Quantitative evaluation of flushing and biodegradation for enhancing in situ dissolution of nonaqueous-phase liquids

Journal of Contaminant Hydrology, 12 (1993) 103-132 Elsevier Science Publishers B.V., Amsterdam

103

Quantitative evaluation of flushing and biodegradation for enhancing in situ dissolution of nonaqueous-phase liquids Eric A. Seagren, Bruce E. Rittmann and Albert J. Valocchi

Environmental Engineering and Science, Department of Civil Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA (Received March 27, 1992; revision accepted August 19, 1992)

ABSTRACT Seagren, E.A., Rittmann, B.E. and Valocchi, A.J., 1993. Quantitative evaluation of flushing and biodegradation for enhancing in situ dissolution of nonaqueous-phase liquids. J. Contam. Hydrol., 12: 103-132. Flushing and in situ biodegradation can enhance the dissolution rate for NAPL contamination by decreasing the solute concentration, which increases the dissolution driving force. NAPL interphase transfer and how flushing and in situ bioremediation enhance it are evaluated using a simple NAPL contamination scenario: one-dimensional flow through a saturated, homogeneous, isotropic medium containing a residual saturation of uniformly distributed, immobilized, single-component NAPL blobs. A mathematical model of the system is developed using a one-dimensional advection-dispersion reaction (ADR) equation incorporating a firstorder interphase mass-transfer relationship and first-order biodegradation kinetics. The analysis is simplified by assuming quasi-steady-state conditions in which NAPL blob size and saturation are constant. Using dimensionless groups that describe the relative rates in the system and analytical solutions to the ADR, criteria are delineated for when equilibrium and nonequilibrium exist and when flushing and biodegradation can effectively enhance NAPL dissolution in the system. These analyses are performed for flushing alone and for flushing and biodegradation in conjunction. The results demonstrate that flushing is effective for enhancing dissolution when the flow rate gives solute concentrations that are neither zero nor the solubility limit throughout the domain. In situ biodegradation can accelerate the dissolution rate when the biodegradation rate becomes large, compared to the mass-transfer rate, and as long as neither the advection rate nor the biodegradation rate is so great that the solute concentration is zero throughout the domain.

Correspondence to: E.A. Seagren, Environmental Engineering and Science, Department of Civil Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois, 61801, USA. 0169-7722/93/$06.00

© 1993 Elsevier Science Publishers B.V. All rights reserved.

INTRODUCTION

Of the 33 synthetic organic contaminants found most frequently in drinking water wells (Council on Environmental Quality, 1981), most are nonaqueous-phase liquids (NAPL's), which are transported or used as separate-phase liquids, have relatively low water solubility and can migrate through the subsurface as a separate phase. Subsurface NAPL multiphase migration is a complicated process in which significant volumes of NAPL can become trapped by surface tension effects as a residual saturation of ganglia or as lenses (e.g., van Dam, 1967; Schwille~ 1967~ 1984, 1988: Mercer and Cohen, 1990). This trapped NAPL represents a long-term source of groundwater contamination via dissolution or volatilization. The NAPL, or components of a multi-component NAPL, dissolve directly into the groundwater when NAPL is in contact with the capillary fringe or is below the water table. In addition, infiltrating water (e.g., from precipitation) can dissolve residual NAPL or vapor trapped in the unsaturated zone. The physicochemical process of NAPL dissolution is critical for understanding N A P L subsurface multiphase transport and the design of several NAPL remediation techniques ...... including flushing (Powers et al., 1991) and in situ bioremediation (Luthy, 1991). The goal of this work is to advance the understanding of the interactions among NAPL dissolution, flushing and biodegradation. A simple NAPL contamination scenario and mathematical formulations for NAPL dissolution, solute transport and biodegradation are used to develop quantitative tools and criteria for assessing when flushing and in situ biodegradation can effectively accelerate the NAPL dissolution rate. See the Notation for symbols used in this paper. BACKGROUND

Interphase mass transfer of a chemical species depends on a deviation from equilibrium between the bulk concentrations of that species within each phase (Welty et al., 1984). When that deviation exists, interphase mass transfer occurs via three steps: transfer of mass through one bulk phase to the interface, transfer across the interface to the second phase and transfer into the second bulk phase. The process is often modeled using two-resistance theory, which assumes that the interphase mass-transfer rate is a function of the diffusion rates through the phases on each side of the interface, while no mass-transfer resistance occurs at the interface. For mass transfer from a N A P L into the aqueous phase, the resistance to mass transfer in the aqueous phase normally is assumed to be greater than that in the NAPL phase; therefore, the dissolution rate is controlled by the rate of transfer through a boundary layer on the water side of the N A P L -

105

ENHANCING IN SITU DISSOLUTION OF NONAQUEOUS PHASE LIQUIDS

NOTATION List of symbols used in this paper Symbol

Description

Dimension

Fundamental quantities: L M M, Mx T

length mass, in general mass of solute mass of bacteria time

English symbols: ana ana

Ax C C*

c, dia

dp Da) Da2 Da3

Do Ox J kl K

KB~ KI L n

Pe

qx rd rd' rd,max rd,max i

rd* R

RB RD Re

s. sw

specific interfacial area between NAPL and aqueous phase interfacial area between NAPL and aqueous phase domain cross-sectional area aqueous-phase solute concentration dimensionless aqueous-phase solute concentration aqueous-phase solute solubility concentration column diameter particle diameter Damk6hler number 1 Damk6hler number 2 Damk6hler number 3 free liquid diffusivity of the solute longitudinal dispersion coefficient dissolution flux mass-transfer coefficient half-maximum rate constant lumped, first-order biodegradation kinetic coefficient lumped mass-transfer rate coefficient length of the contaminated region porosity P6clet number specific discharge NAPL dissolution rate dimensionless NAPL dissolution rate maximum NAPL dissolution rate dimensionless maximum NAPL dissolution rate normalized NAPL dissolution rate source/sink term dissolved NAPL biodegradation sink term NAPL dissolution source term Reynolds number NAPL saturation water saturation

[L ~l] [L2] [L2I [M, L -31 [M, L

3]

/El [L]

[L2 T -l] [L2 T -l] [M~ L -2 T -l] [L T - ' I

[M, L-31 [T-l] [T-'] [LI [L T -I] [M, T-'] [M~ T ~-1]

[M~ L -3 T -I] [M~ L -3 T -I]

[M, L -3 T -l]

]0(I

) A ~,t \ ~ ; P , [ N 11 "~;

NOTATION (continued) Symbol

Description

l)imcnsion

t v~ V x x* X Y

time average pore water velocity total system volume spatial dimension dimensionless distance biomass concentration true yield coefficient

[T] [L T J] [L~[ [L] [M~ L ~] [M, M~ ~]

Greek symbols: ~ ). tZm.~ /~w Pw r

longitudinal dispersivity exponent on vx in mass-transfer correlations maximum specific growth rate dynamic viscosity of water density of water tortuosity factor

[L] [T ~] [M L ~ T ~] [M L ~]

water interface, and the dissolution flux, J, from a pure compound NAPL can be expressed mathematically by a single-resistance model with a linear driving force (e.g., Sleep and Sykes, 1989; Miller et al., 1990; Powers et al., 1991): J = k~(c~

c)

(1)

where k I = mass-transfer coefficient [L T--I]; C~ = water solubility of the chemical [M~ L-3]; and C = average solute concentration at that point [M~ L-3].

The dissolution flux can be enhanced by increasing kl or by decreasing C. Two techniques for achieving this are aquifer flushing and in situ biodegradation. With flushing, the increased groundwater flow rate can increase k~, and it also can increase the concentration gradient by increasing the advective sink term (i.e. flushing out dissolved solute to lower C). These effects of flushing have been demonstrated experimentally (Miller et al.. 1990) and theoretically (Powers et al., 1991). Based on fermenter studies with liquid hydrocarbons, there are three possible mass-transfer pathways by which NAPL growth substrate can reach the microbial cell, depending on the microorganism's properties, the type of NAPL and the environmental conditions: (1) uptake through direct contact between the cells and large NAPL drops; (2) uptake through direct contact of the cells with NAPL droplets of sub-#m size (pseudosolubilization); and (3) uptake of dissolved NAPL (Nakahara et al., 1977). In the case of dissolved NAPL utilization, biodegradation can increase the concentration gradient by being a reaction sink that decreases C. In addition to increasing the NAPL

ENHANCING IN SITU DISSOLUTION OF NONAQUEOUS PHASE LIQUIDS

107

dissolution rate, biological activity concomitantly mineralizes or transforms the solute in situ. Although no experimental evidence for biological enhancement of NAPL dissolution by solute degradation exists, this mechanism has been proposed as an explanation (van Loosdrecht et al., 1990) for experimental observations of the analogous microbial enhancement of desorption from solids (Wszolek and Alexander, 1979; Rijnaarts et al., 1990) and dissolution of solid organic compounds (Thomas et al., 1986). Inherent in this discussion is the requirement of nonequilibrium conditions, i.e. C < Cs. The other possible condition is local equilibrium, which means that C = Cs for a pure compound NAPL. Then, the dissolution rate is no longer controlled by the rate of transfer from the NAPL phase to the aqueous phase, but by the rate at which solute, present at C = Cs, is removed from the interphase boundary by advection and other sink mechanisms. Obviously, the existence or degree of nonequilibrium is an important factor influencing the effect of flushing and biodegradation on the dissolution flux. For example, if the system is already far from equilibrium (i.e. C is already much less than Cs), flushing and biodegradation cannot be effective at enhancing the dissolution rate by decreasing C further. While this sort of generalization can be made, no quantitative criteria are available to predict when equilibrium or nonequilibrium conditions exist. Often, interphase equilibrium is assumed to simplify calculations in models of the subsurface multiphase flow of organic contaminants and the subsurface transport of the miscible phases alone (i.e. aqueous- and gas-phase NAPL components) (e.g., Fried et al., 1979; Abriola and Pinder, 1985a, b; Baehr, 1987; Baehr and Corapcioglu, 1987; Corapcioglu and Baehr, 1987; Hunt et al., 1988a; Falta et al., 1989). In these models, once the contaminant concentration is known in one phase, equilibrium partitioning is used to calculate the concentration in the other phase(s) at the same spatial location. Although this procedure is easy to implement, it can lead to serious errors in predictions for cleanup efforts if the equilibrium assumption is incorrect (Powers et al., 1991). Significant experimental evidence supports that the local equilibrium assumption can be accurate in certain circumstances. Results from several experimental studies on the dissolution of NAPL ganglia indicate that, for the specific experimental conditions, the NAPL and aqueous phase were at equilibrium (e.g., van der Waarden et al., 1971; Fried et al., 1979; Hunt et al., 1988b; Schwille, 1988; Imhoffet al., 1989, 1990). However, Miller et al. (1990) criticized much of the previously performed work because: (1) NAPL saturation was not held constant or monitored as a function of time; (2) small ranges of relatively high NAPL saturation were studied; and (3) systematic and quantitative correlations of interphase mass-transfer coefficients with system variables were not made. To avoid some of these problems, Miller et

al. (1990) performed experiments in glass-bead packed columns, employed toluene uniformly distributed at various residual saturations, and kept the residual saturation decrease during an experiment to ~< 10%. Although ( sometimes was far below C, (C/C~ ranged from 0.12 to 1.0), the calculated mass-transfer rate coefficients were high (ranging from 179 to 6604 day E averaging 2130 d a y ~), indicating that equilibrium could be achieved rapidly in the experimental system. Nevertheless, other experimental work demonstrates that nonequilibrium conditions do exist, at least under certain conditions. In column studies of the dissolution of residual tetrachloroethene (Imhoff et al., 1989) and trichloroethene (lmhoff et al., 1990), effluent solute concentrations initially were at solubility levels; however, as water passed through the columns, solute concentrations eventually began to decrease. These results imply that nonequilibrium occurred after the residual saturation had decreased below a certain level. Geller and Hunt (1989) experimentally studied the dissolution of a large immobilized blob of a single-component (toluene) NAPL and a two-component (50% toluene, 50% benzene by volume) NAPL injected into the center of a water-saturated, glass-bead packed column. At velocities representative of groundwater, the effluent solute concentrations were well below the expected aqueous solubilities for both cases. Finally, groundwater field data from sites with residual NAPL contamination also often reveal organic solute concentrations below equilibrium values (Mackay et al., 1985: Sitar et al., 1987; SchwiUe, 1988). Several hypotheses have been proposed for explaining these nonequilibrium findings (Powers et al., 1991). The focus here is on rate-limited interphase mass transfer, which may apply to all situations, whether or not any of the other hypotheses also are true. Theoretical assessments of the significance of rate-limited interphase mass transfer in porous-medium transport have indicated that nonequilibrium conditions may be important under certain conditions. Hunt et al. (1988a) used one-dimensional plug flow, spherical NAPL drops, first-order NAPL dissolution and a mass-transfer coefficient correlated for dissolution of packed beds of solid spheres of benzoic acid. Using initial conditions representing either a volume fraction (volume NAPL/total medium volume) of 0.01 over a length of 10m or a volume fraction of 0.1 over 1 m, they predicted that, at steady state and before the NAPL volume is significantly reduced, nonequilibrium conditions are important for large blobs and high Darcy velocities. Powers et al. (1991) studied the sensitivity of rate-limited, steadystate NAPL-interphase mass transfer to porosity, Darcy velocity, blob shape and size, residual saturation, dispersivity, mass-transfer coefficient correlation, type of aquifer, and exposed surface area. For small (areal extent) spills, high Darcy velocities, large blob sizes and low residual NAPL saturations, e0uilibrium was not achieved.

ENHANCING IN SITUDISSOLUTIONOF NONAQUEOUSPHASELIQUIDS

Key: • ]

109

NAPL blob Porous medium

Fig. 1. Problem domain for developing the mathematical formulation.

Because NAPL interphase transfer plays an integral role in subsurface NAPL remediation techniques, such as flushing and bioremediation, quantitative tools, and criteria for accurately evaluating NAPL interphase transfer and how it can be enhanced are essential for the appropriate selection and design of these remediation methods. This paper develops such quantitative tools and criteria for a simple NAPL contamination scenario and uses them to assess when flushing and in situ biodegradation can significantly accelerate NAPL dissolution for that scenario. MATHEMATICAL MODEL

Domam

-

The interactions of NAPL dissolution, biodegradation and solute transport are complex; hence, this evaluation is performed using a very simple domain a saturated, homogeneous, isotropic medium with one-dimensional flow in the x-direction. The NAPL is a single component and present as residual saturation of immobilized blobs uniformly distributed throughout the flow regime. NAPL saturation is described assuming the continuum approach. This scenario is illustrated in Fig. 1. -

Transport of dissolved NAPL components For this problem, the water solubility of the NAPL is assumed to be low enough that the solute concentration does not affect the density of the contaminated water or its transport, even at saturation. Therefore, the transport of dissolved NAPL components in saturated, isotropic porous media can be described using the following form of the one-dimensional advection-dispersion reaction (ADR) equation for a homogeneous medium with steady flow in the x-direction: ~C ~2 C ~ - ~ - Oxsx~

qx dC n-~-w~--~x R

(2)

where t = time [T]; Dx = longitudinal dispersion coefficient [L2 T-I]; x =

distance in direction of flow [L]; q,. = specific discharge [L T ~]; n = porosity: S,, - water saturation: and R = source/sink term [M, L 3 y ~]. The water saturation must be taken into account, because not all of the pore volume is available for water flow, due to the NAPI, blobs, The two reaction processe~ investigated here are NAPL dissolution from ~l separate phase, b,'f,, and biodegradation of dissolved NAPL components, RI~.

Dissolution Since the mass-transfer limited modeling approach for NAPL dissolution converges to the local equilibrium case when k~ is large and/or sinks for C are small enough that C approaches Cs, the mass-transfer approach is used here as the basis of the mathematical formulation of NAPL dissolution. To incorporate dissolution as a source term, eq. 1 is modified by multiplying J by the interfacial area between the NAPL and aqueous phases, A.a [L2], and dividing by the porosity, the water saturation and the total system volume, V [L 3] (Miller et al., 1990):

Ana aria kl ana R° = J n S w ~ - J--~'S~ - nS~i ( C ~ - C ) = K,(C~-C)

(3)

where an~ = A,,/V = specific NAPL-aqueous phase interfacial surface area [L-l]; and K~ = a,ak~/nSw = the lumped mass-transfer rate coefficient [T ~]. Use of the lumped mass-transfer rate coefficient, K~, restricts the resulting model to conditions in which a,a and Sw are not changing over time (Powers et al., 1991); however, K~, rather than k~, generally is estimable from experimental data. Although quantification of the actual interfacial area is important if k~ is to be obtained, the heterogeneous nature of the porous media, the time dependence of the interfacial area and the varying accessibility of different portions of the NAPL ganglia interfacial area to the flowing aqueous phase make estimation of k~ difficult (Miller et al., 1990). Incorporation of eq. 3 into the A D R equation gives:

OC OzC ~t - Dx~-~

qx OC nS,~m~x + K t ( C ~ - C )

(4)

Biodegradation Some NAPL's (e.g., liquid aromatic hydrocarbons) that can be used by microorganisms as their sole carbon and energy source have high enough water solubilities to support substantial growth on the dissolved phase; therefore, growth on these NAPL's is described using soluble substrate biodegradation models. The different models for describing bacterial growth and transport of soluble biodegradable substrates in saturated .porous media are

ENHANCING IN SITU DISSOLUTION OF NONAQUEOUS PHASE LIQUIDS

111

categorized as strictly macroscopic, microcolony and biofilm (Baveye and Valocchi, 1989). Odencrantz et al. (1990) used a two-dimensional model to compare the performance of the strictly macroscopic and biofilm models when they were combined with advection and dispersion. Using parameters appropriate for groundwater, they found that the two solutions converged for the organic substrate plume and the biomass distribution in the domain, and they concluded that the added complexity of the biofilm model (and the microcolony model, as well) was not needed for most groundwater situations. Therefore, the strictly macroscopic model is used here. Either Monod or Haldane kinetics may be appropriate macroscopic models, depending on the NAPL contaminant. Both of these kinetic models are nonlinear and do not give rise to analytical solutions; however, for low substrate concentrations, both reduce to first-order kinetics with respect to C: R B = - (/lmax/YK)CX

(5)

where lamax = maximum specific growth rate [T-l]; Y = true yield coefficient [Mx Ms -~]; X = biomass concentration [Mx L-3]; and K = half-maximum rate constant [Ms L-3]. In this work, this simplification is assumed to be correct for all solute concentrations. When the biomass is at steady state, X is constant and can be included with the kinetic coefficients into a lumped, first-order biodegradation kinetic coefficient, KB1 [T-I]: R B =

-- (~maxX/Yg)C

=

-

KBI C

(6)

Adding the lumped first-order biodegradation term to eq. 4 gives:

OC 02C Ot = Dx Ox2

qx OC+K,(Cs_C)_KBIC nSw Ox

(7)

Model evaluation and application Experimental results from the literature are used to evaluate the modeling results and demonstrate their application for quantifying the dissolution rate and its acceleration in a physical system. The modeling results for flushing alone are evaluated and demonstrated using the previously described results of Miller et al. (1990), whose experimental conditions closely approximated the model domain [see Miller et al. (1990) for detailed experimental description]. Values read from Miller et al.'s plot of normalized effluent concentrations vs. Reynolds number for a NAPL saturation Sn ( = volume NAPL/ volume voids) of 4.0% are listed in Table 1. The flushing and biodegradation modeling results are demonstrated using the Miller et al. (1990) results and the first-order toluene biotransformation rate of 0.5 day -l reported in Ghiorse and Wilson (1988) for a subsurface

112

I .\ S[ X~(iic.~.N t l

\~

TABLE I Experimental results from Miller et al. (1990) for S,, =- 4.0°~ and Re ~*~

C*( 1 )

%' * ~'

(mday 0.0040 0.015 0.040 0.064 0.097

0.86 0.75 0.57 0.47 0.40

0.47 1.78 4.75 7.59 11.5I

D ~ ,!,

l)

1" :: 25°C

pc ~,4~

[)ar~ ,5~

K~ ,~., (day ~)

7.11 7.5 7.4 7.2 7.6

2.2 1.4 0.82 0.60 0.48

98 237 371 434 526

(m e day ~) 7.1 • 10 2.5" 10 6.7" 10 1.1-10 1,6. I0

4 ~ ~ ~ :

*1Re = (v~pwdp/#w), where v~ = average pore water velocity [L T J], p~ = water density [M L ~], dp = particle diameter [L] and #,, = dynamic viscosity of water [M L ~ T ~]. *2Calculated from Re. *~D, = :~v~ + z D o, where ~, = longitudinal dispersivity [L], z = tortuosity factor and D,, = aqueous diffusion coefficient [L2T i]. *4Calculated using definition in Table 2. *~Calculated by trial and error using eq. 11. *rCalculated using definition of Da~ in Table 2.

sample of very transmissive sands and gravels from a pristine site near Lula, Oklahoma (DO = 2.6 mg L -t , pH = 7.1 and temperature = 17°C). Bacterial numbers determined by acridine orange direct count in other subsurface samples from the site were on the order of 10 6 g-~. FLUSHING

ANALYSIS

Governing equation Analytical solution. The first step in assessing the effect of flushing on the N A P L dissolution rate is to solve the governing equation for advectiondispersion and dissolution, eq. 4. Eq. 4's solution is simplified by assuming quasi-steady-state conditions, which are valid once a steady-state concentration profile has developed in the contaminated region, but before changes in blob size and N A P L saturation due to dissolution appreciably alter ana or Sw. This assumption was used by Powers et al. (1991) in their sensitivity analysis of N A P L blob dissolution. Furthermore, it has been experimentally demonstrated in column studies of residual N A P L dissolution that effluent solute concentrations initially are approximately constant for a number of pore volumes both for nonequihbrium initial conditions (Geller and Hunt. 1989) and equilibrium initial conditions (Imhoff et al., 1989, 1990). At steady state, eq. 4 can be transformed to a nondimensional form by defining x* = x/L (where L = length of the contaminated region through which groundwater is flowing), C* = C/C~, and the dimensionless group parameters Pe and Da~ found in Table 2. In nondimensionalized form, eq. 4

113

ENHANCING IN SITU DISSOLUTION OF NONAQUEOUS PHASE LIQUIDS

TABL E 2 Definitions of nondimensional coefficients Pe, Da~, Da 2 and D a 3

Pe = P+clet number

(advection rate) (dispersion rate)

qxL D~nS,,,

vxL Dx

Da~ = Damk6hler number 1 =

(mass-transfer rate) (advection rate)

klana L qx

Da2 = Damk6hler number 2 =

(biodegradation rate) (advection rate)

K.t L v~

Da 3 = Damk6hler number 3 =

(biodegradation rate) (mass-transfer rate)

Da2 Da~

KIL Vx

KB~ K~

v~ = average pore water velocity = q:,/nSw. D,, = axV,, +'rDo, where ~tx = longitudinal dispersivity [L], T = tortuosity factor and Do = aqueous diffusion coefficient [L 2 T - t ] .

becomes at steady state: 1 dzC *

0 = Pe

dx .2

dC* dx*

DaiC*+Dal

(8)

Solution of eq. 8 requires specification of two boundary conditions. The influent stream is uncontaminated and a third-type boundary condition is applied at the inlet boundary (x = 0) to ensure conservation of flux: (

ldC* ) Pe dx* t-C* x*=0 = 0

(9)

To simplify the mathematical analyses, we assume that the column domain is semi-infinite and we apply a second-type boundary condition at the outlet: dC*(oo) dx* - 0

(10)

Use of the boundary condition in eq. 10 and the semi-infinite domain approximation has been discussed by Nauman and Buffham (1983) and van Genuchten and Parker (1984). The assumption of a semi-infinite domain at the outlet may result in some errors when the analytical solution is used to determine effluent curves from finite columns (van Genuchten and Alves, 1982). When compared to the solution for eq. 8 obtained assuming a finite domain, dC*(L)/dx* = 0, the semi-infinite solution predicts higher solute concentrations near the end of the column, with the difference decreasing as Pe is increased. With the boundary conditions in eqs. 9 and 10, the analytical solution to

1.0t

l i

/ //

111%=0'01

//

. ,..lO

II

0,6i

I

,//

0.2!

__,..,o

~

•

oo]

Pe=lO0

• o.,ooo

li) & 10 3

10 4

lO 5 10 4

10 3

10 2

10 1 10 0

101

10 2

10 3

10 a

10 5

10 6

10 7

11)8

Da~ Fig. 2. C*(x* = 1) vs. Dal for Pe rangingfrom 0.001 to 1000. eq. 8 is (van Genuchten and Alves, 1982):

C*(x*) = 1 -

i 1 +(1 + 4 D2a , / P e ) ~/2) exp[(½x*Pe){1-(1

+4Da,/Pe)*/2}]

(11)

Trends. Eq. 11 is plotted in Fig. 2; each curve shows C*(x* = 1) vs. Da~ for a given Pe. x* = 1 is used as the reference location, because C* is at its m a x i m u m for the domain, and the concentration exiting the contaminated zone generally is the one of interest. Pe is varied from 0.001 to 1000, and Da~ from 10 -8 to 108. These ranges illustrate the two limiting cases at the downstream boundary - - local equilibrium [C*(1) = 1,0] and the m a x i m u m dissolution driving force [C*(1) = 0] - - as well as the intervening nonequilibrium region where C varies between 0 and (7=. Dal is the critical dimensionless group defining the regions. Local equilibrium [defined as C*(1)~>0.999] is true for all Pe when Da~/> 103; however, as Pe increases from 10 -3 to l01 , the Da~ at which local equilibrium holds extends to as low as 101, Therefore, for 10 -3 ~
ENHANCING IN SITU DISSOLUTION OF NONAQUEOUS PHASE LIQUIDS

1 15

ficients, large specific NAPL-aqueous phase interfacial surface areas (i.e. small blobs), long domains, large NAPL saturations and small average pore water velocities - - in short, conditions allowing the mass-transfer rate to be much faster than the advective transport of solute away from the NAPL. As hydrodynamic dispersion becomes more significant than advection, causing Pe to decrease, the range of Da~ for the transition from C*(1) = 0 to C*(1) = 1 widens: the absolute value of Dal needed to achieve local equilibrium increases, while the absolute value of Dal needed to have the maximum dissolution driving force decreases. For all 10 -3 ~
Dissolution rate The solution to the governing equation is used to evaluate, in terms of dimensionless parameters, when flushing can be used to accelerate the NAPL dissolution rate. Although this steady-state analysis cannot be used to follow the long-term course of a flushing scheme to predict cleanup times, it can be used to evaluate conditions in which Sw and ana are approximately constant.

Calculation. At steady-state, eq. 4 can be rearranged and converted to mass/ time by integrating both sides of the equation over the volume of the reactor: L

L

i+x 0

Ox

0

where Ax = domain cross-sectional area. The right-hand side of eq. 12 is equal to the mass flow rate out of the domain at x = L minus the mass/time into the domain at x = 0. The left-hand side is equal to the total mass/time increase in the system due to dissolution and is termed the dissolution rate, r a [M~ T -1]. Eq. 12 can be nondimensionalized using the previously defined dimensionless parameters to give: I

1

Da,~(1-C*)dx* : 0

(

1 dC*~

f d \ C ' - fie dx']

(13)

0

The left-hand side of eq. 13 is the dimensionless dissolution rate, rd': I rd'

= Dal [ ( 1 - C * ) d x * 0

(14)

Replacing C*(x*) in eq. 14 with the previously developed steady-state relationship in eq. 11 and integrating yield: 2 1 + (1 + 4 D a l / P e ) I/2 r d' = - Da, (½Pe)[1 - (1 + 4Da,/pe)l/2] (1 -- exp[(½Pe){ 1 - (1 + 4Da,/Pe)E"2 }]) (15) The m i n i m u m dimensionless dissolution rate, rd I = 0, occurs when C* is 1.0 t h r o u g h o u t the domain. The m a x i m u m dimensionless dissolution rate occurs when C*(O~x*<~ 1) = 0 and is defined as: I rd,max t

= Dal t - ( 1 - 0 ) d x *

= Dal

(16)

0

Note that rd' and rd,ma x' c a n be converted to r~ and rd.r~ax, respectively, by multiplying by (A~v.~Cs). A normalized dissolution rate, r d*, is then defined as: rd rd *

_

rd,ma x

2 1 + (1 + 4Da I/Pe) 1/2 (½Pe)[t - ( 1 + 4Dai/Pe) 1/2] × (1 - e x p [ ( ½ P e ) { 1 - ( 1 +4Da,/Pe)'/2}])

(17)

Trends. Plots of rd* vs. Dal for Pe ranging from 0.001 to 1000 are presented in Fig. 3. First, Fig. 3 is used to delineate general trends in rj* based on the dimensionless groups. Then, means of maximizing rd* and rd as part of a flushing scheme are discussed. F o u r general trends, expressed succinctly through the dimensionless groups, can be observed in Fig. 3: (1) F o r Pe >/10 the curves are very similar, and approximately the same r d * can be expected for a given Dal. (2) The m a x i m u m Daj for which r d* = 1 (defined as r d* 1>0,999) increases linearly from 10 -6 t o 10 -3 as Pe is increased from 10 -3 to 10°, but for Pe~> 10° it is constant at 10-3. (3) For all Pe's considered, when Dal > 103, r d* ~<0.001, and dissolution of immobilized N A P L is limited by transport of solute, present at the solubility limit, away from the N A P L - w a t e r interface; however, although rj is a very small fraction of rd,max, it may not be insignificant if rd,max is very large. (4) For Dal giving r d* between zero and one, when Da~ is fixed, increasing Pe decreases C*(x*) t h r o u g h o u t the domain, thereby increasing r d* If a system's r d * is < 1.0, tWO essential questions remain to be answered: (1) does increasing v~ as part of a flushing scheme work to increase rd*, and, if

117

ENHANCING IN SITU DISSOLUTION OF NONAQUEOUS PHASE LIQUIDS

1.2 t 1.0'

m -

-

-

-

08/

\ \

0.6]

~

04 /

0

\ "x\ ~ \

.

Pc--0.001

2

--*-Po--01

~ \~ \

\ ~

"-'n'--" Pe=10 m

Pe=100

~

0.0 10-8 10.7 10-6 10-S 104 10-3 10-2 10-I 100 101 102 103 104 105 106 107 108 Da1 Fig. 3. Normalized dissolution rate rd* as a function of Da~ for Pe ranging from 0.001 to 1000. so, (2) when do those changes have the greatest effect? Increasing vx can have three effects: increasing Dx, increasing K~ and decreasing C. When vx is sufficiently large that mechanical dispersion (OtxVx) is much greater than molecular diffusion ( z D o ) , Dx is proportional to v x and Pe is constant at L/otx. The correlation model for mass-transfer from toluene blobs developed by Miller et al. (1990) and the majority of the mass-transfer correlations for dissolution of solid organic spheres into a uniform aqueousphase flow field in a packed bed or for diffusion-limited dissolution of fluid spheres suspended in a laminar flow regime [summarized from the literature by Miller et al. (1990) and Powers et al. (1991)], indicate KI is proportional to vx ~, where 2 < 1.0 Therefore, Dal decreases as v~ increases. In summary, an increase in v~ decreases Dal and has no effect on Pe when mechanical dispersion is much greater than molecular diffusion. Fig. 3 shows that r d* increases in this case. For very low v x and low Pe, where the hydrodynamic dispersion is dominated by molecular diffusion, D x is constant at z D o , and increases in v x not only decrease Dal, but also increase Pe by the same degree as the change

in v,. Both effects act in the same direction to increase rd*. For intermediate v, where both mechanical dispersion and molecular diffusion arc significant, increasing v, also decreases Da, and increases Pe both acting to increase r d* but D, and, thus, Pe increase at a slower rate than v,. The conditions allowing the greatest increase in r d * per decrease m Da~ (i.c increase in %) can be illustrated by looking at the derivative drd*/dDa r as a function of Da~. Assuming v, is in the range where Pe can be assumed to be approximately constant (i.e. ~,v, >>'tDo), the derivative ofeq. 17 with respect to Da~ is: dr,,*_

dDai

2a 2a ~1' (~c)[(~e)_(~)+

exp(b)(~-I

'~)1

(18)

where a - [l+{l+(4Da~/Pe)}~:2] -~ b = ½Pe[1 - {1 +(4Da,/Pe)} ~'2] c = [1 +(4Da,/Pe)] ~:2 Fig. 4 is a plot of -(dr~*/dDa~) vs. Dal for the particular case of Pe = 1.0. For large values of Da~, where equilibrium occurs throughout the system (for Pe = 1.0, rd* ~<0.001 for Da~ > 103), Idrd*/dDa~ I is very small. In this regime, the mass-transfer rate is much greater than the limiting advection rate. which cannot be increased enough to decrease C or increase K] sufficiently to effect a large change in rd *. When Dal is small enough to be in the range where mass transfer just becomes limiting (for Pe = 1.0, Da~ < 103), Idrd*/dDa, l begins to rapidly increase as Da] decreases. Eventually, as Da~ is decreased further. Idrd */dDa~ I plateaus at a maximum value that holds until the point where Da~ and, thus, C*(0 ~
Model evaluation and application Miller et al.'s (1990) data for Sn = 4.0% (Table 1) were converted into a form appropriate for evaluating the model (i,e. %, Dx, Pe, Da~ a n d Kj were determined), using the constant parameters listed in Table 3. The experimental values of C*(1) vs. Da~ are plotted in Fig. 5, along with the theoretical curve calculated using eq. 11 and the average ex~rimental P e of 7.3. The experimental data follow the theoretical curve very closely. These results also

119

ENHANCING IN SITU DISSOLUTION OF NONAQUEOUS PHASE LIQUIDS

2.0'

t:) "(3

1.0'

"13 I

0.0 ':, 10 -10 10 -9

i

10 "8 10 .7

10 -6 10"5 10 4

10 .3

10 -2 10 -1

10 0

101

10 2

10 3

10 4

l0 S

Da 1

Fig. 4. - d r d * / d D a I as a function of Dal for Pe = 1.0.

TABLE 3 Values used in calculation of parameters in Table 1 Parameter

Value

Reference*

Particle diameter, dp Column length, L Column diameter, dia Dispersivity, ctx Tortuosity factor, r Porosity, n Dynamic viscosity,/~w Density, Pw Aqueous diffusion coefficient, D O

650pm 1.05 cm 2.5 cm 1.4.10 -~ cm 0.67 0.39 0.890-10 -3 N s m -2 997.0 kg m -3 9.02.10 -6 cm 2 s -!

[1] [1] [1] [1] [2] [1] [3] [3] [4]

*References: [1] from Miller et al. (1990); [2] Gillham and Cherry (1982); [3] at 25°C, from Metcalf & Eddy, Inc. (1979); [4] at 25°C, 1 atm, calculated using the Wilke-Chang equation (Welty et a1.,1984).

120

E ~, ~,i

1.0 I

t~ t t l N

i
r"

().8

ji

06t 0"4t

t

/

]i

........

,I

0.2]

i

Theoreticalcurve (Pe=7.3) Data for Sn=4,0%

#

J

0.0

i

1(/-5 104 10.3 10-2

i

10 -1

i

l0 0

1

101

i

102

i

103

i

i

104 105

~

106

i

107

108

Daj

Fig. 5. Experimental data from Miller et al. (1990) for So = 4.0% plotted along with the theoretical curve described by eq. 11 using the average experimental Pe of 7.3.

can be used to evaluate the model solution for the dissolution rate with flushing alone. The dissolution rates in Table 4, calculated using eq. 17. are very close to the estimates obtained by using the experimental effluent values and assuming transport by advection only out the column end. Suppose the Miller et al. (1990) system was to be remediated by flushing. As shown in Table 1, Da~ = 0.48-2.2 and P e ~ 7 . 3 for vx = 0.47-11.51 m day- 1. Locating these points on Fig. 3 (recall that ra * is hardly affected by Pe for Pe on the order o f ~> 10) indicates that flushing would increase rd*: furthermore, based on Fig. 4, the increase in rd* per decrease in Da[ increases as vx increases. However, to achieve the maximum dissolution rate with flushing alone, Dal must be lowered to ~ 10 -2, which, based on the masstransfer coefficient correlation of Miller et al. (1990), requires an unrealistic v~ on the order o f 108 m day -I .

ENHANCING IN SITU DISSOLUTIONOF NONAQUEOUSPHASELIQUIDS

121

TABLE 4

Comparison of theoretical and estimated experimental dissolution rates for the Miller et al. (1990) data with S. = 4.00 C*(1)

0.86 0.75 0.57 0.47 0.40

vx (m day -t )

r d*t *')

0.47 1.78 4.75 7.59 11.51

0.38 0.50 0.64 0.71 0.76

rd(theo)(,2)

rd(exp)(,3~

(g day -t )

(g day -t )

0.099 0.32 0.63 0.82 1.06

0.10 0.34 0.68 0.90 1.16

*~Calculated using eq. 17. *2rd(theo) = (AxvxCs)(Dal rd*), where, for toluene, Cs = 515 mg L-i at 20°C (Verschueren, 1983). *3rd(exp) is estimated by using (AxvxC~)[C'(1)].

FLUSHING

PLUS BIODEGRADATION

ANALYSIS

Governing equation

Analytical solution. At steady-state, eq. 7 is rearranged to give the following: d2C

dC

(19)

0 = Dx -d-ff2-Vx Tx -(K, +KB,)C+K, Cs

Eq. 19 is nondimensionalized using x*, C* and four nondimensional coefficients: Pe and Damk6hler numbers Dal, Da2 and Da3. Pe and Da~ were used in the flushing analysis, while Da2 and Da 3 are new and defined in Table 2. Nondimensionalized, eq. 19 becomes: 1 d2C *

dC*

0 - Pe dx .2

dx*

(Dal +Da2)C*+Da~

(20)

Da 3 does not appear in eq. 20, but is useful for interpretation. The analytical solution to eq. 20, with a third-type inlet boundary condition (eq. 9) and a semi-infinite domain outlet boundary condition (eq. 10), is (van Genuchten and Alves, 1982): Dal C*(x*) = (DaT~--Da2)[1 - (1 + [1 +4(Da, 2 + Da2)/Pe]l/2) x exp ((½x*Pe)[1 - {1 + 4(Da, + Da2)/Pe}'/2])]

(21)

A

Trends. The effect of biodegradation on the solute concentration in the domain is illustrated in Fig. 6, which presents the solution to eq. 21 for an

122

i ,,x ,,~ ,x<;Rt

,~ i i

~

F.2-

Da I !i.Di0 i

1.0 'T

," ,.'"

0.8 j

•

l ) a I =: Z 0

•

Da I = 1000

.'"

°,,," 0.6"

:" Da 3= 0.001

04 -

~

0.2

/ /'

./" D% : 1.0

,"

.

•'°" 7'

O

.

,J

O

y."

,

l

~

10~ I0 7 106 10-5 10 a 10 ,3 10-2 10 -1 i0 ° 101 102 103 10 a 105 106 l07 I(i s

Da, Fig. 6. Representative curves of C*(1) vs. D a z with Pe = 1.0 and Da~ = 0.0001, 1.0 and 1000, representing in the absence of biodegradation, extreme mass-transfer limitation [C*(I) = 0], intermediate mass-transfer limitation, and local equilibrium [C*(1) = I], respectively.

example simulation using Pe = 1.0 and three values of Dal: 10-4, 10 0 and 10 3. C*(1) is plotted for each Da~ as a function of Da2, which is varied between t0 -8 and l0 ~°. Based on Fig. 2, the selected Dal-values represent, in the absence of biodegradation, the three mass-transfer regimes of interest: extreme mass-transfer limitation ( C * ( 1 ) ~ 0 ) , intermediate mass-transfer limitation and local equilibrium (C*(1) = l). Observations on how biodegradation affects C*(1) in these regions are helpful in explaining how biodegradation affects the dissolution rate. In general, for a given Pe and Da~, Da2 or Da3 can be used to define the region where biodegradation can affect C*(l), i.e. the region where the biodegradation kinetics are fast enough compared to the mass-transfer rate and flow rate to affect C*(1). A rough line of demarcation is provided by the line connecting points for which Da2 = Dai (i.e. Da 3 = 1), which is an inflection point on the C*(x* = 1) vs. Da2 curve. Above the Da3 = 1 line, where Da 3 << 1, is the b i o d ~ a d a t i o n - l i m i t e d regime, because the maximum biodegradation rate is much slower t ~ n the mass-transfer rate; below the Da3 =

123

ENHANCING IN SITU DISSOLUTION OF NONAQUEOUS PHASE LIQUIDS

1 line, where Da 3 >> 1, is the dissolution-limited regime, because the maximum biodegradation rate is much greater than the maximum masstransfer rate. These concepts are most readily illustrated using the three example cases presented in Fig. 6. In the equilibrium regime for dissolution alone (Dal = 103), biodegradation has no effect on C* for Da2 ~< 1.0. As Da2 becomes > 1.0, the biodegradation rate becomes greater than the advection rate, allowing a decrease in C* and, thereby, making the system go from being at equilibrium to being at nonequilibrium. Therefore, when Pe = 1.0 and Da~ = 10 3, Da2 must also be <~1.0 for the equilibrium assumption to be appropriate. In the intermediate nonequilibrium regime (Dal = 1.0), as Da2 is increased above 10 -3, the effects of biodegradation on C*(x*) become more significant. When Da~ = 10 -4 (i.e. extremely mass transfer limited), biodegradation has an effect on C*(1) at low Da2, but the concentration already is so low from advection that the effect is negligible. So, if the system is extremely masstransfer limited, biodegradation has no effect no matter how fast the firstorder biodegradation rate. Fig. 6 is the same for all P~clet numbers in the range 10 -3 ~ 102.

Dissolution rate The model is used to develop quantitative criteria, in terms of dimensionless parameters, for assessing when biodegradation and flushing techniques can accelerate the N A P L dissolution rate. These dissolution rate results are subject to the same steady-state restrictions as those for the analysis of flushing alone.

Calculation. First, the normalized dissolution rate is defined using the same approach as for the case of flushing alone. Eq. 19 can be rearranged and converted to mass/time by integrating both sides of the equation over the volume of the reactor: L

L =

0

L

f (o C- x 0

22, 0

The right-hand side of eq. 22 is equal to the mass/time out of the domain at x = L minus the mass/time into the domain at x = 0 plus the total mass/time decrease in the system due to biodegradation; the left-hand side is equal to the total mass/time increase in the system due to dissolution and, as before, is termed the dissolution rate, r d [Ms T-l]. Eq. 22 can be nondimensionalized

124

i.,~

51:/\tiRI:N

K I ',

using the previously defined dimensionless parameters to give: t

i

i,,

i

fd( *

Da~ ~,

~, .

' am

Pe d-~Y *I+Da~

iC*dx*

(23)

The left-hand side ofeq. 23 is the previously defined dimensionless dissolution rate rd' (eq. 14). Replacing in eq. 14 with the steady-state relationship in eq. 21 and integrating give:

C*(x*)

I

rd' = Da , 1 -(D~a,~ ~ -

fa,--~7-')(l+(l+-4w/Pe)'/2) 2 t -1

x (1 - exp[(½Pe){ 1 - (1 + 4w/Pe)'"2 }]) /

(24)

_i where w = Da~ + Da2. Again, rd' and ra,max' can be converted to r d and rd.m,x, respectively, by multiplying by Based upon the same definition of the maximum dissolution rate (eq. 16), a normalized dissolution rate is defined as follows:

(AxvxCs).

I

Dal

1-(-~L)-

rd*=

2

{(---W--)(l+(l+4w/Pe)l:2)t 1 ½Pe[l_(l+4w/Pe)l/2]J -1

x

Trends.

exp[(½Pe){ 1 - (1 + 4w/Pe) ~/z}]) /

(25)

A

An example simulation illustrating the effect of biodegradation on the normalized dissolution rate is presented in Fig. 7. Eq. 25 was used to plot rd* VS. Da2 (ranging from 10 -6 to 10 t°) for Pe = 1.0 and Dal ranging from 10 -3 to 10 3. Fig. 7 is the same for all 10 --3 ~102. As the first step in this analysis, Fig. 7 is used to delineate general trends in the dissolution rate when biodegradation and flushing are occurring. Second, means of maximizing r~* and rd are examined. Two limiting cases in which r d* is at its maximum can be delineated in Fig. 7. For Daj ~<0.001, biodegradation has essentially no effect on rd* (i,e. rd* >~0.999 for all Da2). In this range, the advection rate is so large that the

ENHANCING IN SITU DISSOLUTIONOF NONAQUEOUSPHASE LIQUIDS

| 25

1.2

1,0" ""*%%%°"'x "~°'% "'%%

08 •

~'..

06 •~o

"'..

"~

"" 1.o,

" ~ . .

•

o~.oo,..... '... -/ " \~. 0.4--\ \

/"'\

/

/

/

8

",,./ / / /'"tl / //

• Oa,:O., " °a,='

-\\111

0.2 "

~

~

•

-..//

i

~=

•

"

~'""~"'%". ~. 7

0.0.7-

~-

)

i

.=-- ; - " T

106 10-5 10-4 10-3 10.2 10-] 10°

Da'=O'O1

.,:,o

--------a---- Da 1= 100

i), .

.

.

.

.

Dal= 1000 .

.

.

101 102 103 104 105 106 107 108 109 1010 Da 2

Fig. 7. Representative curves of normalized dissolution rate r d* vs. Da 2 with Pe = 1.0 are presented for Dal = 10 -3, 10 -2, 10 -t , I0 °, 101 , 102 and 103.

system is extremely mass-transfer limited and the dissolution rate is at its maximum. So, even when the biodegradation rate is very high, the dissolution rate is not increased significantly, because advection already is keeping the solute concentration low. At the other extreme, when Da 3 >/1000, r d * is at or near its maximum of 1.0 for all Dal. Here changes to the flushing rate (Dat) have no effect on the dissolution rate, because the biodegradation is fast enough to give the maximum dissolution rate. Between these extremes, rd*< 1.0 and is a function of both Da, and Da2. Ifrd* < 1.0 for a system in which flushing and biodegradation are occurring, understanding how to maximize rd* and rd requires answers to three important questions: (1) when is increasing Vx as part of a flushing scheme the best technique for increasing rd*; (2) when can in situ biodegradation accelerate r d* above that resulting from the system's Vx; and (3) under what conditions is the effect of biodegradation the greatest? Between the two extremes described above the point at which biodegradation begins to affect rd* can be described best using Da 3, the ratio of the biodegradation rate to the mass-transfer rate. For a fixed Da) ~>10, the effects

of biodegradation on r d * begin to be evident tor D a 3 > 0.001 (i.e. r~ * increases by at least approximately 0.01 per factor of 10 increase in Da2 ), with the most significant effects found for Da~ > 0.1. The biodegradation effects increase as Da~ is increased further until the m a x i m u m is reached at Da 3 >~ I000. For a fixed Da~ < 10, a larger Da3 is necessary for biodegradation effects to become obvious. For example, with Dat fixed at 1.0 and 0. l, the effects of biodegradation begin to become evident for Da~ > 0.01 and Da~ > 0.1, respectively. For the small Da~-values at which biodegradation has no effect on N A P L dissolution, the onlyway to increase the dissolution rate is to increase flushing, in which case the system reacts to changes in v~ exactly as described in the preceding section describing flushing alone. When Da3 lies in the range in which biodegradation has an ettect (i.e. 10 ~ < D a 3 < 103), the most likely strategy for increasing KB~ and, m turn, Da,, is to increase the a m o u n t of active biomass. X. This moves the position on the r d* vs. Da, curve from left to right, increasing r d*. Thus, depending on the other parameters, increasing active biomass by an order of magnitude, e.g., from 107 to 10 s cells/g dry soil, could significantly increase rd* When flushing and biodegradation can affect r d*, the effects of changing v, and KB~ must be balanced to achieve the o p t i m u m r d*. Increasing K m only increases Da: and thereby increases r d*. On the other hand, increasing v, decreases Da, and Da:. Which effect will have greater impact depends on the initial values of Da~ and Da,. The conditions for which increasing biodegradation causes the greatest increase in r d* per increase in Da 2 (i.e. increase in Kin) can be illustrated by looking at the derivative dr d*/dDa2 as a function of Da2, assuming that v,. and thus Pe and Dat, are constant: drd* _ ( Da~ \(Da, + D a 2 ) 2 ] - \ [

[1 - exp(c)]~

(ab

exp(c)~ -~ J

ab 2 cdPe

bDa, c(Da, + D a 2 ) 2 +

ab )

(26)

where a = Dal/(Dal + Da2) b = 211 + { 1 + 4(Dal + Da2)/Pe}'/2]-' c = ½Pe [1 - {1 + 4 ( D a ,

+Da2)/Pe} '/2]

d = [1 +(4/Pe)(Da, +Da2)] °5 Fig. 8 presents the solution of eq. 26 for Pe = 1.0 and Da, = 0.0001, 1.0 and 1000. For all Dal, the greatest increase in ra* per unit increase in Da2 occurs when Da2 is small, i.e. when biodegradation currently has the smallest

ENHANCING IN SITU DISSOLUTION OF NONAQUEOUS PHASE LIQUIDS

127

100 -7 101 ] 10-2 10-3 l--I--104 10-5 10-5 10 7 10~ 10-9 "o

10-10 Da I =0.0001

10-11. "12

10-12-

Dal= 1.0

10-13. D~q = 1000

10-14. 10-1510"161 10"17t 10-18 10d9 10-20+ 10-6

10 .5

104

10 .3

10 .2

10 -I

100

10 j

102

103

104

105

106

107

108

Da 2 Fig. 8. dra*/dDa 2 as a function o f D a 2 for Pe = 1.0 and Da~ = 0.0001, 1.0 and 1000.

effect. With little biodegradation, C*(0 ~
12~

~ \,!-,I ~ ( , R t N t l

,~

i2-r I

1.0-~

4J (}.8"

l)a ~= (I.48 ~

o

0.6"

Da~ =0.6

E~

__./

0.4"

Da~ = 0.82 a

I)a ~= 1.4

•

Da 1=2.2

[]

Example

I

0.2'

0.0

i

t0 6

10-5

i

10~

J

104

i

10 2

i

10-I

i

•

100

101

i

102

~

10 ~

~

i

104

]05

106

l)a, Fig. 9. The effects o f increased flushing (a decrease in Da~ and Da2) and increased biodegradation (an increase in Da2) on rd* for the experimental set-up o f Miller et al. (1990) with Sn = 4.0%.

biodegradation can affect C*(x*). This greatest maximum is ~ 200 and 1000 times greater than for the extreme cases of equilibrium and extreme masstransfer limitation, respectively.

Model application Application of the model including dissolution and biodegradation can be demonstrated using the data of Miller et al. (1990) (Table I) and the value of Km = 0.5 day-I from Ghiorse and Wilson (1988). An example scenario is presented in Fig. 9, in which rd* is plotted vs. Da2 for the Da~ -values from the Miller et al. (t990) data, using the average Pe = 7.3. If initially v~ -- 0.47m day -t, then Da~ = 2.2 and Da2 = 0.011. This corresponds to a rd* of 0.38 or rd of 0.099 g day-I (point 1 in Fig. 9), which is the same as for flushing alone (Table 4); therefore, the background level of in situ biological activity has no effect on rd*. There are then three choices for increasing rd*: (1) increase flushing alone, (2) increase the biological activity alone, or (3) increase both flushing and biodegradation.

ENHANCING IN SITU DISSOLUTION OF NONAQUEOUS PHASE LIQUIDS

129

I f v x in the system is increased to 11.51 m day -1 , Dal decreases to 0.48, Da2 decreases to 4.6. l0 -4, and rd* increases to 0.76 or r d = 1.1 g day -l (point 2). Again, the background level of biological activity did not increase rd* over what it would be if no biological activity existed (Table 4). If Vx were left at 0.47 m day-~ and the active biomass, X, and, thus, KBI were increased by 500 times (,-~2.7 orders of magnitude, which is not unreasonable), then Da2 increases to 5.6 and tO* increases to 0.75 (r d -----0.20), which is approximately double the dissolution rate with the background biodegradation (point 3). If v x is increased from 0.47 to 11.51 m day -~ and KBI is increased by 500 times, Dal = 0.48, Da2 = 0.23, and rd* only increases to 0.78 (point 4). Compared to the background cases, the increase in active biomass of 2.7 orders of magnitude had a greater effect at the lower v x than at the higher vx. This occurs because biodegradation is a function of C * ( x * ) and X. Increasing flushing decreases C*(x*), which decreases the biodegradation rate and its enhancement effect on the dissolution rate. This illustrates the need to balance the effects of changing Vx and Ka~ when flushing and biodegradation are effective at increasing r d*.

SUMMARY AND CONCLUSIONS

The solution to the ADR equation for one-dimensional flow through a saturated, homogeneous, isotropic medium containing a residual saturation of uniformly distributed, immobilized, single component NAPL blobs was used to develop quantitative tools and criteria for assessing the effect of flushing and biodegradation on NAPL dissolution. The analysis is simplified by assuming quasi-steady-state conditions, which are valid once a steady-state concentration profile has developed in the contaminated region, but before changes in blob size and NAPL saturation due to dissolution appreciably reduce K I by altering ana o r S w. Three conclusions can be made based on the mathematical development for flushing alone: (1) For 101~10 I, and C*(1) approaches zero for Dal ~<10 -3. For P e < 101, the Dal range for transition from C*(1) = 0 to C*(1) = 1 widens. The large Dal necessary for equilibrium correspond to large k~, large a,a, long L, large S,, or small vx. These conditions concur with the results of previous theoretical assessments (Hunt et al., 1988a; Powers et al., 1991). (2) For 10° ~
The results presented in the flushing and biodegradation analysis demonstrate that when the system is not already extremely mass-transfer limited due to flushing, biodegradation can decrease C*(x*) and thereby increase the dissolution rate. For the particular case of Pe - 1.0, the following specitic trends can be delineated: (1) If D a 3 > l0 ~3, biodegradation decreases C*(I), unless the system is already extremely mass-transfer limited (e.g., Da~ < 10 3t as a result of' flushing alone. (2) Biodegradation is effective for increasing the dissolution rate when Da, increases in the range t0 3 10 3 (3) For all Da~, the greatest dr d*/dDa2 occurs as Da2 approaches zero. The maximum dr d*/dDa? is greatly influenced by the magnitude of Da~. ACKNOWLEDGMENTS The research described in this article was supported by grant DE-FG-0289ER60773 from the Subsurface Science Program of the Office of Health and Environmental Research, U.S. Department of Energy (DOE). This paper has not been subjected to the DOE's peer or administrative review and therefore does not necessarily reflect the views of the Department and no official endorsement should be inferred. REFERENCES Abriola, L.M. and Pinder, G.F., 1985a. A multiphase approach to the modeling of porous media contaminated by organic compounds, 1. Equation development.Water Resour. Res., 21: 11-18. Abriola, L.M. and Pinder, G.F., 1985b. A multiphase approach to the modeling of porous media contaminated by organic compounds, 2. Numerical simulation. Water Resour. Res., 21: 19-26. Baehr, A.L., 1987, Selectivetransport of hydrocarbons in the unsaturated zone due to aqueous and vapor phase partitioning. Water Resour. Res.~ 23: 1926-1938. Baehr, A i . and Corapcioglu, M.Y., 1987. A compositional multiphase model for groundwater contamination by petroleum products, 2. Numerical solution. Water Resour. Res., 23: 201-213. Baveye, P. and Valocchi, A., 1989. An evaluation of mathematical models of the transport of biologically reacting solutes in saturated soils and aquifers. Water Resour. Res., 25: 14131421. Corapcioglu, M.Y. and Baehr, A.L., 1987. A compositionalmultiphase model for groundwater contamination by petroleum products, 1. Theoretical considerations. Water Resour. Res., 23: 191-200. Council on Environmental Quality, 1981. Contamination of ground water by toxic organic chemicals. Counc. Environ. Qual., Washington, DC, 84 pp. Falta, R.W., Javendel, I., Pruess, K. and Witherspoon, P.A., 1989. Density-drivenflow of gas in the unsaturated zone due to evaporation of volatile organic compounds. Water Resour. Res.. 25: 2159-2169.

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