution calculations for a representative unsaturated, fine-grained soil, up to 78% of the PFOA and PFOS mass will accumulate at the air−water interface, with the remaining mass dissolved in water and adsorbed on the solids.

One contribution of 12 to a theme issue 'Energy and the subsurface' . We propose a new composite similarity variable, based on which a similarity solution is derived for reaction front propagation in fracture-matrix systems. The similarity solution neglects diffusion/dispersion within the fracture and assumes the existence of a sharp reaction front in the rock matrix. The reaction front location in the rock matrix is shown to follow a linear decrease with distance along the fracture. The reaction front propagation along the fracture is shown to scale like diffusion (i.e. as the square root of time). The similarity solution using the composite similarity variable appears to be applicable to a broad class of reactive transport problems involving mineral reactions in fracturematrix systems. It also reproduces the solutions for non-reactive solute and heat transport when diffusion/dispersion/conduction are neglected in the fracture. We compared our similarity solution against numerical simulations for nonlinear reactive transport of an aqueous species with a mineral in the rock matrix. The similarity solutions agree very well with the numerical solutions, especially at later times when diffusion limitations are more pronounced.This article is part of the themed issue 'Energy and the subsurface'.

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Chemical oxidation of dense nonaqueous-phase liquids (DNAPLs) by permanganate has emerged as an effective remediation strategy in fractured rock. We present high-resolution experimental investigations in transparent analog variable-aperture fractures to improve understanding of chemical oxidation of residual entrapped trichloroethylene (TCE) in fractures. Four experiments were performed with different permanganate concentrations, flow rates, and initial TCE phase geometry. The initial aperture field and evolving entrapped-phase geometry were quantified for each experiment. The integrated mass transfer rate from the TCE phase for all experiments exhibited three time regimes: an early-time regime with slower mass transfer rates limited by low specific interfacial area; an intermediate-time regime with higher mass transfer rates resulting from breakup of large TCE blobs, which greatly increases specific interfacial area; and a late-time regime with low mass transfer rates due to the deposition of MnO 2 precipitates. In two experiments, mass balance analyses suggested that TCE mass removal rates exceeded the maximum upper bound mass removal rates derived by assuming that oxidation and dissolution are the only mechanisms for TCE mass removal. We propose incomplete oxidation by permanganate and TCE solubility enhancement by intermediate reaction products as potential mechanisms to explain this behavior. We also speculate that some intermediate reaction products with surfactant-like properties may play a role in lowering the TCEwater interfacial tension, thus causing breakup of large TCE blobs. Our quantitative experimental measurements will be useful in the context of developing accurate computational models for chemical oxidation of TCE in fractures.

Per-and polyfluoralkyl substances (PFAS) are known to accumulate at interfaces, and the presence of nonaqueous-phase liquids (NAPLs) could influence the PFAS fate in the subsurface. Experimental and mathematical modeling studies were conducted to investigate the effect of a representative NAPL, tetrachloroethene (PCE), on the transport behavior of PFAS in a quartz sand. Perfluorooctanesulfonate (PFOS), perfluorononanoic acid (PFNA), a 1:1 mixture of PFOS and PFNA, and a mixture of six PFAS (PFOS, PFNA, perfluorooctanoic acid (PFOA), perfluoroheptanoic acid (PFHpA), perfluorohexanesulfonate (PFHxS), and perfluorobutanesulfonate (PFBS)) were used to assess PFAS interactions with PCE-NAPL. Batch studies indicated that PFAS partitioning into PCE-NAPL (K nw < 0.1) and adsorption on 60−80 mesh Ottawa sand (K d < 6 × 10 −5 L/g) were minimal. Column studies demonstrated that the presence of residual PCE-NAPL (∼16% saturation) delayed the breakthrough of PFOS and PFNA, with minimal effects on the mobility of PFBS, PFHpA, PFHxS, and PFOA. Breakthrough curves (BTCs) obtained for PFNA and PFOS alone and in mixtures were nearly identical, indicating the absence of competitive adsorption effects. A mathematical model that accounts for NAPL−water interfacial sorption accurately reproduced PFAS BTCs, providing a tool to predict PFAS fate and transport in cocontaminated subsurface environments.

Numerical simulations of diffusion with bimolecular reaction demonstrate a transition in the spatially integrated reaction rate-increasing with time initially, and transitioning to a decrease with time. In previous work, this reaction-diffusion problem has been analyzed as a Stefan problem involving a distinct moving boundary (reaction front), leading to predictions that front motion scales as ffiffi t p , and correspondingly the spatially integrated reaction rate decreases as the square root of time 1= ffiffi t p . We present a general nondimensionalization of the problem and a perturbation analysis to show that there is an early time regime where the spatially integrated reaction rate scales as ffiffi t p rather than 1= ffiffi t p . The duration of this early time regime (where the spatially integrated reaction rate is kinetically rather than diffusion controlled) is shown to depend on the kinetic rate parameters, diffusion coefficients, and initial concentrations of the two species. Numerical simulation results confirm the theoretical estimates of the transition time. We present illustrative calculations in the context of in situ chemical oxidation for remediation of fractured rock systems where contaminants are largely dissolved in the rock matrix. We consider different contaminants of concern (COCs), including TCE, PCE, MTBE, and RDX. While the early time regime is very short lived for TCE, it can persist over months to years for MTBE and RDX, due to slow oxidation kinetics.

A novel statistical approach is developed and implemented for the stochastic reconstruction of nonaqueous phase liquid (NAPL) source zone realizations and the quantification of source zone metrics and associated uncertainty. The approach employs discriminative random field (DRF) models, to simulate the spatial distributions and relationships among source zone properties (i.e., permeability, NAPL saturation, and aqueous concentration distributions) consistent with commonly collected field data. Application of DRF models requires a limited number of full‐scale simulations to train the model parameters. Monte Carlo sampling methods based on these trained models then provide an efficient method to generate contaminant mass realizations conditioned on measured boreholes, bypassing the need to run computationally intensive, partial differential equation‐based simulations of physical flow and transport. Postprocessing of these realizations yields approximations of uncertainty to inform further sampling for characterization and remediation. The reconstructed contaminant mass realizations provide sufficient information for calculating averaged characterization metrics, such as total contaminant mass and pool fraction, used to predict source zone longevity, mass recovery behavior, and remedial performance. The model performance is evaluated through comparisons of these predicted source zone metrics with those obtained from the “true” mass distributions generated with validated flow and transport models. These comparisons clearly demonstrate that stochastic application of a DRF model can reconstruct realistic saturation and concentration fields, conditioned to borehole data at different times. The present study should be viewed as the first step in generating a three‐dimensional characterization tool that can be applied over a wide range of conditions observed at contaminated sites.

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