PFOS Mass Flux Reduction / Mass Removal: Impacts of Lower Permeability Sand Lens Within Otherwise Homogeneous Systems

Abstract

Perfluorooctane sulfonic acid (PFOS) is one of the most common per- and polyfluorinated alkyl 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 (NaCl), pentafluorobenzoic acid (PFBA), and β-cyclodextrin, were used to characterize the influence of diffusive mass transfer on transport for comparison to PFOS results. The results confirm that the attenuation and subsequent mass removal of the nonreactive tracers and PFOS was 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 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.

1. INTRODUCTION

Per- and polyfluoroalkyl substances (PFAS) are a group of anthropogenic, organic compounds that have been widely used in many industrial, commercial, and military applications. These compounds are generally extremely recalcitrant and persistent in the environment due to their unique molecular structure comprising multiple carbon-fluorine bonds, which are among the strongest that exist. The persistence and ubiquity of PFAS has resulted in widespread distribution in the environment^1–4, including global contamination of freshwater resources. This has sparked an immense interest in research on the distribution, transport and fate, and mitigation of PFAS in the environment, as evidenced by the numerous studies cited in several recent review papers^5–23.

PFAS typically experience retention and retardation to some degree during transport in porous media. This retention can be caused by a number of processes. For example, the results of miscible-displacement lab experiments have demonstrated that sorption by the solid phase of soils and aquifer media contributes to PFAS retention during transport^24–31. In addition, miscible-displacement lab experiments and mathematical-modeling studies have demonstrated the impact of air-water interfacial adsorption on PFAS transport in unsaturated media^{27, 32–40}. Another process that can cause contaminant attenuation is the retention and subsequent release of aqueous contaminants in lower-permeability zones in heterogeneous media, referred to as back diffusion^41–43 or diffusive mass transfer, which is likely ubiquitous in heterogeneous subsurface systems and impacts contaminant transport characterization and remediation^44–46. The diffusive mass transfer effects can happen for subsurface systems with low hydraulic conductivity zones such that mainly diffusion removes mass from those zones. Diffusive mass transfer also effects systems with more moderate differences in hydraulic conductivity, where both advection and diffusion can remove mass, but the mass removal is still delayed compared to a homogeneous system^47–49.

The contaminant mass flux or mass discharge emanating from a source zone has become an important metric for risk and remediation assessment associated with subsurface contamination⁵⁰. Regression between mass removal reductions (MR) and reductions in contaminant mass flux (MFR) has been developed as a method for characterizing contamination sources and remediation of contaminants in heterogeneous porous media^{51, 52}. Some authors use a different formulation by correlating relative concentration with relative mass⁵³. These assessments have focused on remediation of NAPL contaminant source zones^{42, 52, 54–65}, with some examination of volatile-source vapor extraction^66–71, and also extension to groundwater-contaminant plume extraction and treatment^{72, 73}. Difilippo et al.⁵⁹ found that a single exponential function correlating MFR to MR was not appropriate when multiple NAPL sources existed, and they observed a nonsingular, or multi-step, nonlinear MFR/MR trend for the heterogeneous source-zone systems. Thus, a non-singular or multi-step regression was needed for characterization of the heterogeneous contaminant distribution. They also noted that concave MFR/MR functions are typical for sources in homogeneous media (higher hydraulic accessibility) and convex MFR/MR functions are generally observed for sources in heterogeneous media (lower hydraulic accessibility), which tend to undergo back diffusion and diffusive mass transfer limitations. Additional lab-scale and modelling studies have attempted to develop predictive methods for contaminant persistence influenced by back diffusion^{43, 45, 74–78}. While these studies have provided insight into the relevant processes, additional questions remain, such as differences in the impacts of diffusive mass-transfer limitations in layered systems for solutes comprising different molecular structures and associated diffusion coefficients.

Quantification of diffusive mass transfer limitations for media with lower-permeability or hydraulically less accessible zones, especially using MFR/MR functions, has focused primarily on NAPL-contaminated systems. In contrast, there has been limited investigations for source zones comprising large masses of aqueous and sorbed contaminants such as are typical for PFAS impacted sites. Two recent modeling studies have investigated this issue for PFAS using the REMChlor-MD matrix diffusion model^79,80. However, to our knowledge, there have been no controlled experiments conducted to date to investigate this issue specifically for PFAS.

The objective of this research was to investigate the impact of layered heterogeneity on the transport, attenuation, and mass removal of PFAS. Two aquifer sands with a relatively moderate difference in hydraulic conductivity were used to develop a model heterogeneous two-dimensional (2-D) flow-cell system. Tracer experiments were conducted with perfluorooctane sulfonate (PFOS) as the representative PFAS and three nonreactive aqueous tracers that have different diffusion coefficients both larger and smaller than that of PFOS. Multi-step MFR/MR regression and flow and transport modeling were both applied to quantify transport behavior and efficiency of tracer and contaminant removal.

2. MATERIALS AND METHODS

2.1. Flow Cell Experiments

Laboratory-scale experiments were conducted with two well-sorted quartz sands (Unimin Accusand). One consists of 20–30 mesh size range (corresponding to grain diameters ranging between 0.59 and 0.84 mm) and the other 50–70 mesh (grain diameters range of 0.21–0.30 mm). Accusand is a fine quartz sand with low organic and oxide-mineral contents. The hydraulic conductivity, porosity, and bulk density of the 20–30 sand is 0.14 cm/s, 33%, and 1.78 g/cm³, whereas they are 0.03 cm/s, 39%, and 1.62 g/cm³ for the 50–70. The factor of 5 difference in hydraulic conductivity is relatively minor compared to the wide range of natural variability observed in the field (i.e., >10 orders of magnitude)⁸¹. However, even relatively small differences in hydraulic conductivity cause perturbations in the flow field and therefore can impact transport behavior. As will be discussed in the Results section, both the experiments and mathematical modeling demonstrate impacts of a nonuniform flow field for the heterogeneous flow-cell system.

Although thousands of PFAS and precursors exist, and there may be many tens to hundreds in a given PFAS mixture, terminal perfluoroalkyl acids (PFAA), including PFOS, are of the highest concern as they were the first to be produced, were produced in large quantities, and are generated through precursor transformations that terminate in production of these end product contaminants. In addition, PFOS is one of the very few PFAS for which the EPA has established lifetime health advisory limits. Thus, PFOS was the model PFAS employed for this study, and PFOS was used as an injected tracer solution in these experiments. Separate experiments conducted individually included tracer injection of three other aqueous tracers (sodium chloride (NaCl), pentafluorobenzoic acid (PFBA), and β-cyclodextrin (cyclodextrin)), which were all reagent grade, ≥99.0% purity (Sigma-Aldrich). It is important to note that the PFBA used herein is not a PFAS. Diffusion coefficients were calculated for each of the tracers from estimated molecular volumes (V = molar volume/density), and application of the molecular diffusivity equation⁸²:

$${\text{D}}_{\mathrm{w}}=\left(13.26\times {10}^{-5}\right)/\left({\mu }^{1.14}\ast {\text{V}}^{0.589}\right)$$ (1)

where D_w = Molecular Diffusion Coefficient in Water (cm² / s), μ = Solution viscosity in centipoise (10⁻² g / cm*s), and V = molar volume of tracer (cm³ / mol). Measured diffusion coefficients (Table S6 Supporting Information (SI)) were also compared to the calculated values. Of these tracers, PFOS is the only one that is generally considered a reactive tracer, which exhibits nonideal transport characteristics including rate-limited (and potentially nonlinear) adsorption²⁹.

Two-dimensional flow experiments were conducted with a 12.5 cm × 38.5 cm (2 cm in width) flow cell constructed of stainless steel and glass. Since PFOS is known to adsorb to glass, a high-density polyethylene (HDPE) plastic lining was placed on the inside of the glass. The Heterogeneous experiments consisted of a matrix of 20/30 (higher-permeability) sand with one lenticular zone of finer (50–70, lower-permeability) sand. The 4.0 cm × 12.0 cm rectangular lens of lower-permeability sand was centered in the flow cell (Fig. S1). The Homogeneous experiments contained only 20/30 (higher-permeability) sand (Fig. S1). The flow cells were packed under ponded water conditions to ensure complete saturation with deionized water.

PFOS tracer solution was injected at a concentration of 400 μg/L, which is within the range of concentrations observed near AFFF source zones^{23, 83–85}. The three nonreactive tracers (i.e., NaCl, PFBA, and cyclodextrin) were individually injected at a concentration of 250 mg/L in deionized water. High performance liquid chromatographic pumps (Shimadzu LC-10AD HPLC piston pump, Japan) were used for aqueous tracer solution injection at 1.0 ml/min for 330 ml, which is equivalent to approximately 0.65 pore volumes. Tracer injection was followed by 4 days of no-flow (or flow interruption) in order to allow diffusion into the lower-permeability zone. The 4 day flow interruption is a relatively short time for diffusive mass-transfer processes to distribute mass in heterogeneous systems, and was not sufficient to attain uniform concentrations within the lower-permeability unit. This condition was by design, as it is likely that concentrations are not uniform at many field sites. The distribution of tracer concentrations and the implications for attenuation and mass removal will be discussed in the Results section. After 4 days of flow interruption, tracer-free deionized water was then pumped into the flow cell at 0.2 ml/min for 1.8 pore volumes to elute the tracer, which was at constant flow rate equivalent to an average pore-water velocity of approximately 30 cm/day. The total flow was evenly distributed along the influent and effluent cross-sectional areas confirmed by visual inspection of preliminary dye tracer tests. Elution samples were collected at regular time intervals until tracer concentrations decreased to below limits of quantification.

The Heterogeneous experiments were repeated three times for each nonreactive tracer and two times for PFOS. The flow cell was then repacked homogeneously with higher-permeability sand, without the lower-permeability zone, and the Homogeneous experiments were also repeated three times for each nonreactive tracer and two times for PFOS. The reported concentrations represent the means of the triplicate (or duplicate for PFOS) measurements. Control flow-cell experiments with the Homogeneous and Heterogeneous sand distributions were also performed (NaCl only), which only differed by the exclusion of the flow interruption period between tracer injection and elution to observe the impact of the flow interruption and associated diffusive transport. Additional control 1-D experiments were conducted for each tracer including PFOS using a 2.5 cm diameter and 20 cm long stainless steel column. These experiments were conducted with each of the two sand media individually to observe the difference between 1-D and 2-D transport and to obtain parameter values for simulating the 2-D experiments.

Each tracer experiment sample was chemically analyzed to quantify the aqueous concentration, and each tracer solute required a different chemical analysis method (further described in SI). PFOS concentration analysis was performed with a Waters Alliance liquid chromatograph with Quattro Ultima triple quad mass spectrometer (LCMS), using negative electrospray ionization (ESI). Analysis of chloride was performed with a Metrohm 940 Professional IC Vario ion chromatograph. β-Cyclodextrin analysis was performed with a Molecular Devices Spectramax M2 Multi-mode plate reader. Sample aliquots of 4.5 ml were mixed with 0.5 ml of toluidine-2-naphihalenesulfonic acid (TNS) at 10 mg/L, which allowed for concentration analysis via fluorescence. Emission intensity of fluorescence was measured at 450 nm after excitation at 387 nm. Finally, PFBA was analyzed using the Spectramax M2, with measured absorbance of visible light at 254 nm. Tracer reservoir concentrations were sampled in duplicate, and all chemical analysis methods employed standard quality assurance and quality control protocols including blanks, duplicates, and background samples.

2.2. Data Analysis

Measured effluent concentrations of samples were used to construct breakthrough curves (BTCs) as relative concentrations (normalized by injection concentration) as a function of pore volumes eluted. The product of effluent concentration and flow rate was used to determine the transient mass discharge. Effluent concentrations and measured flow velocity were also used for moment analysis and mass balance calculations. Retardation coefficients from moment analysis were calculated to evaluate sorption and provide comparison between PFOS and non-sorbing or nonreactive tracers and between one-dimensional flow and two-dimensional flow experiments. Retardation coefficients describe mean travel time (i.e., 1^st moment) of tracer, and they are defined as: R = (water velocity) / (velocity of sorbing contaminant). Mass balance was determined by 0^th moment (i.e., integration of effluent concentration) compared to injection, which was also used to determine transient mass removed during elution.

The Hydrus 3.04 version modeling software was used to simulate the flow and solute transport for each of the experiments⁸⁶. Values for all input parameters were determined from independent sources (Tables S7 and S8). The dispersivities were determined by inverse modeling conducted for the 1-D column experiments. Equilibrium and kinetic sorption coefficients for PFOS were determined from the 1-D column experiments. Hydrus was used to simulate the transient flow including flow interruption and the transient transport including diffusion during the flow interruption.

The power function for relating MFR as a function of MR was as follows:

$$1-{\text{J}}_{\mathrm{f}}/{\text{J}}_{\mathrm{i}}={\left(1-{\text{M}}_{\mathrm{f}}/{\text{M}}_{\mathrm{i}}\right)}^{\text{n}}$$ (2)

where J is mass flux, M is source zone mass, f and i represent transient/final and initial values respectively, and n is a fitting parameter. Mass flux, J, is calculated by sample concentrations and flow rate (i.e., J (mass/time) = flow rate (volume/time) * sample concentration (mass/volume)). Source zone mass, M, is calculated with mass balance of sample concentration (i.e., M (mass) = injected tracer mass (mass) – sample concentration (mass/volume) * eluted volume (volume)). The MFR/MR of PFOS could include groundwater contamination from a variety of types of sources, and back diffusion from PFOS retained within a lower permeability zone acts as a secondary source of contaminant release to the higher permeability matrix.

3. RESULTS AND DISCUSSION

3.1. Flow Cell Experiments

Eight sets of flow cell experiments were conducted including independent experiments with each of the four tracers conducted in both the homogeneous-packed flow cell and heterogeneous-packed flow cell. Replicate trials for each experiment were conducted, giving very similar results (Fig. S11), and the means from the triplicate trials are presented here. Fig. 1 shows BTCs for all four tracers with a comparison of results from the Homogeneous and Heterogeneous flow cell experiments.

Fig. 1.

Break through curve comparisons of heterogeneous and homogeneous flow cell experiments for (a): NaCl; (b): PFBA; (c): Cyclodextrin; and (d): PFOS tracers. The symbols represent measured data, and the lines are the model simulation results.

For all tracers, the midpoint concentrations (C/C₀ = 0.5) of the arrival fronts eluted prior to 1 pore volume due to longitudinal diffusion during the flow interruption. The BTCs for the Heterogeneous experiments exhibit earlier arrival and increased concentrations at later times (concentration tailing) compared to the Homogeneous experiments. The early arrival was attributed to the decreased cross-sectional area of higher-permeability media in the flow cell, causing increased flow velocity around the lower-permeability zone (i.e., preferential flow). The NaCl BTC (Fig. S2) for the control Homogeneous and control Heterogeneous flow cell experiments, without flow interruption, show consistency with the early arrival of tracer concentration in the Heterogeneous experiments. The enhanced elution concentration tailing was greatest for the NaCl tracer (Fig. 1a). This nonideal transport concentration tailing for nonreactive tracers is indicative of physical nonequilibrium conditions for dual-domain systems, wherein preferential flow and lower hydraulic accessibility leads to diffusive mass transfer limitations. The more significant tailing behavior observed for NaCl is consistent with the fact that Cl⁻ ion has the smallest molecular volume and largest diffusion coefficient (Table S6). The arrival and elution timing difference between the Homogeneous and Heterogeneous experiments was most prominent for PFOS (Fig. 1d), PFOS also had less early arrival, and PFOS had significant concentration elution tailing for both Homogeneous and Heterogeneous experiments. These differences for PFOS transport compared to that of the nonreactive tracers were attributed to additional nonideal transport (i.e., extensive concentration elution tailing) caused by rate-limited sorption to the Accusand sediments. The impact of rate-limited sorption to sand and soils on PFOS transport has been demonstrated in prior experiments.^26–30

1-D homogenous column control experiments were used to characterize transport within the 20/30 and 50/70 sands independently (Fig. S5–S8). Moment analysis calculations were conducted to obtain R coefficients of tracer transport for all 1-D column and 2-D flow cell experiments (Table S2 and S3). R coefficients close to 1 verify nonreactive transport behavior for NaCl, PFBA, and cyclodextrin. R values were 1.37 and 1.58 for 20/30 and 50/70 mesh ranges, respectively. This verifies that PFOS transport was impacted due to sorption, and is similar to R coefficients for PFOS in Accusand found in previous literature²⁹. Inverse modeling estimated dispersivity values from nonreactive tracer results were used for PFOS, only PFOS required parameter estimation for rate-limited sorption, and these parameters estimated from the 1-D column experiments were used for simulation of the 2-D flow cell experiments.

The results of the mathematical modeling are presented in Fig. 1 where the dashed lines represent the flow and transport model simulation results in comparison to the observed data from each of the flow cell experiments. It is observed that the simulations match the measured BTCs reasonably well, especially considering that they are independent predictions. These results indicate that all processes contributing to the observed transport behavior are identified and adequately represented. The model was used to simulate the distribution of the tracer concentrations within the flow cell at different stages of the experiments. Inspection of Fig. S9a shows significant nonuniform concentration distributions for all four tracers at the end of the tracer injection. The tracer solution fronts migrated farther in the coarser medium and lagged behind in the lower-permeability layer. This is evidence of the impact of preferential flow on tracer transport, which is consistent with the simulated flow lines (Fig. S9b). The results also show that the tracer fronts did migrate to some extent into the lower-permeability layer, primarily due to advection as shown by the flow-line simulations. The primary contribution of advective flux is also supported by the observation that the concentration distributions are nearly identical for NaCl, PFBA, and cyclodextrin despite their different diffusion coefficients.

The simulated concentration distributions at the end of the flow interruption period show that there was diffusive mass transfer of tracer into the lower-permeability layer. The distributions are moderately different between NaCl, PFBA, and cyclodextrin, indicating the impact of different magnitudes of diffusive mass transfer, as expected. The distributions after one day of elution for PFBA and cyclodextrin are similar to that of NaCl, indicating the contributions of both advective and diffusive flux to mass removal. The distributions for PFOS differ from the other three tracers, exhibiting the impact of sorption. In particular, there is a diffusion gradient inward as well as outward for PFOS within the lower-K zone. It is likely that this situation exists for many field sites, and would be anticipated to have some impact on mass removal.

3.2. Mass Flux Reduction / Mass Removal Behavior

Data points that occur after peak concentration and end of tracer injection (upon the switch to tracer free water injection) in the BTC data were used to create graphs of MFR versus MR (Fig. 2), which contain comparison plots with both Heterogeneous and Homogeneous results for each tracer and Fig. 2e and 2f compare all tracers from Homogeneous and Heterogeneous experiments, respectively. Homogeneous experiments for all tracers show a uniform, concave MFR/MR curve. PFOS tracer exhibits the least concave curve, approaching a linear trend (Fig. 2d), which was attributed to the nonideal transport and sorption behavior of PFOS that differs from the other tracers. The general behavior observed for the Homogeneous experiments (and 1-D column experiments in Fig. S4) is expected for systems wherein the contaminant is distributed relatively homogeneously and is hydraulically accessible to clean water inflow, illustrating the impact of relatively ideal mass-transfer and displacement on MFR/MR behavior, as observed in prior studies^{59, 87}.

Fig. 2.

MFR/MR comparisons of heterogeneous and homogeneous flow cell experiments for (a): NaCl; (b): PFBA; (c): Cyclodextrin; and (d): PFOS tracers. (e) and (f) include MFR/MR comparisons of all homogeneous and all heterogeneous experiments, respectively.

MFR/MR curves for the Heterogeneous experiments show two distinct function shapes at two different portions of the mass removal (Fig. 2). These include a concave profile at low to moderate MR, similar to the homogeneous experiments, followed by a convex profile for high MR. The slope change between early/low MR and late stage MR is characterized as a multi-stage MFR/MR mass removal, which has been observed upon transition from a primary to a secondary contaminant source or with significant alteration in source-zone architecture⁵⁹. During the early/low MR phase of the experiments, the mass flux from the flow cell continued to decrease until all of the highly-accessible contaminant or tracer mass was removed (i.e., elution from the higher-permeability sand surrounding the lower-permeability zone). Then, during the final stage of MR, the MFR/MR relationship reflects the removal of the contaminant or tracer mass from within the lower-permeability zone, which can be considered the more poorly-accessible portion of the mass distribution. Based on the setup of these experiments, the primary and secondary sources were most likely solute retention and elution from the coarser sand matrix and the lower-permeability sand layer, respectively.

Concavity in MFR/MR curves is associated with efficient mass removal, therefore the secondary phase of mass removal in the Heterogeneous experiments show a comparatively less efficient removal of the tracers and PFOS. Less efficient mass removal would be expected since, as noted above, the secondary phase was likely solute retained in and released from the lower permeability layer. The lower velocity within that lower permeability zone generally caused the lower hydraulic accessibility, which led to preferential flow and diffusive mass transfer limitations impacting the mass-removal behavior.

As these two phases of heterogeneous MFR/MR curves are diagnostic of the source elution behavior, they can be used to characterize the dissolved contaminant source configuration and the MFR/MR relationships can be used to determine the transition between solute removal from the higher-permeability sand to the subsequent solute removal from the lower-permeability zone. Efficient mass removal from the primary source of higher-permeability media is controlled by advection and flow velocity, while the comparatively inefficient mass removal from the secondary source within the lower-permeability media is also influenced by diffusive mass transfer of the respective tracers.

The point of inflection in the MFR/MR curve for the heterogeneous experiments was not constant between tracers (Fig. 2f), and occurs earliest (lowest MR) for NaCl (Fig. 2a) and latest (largest MR) for cyclodextrin (Fig. 2c). This trend is consistent with the differences in the diffusion coefficients, as cyclodextrin has the smallest diffusion coefficient whereas Cl⁻ has the largest diffusion coefficient. The early inflection of MFR at lowest MR for the Cl⁻ ion suggests that this tracer had the largest amount of mass retained in the lower-permeability zone due to the 4 hour flow interruption, which is consistent with that tracer having the largest diffusion coefficient. The opposite was also consistent for cyclodextrin having the smallest diffusion coefficient and the least amount of mass in the lower-permeability zone indicated by it having the largest MR value for the inflection point. These results confirm the diffusive mass transfer and back diffusion did impact the solute elution behavior, whereas advection and the velocity variability between the two sand media also impacted tracer retention and elution behavior.

3.3. Homogeneous Flow Cell Power Function Models

Regression analysis was used to match the power function (Equation 2) to the observed MFR/MR curves for the homogeneous flow cell experiments, shown in Fig. 3. Parameter optimization of the exponent, n, of the power function was used to minimize the root mean squared error of a least squares regression between the observed data and the power function. The low root mean squared error and R² values close to unity confirm the goodness of the match between the observations and the power function for the homogeneous experiment curves. The value of n was similar for all nonreactive tracers (i.e., NaCl, PFBA, and cyclodextrin), between values of 3.6 to 3.9 (Fig. 3a – 3c). For the PFOS homogeneous experiment, the value of n was significantly lower at 2.82 (ANOVA test reveals p= 0.022), which suggests less efficient mass removal. This change in n confirms less efficient elution and mass removal of PFOS compared to the nonreactive tracers. We attribute this behavior to the above mentioned nonideal transport and sorption behavior.

Fig. 3.

Comparisons of MFR/MR observed data (symbols) with fitted power functions (lines) of homogeneous flow cell experiments for (a): NaCl; (b): PFBA; (c): Cyclodextrin; and (d): PFOS tracers.

Control, 2-D flow cell experiments were conducted without flow interruption, and homogeneous 1-D column experiments were also conducted without flow interruption. MFR/MR curves with fitted power functions for control flow cell and column experiments are shown in Fig. S3 and S4, respectively. Root mean squared error and R² values of least squared regression show good fits of the simple power function to these MFR/MR curves. Values of n were slightly lower those of the non-control experiments (ANOVA test reveals p=0.044). The difference in n between control and non-control experiments reveal that the diffusion period had a minor effect on MFR/MR behavior.

3.4. Heterogeneous Flow Cell Power Function Models

The two distinct phases of mass removal for the Heterogeneous experiment MFR/MR curves did not allow for a single power function to be fit to all of the data. This multi-stage or nonsingular MFR/MR behavior resembles MFR/MR data from previous flow cell experiments and field observations, which contained multiple sources of NAPL contamination in heterogeneous media⁵⁹. A multi-step, or piece-wise, regression approach was used to characterize the nonsingular behavior using different values of n estimated for each phase of the mass removal. Two power functions were fit to MFR/MR data from each experiment, with a transition from a first power function to a second function once the inflection point in MR was reached. Fitting a multi-step MFR/MR function to a non-uniform curve was developed for complex NAPL sources⁵⁹, which was also the approach applied here for aqueous tracers.

The Heterogeneous experiment multi-step functions are shown with comparison to the measured data in Fig. 4. The first phase of mass removal was concave but the second phase was convex, and this change in shape was attributed to the change in dominant zone of transport and elution (noted above), which occurs high mass removal ranges. The multi-step regression was able to match the multiple phases of mass removal in the observed data throughout each entire experiment. As there is a significant change in the MFR/MR shape, slope, and n parameter associated with the transition in solute elution from the primary to secondary solute source zone (i.e., higher to lower permeability zone), this approach can be used to characterize heterogeneous transport, back diffusion, secondary source elution even for relatively small amounts of heterogeneity, as was the case for the two aquifer sands used herein.

Fig. 4.

Comparisons of MFR/MR observed data (symbols) with fitted multi-step power functions (lines) for heterogeneous flow cell experiments for (a): NaCl; (b): PFBA; (c): Cyclodextrin; and (d): PFOS tracers.

The lower MR, initial, phase resulted in fitting parameter, n₁, values that were all greater than unity and concave, which confirms that the initial phase had efficient elution typical for sources within higher permeability and high hydraulically accessibility zones. The initial phase of mass removal for nonreactive tracers resulted in fitting parameters that are related to the timing of the inflection point. The observed general trend was that earlier (i.e., lower MR) inflection point was generally associated with a smaller value for the n₁ (Fig. 4), which was NaCl<PFBA<cyclodextrin for the tracers used herein. The results for the PFOS tracer deviate from this relationship (Fig. 4d). Fitting parameters for the secondary phase, n₂, were less than unity (n=1) and convex, which confirms the transition to inefficient elution typical for sources within lower permeability and lower hydraulic accessibility zones (Fig. 4a – 4d). The values of n₂, were between 0.54 and 0.81, and did not appear to vary following a trend.

Fig. 5 presents the comparison of observations with the flow and transport model simulation results for Homogeneous and Heterogeneous experiments plotted as MFR versus MR. The model results were comparable to the entire series of data, even matching the two stages before and after the inflection in the Heterogeneous experiments. These results suggest that multi-stage MFR/MR regression results were also comparable to the flow and transport modeling. The model is a physically-based, mechanistic, approach whereas the regression is an empirical approach, but both provide quantification of the transport behavior.

Fig. 5.

Comparisons of MFR/MR observed data (symbols) with model simulation results (lines) for the homogeneous and heterogeneous flow cell experiments for (a): NaCl; (b): PFBA; (c): Cyclodextrin; and (d): PFOS tracers.

3.5. Comparisons of Experiments and n Values

The occurrence of the MFR/MR inflection point during the heterogeneous flow cell experiments indicated a relationship with fitted power functions. This inflection point is the transition between the mass removal from the higher-permeability to the mass removal from the lower-permeability zone. This can also be interpreted as the amount of tracer mass that initially diffused into and was retained in the low permeability lens during the flow interruption period. The tracer mass of the secondary source might therefore be expected to correlate to molecular diffusion coefficients of tracers, which is verified in Fig. S10. In log-log space, a linear trend between molecular diffusion coefficients and secondary source mass was observed (Table S4 and S6). This confirms that the secondary source mass estimated based on the inflection point of the MFR/MR relationship is dependent on the molecular diffusion associated with the flow interruption and any additional diffusive mass transport during the experiments. Additionally, evaluation of the MFR/MR behavior can be used to characterize back-diffusion and diffusive mass transfer for PFOS and other contaminants eluting from lower-permeability zones within heterogeneous systems, which was even confirmed herein for two aquifer sands with relatively low differences in hydraulic conductivity.

Fig. S10 illustrates that the relationship between secondary source mass and diffusion coefficient was applicable to all the tracers considered including PFOS, and including both larger and smaller diffusion coefficients. Despite PFOS experiment inconsistency with the behavior of the nonreactive tracers with respect to n values, secondary source mass during heterogeneous PFOS experiments reveal behavior that is consistent with other tracers. This means that the sorption behavior may be impacting the n values of MFR/MR curves for the Homogeneous experiments and the early mass recovery phase of Heterogeneous experiments when compared to nonreactive tracers. However, sorption of PFOS does not seem to impact the mass accumulated in the lower-permeability zone in the Heterogeneous experiments after a relatively long time for diffusion to occur.

4. ENVIRONMENTAL IMPLICATIONS

The 2-D flow cell experiments presented herein represent to the authors’ knowledge the first to investigate the impact of permeability heterogeneity on preferential flow, diffusive mass transfer, and mass removal for PFAS. Overall, these data provide novel quantitative characteristics of diffusive mass transfer and back diffusion in heterogeneous media, even as illustrated with this single lens of lower permeability sand interbedded within a coarser sand matrix, which would be representative of relatively homogeneous aquifers. The results have implications for natural attenuation processes that impact solute plume migration. In addition, the issue of back diffusion influencing mass removal likely impacts any groundwater system that is heterogeneous with respect to hydraulic conductivities of geologic material⁸¹.

The MFR/MR analysis approach, which typically has been used for NAPL-contaminated sources, was demonstrated to be useful for characterizing mass removal for a dissolved solute source, which is representative of PFAS-impacted sites. This can aide in the risk assessment and analysis of treatment efficacy for aqueous contaminants in heterogeneous groundwater systems. For example, the approach used herein may support Monitored Natural Attenuation feasibility analysis⁸⁸, and these results also relate to evaluation of contaminated groundwater pumping for remediation.

Synopsis:

The results of flow-cell experiments demonstrated that the transport, attenuation, and removal of PFOS from heterogeneous porous media is constrained by hydraulic accessibility (velocity variability) and back diffusion, which was assessed using both mathematical modeling and multi-step regression of mass-removal reductions and reductions in contaminant mass flux (MFR/MR).