Investigating rate-limited sorption, sorption to air-water interfaces, and colloid-facilitated transport during PFAS leaching.

Various sorption processes affect leaching of per- and polyfluoroalkyl substances (PFAS) such as PFOA and PFOS. The objectives of this study are to (1) compare rate-limited leaching in column and lysimeter experiments, (2) investigate the relevance of sorption to air-water interfaces (AWI), and (3) examine colloid-facilitated transport as a process explaining early experimental breakthrough. A continuum model (CM) with two-domain sorption is used to simulate equilibrium and rate-limited sorption. A random walk particle tracking (PT) model was developed and applied to analyze complex leaching characteristics. Results show that sorption parameters derived from column experiments underestimate long-term PFOA leaching in lysimeter experiments due to early depletion, suggesting that transformation of precursors contributes to the observed long-term leaching in the lysimeters (approximately 0.003 µg/kg/d PFOA). Both models demonstrate that sorption to AWI is the dominant retention mechanism for PFOS in lysimeter experiments, with retardation due to AWI being 3 (CM) to 3.7 (PT) times higher than retardation due to solid phase sorption. Notably, despite a simplified conception of AWI sorption, the PT results are closer to the observations. The PT simulations demonstrate possible colloid-facilitated transport at early time; however, results using substance-specific varying transport parameters align better with the observations, which should be equal if colloid-facilitated transport without additional kinetics is the sole mechanism affecting early breakthrough. Possibly, rate-limited sorption to AWI is relevant during the early stages of the lysimeter experiment. Our findings demonstrate that rate-limited sorption is less relevant for long-term leaching under field conditions compared to transformation of precursors and that sorption to AWI can be the dominant retention mechanism on contaminated sites. Moreover, they highlight the potential of random walk particle tracking as a practical alternative to continuum models for estimating the relative contributions of various retention mechanisms.

A Practical Modeling Framework for Non-Fickian Transport and Multi-Species Sequential First-Order Reaction.

Many studies indicate that small-scale heterogeneity and/or mobile-immobile mass exchange produce transient non-Fickian plume behavior that is not well captured by the use of the standard, deterministic advection-dispersion equation (ADE). An extended ADE modeling framework is presented here that is based on continuous time random walk theory. It can be used to characterize non-Fickian transport coupled with simultaneous sequential first-order reactions (e.g., biodegradation or radioactive decay) for multiple degrading contaminants such as chlorinated solvents, royal demolition explosive, pesticides, and radionuclides. To demonstrate this modeling framework, new transient analytical solutions are derived and are inverted in Laplace space. Closed-form, steady-state, multi-species analytical solutions are also derived for non-Fickian transport in highly heterogeneous aquifers with linear sorption-desorption and matrix diffusion for use in spreadsheets. The solutions are general enough to allow different degradation rates for the mobile and immobile zones. The transient solutions for multi-species transport are applied to examine the effects of source remediation on the natural attenuation of downgradient plumes of both parent and degradation products in highly heterogeneous aquifers. Results for representative settings show that the use of the standard, deterministic ADE can over-estimate cleanup rates and under-predict the cleanup timeframe in comparison to the extended ADE analytical model. The modeling framework and calculations introduced here are also applied for a 30 year groundwater cleanup program at a site in Palm Bay, Florida. The simulated plume concentrations using the extended ADE exhibited agreement with observed long concentration tails of trichloroethene, cis 1,2 DCE, and VC that remained above cleanup goals.

Local Equilibrium and Retardation Revisited.

In modeling solute transport with mobile-immobile mass transfer (MIMT), it is common to use an advection-dispersion equation (ADE) with a retardation factor, or retarded ADE. This is commonly referred to as making the local equilibrium assumption (LEA). Assuming local equilibrium, Eulerian textbook treatments derive the retarded ADE, ostensibly exactly. However, other authors have presented rigorous mathematical derivations of the dispersive effect of MIMT, applicable even in the case of arbitrarily fast mass transfer. We resolve the apparent contradiction between these seemingly exact derivations by adopting a Lagrangian point of view. We show that local equilibrium constrains the expected time immobile, whereas the retarded ADE actually embeds a stronger, nonphysical, constraint: that all particles spend the same amount of every time increment immobile. Eulerian derivations of the retarded ADE thus silently commit the gambler's fallacy, leading them to ignore dispersion due to mass transfer that is correctly modeled by other approaches. We then present a particle tracking simulation illustrating how poor an approximation the retarded ADE may be, even when mobile and immobile plumes are continually near local equilibrium. We note that classic "LEA" (actually, retarded ADE validity) criteria test for insignificance of MIMT-driven dispersion relative to hydrodynamic dispersion, rather than for local equilibrium.

Contaminant point source localization error estimates as functions of data quantity and model quality.

We develop empirically-grounded error envelopes for localization of a point contamination release event in the saturated zone of a previously uncharacterized heterogeneous aquifer into which a number of plume-intercepting wells have been drilled. We assume that flow direction in the aquifer is known exactly and velocity is known to within a factor of two of our best guess from well observations prior to source identification. Other aquifer and source parameters must be estimated by interpretation of well breakthrough data via the advection-dispersion equation. We employ high performance computing to generate numerous random realizations of aquifer parameters and well locations, simulate well breakthrough data, and then employ unsupervised machine optimization techniques to estimate the most likely spatial (or space-time) location of the source. Tabulating the accuracy of these estimates from the multiple realizations, we relate the size of 90% and 95% confidence envelopes to the data quantity (number of wells) and model quality (fidelity of ADE interpretation model to actual concentrations in a heterogeneous aquifer with channelized flow). We find that for purely spatial localization of the contaminant source, increased data quantities can make up for reduced model quality. For space-time localization, we find similar qualitative behavior, but significantly degraded spatial localization reliability and less improvement from extra data collection. Since the space-time source localization problem is much more challenging, we also tried a multiple-initial-guess optimization strategy. This greatly enhanced performance, but gains from additional data collection remained limited.

Integrodifferential formulations of the continuous-time random walk for solute transport subject to bimolecular A+B→0 reactions: From micro- to mesoscopic.

We develop continuous-time random walk (CTRW) equations governing the transport of two species that annihilate when in proximity to one another. In comparison with catalytic or spontaneous transformation reactions that have been previously considered in concert with CTRW, both species have spatially variant concentrations that require consideration. We develop two distinct formulations. The first treats transport and reaction microscopically, potentially capturing behavior at sharp fronts, but at the cost of being strongly nonlinear. The second, mesoscopic, formulation relies on a separation-of-scales technique we develop to separate microscopic-scale reaction and upscaled transport. This simplifies the governing equations and allows treatment of more general reaction dynamics, but requires stronger smoothness assumptions of the solution. The mesoscopic formulation is easily tractable using an existing solution from the literature (we also provide an alternative derivation), and the generalized master equation (GME) for particles undergoing A+B→0 reactions is presented. We show that this GME simplifies, under appropriate circumstances, to both the GME for the unreactive CTRW and to the advection-dispersion-reaction equation. An additional major contribution of this work is on the numerical side: to corroborate our development, we develop an indirect particle-tracking-partial-integro-differential-equation (PIDE) hybrid verification technique which could be applicable widely in reactive anomalous transport. Numerical simulations support the mesoscopic analysis.