the role of biofilm growth in bacteria-facilitated contaminant transport in porous media

Transport in Porous Media 26: 161–181, 1997. 161c 1997 Kluwer Academic Publishers. Printed in the Netherlands.

The Role of Biofilm Growth in Bacteria-FacilitatedContaminant Transport in Porous Media

SEUNGHYUN KIM1 and M. YAVUZ CORAPCIOGLU21Department of Environmental Engineering, Yeungnam University, Kyungsan 713-749, Korea.e-mail: [email protected] of Civil Engineering, Texas A&M University, College Station, TX 77843-3136, USA.e-mail: [email protected]

(Received: 29 March 1996; in final form: 23 September 1996)

Abstract. Groundwater contaminants adhered to colloid surfaces may migrate to greater distancesthan predicted by using the conventional advective-dispersive transport equation. Introduction ofexogenous bacteria in a bioremediation operation or mobilization of indigenous bacteria in ground-water aquifers can enhance the transport of contaminants in groundwater by reducing the retardationeffects. Because of their colloidal size and favorable surface conditions, bacteria can be efficientcontaminant carriers. In cases where contaminants have low mobility because of their high partitionwith aquifer solids, facilitated contaminant transport by mobile bacteria can create high contaminantfluxes. In this paper, we developed a methodology to describe the bacteria-facilitated contaminanttransport in a subsurface environment using the biofilm theory. The model is based on mass bal-ance equations for bacteria and contaminant. The contaminant is utilized as a substrate for bacterialgrowth. Bacteria are attached to solid surfaces as a biofilm. We investigate the role of the contaminantadsorption on both biofilm and mobile bacteria on groundwater contaminant transport. Also, theeffect of bacterial injection on the contaminant transport is evaluated in the presence of indigenousbacteria in porous media. The model was solved numerically and validated by experimental datareported in the literature. Sensitivity analyses were conducted to deduce the effect of critical modelparameters. Results show that biofilm grows rapidly near the top of the column where the bacteria andcontaminant are injected, and is detached by increasing fluid shear stress and re-attach downstream.The adsorption of contaminant on bacterial surfaces reduces contaminant mobility remarkably in thepresence of a biofilm. The contaminant concentration decreases significantly along the biofilm whencontaminant partition into bacteria. Bacterial injection and migration in subsurface environments canbe important in bioremediation operations regardless of the presence of indigenous bacteria.

Key words: biofilm, contaminant transport, bacterial transport, facilitated transport, bioremediation.

1. Introduction

Retardation of contaminants in groundwater can be short-circuited by colloid-facilitated transport. Contaminants adhered to colloid surfaces can travel to greaterdistances than those predicted by using their nominal retardation values. As notedby McCarthy and Zachara (1989), inorganic ions and biocolloids such as bacteriamigrate to groundwater from the vadose zone (Harvey et al., 1989). Furthermore,the introduction of exogenous bacteria in a bioremediation operation can short-circuit the effort by bacteria-facilitated contaminant transport. Likewise, indigenoussubsurface bacteria mobilized by changes in physical and chemical conditions

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162 SEUNGHYUN KIM AND M. YAVUZ CORAPCIOGLU

in groundwater can contribute to facilitated groundwater contaminant transport.Bacterial surfaces in most natural environments are negatively charged like mostother colloids, and bacterial density is slightly greater than that of water. As a resultof these properties, bacteria tend to form stable colloidal suspensions (Marshall,1986). Hydrophobic contaminants partition into the surfaces of bacteria and alsocan desorb to some extent (Canton et al., 1977).

Recently, Bellin and Rao (1993) noted that the presence of bacteria in subsurfaceenvironments may affect polynuclear aromatic hydrocarbon (PAH) migration byaltering the sorption characteristics of soil solids. Jenkins and Lion (1993) haveindicated that bacteria may enhance the transport of PAHs in the subsurface. Ina review paper, Baughman and Paris (1981) concluded that sorption of organicsolutes occurs at least to the same extent in dead cells as in live cells for mostspecies. Similar conclusions were later reached by other researchers with a varietyof organic substances such as lindane, pentachlorophenol, and diazinon (Tsezos andBell, 1989; McRea, 1985). Bell and Tsezos (1987) and Tsezos and Bell (1989) havefurther shown that aqueous phase pollutants are reversibly bound to microorganismsurfaces. Thus, based on these experimental evidences, we can expect adsorptionand desorption of organic solutes on surfaces of microorganism as they migrate insubsurface environments.

Corapcioglu and Haridas (1984 and 1985) modeled the migration of bacteria inporous media. Hornberger et al. (1992) conducted a laboratory column experimentsand concluded that the model of Corapcioglu and Haridas (1985) can successfullydescribe some of the important characteristics of the transport of bacteria throughporous media. Corapcioglu and Jiang (1993) presented a methodology to developa predictive model of colloid facilitated groundwater contaminant transport basedon a conceptualization of the problem as a three-phase medium. Experimental dataof Magee et al. (1991) matched favorably with the numerical results of the model.Recently Corapcioglu and Kim (1995) and Kim and Corapcioglu (1996) presentedmodels to simulate the facilitated contaminant transport by mobile bacteria.

Bacteria in groundwater aquifers, mostly under oligotrophic or starvation sur-vival conditions, would shift their metabolic balance away from the biosynthesisand reproduction and toward the acquisition of energy for existing biological func-tions (Kurath and Morita, 1983). They have a wide selectivity for their substrateand can uptake variety of materials as nutrients for their growth and maintenance(Poindexter, 1981). As a result, bacteria can migrate in porous media carryinghydrophobic contaminants on their surface as uptaking them as substrates.

When bacteria flow through an established porous medium, they migrate to thesurface of the solid matrix. They are captured on the solid matrix by mechanismscaused by the action of forces of fluid-mechanical origin along with other forcesacting between the bacteria and solid matrix. Bacterial capture on solid matrixis generally affected by several factors such as temperature, pH, ionic strength(Fletcher and Loeb, 1979). After a bacterium stays for some critical residencetime on the solid matrix surface, the irreversible attachment or anchoring begins,

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BIOFILM GROWTH IN BACTERIA-FACILITATED TRANSPORT 163

resulting in biofilm formation (Characklis, 1984). This mechanism is biologicalin nature and is mainly attributed to the production of extracellular polymericsubstances (Bashan and Holguin, 1993). A recent study by Rijnaarts et al. (1995)shows that irreversible attachment mediated by bacterial surface polymers may beinstantaneous.

Biofilm concept (i.e., continuous phase coverage by biofilm rather than patchycolonization) was employed in environmental engineering to model substrateutilization in wastewater treatment systems and groundwater by bacterial films(Williamson and McCarty, 1976). Taylor et al. (1990) studied the effects of biofilmdevelopment on the changes in physical properties of a porous medium. Taylor andJaffe (1990b) included these effects in their modeling of bacterial and substratetransport. Taylor and Jaffe employed the steady state substrate concentration pro-file assumption within the biofilm. Furthermore, they assumed that the substrateconcentration is constant throughout the entire biofilm. Their model predictionswere verified against the experimental data.

In this paper, following the works of Corapcioglu and Haridas (1985), Taylorand Jaffe (1990b), and Corapcioglu and Jiang (1993), we investigate the role ofthe contaminant attachment to both mobile and immobile (biofilm) bacteria ongroundwater contaminant transport. Also, the effect of bacterial injection on thecontaminant transport is evaluated in the presence of indigenous bacteria in porousmedia.

2. Formulation of the Problem

In this section, we present a formulation for simultaneous transport of a dissolvedcontaminant and bacteria in porous media. The methodology is based on a concep-tualization of the problem as a three-phase medium (Figure 1). The system has twosolid phases, i.e., soil solids and mobile biocolloids (bacteria) and a fluid phase(water). Bacteria form a biofilm on solid surfaces, i.e., immobile bacteria. Since ourobjective is to study the role of biofilm growth and bacterial migration on contam-inant transport, we neglect the adsorption of contaminant on solid surfaces. Suchan approach is justifiable when the porous medium comprises particles with lowadsorption capacity such as silica surfaces. However, we take into considerationthe sorption of contaminant on bacterial surfaces. The contaminant is utilized as asubstrate for bacterial growth. We also assume that other components of bacterialgrowth such as electron acceptors and inorganic compounds are abundantly avail-able and not rate-limiting. Bacteria are assumed to grow both in the aqueous andbiofilm phases. Biofilm is assumed to consist of a gel throughout which the bacteriaare uniformly scattered, i.e., the film volume is directly proportional to the activebiomass in it (LaMotta, 1976). At this point we should note that although someresearchers assume continuous coverage of attached bacteria on solids, others arguepatchy colonization (Rittman, 1993). Due to lack of significant evidence, the fate ofdead bacteria is not considered although it may contribute to the process. Instead,

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Figure 1. Schematic diagram of a porous medium with biofilm.

we assume that a constant fraction of bacterial mass in the biofilm comprises deadbacteria.

2.1. BACTERIAL TRANSPORT IN AQUEOUS PHASE

Our starting point in modeling the facilitated transport of contaminants by bacteriais the mass balance equation for mobile bacterial particles suspended in the aqueousphase. We assume that the amount of contaminant mass adsorbed on bacteria isnegligible in comparison to the mass of bacteria (Corapcioglu and Haridas, 1985)

@

@t(�CC) = �r � JC + rc� � rd� �QC ; (1)

where � = n� �f ; n is the porosity, �f is the volume fraction of the biofilm, CCis the bacterial mass concentration in the aqueous phase, JC is the specific massdischarge of bacteria, rc is the bacterial growth rate, rd is the bacterial decay rate,and QC is the net mass transfer rate of bacteria from the aqueous phase to biofilm.

Assuming that suspended bacteria migrate with a velocity equal to that of theaqueous phase, the specific mass discharge of bacteria can be expressed by

JC = JMD + qwCC = �DCr(�CC) + �vCC ; (2)

where JMD denotes the bacterial mass flux by dispersion, qw is the specific dis-charge of water phase, v is the flow velocity, andDC is the bacterial hydrodynamicdispersion coefficient. In Equation (2), the other bacterial motions such as tumblingand chemotaxis were neglected.

Bacterial growth occurs with the utilization of a substrate (contaminant). Thegrowth of bacteria is assumed to follow the Monod equation. The Monod equation

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describes a relationship between the concentration of a limiting nutrient and thegrowth rate of microorganisms. Since bacterial growth in a subsurface environmentis slow, and groundwater contaminants such as dissolved hydrocarbons can serveas growth substrates, the use of the Monod equation to describe contaminantutilization by bacteria is warranted

rc =�maxCD

KD + CDCC ; (3)

where CD is the contaminant mass concentration in the aqueous phase, �max is themaximum specific growth rate achievable when KD � CD, i.e., zero order withrespect to CD, and the concentration of all other essential nutrients is unchanged.KD, Monod half-saturation constant, is the value of the concentration of the sub-strate where the specific growth rate has half its maximum value. Roughly speaking,it is the division between the lower concentration range where rc is linearly depen-dent on CD, and the higher range, where rc becomes independent of CD. Thecontribution of sorbed contaminant on bacterial surfaces to the bacterial growthwas neglected because of its negligible mass compared to that of the aqueous phasecontaminant. The bacterial decay rate can be expressed by a first-order kineticequation

rd = kdCC ; (4)

where kd is bacterial decay rate coefficient. The net mass transfer rate of bacteriaon biofilm is the sum of deposition and detachment rates

QC = Rd �Rs; (5)

where Rd is the deposition rate of bacteria and Rs is the shear loss rate of biofilm.Rd can be expressed by Iwasaki’s (1937) model as

Rd = (c1�f + c2)�CC ; (6)

where the second term, c2�CC corresponds to the capture rate in an initially cleanmedium free of biofilm. The first term c1�f�CC introduces the effect of biofilm onbacterial capture and �f is the volume fraction of the biofilm.

The detachment of captured bacteria from the solid surfaces can be quantified ina number of ways. Corapcioglu and Haridas (1985) employed a first-order kineticmodel to describe the detachment process. An alternative approach which is used inconjunction with biofilms is a model based on shear of biomass. As biofilm thick-ness increases with growing biomass, the detachment rate of biomass increases withfluid shear stress at the biofilm surfaces (Characklis, 1984). Rittmann (1982) notedthat shear losses of biofilm can be significant for sandy media. Based on experi-mental data obtained in granular-activated carbon columns, Speitel and DiGiano

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(1987) proposed a model of biofilm shearing. Then we express the detachment rateof biofilm as

Rs = bdetxf�f + �b0

det�max(CD + �cmxf )

KD + (CD + �cmxf )xf�f ; (7)

where bdet is the detachment rate coefficient, b0det is a dimensionless parameterdescribing the bacterial growth effects on shearing at the biofilm/water interface,xf is the biofilm density, � is the effectiveness factor of biofilm reaction, �cm isthe mass fraction of contaminant adhered to bacterial surfaces per unit mass ofbacteria. Since adsorption and desorption of hydrophobic substances on bacterialsurfaces are considered reversible and very fast (Canton et al., 1977), �cm can beexpressed by an equilibrium relationship in terms of the aqueous phase contaminantconcentration as

�cm = K5CD; (8)

where K5 is the equilibrium distribution coefficient for the contaminant with bac-terial surfaces.

The biofilm detachment rate coefficient is given as (Rittmann, 1982)

bdet = 8:42� 10�2�

0:58 (Lf 6 0:003 cm);

= 8:42� 10�2

"�

1 + 443:2(Lf � 0:003)

#0:58

(Lf > 0:003 cm); (9)

where Lf is the biofilm thickness and � is the shear stress (dyne/cm2) which canbe computed for a spherical medium as (Rittmann, 1982)

� =100�wqw(1� �)3

7:46� 109d2�3a; (10)

where �w is the viscosity of fluid, d is the particle diameter and a is the specificsurface of the biofilm/water interface based on the total volume of the column.Equation (10) can be rewritten by introducing the permeability of the mediumfrom the Kozeny–Carman equation for spherical grains (Bear, 1972, p. 166)

� =5

9� 7:46� 109

�wqw(1 � �)

ka; (11)

where k is permeability of the medium.

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Substitution of Equations (2)–(8) into Equation (1) yields

@

@t(�CC) = �r � [�DCr(�CC) + qwCC ]

+�maxCD

KD + CD�CC � kd�CC � (c1�f + c2)�CC

+

"�b

0

det�maxCD(1 +K5xf )

KD + CD(1 +K5xf )+ bdet

#xf�f : (12)

2.2. CONTAMINANT TRANSPORT IN THE AQUEOUS PHASE

Contaminant mass balance in the aqueous phase can be expressed by

@

@t(�CD + �CC�cm) = �r � JD �r � (JC�cm)� rs� �Qs; (13)

where JD is the specific mass discharge of contaminant in the aqueous phase, rs isthe contaminant utilization rate by bacteria in the aqueous phase, and Qs is the nettransfer rate of contaminant from the aqueous phase to the biofilm phase. As notedearlier, we neglect the adsorption of contaminant on solid. Such an approach is jus-tifiable when the porous medium comprises particles with low adsorption capacitysuch as silica surfaces. This assumption is further justified because the biofilmis composed of bacteria and their charged exopolymers completely covering thegrain surfaces. These constituents are considered to occupy the possible adsorptionsites for contaminants on solid surfaces (Marshall, 1986). However, we take intoconsideration the sorption of contaminant on bacterial surfaces. The second termwithin the parentheses of the left hand side denotes the contaminant mass sorbed onmobile bacteria. The second term on the right hand side stands for the contaminantmigration adsorbed on mobile bacteria.

Assuming that dissolved contaminant migrates with a velocity equal to that ofthe aqueous phase, the specific mass discharge of aqueous phase contaminant isexpressed as

JD = �DDr(�CD) + qwCD; (14)

whereDD denotes the hydrodynamic dispersion coefficient of contaminant and canbe thought of as identical with the bacterial hydrodynamic dispersion coefficientDC , with the assumption of negligible molecular diffusion.

Assuming the existence of a stoichiometric ratioY between the mass of substrateutilized and microbes formed, the net rate of consumption of substrate becomes

rs =1Y

�maxCD

KD + CDCC ; (15)

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where Y is called the yield coefficient.In this study, we assume that bacteria attach to soil solids as a biofilm. Biofilm

is a continuous layer of aggregation of bacteria attached to solid surfaces. Theirthickness can be assumed to be evenly distributed on a soil particle. The biofilm isassumed to be a flat plate although the surface of biofilm is irregular in shape. Innatural systems with a high specific surface area and low nutrient concentrationssuch as in an aquifer, biofilm concept can be applied even with low bacterialpopulations. Based on the measurements of Wilson and McNabb (1983), McCarty(1984) commented that a groundwater microbial population of 106/ml–107/ml,which corresponds to about one microorganism per grain of sand, can utilizegroundwater contaminants.

The mass transfer rate of contaminant from the aqueous phase to the biofilm isthe interface mass transfer at the biofilm surface. It is reasonable to assume that theinterface contaminant mass transfer rate is basically the same as the contaminantutilization rate in the biofilm with the assumption of a steady state conditionwithin the biofilm, if no contaminant is released from the substratum. With thisassumption, contaminant transfer rate can be expressed by

Qs =�

Y

�maxCD(1 +K5xf )

KD + CD(1 +K5xf )xf�f ; (16)

where the effectiveness factor � is defined as � =R Lf

0 rc(�) d�=[Lf rc(0)], in which� is the distance measured from the biofilm/water interface, rc(�) is the bacterialgrowth rate, and rc(0) is the bacterial growth rate at the biofilm/water interface(Froment and Bischop, 1979). The parameters for the growth rate in the biofilmare assumed to be the same as those in the aqueous phase (Characklis, 1984).In Equation (16), we consider only unidirectional contaminant fluxes from theaqueous phase to the biofilm.

Substitution of Equations (14)–(16) into Equation (13) yields

@

@t(�CD + �CCK5CD)

= �r � [�DDr(�CD) + qwCD]

�r � f[�DCr(�CC) + qwCC ]K5CDg �1Y

�maxCD

KD + CD�CC

��

Y

�maxCD(1 +K5xf )

KD +CD(1 +K5xf )xf�f : (17)

2.3. BIOFILM GROWTH AND CONTAMINANT UTILIZATION WITHIN THE BIOFILM

If the bacterial growth is rate limiting and the contaminant diffuses rapidly, thecontaminant concentration in the biofilm can be assumed to be constant throughout

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the biofilm in the case of low aquifer temperature. However, if the temperature ofthe water entering the aquifer is not low, in other words, if the bacterial growthrate is not low in comparison to the diffusion of contaminant within the biofilm,� becomes less than unity. Then the concentration variation within the biofilmshould be taken into consideration. If the resistance at the biofilm/water interfaceis negligible, contaminant concentration at the interface is identical with that in theaqueous phase and the biofilm growth can be described by

@

@t(xf�f ) = �(1� b

0

det)�maxCD(1 +K5xf )

KD + CD(1 +K5xf )xf�f

�kdxf�f + (c1�f + c2)�CC � bdetxf�f ; (18)

where the bacterial concentration in the biofilm is considered to be constant(LaMotta, 1976).

When the contaminant concentration in the biofilm is not constant, the contami-nant mass balance in the biofilm can be described under the steady-state assumptionas

Df

d2CDf

d�2 =xf

Y

�maxCDf (1 +K5xf )

KD +CDf (1 +K5xf ); (19)

whereCDf is the contaminant concentration in biofilm,Df is the effective diffusioncoefficient of contaminant in the biofilm. � can be calculated by solving Equation(19). In Equation (18), �f can be approximated as

�f = [Mb0(1 � n) +Mb(1� �)]Lf=2; (20)

where Mb is the specific surface based on solid volume including the biofilm, Mb0

is the initial specific surface with no biofilm.Substitution of Equation (20) into Equation (18) yields

dLfdt

= �(1 � b0

det)�maxCD(1 +K5xf )

KD + CD(1 +K5xf )Lf � kdLf

+2(c1�f + c2)�CC

[Mb0(1 � n) +Mb(1� �)]xf� bdetLf : (21)

Because a sequential method is employed in the solution of the governing equations,Mb and � were regarded as constants through a time step.

2.4. POROUS MEDIUM PROPERTIES

As the biofilm grows, the porous medium properties such as porosity, dispersivity,and specific surface change due to alterations of pore structure. Changes in these

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parameters affect the bacterial and contaminant transport. In this study, we employthe functional relationship proposed by Taylor and Jaffe (1990a) and Taylor et al.(1990) between these medium parameters and the biofilm thickness. The porosityis expressed by

�=1��

�m

"(2�m)

12

�2Lfd

�3

+(4�m)

8

�2Lfd

�2

+12

�2Lfd

�+

16

#: (22)

The dispersivity is given by

� = �0 exp(13:6Lf=R); (23)

whereR is the maximum pore radius. The expression for the specific surface basedon bulk porous medium volume is

a =�

�md

"(2�m)

2

�2Lfd

�2

+(4�m)

2

�2Lfd

�+ 1

#: (24)

In Equations (22)–(24), �0 is the initial dispersivity, m is the number of contactpoints which is used to characterize the packing arrangement of grains, R is themaximum pore radius, d is the grain diameter, and �m is the packing arrangementfactor. In this study, m = 8 and �m = 0:866 are employed.

The changes in permeability due to biofilm growth are handled by modifyingthe Kozeny–Carman equation as

k = c0�3

a2 ; (25)

where c0 is Kozeny’s constant.

3. Solution to the Model Equations

Equations (12), (17), (19), and (21) constitute the set of governing equations withunknowns CC ; CD; CDf , and Lf . Equations (22)–(25) are employed to calculatevariable material parameters. Equations (12) and (17) can be rewritten in one-dimensional form respectively as

@

@t(�CC) =

@

@x

�DC

@

@x(�CC)

�� qw

@CC

@x

+�maxCD

KD + CD�CC � kd�CC � (c1�f + c2)�CC

+

"bdet + �b

0

det�maxCD(1 +K5xf )

KD + CD(1 +K5xf )

#xf�f (26)

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and

@

@t[(1 +K5CC)�CD]

=@

@x

�DD

@

@x(�CD)

�� qw

@CD

@x

+K5DC

@(CD)

@x

@(�CC)

@x+K5DCCD

@2(�CC)

@x2

�K5qw@(CCCD)

@x�

1Y

�maxCD

KD + CD�CC

��

Y

�maxCD(1 +K5xf )

KD +CD(1 +K5xf )xf�f : (27)

A numerical solution of the Equations (26) and (27) is obtained by a fullyimplicit finite-difference method which employs a two-point backward differenceapproximation for the time derivatives and a central difference approximation forthe spatial derivatives. This method leads to a system of linear algebraic equationsfor Equation (26) with a tridiagonal coefficient matrix, which can be directly solvedby the Thomas algorithm. The method when applied to Equation (27) leads to asystem of non-linear equations due to non-linear contaminant utilization terms.These non-linear equations are solved by the Newton–Raphson iteration methodincorporated with the Thomas algorithm. First, Equation (26) is solved for CC atthe time step (n + 1) where n is the previous time step at which all variables areknown. Once (26) is solved for CC at the time step (n+ 1), we move to Equation(27) for CD at the time step (n+ 1).

The boundary conditions of Taylor and Jaffe’s (1990b) experiment are simulatedby the third kind boundary conditions. Parker and van Genuchten (1984) noted thatthe third kind boundary condition can describe the mass transport phenomenon ina column experiment more rigorously than the first type. The initial and boundaryconditions imposed in the model are

CC(x; 0) = 0; CD(x; 0) = 0; (28)

CC0 = CC(0; t)��DC

qw

@CC

@x(0; t); 0 6 t 6 t0

= 0; t0 6 t;

(29)

CD0 = CD(0; t)��DD

qw

@CD

@x(0; t) + CC0K5CD(0; t); (30)

@CC

@x(L; t) = 0;

@CD

@x(L; t) = 0; (31)

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where CC0 is the influent bacterial concentration and CD0 is the influent aqueousphase contaminant concentration. Equations (29) and (30) denote the constant fluxtype boundary conditions and the third term on the right-hand side of Equation(30) represents the contaminant flux adhered to bacteria entering the column.Equation (21) can be solved by the Runge–Kutta method with the initial conditionof Lf (x; 0) = 0 when there is no initial biofilm.

The next step is to calculate the effectiveness factor �, by solving Equation (19)by employing the Newton–Raphson method with

CDf = CD(x; t) @ � = 0; (32)

dCDfd�

= 0 @ � = Le: (33)

In Equation (33),Le is the effective biofilm thickness penetrated by the contaminant(Figure 2). Le is not constant when the contaminant consumption rate is greaterthan the diffusion rate. In this solution procedure, the lower boundary condition,i.e., Equation (33), depends on the contaminant penetration in the biofilm (LaMot-ta, 1976). First, we assume a complete contaminant penetration of the biofilm withEquation (33) at � = Lf . Then, Equation (19) is solved subject to Equations (32)and (33) with the complete contaminant penetration assumption. If the solutionindicates a partial contaminant penetration, then Equation (19) is solved subject toEquations (32) and (33) with � = Le whereLe is determined from the contaminantconcentration profile obtained previously. This iteration is repeated till Equation(33) is satisfied. After the concentration profile in the biofilm is obtained, the effec-tiveness factor �, can be calculated by substituting Equation (3) and the solution of(19) into the definition of � as

� =KD + CD(1 +K5xf )

LfCD(1 +K5xf )

Z Lf

0

CDf (1 +K5xf )

KD + CDf (1 +K5xf )d�: (34)

The trapezoidal rule is employed for numerical integration. The solution of Equa-tion (21) is used to estimate the porous medium properties, i.e., Equations (22)–(25),for the next time step of calculations.

4. Model Application and Sensitivity Analysis

The model developed in this study is compared with the experimental data of Taylorand Jaffe (1990b). Taylor and Jaffe measured biofilm thickness and contaminantconcentration in a sand-packed column experiment as described in their paper. Themodel parameters are listed in Table I. Mostly, they are from Taylor and Jaffe’s(1990b) data. However, there are some modifications because of the assumptionof uniform sized spherical grains. First, the effectiveness factor was taken as unityfor model application purposes. The experimental data and model predictions are

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Figure 2. Schematic diagram of a biofilm.

compared for the biofilm thickness and substrate concentration with no contaminantadsorption on bacteria, i.e., K5 = 0, in Figures 3 and 4, respectively. The modelpredictions match relatively favorably with the experimental data with parametersc1 = 3000=day; c2 = 400=day and b0det = 0:665. The differences between theexperimental data and model predictions seem to be due partly to the assumptionof constant fraction of dead bacteria in the biofilm which was taken as 30 percentof the total mass in the biofilm, and partly to the assumption of uniform-sizedspherical grains.

Then, the Equation (18) governing the contaminant diffusion in the biofilmwas solved to compare with the results obtained with uniform contaminant profileassumption along the biofilm, i.e., � = 1. The effective biofilm diffusion coefficientof methanol which is used as a substrate by Taylor and Jaffe (1990b), is 0.9 cm2/day.This value is 80 percent of the aqueous phase diffusion coefficient as reported byWilliamson and McCarty (1976). Results show that the effectiveness factor alongthe column calculated for the experimental conditions was over 0.98 and the lowestcontaminant concentration within the biofilm reached 97.5 percent of the aqueousphase concentration. Thus the assumption of � = 1 is a reasonable one for theexperimental data of Taylor and Jaffe (1990b).

After the verification of the model with Taylor and Jaffe’s experimental results,the model was extended to various cases of practical interest. At this stage,we consider an organic substance which is not easily biodegradable and high-ly hydrophobic. The realizable parameters of a substance of this nature can betaken as �max = 0:53/day, KD = 100 mg COD/L, Y = 0:2 mg BOC/mg COD,kd = 0:02/day and Df = 0:463 cm2/day at 20�C (Mavinic, 1984). Dimensionlessmodel parameter values of the bacterial capture, c1 and c2, were taken as 3000 and

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Figure 3. Comparison of model predicted biofilm thickness profiles with experimental data ofTaylor and Jaffe (1990b).

Figure 4. Comparison of model predicted concentration profiles with experimental data ofTaylor and Jaffe (1990b).

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Table I. Parameters used in model validation.

Parameter Notation Value Unit

Mean grain diameter d 0:13 cmInitial porosity n 0:336 —-Maximum pore radius R 0:03 cmSpecific surface a 51:8 cm�1

Initial permeability —- 2:93� 10�6 cm2

Initial dispersivity �0 0:09 cmViscosity of water (15�C) �w 982 dyne/cm2

Maximum specific growth rate �max 0:8 d�1

Monod half saturation coefficient KD 0:8 mg/lBacterial decay rate constant kd 0:013 d�1

Yield coefficient Y 0:22 mg BOC/mg methanolDarcy velocity v 944 cm/dayBacterial concentration in biofilm xf 3000 mg BOC/lKozeny constant c0 0:53 —-

400 respectively as obtained earlier. The specific discharge of water is assumedto be 500 cm/day through a one-meter column with medium properties listed inTable I. Constant flux boundary conditions of Equations (28) and (29) were usedwith CC0 = 10 mg/l, CD0 = 10 mg/l respectively. The column was free of anycontaminant and bacteria initially.

Figure 5 shows the effect of facilitated contaminant transport on bacterial andcontaminant mobility with bacterial injection at the column surface at a concen-tration of CC(x = 0) = 10 mg/l. We observe that bacterial and contaminantconcentrations decrease significantly along the column, which indicates that bac-teria grow rapidly at the vicinity of injection point by uptaking the most of thecontaminant supplied. Also, we find that contaminant migration decreases signifi-cantly with increasing partition coefficient of dissolved contaminant with bacteria,K5. However, bacterial mobility is not affected as much as contaminant mobilitywith increasing K5. This can be attributed to the increase in substrate utilizationrate with increasing K5. This observation leads to the expected conclusion that notall contaminant utilized yield biomass and only a fraction of the energy derivedfrom the substrate contributes to cell growth while the remainder is used for cellmaintenance (note that Y < 1).

Figures 6 and 7 illustrate the spatial variations of biofilm thickness and mobilityrespectively at different times. We observe that, at a given time, the biofilm thicknessdecreases rapidly although the aqueous phase bacterial concentration decreasesgradually along the column. This is because the biofilm in the vicinity of theinjection point can hardly grow more than some critical thickness which is about0.015 cm (see Figure 6), due to the increasing fluid shear stress. The detached

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Figure 5. Effect of facilitated contaminant transport on bacterial and contaminant mobility att = 100 days.

biomass builds up downgradient until it reaches the critical thickness. As a result,downgradient propagation of bacteria produced near the injection point is moresignificant than the downgradient bacterial growth.

Figure 8 presents the simultaneous effects of contaminant partition coefficientwith bacterial surface and temperature on the biofilm contaminant concentrationprofile. The contaminant utilization rate varies with the temperature followingArrhenius’s law. The diffusion coefficient follows the Stokes–Einstein equation.As seen in Figure 8, the contaminant concentration can be assumed to be uniformalong the biofilm at all temperatures when the contaminant does not adsorb onbacteria. However, the contaminant concentration decreases along the biofilm whencontaminant adheres on bacterial surfaces.

We also investigated the effect of bacterial injection on contaminant mobili-ty. As noted earlier, we assumed that the column was free of biomass initiallyin our previous analyses. At this point, we introduce an initial biomass into thesystem, i.e., initially present indigenous bacteria with a uniform biofilm thicknessof 10�4 cm. Figure 9 illustrates the effect of contaminant adsorption and bacterialinjection on contaminant mobility. It is observed that bacterial injection reducescontaminant mobility dramatically although the native bacteria were present in thesystem. The adsorption of contaminant on bacterial surfaces reduces contaminantmobility remarkably. This trend is also demonstrated in Figure 10 which shows thesimultaneous effect of contaminant adsorption and bacterial injection on biofilm

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Figure 6. Propagation of biofilm growth with K5 = 0:01 mg contaminant attached tobacteria/mg bacteria.

Figure 7. Bacterial mobility withK5 = 0:01 mg contaminant attached to bacteria/mg bacteria.

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Figure 8. Effects of contaminant partitioning coefficient and temperature on contaminantconcentration profile along the biofilm.

thickness. As the amount of contaminant attached to bacteria increases, i.e., increas-ingK5, biofilm growth increases (see Figure 10) and the contaminant concentrationdecreases (see Figure 9). In the aqueous phase, this effect is not significant becauseof low bacterial concentrations. However, it becomes important within the biofilm.In Figure 10, we also observe that bacterial injection enhances the biofilm growthdramatically and it is further increased by contaminant adsorption on bacterialsurfaces.

5. Summary and Conclusions

In this study, we present a model to describe biocolloid-facilitated transport ofa biodegradable contaminant. Bacteria are assumed to grow both in the aqueousand biofilm phases. The contaminant diffusion within the biofilm is formulatedbased on the mass balance equation. The Monod model was employed for bacterialgrowth and substrate utilization. An equilibrium relation was employed to partitioncontaminant mass between the aqueous phase and bacterial surfaces. Model wassolved numerically and compared with the experimental data of Taylor and Jaffe(1990b).

Sensitivity analyses conducted to deduce the effect of critical model parameterson contaminant and bacterial mobility indicate that the presence of biofilm andcontaminant adsorption on bacteria greatly reduce the contaminant mobility. This

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Figure 9. Effect of contaminant adsorption and bacterial injection on contaminant mobilitywith an initial biofilm thickness = 10�4 cm at t = 10 days.

Figure 10. Effect of contaminant adsorption and bacterial injection on biofilm formation withan initial biofilm thickness = 10�4 cm at t = 30 days.

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observation suggests that the contaminant adsorption on bacterial surfaces shouldbe taken into account when hydrophobic contaminants are present in the system.Furthermore, contaminant concentration variation within the biofilm was found notto be negligible if the contaminant adsorbs on bacterial surfaces. We also observethat biomass in the biofilm grows rapidly near the injection point and is detachedby increasing fluid shear stress and re-attach downstream. Therefore, bacterialinjection and migration can be important in bioremediation operations regardlessof the presence of indigenous bacteria.

Finally, we should note that high desorption rates for bacteria and resulting poreclogging hinder rather than facilitate the contaminant transport. Development ofhigh flow velocities due to reduction in pore space and shearing of biofilm movethe bacteria slightly downstream. However, bacteria with less tendency to attachwould lead to significant bacteria-facilitated contaminant transport. Therefore, thebacterial deposition is the most critical factor in facilitated contaminant transport.

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the role of biofilm growth in bacteria-facilitated contaminant transport in porous media

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