Pulsing of multiple nutrients as a strategy to achieve ...clemept/publsihed_pdf/marley.pdf · For the speciﬁc problem solved here, the governing transport model with appro-priate

Computational Geosciences 1 (1997) 271–288 271

Pulsing of multiple nutrients as a strategy to achieve largebiologically active zones during in situ carbon

tetrachloride remediation

Marlee E.L. Franzen a, James N. Petersen a,∗, T. Prabhakar Clement b,Brian S. Hooker b and Rodney S. Skeen b

a Chemical Engineering Department, Washington State University, Pullman, WA 99164-2710, USAb Bioprocessing Group, Battelle Pacific Northwest National Laboratory, Richland, WA 99352, USA

Received 5 September 1996; revised 8 July 1997

When injecting nutrients during active bioremediation, various nutrient addition strategiescan be employed in order to remediate the site at minimal expense. In particular, if more thanone nutrient is required, a pulse addition strategy can be devised in which these nutrientsare added as temporally separated pulses such that the biostimulated portion of the flowfield can be maximized. In this manuscript, results of numerical simulations are reportedwhich demonstrate this effect. Previously published kinetic expressions describing microbialgrowth and carbon tetrachloride degradation under denitrifying conditions are used in thesesimulations. The simulations indicate that volumetric treatment can be accomplished byinjecting long duration nutrient pulses of different nutrients that are separated by a longperiod where only unamended water is injected. This strategy will cause the nutrient pulses tooverlap at a considerable distance from the injection point, while maintaining concentrationsthat are high enough to ensure significant biomass growth and contaminant destruction.

Keywords: bioremediation, numerical simulation, carbon tetrachloride, denitrification

1. Introduction

Groundwater contamination originates from a variety of sources including surfacedisposal trenches and cribs, underground storage and septic tanks, and landfills [18]. Inaddition, agricultural and industrial activities have generated a variety of groundwatercontaminants, including synthetic organic chemicals, metal ions, petroleum products,volatile organic compounds, pesticides, and nitrates [6]. At the Department of EnergyHanford Site, located in Southeastern Washington State, various contaminants wereintroduced to the subsurface during the more than 40 years of production of weaponsgrade plutonium. Characterization of the groundwater at this site indicates that carbontetrachloride (CT) and nitrate contamination covers at least 5 km2. Within this area,CT concentrations up to 1,000 times the EPA drinking water standard of 5 ppb, and

∗ Corresponding author. E-mail: [email protected].

Baltzer Science Publishers BV

272 M.E.L. Franzen et al. / Effects of nutrient pulsing strategies

nitrate concentrations up to ten times the EPA drinking water standard of 44 ppm havebeen found [14]. Cost effective treatment methods must be developed to facilitateclean-up of such contaminated groundwaters.

In situ bioremediation has the potential to reduce CT and nitrate groundwa-ter contamination to acceptable levels at lower cost than pump-and-treat technology[14]. Furthermore, laboratory tests have demonstrated that the Hanford aquifer hasindigenous denitrifying bacteria possessing the ability to degrade CT and nitrate tononhazardous products [8,11,15,16]. For these organisms, acetate was shown to be aneffective electron donor while nitrate and nitrite serve as electron acceptors. However,even though the metabolic potential to degrade these contaminants is present at thissite, several engineering issues need to be addressed before in situ bioremediation canbe successfully applied at full-scale. For example, treatment strategies must be devel-oped that allow large portions of the aquifer to be remediated at minimum expense [5].This issue is especially pertinent to sites that have deep water tables, such as Hanford,because the cost of drilling is high.

To accomplish cost effective treatment, nutrient addition strategies must be de-veloped to maximize the volume of the treated zone. One potential method to increasethe biologically active zone is independent injection of the electron donor and accep-tor. Such control is possible when denitrifying bacteria are used to accomplish theremediation. Previous simulation and laboratory work has demonstrated that addingelectron donors and acceptors in pulses which are separated in time can increase theremediated volume of the porous medium. This strategy avoids overlap of the electrondonor and electron acceptor in the porous medium directly adjacent to the injectionwell, thereby slowing the rate of biomass production in this region and extending thebioactive zone. Nutrients can then flow further out into the field where the electrondonor and acceptor pulses eventually mix due to dispersion [5,9,10,12,13]. In con-trast, simultaneous addition of both nutrients leads to large biomass production nearthe injection point and clogging of the pore spaces with biomass [3,7].

Experimental support of these concepts was recently obtained by Peyton [9]. Incolumn tests using the Hanford denitrifying consortium, he demonstrated that a moreuniform distribution of the biomass in a column resulted if the nutrients were addedin a pulse fashion. Peyton found that when acetate and nitrate were added as temporalpulses separated in time by injection of nutrient-free water, the biomass level variedby only a factor of two over the first 30 cm and a factor of six over the entire 90 cmcolumn. In contrast, when the same pulses were injected simultaneously, biomass grewpreferentially near the inlet. Under these conditions, the biomass level diminished byan order of magnitude in the first 30 cm. When the same daily acetate and nitrateloadings were used, but concentrations were lowered so that both materials were addedcontinuously, the preferential biomass growth at the injection point was even moreevident. Then, the maximum biomass was located at the column inlet and diminishedby more than two orders of magnitude in the first 30 centimeters. Hence, even thoughPeyton has experimentally illustrated the benefits of pulse addition strategies for smallscale systems, no tests have been performed at the field scale to verify these concepts.

M.E.L. Franzen et al. / Effects of nutrient pulsing strategies 273

The purpose of this study is to extend the concepts demonstrated by Peyton and,using numerical simulations of biologically reactive flow and transport, to examine theeffects of nutrient pulse characteristics on the volume of aquifer that is biologicallystimulated.

2. Pulse characteristics

Denitrifying activity, stimulated by pulse addition of acetate as the electron donorand nitrate as the electron acceptor are the basis for this work. Such pulse additionof nutrients allows the electron donor and the electron acceptor to be added to thesubsurface in an independent fashion. The characteristics of the pulses are definedusing four distinct parameters: pulse cycle time PT, pulse width PW, pulse skew PS,and pulse concentration (see figure 1). The pulse cycle time, PT, is defined as thetime that elapses from the leading edge of one acetate pulse to the leading edge of thesubsequent acetate pulse. The pulse width, PW, is the duration period of the injection ofa particular nutrient into the flow field. In all simulations reported here, the pulse widthof the electron donor was set equal to the pulse width of the electron acceptor. Thepulse skew, PS, which can be calculated from the pulse cycle time and the pulse width,is defined as the duration period that elapses from the trailing edge of one pulse to theleading edge of a subsequent pulse of the same species. Finally, the concentrations of

Figure 1. Pulsing characteristics for the 48 hr and 96 hr pulse cycle time cases.


the acetate and nitrate pulses were adjusted together so that stoichiometric quantitieswere added. This stoichiometric relationship is based on [4].

3. Model development

3.1. Biochemical reaction model

In this study, the biological reactions described previously by Hooker et al. [4]have been employed. The kinetic expressions they presented are based on assimilatoryand dissimilatory denitrification reactions using both nitrate and nitrite as electronacceptors. The stoichiometry of the balanced chemical reactions are:

Dissimilatory denitrification

8NO−3 + 2CH3COO− + 2H+ → 4CO2 + 8NO−2 + 4H2O, (1)

8NO−2 + 3CH3COO− + 11H+ → 6CO2 + 4N2 + 10H2O. (2)

Assimilatory denitrification

3.5CH3COO− + NO−3 + 4.5H+ → 2CO2 + 3H2O + C5H9O3N, (3)

3.25CH3COO− + NO−2 + 4.25H+ → 1.5CO2 + 2.5H2O + C5H9O3N, (4)

where C5H9O3N is the empirical formula for cell mass. Based on the above reactionmechanisms, specific reaction rate (rate per unit concentration of bacteria) expressionswere developed for acetate, nitrate, and nitrite uptake in these pathways and are givenby the kinetic expressions:

rD,NO3 =µD,NO3 [NO3]

1 +KSD/[Ac]KiD,NO2

KiD,NO2 + [NO2], (5)

rD,NO2 =µD,NO2

1 +KSD/[Ac]1

1 +KNO2/[NO2] + [NO2]/Ki,NO2

, (6)

rA,NO3 =µA,NO3[NO3]

1 +KSA/[Ac] + [Ac]/KiA

(KiA,NO2

KiA,NO2 + [NO2]

)m, (7)

rA,NO2 =µA,NO2

1 +KSA/[Ac]1

1 +KNO2/[NO2] + [NO2]/Ki,NO2

. (8)

The details of various kinetics constants used in equations (5) to (8) are describedin Hooker et al. [4]. In that work, the values of each of the kinetic constants wereestimated based on laboratory data for the Hanford denitrifying consortium of microbes.

3.2. Fate and transport model

The numerical flow and transport simulator used in this study is a modified versionof a model developed previously [2]. Using this model, reactive flow from a single


injection well in a radial, homogeneous flow field can be described. In the model,changes in the concentration of the aqueous phase, mobile species were representedby a set of radial, one-dimensional transport equations of the form

∂[cspecies]∂t

= αVr∂2[cspecies]

∂r2 − Vr∂[cspecies]

∂r+Rspecies

φ, species = 1, 2, . . . , NM, (9)

while temporal changes in the concentration of immobile species attached to the soilmatrix were represented by equations of the form

∂[cspecies]∂t

=Rspecies

φ, species = 1, 2, . . . , NIM, (10)

where NM is the number of mobile species, NIM is the number of immobile species,and Rspecies is the reaction term for the species. In equation (9), the pore velocity, Vr,is a function of the radial distance from the injection point and is given by

Vr =Q

2πrbφ, (11)

where Q is the volumetric injection rate (L3T−1), b is the aquifer thickness (L), r isthe radial distance, and φ is the soil porosity.

3.3. Reactive transport model for the denitrifying system

For the specific problem solved here, the governing transport model with appro-priate reaction terms can be written for six mobile species and two immobile species.The six mobile species are: nitrate (NO3), nitrite (NO2), acetate (Ac), carbon tetra-chloride (CT), active, liquid-phase biomass (Xa), and inactive, liquid-phase biomass(Xi). The two immobile species are the live biomass attached to the solid phase (X̃a),and the inactive biomass attached to the solid phase (X̃i). For each of these eightspecies, the appropriate reaction rate (R/φ) is given in table 1.

In the biochemical model, both nitrate and nitrite are described as being consumedby either assimilatory or dissimilatory denitrification, with associated consumption ofacetate. When nitrate is consumed by dissimilatory denitrification, however, it isconverted to nitrite. Hence, the reaction term for nitrite accounts for the production ofnitrite by dissimilatory consumption of nitrate. Carbon tetrachloride (CT) destructionis first order in CT concentration, but is inhibited by high nitrate concentrations. All ofthese reactions are catalyzed by active biomass, that either is suspended in the aqueousphase or attached to the soil surface.

The reaction terms in the equations describing the biomass concentrations accountfor the fact that biomass can be either suspended in the aqueous phase or attached tothe solid surface. Kinetic terms are included to account for the transfer of the biomassbetween these two phases. Further, as the biomass ages, it may become inactive andno longer catalyze the biological reactions. Hence, terms are included to account forthis process. Other terms used in these reaction terms include, Katt, the bacterial


Table 1Reactive terms for each species.

Species name Species Reactive termsymbol

Nitrate [NO3] −(Xa + ρX̃a

φ

)(rD,NO3 + rA,NO3 )

Nitrite [NO2] −(Xa + ρX̃a

φ

)(−rD,NO3 + rD,NO2 + rA,NO2 )

Acetate [Ac] −(Xa + ρX̃a

φ

)(0.25rD,NO3 + 0.375rD,NO2 + 3.5rA,NO3 + 3.25rA,NO2 )

Carbon tetrachloride [CT] −(Xa + ρX̃a

φ

)(µCT[CT]

1+[NO3]/Ki,CT

)Aqueous phase, [Xa] −Katt[Xa] +

(Kdetρ[X̃a]

φ

)+ (rA,NO3 + rA,NO2 −Kd)[Xa]

active biomass

Aqueous phase, [Xi] −Katt[Xi] +(Kdetρ[X̃i]

φ

)+ (Kd(1− Fd)[Xa])

inactive biomass

Attached phase, [X̃a] −(φKdet[X̃a]

ρ

)+Katt[Xa] + (rA,NO3 + rA,NO2 −Kd)[X̃a]

active biomass

Attached phase, [X̃i] −(φKdet[X̃i]

ρ

)+Katt[Xi] + (Kd(1− Fd)[X̃a])

inactive biomass

attachment rate (0.38 d−1), Kdet, the bacterial detachment rate (0.001 d−1), Kd, thecell decay rate (4.8 × 10−5 d−1), Fd, the fraction of dead cells that solubilize (0.5),and ρ, the bulk density of the soil matrix (1.56 × 103 kg/m3).

Two additional assumptions were made. First, field observations indicate thatsubsurface denitrifiers in a starvation state are incapable of destroying contaminants.Hence, we assumed that if both the electron donor and the acceptor were not present atconcentrations greater than 1 mg/l for 14 days, the contaminant degradation rate linearlydiminished to zero by the end of day 15. The second assumption involves the observedminimum levels of attached biomass. Here, it was assumed that if the attached livebiomass concentration fell below its undisturbed aquifer level of 1.66× 10−7 g-DW/gsoil, biomass death and detachment did not take place. This assumption sets a lowerlimit on the subsurface, attached phase biomass concentration, similar to that observedin pristine aquifers.

3.4. Initial and boundary conditions for the reactive transport model

Boundary and initial conditions for each of the species are provided in table 2.Initially, the concentration of all the transported species is assumed to be zero through-out the field, except CT. The CT concentration is assumed to be 2 mg/l. In addition,all the biomass was assumed to be initially active and attached to the soil surface.

The boundary conditions provided in table 2 specify that the gradient in concen-tration at the outer edge of the simulation domain must be equal to zero and that onlyacetate, nitrate and CT are contained in the feed stream at the center of the flow field.


Table 2Initial and boundary conditions used for each species. Note that the attached phase biomass is nottransported, so these species are described by ordinary differential equations requiring the definition of

only the initial condition.

Species name Initial condition Boundary condition 1 Boundaryt = 0, t > 0, r = rwell condition 2

0 6 r 6∞ t > 0, r = rmax

Nitrate [NO3] = 0 [NO3] = [NO3]f

{∑∞n=0

u(t− Ps − PW − nPT) d[NO3]dr = 0

−u(t− Ps − 2PW − nPT)}

Nitrite [NO2] = 0 [NO2] = 0 d[NO2]dr = 0

Acetate [Ac] = 0 [Ac] = [Ac]f

{∑∞n=0

u(t− nPT) d[Ac]dr = 0

−u(t− nPT − PW)}

Carbon [CT] = [CT]i [CT] = [CT]fd[CT]

dr = 0tetrachloride = 2 mg/l = 2 mg/lAqueous phase, [Xa] = 0 [Xa] = 0 d[Xa]

dr = 0active biomassAqueous phase, [Xi] = 0 [Xi] = 0 d[Xi]

dr = 0inactive biomass

Attached phase, [X̃a] = [X̃a]0

active biomass

Attached phase, [X̃i] = 0inactive biomass

Acetate and nitrate are fed in a pulse fashion, as described in the previous sectionof this manuscript, while CT is fed continuously at a concentration of 2 mg/l. Tomathematically describe this pulse feeding strategy, the Heaviside step function u(τ )is used. This function is defined as

u(τ ) =

{0, τ < 0,1, τ > 0.

(12)

The system of eight coupled, non-linear, partial/ordinary differential equationswas solved by a Eulerian–Lagrangian, three stage, split operator, radial flow and re-active transport code described in [2]. The numerical model uses the operator splitstrategy to divide the flow and transport equations into advection, dispersion, and reac-tion portions. The advection portion was solved by a radial particle tracking procedure[2], the dispersion portion was solved by the fully-implicit method, and the coupledreaction portion was solved by 4th order Runge–Kutta procedure. Further numericaldetails of the solution procedure are described, for the case of a simplified aerobicproblem, in [2].

In all simulations, we assumed that the CT was injected into the field at a con-centration of [CT]f = 2 mg/l and that contaminant sorption could be neglected. Simu-lations were performed using a maximum radius of at least 35 m. Larger systems wereused if necessary to ensure that the biomass concentration was equal to the undisturbed


Table 3Summary of pulse characteristics examined in the first phase of the

study.

Pulse cycle time (hr) Pulse width (hr) Pulse skew (hr)

12 0.25 5.7524 0.5 11.548 1 2396 2 46

144 3 69192 4 92384 8 184

aquifer level at the downstream boundary of the flow field. The well radius was as-sumed to be 0.1 m. The injection flow rate, Q, was set at 27.25 m3/d (5 gpm). Fieldporosity, φ, and dispersivity, α, were set at 0.4 and 0.5 m, respectively. The thicknessof the aquifer was set at 1 m and 470 days of operation were simulated in each case.All calculations were performed in double precision on a DEC 3000 workstation usingDigital FORTRAN 77.

A set of simulations was completed to test the implications of various pulsecharacteristics on biomass development and CT destruction. This study was carriedout in three phases. In the first phase, the pulse cycle time was varied, while adjustingthe pulse width to ensure that the total amount of mass injected over the simulationperiod remained constant. In the second phase, the nutrient feed concentrations werevaried. Finally, in the third phase of the study, the total amount of nutrient added tothe field was varied by simultaneously adjusting the pulse width and pulse skew.

4. Results and discussion

4.1. Effects of pulse cycle time

The seven sets of pulse characteristics shown in table 3 were tested to assessthe effect of this parameter on the distribution of the biomass in the flow field. Foreach pulse cycle time, the injected acetate and nitrate concentrations were constant at20.0 and 28.0 g/l, respectively, and the pulse width was adjusted to ensure that thetotal mass of each nutrient fed was the same in all cases. This strategy is depictedgraphically in figure 1, where the 48 hr and 96 hr pulse cycles are shown as a functionof time over a 100 hr time interval. Over 4 days, only one pulse of each nutrient isinjected in the 96 hr cycle while two pulses of each nutrient are injected in the 48 hrcase. In the same fashion, pulse width and pulse cycle time were varied in the otherexamined cases.

In figure 2, the biomass concentration predicted after 470 days is plotted as afunction of distance from the nutrient injection well for each pulse cycle time. It isevident that a longer pulse cycle time produces a broader biomass distribution and that


Figure 2. Attached biomass concentration as a function of distance from the well for various pulseperiods.

the location of the maximum biomass concentration moves further from the injectionpoint. In addition, the maximum biomass concentration decreases with increasing pulsecycle times. In contrast, the same total amount of biomass develops in each case shownin figure 2. Integrating the biomass levels over the flow field after 470 days reveals thatthe average biomass level (± standard deviation) was 2.36× 105 ± 3.73× 103 g-DW.This result is expected since the same total nutrient loading was added in each case,and all nutrients were consumed in the flow field.

The predicted biomass distribution is a direct result of nutrient dispersion. Nobiomass growth can occur until both the electron donor and acceptor are present atthe same location. Eventually, dispersion spreads the leading and trailing edges oftwo adjacent pulses such that the two materials mix, which is a prerequisite for thebiological reactions. Since this mixing takes time, a region exists near the injectionpoint where these materials never meet and no biomass growth occurs. The radius ofthis region in which no growth occurs increases as the time between pulses increases,since a longer period is required before the pulses mix. Biomass growth will, however,occur over an extended region defined by the distance traveled by the nutrient pulsesafter they first mix, but before all material has reacted. Since dispersion lowers theconcentration in the mixing tails, biomass is further distributed as the pulse cycle timeincreases, resulting in lower growth and nutrient consumption rates.

The volume of aquifer biostimulated as a function of pulse cycle time was alsoevaluated. This volume was assumed to extend from the point where biomass con-centration was 5% more than the base biofilm level to the point where the biomass


Figure 3. Volume of the biostimulated portion of the flow field as a function of pulse cycle time.

concentration returned to within 5% of the base biofilm level. The volume of thisannulus is shown as the solid line in figure 3, using the same nutrient conditions aswere employed in figure 2. Data for two other nutrient concentrations (see section 4.2)are also shown in this figure. It is evident that, for each nutrient concentration, thevolume of the annulus containing the biomass increases with the pulse cycle time.This increase is a result of the radial nature of the flow field. Since higher pulse cycletimes cause the biomass to grow further from the well, the volume of the biologicallyactive zone also increases.

Even better volumetric coverage may be achieved if a combination of long andshort pulse cycle times were employed. For example, from the distributions shownin figure 2, it is evident that almost complete coverage of the region within 25 m ofthe injection well could be accomplished if a combination of 24 hr and 384 hr pulseswere used to develop a bimodal distribution of biomass around the injection point.

4.2. Effect of nutrient concentration

To determine the effects of the nutrient concentration on the total amount ofbiomass developed in the field, 470 day simulations were performed using three nutrientconcentrations (designated high, medium, and low) at each of the seven pulse cycletimes. The high nutrient level is identical to that used in the previous portion of thisstudy (28 g/l nitrate, 20 g/l acetate). The medium nutrient level was 20% of the highlevel (5.6 g/l nitrate and 4 g/l acetate). The low level was 10% of the high case (2.8 g/lnitrate and 2.0 g/l acetate).

Both the medium and low nutrient levels generated biomass distributions whichwere qualitatively similar to those of the high nutrient case are shown in figure 2. That


is, the location of the maximum biomass concentration and the width of the biomasspeak increased with increasing pulse cycle time. However, for a given pulse cycle time,lowering the nutrient concentration resulted in lower levels of total biomass in bothcases. Numerical integration of the biomass profiles indicates that the total amount ofbiomass produced was independent of pulse cycle time for all three cases, but decreasedas the nutrient concentration decreased. The average amounts of biomass produced(± standard deviations) for the high, medium, and low nutrient concentration caseswere 2.36×105±3.73×103, 3.18×104±1.15×103 and 1.18×104±4.12×102 g-DW,respectively.

A decrease in the total biomass with nutrient concentration is expected sincelower amounts of nutrients lead to lower growth. However, the amount of biomassproduced was not directly proportional to the total amount of nutrients added. In themedium and low cases, only 20% and 10% of the nutrients used in the high casewere added to the field. However, for these two cases, the average total amounts ofbiomass produced were 13% and 5% of the high concentration case. This shift ingrowth yields is consistent with the kinetics reported by Hooker et al. [4], since at lownutrient concentrations a larger fraction of the nutrients will be used to support cellgrowth (assimilatory denitrification). Others have reported experimental observationsof similar shifts in growth yields with lower nutrient levels [17].

The implications of this phenomenon on in situ remediation of co-metabolicallydegraded compounds such as CT is significant since, for these systems, large amountsof unwanted biomass are produced during contaminant destruction [1]. This materialcould be minimized by adjusting nutrient feeding strategies to first build up a largeamount of biomass by introducing high levels of nutrients and then lowering thesubstrate level to maintain the organisms in a state that diverts more of the added energyto catabolism and less to reproduction. However, this approach will not completelyeliminate the problem of unwanted biomass since a lower limit on nutrient requirementsis dictated by the amount of substrate needed to achieve a steady state contaminantremoval required to meet the clean-up goal.

As shown in figure 3, the volume of the biostimulated region decreases as theconcentration of the nutrients in the feed pulses is reduced. For the cases shown here,the biostimulated volume for the high concentration case is 7% to 36% more than thebiostimulated volume obtained using the low concentration feed condition.

4.3. Effects of pulse width

The total amount of nutrients added to the subsurface can also be adjusted bymanipulating the width of the nutrient pulses. To test the effect of this parameteron biomass development, 470 days of nutrient injection were simulated using a pulsecycle time of 384 hr, a high nutrient feed concentration, and five different pulse widths(8, 16, 40, 64, and 128 hr). In each case, the pulse skew was adjusted to keep thepulse cycle time constant.


Table 4Effects of pulse width on biomass and CT destruction.

Pulse width Total Biostimulated Average Assimilatory Dissimilatory CT destroyed(hr) biomass volume nitrite conc. nitrite nitrite (kg)

(kg) (m3) (mg/l) inhibition inhibitionmultiplier multiplier

8 230 6851 2.5× 10−2 1.0 1.0 8.516 526 7187 2.9× 10−2 1.0 1.0 13.340 1506 7562 4.0× 10−2 1.0 1.0 16.164 2518 7538 3.5× 10−2 1.0 1.0 19.9

128 2194 11882 2922 0.000120 0.008200 9.1

Table 4 shows the total amount of biomass that is predicted to be developed inthe flow field, and the associated volume of the biostimulated region after 470 daysof operation as a function of pulse width. As is seen in this table, the total amount ofbiomass developed increases with pulse width up to a pulse width of 128 hours. Inthis last case, the amount of biomass is slightly less than that predicted for the 64 hrcase. In contrast, the volume of the biostimulated portion of the flow field increasesin every case and is significantly higher in the 128 hr case than it is in the 64 hrcase.

To better understand these results, the concentrations of the acetate, nitrate, nitrite,and attached biomass are plotted in figure 4 as a function of distance from the injectionwell after 470 days of simulated time for the 64 hr and 128 hr cases. In the 64 hr case,a single biomass peak developed, having a shape similar to those shown in figure 2.However, for the 128 hr case, two biomass peaks are predicted. One peak developsnear the injection point and another sharp peak is predicted to develop much fartherfrom the injection point, at about 55 m. Examination of the acetate, nitrate, and nitritelevels in the flow field reveals the reason for the bimodal biomass profile. For allcases except the 128 hr pulse width, virtually all the nutrients were consumed withinthe flow field. For this 128 hr case, however, the bulk of the nitrate is first convertedonly to nitrite which then builds up to inhibitory levels. Table 4 shows the averagenitrite level at 35 m from the injection point during the final 16 days of each caseexamined. For a 128 hr pulse width, the nitrite concentration was nearly 3000 mg/l,while its concentration is less than 1 mg/l for all other pulse widths. As reported byHooker et al. [4], nitrite inhibits both dissimilatory and assimilatory denitrification inthese organisms. Using the nitrite concentrations from column 4 of table 4, the valuesof the nitrite inhibition multiplier for assimilatory and dissimilatory nitrate consumingbiological reactions reported by Hooker et al. [4] are shown in the fifth and sixthcolumns in table 4. Obviously, little microbial growth would occur at the nitriteconcentrations predicted in this portion of the flow field in the 128 hr case. Thisinhibition of microbial activity will limit the volume of the biostimulated portion ofthe flow field near the injection point. Eventually, however, because of dispersion andslow reaction, the nitrite concentration drops to levels that are not inhibitory, and rapid


Figure 4. Acetate (A), nitrate (B), nitrite (C), and attached biomass (D) concentrations as functions ofdistance from the injection point for pulse widths of 64 hr and 128 hr.

cell growth commences. In this case, this growth is predicted to occur approximately55 m from the injection point.

It is important to note that, although dispersion will eventually cause the nitriteconcentration to drop to levels that will allow reaction, in realistic field-scale systemssubsurface heterogeneity would broaden this latter peak. Further, since nitrite is pre-dicted to be at inhibitory levels in much of the flow field, one should not use a strategythat takes advantage of inhibition to maximize the volume of the treated zone.


4.4. CT degradation

The amount of CT destroyed by the biomass was calculated as a function of thepulse cycle time, the nutrient concentration, and the pulse width. The average totalCT destroyed in the high, medium, and low concentration cases at various pulse cycletimes and a pulse width of 8 hr were 8.60± 0.15, 2.14± 0.05 and 1.15± 0.04 kg CT,respectively. Hence, the total amount of CT destroyed was nearly independent of pulsecycle time, but was highly dependent on the nutrient concentration employed. Thisbehavior is similar to that observed for the total amount of biomass produced.

Note that although the amounts of nutrients added in the medium and low concen-tration cases were, respectively, 20% and 10% of that added in the high concentrationcase, the amount of CT destroyed in the medium and low concentration cases was25% and 14% of that destroyed in the high concentration cases. Hence, althoughmore biomass was produced per unit nutrient added in the higher concentration cases,more CT was destroyed per unit of nutrient fed in the lower concentration cases. Thisbehavior is caused by nitrate inhibition of CT destruction; even though more biomasswas grown, the high nitrate concentrations did not allow the biomass to effectivelydestroy the contaminant [4].

Table 4 also shows the amount of CT that is predicted to be destroyed in the fieldas a function of the pulse width. In all cases except the 128 hr case, the last columnlists the total amount of CT that is predicted to be destroyed in the system; in case ofthe 128 hr pulse width, only the degradation due to the biomass near the injection pointis included. These data demonstrate that increasing the pulse width also increases CTdestruction. However, the amount of CT that is destroyed is not proportional to theamount of biomass that is produced because CT transformation is inhibited by high ni-trate concentrations. In every case, the nitrate concentration is predicted to be inhibitoryin much of the flow field. Hence, although more biomass is grown in the cases witha high pulse width, much of this biomass can not be effectively used to degrade CT.

Combining these CT destruction predictions with the information presented earlieron the effect of pulse width on the biostimulated volume provides insight into the waythat a field site should be operated. These data indicate that, because the biostimulatedvolume is not a strong function of the pulse width, a field site should be operatedin a fashion that maximizes the amount of CT degraded per unit of nutrient injected,while also maximizing the volume of the biostimulated portion of the flow field. Thiscondition can be achieved by injecting long pulses that are separated by long periodswhere only unamended water is injected. This strategy will cause the nutrient pulsesto overlap at a considerable distance from the well, while still having concentrationshigh enough to ensure significant biomass growth.

5. Conclusions

The effects of pulse characteristics on the volume of the biologically activezone during an in situ bioremediation process were determined using a radial, one-


dimensional, numerical model of a homogeneous confined aquifer. Four major con-clusions follow from this work:

(1) The volume of the biologically active zone is nearly independent of the nutrientconcentration, but increases with pulse cycle time. Even larger biostimulatedvolumes may be achievable if a combination of long and short pulse cycle timeswere used.

(2) The total biomass produced is independent of the pulse cycle time but increaseswith the nutrient concentration. In addition, increasing the pulse width also in-creases the total biomass in the flow field, up to the point where inhibitory productsbegin to develop. However, for wide pulses, biomass may not be effective in de-grading CT if the nitrate concentration is above inhibitory levels in a large portionof the flow field.

(3) CT destruction is nearly independent of the pulse period, but highly dependentupon nutrient feed concentration since it is related in a first order fashion to thebiomass concentration as long as the nitrate concentration is below the inhibitorylevel. The high feed condition had the highest rate of contaminant destruction.

(4) Large pulse periods lead to large quantities of biomass in the field, provided thatinhibitory levels of nitrate are not produced.

These results indicate that volumetric treatment can be accomplished by inject-ing long pulses that are separated by long periods in which only unamended wateris injected. This strategy will cause the nutrient pulses to overlap at a considerabledistance from the well, while still having concentrations high enough to ensure sig-nificant biomass growth. Finally, note that these results are limited by the radial,one-dimensional nature of the flow and transport model. Subsurface heterogeneitieswould cause variable dispersivity, resulting in the region of biomass growth to notbe exactly as predicted here. In addition, an upper bound on nutrient pulsing willbe dictated by design constraints such as those caused by well-to-well communica-tion.

Appendix. Notation

[Ac] acetate concentration M l−3

b aquifer thickness l[cspecies] species concentration M l−3

[CT] carbon tetrachloride concentration M l−3

Fd fraction of total inactive biomass that solubilizeskdecay active biomass decay rate parameter T−1

Katt bacterial attachment rate T−1

Kdet bacterial detachment rate T−1

KiA Monod acetate inhibition parameter for assimilatory uptake of nitrate M l−3


KiA,NO2 nitrite inhibition parameter for the assimilatory uptake of nitrate M l−3

Ki,CCl4 nitrate inhibition for CT destruction M l−3

KiD,NO2 nitrate inhibition parameter for the dissimilatory uptake of nitrate M l−3

Ki,NO2 Monod nitrite inhibition parameter for assimilatory and dissimilatory uptakeof nitrite M l−3

KNO2 Monod parameter on nitrite for assimilatory and dissimilatory uptake ofnitrite M l−3

KSA Monod parameter on acetate for assimilatory uptake of nitrate and nitriteM l−3

KSD Monod parameter on acetate for dissimilatory uptake of nitrate and nitriteM l−3

m exponent on the nitrite inhibition term for the assimilatory uptake of nitrateNM number of mobile speciesNIM number of immobile species[NO3] nitrate concentration M l−3

[NO2] nitrite concentration M l−3

PS pulse skew TPT pulse cycle time TPW pulse width TQ volumetric injection rate l3 T−1

u(τ ) Heaviside step functionr radial position lrA,NO3 specific overall rate of assimilatory uptake of nitrate T−1

rA,NO2 specific overall rate of assimilatory uptake of nitrite T−1

rD,NO3 specific overall rate of dissimilatory uptake of nitrate T−1

rD,NO2 specific overall rate of dissimilatory uptake of nitrite T−1

R total reaction rate M l−3 T−1

t time TVr fluid velocity in the radial direction l T−1

[Xi] inactive, liquid-phase biomass concentration M l−3

[X̃i] inactive, attached-phase biomass concentration M l−3

[Xa] active, liquid-phase biomass concentration M l−3

[X̃a] active, attached-phase biomass concentration M l−3

α dispersivity lµA,NO3 maximum rate parameter for the assimilatory uptake of nitrate l3 M−1 T−1

µA,NO2 maximum rate parameter for the assimilatory uptake of nitrite T−1

µCCl4 first order rate parameter for CT destruction l3 M−1 T−1

µD,NO3 maximum rate parameter for the dissimilatory uptake of nitrate l3 M−1 T−1

µD,NO2 maximum rate parameter for the dissimilatory uptake of nitrite T−1

ρ bulk density of the soil matrix M l−3

φ porosity


Acknowledgements

This work was supported by the US Department of Energy Office of TechnologyDevelopment, the VOC-Arid Integrated Demonstration and by the former In Situ Re-mediation Integrated Program. The portion of this work conducted at Washington StateUniversity was supported by a contract from the Pacific Northwest Laboratory. Dr.Petersen was supported by the Associated Western Universities, Inc., Western Divisionunder grant DE-FG06-89ER-7522 with the US Department of Energy. Ms. Franzenwas supported by the Chemical Engineering Department at WSU. Pacific NorthwestLaboratory is operated by Battelle Memorial Institute for the US Department of Energyunder contract DE-AC-6-76RLO 1830.

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