HOME HELP FEEDBACK SUBSCRIPTIONS ARCHIVE SEARCH TABLE OF CONTENTS		QUICK SEARCH:   [advanced] Author: Keyword(s): Year:  Vol:  Page:

This Article Abstract Figures Only Full Text (PDF) Free Alert me when this article is cited Alert me if a correction is posted Services Similar articles in this journal Similar articles in PubMed Alert me to new issues of the journal Download to citation manager Citing Articles Citing Articles via Google Scholar Google Scholar Articles by Haws, N. W. Articles by Bouwer, E. J. Search for Related Content PubMed PubMed Citation Articles by Haws, N. W. Articles by Bouwer, E. J. GeoRef GeoRef Citation Agricola Articles by Haws, N. W. Articles by Bouwer, E. J. Related Collections Remediation Nonequilibrium Transport Bioremediation and Biodegradation

Effects of Initial Solute Distribution on Contaminant Availability, Desorption Modeling, and Subsurface Remediation

^a Hydro Geo Chem, Inc., Tucson, AZ 85705
^b Dep. of Geography and Environmental Engineering, Johns Hopkins Univ., 3400 Charles St., Baltimore, MD 21218

^* Corresponding author (bball{at}jhu.edu).

Received for publication October 31, 2006.

	ABSTRACT

TOP NOTES ABSTRACT INTRODUCTION Materials and Methods Results and Discussion Conclusions Appendix: Modeling Equations and... REFERENCES

 
Low permeability regions in which solute movement is governed by diffusion reduce the availability of pollutants for remediation and can function as long-term sources of groundwater contamination. The inherent difficulty in understanding mass transfer from these regions of sequestered contamination is further complicated by unknown solute distributions within the low-permeability regions (sequestering regions). When models are calibrated to reproduce temporal histories of solute release from a sequestering region (desorption), the fitted parameter values are used to infer the physical or chemical characteristics of the media; however, the calibrated parameters also reflect the case-specific initial conditions (i.e., the solute distribution within the sequestering region domain at the onset of desorption). This phenomenon is demonstrated using model simulations of solute diffusion from hypothetical solids with characteristics similar to those of the well studied Borden, Ontario aquifer system. Solute release from the solids is simulated using a batch diffusion model under different initial solute distributions within the solids. The results of these model simulations are used to calibrate parameters of a multiple first-order rate desorption model (MRM) to illustrate how the fitted MRM parameters increase or decrease depending on the initial "aging" of the solids. Further numerical simulations are conducted for a one-dimensional flow system under steady-state and variable-rate hydraulic flushing. These simulations show that although aging reduces desorptive mass flux during early stages of flushing, aged sites have greater desorptive mass flux (greater solute availability) than "freshly" contaminated media during the later stages of remediation. Overall, the results demonstrate why the physicochemical meaning of observed desorption rates cannot be accurately deduced without first understanding the initial solute distribution within the media.

Abbreviations: MRM, multiple first-order rate desorption model • PDM, pore diffusion model

	INTRODUCTION

TOP NOTES ABSTRACT INTRODUCTION Materials and Methods Results and Discussion Conclusions Appendix: Modeling Equations and... REFERENCES

 
THE success of bioremediation or most other remediation schemes that target the aqueous phase of contaminant plumes depends on how available the contaminants are to the interparticle pore-water of the aquifer region. Thus, the effectiveness of remediation can be controlled by solute migration into low-permeability "sequestering" regions. Such regions can be manifest at any spatial scale where solute movement is dominated by diffusion and can include such features as intraparticle pore spaces (e.g., Ball and Roberts, 1991a,b, Shor et al., 2003; Basagaoglu et al., 2004), fine-grained (aquitard) strata (Ball et al., 1997; Liu and Ball, 1998; Wassenaar and Hendry, 2000), and rock matrices (e.g., Jardine et al., 1999; Shapiro, 2001; Reimus et al., 2003; Liu et al., 2007). When solute movement from these regions is slow relative to contaminant depletion rates in the permeable ("available") region (hereafter referred to as the "bulk aqueous phase"), the remediation timeline is characterized by an initial rapid drop in bulk aqueous phase contaminant concentrations, followed by very slow solute mass recoveries as contaminants from the sequestering region gradually desorb and diffuse back into the bulk aqueous phase where they become available for removal processes such as biological uptake and transformation.

The fraction of total solute mass readily available for remediation and the associated desorption rates for this mass are generally difficult to predict because of complex heterogeneities and sorption kinetics within the low-permeability region (hereafter referred to as "sequestering region"). The release of solute from sequestering regions (desorption) can be difficult to predict even for homogeneous soils of known geometry and simple chemical processes because the observed desorption rates are affected by the (usually unknown) initial distribution of solute concentration within the region. An important concept in this regard is "aging," or the length of time a site has been exposed to a contaminant source (Alexander, 2000). Aging phenomena have been attributed to physical mechanism (i.e., diffusion deeper into the sequestering region) (e.g., Kleineidam et al., 1999, 2004; Sabbah et al., 2005) and/or chemical processes (i.e., sorption to kinetically slow sites) or often to some unspecified combination of the two (Weissenfels et al., 1992; Connaughton et al., 1993; Sharer et al., 2003; Sun et al., 2003; Park et al., 2004; Ahmed and Chen, 2006). Both processes result in a slower release of contaminants from the sequestering zone such that the interpretation of the governing aging process can be obscure. This work focuses on diffusion as a mechanism for aging.

In a prior work by Sabbah et al. (2005), a diffusion-based numerical model was used to simulate desorption of phenanthrene from soil particles in several hypothetical batch systems that differed only in the amount of time between phenanthrene introduction into the system and the onset of desorption (i.e., aging period). These simulations demonstrated how a poor understanding of a solute's state of physical/chemical equilibrium with the solids can lead to a misinterpretation of kinetic and rate parameters and incorrect presumptions of sorption hysteresis (Kleineidam et al., 2004).

We use an analytical three-domain desorption model and numerical diffusion models to more explicitly consider effects that the initial solute distribution can have on the short- and long-term desorption rate and the corresponding solute availability. In contrast to the prior work of Sabbah et al. (2005), we assumed that actual equilibrium relations were well known such that the same (known) sorption isotherms could be applied to all modeling. This allowed a more specific focus on the effect of initial condition on diffusion-based release. Using some hypothetical conditions of remediation, we simulate phenanthrene desorption from aquifer solids in which mass transfer is controlled by Fickian diffusion within intraparticle pores. The cases selected were hypothetical and well defined yet sufficiently realistic to be indicative of effects that may be manifest in actual porous media. These hypothetical case studies show how initial intraparticle solute distributions affect the interpretation of aging and complicate remediation predictions.

The case studies are based on diffusive rate parameters that have been well developed for 0.25- to 0.40-mm-diameter calcareous and sparingly porous aquifer sand from Borden, Ontario (Ball and Roberts, 1991a,b). We avoid an explicit discussion of absolute length scale of the diffusive zone. Our intent here is to highlight that the manifestation of "non-equilibrium" in sorbing solute transport is controlled not so much by the absolute length- and time scales of the system as by the relative rates of flux in the available and sequestering regions—that is, by the ratio defined by dividing the characteristic diffusion rate (₂D_p/a², where symbols are as defined in the Appendix) by a characteristic advection rate (e.g., the velocity over transport length, v/L). The simulations discussed in this study are intended to illustrate the kind of effects that might be observed for any flow scenarios with similar ratios of characteristic diffusion rate to characteristic advection rate (e.g., Connaughton et al., 1993; Culver et al., 1997; Johnson et al., 2001). For example, contamination scenarios in a layered aquitard underlying Dover AFB, Delaware, USA have shown age-related diffusion profiles analogous to that conceptualized for intraparticle diffusion (Ball et al., 1997; Liu and Ball, 1998).

	Materials and Methods

TOP NOTES ABSTRACT INTRODUCTION Materials and Methods Results and Discussion Conclusions Appendix: Modeling Equations and... REFERENCES

 
Model Systems
This study considered two model systems: (i) a well mixed batch system (e.g., a batch sorption reactor or other isolated closed environment with no inflow or outflow and where solute concentration in the bulk aqueous phase was completely mixed) and (ii) an advective system with one-dimensional water flow (e.g., a water-saturated column of porous media with a single inlet, a single outlet, and uni-dimensional advective transport). The sequestering zone in both model systems was assumed to be at the scale of grains or small aggregates, although the results can apply to larger scales of sequestering zones if advective transport is also at much larger spatial and temporal scale. For illustrative purposes, we limit our sequestering region in the batch and column systems to homogeneous, spherical particles with an internal pore structure. Water and solute are assumed to exist in two regions: Region 1, a bulk aqueous phase, and Region 2, a sequestering region (Fig. 1 ). Within Region 1, solute is completely mixed (for the batch system) or transported one-dimensionally by advection and hydrodynamic dispersion (for the flow system). Water is stagnant in Region 2; however, solute can move radially through Region 2 by Fickian diffusion while being simultaneously affected by interactions with the solid surfaces or phases (sorptive retardation).

View larger version (20K): [in this window] [in a new window]   Fig. 1. Schematic representations of the batch (top) and flow (bottom) systems.

The modeling equations for both batch and flow systems are provided in the Appendix. These equations are based on assumptions of uniform-sized, spherical particles with identical internal pore structure. These and other assumptions (see Model Parameters section) are obvious over-simplifications of real aquifers where solids have a complex assortment of shapes, sizes, and internal pore structures and where more intricate sorption processes dominate. The use of such assumptions in this study is advantageous for isolating and highlighting the effects of the initial solute distribution; these assumptions do not imply that heterogeneity and other physical and chemical complexities are inconsequential. The effects of these complexities on contaminant availability and the desorptive flux have been illustrated in previous studies (e.g., Kleineidam et al., 1999; Karapanagioti et al., 2001; Basagaoglu et al., 2002).

The specific systems modeled are further described in the following section. The diffusion time scale represented by the chosen system was on the order of 10³ days (95% mass release under infinite solution conditions in a batch system). Because time-scales for immobile zone access vary widely in the environment, this time scale is exemplary rather than representative; nonetheless, it is known to be realistic for retarded particle-scale diffusion of some contaminants in sand-sized microporous calcite particles (Ball and Roberts, 1991; Sabbah et al., 2005) and could also be accurate for faster diffusion at larger length scales. The batch and flow models used the same spatial and temporal discretization. The time-step was set at 0.2 d, and Region 2 was divided into 100 radial nodes. Region 1 of the flow model had 100 longitudinal nodes. This model construction provided stable results that did not change with increased discretization.

Model Parameters
Region 2 diffusion rates are based on aquifer solid characteristics that are hypothetical but have average chemical and physical characteristics that are similar to those of some sands from the aquifer in Borden, Ontario, on which prior studies have been conducted (Mackay et al., 1986; Roberts et al., 1986; Curtis et al., 1986; Ball and Roberts, 1991). The basic properties of the solids and contaminant (Table 1) are similar to those used in Sabbah et al. (2005), with the exception of additional simplifying assumptions that are advantageous for isolating and discussing the effects of the initial solute distribution. One simplifying assumption is that the fraction of total sorption sites at instantaneous local equilibrium with the bulk fluid (f) was set to a negligible amount (0.001). This small f value effectively negated any instantaneous sorption directly from the bulk aqueous phase so that all solute uptake and release would be attributable to diffusion gradients between Region 1 and Region 2. Another simplifying assumption was the use of a linear, rather than a nonlinear, isotherm to simulate the sorption of phenanthrene. The linear isotherm assumption allowed a more straightforward interpretation of results—use of the actual nonlinear isotherm would have complicated our ability to distinguish the effects of the initial spatial distribution from the impacts of concentration-dependent sorption on the retardation of intragranular diffusion.

View larger version (20K): [in this window] [in a new window]   Fig. 2. Relative solute concentration profiles for the equilibrium (EQ), gradient in (Grad-In), and gradient out (Grad-Out) scenarios. Each scenario has the same initial mass.

The bulk aqueous concentration for sorption and desorption in the batch simulations were kept constant at high or zero values to provide maximum sorption and desorption rates, respectively. These conditions correspond to an infinite sink in the aqueous phase, such as has been applied in experimental batch desorption experiments (e.g., Pignatello, 1990; Cornelissen et al., 1997) or as might be approached for a scenario where the potential biodegradation rate is much greater than the maximum diffusive mass transfer rate. For the flow scenarios, the concentration in the bulk aqueous region (C₁) was initially set to be equivalent to the initial EQ solute concentration inside the particle (_o), and the influent concentration (C_in) was free of solute (i.e., C_in = 0). This condition allows for continuous elution of the resident contaminant and is representative of hydraulic flushing. In such a case, the desorption is maximum at the upstream end of the porous medium and minimum at the most downstream end, where diffusion is into solute-laden water. Average results, however, depend only on the time of pumping and the relative ratio of D_p/a² (in Region 2) to v/L (in Region 1), with terms as defined in the Appendix. Moreover, the fraction of initial mass removed depends only on D_p/a² and the groundwater velocity (v), when the time is expressed in terms of the number of pore volumes fed (PV = vt/L).

Multi-Site First-Order Rate Model
Desorption from a sequestering region is often approximated using first-order rate models. Although these models are mathematically simple, they often fail to accurately represent soil sorption/desorption dynamics, particularly the longer-term behavior (Rao et al., 1980a,b; Young and Ball, 1995; Griffioen, 1998). To overcome this shortcoming, several researchers have used multi-site first-order rate models (MRM) to improve model fits to observed desorption data across a wide range of time scales. Some MRMs comprise two or three rate-limited sorption regions or "compartments" (e.g., Brusseau and Rao, 1989; Gamerdinger et al., 1990; Cornelissen et al., 1998; Johnson et al., 2001; Park et al., 2004; van Noort et al., 2004; Wells et al., 2004; Saffron et al., 2006), each of which has its own sorption equilibrium and first-order rate constant. Other MRMs assume a continuum of compartments and rate constants but assume that the distribution of rates (and sometimes also equilibrium capacity) can be represented by well defined statistical distributions (e.g., Connaughton et al., 1993; Pedit and Miller, 1994; Culver et al., 1997). The assumption of multiple rates in such models is typically attributed to the unknown heterogeneities in media properties, including the shapes, sizes, porosities, and organic phase distributions in the immobile water and sorption zones (Cornelissen et al., 1998; Kleineidam et al., 1999; Basagaoglu et al., 2002, 2004; Heyse et al., 2002; van Noort et al., 2004). Although such heterogeneities lead to complexity of rate modeling, they do not necessarily account for all observed phenomena in desorption studies in the field or laboratory. In particular, some rate effects, such as slower fitted desorption rates for more highly aged samples, can also arise from variation in the initial spatial distributions of solute within the sequestering region. Such initial distributions are usually unknown and vary as a function of exposure time (aging) during the adsorption phase. Numerous investigators have used model simulations to show how longer exposure times can lead to increased proportions of solute mass being located in more slowly accessed sequestering regions (Connaughton et al., 1993; Park et al., 2004; Sharer et al., 2003; Sun et al., 2003; Gamst et al., 2004; Sabbah et al., 2005). To better elucidate the manner in which the fitted parameters for a selected MRM are influenced by initial solute distributions, we have calibrated the model parameters for the selected MRM to external concentration histories that would be observed for well defined systems that are controlled by a simple and reversible diffusion process. More specifically, we have generated alternative scenarios of "synthetic" sorbed-phase solute mass distributions with the PDM for each of the three initial solute concentration cases (EQ, Grad-In, and Grad-Out), and we have then interpreted these histories using a three-region MRM. Although many MRMs are extant in the literature, the three-region MRM used by Johnson et al. (2001) and others (e.g., Culver et al., 1997; Cornelissen et al., 1998; van Noort et al., 2004; Wells et al., 2004; Jonker et al., 2005; Saffron et al., 2006) was chosen for this study because of the combination of its potential accuracy and simplicity, as described by Johnson et al. (2001). The MRM model is given by:

[1a]

[1b]

where S_o is the initial Region 2 sorbed-phase mass, and S(t) is the sorbed mass at time (t); k_r, k_s, k_vs (T^–1) are the first-order rate constants in the rapid, slow, and very slow compartments, respectively; f_r, f_s, and f_vs (-) represent the fraction (f ) of total sorption sites in the rapid, slow, and very slow sorption regions, respectively.

The MRM parameters were calibrated to the PDM data by minimizing the sum of the relative squared errors:

[2]

where S_i^PDM is the sorbed concentration from the PDM model at t, S_i^MRM is the sorbed concentration from the MRM model at t, and T is the total simulation time. The MS Excel Solver was used to perform the parameter calibration.

Flow System: Steady Pumping and Variable Pumping Simulations
The simulations for the flow system were conducted using a maximum pumping rate that corresponded to a Darcy flux, (q) of 0.5 m d^–1, or a linear one-dimensional pore-water velocity (v) of 1.39 m d^–1. This Darcy flux was chosen to produce a column Peclet number (P_e) of 100, which is consistent with an advection-dominated regime and with column studies performed by Young and Ball (1997). In the first set of simulations for the flow system (steady pumping), the modeling domain was assumed to be flushed continuously at the maximum pumping rate. The steady pumping simulations were designed to provide a base case for how the initial solute distributions influenced mass removal during hydraulic flushing.

Continuous pumping at a maximum rate is not the most efficient mass removal strategy in terms of pumped volume when slow immobile-region diffusion rates limit solute availability in the bulk aqueous phase. Pulsed pumping (i.e., periodically resting the pumps until concentrations in the bulk aqueous region rebound to near pre-pumping levels) is often used to cope with mass transfer rate limitations and to enhance pumping efficiency (Mackay et al.. 2000 and references therein). As shown by Harvey et al. (1994), however, pulsed pumping is less efficient in terms of pumped volume savings than continuously pumping at some appropriately selected lower rate. In fact, the theoretically optimal rate based on pumped volume savings would be achieved by pumping at a rate that approached zero. Very low pumping rates are often impractical because they can lead to long clean-up times for remediation and are also perhaps less effective at controlling groundwater flow (Harvey et al., 1994). In addition, some scenarios of slow pumping lead to unacceptably high well-water concentrations for an unacceptably long time, and usually gainful use can be made of pumped groundwater long before subsurface cleanup is deemed to be sufficient.

Under situations where the goal is to achieve a balance between pumped volume and rapid lowering of aqueous concentrations in pumped water, alternative scenarios of cleanup can be envisioned that would involve an initially rapid rate of pumping followed by variable pumping rates over time in response to observed variations in the field. To simulate such an "adaptive management" approach (National Research Council, 2003), we performed a second set of simulations in which the pumping rates were initially at the maximum rate but were then varied over the course of the simulation to minimize the volume of water pumped within the constraint that effluent concentrations remain below some required value (arbitrarily set at C/C_o = 0.3 for the purposes of our simulations). After the initial rapid flush to reach this level, the pumping rates were continually adjusted to prevent the relative effluent concentration from rising above the required level. This simulation was implemented numerically by starting pumping at the maximum rate (q_max = 0.5 m d^–1) and then, at each time step (0.2 d), decreasing the pumping rate by 10% if C/C_o < 0.3 or increasing the pumping rate by 10% (not to exceed q_max) if C/C_o > 0.3. This strategy was continued until sufficient mass was removed so that M/M_o = 0.3, meaning that pumping could be terminated without concentrations exceeding the effluent criterion. A similar scheme might be implemented at a contaminated field site by periodically increasing or decreasing the pumping rate or by increasing or decreasing the number of active pumps.

	Results and Discussion

TOP NOTES ABSTRACT INTRODUCTION Materials and Methods Results and Discussion Conclusions Appendix: Modeling Equations and... REFERENCES

 
Initial Concentration Profile Effects on MRM Parameters (Batch Simulations)
The results of the batch PDM simulations and the MRM fits for the EQ, Grad-In, and Grad-Out initial concentration profiles are shown in Fig. 3 . To appropriately highlight the results of the simulations, Fig. 3 is plotted on a linear scale for the first 2500 d and on a semi-log scale for the next 2500 d. Consistent with laboratory and field observations, the initial desorption in the Grad-In scenario (corresponding to a "freshly contaminated" site) was much more rapid than those observed in the other two scenarios (more representative of "aged" sites). The MRM fits provide an excellent match to the desorption profiles of each of the initial solute distribution scenarios and are indistinguishable from the PDM-generated curves.

View larger version (16K): [in this window] [in a new window]   Fig. 3. Average relative sorbed concentrations for the equilibrium (EQ), gradient in (Grad-In), and gradient out (Grad-Out) scenarios with the multiple first-order rate desorption model fits to each scenario. The plot is shown on a linear scale (left ordinate scale) for 0 to 2500 d and on a semi-log scale (right ordinate scale) for 2500 to 5000 d.

Steady-State Pumping
Figure 4 shows the relative concentration at the mobile domain exit (e.g., a compliance boundary, column outlet, extraction well) and the relative mass remaining in the system over a steady pumping period of 1000 pore volumes. Because the simulations were conducted using a steady pumping rate, the solute concentration at the outlet is directly proportional to solute mass flux at the exit and therefore can be used as an indicator of the relative rate of clean-up. The Grad-Out case showed an earlier drop in effluent concentration as a result of initially low desorption fluxes in response to the lower concentration gradient between the outer area of the sequestering region and the bulk aqueous phase. Conversely, the effluent concentration for the Grad-In scenario dropped off much more slowly due to higher desorption fluxes associated with an initially steeper concentration gradient in the outer area of the sequestering region.

View larger version (21K): [in this window] [in a new window]   Fig. 4. Effluent concentrations and mass remaining with pore volumes pumped for the equilibrium (EQ), gradient in (Grad-In), and gradient out (Grad-Out) scenarios in the steady pumping simulations.

View larger version (20K): [in this window] [in a new window]   Fig. 5. Intraparticle concentration profiles for the equilibrium (EQ), gradient in (Grad-In), and gradient out (Grad-Out) scenarios for three different pumped pore volumes (PV) in the steady pumping simulations.

Variable-Rate Pumping
The relative mass remaining with pore volumes flushed and with total time for the simulations with variable pumping rates are shown in Fig. 6a and 6b , respectively. The mass remaining for the steady-state pumping simulations is also shown in these figures for comparison. For the variable pumping case, Fig. 7a shows how the relative pumping rate (q/q_max, where q_max is the steady pumping rate) varied with the number of pore volumes pumped (Fig. 7a) and with time (Fig. 7b). (In Fig. 6 and Fig. 7, the number of pore volumes flushed and the elapsed time are not directly proportional because the pumping rate was not held constant.) Variable pumping provides considerable savings in volume of water pumped relative to continuous pumping at q_max to reach the same amount of mass removal, but the variable (and, on average, slower) pumping necessarily required more time to reach the cleanup goal (Rabideau and Miller, 1994; Harvey et al., 1994). The pumping durations in pore volumes flushed and in actual time are provided in Table 3, along with an indicator of the savings in pumped water volume, calculated as the ratio of variable-rate to steady-state pumped volumes at 70% clean-up (V:S). As outlined in Table 3, the variable pumping scheme reduced the required pumping volume to between 16 and 31% of the steady pumping requirement, dependent on the initial condition assumed. On the other hand, the variable pumping scheme needed between 53 and 79% more time to achieve the same cleanup goal.

View larger version (26K): [in this window] [in a new window]   Fig. 6. Relative mass remaining (M/Mo) with pore volumes pumped (top) and with time (bottom) for the simulations with the variable (vble) pumping rates and the steady (stdy) pumping rates. The plots are truncated at M/Mo = 0.3, which is the fraction of remaining mass that was arbitrarily selected as sufficient to meet cleanup criteria without pumping. Variable pumping was initially set at the maximum rate but was then allowed to drop as needed to keep effluent concentrations at a maximum allowable value of C/C0 = 0.3. The pore volumes pumped and time scales are not easily related because pumping is not at a steady rate.

View larger version (20K): [in this window] [in a new window]   Fig. 7. Relative pumping rate, q/qmax, as a function of number of pore volumes pumped (top) and time (bottom) for the simulations with the variable pumping rate. qmax is the steady pumping rate used to generate the data in Fig. 6a and 6b. Variable pumping was initially set at the maximum rate but was then allowed to drop as needed to keep effluent concentrations at a maximum allowable value of C/C0 = 0.3. The pore volumes pumped and time scales are not easily related because pumping is not at a steady rate.

The variable-rate pumping case described above is an illustration of an adaptive approach that continually meets some water quality criteria, thus providing a balance between cleanup needs and efficient remediation with respect to volume of water pumped. The results of Fig. 6 show that variable speed pumping not only affects the overall required clean-up volume and time, but also the variability that exists in such volume and time as a result of initial conditions. Compared with the wide range in potentially required pore volumes flushed for the steady pumping simulations, the required pore volumes for the three initial concentration scenarios under variable pumping is essentially the same. On the other hand, the range of time requirements associated with different scenarios of initial conditions is seen to increase under the variable pumping scheme. In cases of unknown spatial distributions of contamination at the time of remediation onset, variable or pulsed pumping may be one strategy for improving predictability for the volume of water pumped but will weaken predictability for the total remediation time. These conclusions come with the caveat that the differences reported in Table 3 are relatively small compared with the compounding uncertainties that arise in real systems (e.g., media heterogeneities, nonlinear/non-equilibrium sorption, and chemical transformations). Additional research should further address adaptive means of reducing the effects of uncertainties on subsurface remediation.

	Conclusions

TOP NOTES ABSTRACT INTRODUCTION Materials and Methods Results and Discussion Conclusions Appendix: Modeling Equations and... REFERENCES

 
Diffusion from sequestering regions is often the limiting process for remediation strategies because it controls the speed at which contaminants become available for uptake and removal. One of the difficulties in properly understanding and predicting solute release to available regions is the initial solute distribution within a sequestering region. Because initial solute distributions are typically unknown, they complicate the calibration and interpretation of models of solute release and the short- and long-term availability of contaminants. If the effects of the initial solute distribution on the apparent aging effect are not considered, erroneous conclusions will likely be made regarding desorption sites and desorption model parameters. This study demonstrates these concepts for a hypothetical system of particle scale diffusion, but the concepts are generally applicable to solute migration through sequestering regions at other scales (e.g., aquitards and clay lenses).

The batch simulations conducted in this study demonstrate that the distribution of sorption "site types" calibrated from fitting a multi-site, first-order mass transfer model can be strongly influenced by initial conditions. In particular, the simulations illustrate how diffusion-related changes in initial condition (before desorption) may be a viable alternative explanation for situations where "aging" is observed to cause a given contaminant to become less available to remediation or biological uptake. More generally, because mathematical simulations through differential equations are always strongly dependent on initial and boundary conditions, model calibration cannot be decoupled from the initial conditions. Therefore, the calibrated parameters will not have a clear physical or chemical meaning if based on inappropriate assumptions regarding initial conditions. Moreover, subsequent predictions made on the basis of such models may be invalid when applied to the same system but under a different set of starting conditions.

The one-dimensional flow simulations illustrate that initial solute distribution affects short- and long-term contaminant flushing, and in different ways, for steady- and variable-rate pumping. Results with either pumping scheme show that solute in a Grad-In scenario is initially more available (with a greater fraction of contaminant mass being removed at a given time and pumping rate) but that such scenarios can be associated with long-term desorption flux rates that are less than those from more aged samples with similar levels of total contamination. This change in short-term and long-term solute availability affects the efficiency of contaminant removal by pumping or other management strategies that target the bulk aqueous phase. For example, a comparison of the variable pumping and the steady pumping simulations shows greater benefit (in volumes pumped) for an aged site (Grad-Out or EQ) than for a freshly contaminated site (Grad-In). In addition, variable-speed pumping was shown to give less uncertainty in the required volume of flushing water (and greater uncertainty for overall pumping time) for a given level of cleanup under conditions of unknown spatial distribution. As with the other comparisons to steady pumping, these differences were greater for the well aged (EQ or Grad-Out) scenarios than for fresh contamination (Grad-In).

Taken together, these results demonstrate that short-term and long-term solute availability to the bulk aqueous phase is influenced by the initial solute distributions within the media. Because initial solute concentrations for real systems are rarely, if ever, known, all models that are calibrated from desorption data should be regarded as empirical simulation tools that are likely to be case-, time-, and site specific unless their mechanistic assumptions can be verified through independent study. Our results also illustrate how the implementation and effectiveness of adaptive approaches to remediation (such as pumping rate variations in response to effluent concentrations) can be dependent on the initial spatial distributions of contaminants.

	Appendix: Modeling Equations and Parameter Definitions

TOP NOTES ABSTRACT INTRODUCTION Materials and Methods Results and Discussion Conclusions Appendix: Modeling Equations and... REFERENCES

 
Modeling Equations
For the batch system, aqueous solute concentrations in Region 1 are completely mixed throughout the finite volume reactor. The mass balance for the batch system is (all parameters are defined in Section A.2):

[3]

The variables ₂(t) and ₂(t) are averaged quantities computed as follows:

[4a]

[4b]

Sorbed concentrations in each region are related to their local aqueous phase concentrations through the sorption isotherm, which is assumed to be linear for the purposes of our current work. In other words, S = K_dC, where K_d has units of L³ M^–1. Thus, we have:

[5a]

and

[5b]

Region 2 is composed of homogeneous spherical particles. Solute movement within the particles of Region 2 is governed by Fickian diffusion, given by:

[6]

The boundary condition at the particle interface with the bulk fluid is:

[7]

For the flow system, solute in Region 1 is mobile and transported by advection and hydrodynamic dispersion through the column. The governing equation for one-dimensional solute movement in a homogeneous porous medium is as follows:

[8]

where

[9]

[10]

Interfacial concentrations at the Region1/Region 2 interface thus depend on longitudinal location (x), and the concentration distributions and mass transfer in Region 2 are governed by Fickian diffusion based on homogeneous spherical particles, similar to the batch reactor (Eq. [4]), and relations between sorbed and aqueous concentrations at any longitudinal position are also as previously defined for the batch system (Eq. [2a], [2b], [3a], and [3b]).

The boundary conditions at the inlet and outlet of the flow system are:

[11a]

[11b]

where C_o is the solute concentration at the column inlet, and L is the column length.

Parameter Definitions
a = particle radius (L)

C₁ = aqueous solute concentration in Region 1 (M L^–3)

C₂ = aqueous solute concentration in Region 2 (M L^–3)

C_o = initial aqueous solute concentration (M L^–3)

_o = average initial solute concentration in Region 2 (M L^–3)

D = hydrodynamic dispersion coefficient (L² T^–1)

D_p = pore-diffusion coefficient (L² T^–1)

(D_p)/(a²) = characteristic diffusion rate (1 T^–1)

f = fraction of instantaneous sorption sites (-)

f_r = fraction of rapid kinetic sorption sites (-)

f_s = fraction of slow kinetic sorption sites (-)

f_vs = fraction of very slow kinetic sorption sites (-)

K_d = linear sorption coefficient =(dS)/(dC) (L³ M^–1)

L = domain length (L)

M₁ = solute mass in Region 1 (M)

M₂ = solute mass in Region 2 (M)

M_o = initial solute mass (M)

m_s = particle mass (M)]

p_b = bulk density (M L^–3)

p_g = grain density (M L^–3)

r = radial distance coordinate (L)

t = time coordinate (T)

S₁ = sorbed solute concentration in Region 1 (M M^–1)

S₂ = sorbed solute concentration in Region 2 (M M^–1)

S_o = initial sorbed solute (M M^–1)

v = fluid advective velocity (L T^–1)

V_w = total fluid volume (L³)

x = one-dimensional distance coordinate (L)

₁ = interparticle porosity

₂ = intraparticle porosity

	ACKNOWLEDGMENTS

 
This research was supported under Agreement Number R828771-0-01 from the United States Environmental Protection Agency, Science to Achieve Results (STAR) program. The authors thank Dirk F. Young and Michael R. Paraskewich for useful discussions regarding the numerical models used in this research.

	NOTES

TOP NOTES ABSTRACT INTRODUCTION Materials and Methods Results and Discussion Conclusions Appendix: Modeling Equations and... REFERENCES

 
All rights reserved. No part of this periodical may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher.

	REFERENCES

TOP NOTES ABSTRACT INTRODUCTION Materials and Methods Results and Discussion Conclusions Appendix: Modeling Equations and... REFERENCES

 

• Ahmed, A.A., and D. Chen. 2006. Effects of contamination age on phenanthrene desorption from aquifers. J. Environ. Sci. Health Part A 41:1–15.
• Alexander, M. 2000. Aging, bioavailability, and overestimation of risk from environmental pollutants. Environ. Sci. Technol. 34:4259–4264.
• Ball, W.P., C. Liu, G. Xia, and D.F. Young. 1997. A diffusion-based interpretation of tetrachloroethene and trichloroethene concentration profiles in a groundwater aquitard. Water Resour. Res. 33:2741–2758.[CrossRef]
• Ball W.P., and P.V. Roberts. 1991a. Long-term sorption of halogenated organic-chemicals by aquifer material: I. Equilibrium. Environ. Sci. Technol. 25:1223–1237.
• Ball, W.P., and P.V. Roberts. 1991b. Long-term sorption of halogenated organic-chemicals by aquifer material: II. Intraparticle diffusion. Environ. Sci. Technol. 25:1237–1249.
• Basagaoglu, H., B.J. McCoy, T.R. Ginn, F.J. Loge, and J.P. Dietrich. 2002. A diffusion limited sorption kinetics model with polydispersed particles of distinct sizes and shapes. Adv. Water Resour. 25:755–772.[CrossRef]
• Basagaoglu, H., T.R. Ginn, and B.J. McCoy. 2004. Radial pore diffusion with nonuniform intraparticle porosities. J. Environ. Eng. 130:1170–1179.[CrossRef]
• Brusseau, M.L., and P.S.C. Rao. 1989. The influence of sorbate-organic matter interactions on sorption nonequilibrium. Chemosphere 18:1691–1706.
• Connaughton, D.F., J.R. Stedinger, L.W. Lion, and M.I. Shuler. 1993. Description of time-varying desorption-kinetics release of naphthalene from contaminated soils. Environ. Sci. Technol. 27:2397–2403.
• Cornelissen, G., P.C.M. van Noort, and H.A.J. Govers. 1998. Mechanisms of slow desorption of organic compounds from sediments: A study using model sorbents. Environ. Sci. Technol. 32:3124–3131.
• Cornelissen, G., P.C. van Noort, J.R. Parsons, and H.A. Govers. 1997. Temperature dependence of slow adsorption and desorption kinetics of organic compounds in sediments. Environ. Sci. Technol. 31:454–460.
• Culver, T.B., S.P. Hallisey, D. Sahoo, J.J. Deitsch, and J.A. Smith. 1997. Modeling the desorption of organic contaminants from long-term contaminated soil using distributed mass transfer rates. Environ. Sci. Technol. 31:1581–1588.
• Curtis, G.P., P.V. Roberts, and M. Reinhard. 1986. A natural gradient experiment on solute transport in a sand aquifer: IV. Sorption of organic solutes and its influence on mobility. Water Resour. Res. 22:2059–2067.
• Gamerdinger, A.P., R.J. Wagenet, and M.T. van Genuchten. 1990. Application of two-site two-region models for studying simultaneous nonequilibrium transport and degradation of pesticides. Soil Sci. Soc. Am. J. 54:957–963.[Abstract/Free Full Text]
• Gamst, J., P. Moldrup, D.E. Rolston, K.M. Scow, K. Hendriksen, and T. Komatsu. 2004. Time-dependency of naphthalene sorption in soil: Simple rate-, diffusion-, and isotherm-parameter-based models. Soil Sci. 169:342–354.[CrossRef]
• Griffioen, J. 1998. Suitability of the first-order mass transfer concept for describing cyclic diffusive mass transfer in stagnant zones. J. Contam. Hydrol. 34:155–165.[CrossRef][Web of Science]
• Harvey, C.F., R. Haggerty, and S.M. Gorelick. 1994. Aquifer remediation: A method for estimating mass transfer rate coefficients and an evaluation of pulsed pumping. Water Resour. Res. 30:1979–1991.[CrossRef]
• Heyse, E., D. Augustijn, P.S.C. Rao, and J.J. Delfino. 2002. Nonaqueous phase liquid dissolution and soil organic matter sorption in porous media: Review of system similarities. Crit. Rev. Environ. Sci. Technol. 32:337–397.[CrossRef]
• Jardine, P.M., W.E. Sanford, J.P. Gwo, O.C. Reedy, D.S. Hicks, J.S. Riggs, and W.B. Bailey. 1999. Quantifying diffusive mass transfer in fractured shale bedrock. Water Resour. Res. 35:2015–2030.[CrossRef]
• Johnson, M.D., T.M. Kienath, II, and W.J. Weber, Jr. 2001. A distributed reactivity model for sorption by soils and sediments: XIV. Characterization and modeling of phenanthrene desorption rates. Environ. Sci. Technol. 35:1688–1695.[Medline]
• Jonker, M.T.O., S.B. Hawthorne, and A.A. Koehlmans. 2005. Extremely slowly desorbing polycyclic aromatic hydrocarbons from soot and soot-like materials: Evidence by supercritical fluid extraction. Environ. Sci. Technol. 39:7889–7895.[Medline]
• Karapanagioti, H.K., C.M. Gossard, K.A. Strevett, R.L. Kolar, and D.A. Sabatini. 2001. Model coupling intraparticle diffusion/sorption, nonlinear sorption, and biodegradation processes. J. Contam. Hydrol. 48:1–21.[CrossRef][Web of Science][Medline]
• Kleineidam, S., H. Rugner, and P. Grathwohl. 1999. Impact of grain scale heterogeneity on slow sorption kinetics. Environ. Toxicol. Chem. 18:1673–1678.[CrossRef][Web of Science]
• Kleineidam, S., H. Rugner, and P. Grathwohl. 2004. Desorption kinetics of phenanthrene in aquifer material lacks hysteresis. Environ. Sci. Technol. 38:4169–4175.[Medline]
• Liu, C., and W.P. Ball. 1998. Analytical modeling of diffusion-limited contamination and decontamination in a two-layer porous medium. Adv. Water Resour. 24:297–313.
• Liu, H.H., Y.Q. Zhang, Q. Zhou, and F.J. Molz. 2007. An interpretation of potential scale dependence of the effective matrix diffusion coefficient. J. Contam. Hydrol. 90:41–57.[CrossRef][Web of Science][Medline]
• Mackay, D.M., D.L. Freyberg, and P.V. Roberts. 1986. A natural gradient experiment on solute transport in a sand aquifer: I. Approach and overview of plume movement. Water Resour. Res. 22:2017–2029.
• Mackay, D.M., R.D. Wilson, D.J. Brown, W.P. Ball, G. Xia, and D.J. Durfee. 2000. A controlled field evaluation of pulsed pump-and-treat remediation of a VOC-contaminated aquifer: Site characterization, experimental set-up, and overview of results. J. Contam. Hydrol. 41:81–131.[CrossRef][Web of Science]
• National Research Council. 2003. Environmental cleanup at Navy facilities: Adaptive site management. The National Academies Press, Washington, DC.
• Park, J.-H., Y. Feng, Y.C. Sung, T.C. Voice, and S.A. Boyd. 2004. Sorbed atrazine shifts into non-desorbable sites of soil organic matter during aging. Water Res. 38:3881–3892.[Medline]
• Pedit, J.A., and C.T. Miller. 1994. Heterogeneous sorption processes in subsurface systems: I. Model formulations and applications. Environ. Sci. Technol. 28:2094–2104.
• Pignatello, J.J. 1990. Slowly reversible sorption of aliphatic halocarbons in soils: I. Formation of residual fractions. Environ. Toxicol. Chem. 9:1107–1115.[CrossRef][Web of Science]
• Rabideau, A.J., and C.T. Miller. 1994. Two-dimensional modeling of aquifer remediation influenced by sorption nonequilibrium and hydraulic conductivity heterogeneity. Water Resour. Res. 30:1457–1470.[CrossRef]
• Rao, P.S.C., R.E. Jessup, D.E. Rolston, J.M. Davidson, and D.P. Kilcrease. 1980a. Experimental and mathematical-description of non-adsorbed solute transfer by diffusion in spherical aggregates. Soil Sci. Soc. Am. J. 44:684–688.[Abstract/Free Full Text]
• Rao, P.S.C., D.E. Rolston, R.E. Jessup, and J.M. Davidson. 1980b. Solute transport in aggregate porous media: Theoretical and experimental evaluation. Soil Sci. Soc. Am. J. 44:1139–1146.[Web of Science]
• Reimus, P.W., M.J. Haga, A.I. Adams, T.J. Callahan, H.J. Turin, and D.A. Counce. 2003. Testing and parameterizing a conceptual solute transport model in saturated fractured tuff using sorbing and nonsorbing tracers in cross-hole tracer tests. J. Contam. Hydrol. 62–3:613–636.
• Roberts, P.V., P. Cornel, and R.S. Summers. 1985. External mass-transfer rate in fixed-bed adsorption. J. Environ. Eng. 111:891–905.
• Roberts, P.V., M.N. Goltz, and D.M. Mackay. 1986. A natural gradient experiment on solute transport in a sand aquifer: III. Retardation estimates and mass balances for organic solutes. Water Resour. Res. 22:2047–2058.
• Saffron, C.M., J.H. Park, B.E. Dale, and Voice. T.C. 2006. Kinetics of contaminant desorption from soil: Comparison of model formulations using the akaike information criterion. Environ. Sci. Technol. 40:7662–7667.[Medline]
• Sabbah, I., W.P. Ball, D.F. Young, and E.J. Bouwer. 2005. Misinterpretations in the modeling of contaminant desorption from environmental solids when equilibrium conditions are not fully understood. Environ. Eng. Sci. 22:350–356.[CrossRef]
• Shapiro, A.M. 2001. Effective matrix diffusion in kilometer-scale transport in fractured crystalline rock. Water Resour. Res. 37:507–522.[CrossRef]
• Sharer, M., J.-H. Park, T.C. Voice, and S.A. Boyd. 2003. Time dependence of chlorobenzene sorption/desorption by soils. Soil Sci. Soc. Am. J. 67:1740–1745.[Abstract/Free Full Text]
• Shor, L.M., K.J. Rockne, G.L. Taghon, L.Y. Young, and D.S. Kosson. 2003. Desorption kinetics for field-aged polycyclic aromatic hydrocarbons from sediments. Environ. Sci. Technol. 37:1535–1544.[Medline]
• Sun, H., M. Teteda, M. Ike, and M. Fujita. 2003. Short- and long-term sorption/desorption of polycyclic aromatic hydrocarbons onto artificial solids: Effects of particle and pore sizes and organic matters. Water Res. 37:2960–2968.[Medline]
• van Noort, P.C.M., M.T.O. Jonker, and A.A. Koelmans. 2004. Modeling maximum adsorption capacities of soot and soot-like materials for PAHs and PCBs. Environ. Sci. Technol. 38:3305–3308.[Medline]
• Wassenaar, L.I., and M.J. Hendry. 2000. Mechanisms controlling the distribution and transport of C-14 in a clay-rich till aquitard. Ground Water 38:343–349.[CrossRef][Web of Science]
• Weissenfels, W.D., H.J. Klewer, and J. Langhoff. 1992. Adsorption of polycyclic aromatic-hydrocarbons (PAHs) by soil particles: Influence on biodegradability and biotoxicity. Appl. Microbiol. Biotechnol. 36:689–696.[Web of Science][Medline]
• Wells, M., L.Y. Wick, and H. Harms. 2004. Perspectives on modeling the release of hydrophobic organic contaminants drawn from model polymer release systems. J. Mater. Chem. 14:2461–2472.[CrossRef]
• Young, D.F., and W.P. Ball. 1994. A-priori simulation of tetrachloroethene transport through aquifer material using an intraparticle diffusion-model. Environ. Prog. 13:9–20.[CrossRef]
• Young, D.F., and W.P. Ball. 1995. Effects of column conditions on the first-order rate modeling of nonequilibrium solute breakthrough. Water Resour. Res. 31:2181–2192.[CrossRef]
• Young, D.F., and W.P. Ball. 1999. Two-region linear/nonlinear sorption modeling: Batch and column experiments. Environ. Toxicol. Chem. 18:1686–1693.[CrossRef][Web of Science]

This Article Abstract Figures Only Full Text (PDF) Free Alert me when this article is cited Alert me if a correction is posted Services Similar articles in this journal Similar articles in PubMed Alert me to new issues of the journal Download to citation manager Citing Articles Citing Articles via Google Scholar Google Scholar Articles by Haws, N. W. Articles by Bouwer, E. J. Search for Related Content PubMed PubMed Citation Articles by Haws, N. W. Articles by Bouwer, E. J. GeoRef GeoRef Citation Agricola Articles by Haws, N. W. Articles by Bouwer, E. J. Related Collections Remediation Nonequilibrium Transport Bioremediation and Biodegradation