A novel concept, the Fe0 fracture reactive barrier (Fe0 FRB), is proposed to clean up chlorinated solvent pollution of groundwater in a chalk aquifer. Iron particles, suspended in a viscous biodegradable gel, can be injected into selected fractures to create an extended reactive zone of partly iron-filled fractures. To evaluate the feasibility of Fe0 FRB as a remediation strategy, we conducted numerical modeling simulations to assess the treatment performance of an Fe0 FRB in a hypothetical chalk aquifer. The assessment was carried out using a numerical model for flow and solute transport in a discretely fractured porous medium coupled with an analytical expression representing degradation by iron. The hypothetical chalk aquifer was represented by a three-dimensional discrete fracture network model that was developed using data from a number of chalk sites. Trichloroethylene reactive transport in the Fe0 FRB and mass exchange of solute between fractures and the porous matrix were fully accounted for in the model. This modeling revealed that the success of the remediation technology lies in creating a highly reactive Fe0 FRB without reducing fracture permeability, which could lead to the plume being diverted around the barrier. A parametric study of various design parameters for the Fe0 FRB suggested that high treatment efficiency could be achieved by employing highly reactive nanoscale iron or by using a high proportion of microscale iron fill and fracture enlargement. The model study also provided some preliminary conclusions on sensitive design parameters of an Fe0 FRB such as the proportion of iron fill, the size of the FRB, and the amount of fracture enlargement. A preliminary analysis suggests that an Fe0 FRB containing a small amount of highly reactive nanoscale iron could provide satisfactory treatment for up to 50 years, depending on contaminant mass flux through the barrier.
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 For decades, dense nonaqueous phase liquids (DNAPLs), such as chlorinated solvents, have been widely used in industry as degreasers and dry cleaning agents [Pankow and Cherry, 1996]. Accidental spillage and inappropriate disposal of these chemicals are serious threats to groundwater quality. In industrialized areas, such as Coventry and Birmingham, England, widespread chlorinated solvent contamination by tetrachloroethylene (PCE) and trichloroethylene (TCE) have been found; PCE and TCE concentrations over 1 μg/L were detected in 40% and 73%, respectively, of 101 deep abstraction wells in fractured sandstone aquifers [Rivett et al., 1990a; Burston et al., 1993]. PCE and TCE has been the UK's predominant industrial solvents and its use peaked in the early 1970s, the overall production of TCE and PCE reached over 3.3 million tons by 1990 [Rivett et al., 1990b]. Given that fractured aquifers contribute ∼85% UK groundwater supply [e.g., Downing, 1993; U.K. Groundwater Forum, 1998], PCE and TCE have been reported to be major contaminant sources for a number of sites. For example, at Sawston, southwest of Cambridge, England, a public supply well with a license to abstract 6,800 m3/d from the chalk aquifer was taken out of supply in 1983, when PCE was detected at up to 130 μg/L in the groundwater. The main source of chlorinated solvents was the Eastern Counties Leather tannery, 2 km south east of the water supply well [Lawrence and Foster, 1991; Dames and Moore, 1999].
 The Chalk is the most important aquifer in the UK and contributes ∼60% of the groundwater used in England and Wales [e.g., Downing, 1993; U.K. Groundwater Forum, 1998]. The Chalk usually behaves as a dual-porosity medium, with advection occurring in the fractures while water stored in the highly porous matrix blocks is largely immobile. Solute exchange between mobile fracture and immobile matrix waters is by molecular diffusion [e.g., Price et al., 1993; Younger and Elliot, 1995].
 Chlorinated solvents are denser and less viscous than water. These physical properties imply that they can penetrate aquifers rapidly and deeply in their nonaqueous form. Theoretical study of DNAPL transport in fractures [Kueper and McWhorter, 1991] and field observations in fractured aquifers [e.g., Lawrence and Foster, 1991; U.S. Geological Survey, 2000] suggest that DNAPLs can penetrate many tens of meters and create dissolved chlorinated solvent plumes well below the water table. Chlorinated solvents do not naturally attenuate at any appreciable rate in many subsurface environments, and their low but significant solubility means that the risk to water resources will persist for decades or centuries as they slowly dissolve.
 Zero-valent iron (Fe0) has been shown to be a promising material for the in situ remediation of groundwater contaminants such as chlorinated solvents [Gillham and O'Hannesin, 1994; Matheson and Tratnyek, 1994; O'Hannesin and Gillham, 1998]. In situ treatment of chlorinated solvent plumes using zero-valent iron permeable reactive barriers (Fe0 PRBs) has, on the basis of 10 years of experience, been shown to be an efficient and cost-effective remediation strategy. Technologies have been developed and used for the installation of Fe0 PRBs in aquifers composed of excavatable materials. Fe0 PRBs have been installed at more than 90 chlorinated solvent sites worldwide [O'Hannesin, 2003]. However, the use of this technology at fractured rock sites has not received as much interest. The engineering challenges and high costs of constructing Fe0 PRBs in deep and/or fractured rock aquifers have discouraged their use. However, Marcus and Bonds  and Glazier et al.  demonstrated that Fe0 particles (microscale or nanoscale) could be suspended in a degradable viscous liquid or in potable water, and injected into selected fractures from boreholes. This technique could be used to create an Fe0 fracture reactive barrier (Fe0 FRB) as shown schematically in Figure 1a. There have not been any detailed field trials or systematic studies of the design issues of such barriers.
 The goal of this modeling study is to evaluate the feasibility of the Fe0 FRB as a remediation technology for chlorinated solvent plumes in fractured aquifers. The approach is to conduct a parametric study of the importance of a range of factors such as the proportion of Fe0 fill, the amount of fracture enlargement, the size of the FRB relative to source size, and the reactivity of the Fe0 particles by numerical modeling. We have constructed a hypothetical site, which is based on representative data from a number of chalk sites in England with similar hydrogeological properties to the Sawston site. The results lead to some preliminary conclusions on the optimal design of an Fe0 FRB remediation system.
2. Methods and Parameter Values
 HydroGeoSphere is a fully integrated surface and subsurface flow and transport code [Therrien et al., 2004]. The subsurface module, which is used for this study, is based on the three-dimensional (3-D) subsurface flow and transport code FRAC3DVS [Therrien and Sudicky, 1996]. FRAC3DVS is an efficient and robust numerical model that solves the three-dimensional variably saturated subsurface flow and solute transport equations in nonfractured or discretely fractured media. For discretely fractured media, the three-dimensional system is composed of a porous matrix, discretized with three-dimensional elements and a fracture network represented by three orthogonal sets of fractures, with individual fractures discretized with two-dimensional planar elements. FRAC3DVS uses a standard time-marching Galerkin finite element approach to solve the flow and transport equations. A finite difference discretization for both groundwater flow and solute transport can also be mimicked through the use of influence coefficients [e.g., Huyakorn et al., 1984]. The use of a preconditioned iterative solver and adaptive time stepping allows for the fast solution of matrix equations with tens to hundreds of thousands of unknowns. Fracture networks can be created in HydroGeoSphere by either a built-in fracture generator, or deterministically by inputting individual fracture geometry. Transport processes including advection, dispersion and sorption in both fractures and the porous matrix are fully accounted for, as well as solute exchange between fractures and the porous matrix. For reactive components, separate first-order reaction rates can be specified in fractures and the porous matrix.
2.2. Representing Degradation by Fe0
 If a biodegradable fluid is used to suspend iron in an injection slurry, the resulting Fe0 FRB is likely to consist of a network of predominantly horizontal fractures partly filled with iron that adheres to the lower fracture face (Figure 1b). Modeling of reactive transport in such an Fe0 FRB needs a discrete fracture network model, which can account for all the processes in each partly iron-filled fracture, including the reaction in the open fracture, degradation processes in the iron layer, and mass transfer of solute between the open fracture and the iron layer. By assuming that all reaction processes in a partly filled fracture can be represented by a single first-order degradation rate in the water of the open fracture, we avoid the need to modify the computational framework of HydroGeoSphere to include the Fe0 layer as a third domain. This has been successfully done as explained below.
 An analytical solution for representing solute transport and degradation in a single partly Fe0 filled fracture has been developed by Cai et al.  and is only summarized briefly here. Reaction in the open fracture, the degradation in the iron layer, and the mass transfer of solutes between the open fracture and the iron layer were included in an analytical expression. This enables all three processes to be represented by a single lumped parameter. The development assumes first-order degradation in the open fracture and the iron layer, no advective transport in the iron layer, and diffusive transport between the open fracture and the iron layer. These assumptions ensure that the resulting lumped parameter is a first-order rate which represents steady state degradation by the iron layer in terms of the degradation in the water of the open fracture, and which is expressed by Cai et al.  as
The lumped rate parameter λlumped (T−1) is the sum of the first-order degradation rate coefficient in the open fracture (λf, T−1) and the mass transfer rate coefficient from the open fracture into the iron layer (Kl,iron, T−1); λiron is a first-order degradation rate coefficient (T−1) within the iron; θiron is the iron porosity (dimensionless); D′iron is the effective diffusion coefficient in the iron layer (D′iron = τironD*, L2 T−1); τiron is the tortuosity (dimensionless); D* is the free solution diffusion coefficient (L2 T−1); Riron and Rf are the retardation factors for the iron and fracture (dimensionless), respectively; d is the iron thickness (L) and 2b is the open fracture aperture (L).
 The analytical model can be used on its own to represent reactive solute transport in a single fracture in a closed system with known hydraulic boundaries, such as the laboratory experiment interpreted by Cai  and Cai et al. . However, in a field-scale Fe0 FRB, the Fe0 will be present in multiple fractures, the presence of the Fe0 will alter the flow patterns, and the analytical model cannot be used on its own. The advantage of the analytical solution is that the lumped parameter determined from it can be directly incorporated into HydroGeoSphere, and applied to those parts of the fracture network containing Fe0. By this approach, the iron layer in the fractures does not need to be explicitly represented in the fracture network model, enabling the application of HydroGeoSphere to simulate contaminant transport in an Fe0 FRB.
2.3. Development of a Representative Aquifer Scenario
 In order to simulate the performance of Fe0 FRBs in chalk aquifers, we need to create a numerical model that is representative of some polluted sites. This requires the generation of a realistic fracture network and the selection of appropriate values for parameters such as fracture aperture, porosity and properties of the iron.
2.3.1. Generation of the Fracture Network
 If there are sufficient data available, a discrete fracture network can be generally characterized by statistical distributions that describe all aspects of the network, from the broad classification of fractures into similar sets (e.g., horizontal or vertical fractures, fracture intensity etc.), to more specific classifications such as the location, areal extent and aperture of the fractures [e.g., Reynolds and Kueper, 2003]. In practice, these data can be obtained by a combination of fracture mapping in outcrops and core holes, down-hole video and caliper logs, and hydraulic testing [Nativ et al., 2003]. The statistical characterization of a fracture network can provide parameter values such as fracture density, distribution of fractures, fracture length and aperture distributions, and a discrete fracture network can be created by HydroGeoSphere's inbuilt fracture generator. For the cases where the statistical parameters of the fracture network are not available but the geometry of a particular fracture network is available, e.g., from mapping an outcrop, a realistic fracture network can be created in HydroGeoSphere by inputting fracture coordinates deterministically.
 Although there have been many hydrogeological studies of the Chalk to date [Downing et al., 1993], none has provided the highly detailed fracture data that is available from hard rock repository investigations such as those at Aspo in Sweden [e.g., Gylling et al., 1998; Selroos et al., 2002]. Because of a lack of statistical data, a single outcrop of the Chalk at Play Hatch Quarry in the south of England [Bloomfield, 1996] was the primary source of data used to construct a representative 3-D fracture network for this study. The coordinates of the bedding fractures and faults from this 25 × 8 m outcrop were determined from the mapped section (Figure 2) and were adapted into an orthogonal fracture network as required for HydroGeoSphere. The data on horizontal fractures and one of two sets of vertical fractures in this 2-D outcrop were then transformed into a 25 × 25 × 8 m 3-D network as follows. As bedding plane fractures are believed to provide the major pathways for flow and solute transport in the chalk [Reeves, 1979], the mapped horizontal fractures were transferred directly to HydroGeoSphere. Each horizontal fracture was assumed to be a square in the x–y plane, with the x and z location as measured in the outcrop. The y positions were randomly generated; any part of a horizontal fracture that fell outside of the domain was wrapped to appear on the other side. Some extra horizontal fractures were also added to the 3-D domain to ensure the horizontal fracture density was similar in all planes to that observed in the 2-D outcrop. The domain was assumed to have two sets of vertical fractures, one in each of the x–z and y–z planes. The vertical fractures in the outcrop have a fracture density of 4 fractures/25 m and fracture lengths from 1.2 to 5 m. These parameters were used for both sets by assuming a uniform distribution of fracture length, and each fracture was again assumed to be a square in the vertical plane. The vertical fracture sets were created by HydroGeoSphere using the built-in fracture generator.
2.3.2. Selection of Values for Parameters
 The aperture data from Play Hatch Quarry outcrop were not used for characterizing the model, because only some of the fracture apertures were reported. Also, the fractures at the outcrop are likely to be enlarged by overburden removal and weathering and so may not represent the fractures at depth [Reeves, 1979; Younger and Elliot, 1995]. A mean fracture aperture of 0.5 mm was selected on the basis of a study of a number of Chalk sites in England where the fracture apertures were estimated from radon activities in the groundwater samples [Younger and Elliot, 1995]. The values of the hydraulic parameters for the rock matrix (i.e., hydraulic conductivity, porosity and tortuosity) were chosen from previous studies in England and Israel [Price et al., 1993; Little et al., 1996; Nativ et al., 2003], and are listed in Table 1. The median hydraulic head gradient of 7‰ for the domain was based on field observations of regional gradients at three chalk sites in England [Dames and Moore, 1999; Schurch and Buckley, 2002; Schurch et al., 2004]. The aquifer storage coefficient, with a median of 0.008, was determined from data gathered at 286 pump tests in the unconfined chalk aquifers in England [MacDonald and Allen, 2001].
 The value for dispersivity for the fracture network is the least rigorous, as few, if any, field-scale observations of hydrodynamic dispersion in Chalk fractures are available. Gelhar et al.  suggested that the dispersivities in porous and fractured media are similar, and that the longitudinal dispersivity in a 25 m long fractured aquifer is in the range ∼0.5–5 m. A longitudinal dispersivity of 0.5 m was selected for the fracture network. The reviewed and selected values for the parameters for the synthetic fractured aquifer are listed in Table 1. The parameter values selected for the Fe0 and TCE are summarized in Table 2, together with the references from which they are derived.
Table 1. Summary of the Hydraulic Parameter Values Adopted for the Fracture Domain
The same values are used in the nanoscale iron cases, as the selected porosity (0.5) for the nanoscale iron and its estimated tortuosity (0.4) are consistent with lab observations of nanoparticles (porosity, 0.4–0.6; and tortuosity, 0.3–0.44) [Haugaard and Livbjerg, 1998; Lehmann et al., 2002].
TCE sorption to iron is not considered. Sorption to iron particles is an important mechanism for iron dechlorination [Burris et al., 1995]. However, the TCE degradation rate used here has accounted for the effects of both sorption and reduction.
 To implement the hypothetical site in HydroGeoSphere, the aquifer domain of 25 m by 25 m by 8 m was discretized into 304704 3-D elements (64 by 69 by 69 in the x, y and z directions respectively) for the porous matrix. The finer discretization in the z direction ensured there was at least one gridline between each pair of horizontal fractures. The total number of rectangular plane elements representing all fractures is 39669. Constant head inflow (x = 0) and outflow (x = 25) boundaries provided the head gradient shown in Table 1. The remaining boundaries are impermeable.
2.5. TCE Source Term and Initial Conditions
 A constant source of dissolved TCE, which extended from 10 to15 m in the y direction and from 3 to 5 m in the z direction, was specified on the inflow boundary at x = 0. Initially, TCE concentrations were set to zero throughout the domain. In the initial simulation, a steady state flow field was first established, and then a TCE plume was allowed to migrate untreated for a period of 10 years. The year 10 concentration distributions were then used as starting concentrations for all simulations of the Fe0 FRB simulations.
2.6. Scenarios Examined
 In order to evaluate treatment performance, a range of Fe0 FRB scenarios were simulated using HydroGeoSphere, coupled with the lumped parameter approach. All scenarios assume that a dissolved contaminant source (TCE) has developed in the fractured rock over a period of 10 years, at which time an Fe0 FRB is installed. Injection of the iron containing gel would displace the dissolved TCE plume from the fractures for a short period. The gel would be made with a degradable polymer with added enzymes such as those widely used to make drilling fluids and would degrade within a few weeks. Biomass clogging is not considered in this study, as we assume that bacterial growth will stop following depletion of the gel, and that the accumulated bacteria will gradually detach and be removed from the system. Once the gel had degraded, advection from the source, and back diffusion from the matrix, would quickly reestablish the plume. These transient effects were neglected in the modeling. The model is then run for an additional 10-year period of remediation, at the end of which the treatment performance is assessed.
 The scenarios are summarized in Table 3, and briefly described here. Case A investigates the effect of the proportion of the fracture aperture which contains iron. Cases B–D expand case A to investigate the effect of fracture enlargement and the percentage of iron fill. Cases E–F examine the effect of the size of the FRB, both in cross-sectional area and length. Cases G–H look at the effect of iron reactivity, comparing conventional iron with nanoscale particles.
A range of values is shown for the parameter which was varied for the runs in each scenario.
Cross-sectional area in the y–z plane of FRB expressed as a ratio to the cross-sectional area in the y–z plane of the source zone, AFRB/ASZ. The cross-sectional area of the source zone (ASZ) is 10 m2 (2 m by 5 m).
Distance from the source zone to the front of FRB.
Factor by which the total aperture (d + 2b) has been increased relative to the original value of 0.5 mm used in scenario A.
Proportion of the enlarged facture aperture which contains Fe0, d/(d + 2b).
Estimated by the highest values.
Reactivity of the Fe0, λiron,TCE.
In this case, the end of the FRB was kept at 15 m in the x direction, so the distance from the source zone to the front of the FRB varies with the length of FRB applied.
 Only the horizontal fractures in the FRB are assumed to be filled by iron, or to be enlarged if fracture enlargement techniques are applied. For the cases where the fractures in the FRB were fully filled by iron, the hydraulic conductivities of the fractures were estimated by the Kozeny-Carmen equation [Bear, 1972] for a mean iron grain size of 0.3 mm. For the cases where fractures are partly filled, a finer iron particle size (e.g., 30–100 μm) would be used to avoid the clogging of the fracture. Our study [Cai et al., 2006] of the hydraulic conductivity of the iron layer (estimated by Kozeny-Carmen) and the open fractures (estimated by the cubic law) in partly iron-filled factures showed that, for an iron particle ≤0.1 mm and open fracture aperture ≥0.1 mm, the ratios of hydraulic conductivity of the iron layer and the open fracture are <10−2. The results suggested that advective transport in the iron layer is insignificant compared to that in the open fracture, and that the assumption of diffusive transport within the iron layer is valid when the open fracture aperture is ≥0.1 mm. The larger iron particle size proposed in the fully iron-filled fracture case is intended to prevent flow from bypassing the filled fracture due to a significant reduction of fracture hydraulic conductivity.
3. Results and Discussions
3.1. Simulated Fracture Network and Initial Plume
 Given the lack of both 3-D information and statistical data on chalk fracture patterns, the intention was to generate a subjectively realistic fracture network. The simulated network contains 92 vertical and 38 horizontal fractures, and is illustrated in Figure 3. The longitudinal and cross sections of the simulated network capture the character of the outcrop shown in Figure 2. With the hydraulic parameters values listed in Table 1, a steady state flow simulation by HydroGeoSphere indicates that the flow rate through the domain is 1380 m3/yr. Thus the effective hydraulic conductivity of the network can be estimated to be ∼3 × 10−5 m s−1, which is in the range of 10−5–10−3 m s−1 reported from field observations in chalk aquifers [Price et al., 1993; Nativ et al., 2003].
 With the selected TCE parameters, untreated TCE transport (without Fe0 FRB) was simulated for a 10-year period, with initial TCE concentrations of zero everywhere except the source. By the end of the simulation solute transport in the domain is close to steady state, with a rate of change of mass stored of ∼1‰ per year. The resulting concentrations are presented in Figure 4. They show that TCE advective transport is limited to a few interconnected fractures, while the transport process in the porous matrix is dominated by diffusion exchange with the fractures. The TCE mass flux from the source zone is 21.1 kg/yr when a constant released concentration of 100 mg/L is applied from the source zone. Only ∼5% of the TCE flux into the domain over the 10 year period is stored in the porous matrix, and most of TCE mass (∼95%) has been carried out of this small domain by advection.
3.2. Amount of Iron Fill and Fracture Enlargement (Cases A–D)
 Once an Fe0 FRB is emplaced, the flow pattern in the fracture network will be altered because of changes in the fracture aperture. Although a thicker iron layer in a fracture provides more overall reactivity, it will decrease the effective permeability of the fracture. Because fracture conductivity is proportional to the square of the aperture, this could cause significant reductions in the flow capacity of the fracture. This could cause flow to bypass the filled fractures and the FRB, and potentially reduce the overall effectiveness. However, fracture enlargement techniques such as hydrofracturing could be used during Fe0 emplacement to maintain or expand the fracture openings [e.g., Marcus and Bonds, 1999]. This could reverse the effect of fracture clogging by increasing the transmissivity of the FRB, and potentially draw in more flow than was previously passing through the zone. Cases A–D were carried out to explore the effect of the proportion of Fe0 fill and the amount of fracture enlargement on the flow and treatment performance of an Fe0 FRB.
Figure 5 shows the effect of the open fracture aperture on the hydraulics of the Fe0 FRB. The range of fracture enlargements and amounts of Fe0 infill are expressed as ratios of the open (i.e., unfilled) apertures in the FRB after and before filling, i.e., 2bFRB,Fe/2bFRB,ini. The y axis is the proportion of the total flow through the domain which passes through the front face of the FRB. The simulations show that the flow into the FRB varies from ∼25% to ∼65% of the total flow over the range of cases tested. Note that the model might underestimate the proportion of the total flow that passes through the barrier. This is because the closeness of the lateral no-flow boundaries (the distance from the edges of the barrier to no flow boundaries is 7.5 m) might prevent as much convergence of flow as would occur in a field situation where the boundaries are further away. Nevertheless, the lowest flow was found for case A when 80% of initial fracture aperture is filled by iron (2bFRB,Fe/2bFRB,ini = 0.2), while the highest value was found in cases C and D when the amount of the fracture enlargement is sufficient to ensure that 2bFRB,Fe/2bFRB,ini is greater than 3. The flow into the FRB increases with the size of the open apertures, suggesting that fracture enlargement is essential to maintain or increase the effectiveness of the Fe0 FRB. Up to ∼50% of initial (i.e., undisturbed) flow into the FRB bypasses the FRB in case A, when high percentages of the aperture (≥60%) are filled by iron and there is no enlargement. Thus, if a high percentage of Fe0 fill is needed to achieve a desired level of treatment, fracture enlargement will be required. The amount of fracture enlargement can be determined by the fracture opening ratio and percentage of Fe0 fill as (2bFRB,Fe/2bFRB,ini)/(1-%Fe0 fill). A ratio of 2bFRB,Fe/2bFRB,ini of 3–4 times is sufficient to achieve the maximum flow into the FRB.
 The effects of Fe0 fill and fracture enlargement on treatment efficiency are shown in Figure 6a. Without fracture enlargement (case A), the TCE removal efficiency increases with the amount of iron fill and reaches a maximum of ∼20% when the fractures are 40–60% filled. Removal efficiency decreases with further increases of iron fill even though the lumped decay rate continues to increase (Figure 6b) because of flow bypassing the FRB as the iron fill reduces fracture transmissivity. Thus bypassing flow can have a significant effect on the success of the remediation strategy. These numerical investigations suggest that the iron fill should not exceed 60% of the fracture aperture if no fracture enlargement is employed during iron emplacement.
 When the horizontal fractures in the Fe0 FRB are enlarged by 2–8 times during iron emplacement (cases B–D), the trend of removal efficiency with the amount of iron fill is similar to that of case A (Figure 6a). High removal efficiency is found in the range of 40–80% iron fill, with the highest efficiency generally found at 60% fill. Fracture enlargement improves the performance of the Fe0 FRB and the maximum efficiency in case D (8 times fracture enlargement) is about 2.5 times that of case A (no enlargement). However the relative benefit decreases with successive doubling of the aperture, as the rate of increase in the lumped decay rate drops with increasing open fracture aperture (Figure 6b). These simulations suggest that fracture enlargement will play an important role in the success of the remediation technology. For the fracture network used in these simulations, a fracture enlargement of 4–8 times with ∼60% iron fill is optimum. Also, fully filling the fractures is not recommended since it diverts flows significantly and reduces the effectiveness of the Fe0 FRB.
 Brittle geologic media (i.e., chalk) usually exhibit good self-propping because irregularities along the fracture wall prevent closure [Schuring, 2002]. In some cases, however, the injection of a proppant may be desirable or required to maintain a certain aperture enhancement. We recognize that the presence of a proppant will, to a certain degree, reduce the permeability of what would be open water above the iron. For the purposes of this analysis, however, we elected to ignore that effect: the overall enhancement of barrier permeability resulting from hydrofracturing is more significant than the incremental decrease due to the presence of a proppant.
3.3. Size of the FRB (Cases E–F)
 As expected, the mass removal rate increases with the cross-sectional area of the FRB (Figure 7a, case E), with a large increase occurring as the FRB to the source zone area ratio (AFRB/ASZ) increases from 1 to 4 times, but with no significant increase thereafter. This limiting area ratio of 4 times may vary with the geometry of the fracture network and the location of the FRB. For example, an FRB with a smaller cross-sectional area could be positioned closer to source zone and still capture most of plume, since dispersion processes cause the plume to spread as it moves away from the source, as shown in Figures 4a and 4c.
 The length of the FRB in the direction of flow has a significant effect on the treatment efficiency (Figure 7b, case F). The removal rate increases more than 25% as the length of the FRB increases from 5 to 12.5 m for all fracture enlargements. The effect of increasing the length from 10 m to 12.5 m is not the same in all cases, only making a noticeable difference with a fracture enlargement factor of 2. Interpretation of these differences is difficult, because the fracture enlargement and the change of length of the FRB can alter the flow pattern in the surrounding fracture network domain as well as in the FRB. In theory, contaminant retention time in the FRB will increase as its length increases, resulting in higher removal efficiency as long as flow in the FRB remains unchanged. In general, the peak mass removal efficiency is found to be ∼75% for all the cases with fracture enlargement. Again, simulations show the fracture enlargement plays a vital role in enhancing the overall removal efficiency.
3.4. Iron Reactivity (Cases G–H)
 Recent studies of nanoscale zero-valent iron [e.g., Wang and Zhang, 1997; Zhang, 2003; Liu et al., 2005] suggest that its reactivity to chlorinated solvents can be 10–100 times higher than for iron filings [Johnson et al., 1996]. The high specific surface area (∼30 m2 g−1) and small particle size (1–100 nm) of nanoscale iron imply that only a small amount would be needed to create an effective FRB. Thus, in cases where fracture enlargement cannot be implemented, the use of nanoscale iron could overcome the problem of flow bypass caused by fracture clogging. A scoping study of the treatment of chlorinated solvent plumes in fractured aquifers has suggested that the use of highly reactive nanoscale iron is very effective [Glazier et al., 2003].
 In order to explore the effect of iron reactivity on FRB design, a nanoscale iron with reactivity to TCE of 120–480 d−1, which is 5–20 times higher than the reactivity used for previous simulations (λTCE, iron = 24 d−1), was simulated without fracture enlargement (case G). The simulations (Figure 8a) show the removal efficiency has been dramatically promoted by the high reactivity, with the maximum efficiency increased from ∼40% for iron filings (reactivity of 24 d−1) to ∼80% for nanoscale iron (480 d−1). Also for the increased iron reactivity, the maximum efficiency occurs at lower percentages of iron fill. Thus the maximum overall removal rate can be obtained by 20–40% of fill by nanoscale iron instead of 40–60% for iron filings, because the nanoscale iron achieves a higher lumped decay rate at lower proportions of fill (Figure 8b), and reduces the amount of flow that bypasses the FRB (Figure 5).
 The lumped degradation rate is greater than 30 d−1 with ∼20% nanoscale iron fill with reactivity greater than 240 d−1. With these degradation rates, 99% of the TCE flux into a partly iron-filled fracture is destroyed in less than 0.07 days. This would be equivalent to a nonsorbing solute traveling through a 10 m fracture at a flow velocity of ∼140 m/d. In a 10 m long FRB, the degradation rate in the fractures is rapid enough to remove all the mass entering, and the overall efficiency is determined by the efficiency of capture by the FRB. A low percentage of iron fill in the fracture means that it will maintain the amount of mass flux into the FRB and thus achieve a higher removal efficiency. Overall, these simulations suggest that nanoscale iron has great potential to improve the performance of the Fe0 FRB.
 Unlike the findings for the low iron reactivity FRB (λiron, TCE = 24 d−1, Figure 7a, cases B–D), the maximum increase in removal efficiency due to fracture enlargement in a high iron reactivity FRB (λiron, TCE = 240 d−1, Figure 9, case H) is found to be ∼5%, suggesting that fracture enlargement might not be necessary in this case.
3.5. Longevity of a Nanoscale Fe0 FRB
 An FRB contains less iron per m3 than a conventional PRB, and so there may be some concerns about its longevity, particularly if it uses a nanoscale iron with its higher efficiency. Moreover, it has been reported that H2 gas is evolved from nanoscale iron in water [Schrick et al., 2002; Liu et al., 2005], which would reduce the amount of iron available for dechlorination. In this section, we report a simple analysis of the lifetime of an FRB containing nanoscale iron which takes account of the two potential problems above.
Liu et al.  investigated the TCE dechlorination rates, pathways and efficiency by nanoscale iron particles with different properties. The mass of TCE dechlorinated per mass of Fe0 was evaluated by the following possible pathways:
Electrons from Fe0 oxidation can be used to dechlorinate TCE (equation (4)) or to produce H2 gas (equation (5)). Values of n in equation (4) are 6, 4, 8, 6, 7, and 6.7 for the observed production of ethene, acetylene, ethane, butylenes, butane, and hexane, respectively [Liu et al., 2005].
Liu et al.  used two types of nanoscale iron particles (Fe/B and RNIP) to determine the TCE dechlorination rates and pathways by Fe0. The results show that both types have high reactivity with TCE (one to two orders of magnitude higher than iron filings [Johnson et al., 1996]), and that Fe/B produces H2 at a high rate while the commercially available RNIP does not. This suggested that the high reactivity of Fe/B particles may be not practical for in situ application to remediate TCE, since the rapid H2 gas evolution would consume much of the iron. Therefore we used RNIP particles (0.15 g of TCE dechlorinated per gram of iron based on the work of Liu et al. ), a defined TCE mass flux through the FRB and a known total starting mass of iron to estimate the longevity of a nanoscale Fe0 FRB. For our estimate, we assume that the FRB consists of 5 horizontal fractures, each with an area of 10 × 10 m, an aperture of 0.5 mm with a 20% iron fill, a flow rate into the FRB of 600 m3/yr (obtained from case G), a range of TCE plume concentrations from 1–10 mg/L [Lawrence and Foster, 1991] and a bulk density of iron that is assumed to be similar to microscale iron (∼4 kg/L) [Merly and Lerner, 2002].
 Under these conditions, the estimated FRB lifetime is between 5 and 50 years depending on input concentration. We recognize that there are many uncertainties in the estimate; for example we have not accounted for the deactivation of iron particles [Liu et al., 2005] that might be caused by Fe0 corrosion [O'Hannesin and Gillham, 1998]. Nevertheless, this first estimate of the lifetime suggests that such a nanoscale Fe0 FRB could be practical, especially as multiple iron injections might be feasible if longer treatment period is required. Moreover, longer lifetimes could be achieved by increasing the iron content in the particles, or by emplacing more iron in the FRB through using a high percentage of iron fill (i.e., 40%) and fracture enlargement.
 The application of nanoscale iron particles may be limited if the particles prove to be mobile: recent research shows that nanoscale iron particles are mobile in groundwater systems, but they may attach strongly to solid surfaces and form aggregate clusters. Their high density (particle specific gravity of 7) is likely to result in gravitational deposition if the groundwater flow rate decreases significantly (A. Keller, personal communication, 2006). The estimation based on the Shield equation [Shields, 1936] shows that, once these particles are placed on the lower fracture face, a velocity >400 m/d would be required for incipient particle movement (fracture aperture of 1 mm, particle diameter >1 μm, particle specific gravity of 7) [Cai et al., 2006].
3.6. Optimal Design
 Within the boundary of the simulations run and the idealized Chalk site, the study suggests the following optimal designs for an Fe0 FRB. For microscale iron (λFe,TCE ∼24 d−1), the optimal design parameters for a FRB in this case are: cross-sectional area of 4 times the source zone, length of 10 m, factor of fracture enlargement of 4 and 60% iron fill in the enlarged fracture aperture. The overall treatment efficiency of the FRB is ∼70% and the TCE concentration profile along the longitudinal section (y = 13 m) after 10 years installation is shown in Figure 10a. In a simple sensitivity analysis, a low-reactivity iron (λFe,TCE ∼ 0.5 d−1) was simulated for this scenario. The treatment efficiency was <40%, a reduction by a factor of about 2 for a 48-fold reduction in reactivity. This implies that a wide range of reactivity values would create a useful barrier, but clearly higher rates are more efficient. With the same design parameters as above but no fracture enlargement and only 20% Fe0 fill, a similar treatment efficiency (∼75%) can be achieved by using nanoscale iron (λFe,TCE ∼ 240 d−1). The concentration profile is presented by Figure 10b. A case with the TCE source zone depleted because of source remediation or dissolution of the free phase was simulated when the above microscale iron FRB is installed, showed that about 65% of the mass released from the rock matrix was destroyed by the FRB. The concentration in the rock matrix after 10 years of treatment is shown in Figure 10c. Higher treatment efficiencies could be obtained by lengthening the FRB or increasing its cross-sectional area relative to the source area; but these options have not been simulated because of size limitations of the current model grid.
 This design optimization analysis is limited to an FRB comprising uniform fractures filled with a uniform thickness of Fe0, and is based on a single realization of a hypothetical chalk site. Ideally, uncertainties in both the distribution and variability of the materials comprising such a complex, discretely fractured porous medium should be reflected in an assessment of the treatment performance of an Fe0 FRB. Therefore future work is planned whereby data, describing all relevant aspects of the domain, would be gathered from a contaminated chalk site such as the Sawston site. This data would then be used to define distributions of statistical parameters that accurately reflect the properties of the discretely fractured porous medium. A number of realizations of fracture networks could then be generated on the basis of the statistical parameters and numerical simulations would be carried out to see how parameters such as the geometry of the fracture network and the variability of the fracture aperture and the iron thickness affect the performance and optimal design of an Fe0 FRB. Moreover, the simulated domain should be large enough to prevent the effect of the lateral no-flow boundaries on the flow regime.
 This conceptual analysis suggests that it is feasible to treat a plume of TCE contaminated water in a fractured chalk by an emplaced Fe0 FRB. The numerical simulations show that although severe reductions in the fracture aperture by iron fill can cause flow to bypass the FRB and render it ineffective, these effects can be minimized or even eliminated by reducing the proportion of iron fill in the fractures and by applying fracture enlargement techniques during iron emplacement. This modeling investigation indicates that the open fracture aperture after iron emplacement should not be less than ∼40% of its original size. This criterion is suitable for cases with or without fracture enlargement. The amount of fracture enlargement is determined by the proportion of iron fill in the fractures and the ratio of the fracture opening before and after iron emplacement (2bFRB, Fe/2bFRB,ini). This can be calculated by (2bFRB, Fe/2bFRB,ini)/(1-% Fe0 fill). To obtain maximum flow through the FRB, we suggest a optimal value for the ratio of 2bFRB,Fe/2bFRB,ini of 3 times.
 For an iron reactivity to TCE (λiron, TCE) of ≤24 d−1, the study shows that >50% treatment efficiency is unlikely to be achieved without fracture enlargement. However, higher treatment efficiencies can be obtained by a combination of fracture enlargement and a high proportion of iron fill in the fractures. The simulations demonstrate that by using 40–80% iron fill and a fracture enlargement of ∼4–8 times, a treatment efficiency of ∼75% can be achieved for a 10 m long Fe0 FRB. The size of the FRB does have some effect on the treatment efficiency, and generally, the cross-sectional area should be big enough to capture most of the plume. The length of the FRB recommended from this study is ∼10 m.
 Because of its high reactivity, nanoscale iron offers great opportunities for the success of Fe0 FRBs in chalk aquifers. The simulations demonstrate that in a nanoscale Fe0 FRB without fracture enlargement, ∼80% treatment efficiency of TCE can be achieved even with a proportion of iron fill in the fractures of ∼20%. Because of its small particle size (1–100 nm), a nanoscale iron layer could potentially be emplaced in a tiny fracture and cause just a small reduction in its aperture, thereby reducing the clogging which causes flow to bypass the FRB. Because of its highly reactive nature, such a thin layer of nanoscale iron could still ensure an effective FRB.
 Preliminary analysis showed that the lifetime of a typical nanoscale Fe0 FRB (which contains less iron than one constructed with microscale iron) is 5 to 50 years, depending on the incoming TCE mass flux. The effectiveness of such an FRB could be prolonged by employing higher iron content particles or by using a high proportion of iron fill and fracture enlargement.
 This research was supported by the U.K. Engineering and Physical Sciences Research Council and Environment Agency for England and Wales. This paper benefited from numerous discussions with Neil R. Thomson from the University of Waterloo and Sascha E. Oswald from the University of Sheffield (now with UFZ Leipzig).