Modeling of DNAPL-Dissolution, Rate-Limited Sorption and Biodegradation Reactions in Groundwater Systems

Bioremediation Journal, 81 2):47 64, 2004 Copyright c 2004 Taylor and Francis Inc. ISSN: 1040-8371 DOI: 10.1080/10889860490453177 Modeling of DNAPL-Dissolution, Rate-Limited Sorption and Biodegradation Reactions in Groundwater Systems T. Prabhakar Clement Department of Civil Engineering, Auburn University, Auburn, Alabama, USA Tirtha R. Gautam Department of Civil Engineering, Auburn University, Auburn, Alabama, USA; Center for Water Research, University of Western Australia, Perth, Australia Kang Kun Lee School of Earth and Environmental Science, Seoul National University, Korea Michael J. Truex Pacific Northwest National Laboratory, Richland, Washington, USA Greg B. Davis CSIRO Land and Water, Perth, Australia ABSTRACT This article presents an approach for modeling the dissolution process of single component dense non-aqueous phase liquids DNAPL), such as tetrachloroethene and trichloroethene, in a biologically reactive porous medium. In the proposed approach, the overall transport processes are conceptualized as three distinct reactions. Firstly, the dissolution or dissolving) process of a residual DNAPL source zone is conceptualized as a mass-transfer limited reaction. Secondly, the contaminants dissolved from the DNAPL source are allowed to partition between sediment and water phases through a rate-limited sorption reaction. Finally, the contaminants in the solid and liquid phases are allowed to degrade by a set of kinetic-limited biological reactions. Although all of these three reaction processes have been researched in the past, little progress has been made towards understanding the combined effects of these processes. This work provides a rigorous mathematical model for describing the coupled effects of these three fundamental reactive transport mechanisms. The model equations are then solved using the general-purpose reactive transport code RT3D Clement, 1997). KEYWORDS NAPL dissolution, rate limited sorption, biodegradation, solute transport, chlorinated solvent INTRODUCTION Address correspondence to T. Prabhakar Clement, Department of Civil Engineering, Auburn University, Auburn, AL 36849, USA. E-mail: clement@eng.auburn.edu Chlorinated solvents e.g., tetrachloroethene [PCE] and trichloroethene [TCE]) are commonly observed soil and groundwater contaminants Wiedemeier et al., 1999). Because of their physical properties, PCE and TCE can contaminate the environment as non-aqueous phase liquids NAPL). Since chlorinated compounds are denser than water they are further classified as DNAPL. If sufficient contaminant mass is discharged at a hazardous waste site, the DNAPL products can rapidly migrate into the deeper regions of the saturated groundwater zone, contaminating large volumes of the aquifer. Within this contaminated region, 47

FIGURE 1 Conceptual representation of various rate-limited reactive transport processes considered in the numerical model. the DNAPL will eventually be trapped in the form of blobs. These trapped DNAPL-contaminated regions can act as long-term residual sources. Figure 1 is a conceptual model that illustrates various contaminant transport processes occurring within a DNAPL contaminated aquifer. The important fate-and-transport processes identified in the conceptual model include: 1) DNAPL dissolution processes, which will control the rate at which the contaminant mass dissolves from the trapped DNAPL into the surrounding groundwater; 2) sorption processes, which will control the rate at which the dissolved contaminants will partition on to the surrounding soil material; and 3) biodegradation reaction processes, which will control the rate of contaminant transformation. At several contaminated sites, these physical, chemical, and biological processes can be mediated by kinetically-controlled, rate-limiting mechanisms. Designing a remediation system for treating the groundwater systems contaminated with DNAPL products would first require a thorough understanding of the dissolution kinetics of the DNAPL source. DNAPL dissolution is a complex process that can be influenced by several factors. Miller et al. 1990) concluded that the inter-phase mass transfer rate of contaminants from an NAPL source depends on at least ten non-dimensional parameters, which are in turn functions of several other flow and transport parameters. Unfortunately, the experimental research required to quantify the system in terms of all of these parameters has not been accomplished even 48 under ideal laboratory conditions. Therefore, in most practical field problems, if an NAPL source is known or suspected to be present in the system, a partitioning relationship is often used to model the source region having concentrations close to the saturations e.g., Schafer and Therrien, 1995) or by fixing the source zone concentrations at those levels observed in the field e.g., Burnell, 2002). Others have also used a set of imaginary injection wells to recreate observed source concentration levels e.g., Rifai et al., 1988). However, none of these fixed source-zone models may be valid for sources that are expected to deplete considerably over the simulation period. Furthermore, field studies have shown that the dissolved phase concentrations near an NAPL source zone can be significantly lower than the expected solubility level e.g., Clement et al., 2002), thereby indicating that the dissolution of NAPL is often a rate-limited exchange process. As illustrated in Figure 1, the dissolved contaminant mass transferred from a DNAPL source zone may partition between the sediment and water phases due to sorption reactions. Sorption is often modeled using the retardation approach, which assumes an equilibrium relationship between solid and liquid phases. The retardation approach for modeling sorption may provide an adequate description for modeling transport in slow natural groundwater flow systems. However, when considerable external pumping and injection stresses are imposed on the system e.g., using a pump- and-treat system), then the system may diverge from the equilibrium transport conditions CLEMENT ET AL.

Harvey et al., 1994). Under these conditions, nonequilibrium effects such as the plume tailing effect where low persistent contaminant levels are observed at the pumping well for long periods) and the rebounding effect where a remediated aquifer shows considerable increase in contaminant concentration levels when the pumps are shut down) are commonly observed. These non-equilibrium effects cannot be simulated using retardation models. They can, however, be modeled using mass-transfer limited sorption models, where the contaminant mass exchange between the soil and groundwater is assumed to be a rate-limited kinetic process e.g., Clement et al., 1998; Haggerty and Gorelick, 1994; Zhang and Brusseau, 1999). Recent field studies have shown that natural microbial populations present in groundwater aquifers have the ability to degrade several anthropogenic chemicals including the chlorinated solvents e.g., McCarty, 1997; Lu et al., 1999; Clement et al., 2000). These observations have led to the development of various types of bioremediation technologies for cleaning contaminated groundwater systems. Application of bioremediation processes to remediate contaminated sites includes two distinct approaches: the passive bioremediation approach and the active bioremediation approach. The passive approach is also known as natural attenuation or monitored natural attenuation. The natural attenuation approach is a long-term management strategy, which relies on the natural assimilative capacity of the system to control contaminant migration and support site-specific remediation goals. The active bioremediation approach, on the other hand, is an accelerated cleanup strategy which is usually accomplished by enhancing the activities of an indigenous or a nonindigenous microbial population within the contaminated region e.g., Truex, 1995; Duba et al., 1996). Both passive and active bioremediation systems are mediated by rate-limited microbial degradation reactions Hooker et al., 1998; Clement et al., 2000). Determining the feasibility of a bioremediation system at chlorinated solvent-contaminated sites with complex hydrogeological conditions will require simulation of a set of coupled rate-limited processes that describe the effects of DNAPLdissolution, sorption and biodegradation reactions. Although all of these three rate-limited processes have been researched in the past, little progress has been made towards understanding the combined effects of these processes. The objective of this work is to develop a mathematical model for predicting the combined effects of NAPL-dissolution, ratelimited sorption, and biological reactions in a saturated porous medium. The coupled model equations are solved by the reactive transport code RT3D Clement, 1997; Clement et al., 1998). The model was used to simulate a test problem to demonstrate the use of the approach for describing the bio-attenuation patterns of contaminants emanating from a residual DNAPL source. A detailed simulation analysis was also completed to quantify the effects of parameter variations. MODEL DEVELOPMENT In this section, a kinetic modeling framework is developed to describe the fate and transport processes occurring at a site contaminated with PCE-DNAPL products. PCE is selected as the DNAPL specie because it is a widely used industrial solvent; further, there are multiple reported cases of soil and groundwater contamination problems associated with PCE spills Wiedemeier et al., 1999). Also, the physical and chemical properties of PCE are well understood since it is a commonly used DNAPL species in laboratory-scale column experiments e.g., Bradford and Abriola, 2001). PCE can be biologically dechlorinated under anaerobic conditions via the following sequential reaction chain McCarty, 1997): PCE Trichloroethene TCE) Dichloroethene DCE) Vinyl Chloride VC) Ethene. PCE and its biotransformation products are regulated contaminant species; therefore, remediation of PCEcontaminated sites requires careful consideration of the fate of PCE and all its degradation products. The details of various reactive transport processes considered in this study are illustrated in Figure 1. As shown in the figure, three coupled reaction mechanisms, which include DNAPL dissolution, rate-limited sorption, and biodegradation, are considered. The following three sections summarize the mathematical descriptions used for modeling DNAPL dissolution, rate-limited sorption, and biological processes, respectively. Modeling of DNAPL Dissolution and Solute Transport Processes A detailed review of the NAPL dissolution and related laboratory studies can be found in Miller et al. MODELING OF BIOREMEDIATION SYSTEMS 49

1998). In several DNAPL modeling studies, a quasisteady state form of Fick s linear dissolution model is used to describe the contaminant mass exchange from the NAPL phase to the aqueous phase e.g., Miller et al., 1990; Powers et al., 1994; Saenton et al., 2002). Using the linear dissolution model, the fate and transport of a contaminant plume emanating from an aquifer contaminated with residual DNAPL products can be written as: C = ) C D ij v i C) + k La C C) ± F t x i x j x i 1) where C is the aqueous-phase concentration of the DNAPL contaminant [ML 3 ], C is equilibrium aqueous phase concentration the solubility limit) of the contaminant [ML 3 ], D is the hydrodynamic dispersion coefficient [L 2 T 1 ], v is the pore water velocity [LT 1 ], k La is the DNAPL dissolution rate constant [T 1 ], and the factor F represents all other physical, bio/geo-chemical reactions [ML 3 T 1 ]. In this work, DNAPL is assumed to be trapped in the subsurface as an immobile phase, and the influence of the trapped DNAPL on aquifer porosity and hydraulic conductivity are assumed to be negligible. These assumptions are valid at very low DNAPL saturation levels Zhu and Sykes, 2000). The changes in the DNAPL mass associated with the contaminated sediment can be modeled by using the following equation: ρ C N = k La C C) 2) φ t where ρ is the dry bulk density of the soil matrix [ML 3 ]; φ is the porosity; and C N is the mass fraction of the residual DNAPL in the sediment [mass of trapped NAPL per unit dry mass of porous media, MM 1 ]. Note, traditionally, the presence of NAPL in a porous medium is represented by its volumetric fraction θ N. The value of DNAPL-mass fraction C N can be computed from the value of θ N using the relationship: C N = ρ Nθ N 3) ρ where ρ N is the DNAPL density [ML 3 ]. We used the following empirical expression for computing the DNAPL dissolution rate constant k La see Appendix A): ) β k La = kla max CN 4) C o N where kla max is the initial maximum dissolution rate constant, which can be calculated based on the properties of the porous medium Appendix A), β is an empirical constant and CN o is the initial mass fraction of the residual DNAPL in the sediment. Equation 4) is a scaling-type model for estimating the value of k La for different amounts of residual DNAPL. Note when β = 1, the model reduces to a simple expression that scales the initial k La value based on the fraction of DNAPL concentration remaining in the system. Powers et al. 1994) presented a detailed dissolution model that has a format similar to 4). In Appendix A, we review the details of the Powers et al. 1994) work and relate Equation 3) to the Powers model. The appendix also provides expressions for computing the values of the model parameters kla max and β. It is important to note that the Powers et al. 1994) model was originally developed based on data obtained from one-dimensional experiments conducted using homogeneous sandy soils. This simple model will not be directly applicable for heterogeneous multi-dimensional flow domains. Others have attempted to extend this model for use in heterogeneous systems involving non-uniform DNAPL sources. For example, Zhang and Brusseau 1999) identified one of the Powers model parameters as a calibration parameter and used the calibrated model to predict the regional-scale behavior of a trichloroethene plume at a Superfund site in Tucson, Arizona. Brusseau et al. 2002) used a simple ratio approach to estimate the discrete dissolution values for a three-dimensional grid using the Powers model based values estimated from local-scale column experiments. The scaling approach given in the appendix is similar to the Brusseau et al. 2002) approach. However, it is important to note that field heterogeneity and NAPL source geometry can greatly influence the dissolution behavior, especially in a multi-dimensional aquifer where transient flow bypassing effects can be dominant Saenton et al., 2002; Brusseau et al., 2000). Further, DNAPL dissolution processes can also be affected by the biological processes active near the NAPL source Seagren et al., 1994; Yang and McCarty, 2000; Chu et al., 2003). The Powers dissolution model used in this work is a simplified approach, and it ignores several issues including multi-dimensional by-pass flows, soil heterogeneities, source heterogeneities, and biological effects of NAPL dissolution. The overall modeling framework described, however, is a general approach 50 CLEMENT ET AL.

and can be easily adapted for more complex situations by replacing the Powers approach with an appropriate dissolution model. Modeling of Rate-Limited Sorption and Solute Transport Processes When the partitioning of dissolved contaminants between the solid and liquid phases is assumed to be rate-limited, the contaminant concentration levels in both solid and liquid phases must be simulated by the model. Following Haggerty and Gorelick s 1994) approach, the fate and transport of a sorbing solute in aqueous and soil phases can be predicted using the following transport equations: C + ρ C = ) C D ij ν i C) ± F 5) t φ t xi xj xj ρ C = ξ C ) C 6) φ t λ where C is the concentration of the contaminant in the aqueous phase [ML 3 ]; C is the concentration of the contaminant in the sorbed phase [mass of sorbed contaminant per unit dry mass of porous media, MM 1 ]; ξ is the mass-transfer rate parameter [T 1 ]; λ is the linear partitioning coefficient [L 3 M 1 ]; and the factor F represents all possible aqueous-phase physical, bio/geo-chemical reactions [ML 3 T 1 ]. It can be shown that the above nonequilibrium model relaxes to an equivalent equilibrium retardation model formulation when the value of ξ is large, and relaxes to non-sorbing tracer model when the value of ξ is small Clement et al., 1998). Modeling of Coupled DNAPL-Dissolution, Rate-Limited Sorption, and Biological Reaction Processes In this section we couple the rate-limited dissolution and sorption models discussed above with a rate-limited biodegradation reaction model to predict the overall fate and transport of the dissolved PCE plume originating from a PCE-DNAPL source. The biodegradation model assumes that PCE will be degraded by a uniformly distributed stable microbial population present in the aquifer. The model also assumes biodegradation by anaerobic reductive dechlorination processes yielding the following sequential degradation pathway: PCE TCE DCE VC. The true reaction mechanisms of microbially-mediated reductive dechlorination processes are indeed complex and will be influenced by several biogeochemical factors Maymo-Gatell et al., 1997). For instance, the rate of biodegradation would strongly depend on the types and number of microorganisms present in the subsurface, and the types and amounts of the electron donors available for supporting the dechlorination reaction. However, in most practical, field-scale applications, chlorinated solvent degradation steps can be conceptualized as lumped first-order decay reactions e.g., Wiedemeier et al., 1999; Clement et al., 2000). Assuming first order, sequential decay kinetics for describing the PCE biodegradation process, the governing equations for the coupled reactive transport system can be written as: [PCE] + ρ t φ = xi [P CE] t [PCE] D ij x j ) x i ν i [PCE]) + q s φ [PCE] s + k La [PCE] [PCE]) k a Pce [PCE] ρ φ ks Pce [P CE] ρ [T CE] φ t = [TCE] D ij xi xj + Y Tce/Pce k a PCE [PCE] ka Tce [TCE] [TCE] ) xi ν i [TCE]) + q s φ [TCE] s 7) + ρ φ Y Tce/Pce k s Pce [P CE] ρ φ ks Tce [T CE] 8) [DCE] + ρ t φ = xi [D CE] t [DCE] D ij xj + Y Dce/Tce k a Tce [TCE] ka Dce [DCE] [VC] t = xi ) xj ν i [DCE]) + q s φ [DCE] s + ρ φ Y Dce/Tce k s Tce [T CE] ρ φ ks Dce [D CE] 9) + ρ φ [VC] t [VC] D ij xj + Y Vc/Dce k a Dce [DCE] ka Vc [VC] ) xj ν i [VC]) + q s φ [VC] s + ρ φ Y Vc/Dec k s Dec [D CE] ρ φ ks Vc [V C] 10) ρ d[pce NAPL ] = k La [PCE] [PCE]) 11) φ dt MODELING OF BIOREMEDIATION SYSTEMS 51

ρ φ [PCE] = ξ Pce t ρ [T CE] φ t = ξ Tce [TCE] [T [PCE] [P CE] CE] λ Tce λ Pce ) ρ φ ks Pce [P CE] 12) ) + ρ φ Y Tce/Pcek s Pce [P CE] ρ φ ks Pce [T CE] 13) ρ [DCE] φ t = ξ Dce [DCE] [D CE] λ Dce ) + ρ φ Y Dce/Tcek s Tce [T CE] ρ φ ks Dce [D CE] 14) ρ [V C] φ t = ξ Vc [VC] [V C] ) + ρ φ Y Vc/Dcek s Dce [D CE] λ Vc ρ φ ks Vc [V C] 15) where [PCE], [TCE], [DCE], and [VC] represent aqueous phase concentrations of the contaminant species [ML 3 ]; [PCE NAPL ] is the mass fraction of residual PCE NAPL [MM 1 ]; [PCE], [T CE], [DCE] and [V C] represent sorbed phase concentrations of the contaminants [MM 1 ]; [PCE] s,[tce] s, [DCE] s, and [VC] s represent the source/sink concentrations of various contaminant species [ML 3 ]; [PCE ] represents the solubility limit of PCE [ML 3 ]; k a Pce, ka, Tce ka Dce, and ka Vc are the first-order aqueous phase degradation rate constants [T 1 ]; k s Pce, ks, Tce k a Dce, and ks Vc are the first-order sorbed phase degradation rate constants [T 1 ]; ξ Pce, ξ Tce, ξ Dce, and ξ Vc are the first-order sorption mass transfer rate constants of various contaminant species [T 1 ]; λ Pce, λ Tce, λ Dce, and λ Vc are the first-order linear partitioning coefficients of various contaminant species [L 3 M 1 ]; and Y represents various stoichiometric yield values. The values of Y can be calculated from the reaction stoichiometry and the molecular weights; for example, degradation of one mole of PCE would yield one mole of TCE, therefore Y Tce/ Pce = molecular weight of TCE/molecular weight of PCE 131.4/165.8 = 0.79). Based on similar calculations, the values of Y Dce/Tce and Y Vc/Dce can be calculated as 0.74 and 0.64, respectively. It should be noted that the above model assumes that degradation reactions in the aqueous phase would release daughter products into the aqueous phase, and degradation reactions in the sorbed phase would release daughter products into the sorbed phase. Biodegradation in the solid phase is included in the model as a means to simulate the bioavailability of sorbed-phase contaminants. Conceptually, biodegradation in the sorbed phase assumes that microorganisms are in contact with the sedimentbound contaminants and can mediate the release and degradation of the bound contaminant mass. Novak et al. 1995) reviewed several experimental studies where addition of soil amendments has been shown to simulate microbial activity and helped increase the release and degradation rates of bound residues. While it is difficult to directly quantify the effective rates of such solid phase biodegradation reaction rates, inclusion of this mechanism in our theoretical model allowed investigation of the impacts of various types of bioavailability conditions on the overall fate and transport. Several scenarios related to the bioavailability effects are discussed in the simulation analysis section of this work. Equations 7 15) provide the complete set of mathematical equations for describing PCE NAPL dissolution coupled with rate-limited mass transfer and biodegradation reactions. The model equations, together with appropriate initial and boundary conditions, were solved using the general-purpose reactive transport code RT3D Clement, 1997; Clement et al., 1998; Clement et al., 2000). The RT3D code uses the operator-splitting OS) technique which allows representation of various reaction frameworks Clement, 1997). Using the OS technique, the reaction kinetics in Equations 7 15) can be separated from the transport equations to form the following reaction kinetic framework: d[pce] dt d[tce] dt d[dce] dt = kla t [PCE] [PCE]) k a Pce [PCE] ξ Pce [PCE] [P CE] ) 16) λ PceE = Y Tce/Pce k c Pce [PCE] ka Tce [TCE] ξ Tce [TCE] [T CE] ) 17) λ Tce = Y Dce/Tce k c Tce [TCE] ka Dce [DCE] ξ Dce [DCE] [D CE] ) 18) λ Dce 52 CLEMENT ET AL.

d[vc] dt = Y Vc/Dce k c Dce [DCE] ka Vc [VC] ξ Vc [VC] [V C] ) λ Vc 19) d[pce NAPL ] = φkt La dt ρ [PCE] [PCE]) 20) d[pce] = φξ Pce [PCE] [P ) CE] dt ρ λ Pce k s Pce [P CE] 21) d[t CE] = φξ Tce [TCE] [T ) CE] dt ρ λ Tce + Y Tce/Pce k s Pce [P CE] k s Pce [T CE] 22) d[dce] = φξ Dce [DCE] [D ) CE] dt ρ λ DceE +Y Dce/Tce k s Tce [T CE] k s Dce [D CE] 23) d[v C] = φξ Vc [VC] [V ) C] dt ρ λ Vc + Y Vc/Dce k s Dce [D CE] kvc s [V C] 24) In the RT3D model, a subroutine, known as the RT3D reaction package, is used to define the governing reaction kinetics. The reaction kinetics described by Equations 16 24) were programmed as a userdefined reaction package using four mobile components to represent the aqueous phase contaminants and five immobile components to represent the solid phase contaminants. MODEL TESTING Analytical solutions are not available for the multispecies transport equations developed in this work, even for simple one-dimensional cases. Therefore, the new reaction package was first tested against a single-species analytical solution involving source decay, sorption, and biological degradation processes. Later a more complex multi-species case was solved to verify the mass balance characteristics of the numerical solution. Comparison Against an Analytical Solution The objective of this test is to verify the workings of the new RT3D user-defined reaction package. The test problem considers one-dimensional transport of a contaminant degrading via first-order reaction in a sorbing porous medium. The contaminant source is assumed to degrade with time. The governing equation for this problem can be written as: R C = D 2 C t x 2 ν C kc 25) x The initial and boundary conditions for this problem are: Cx, 0) = 0 C0, t) = C s exp µt) 26) C, t) = 0 x where R is the retardation factor; D is the dispersion coefficient [L 2 T 1 ]; k is first-order degradation rate constant [T 1 ]; µ is rate constant of the exponentially decaying source [T 1 ]; C is the contaminant concentration [ML 3 ]; and C s is the initial maximum contaminant source concentration level at the boundary [ML 3 ]. Analytical solution to Equations 24) and 25) is given in van Genuchten and Alves 1982). The numerical modeling framework developed in this study was used to solve the analytical problem described above. In the numerical model, the DNAPL source was assumed to yield an initial source concentration C s ) of 1 mg/l, and this concentration was allowed to decay exponentially. The sorption processes were modeled under two extreme mass transfer conditions: firstly, a large mass transfer rate constant ξ) of 1.5 day 1 was used to model the equilibrium retarded plume condition, and later a very small mass transfer rate constant of 0.000015 day 1 was used to model the no sorption or tracer) condition. The value of the first-order linear partitioning coefficients λ was assumed to be 0.1875 L/kg which would yield a retardation coefficient of R = 2 under high mass transfer conditions), bulk density of the soil is 1.6 kg/l, porosity is 0.3, the degradation rate constant k is 0.01 day 1, the source decay constant µ is 0.005 day 1, transport velocity is 1 m/day, and dispersion coefficient is 0.5 m 2 /day. The column was discretized using 50 uniform grid cells. Figure 2 compares the breakthroughs obtained from the analytical and numerical models at x = 50 m, and the concentration profiles observed along the column after 50 days. Under both tracer transport and equilibrium sorption conditions, the result obtained from the numerical model closely matches the analytical solution. MODELING OF BIOREMEDIATION SYSTEMS 53

FIGURE 2 Comparison of numerical and analytical results a) breakthrough curves at x = 50 m b) Concentration profile in the column after 50 days of transport. Mass Balance Analysis The hypothetical test problem considered for the mass balance study is a 510 m long one-dimensional aquifer. The aquifer is divided into 51 cells of dimensions 10 m 10 m 10 m. This problem is a one-dimensional version of a validation problem discussed in the MT3D manual Zheng, 1990). The model parameters and other numerical parameters assumed in our simulation were similar to those used by Zheng 1990). The aquifer is assumed to be confined with constant head boundaries at either end of the flow domain and no flow boundaries at the top and bottom of the domain. The hydraulic gradient across the aquifer is 1/500, hydraulic conductivity is 50 m/day and porosity is 0.3; these parameters yield an effective transport velocity of 0.33 m/day. The longitudinal dispersivity is assumed to be 10 m and the ratio of transverse to longitudinal dispersivity is assumed to be 0.3. Other transport and reaction parameters assumed are given in Table 1. To simulate the source zone, 20,000 kg of PCE- NAPL was instantaneously discharged into the grid cell centered at x = 155 m resulting in the initial DNAPL mass fraction C N ) of 0.0125 mg/mg or the volumetric NAPL content of 0.0123, yielding 4% residual NAPL saturation). The DNAPL fractions at all other nodes are assumed to be zero. The initial aqueous and sorbed-phase concentrations of all other species are also assumed to be zero. The objective of the first simulation experiment is to verify the code performance by testing the mass balance characteristics of the model. In this test, the fate and transport of PCE emanating from 54 CLEMENT ET AL.

TABLE 1 Summary of model parameters Model parameters Values Reference PCE solubility, PCE at 20 C) 203 mg/l Bradford and Abriola 2001) Dynamic viscosity of water, µ w 0.89 centi poise Bradford and Abriola 2001) Uniformity, U in 1.21 Bradford and Abriola 2001) Median grain size, d 50 0.036 cm Bradford and Abriola 2001) Diameter of mean grain size, d M 0.05 cm Powers et al. 1994) PCE diffusivity, D m 6.56 10 6 cm 2 /sec Bradford and Abriola 2001) Water density, ρ w 1.0 kg/l Assumed NAPL PCE density, ρ m 1.623 kg/l Bradford and Abriola 2001) Bulk density of porous media, ρ b 1.6 kg/l Assumed Partitioning coefficient for PCE, λ Pce 1.0 kg/l 6.3) Clement et al. 2002) Retardation factor for PCE, R Pce ) Partitioning coefficient for TCE, λ Tce 0.57 L/kg 4.0) Clement et al. 2002) Retardation factor for TCE, R Tce ) Partitioning coefficient for DCE, λ Dce 0.25 L/kg 2.4) Clement et al. 2002) Retardation factor for DCE, R Dce ) Partitioning coefficient for VC, λ Vc 0.05 L/kg 1.3) Clement et al. 2002) Retardation factor for VC, R Vc ) Initial dissolution rate constant for PCE 19 day 1 Calculated based on assumed NAPL, k max La porous media properties Empirical constant, β 1 Assumed the DNAPL source was simulated for two years. A short two-year simulation period was selected in this test to avoid the advective loss of contaminant mass through the downstream boundary of the column. Also, in order to close complete mass balance within the column, the degradation rate of VC and the solid-phase biodegradation rates of all the species were set to zero. The aqueous phase biodegradation rates of PCE, TCE, and DCE were set to 0.02 day 1, 0.01 day 1, and 0.002 day 1, respectively. The values of the sorption mass transfer rate constants ξ) for all the species were set to 0.15 day 1. The simulated aqueous phase concentration profiles of all the species at the end of the two-year period are presented in Figure 3a. Mass balance calculations indicated that the model conserved the total mass. At the end of the two-year simulation period, the amount of DNAPL remaining in the NAPL-contaminated node was 1.0101 10 2 mg/mg, which is equivalent to 16,160 kg of DNAPL. Therefore, the remaining 3,840 kg of PCE must have dissolved and either partitioned into the solid phase or degraded. The total PCE equivalent mass of all the contaminants species i.e., the area below all the concentration profiles multiplied by their respective yield and retardation values) is estimated to be 3,880 kg, which is close to the total mass of PCE dissolved into the system. The overall mass balance error at the end of the two-year simulation period is about 0.2% of the initial DNAPL mass. Figure 3b shows the breakthrough curves of various dissolved species at the 20th cell 40 m downstream from the DNAPL source) after 18 years of simulation. It is interesting to note that the concentration of the dissolution product PCE) reaches a quasisteady state condition within two years and remains steady until the DNAPL mass is considerably depleted. All other daughter products also appear to reach a similar quasisteady state condition within three years. Depletion of the DNAPL source zone starts to impact the breakthrough concentration profiles after 12 years, when the concentration profiles appear to relax into a transient mode. MODEL SIMULATIONS RESULTS Obtaining precise values for all the parameters used in the proposed model is a difficult task. Therefore, several sets of simulations were completed to provide a basic understanding of the model behavior under various parameter conditions. The results are summarized by quantifying the response of the model to systematic variations in the values of biodegradation rates, DNAPL dissolution rates, and sorption mass transfer rates. Model Response to Variations in Biodegradation Rates In the first set of simulations, biodegradation rate constants were varied. Simulations were completed MODELING OF BIOREMEDIATION SYSTEMS 55

FIGURE 3 Predicted concentration distribution of PCE, TCE, DCE, and VC a) Profile along the column after two years b) Breakthrough curve at x = 195 m. with aqueous phase biodegradation rate constants as 0.02 day 1, 0.01 day 1, 0.002 day 1, and 0.001 day 1 for PCE, TCE, DCE, and VC, respectively. These assumed values of degradation rate constants are within the range of values reported in the literature Wiedemeier et al., 1999). Biodegradation was assumed to occur in the solid-phase with rates identical to those assumed for the aqueous phase i.e., complete bioavailability is assumed). In order to assess the sensitivity, two sets of simulations were completed by perturbing the base level biodegradation rates of PCE both aqueous and soil phase rates) by an order of magnitude. In all of these simulations, the DNAPL dissolution rate parameter, kla max, was fixed at 19 day 1, and the values of sorption mass transfer rate constant, ξ, were fixed at 0.008 day 1 for all the species. Other flow and transport parameters used were identical to those used in the previous mass balance example problem. Figure 4 shows the results of the model response to variation in PCE biodegradation rate constant at the end of 5 years. The results indicate that when the biodegradation rate for PCE is high, PCE and TCE concentrations decrease rapidly yielding high concentrations of DCE and VC. It should be noted that although higher biodegradation rate for PCE result in rapid removal of PCEand TCE contaminants, the reactions lead to accumulation of daughter products, which could pose several environmental concerns. For example, decay products, such as VC, are more toxic than its parent products TCE and PCE. Therefore, the performance of a chlorinated solvent 56 CLEMENT ET AL.

FIGURE 4 Model predictions for various PCE biodegradation rates t = 5 years). 57

bioremediation system should always be carefully screened for conditions that could possibly lead to the accumulation of more toxic daughter products. Model Response to Variations in DNAPL Dissolution Rates The response of the model to variations in the DNAPL dissolution rate was studied by perturbing the rate constant k max La. Since the overall DNAPL dissolution rate given by Equation [4]) varies linearly with the value of k max La, varying this parameter by a factor will vary the overall DNAPL dissolution rate by a similar factor over the entire simulation period. The variations in the DNAPL dissolution rate was quantified under the following two bioavailability conditions: in the first case, biodegradation was assumed to occur both in aqueous and solid phases complete bioavailability condition), and in the second case biodegradation was assumed to occur only in the aqueous phase i.e., direct solid-phase bioavailability was assumed to be negligible). Three simulations were completed under the two assumed bioavailability conditions with the values of maximum DNAPL dissolution rate constant k max La = 19, 1.9, and 0.19 day 1. The values of ξ were fixed at 0.008 day 1. The values of aqueous phase biodegradation rates were fixed at the baseline values used in section 4.1. Whenever degradation was assumed to occur in the solid phase, the rates were assumed to be identical to aqueous phase degradation rates. Figure 5 summarizes the result for the model response to variation in DNAPL dissolution rate constant. Figures 5a and 5b show the concentration distribution of PCE and VC, respectively, at the end of the five-year simulation period when biodegradation is assumed to occur in both phases. The simulation results showed that the PCE contamination was concentrated to a small region close to the DNAPL source but its immediate daughter product TCE results not shown) was spread over a wider region. Similarly, the DCE concentration profile not shown) was wider than the TCE profile, and finally the VC concentration profile shown in Figure 5b) was wider than the DCE profile. Thus, contamination by a daughter species tends to impact a larger zone when compared to its immediate parent species. Increases in dissolution rate lead to wider concentration profiles and higher concentration peaks. Figures 5c and 5d show the results for the second set of simulations where biodegradation is considered to occur only in the aqueous phase. The observed trends in the predicted concentration profiles were similar to those observed in the previous set of simulations. However, the total amount of PCE mass in the column was relatively high when solid phase biodegradation processes were ignored. Also, the model predicted VC profiles were observed to be relatively insensitive above a critical DNAPL dissolution rate constant of 1.9 day 1.ForPCE, the value of critical limiting rate constant was slightly higher. The overall dissolved concentration level of PCE appears to control the contaminant dissolution process when the dissolution rate constant was above the critical value. Comparison of the results shown in Figures 5a and 5c or 5b and 5d) indicates that the predicted aqueous phase contaminant concentration levels are marginally lower for the case when degradation was assumed to occur in both phases. This is because, when complete bioavailability is assumed, the contaminant mass is consumed on the solid phase leading to lower solid phase concentration levels. This increases the concentration gradient the driving force for mass transfer reactions) towards the solid phase and facilitates increased aqueous phase contaminant mass partitioning onto the solid phase, thus resulting in lower aqueous phase concentration levels. Therefore, for a given solubility limit, aqueous phase concentrations can be expected to be at a lower level when total bioavailability conditions are assumed. Model Response to Variations in Sorption Mass Transfer Rates In this set of simulations the response of the model to variations in the sorption mass transfer rate constant ξ was analyzed. The values of degradation rate constants were fixed similar to the baseline values used in previous simulations. When biodegradation was assumed to occur in both liquid and solid phases, the solid phase biodegradation rates were assumed to be identical to the aqueous phase rates. Three simulations were completed by setting the ξ values of all the species at 0.15, 0.008, and 0.00015 day 1, which are the range of ξ values used in Clement et al. 1998). The value of DNAPL dissolution rate parameter kla max was set at 19 day 1, which was the calculated rate using the assumed porous media properties. 58 CLEMENT ET AL.

FIGURE 5 Model predictions for various DNAPL dissolution rates: a) and b) biodegradation is assumed to occur in both aqueous and solid phases; c) and d) biodegradation is assumed to occur only in the aqueous phase t = 5 years). 59

60 FIGURE 6 Model predictions for various sorption mass transfer rate constants t = 5 years).

The predicted aqueous phase concentration profiles after 5 years, assuming biodegradation to occur in both solid and aqueous phases, are summarized in Figure 6. When sorption mass-transfer rate was high, biodegradation can destroy contaminants in both solid and aqueous phases. Therefore, the total amount of PCE and TCE mass in the column was minimum when ξ = 0.15 day 1. Since the assumed biodegradation rates of DCE and VC are relatively less than the PCE and TCE degradation rates, the column tends to accumulate large amounts of DCE and VC when the value of ξ is high. Unfortunately, it is difficult to observe further definite trends from the results. The overall mass transfer process seems to be controlled by complex nonlinear exchange mechanisms. Therefore, the simulation experiments were re-run for 25 years and a detailed mass balance analysis was completed to interpret the predicted aqueous and sorbed phase concentration profiles. Figure 7a shows the cumulative mass removed by the biodegradation activity within the column over the 25-year simulation period. The mass removed due to biodegradation was computed by deducting the following two components from the initial solvent mass: 1) the mass of various solvent species in PCE-equivalent mass units) remaining within the aquifer column, and 2) the mass of various solvent species flushed through the downgradient boundary. It can be observed from Figure 7a that the cumulative contaminant mass destroyed due to biodegradation increases rapidly with time and reaches a steady level around 15 years, after which the DNAPL source was totally depleted. The total mass destroyed due to biodegradation is high when FIGURE 7 Total solvent mass removed by biodegradation under various values of ξ a) biodegradation is assumed to occur in both aqueous and solid phases; b) biodegradation is assumed to occur only in the aqueous phase. MODELING OF BIOREMEDIATION SYSTEMS 61

the ξ value is high. Note for the low value of ξ, the partitioning rate of contaminants to the solid phase is small and, therefore, under this condition, most of the contaminant mass was advected and lost through the right boundary. This can be clearly seen in Figures 6c and 6d where the predicted aqueous phase concentrations of DCE and VC are considerably high, closer to the right boundary, when ξ values are small. Nonlinear trends, similar to those shown in Figure 6, were also observed for the second set of simulations where the solid phase biodegradation was assumed to be negligible results not shown). Figure 7b shows the mass balance results for these simulations. The mass balance profiles presented in the figure are relatively insensitive to changes in ξ values; this is, in part, due to the fact that the total mass removed via biodegradation was considerably low in this case when compared to the mass removal results predicted for the complete bioavailability case. SUMMARY AND CONCLUSIONS This article presents a mathematical framework for coupling DNAPL dissolution processes with ratelimited sorption and biodegradation processes. The coupled model equations were implemented in a user-defined reaction package and solved by the reactive transport code RT3D. The reaction package was first tested by solving a reactive transport problem for which an analytical solution is available. Numerical performance of the model was further validated through the mass balance analysis of the simulation results. Application of the model was illustrated by using a hypothetical case study. A detailed simulation analysis was completed to explore the effects of changes in various reaction parameters used in the model. The analysis indicated that the sequential PCEdechlorination process could lead to excessive accumulation of certain degradation daughter products. Therefore, chlorinated solvent bioremediation systems should always be carefully monitored for conditions that could possibly lead to accumulation of more toxic degradation byproducts, such as vinyl chloride. Comparison of the simulation result for different bioavailability conditions indicated that the predicted aqueous phase contaminant concentration levels are relatively low under complete bioavailability conditions. This is because when the solid-phase degradation or complete bioavailability) was allowed in the model, more contaminant mass partitioned to the soil phase to compensate for the decayed soil phase mass) and this partitioning process led to lower aqueous phase concentration levels. Therefore, for a given solubility limit, aqueous phase concentrations can be expected to be at lower levels when complete bioavailability conditions are assumed. Predictive simulations for the variations in the rate-limited sorption process rate showed that the mass transfer process assumed in the model appears to be mediated by complex non-linear mass exchange mechanisms. Varying the value of masstransfer rate constant yielded concentration profiles and mass-balance results that help demonstrate these nonlinear effects. This study provides a general framework for modeling DNAPL dissolution processes coupled to ratelimited sorption processes in a biologically reactive porous medium. The framework is a useful tool for developing a better understanding of the combined effects of physical, chemical and biological reactive transport mechanisms in groundwater systems. The proposed framework can serve as a basis for developing rational design methods for quantifying the effectiveness of natural attenuation and/or enhanced bioremediation systems at DNAPL-contaminated field sites. ACKNOWLEDGEMENTS This study was completed at Auburn University and was, in part, funded by a project from the Seoul National University funded by the Frontier Project of the Korea Ministry of Science and Technology. Additional funding for Dr. Gautam was provided by Battelle Pacific Northwest National Laboratory through the Australian Research Council s SPIRT Grant program. REFERENCES Bradford, S. A., and L. M. Abriola. 2001. Dissolution of residual tetrachloroethylene in fractional wettability porous media: Incorporation of interfacial area estimates. Water Resour. Res. 37:1183 1195. Brusseau, M. L., N. T. Nelson, M. Oostrom, Z. Zhang, G. R. Johnson, and T. W. Wietsma. 2000. Influence of heterogeneity and sampling method on aqueous concentrations associated with NAPL dissolution. Environ. Sci. Technol. 34:3657 3664. Brusseau, M. L., Z. Zhang, N. T. Nelson, R. B. Cain, G. R. Tick, and M. Oostrom. 2002. Dissolution of nonuniformly 62 CLEMENT ET AL.

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Simulating regional-scale behavior of a trichloroethene plume during pump-and-treat remediation. Water Resources Research 35:2921 2935. Zheng, C., 1990. MT3D: A modular three-dimensional transport model for simulation of advection, dispersion and chemical reactions of contaminants in groundwater systems. USEPA report. Zhu, J., and J. F. Sykes. 2000. The influence of NAPL dissolution characteristics on field-scale contaminant transport in subsurface. J. Contam. Hydrol. 41:133 154. APPENDIX A: ESTIMATION OF DNAPL DISSOLUTION RATE CONSTANT In this appendix, we modify the model by Powers et al. 1994) to develop a simple scaling-type expression for predicting the transient variations in DNAPL dissolution rates. The first order dissolution rate constant, k La, can be computed using the following empirical model Powers et al., 1994): S h = 4.13R 0.598 e d50 d m ) 0.673 U 0.369 in θn θ Ni ) β A.1) where S h [= k Lad50 2 D m ] is the modified Sherwood number; R e [= νρ wd 50 µ w ] is the Reynolds number; d 50 is the MODELING OF BIOREMEDIATION SYSTEMS 63