Modeling Gas Formation and Mineral Precipitation in a Granular Iron

Chalk River Laboratories, Atomic Energy of Canada Limited, Chalk River, Ontario, Canada K0J 1J0. ‡ Department of Earth and Environmental Sciences, ...
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Modeling Gas Formation and Mineral Precipitation in a Granular Iron Column Sung-Wook Jeen,†,‡ Richard T. Amos,*,‡ and David W. Blowes‡ †

Chalk River Laboratories, Atomic Energy of Canada Limited, Chalk River, Ontario, Canada K0J 1J0 Department of Earth and Environmental Sciences, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1

‡

S Supporting Information *

ABSTRACT: In granular iron permeable reactive barriers (PRBs), hydrogen gas formation, entrapment and release of gas bubbles, and secondary mineral precipitation have been known to affect the permeability and reactivity. The multicomponent reactive transport model MIN3P was enhanced to couple gas formation and release, secondary mineral precipitation, and the effects of these processes on hydraulic properties and iron reactivity. The enhanced model was applied to a granular iron column, which was studied for the treatment of trichloroethene (TCE) in the presence of dissolved CaCO3. The simulation reasonably reproduced trends in gas formation, secondary mineral precipitation, permeability changes, and reactivity changes observed over time. The simulation showed that the accumulation of secondary minerals reduced the reactivity of the granular iron over time, which in turn decreased the rate of mineral accumulation, and also resulted in a gradual decrease in gas formation over time. This study provides a quantitative assessment of the evolving nature of geochemistry and permeability, resulting from coupled processes of gas formation and mineral precipitation, which leads to a better understanding of the processes controlling the granular iron reactivity, and represents an improved method for incorporating these factors into the design of granular iron PRBs.

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INTRODUCTION Gas formation and mineral precipitation are important geochemical processes in many natural and contaminated aquifers. Particularly, for remediation systems, where formation of gas bubbles and mineral precipitation significantly affect the geochemistry and performance of the systems, suitable analysis tools are required to improve system design and predict longterm effectiveness. Permeable reactive barriers (PRBs) containing granular iron are among the remediation systems where gas formation and mineral precipitation are related to iron corrosion and other geochemical reactions. Although granular iron PRBs have been shown to successfully treat a wide range of contaminants for substantial periods of time,1−6 concerns remain with regard to long-term performance. Formation of gas bubbles due to hydrogen gas generation7,8 and precipitation of secondary minerals5,9−11 can reduce permeability and also negatively affect the reactivity of the granular iron. Although there have been many studies on effects of gas formation and mineral precipitation on permeability and reactivity of iron materials,12,13 quantitative analysis tools that address both gas formation and mineral precipitation and their inter-related effects on permeability and reactivity have not been developed. Geochemistry in granular iron PRBs continually evolves as iron materials contact groundwater containing aqueous and gaseous components. The coupled and evolving geochemical interactions, along with groundwater flow and transport, are difficult to understand intuitively without © 2012 American Chemical Society

help of quantitative analysis tools such as reactive transport models. The reactive transport model MIN3P14 is applicable to many geochemical problems, involving kinetically controlled redox and mineral dissolution/precipitation reactions, along with equilibrium hydrolysis, aqueous complexation, ion exchange, and surface complexation reactions. MIN3P includes formulations to describe the formation and collapse of gas bubbles in response to changes in dissolved gas concentrations, entrapment of gas bubbles, and permeability changes as a function of gas saturation.15 Jeen et al.16 developed a version of MIN3P that includes an iron reactivity update option with secondary mineral precipitation in iron PRBs. However, Jeen et al.16 did not include the effect of hydrogen gas accumulation for the calculation of permeability changes in iron materials and noted a significant discrepancy between the measured and simulated hydraulic conductivity. The MIN3P model, enhanced for this study, combined the two previous versions of the model (i.e., Amos and Mayer15 and Jeen et al.16) to incorporate both gas bubble formation and iron reactivity loss due to secondary mineral precipitation, which result in permeability and reactivity changes in iron PRBs. The combined model was applied to an iron column, which was previously studied for the treatment of trichlorReceived: Revised: Accepted: Published: 6742

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oethene (TCE) in the presence of dissolved CaCO3.16,17 The purpose of the simulation presented here was to capture the principal physical and chemical characteristics of the iron column observed over time and specifically to quantitatively evaluate the combined effects of gas bubble production and secondary mineral formation on the evolution of hydraulic conductivity over time. Although the effects of gas bubble formation in granular iron columns have been previously identified, these effects have not been quantitatively assessed in an integrated framework where coupled physical and geochemical changes can be evaluated over time and space. Given the potential importance of gas bubble formation and the interaction between bubble formation and secondary mineral precipitation on the long-term performance of granular iron PRBs, a thorough quantitative assessment is warranted. The model will also have broader applications where gas formation and mineral precipitation are important geochemical processes in groundwater systems.

treatment of chlorinated organics6,16,25 or Cr(VI)26 in the presence of dissolved CaCO3. Integrated Model Formulation. Here, we integrate the model formulations of Amos and Mayer15 and Jeen et al.16 to investigate the combined effects of gas bubble formation and declining iron reactivity on the performance of PRB systems. In general, the model formulations are independent; however, both formulations affect the hydraulic conductivity of the system. The formation and dissolution of gas bubbles is not expected to directly affect iron reactivity. With respect to gas bubble formation, MIN3P describes the relatively permeability with respect to the saturation of the aqueous phase: k ra = Sea l(1 − [1 − Sea1/ m]m )2

where l and m are soil hydraulic function parameters and Sea is the effective gas phase saturation.27 Changes to hydraulic conductivity due to porosity changes as a result of secondary mineral precipitation and iron dissolution are updated based on a normalized version of the Kozeny− Carman relationship:28

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MODEL FORMULATION Reactive Transport Model. The general-purpose numerical model MIN3P was developed for multicomponent reactive transport simulations in variably saturated porous media.14 MIN3P employs a global implicit solution approach,18,19 which enforces a global mass balance between solid, surface, dissolved, and gaseous species. It thus facilitates the investigation of the interactions of reaction and transport processes between various phases. MIN3P has been previously applied to an iron PRB near Elizabeth City, North Carolina,20 and other PRB systems.21−23 Amos and Mayer15 enhanced MIN3P to simulate bubble growth and contraction due to in situ gas production or consumption, bubble entrapment due to water table rise and subsequent re-equilibration of the bubble with ambient groundwater, and permeability changes due to trapped gasphase saturation. The MIN3P gas bubble formulation followed the work of Cirpka and Kitanidis24 to incorporate gas saturation changes as a result of changes in dissolved gas partial pressures and hydrostatic pressure into the multicomponent framework of MIN3P. The MIN3P bubble model was used to simulate gas bubble formation due to biogenic methane production and gas bubble entrapment near the water table in a petroleum contaminated aquifer.15 Jeen et al.16 modified MIN3P to incorporate the declining reactivity of iron resulting from accumulation of secondary precipitates. Jeen et al.16 used an empirical formula (eq 1) relating the decrease in iron reactivity to the accumulation of secondary minerals, and modified the kinetic expressions of MIN3P accordingly: S(x , t ) = S0exp( −∑ αiφi(x , t )) i

(2)

⎡ ϕ3 ⎤t ⎡ (1 − ϕ)2 ⎤initial k rp = ⎢ ⎥ ⎥⎢ ⎣ (1 − ϕ)2 ⎦ ⎣ ϕ3 ⎦

(3)

where ϕ is the porosity (-). The overall influence on hydraulic conductivity is determined as a product of the two relative permeabilities:

kt = ki·k ra·k rp

(4) −1

t

where k is the hydraulic conductivity at time t (m s ), and ki is the initial saturated hydraulic conductivity (m s−1). The model updates hydraulic conductivity at the end of each time step based on updated values for gas phase saturation and porosity changes due to changes in mineral volume fractions of primary and secondary minerals. Gas Phase Formation and Gas Discharge. The formulation of Amos and Mayer15 simulates the formation and contraction of gas bubbles but not discrete gas discharge. To date, no easily implemented theoretical formulation for transport of gas bubbles due to capillary and buoyancy forces within porous media is known. Amos and Mayer29 used an empirically derived formulation to describe transport of gas bubbles due to capillary and buoyancy forces within porous media. However, due to the nature of the formulation, empirically derived constants are required that are dependent on the properties of the porous media and are not readily available. Here, an alternate formulation was implemented that allows gas discharge from a single model cell when a specific maximum gas saturation is approached:

(1)

⎡⎛ S ⎞ g − 1⎟⎟ , R g = kg max⎢⎜⎜ ⎢⎣⎝ Sg,max ⎠

where S(x,t) is the reactive surface area of iron at a specific location along the flow path and time (m2 iron L−1 bulk), S0 is the initial reactive surface area of the iron (m2 iron L−1 bulk), αi is the proportionality constant for mineral phase i, and φi(x,t) is the volume fraction of mineral phase i at a specific location and time (m3 mineral m−3 bulk). Mineral volumes are calculated at each time step from the precipitated mineral masses (see eq 10 below) and densities of the mineral phases. The proportionality constant for a particular mineral phase represents the extent to which that mineral phase contributes to the loss in reactivity of iron. The modified MIN3P model reasonably reproduced the

⎤ 0⎥ ⎥⎦

(5)

where Rg is the degassing rate (mol LH2O−1 s−1), kg is the degassing rate constant (mol LH2O−1 s−1), Sg is the gas saturation (mgas3 mpore volume−3), Sg,max is the maximum gas saturation (mgas3 mpore volume−3), and the function max ensures an irreversible process. This formulation does not mechanistically reproduce the movement and expulsion of gases from the experimental system, but it does allow the experimental 6743

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the simulation was based on the maximum corrosion rates calculated from the laboratory-measured rates of gas generation.30 The initial reactive surface area, which was assumed to be same as the physical surface area measured by the Brunauer−Emmett−Teller (BET) method,32 was 6.80 × 103 m2 iron L−1 bulk. The source solution was purged with CO2 and N2 gases to maintain the pH close to neutral and also to remove oxygen.30 Henry’s law constants for N2 and CO2 are 6.45 × 10−4 mol L−1 atm−1 and 3.41 × 10−2 mol L−1 atm−1, respectively.33,34 TCE degradation was considered to occur according to

observation of gas expulsion to be represented in a quantitative manner. Reaction Network and Model Parameters. The integrated MIN3P code was applied to the observed data for one column that was initially described and simulated by Jeen et al.,16 with additional features of the integrated code examined against the observed behaviors, particularly with respect to gas formation and permeability changes. Column C is a 50 cm long granular iron column, which received 100 mg/L CaCO3 plus 10 mg/L trichloroethene (TCE) as the source solution for a period of 704 days (3056 pore volumes (PVs)). It contained commercially available granular iron (Connelly-GPM, Inc., Chicago, IL), with a grain size of 0.30−2.38 mm, which is the range of typical iron materials installed in the field.16 The flow rate of the column was 0.4 mL/min (Darcy velocity of 1.4 × 10−5 m s−1) resulting in the residence time of 350 min. The detailed column characteristics are provided in Table S1 (Supporting Information) of Jeen et al.30 Briefly, as the source solution was provided to the column and contacted the iron material, carbonate precipitates formed as a result of the changing geochemical conditions. Carbonate precipitates caused a decrease in the reactivity of the iron and more importantly spatially and temporally varying reactivity loss resulted in migration of mineral precipitation fronts, as well as migration of other dissolved constituents such as TCE, alkalinity, calcium, and dissolved iron. Hydraulic conductivities gradually decreased over time as carbonate minerals accumulated. However, permeability loss due to mineral precipitation alone could not fully account for the observed decrease in hydraulic conductivity.30 Experimental and analytical methods for the hydraulic and geochemical parameters are described in Jeen et al.30 The reaction network and model parameters related to mineral precipitation with declining reactivity of iron were the same as those in Jeen et al.16 The fundamental corrosion reaction occurring in the granular iron column is iron corrosion with water according to the following reaction: 0

Fe (s) + 2H 2O → Fe

2+

+ H 2(aq) + 2OH

−

Fe0(s) + 0.3448C2HCl3 + H+ → Fe2 + + 0.0172C2H 2Cl 2 + 0.3275C2H4 + Cl−

with the mixed-order kinetic expression: d[TCE] [TCE] = −k SA − TCE − Fe0·S(x , t ) dt K1/2 + [TCE]

R H2O − Fe

where kSA−TCE−Fe is the rate constant of TCE normalized to iron surface area (mol m−2 iron s−1), [TCE ] is the activity of TCE (mol L−1 H2O), and K1/2 is the TCE concentration at which the transformation rate is half the maximum rate (mol L−1 H2O). Based on previous mineralogical studies,17 aragonite and Fe2(OH)2CO3 are considered the primary carbonate phases in this system. As such, three mineral species (aragonite, Fe2(OH)2CO3(s), and Fe(OH)2(am)) were included for mineral precipitation reactions (see Table S4 of the Supporting Information in Jeen et al.,16 for reaction stoichiometries and equilibrium constants), with the following kinetic expressions: ⎧⎡ ⎡ ⎛ IAPm ⎞−1⎤⎤ ⎪ R im = max⎨⎢keff, i⎢1 − ⎜ mi ⎟ ⎥⎥ , ⎪⎢⎣ ⎢⎣ ⎝ K i ⎠ ⎥⎦⎥⎦ ⎩

⎫ ⎪ 0⎬ ⎪ ⎭

⎫ ⎪ 0⎬ ⎪ ⎭

(10)

where keff,i is an effective rate constant for the precipitation of mineral phase i (mol L−1 H2O s−1), IAPmi is the ion activity product, and Kmi is the corresponding equilibrium constant for mineral dissolution−precipitation reactions. Jeen et al.16 show that dissolution of secondary precipitates is not an important process in this system. Reaction rate constants and proportionality constants for secondary minerals are the same as in Jeen et al.16 and are summarized in Table 1. The 0.5 m long column was discretized using 0.01 m intervals, giving a total of 51 grid points. The flow system was modeled as a variably saturated system with a second type boundary (specified flux) at the influent end and first type boundary (specified head) at the effluent end. The average flow rate for the column was used for the specified flux through the column. Physical parameters used in the simulation are summarized in Table 1. Eleven aqueous components (Ca2+, Cl−, CO32‑, Fe2+, H+, H2(aq), TCE, cis-dichloroethene (cis-DCE), vinyl chloride (VC), ethene, and H2O) and three gases (CO2, N2, and H2) were included to describe the relevant chemical reactions. A total of 12 aqueous complexes (see Table S1 of the Supporting Information of Jeen et al.16) are also included for appropriate determination of mineral solubilities. More details on the reaction parameters and thermodynamic constants are provided in Jeen et al.16 The measured aqueous concentrations and calculated gas concentrations of the source water were used for the boundary conditions for the transport simulation. The

(6)

⎧ ⎡ ⎪ = −max⎨⎢k SA − H2O − Fe0·S(x , t ) ⎪⎢ ⎩⎣ ⎛ IAPH2O − Fe0 ⎞⎤ ⎜⎜1 − ⎟⎥ , K H2O − Fe0 ⎟⎠⎥⎦ ⎝

(9)

0

A Henry’s law constant of 7.515 × 10−4 mol L−1 atm−1 was used to describe equilibration of hydrogen gas between the pore water and the gas bubbles.7 The rate expression for iron corrosion with water is represented by a first-order dependence on iron surface area, and it is assumed that the reaction progress becomes inhibited when equilibrium conditions are approached:

0

(8)

(7)

where kSA−H2O−Fe0 is the rate constant of iron corrosion normalized to iron surface area (mol m−2 iron s−1), IAPH2O−Fe0 is the ion activity product, and KH2O−Fe0 is the equilibrium constant (log KH2O−Fe0 = −11.78) for iron corrosion reaction. As noted by Devlin,31 the first-order dependence on iron surface area is a simplification. The initial iron corrosion rate in 6744

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Table 1. Reactive Transport Model Parameters reaction rate (k) and proportionality constants (α) log kSA−H2O−Fe0 (mol m−2 iron s−1) log kSA−TCE−Fe0 (mol m−2 iron s−1) K1/2 (mol L−1 H2O)

physical parameters

−10.70

column length (m)

0.50

−10.95

porosity (-)

0.55

1.83 × 10−5

log keff,i (mol L−1 H2O s−1) CaCO3(s) (aragonite) −7.44 Fe2(OH)2CO3(s)

−10.89

Fe(OH)2(am)

−8.68

α1: CaCO3(s)

85.0

α2: Fe2(OH)2CO3(s)

5.0

0

Fe volume fraction (-)

0.45

hydraulic conductivity (m s−1)

1.0 × 10−4 0.20

maximum gas phase saturation prior to degassing longitudinal dispersivity (m) diffusion coefficient − aqueous phase (m2 s−1) diffusion coefficient − gas phase (m2 s−1) flow rate (Darcy flux) (m s−1 ) running time (days)

9.9 × 10−4 1.5 × 10−9 2.0 × 10−5 1.4 × 10−5 704

Figure 1. Measured degassing rate and simulated degassing rates for CO2, N2, and H2 gases.

period of autoreduction37 to remove Fe(III) phases from the granular iron surfaces. Thus, it took time to reach the maximum gas generation rate (about 50 days) before the pre-existing passive oxides are removed from the iron surfaces. The simulation used the maximum gas generation rate as the initial iron corrosion rate; thus, there is a discrepancy between measured and simulated degassing rate at early times (Figure 1). This discrepancy also influenced the simulated hydraulic conductivity (see Figure 5). The spatial distribution of gas entrapment evolved over time (Figure 2). At 50 days, hydrogen gas formed from iron

initial conditions for the transport simulation were specified as several orders of magnitude lower concentrations for each constituent, relative to the expected concentrations, because the initial conditions affected the simulations only at a very early time. The reaction network specified in this study only encompasses abiotic reactions (e.g., iron corrosion, gas formation, and carbonate mineral precipitation); thus, application of the model to describe the evolution of fieldbased installation of granular iron, particularly when other biogeochemical reactions, such as microbial sulfate reduction, are important processes, would require refinement of the conceptual model and adjustment of model parameters.

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RESULTS AND DISCUSSION Gas Formation and Degassing. Jeen et al.16 reported enhanced iron corrosion rates in the presence of dissolved carbonate species, which is consistent with previously reported results.9,10,35,36 Upon contact with the incoming carbonated source water, gas bubbles were observed to form on the interior walls of the columns, with occasional bubbles appearing in the effluent line. Gas bubbles in the effluent line were trapped in a sealed tube to measure the rate of gas generation. At later times, passivation of iron was indicated by a decrease in the measured gas generation rate, which indicates the average value over the entire length of the column. Simulated degassing rates for CO2, N2, and H2 indicate that the primary component of the gases collected in the effluent line is H2 until about 350 days (Figure 1). As the iron is passivated due to mineral precipitation, the iron corrosion rate decreased significantly, as indicated by the decrease in H2 degassing rate after 350 days. After 350 days, degassing of N2 gas is the most significant contributor to the total degassing rate. CO2 is a minor contributor to the total degassing rate throughout the experiment, due to its relatively high solubility. The simulation generally reproduces behavior that is consistent with the observed gas generation in the column, which is primarily governed by the decreasing rate of hydrogen gas generation over time (Figure 1). Note that the carbonated source water was provided to the column from the beginning of the experiment without having a

Figure 2. Simulated gas phase saturation along the length of the column at various times. For Day 0, the gas phase saturation throughout the column is zero.

corrosion occupies pore space up to the specified maximum gas phase saturation (i.e., 0.20) prior to degassing throughout the majority of the column. Observed gas saturations slightly exceed 0.20 as the degassing formulation does not strictly limit the saturation to 0.20 but only limits the rate of degassing as the maximum saturation is approached. As the reactivity of iron decreases due to mineral precipitation on the iron surfaces, the rate of hydrogen gas generation decreases, and thus, gas phase saturation is decreased at the influent end of the column (Figure 2). The position of the gas saturation front will be determined by the flow rate and the rate of hydrogen gas production. As the rate of gas production decreases due to iron passivation, the gas saturation front migrates further from the influent end of the column. By 704 days, a significant decrease in iron corrosion rate (almost ceased) was observed in the influent half of the column, and thus, the pore spaces previously occupied by hydrogen and nitrogen gas are filled by water (Figure 2). 6745

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Mineral Precipitation. As the geochemical conditions change to favor carbonate precipitation, carbonate minerals (aragonite and Fe2(OH)2CO3) precipitate beginning near the influent end. However, because the accumulation of secondary carbonate minerals in turn reduces the reactivity of iron in the location where carbonates accumulate (eq 1), the accumulation is spread over the entire length of the column over time rather than limited to the influent end. This pattern is important in that it prohibits complete clogging near the influent end and results in gradual increase of carbonate mineral accumulation over the entire length of the column (Figure 3). Although

The simulated total volume fractions of aragonite and Fe2(OH)2CO3 (total carbonates), averaged along the length of the column, compare well with total carbonate fractions determined from column studies (Supporting Information, Figure S1). Both simulated and measured total carbonate volume fractions show the relatively faster accumulation at early times and more gradual accumulation at later times, which demonstrate again the evolving nature of mineral accumulation and coupling between iron reactivity and mineral accumulation. The maximum porosity loss due to mineral precipitation is 15% (Supporting Information, Figure S2). Hydraulic Conductivity Changes. The changing distribution of hydraulic conductivity throughout the column and over time is determined by a combination of the gas-phase saturation (Figure 2), and the change in porosity due to secondary mineral precipitation (Supporting Information, Figure S2 and Figure 3). At early times (i.e., 50 days), there is minimal accumulation of carbonate minerals in the column and reduction in hydraulic conductivity is predominantly due to the increase in gas-phase saturation (Figure 4). At later times

Figure 4. Spatial distribution of hydraulic conductivity along the length of the column, simulated at various times.

(i.e., 704 days), carbonate minerals have accumulated throughout the column, the gas-phase saturation at the influent end of the column, up to 0.17 m, has reduced to zero, and the gas-phase saturation at the effluent end of the column remains near 20% (Figure 2). At this time, the reduction in hydraulic conductivity at the influent end of the column is due only to the reduction in porosity due to secondary mineral formation, whereas the decrease in hydraulic conductivity at the effluent end is due to a combination of the porosity decrease and the gas-phase saturation (Figure 4). There is an increase in hydraulic conductivity very close to the influent end (i.e., up to 0.01 m from the influent end; Figure 4). This increase is due to the enhanced porosity in this region (Supporting Information, Figure S2) resulting from iron dissolution and minimal carbonate precipitation. Simulations were conducted including only mineral precipitation, including only gas formation, and including both mineral precipitation and gas formation (Figure 5). The effect of porosity loss due to mineral precipitation on hydraulic conductivity is gradual and initially less significant than gas formation. The effect of hydrogen gas formation on hydraulic conductivity is most significant immediately after the source water is introduced into the column and continuously decreases as the iron reactivity decreases due to accumulation of carbonate minerals. The simulated combined effect of mineral precipitation and gas formation results in an immediate and significant decline in hydraulic conductivity primarily due to gas

Figure 3. Simulated volume fractions of (a) aragonite and (b) Fe2(OH)2CO3.

precise measurement of carbonate accumulation was not done for these columns, Wilkin et al.38 found a similar pattern of mineral accumulation in a field-scale barrier, which is consistent with the simulation results. Simulation results indicate that aragonite precipitates closer to the influent end, compared to Fe2(OH)2CO3, because of differences in solubility and rate constants (Table 1). These observations are consistent with mineralogical observations.17 Both of the carbonate minerals accumulated faster at early times, but more slowly at later times, indicating the decreasing reactivity of the Fe0 over time. The maximum volume fractions of aragonite and Fe2(OH)2CO3 by 704 days were 0.036 and 0.078, respectively. The accumulation of Fe2(OH)2CO3 was greater than the accumulation of aragonite in terms of volume fraction, partly due to difference in density (2.95 for aragonite vs. 3.59 g cm−3 for Fe2(OH)2CO3).39,40 In the simulation, it was assumed that aragonite (α1 = 85.0; Table 1) is the major contributor to the reactivity loss rather than Fe2(OH)2CO3 (α2 = 5.0; Table 1). The proportionality constants were determined by fitting to experimental data16 and are consistent with mineralogical observations.17 6746

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average value over the first few days. Thus, the effect of the initial buildup of gas bubbles during the setup of the column with deoxygenated deionized water might be missed. In the simulation, it was assumed that there is no gas generation in the beginning (initial condition), and thus, after the simulation time starts, the hydraulic conductivity declines very quickly from the initial value of 1.0 × 10−4 m s−1 because of the bubble generation (see Figure 5). The maximum gas generation was observed at about 50 days in the laboratory (Figure 1); however, the simulation used that value as the initial iron corrosion rate. Therefore, the simulation does not capture all of the details in the early behavior. The overall magnitude of the decline in hydraulic conductivity was largely governed by formation of gas bubbles, where the maximum effect on hydraulic conductivity is determined by the predefined maximum gas-phase saturation prior to degassing. Simulations with different values of maximum gas phase saturation ranging from 0.05 to 0.20 showed minimum hydraulic conductivity values that vary by a factor of 2. The maximum gas saturation of 0.20 was chosen to be consistent with the calculation of maximum water saturation loss due to gas production (about 20% in Jeen et al.30). Reactivity Changes. Simulated solute concentrations are a function of reaction rate and the water flow velocity in the columns. Although hydraulic conductivity changes significantly both spatially and temporally, these changes have little effect on flow velocity due to the constant flux boundary conditions used for the column experiments and the simulations. Reaction kinetics are simulated in terms of a normalized reaction constant and reactive surface area (eqs 7 and 9). The changes in reactive surface area caused by accumulation of secondary minerals are reflected through eq 1, which result in the changes in reaction rates in a given control volume and time. The decrease in iron reactivity (reactive surface area) is related to the identity of each carbonate mineral through the proportionality constants (Table 1) and the volume fraction of each carbonate mineral at specific location and time (eq 1). As a result, the changes in reactive surface area over time are generally inversely related to the distribution of carbonate minerals and particularly aragonite because it has a greater effect on iron reactivity (compare Figures 3a and 6a). The simulations show that there is more than an order of magnitude decrease in reactive surface area throughout the majority of the column by 704 days. The spatial and temporal change in reactive surface area is incorporated in the TCE degradation rate (eq 9). The consequence of this change is reflected in the shape of TCE degradation profiles over time (Figure 6b). The region close to the influent end, where more carbonate minerals accumulated, shows only little degradation by 704 days (Figure 6b). On the other hand, passivation is less significant at the effluent end of the columns, and TCE degradation generally follows pseudofirst-order kinetics (concave shape). The simulated TCE profiles are generally consistent with the observed profiles over time. In the simulation, “reactive surface area” was used to express the reactivity of iron and thus provides a quantitative basis for representing decreased reactivity of iron. However, although the reactive surface area concept is convenient and useful way of representing reactivity, it has limited mechanistic basis.16 The simulation results provide a quantitative assessment of laboratory observations that indicate that gas bubble formation due to iron corrosion and hydrogen gas production have an

Figure 5. Simulated hydraulic conductivities under various simulation modes, compared to measured hydraulic conductivity. Hydraulic conductivity is the harmonic mean over the entire length of the column.

formation at early times and a gradual decrease over time, primarily due to mineral precipitation. At very late times (i.e., greater than 600 days), the decline in gas generation coupled with the minimal increase in mineral precipitation results in a relatively stable hydraulic conductivity in the simulation and a slight increase in hydraulic conductivity in the laboratory experiment (Figure 5). The hydraulic conductivity rebound is not manifested in the simulation because the simulated increase in mineral accumulation was more rapid than measured in the laboratory experiment (Supporting Information, Figure S1). Although the simulation reproduces the general trends in hydraulic conductivity observed in the laboratory (e.g., moderate decline in hydraulic conductivity at intermediate to late times due to gradual increase of mineral precipitation), it does not precisely match the detailed trends observed. Particularly, before 200 days, although the simulation shows the immediate and substantial decline in hydraulic conductivity due to gas formation, the measured hydraulic conductivity varies significantly and then declines rather gradually after 100 days. This discrepancy is partially due to the uncertainties inherent in the measured hydraulic conductivity. The initial head difference between the inlet and outlet of the column was only a few centimeters across the 50 cm long column, and thus, a slight change in the head measurement could result in a substantial difference in the calculated hydraulic conductivity. The hydraulic conductivities (Figure 5) are the harmonic means along the entire length of the column, because the measured hydraulic conductivities represent the average values across the entire length of the column. The overall hydraulic conductivity through the column is dominated by the portion with the lowest hydraulic conductivity. Thus, a subtle change in permeability in the very narrow area of the column (e.g., near the inlet) may significantly affect the measured hydraulic conductivity. Also, frequent escapes of gas bubbles through the effluent tube and gas entrapment inside the manometer tubes made it difficult to take precise readings. This is somewhat consistent with the earlier study of Zhang and Gillham.12 In their 10 cm columns receiving 300 mg/L CaCO3, there were order of magnitude fluctuations in the calculated hydraulic conductivity values, and there were no discernible changes in hydraulic conductivity over about 1000 pore volumes of the experiments. The measurement of hydraulic conductivity began after the TCE + CaCO3 solution was supplied to the column, and the initial hydraulic conductivity in the simulation was set to be the 6747

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ACKNOWLEDGMENTS Funding for this research was provided through the NSERC/ DuPont/EnviroMetal Industrial Research Chair held by R. W. Gillham, a Canada Research Chair held by D. W. Blowes, and an NSERC postdoctoral fellowship awarded to R. T. Amos. We thank Wayne Noble for the technical assistance in the laboratory.

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Figure 6. (a) Reactive surface area along the distance of the column at various times, calculated from the simulated volume fractions of aragonite and Fe2(OH)2CO3 (Figure 3) and eq 1. (b) Simulated and measured TCE concentrations along the length of the column at various times.

important effect on the permeability of granular iron treatment systems. The simulation results indicate that a majority of the observed permeability loss in the iron material was due to gas bubble formation and to a lesser extent mineral precipitation. In addition, the coupled effects of bubble formation and iron reactivity are demonstrated, with the model reproducing the observed trends in granular iron reactivity and hydraulic conductivity, and the changes in these parameters over time and space. The simulation results also demonstrate the utility of reactive transport models for investigating multiple coupled physical and geochemical processes. Furthermore, the model provides a quantitative tool for incorporating the long-term effects of reactivity and permeability loss in the design of iron PRBs.

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ASSOCIATED CONTENT

S Supporting Information *

Figures showing simulated and measured total carbonate volume fractions over time and spatial distribution of porosity along the length of the column, simulated at various times. This material is available free of charge via the Internet at http:// pubs.acs.org.

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REFERENCES

AUTHOR INFORMATION

Corresponding Author

*Phone: +1 (519) 888-4567; e-mail: [email protected]. Notes

The authors declare no competing financial interest. 6748

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