Mass Transfer and Bioavailability of PAH Compounds in Coal Tar

biotreatment of polynuclear aromatic hydrocarbons (PAHs) released from coal tar NAPL in solid-slurry and liquid-liquid dispersion systems. A multi-ste...
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Environ. Sci. Technol. 1997, 31, 2260-2267

Mass Transfer and Bioavailability of PAH Compounds in Coal Tar NAPL-Slurry Systems. 1. Model Development A N U R A D H A R A M A S W A M I * ,† A N D RICHARD G. LUTHY Department of Civil and Environmental Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213

A modeling framework is developed that addresses mass transfer, bioavailability, and potential biotreatment rates that may be achieved under stable microbial conditions in slurry systems containing multi-component non-aqueousphase liquids (NAPLs). The framework is applied to describe biotreatment of polynuclear aromatic hydrocarbons (PAHs) released from coal tar NAPL in solid-slurry and liquid-liquid dispersion systems. A multi-step mass transport-degradation model considers equilibrium partitioning of PAH compound at the NAPL-water interface, followed by three sequential kinetic processes occurring in the aqueous phase: micropore sorption-diffusion, bulk aqueous-phase transport, and first-order biodegradation of bulk-phase substrate. Dynamic changes in NAPL-water equilibria due to depletion of PAH compound from the NAPL are incorporated into the model. Model results indicate that the overall rate of biotransformation of organic compounds from NAPLs is controlled by NAPL-water equilibrium processes represented by a dimensionless solubility factor, as well as the slowest of three aqueous-phase kinetic processes determined by pair-wise analysis of the dimensionless Biot number, the Thiele modulus, and the Damkohler number. Analytical equations and computer simulations demonstrate the utility of the dimensionless parameters in quantifying bioavailability, identifying dominant rate-limiting processes, and developing simpler models for biotransformation in NAPL-slurry systems. Some aspects of the modeling framework are evaluated in a companion paper using data from controlled laboratory experiments.

Introduction Coal tar is a dense non-aqueous-phase liquid (D-NAPL) often associated with subsurface contamination at former manufactured gas plant (MGP) sites (1). Coal tar is a multicomponent NAPL composed of hundreds of aromatic organic compounds, including polycyclic aromatic hydrocarbon (PAH) compounds such as naphthalene, phenanthrene, chrysene, etc. The composition and physical properties of coal tars may vary widely depending on the chemical process and feedstock used at the MGP facility (2, 3). The complex physicochemical properties of coal tar may be associated with observed changes in NAPL-water interfacial structure upon * Corresponding author e-mail: [email protected]; phone: (303) 556-4734. † Present address: Department of Civil Engineering, University of Colorado, Denver CO 80217.

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aging (4, 5) and corresponding wettability reversals (6, 7). Due to the slow release of organic solutes from the entrapped NAPL, coal tar can function as a long-term source of contamination in subsurface environments. Proposed in situ treatment strategies for source material at NAPL-contaminated sites include steam injection (8), enhanced solubilization by solvents and surfactants (9, 10), and bioremediation (11). In situ treatment methods are primarily constrained by slow rates of mass transfer and uncertainties regarding both location and mobility of NAPLs in the subsurface. Consequently, above-ground treatment of NAPL-contaminated soils may be required as an alternative or as a supplement to in situ approaches. Above-ground biotreatment systems, such as land farms or bioslurry systems, attempt to overcome mass transfer limitations encountered in the subsurface by employing mixing to achieve more uniform distribution of the NAPL and enhanced contact with the aqueous phase. In addition, adequate nutrients and oxygen may be provided to more readily maintain optimal conditions for biotreatment. Such an approach may be particularly appropriate for near-surface contamination by NAPLs like coal tar that are slow to dissolve and persist for long periods of time in soil and sediment matter. At some coal tar-contaminated sites, in-place bioslurry treatment of a top layer of contaminated sediment material has also been proposed as a means to create a ‘clean’ cap over a deeper NAPL-contaminated zone (12). However, little is known about the impact of physicochemical processes on the rate of bioslurry treatment of contaminated media containing complex mixtures such as coal tar.

Mass Transfer and Biotreatment Several bench-scale studies have been conducted with coal tar-contaminated soils in order to assess the potential for above-ground biotreatment (13-15). The results of some of these studies indicate little or no biodegradation (15), while others (14) show that the cumulative fraction of PAH mineralized approaches a limiting value. Several factors that could potentially limit biodegradation, e.g., toxicity and the viability of microbes, have been investigated in some laboratory screening tests and found not to be significant (14, 15). In these instances, examination of the aqueous phase revealed relatively low PAH concentrations, indicating that availability of aqueous-phase PAH substrates to microbes could be the rate-limiting factor. However, bioavailability and rate-limiting factors in the above studies were assessed qualitatively with soils poorly characterized with respect to NAPL content and saturation. Consequently, no generalizable results could be ascertained from those studies. The bioavailability of organic substrates has been quantitatively assessed in a few two-phase, soil(solid)-water systems (16-20). Sorbed organic substrates were found to be unavailable for microbial degradation, and a working hypothesis was developed for two-phase soil-water systems that considers primarily the aqueous-phase organic substrate to be readily bioavailable. Very little is known about bioavailability when a NAPL is introduced into the system. Seagren et al. (21) have theoretically analyzed coupled mass transfer and biodegradation in a laboratory column using a pure one-component NAPL. Efroymson and Alexander (22) studied mass transfer and biodegradation from a simple twocomponent NAPL in a slurry batch reactor. The behavior of a complex NAPL such as coal tar in a bioslurry system has yet to be investigated in a quantitative manner. This paper presents mathematical models that couple physicochemical phenomena with bioavailability and biokinetic processes occurring in slurry systems containing coal tar NAPL. The

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TABLE 1. Summary of Governing Equations for Multi-Step Mass Transport-Degradation Model Describing Slurry Biotreatment of Microporous Solids Contaminated with Coal Tar NAPL location

process

r ) ri initial equilibrium NAPL-water interface dynamic equilibrium depletion of the PAH from the NAPL

mathematical model

C(ri,t)0) ) Cs0 )

[

]

MWct PAH xPAHCpure liq. MWPAH 0

C(ri,t) ) Ceq(t) ) F(PAH t) Cs0

F(PAH t) )

eq

assumptions and references

1

instantaneous equilibrium (25-27) described by Raoult’s law for ideal NAPL (28-30) no change in total coal tar mass due to depletion of more soluble PAHs (31) time-varying PAH mass fraction in coal tar is given by the initial value, xPAH 0 , factored by F(PAH t) , the fraction of initial PAH mass remaining in the NAPL at time, t linear sorption isotherm with coeff, Kd; no solid-phase diffusion; tortuosity, ξ, inversely related to porosity, n (32, 33) equal flux condition with aqueous-phase mass transfer coefficeint, kl

2 3

PAH Mct,( t) PAH Minit.,ct

; F(PAH t)0) ) 1 4

∂F(PAH t)

ri < r < R pore water

sorption-retarded diffusion

-1 Vkla[C(R,t) - C(t)] PAH ∂t Minit.,ct ∂C Den ∂2C 2 ∂C ) + ∂t γ ∂ r2 r ∂r where γ ) n + KdFs(1 - n); De ) Dm/ξ

r)R particle surface

transport thru external aqueous boundary layer

-Den

=

[

NSh )

bulk water

coupled mass transfer and biodegradation

∂C(t) ∂t

[ ]

]

∂C(r,t) ∂r

5

6 r)R

) kl [C(R,t) - C(t)]

[ ] [] [ ]

kl d d4/3 1/3 0.62 ) 2 + 0.47 Dm µ/F Ds 0.17 µ/F Dt Dm

7

chemical engineering correlation for mass transfer from particles and liquid globules in a stirred tank (34, 35)

8

pseudo-first-order biokinetic constant, kbio, for stable microbial populations and low substrate concentration (21) identically sized particles of radius, R, diameter, d, number density, np, and, mass transfer rate coefficient, kla

0.36

) kla [C(R,t) - C(t)] - kbioC(t)

where kla ) 4πR2npkl

9

modeling framework is evaluated through laboratory experiments, which are presented in a companion manuscript (23).

Conceptual Modeling Framework Two bioslurry treatment regimes are considered in this study: (a) a liquid-liquid system comprising coal tar globules dispersed in water and (b) a slurry of coal tar-containing solid aggregates dispersed in water. Mass transfer and biodegradation of PAH compounds from coal tar is schematically illustrated for the two systems in Figure 1a,b. Consistent with recent findings on the biodegradation of sorbed hydrophobic organic compounds in soil-water systems (1620, 24), it may be inferred that it is the bulk aqueous-phase organic substrate that is readily available for microbial degradation. Thus, the overall rate of biotransformation of PAH compounds released from coal tar NAPL may be controlled by the following: (a) Physicochemical equilibrium phenomena related to the partitioning of PAH solutes between NAPL, water, and porous solid. (b) Physicochemical kinetic processes related to the rate of mass transfer of PAH compounds from the organic phase to the bulk aqueous phase. (c) Biokinetic phenomena pertaining to the intrinsic biodegradation rates of the microbes, the competitive utilization of tar-derived substrates, toxic/inhibitory effects of coal tar solutes and/or their degradation products, and limiting aqueous-phase threshold concentrations below which microbial growth and enzymatic activity is not supported. The focus of this paper is on physicochemical equilibrium and kinetic phenomena that influence biotransformation rates; adequate oxygen and nutrients and stable and viable microbial populations are assumed to exist in the NAPLslurry bioreactors. The modeling framework in this study consists of developing a multi-step mass transport-biodegradation model, employing dimensionless groups for identifying dominant

FIGURE 1. Schematic illustrating coal tar bioslurry systems. (a) Coal tar globule in NAPL-Water dispersion system. (b) Coal tarcontaining microporous particle in solid-slurry system. rate-controlling mechanisms in slurry bioreactors. The dimensionless parameters aid in reducing the multi-step mass transport-degradation model to simpler one- or two-step models, the parameters of which may be determined from macroscopic physical and chemical properties of the bioslurry system. The model development primarily addresses coal

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TABLE 2. Governing Equations for Multi-Step NAPL-Slurry Biotreatment Model, Expressed in Dimensionless Forma location

process

r′ ) r′i NAPL-water interface

mathematical representation

dynamic equilibrium

C′(r′i, τ) )

PAH F(τ)

depletion of PAH solute from the NAPL

PAH ∂F(τ)

PAH MWct V Cpure liquid SF [C′(R′,τ) - C′(r)] where SF ) , Da MWPAH Mtot.ct

∂τ

=

[

]

Da ) r′i < r′ < R′ pore water

sorption-retarded diffusion

r ) R′ particle surface

particle surface to bulk water transfer

bulk water

coupled mass transfer & biodegradation

τ ) 0; time ) 0

initial conditions

a

[

]

kbio kla

∂C′(r′,τ) ∂2C′(r′,τ) 2 ∂C′(r′,τ) kbioγ (R - ri)2 2 ) + where φ ) φ2 ∂r r′ ∂ r′ Den ∂ r′ 2 ∂C′(r′,τ) kl (R - ri) ) Bi[C′(R′,τ) - C′(τ)] where Bi ) ∂r′ r′)R′ Den ∂C′(τ) 1 ) [C′ - C′(τ)] - C′(τ) where Da ) kbio/kla ∂r Da (R′,τ) C′(r′i,0) ) 1; C′(r′,0) ) 0 for r′ > r′i; C′(t) ) 0 in bulk water; PAH F(0) ) 1 in NAPL

[ ]

Concentration C′ ) C/Cs0, radius r′ ) r/(R - ri), and, time τ ) kbiot.

tar NAPL-solid slurry systems (Figure 1b); liquid-liquid tarwater dispersions are discussed as a special case of the solidslurry system.

Modeling Coal Tar-Solid Slurry Systems Consider a gently mixed bioslurry system composed of identically-sized spherical microporous aggregates partially saturated with coal tar NAPL (Figure 1b). Coal tar NAPL is shown to have penetrated the micropores of the soil particle in Figure 1b, consistent with observations that coal tar can function as the preferentially wetting fluid in subsurface systems (6, 7). Bacteria are assumed to be size-excluded from the micropores, thus only solubilized aqueous-phase PAH present in the external bulk solution is available for biodegradation. In such a system (Figure 1b), four processes occur in series and result in the solubilization and biodegradation of the PAH compound: (a) PAH dissolution at the intraparticle NAPL-water interface. (b) Intraparticle sorption-retarded diffusion of PAH in pore water. (c) Transport of PAH to bulk water from the surface of the particle. (d) Biodegradation of PAH in the external bulk aqueous phase. The above multiple processes are coupled together and described mathematically in eqs 1-9 summarized in Table 1. Dimensionless Parameters. The multi-step model presented in Table 1 may be expressed in a dimensionless form by normalizing the equations in Table 1 using the following transformations: concentration C′) C/Cs0, radius r′ ) r/(R - ri), and, time τ ) kbiot. The normalized equations are shown in Table 2 and contain three dimensionless rate parameters (Biot number, Damkohler number, and Thiele modulus) and a dimensionless solubility factor. The significance of each of these dimensionless groups is discussed below. Biot Number. The Biot number, Bi, may be expressed as

kl [C(ri) - 0]

Bi )

D en

[

]

C(ri) - 0

)

R - ri maximum external mass flux across particle surface maximum intraparticle diffusive flux at particle surface (10) Systems with Biot numbers smaller than unity indicate rapid

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FIGURE 2. Variation of the Biot number in NAPL-solid slurry systems. The Biot number increases as the tortusity is increased (porosity is varied from 0.8 to 0.2), and the coal tar residual saturation is decreased. intraparticle diffusion processes relative to boundary-layer transport. For a gently mixed slurry system with kl = Dm/R, eq 10 reduces to

( )

Bi = (ξ/n) 1 -

ri R

While the exact position of the tar-water interface, ri, is not known, a conservative estimate may be computed from the microporous NAPL residual saturation, θ [volume of coal tar/volume of voids], in the system. Assuming coal tar to be present near the center of the solid aggregate, a volumetric relationship indicates that ri/R ) θ1/3, from which Bi = (ξ/ n)(1 - θ1/3). The dependence of the Biot number on residual saturation and tortuosity/porosity is illustrated in Figure 2 with ξ ) 1/n. At large residual saturations and/or in more porous, less tortuous media, diffusion occurs much faster than boundary-layer mass transfer yielding Bi , 1. In the limiting case of 100% saturation with the NAPL, no pore water exists, and bulk-phase transport is the dominant mass transfer phenomenon. Porous particles fully saturated with coal tar NAPL or solid particles coated with NAPL films are akin to spherical NAPL globules. Thus, a liquid-liquid dispersion

system may be described as a special case of the solid slurry system, with Bi ) 0. Thiele Modulus. The Thiele modulus may be written as

φ2 )

kbio γ C(ri,t) (R - ri)(particle surface area) Den

[

]

C(ri,t) - 0 R - ri

)

(particle surface area) maximum biokinetic rate (11) maximum diffusion rate

where C(ri,t) is the interfacial equilibrium aqueous concentration, Ceq(t). The denominator represents the maximum intraparticle diffusion rate achieved when the concentration differential is maximum, providing the greatest driving force for diffusion. The numerator represents the maximum potential biodegradation rate that may be achieved if the PAH compound trapped within the microporous particles was available for microbial degradation, i.e., if pore diffusion occurred very rapidly and sorption was minimal. A value for φ2 much greater than unity would indicate that the overall biotransformation rate is constrained by sorption-diffusion occurring within the microporous solid aggregates. Large values of φ2 are obtained for small effective diffusivities, large pore water diffusion distances, large sorption coefficients, and/or rapid biokinetics. Damkohler Number. The Damkohler number represents the ratio of the maximum rate of solute release from the surface of the particles into the external bulk fluid relative to the maximum rate of solute consumption in the bulk aqueous phase by biodegradation. Thus, Da may be written as

Da )

FIGURE 3. Flow chart depicting the simplification of the multi-step mass transport degradation model. fraction of PAH in coal tar, the solubility factor can be rewritten as

kbio C(R)

) kla C(R) maximum rate of solute biodegradation in bulk fluid maximum rate of solute release to bulk fluid (12)

Values of Da less than unity indicate that the rate at which solute is released from the particle surfaces is much faster than the rate of biodegradation, thus the overall rate of biotransformation will be limited by biokinetic phenomena. Conversely, a value of Da greater than unity would indicate that the overall rate of biotransformation is limited by the rate of release of solute from the surface of the particles to the bulk aqueous phase. The Da number will be large for small a, i.e., small specific surface areas for mass transfer, slow mass transfer coefficients, kl, and large values of kbio, i.e., rapid biokinetics. Solubility Factor. The dimensionless solubility factor compares the maximum PAH mass that may partition to the aqueous phase at the start of bioslurry treatment with the PAH PAH mass initially present in NAPL coal tar, Minit.,ct . Thus, the solubility factor represents the maximum fraction of the NAPL-derived PAH mass that may be available in the aqueous phase for flushing, biodegradation, or other aqueous-phase operations:

SF )

V Cs0 PAH Minit.,ct

)

max mass of PAH solute in bulk fluid PAH mass initially present in coal tar (13)

The SF functions as a scale factor that quantitatively relates the transport and fate of a PAH compound in bulk water with the depletion of that PAH compound from coal tar NAPL. A large value of SF indicates greater response of the PAH mass in coal tar NAPL to flushing and biodegradation in the aqueous PAH phase. Using eq 1 to describe Cs0, and writing Minit.,ct ) PAH x0 Mtot.ct, where Mtot.ct represents the total invariant mass of coal tar present in the system and xPAH is the initial mass 0

SF )

[

]

PAH MWct VCpure liq. MWPAH Mtot.ct

(14)

SF is independent of kinetic parameters and may readily be computed from PAH compound solubility data. Large values of SF are indicated in bioslurry systems with large bulk waterNAPL (V/Mtot.ct) ratios and for those PAH compounds with a greater solubility in water.

Developing Simplified Models The three dimensionless rate parameters (Bi, φ2, and Da) offer a pair-wise comparison of three sequential kinetic processes occurring in the aqueous phase and can together be used to identify the slowest rate-limiting process that dominates the system. As shown in the flow chart in Figure 3, the identification of slowly occurring rate processes can result in simplification of the multi-step model into simpler one- and two-step models. Two-Step Models. The companion laboratory experiments conducted as part of this research employ porous silica particles with a fairly high residual saturation of coal tar (23). For such a slurry system, a conservative estimate of the Biot number yields Bi < 1, and rapid intrapore diffusion results in the concentration at the surface of the particles being very nearly equal to the intrapore interfacial equilibrium concentration, i.e., C(R,t) = C(ri,t) = Ceq(t). In such systems, pore diffusion processes may be neglected and a two-step dissolution-degradation model can be developed that couples external boundary layer transport with bulk-phase biodegradation. The two-step model may be written as

∂C(t) ∂t

) kla[Ceq(t) - C(t)] - kbioC(t)

for Bi < 1

(15)

Equation 15 is a mass balance equation for aqueous phase PAH in the bioslurry system. Dynamic changes in equilibrium concentration may be represented by the Raoult’s law

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expressions in eqs 1-3 (Table 1). Equations 1-3 and 15 together constitute a simplified two-step dissolutiondegradation model. One-Step Models. Analytical solution of eq 15 for conditions of slow variations in Ceq(t) enables further reduction of the two-step model into single step models, based on the value of the Damkohler number. It can be shown that when kla . kbio, i.e., when mass transfer occurs much faster than biodegradation, the aqueous-phase PAH concentration in the bioslurry system is very close to equilibrium such that C(t) = Ceq(t). Assuming zero growth of microorganisms and no accumulation of intermediate degradation products, the rate of mineralization of a PAH compound is given by the rate of removal of aqueous phase PAH by degradation as

∂CCO2 ∂t

) kbioC(t) = kbioCeq(t)

Tot ∂MCO 2(t)

PAH Minit.,ct

∂t

)

V

∂CCO2

PAH Minit.,ct

∂t

=

V kbio Ceq(t) PAH Minit.,ct for kbio , kla (17)

PAH where Minit.,ct is the mass of a PAH compound initially Tot present in the coal tar NAPL in the bioreactor, and MCO is 2(t) the cumulative mass of that PAH compound that has been mineralized upto a time, t. Using eq 2 to describe the PAH equilibrium concentration, Ceq(t), and writing Minit.,ct ) xPAH M , eq 17 becomes tot.ct 0

Tot ∂MCO 2(t)

1 PAH Minit.,ct

∂t

= SF × FPAH (t) kbio

for Da , 1

(18)

where FPAH represents the fraction of the target PAH com(t) pound remaining in the tar phase at time, t, and SF is the solubility factor defined in eq 14. The term SF × FPAH (t) is akin to a time-varying solubility factor, SF(t), that accounts for reduced fractions of the initial tar-derived PAH mass partitioning into the aqueous phase due to the decreasing PAH mole fraction in coal tar NAPL (eq 2). Equation 18 indicates that in coal tar NAPL-bioslurry systems characterized by rapid mass transfer relative to biodegradation (Da , 1 ), the rate of mineralization of PAH compound from coal tar NAPL depends on the aqueous-phase biokinetic rate constant, kbio, as well as NAPL-water equilibrium processes represented by the solubility factor, SF(t). When mass transfer occurs much slower than biodegradation, analysis of eq 15 shows that the aqueous-phase PAH concentration in the bioslurry system is small compared to the equilibrium concentration: C(t) = (kla/kbio)Ceq(t). Following the same sequence of steps outlined above, the fractional biomineralization rate for a PAH compound in coal tar NAPL is given by Tot ∂MCO 2(t)

1 PAH Minit.,ct

∂t

=

V klaCeq(t) = SF × FPAH (t) kla PAH Minit.,ct for Da . 1 (19)

In systems constrained by slow mass transfer rates, the

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system

parameter values

A; Bi ) 0.11

R ) radius of particles ) 0.125 cm np ) number density of particles ) 5/mL Kd ) sorption coefficient ) 2 mL/g n ) porosity ) 0.8 ξ ) tortuosity ) 1.25 θ ) residual tar saturation ) 0.8 R ) radius of particles ) 0.125 cm np ) number density of particles ) 80/mL Kd ) sorption coefficient ) 2 mL/g n ) porosity ) 0.2 ξ ) tortuosity ) 5 θ ) residual tar saturation ) 0.2

B; Bi ) 10

for kbio , kla (16)

where the left-hand side of eq 16 represents the increment of PAH mass converted to CO2 per unit time, per unit aqueous volume in the reactor. Biomineralization data are often reported in terms of a fraction of the contaminant mass initially present in the system. Thus, using eq 16, the rate of PAH mineralization from the entire bioreactor aqueous volume, V, may be expressed as a fraction of the PAH mass present initially in the coal tar NAPL:

1

TABLE 3. Base Case Solid-Slurry Parameters Used in Computer Simulations

ENVIRONMENTAL SCIENCE & TECHNOLOGY / VOL. 31, NO. 8, 1997

apparent rate of biomineralization of PAH compound from coal tar NAPL is directly related to the aqueous-phase mass transfer rate coefficient, kla, through the time-varying solubility factor, SF(t) given as SF(t) ) SF ×FPAH (t) .

Computer Simulations The performance of the mathematical models and the utility of the different dimensionless parameters was evaluated by simulating the biotransformation of naphthalene from coal tar present at residual saturation within microporous media. The simulations depict the biotransformation of a coal tar NAPL with 2.2% naphthalene, as employed in the experimental studies. The efficacy of the dimensionless parameters was evaluated by comparing PAH concentration and biomineralization profiles obtained from the multi-step mass transport-degradation model with those predicted from the simpler models described above. Both the multi-step mass transport-degradation model and the simplified one-step models were implemented using a numerical finite difference technique. In the case of the multi-step model, the transformation u ) C′r′ (36) was used to linearize the radial-spherical equations summarized in Table 2. The accuracy of the numerical scheme was verified by computing a mass balance for the PAH compound in the system at the end of each time step. The sensitivity of the numerical scheme to changes in the magnitudes of the time and distance increments was studied. The simulations were executed at time increments of ∆τ ) 10-4 and distance increments of ∆r′ ) 0.05, which resulted in less than a 2% mass balance error in the system. In order to assess the utility of the dimensionless parameters, independent simulations were conducted in which the dimensionless parameters were varied over a broad range of values by changing the physical and chemical properties of the porous matrix (e.g., particle size, number density, sorption capacity, etc.). Two contrasting systems, A and B, with Bi < 1 and Bi > 1, respectively, were employed in a base-case study. Parameters describing these two systems are summarized in Table 3; properties of the porous particles in system A are similar to those employed in the companion laboratory experiments (23). Compared to system A, system B is characterized by reduced porosity and reduced NAPL residual saturation, while maintaining the same mass of coal tar in the two systems. In subsequent simulations, the magnitude of Da was varied by varying the particle size of system A while maintaining a constant solids loading (mass of solids/aqueous volume of bioreactor) in the system. The Thiele modulus, φ2, was varied over several orders of magnitude by varying the the sorption coefficient, Kd, and thereby the sorption parameter, γ, in system B. Simulation Results. Simulation results are shown in Figures 4-7. The effect of the Biot number on concentration

FIGURE 4. Simulation results: effect of the Biot number on concentration profiles. (a) System A, Bi < 1. The concentration at the surface of the particles, C(R,t), approaches the interfacial equilibrium concentration, C(ri,t), while the bulk aqueous-phase concentration, C(t), shows a large departure from equilibrium, indicating dominant external boundary layer resistances to mass transfer; (b) System B, Bi > 1. The concentration at the surface of the particles, C(R,t), is similar to the bulk aqueous-phase concentration, C(t), both of which show a large departure from the interfacial equilibrium concentration, C(ri,t), indicating micropore sorptiondiffusion effects. profiles is shown in Figure 4. For system A with Bi < 1, pore diffusion occurs much faster than boundary-layer transport. Thus, as shown in Figure 4a, the aqueous-phase PAH concentration at the surface of the aggregates is close to the interfacial equilibrium concentration, while the bulk-phase concentration shows a large departure from the surface concentration due to slow boundary-layer mass transfer. Conversely, when Bi > 1 (system B), the PAH concentration in the bulk aqueous phase is very nearly equal to the concentration at the surface of the particles, and the surface concentration shows a large departure from the interfacial equilibrium concentration, due to slow pore diffusion rates. By simulating effects of particle size and number density, the Damkohler number in system A was varied from 0.035 to 14. The effect of Da on concentration and fractional biomineralization profiles is shown in Figure 5. When a dense slurry of small solid particles is used, the specific surface area and the mass transfer rate coefficients are large. For such a system, the Damkohler number is predicted to be much smaller than unity, indicating biokinetic control. Cor-

FIGURE 5. Simulation results: effect of the Damkohler number on naphthalene concentration and biomineralization profiles. Da was varied by increasing the particle size of the slurry solids, while maintaining a constant solids loading in the system. (a) Bulk aqueousphase concentrations for systems with Da , 1 approach equilibrium, while those for Da . 1 show a large departure from equilibrium, indicating mass transfer limitations. (b) Biomineralization profiles vary as the particle size and Da are varied. For Da , 1, the fractional biomineralization rate is the same as the biokinetically controlled rate shown in eq 18, indicating biokinetic control. For Da . 1, the biomineralization profile collapses into the mass transfer-controlled regime described by eq 19. respondingly, the aqueous concentrations are close to equilibrium (Figure 5a), and the biomineralization profile collapses to a one-step biokinetically controlled system represented by eq 18 (Figure 5b). As the particle size is increased while maintaining a constant solids mass loading per unit volume, the value of the Damkohler number approaches unity, the bulk aqueous-phase concentration shows a departure from equilibrium (Figure 5a), and the biomineralization profile is intermediate between the mass transfer- and biokineticcontrolled regimes (Figure 5b). Further increase in the particle size represents a slurry comprising a few large particles. Lumped mass transfer rate coefficients are small due to the small specific surface area for mass transfer and the Damkohler number is predicted to be much larger than unity. In this case, the aqueous-phase PAH concentration is small relative to equilibrium (Figure 5a), and the overall biomineralization profile collapses into the one-step dissolutioncontrolled profile shown in eq 19 (Figure 5b). The fractional biomineralization rates in eqs 18 and 19 depend also on the time-varying solubility factor SF(t), which decreases with the progress of biotreatment as the fraction of PAH remaining in the tar phase, FPAH (t) , diminishes. This effect is observed in Figure 5b, which shows rapid miner-

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FIGURE 6. Simulation results: effect of compound solubility on biomineralization profiles. Biomineralization profiles are presented for a compound with pure liquid solubility in water half that of naphthalene. The biomineralization profiles are scaled down by a factor of approximately 0.5 relative to those obtained for naphthalene in Figure 5b, depicting the effect of aqueous solubility on bioavailability. alization during the initial stages of biotreatment, following which the biomineralization rates attenuate due to a decrease in the bioavailable equilibrium aqueous phase PAH concentrations. The effect of pure compound solubility on fractional biomineralization rates is depicted in Figure 6, which describes the biotreatment of a hypothetical NAPL-derived aromatic solute with a pure compound (liquid) solubility half that of naphthalene. Aqueous molecular diffusion coefficients for most organic solutes being similar in magnitude (of the order of 10-5 cm2/s; 30), the mass transfer coefficients kla in the slurry system are also predicted to be similar. Thus, biomineralization profiles for the hypothetical solute (Figure 6) are similar in structure to those for naphthalene (Figure 5b), but scaled down by a factor of approximately 0.5, commensurate with the reduction in the solubility factor, SF, due to the reduced bioavailability of the hypothetical solute. Note, that differences in kbio for the two compounds are absorbed in the dimensionless time axis: τ ) kbiot. The significance of the Thiele modulus, φ2, is evaluated by simulating systems in which micropore diffusion processes are important (system B, Bi > 1; Table 3). The effect of particle size on the Thiele number is assessed by comparing results for two particle sizes, 0.12 cm in diameter and 0.012 cm diameter, while maintaining a constant solids mass loading in the system. For each slurry system, the parameter φ2 in the simulations was varied by varying the sorption coefficient (Kd) across a range of values appropriate for porous media. Results from these simulations are presented in Figure 7a,b. Figure 7a describes the biomineralization profiles obtained with the smaller solid aggregates. As the sorption coefficient was increased from 2 to 200 mL/g, the Thiele modulus increased from 0.08 to 8. For solids with a low sorptive capacity, the Thiele modulus was less than unity and the biomineralization profile collapsed to the one-step biokinetic regime described in eq 18, indicating biokinetic control. As the sorption capacity of the solid increased, the Thiele modulus became larger than unity and departures from the biokinetically controlled regime are seen, indicating that sorption-diffusion effects were constraining biotransformation rates. The effect of sorption-diffusion on biotreatment rates is more pronounced, and greater departures from the biokinetically controlled regime were obtained for the larger solid aggregates, as shown in Figure 7b.

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FIGURE 7. Simulation results: effect of Thiele modulus on biomineralization profiles for two particle sizes. For each particle size, the Thiele number was varied by varying the sorption coefficient (Kd) of the porous medium. (a) For a slurry particle size of 0.0125 cm, the Thiele modulus varied from 0.08 to 8 as the sorption coefficient, Kd was varied from 2 to 200 mL/g. Departures from the biokineticallycontrolled regime are seen for Thiele . 1, indicating sorptiondiffusion constraints on biotransformation rates. (b) For a larger slurry particle size, the Thiele moduli are also larger, resulting in greater departures from the biokinetically-controlled regime. Significance for Design of NAPL-Bioslurry Treatment Systems. The analysis presented above leads to several conclusions of relevance to the engineering and design of multi-component NAPL-slurry biotreatment systems: (1) The overall rate of biotransformation of contaminants from NAPLs is controlled by equilibrium NAPL-water partitioning processes as well as the slowest of three aqueousphase kinetic processes: micropore diffusion, external boundary layer transport, and bulk-phase biodegradation. (2) The kinetic process that controls contaminant transport and transformation in the aqueous phase may be identified by pair-wise analysis of three dimensionless rate parameters Bi, φ2, and Da. Systems that are indicated to be limited by external mass transfer rates (Bi < 1, Da > 1) may be engineered to enhance mass transfer and biotransformation rates by increased mixing and/or by increasing the specific surface area for mass transfer. For systems limited by micropore diffusion processes (Bi > 1, φ2 > 1), increased mixing of the bulk phase to enhance mass transfer will be ineffective unless particle attrition or disaggregation occurs to decrease the diffusion path length through particle size reduction. Systems constrained by biokinetic phenomena may be addressed by evaluating microbial populations and their viability. (3) The rate-limiting aqueous-phase kinetic process may be scaled by a solubility factor, SF(t), to quantify the rate of

contaminant depletion from the NAPL. The solubility factor reflects the effect of NAPL-water partitioning on contaminant bioavailability. Slower rates of contaminant depletion from the NAPL are indicated for less soluble compounds and also with the progress of biotreatment, due to a decrease in bioavailable equilibrium aqueous-phase contaminant concentrations. (4) In the case of coal tar NAPL, the more insoluble, higher ring PAH compounds typically also exhibit slower biokinetic rates (37); the combination of intrinsically slow biokinetics and low bioavailability may result in little or no removal of higher ring PAH compounds from coal tar. Complex mixture interactions may also arise from the fact that while biotransformation of lower ring PAH compounds may be mass transfer limited, biokinetics may limit transformation of the higher ring PAHs. In addition, the multiple substrates present in coal tar and other multi-component NAPLs may also affect the biokinetic rate coefficient for individual contaminants through potential competitive, toxic, or inhibitory effects. Microbial growth or decay may result in time-varying biokinetic coefficients, giving rise to the possibility that a system may shift from mass transfer control to biokinetic control, or vice versa, with the progress of time. Extremely low substrate concentrations may not support microbial biomass leading to biokinetic limitations. Periodic monitoring of microbial parameters and independent assessment of mass transfer phenomena will be required to quantify contaminant biotransformation in NAPL-slurry biotreatment systems.

Acknowledgments This work was sponsored by Texaco Research Inc., Beacon, NY, and another industrial sponsor. A glossary explaining the mathematical notation used in this work is provided at the end of the companion manuscript.

Literature Cited (1) Luthy, R. G.; Dzombak, D. A.; Peters, C. A.; Roy, S. B.; Ramaswami, A.; Nakles, D. V.; Nott, B. R. Environ. Sci. Technol. 1994, 28, 266A-276A. (2) Rhodes, E. O. The History of Coal Tar and Light Oil; Drieger Publishing Co.: 1979. (3) Harkins, S. M.; Truesdale, R. S.; Hill, R.; Hoffman, P.; Winters, S. U.S. Production of Manufactured Gases: Assessment of Past Disposal Practices; EPA/600/S2-88/012: U.S. Government Printing Office: Washington, DC, 1988. (4) Luthy, R. G.; Ramaswami, A.; Ghoshal, S. G.; Merkel, W. M. Environ. Sci. Technol. 1993, 27, 2914-2918. (5) Nelson, E. C.; Ghoshal, S.; Edwards, J. C.; Marsh, G. X.; Luthy, R. G. Environ. Sci. Technol. 1996, 30, 1014-1022. (6) Huling, S. G.; Weaver, J. W. Dense Nonaqueous Phase Liquids; EPA Ground Water Issue; EPA/540/4-91-002; U.S. EPA: Washington, DC, 1991. (7) Barranco, F. T.; Dawson, H. E. A Study of the Wettability of Coal Tar in Aquifer Material. Paper presented at the 13th Rocky Mountain Regional Meeting of the American Chemical Society, June 9-12, 1996. (8) Hunt, J. R.; Sitar, N.; Udell, K. S. Water Resour. Res. 1988, 24 (8), 1247-1258. (9) Luthy, R. G.; et al. Solvent Extraction for Remediation of Manufactured Gas Plant Sites; EPRI TR-101845, Project 3072-2; Carnegie Mellon University: Pittsburgh, PA, 1992.

(10) Villaume, J. F. Ground Water Monit. Rev. 1985, 5 (2), 60-74. (11) Muraka, I. Manufactured Gas Plant Site Investigations. EPRI J. 1990. (12) RETEC. Harbor Sediments: In Situ Bioslurry Treatment Demonstration Work Plan; Remediation Technologies Inc.: Austin, TX, 1994; 3-0844/341. (13) Smith, J. R.; Nakles, D. V., Neuhauser, E. F.; Loehr, R. C.; Erickson, D. Paper presented at the Third International Conference on New Frontiers for Hazardous Waste Management, Pittsburgh, PA, 1989. (14) Morgan, D. J.; Battaglia, A.; Hall, B. J.; Vernieri, L. A.; Cushey, M. A. The GRI Accelerated Biotreatability Protocol for Assessing Conventional Biological Treatment of Soils: Development and Evaluation using Soils from Manufactured Gas Plant Sites; Gas Research Institute: Chicago, IL, 1992; GRI-92/0499. (15) Erickson, D. C.; Loehr, R. C.; Neuhauser, E. F. Water Res. 1993, 27 (5), 911-919. (16) Rijnaarts, H. H. M.; Bachmann A.; Jumelet J. C.; Zehnder A. J. B. Environ. Sci. Technol. 1990, 24, 1349-1354. (17) Alvarez-Cohen, L. M. Ph.D. Dissertation, Stanford University, 1991. (18) Bosma, T. N. P. Ph.D. Dissertation, Wageningen Agricultural University, The Netherlands, 1991. (19) Mihelcic, J. R.; Luthy, R. G. Environ. Sci. Technol. 1991, 25, 169177. (20) Scow, K. M.; Alexander, M. Soil Sci. Soc. Am. J. 1992, 51, 128134. (21) Seagren, E. A.; Rittmann, B. E.; Valochhi, J. A. Environ. Sci. Technol. 1994, 28, 833-839. (22) Efroymson, R. A.; Alexander, M. Environ. Sci. Technol. 1994, 28, 1172-1179. (23) Ramaswami, A.; Ghoshal, S.; Luthy, R. G. Environ. Sci. Technol. 1997, 31, 2268-2276. (24) Ogram, A. V.; Jessup, R. E.; Ou, L. T.; Rao, P. S. C. Appl. Environ. Biol. 1985, 49, 582-587. (25) Miller, C. T.; Poirier-McNeill, M. M.; Mayer, A. S. Water Resour. Res. 1990, 26 (11), 2783-2796. (26) Powers, S. E.; Loureiro, C. O.; Abriola, L. M.; Weber, W. J. Water Resour. Res. 1991, 27 (4), 463-477. (27) Geller, J. T.; Hunt, J. R. Water Resour. Res. 1993, 29 (4), 233-245. (28) Mackay, D. M.; Shiu, W. Y.; Maijanen, A.; Feenstra, S. J. Contam. Hydrol. 1991, 8, 23-42. (29) Lee, L. S.; Rao, P. S. C.; Okuda, I. Environ. Sci. Technol. 1992, 26, 2110-2115. (30) Schwarzenbach, R. P.; Gschwend, P. M.; Imboden, D. M. Environmental Organic Chemistry; John Wiley & Sons Inc.: New York, 1993. (31) Peters, C. A.; Luthy, R. G. Environ. Sci. Technol. 1993, 27, 28312843. (32) Wu, S.; Gschwend, P. M. Water Resour. Res. 1988, 24 (8), 13731383. (33) Chung, G.; McCoy, B. J.; Scow, K. M. Biotechnol. Bioeng. 1993, 41, 625-632. (34) Levins, D. M.; Glastonbury, J. R. Trans. Inst. Chem. Eng. Sci. 1972, 50, 132-145. (35) Ahn, B. S.; Lee, W. K. Ind. Eng. Chem. Res. 1990, 29, 1927-1935. (36) Crank, J. The Mathematics of Diffusion; Clarendon: Oxford, 1975. (37) Simms, R. C.; Overcash, M. R. Fate of Polynuclear Aromatic Compounds in Soil-Plant Systems. Residue Rev. 1988, 88.

Received for review October 4, 1996. Revised manuscript received March 17, 1997. Accepted April 3, 1997.X ES9608499 X

Abstract published in Advance ACS Abstracts, June 1, 1997.

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