Characterization and optimization of long-term controlled release system for groundwater remediation: A generalized modeling approach

Chemosphere 69 (2007) 247–253 www.elsevier.com/locate/chemosphere

Characterization and optimization of long-term controlled release system for groundwater remediation: A generalized modeling approach Eung Seok Lee *, Franklin W. Schwartz School of Earth Sciences, The Ohio State University, Columbus, OH 43210, USA Received 6 November 2006; received in revised form 2 April 2007; accepted 3 April 2007 Available online 5 June 2007

Abstract A well-based reactive barrier system using controlled-release KMnO4 has been recently developed as a long-term in situ treatment option for plumes of dense and non-aqueous phase liquids in groundwater. In order to take advantage of the merits of controlled release systems (CRS) in environmental remediation, the release behavior needs to be optimized for the hydrologic and environmental conditions of target treatment zone. Where release systems are expected to be operated over long times, like for the reactive barriers, it may only be practical to describe the long-term behavior numerically. We developed a numerical model capable of describing release characteristics associated with variable forms and structures of longterm CRS. Sensitivity analyses and illustrative simulations showed that the release kinetics and durations would be constrained by changes in agent solubility, bulk diffusion coefficients, or structures of the release devices. The generality of the numerical model was demonstrated through simulations for CRS with monolithic and double-layered matrices. The generalized model was then used for actual design and analyses of an encapsulated-matrix CRS, which can yield constant release kinetics for several years. A well-based reactive barrier system (4.05 · 103 m3) using the encapsulated-matrix CRS can release 1.65 kg of active agent (here MnO 4 ) daily over the next 6.6 yr, creating prolonged reaction zone in the subsurface. The generalized model-based, target-specific approach using the longterm CRS could provide practical tool for improving the efficacy of advanced in situ remediation schemes such as in situ chemical oxidation, bioremediation, or in situ redox manipulation. Development of techniques for adjusting the bulk diffusion coefficients of the release matrices and facilitating the lateral spreading of the released agent is warranted.  2007 Elsevier Ltd. All rights reserved. Keywords: Controlled release system; Environment; Groundwater; Remediation; Modeling; Reactive barrier

1. Introduction In problems of environmental remediation, successful use of advanced schemes for contaminated soils and water often requires continuous supply of active agents to the target area. For example, in situ redox manipulation involves creating a permeable treatment zone downstream of a contaminant plume or contaminant source by injecting chemical agents such as sodium dithionite (Na2S2O4) to alter the redox potential of aquifer fluids and sediments (Vermeul *

Corresponding author. Tel.: +1 614 292 6193; fax: +1 614 292 7688. E-mail address: [email protected] (E.S. Lee).

0045-6535/$ - see front matter  2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.chemosphere.2007.04.037

et al., 2002). In situ chemical oxidation (ISCO) approach requires introduction of chemical oxidants like potassium permanganate (KMnO4) to target subsurface zones (Schnarr et al., 1998; Siegrist et al., 2001; Lee et al., 2003; Li and Schwartz, 2004; Lee and Schwartz, 2007). Enhanced bioremediation schemes also involve introduction of additional electron acceptors like sulfate or nitrate into the aquifer (Barbaro et al., 1992; Sweed et al., 1996; Wiesner et al., 1996; Hutchins et al., 1998; Anderson and Lovley, 2000; Cunningham et al., 2001). The dilemma in developing strategies for better utilizing these methods has been how to control the tendency for rapid dissolution of agents in water. Rapid dissolution can not only create undesirably

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high concentrations of chemical agents but also make the treatment schemes short-term in nature, thus requiring major operational cost. In these remediation schemes, maintaining optimal agent concentration in the target hosts for prolonged period of time is the key for successful and efficient treatment. Controlled release system (CRS) works by transferring agents from a reservoir to a target host, i.e., a contaminated site, while maintaining a predetermined release pattern for a specified period of time. By controlling the precise level and/or location of agents in the target contaminated compartment, risks of secondary contamination and ineffectiveness can be eliminated, long-term control of pollutants is feasible, or needs for maintenance and operational cost can be reduced. Lee and Schwartz (2007) have recently developed a long-term ISCO scheme using controlled-release KMnO4 as an active component in the well-based reactive barrier system. Through experiments and model simulations, they demonstrated that the reactive barrier system using the CRS could potentially be developed as a practical approach for long-term in situ remediation of contaminated aquifers. In order to take advantage of the merits of CRS in environmental remediation, however, the release behavior needs to be optimized for the hydrologic and environmental conditions of target treatment zone. For example, consideration of natural oxidant demand, lateral spreading of permanganate, and volume and concentration of contaminant plume must be made in field applications (Lee and Schwartz, 2007). There are two types of CRS: reservoirs and matrices. In both cases, diffusion controls the release process. Diffusion occurs through a reservoir, in which an agent core is encapsulated (i.e., covered by a coating), or in a matrix, where the agent is uniformly dispersed through the polymeric system (e.g., Langer, 1990). Increasingly sophisticated encapsulation techniques are being developed to construct CRS that can meet the demanding requirements in the biomedical applications. These approaches use fluid extrusion (Loscertales et al., 2002), electrospray (Decher, 1997; Caruso et al., 1998; Tiarks et al., 2001), selective withdrawal (Cohen et al., 2001), flow focusing (Bocanegra et al., 2005), electrohydrodynamic force techniques (Chaikof, 1999), or self-assembly process (Dinsmore et al., 2002) to generate coatings comprising colloids with diameters in the micrometer/nanometer range. Despite the enormous progress in encapsulation technologies, however, these methods are often limited in their applicability, durations, range of materials that can be used, in the uniformity of pore sizes and the associated agent diffusivity, ease of synthesis, filling efficiency, stability (i.e., risks of agent dumping by rupture), or control and estimation of release rates (e.g., Dinsmore et al., 2002). In matrix-type release systems, the dissolution of granules of agents dispersed in the matrix develops secondary porosity and permeability, through which dissolved agent is released by diffusion. Compared with reservoir-encapsulation systems, matrix systems have advantages of low cost, easy fabrication, longer durations,

more stable release rates, and less risk of agent dumping which mainly results from damage in the encapsulation (e.g., Zhou and Wu, 1997). Advanced manufacturing techniques have been developed for matrix systems of variable structures (Lu and Anseth, 1999; Pohja et al., 2004; Vaz et al., 2004). Model development is useful because prototype CRS can be analyzed quickly and efficiently. These models compliment conventional experimental testing. Where release systems are expected to be operated over long times, like for the passive treatment schemes, it may only be practical to describe the long-term behavior numerically. In this way, model simulations can provide great efficiency in the design and optimization of long-term CRS meeting variable concentration/time requirements. The main objective of this study was to develop a generalized numerical model for the design and analyses of long-term CRS optimized for hydrologic and environmental conditions of target treatment zone. The finite difference model was designed to simulate reaction-diffusion problems in polymeric release devices and could account for time varying fluxes from the media, moving reaction boundaries, and variable matrix structures and initial agent loadings. Examples are presented illustrating parameters controlling the time varying concentration gradients and release kinetics of chemicals for simple monolithic media. This basic program formed the nucleus of the modified programs that were intended for predicting release kinetics associated with devices of variable structures and non-homogeneous initial agent loadings. Simulation results were presented, demonstrating the generality of the model in describing the release kinetics associated with varied forms of CRS. In addition, the generalized model was used to actually design and analyze an encapsulated matrix system, which could yield constant release kinetics over several years and perhaps decades. 2. Model development 2.1. Model formulation Finite difference approaches capable of solving forms of the diffusion equation have been around for more than three decades. Alternative direction implicit schemes are easy to implement in simple, short codes (e.g., Peaceman and Rachford, 1955; Price et al., 1961; Chen et al., 2002). Simple, non-reactive transport through some type of polymeric matrix can be described by Fick’s law of diffusion, J ¼ Dd n

oC ox

ð1Þ

where J is the solute mass flux, C is the concentration of the solute, Dd is the bulk diffusion coefficient, n is porosity, and x is a coordinate direction. Using principles of mass conservation, an equation describing solute mass transport in a constant porosity, porous medium subject to diffusion and reaction can be written as follows:

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    o oC o oC r oC Dd Dd þ þ ¼ ox ox oy oy n ot

ð2Þ

where r is a source term defined by a rate law, t is time, n is porosity, and x, y are coordinate axes. Solutions of this equation are complicated by the need to account for porosity development as reactions are occurring. In effect, the active part of the matrix is dissolving with time to form a connected pore system, i.e., capillary secondary permeability. Thus, essentially non-porous solid gradually develops connected porosity as the active chemical dissolves from the outside of the solid inward. Agent further inside is then released by diffusion through the secondary permeability in the depleted cells. This conceptual model is illustrated in Fig. 1 in more details. Panels are cross-sectional areas (top views) of a cuboidal form. Fig. 1a shows a monolithic matrix system immediately after release began. Fig. 1b shows a monolithic matrix system that is being leached. Here, lithic (squares with filled circles), dissolving (squares with dotted circle), and depleted (squares with open circle) cells (1 mm · 1 mm) represent the areas where dissolution diffusion is yet to begin, where dissolution occurs (reaction fronts), and where the amount of agent left in the cells is less than the solubility level, respectively. Concentrations in the dissolving cells are assumed to be the solubility of the agent. Concentrations in the depleted cells are controlled by diffusion of dissolved agent in the secondary permeability. The details of the porosity development and extent of interconnection are broadly determined by the original design of the solid, such as the relative proportion of reactive versus non reactive components in the solid and grain-size of the reactive particles. Because the early dissolution-controlled releases are typically much greater than later diffusion-controlled releases, the result is the so-called ‘‘burst release’’, or initial concentration spike at early time (e.g., Zhou and Wu, 1997). There are several ways to incorporate these reactive processes into a numerical model. One approach is to formally provide kinetic expressions for each model cell describing release rates as a function of

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time as shown in Eq. (2). For many compounds of interests, these kinetic rate laws are unknown. We have chosen to use a simple moving boundary approach. In effect, the solid releases mass at the rate diffusion removes it. Thus, an inherent assumption is that the dissolution rate is greater than the rate of diffusion. Both our experiments and simulation results indicate that this assumption is valid. Operationally, the model ‘turns on’ the lithic and dissolving cells as constant concentration nodes (infinite storage) until they become ‘depleted’. This approach maintains concentration of the dissolving agents in the lithic and dissolving cells at the solubility of agent. In practice, the size of individual cells is kept small to minimize the gradients within cells. Continued release of agent from the matrix creates concentration gradients among the dissolving and depleted cells. These concentration gradients drive agent release in a sustained fashion. While the interior of the solid is represented by a moving boundary, the outside boundary is fixed location-wise and represented by a constant concentration of zero (e.g., perfect sink condition in flowing water). Thus, mass reaching the external boundaries of the solid is assumed to be efficiently released. At this external boundary, for each time step, release rates are calculated (g d1) using the corresponding modeled concentration gradients. Finally, the cumulative amount of agent (g) released from some three-dimensional volume can be calculated from the release rate for a finite slice. The model was programmed in FORTRAN 95 (Lahey/ Fujitsu ED4W). The program was run using a time step of 1 min. To ensure that the model had no undetected programming or logic errors, it was successfully verified against an analytical solution for one-dimensional diffusion (from Crank, 1983): x C ¼ C 0 erfc pffiffiffiffiffiffiffiffiffi 2 ðDtÞ

ð3Þ

where erfcz ¼ 1  erfz

ð4Þ

Fig. 1. Conceptual model showing some imaginary monolithic system. Figures are cross-sectional areas (top views) of a cuboidal form. The squares (1 mm · 1 mm) containing open, checked, and dotted circles represent depleted, dissolving, and lithic cells, respectively. Panel (a) shows a monolithic matrix system immediately after release began. Panel (b) shows a monolithic matrix system that is being leached.

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In addition, the model was tested with representative sets of reaction-diffusion parameters. Sensitivity analyses of this type involve the systematic variation of one or more model parameters while the others are held constant. For this study, three parameters were chosen to examine their influence on the release rates and durations of several hypothetical controlled release devices. The parameters of interests were: (i) solubility of agent; (ii) bulk diffusion coefficient of the matrix, and (iii) pattern of initial agent loadings. Among these parameters, bulk diffusion coefficient and agent solubility were used for sensitivity analyses. The effect of initial agent loading to release kinetics is discussed in the subsequent section for system optimization. All model simulations yielded excellent chemical mass balances with 60.8% errors. The CRS forming the basis for the sensitivity analyses represented a set of conditions that would be typical for simple monolithic, i.e., very narrow pore size distribution, agent-dispersed matrix system described in the literature (Higuchi, 1963).

sions h · x · y = 50 mm · 24 mm · 24 mm, and containing 25 g of agent salt (KMnO4; water solubility: 64 g l1, molar mass: 158 g mol1) are shown in Fig. 2. Bulk diffusion coefficient for the depleted portion of the matrix was assumed to be 5.79 · 107 cm2 s1. This value was within the typical range of agent diffusion coefficients (106–107 cm2 s1) in rubbery polymer (Narasimhan, 2000). In 200 d (Fig. 2a), the dissolution front receded approximately 2 mm from the surface, creating 62 mm-long diffusion path in the secondary permeability (depleted cells in Fig. 1). In 550 (Fig. 2b) and 900 d (Fig. 2c), the dissolution fronts further receded creating approximately 65.5 mm-long and 68 mm-long diffusion paths in the depleted cells, respectively. In 1250 d (Fig. 2d), all monolithic cells were depleted, showing agent concentrations 612.9 lg mm3 with maximum concentrations in the core nodes. In all time steps, the simulated concentration data facilitated estimates of fluxes, system, i.e., agent solubility (C), total mass stored (S), and bulk diffusion coefficient release rates, and agent release profiles. Three major parameters controlling the reaction-diffusion in polymeric release (Dd ) work interchangeably along with dimensions and structures of matrices to control release kinetics and durations of the release devices. To investigate how release kinetics and durations respond to these parameters, simulation trials were undertaken where values of C, S, and Dd were varied.

2.2. Illustrative results

2.3. Sensitivity analysis – monolithic system

Temporal and spatial changes in agent concentrations within a monolithic parallelepiped device having dimen-

The sensitivity analysis was based on a monolithic system having dimensions h · x · y = 20 mm · 12 mm ·

with the boundary condition C ¼ C0;

x ¼ 0; t > 0

and the initial condition C ¼ 0;

x > 0; t ¼ 0

Fig. 2. Simulation data showing the temporal and spatial variations in the agent concentrations (lg mm3) within the monolithic system (24 mm · 24 mm · 50 mm). Figures are cross-sectional areas (top views) of the parallelepiped monolithic system. (unit of x, y dimension: mm, unit of concentration: lg mm3).

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12 mm and containing 4 g of KMnO4. The system was subdivided into total of 144 vector volumes, each having dimensions h · Dx · Dy = 20 mm · 1 mm · 1 mm Simulations were then performed using a 2D finite grid (difference) system (12 mm · 12 mm) comprising 144 square units (cells) having dimensions DxDy = 1 mm · 1 mm. Release patters for two monolithic systems having the same dimensions and agent but different bulk diffusion coefficients are shown in Fig. 3a. Bulk diffusion coefficients in the depleted portions of the matrices were assumed to be 1.16 · 106, and 2.31 · 106 cm2 s1, respectively. In the monolithic system, the release rates were initially high (burst effect), then these rates declined following first-order decay. The duration of the release was estimated as 150 d and 260 d for systems having bulk diffusion coefficients of 2.31 · 106 cm2 s1 and 1.16 · 106 cm2 s1, respectively, demonstrating decrease in the release rates with smaller diffusion coefficients. The first-order release kinetics of the monolithic system was attributed to the recession of the dissolution fronts as described in Figs. 1 and 2. As the diffusion path length increases, the release rates decrease with time. These simulation results are in keeping with the simulation and experimental data presented in the literature for monolithic, dispersed-agent matrix systems (Higuchi, 1963; Narasimhan, 2000; Lee and Schwartz, 2007). Here, the Dd values are constrained by the free volume of the

Amount Released (g)

4

3

2 D=1.16E-6 D=2.32E-6

1

0

Amount released (g)

4

3

2 solubility = 32 g/L solubility = 64 g/L

1

0 0

100

200

300

Time (Days)

Fig. 3. Release kinetics of an agent from monolithic systems with different (a) solubility and (b) bulk diffusion coefficients. Dissolution of 4 g of agent would generate 3.01 g of active dissolved ingredient according to moleto-mole dissolution ratio. D denotes bulk diffusion coefficient (Unit: cm2 s1).

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matrix, which in our case is essentially a function of two parameters, i.e., agent/matrix volume ratios and initial agent loadings. This means that the release kinetics can be predetermined by adjusting the two parameters during the manufacturing process. Mathematical and experimental studies investigating the correlations among these factors are currently underway. Release kinetics of two monolithic systems having same dimensions and diffusion coefficients but containing agent with different solubility were simulated and presented in Fig. 3b. The bulk diffusion coefficient was assumed to be 2.31 · 106 cm2 s1. Duration was estimated as 150 d and 260 d for systems having solubility of 64 lg mm3 and 32 lg mm3, respectively, demonstrating that the rates of decrease in the release kinetics are linearly correlated between the rates of decrease in diffusion coefficient and agent solubility. These observations from the sensitivity analysis suggested that release kinetics of an agent from same monolithic system may be controlled by adjusting bulk diffusion coefficients or agent solubility. 2.4. System optimization and design The monolithic systems that produce release pattern of initial concentration spike followed by first-order decay in release kinetics may not be desirable for remedial schemes that require maintenance of optimal agent level in the target contaminated zone for extended period of time. This problem may be solved by using release systems providing long-term ‘constant’ or ‘zero-order’ releases, i.e., delivering the same amount of agent to a target host over its entire life span. For this study, the generalized model was used to actually design a release device that can deliver active ingredient to the flowing water at a constant rate over extended time periods of years and possibly decades without replenishment. Release kinetics associated with matrices of variable structures was analyzed using the generalized model. For an illustrative simulation, a conceptual double-layered parallelepiped matrix system was proposed, having dimensions h · x · y = 20 mm · 12 mm · 12 mm and containing 2 g of agent (KMnO4) in the inner portion (h · x · y = 20 mm · 6 mm · 6 mm) and 2 g of KMnO4 in the outer region. The Dd values of the inner and the outer matrices were assumed to be 3.0 · 107 cm2 s1 and 1.5 · 107 cm2 s1, respectively. Fig. 4 shows the simulated release kinetics of the monolithic and double- layered matrix systems. Compared to the monolithic system with the same dimensions, same total mass of KMnO4, and constant Dd of 1.16 · 106 cm2 s1, the initial concentration spike and the subsequent decrease in the release rates were considerably moderated in the double-layered system. Overall, the double-layered system yielded much less variable release rates over longer period of time (390 d) compared to the monolithic system (Fig. 4), indicating that non-uniform initial agent loadings could moderate initial burst effect and time variations of the underlying release rates.

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1200

2

Single Double

1

2700 800 1800 400

Release rate

Amount released (mg)

3600

3 Release rate (μg/day)

Amount Released (g)

4500

1600

4

900

Amount released

0 0

100

200 300 Time (Days)

400

500 0 0

Fig. 4. Release kinetics of an agent from monolithic (single-layered) and double-layered matrices (h · x · y = 20 mm · 12 mm · 12 mm). Dissolution of 4 g of agent would generate 3.01 g of active dissolved ingredient according to mole-to-mole dissolution ratio. In the double-layered system, 2 g of agents were dispersed in the core (h · x · y = 20 mm · 6 mm · 6 mm) and the outer part the matrix, respectively.

Through a number of simulations of release kinetics from various forms and structures of release devices with non-uniform initial agent loadings, a new long-term, constant-release encapsulated-matrix system was designed. This system differs from the reservoir-encapsulation system in that the core portion is comprised of a dispersed-agent polymeric matrix. It also differs from the matrix systems because the matrix is encapsulated by low-permeability polymer. For an illustrative simulation of the release kinetics, we used a release device in which a dispersed-agent monolithic cube (9 mm · 9 mm · 9 mm) was encapsulated by polymeric micro-particles creating a 1 mm-thick lowpermeability coating. Same agent (mass of KMnO4 = 5.16 g; mass of MnO 4 ¼ 3:88 g) was used and bulk diffusion coefficients were assumed to be 2.31 · 106 cm2 s1 and 1.16 · 109 cm2 s1 for the matrix and the encapsulation, respectively. These values were within the typical ranges for drug diffusion in rubbery polymers (107– 106 cm2 s1) and in glassy polymers (1012–107 cm2 s1), respectively (Narasimhan, 2000). For the 2D simulation, the top and bottom of the matrix were assumed to be zero mass flux boundaries. The 2D simulation can be extended to describe reaction kinetics of infinite-length system, i.e., long parallelepiped systems. The simulation results are presented in Fig. 5. The initial release rates were 1.4 mg d1 on day 1, slightly increased to 1.5 mg d1 on day 136, then remained constant until day 2397 (6.6 yr), yielding a long-term zero-order release without the initial concentration spike. Approximately 90% of agent was estimated to be released during the first 6.6 yr, with constant release rate (1.5 mg d1). Release rates then rapidly decreased to become 0.4 mg d1 over the next 700 d, and gradually approached zero. In a previous study, liquid crystal was used as matrix for constructing the controlled-release KMnO4 (CRP) cylinders (Lee and Schwartz, 2007). This organic crystalline matrix would be rigid enough to hold original shape of a long parallelepiped monolithic system, for example, having

1000

2000 Time (days)

3000

0 4000

Fig. 5. Long-term, constant-release of agent from an encapsulated-matrix system.

dimension h · x · y = 135 cm · 0.9 cm · 0.9 cm even after all dispersed KMnO4 granules are leached out. The monolithic system can be then encapsulated by polymeric microparticles creating a 1 mm-thick low-permeability coating. Let us assume a well-based CRP reactive barrier system comprising five discrete barriers installed at 2-m interval downstream normal to a dissolved contaminant TCE plume. Each barrier is composed of 10 delivery wells (ID = 14 cm) spaced in 2-m intervals, and each well contains 10 lines of encapsulated-matrix CRP (each encapsulated-matrix CRP with total mass of MnO 4 ¼ 582g; h · x · y = 135 cm · 1.1 cm · 1.1 cm) embedded at 2 cm interval within the uniform-sized large spherical silica beads that fill the empty space of the screened well casing. Here, each line has 15 encapsulated-matrix CRP placed on top of each other (total length of a line = 20.3 m). The simulation data suggested that the well-based encapsulatedmatrix CRP reactive barrier (w · l · d = 20 m · 10 m · 20.3 m) containing total of 4370 kg of active agent  (MnO 4 ) could release 1.65 kg of MnO4 daily over the next 6.6 yr (mass of total released MnO over 6.6 yr = 4 3950 kg), creating 4050 m3 of prolonged chemically active zone with almost constant MnO 4 level in the subsurface. 3. Conclusions A generalized computer model capable of describing release characteristics of variable forms and structures of CRS was developed and used for actual design and analyses of encapsulated-matrix system, a new long-term constant release device. The release kinetics and durations of the encapsulated-matrix system and other long-term CRS can be adjusted to meet the specific requirements of target hosts by constructing systems of appropriate dimensions, structures, agent solubility, and bulk diffusion coefficients. For example, various environmental and hydrologic factors including aquifer characteristics, volume and concentration of contaminant plume, natural demands for active agents, reaction kinetics, or spreading of released agent must be considered. Here, utilization of the generalized

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model for system design and optimization can provide great efficiency in the construction of target-specific long-term controlled release devices by complementing the need for time-consuming and costly preliminary release experiments. When these factors are well addressed, the model-based, target-specific, long-term controlled release approach could provide promising tools for improving the efficacy of advanced remedial schemes like in situ redox manipulation, in situ chemical oxidation, and bioremediation. Perhaps, the most important research need with the controlled release approach would be to develop techniques for precisely adjusting the bulk diffusion coefficients of the release matrices and facilitating the lateral spreading of the released agent in the subsurface. Acknowledgement This material is based upon work supported by the Department of Energy under Grant FG07-02ER63487. References Anderson, R.T., Lovley, D.R., 2000. Anaerobic bioremediation of benzene under sulfate-reducing conditions in a petroleum-contaminated aquifer. Environ. Sci. Technol. 34, 2261–2266. Barbaro, J.R., Barker, J.F., Lemon, L.A., Mayfield, C.I., 1992. Biotransformation of BTEX under anaerobic, denitrifying conditions: field and laboratory observations. J. Contam. Hydrol. 11, 245–272. Bocanegra, R., Sampedro, J.L., Ganan-Calvo, A., Marquez, M., 2005. Monodisperse structured multi-vesicle microencapsulation using flowfocusing and controlled disturbance. J. Microencapsul. 22, 745–759. Caruso, F., Caruso, R.A., Mohwald, H., 1998. Nanoengineering of inorganic and hybrid hollow spheres by colloidal templating. Science 282, 1111–1114. Chaikof, E.L., 1999. Engineering and material considerations in islet cell transplantation. Annu. Rev. Biomed. Eng. 1, 103–127. Chen, J., Wang, Z., Chen, Y.C., 2002. Higher-order alternative direction implicit FDTD method. Electron. Lett. 38, 1321–1322. Cohen, I., Li, H., Hougland, J.L., Mrksich, M., Nagel, S.R., 2001. Using selective withdrawal to coat microparticles. Science 292, 265–267. Crank, J., 1983. The Mathematics of Diffusion. second ed.. Clarendon Press, Oxford. Cunningham, J.A., Rahme, H., Hopkins, G.E., Lebron, C., Reinhard, M., 2001. Enhanced in situ bioremediation of BTEX-contaminated groundwater by combined injection of nitrate and sulfate. Environ. Sci. Technol. 35, 1663–1670. Decher, G., 1997. Fuzzy nanoassemblies: toward layered polymeric multicomposites. Science 277, 1232–1237. Dinsmore, A.D., Hsu, M.F., Nikolaides, M.G., Marquez, M., Bausch, A.R., Weitz, D.A., 2002. Colloidosomes: selectively permeable capsules composed of colloidal particles. Science 298, 1006–1009. Higuchi, T., 1963. Mechanism of sustained-action medication-theoretical analysis of rate of release of solid drugs dispersed in solid matrices. J. Pharm. Sci. 52, 1145–1149. Hutchins, S.R., Miller, D.E., Thomas, A., 1998. Combined laboratory/ field study on the use of nitrate for in situ bioremediation of a fuelcontaminated aquifer. Environ. Sci. Technol. 32, 1832–1840.

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