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WATER RESOURCES RESEARCH, VOL. 42, W12S10, doi:10.1029/2006WR004896, 2006

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Full
ArticleEvaluation of bacteria-facilitated cadmium transport
in gravel columns using the HYDRUS colloid-facilitatedsolute transport model
Liping Pang1 and Jirka Šimůnek2
Received 13 January 2006; revised 8 May 2006; accepted 29 June 2006; published 21 October 2006.

[1] The colloid-facilitated solute transport model, based on HYDRUS-1D, was evaluatedusing the column experimental data of Pang et al. (2005) for cadmium (Cd) transportfacilitated by B. subtilis spores or E. coli in saturated coarse alluvial gravels. We simulated
Cd transport involving convection, dispersion, kinetic adsorption/desorption to/from theaquifer media and to/from mobile/immobile bacteria, and kinetic attachment/detachmentof the bacteria to/from the aquifer media. To reduce the number of parameters to be
optimized, we independently estimated Cd sorption/desorption rates to mobile bacteria
from a batch study. The model described the collected experimental data reasonably well.
Extensive sensitivity analysis to various reaction parameters was carried out to obtain anunderstanding of the relative importance of individual model parameters on model
predictions. Our modeling results suggest that the rates of Cd sorption or desorption differ
not only between different bacterial species but also between unattached and depositedbacteria. The results of the sensitivity analysis indicated that the Cd sorption rate tounattached bacteria had a significantly greater impact on the model results than its sorption
rate to deposited bacteria. For the experimental system investigated here, model results
were most sensitive to parameters describing interactions between Cd-aquifer media,
bacteria-aquifer media, and Cd-mobile bacteria, and they were less sensitive tointeractions between Cd-immobile bacteria and desorption rate from mobile bacteria.
Citation: Pang, L., and J. Šimůnek (2006), Evaluation of bacteria-facilitated cadmium transport in gravel columns using the
HYDRUS colloid-facilitated solute transport model, Water Resour. Res., 42, W12S10, doi:10.1029/2006WR004896.

1. Introduction[2] The classical view that strongly sorbing contaminants(i.e., heavy metals, radionuclides, some pesticides) movevery slowly through soils and aquifers has been challenged
recently by the evidence that their transport velocity inporous media can be from a few times up to several
thousand times faster when they are adsorbed to mobile
colloids [Newman et al., 1993; Grolimund et al., 1996;
Saiers and Hornberger, 1996; McCarthy et al., 1998; Pang
and Close, 1999; Karathanasis, 1999, 2000; Artinger et al.,2002]. Colloids (e.g., humic substances, bacteria, clays, andmetal oxides) have a considerable adsorption capacity forother species present in water because of their large specificsurface areas and their high concentrations in groundwaterand soil-water. Colloids can be the most mobile constituent
in groundwater and can thus provide a vehicle for the rapidtransport of smaller, less mobile contaminants. On the other
hand, colloids can be subject to straining and filtration in
porous media and can thus also act as inhibitors of contaminant migration if the contaminants are adsorbed to them.
Understanding this twofold role of colloids on the transport
1
Institute of Environmental Science and Research Ltd., Christchurch,
New Zealand.
2
Department of Environmental Sciences, University of California,
Riverside, California, USA.

Copyright 2006 by the American Geophysical Union.
0043-1397/06/2006WR004896$09.00

and attenuation of contaminants has important implications
for risk analysis and remediation of contaminated sites.
[3] Over the last decade, a number of computer models
have been developed to simulate colloid-facilitated solutetransport in porous media [Mills et al., 1991; Dunnivant
et al., 1992; Corapcioglu and Jiang, 1993; Jiang andCorapcioglu, 1993; Corapcioglu and Kim, 1995; Saiersand Hornberger, 1996; van de Weerd and Leijnse, 1997].
Three-phase colloid-facilitated solute transport models(CFMs) can simultaneously simulate interactions among
solutes, colloids and porous media and are superior toconventional two-phase contaminant transport models,
which only address interactions between contaminants andporous media. CFMs address the coupled transport of solutes
that are dissolved in the aqueous phase or adsorbed to porous
media and mobile/immobile colloids, with the transport ofcolloids that are suspended in solution (mobile colloids) or
attached to the porous media (immobile colloids). CFMs are
generally based on mass balance equations of these individual components [e.g., Corapcioglu and Jiang, 1993; van deWeerd et al., 1998; Corapcioglu and Kim, 1995]. However,various assumptions and simplifications are made in different CFMs about interactions between colloids and solutes(e.g., kinetics/equilibrium, linear/nonlinear, reversible/
irreversible etc), as well as the aquifer transport properties(e.g., different velocities and dispersivities of colloids andsolutes). Descriptions of different assumptions in some
CFMs are given by van de Weerd et al. [1998].

W12S101 of 13W12S10PANG AND ŠIMŮNEK: BACTERIA-FACILITATED Cd TRANSPORT IN GRAVEL COLUMNS[4] Colloid-facilitated solute transport has recently been
incorporated into the HYDRUS-1D software package[Šimůnek et al., 2006]. The existing HYDRUS-1D model
is a widely used solute transport model for variably saturated porous media [e.g., Vanderborght et al., 2005]. Likeother CFMs, the HYDRUS CFM considers interactions
among colloids, solutes, and porous media, but it also
contains some features that are usually not included in other
CFMs. Šimůnek et al. [2006] describe the major differences
between the HYDRUS CFM and most other CFMs.
These differences include considerations of (1) the velocity
enhancement of colloids and colloid-facilitated solute transport due to size and anion exclusion (thus different porevelocities and dispersivities for colloids and solutes),(2) irreversible straining and nonlinear blocking, (3) watercontents, water fluxes, and air-water interfacial areas that
may change in time and space (i.e., transient variably
saturated water flow), (4) the presence of the air-waterinterface colloids, and (5) adjustment of all kinetic rates tothe number of colloids present in the system.
[5] Although the newly developed CFMs are more appropriate than conventional solute transport models ininterpreting coupled solute and colloid transport in natural
subsurface conditions, the models’ abilities need to beevaluated using actual experimental data. Model evaluationmust be an essential part of model development. In comparison with solute transport models, many more parameters
are employed in CFMs and some of these parameters are
difficult, if not impossible, to estimate experimentally. Thissignificantly increases the uncertainty of parameter estimation, especially for parameters that are closely correlated.
Thus, without experimental verification it is uncertain how
capable and applicable these CFMs are in addressing real
problems. Although a number of CFMs have been developed, model verification against experimental data is still
relatively limited [Saiers, 2002].
[6] The purpose of this paper is twofold. The firstobjective is to evaluate the newly developed HYDRUS
CFM using the column experimental data of Pang et al.
[2005] for cadmium (Cd) transport in the presence ofbacteria (B. subtilis spores or E. coli) in saturated coarse
alluvial gravels. By using experimental evaluation, we aim
to identify the most important processes that govern bacteria-facilitated Cd transport and the key parameters that
describe these processes. The second objective is to examine
whether exchange processes between liquid, solid, andcolloid phases can be adequately described using linear
exchange models. As part of the model evaluation, sensitivity tests were also undertaken to systematically assess theimpact of model input parameters on the model’s output andto provide an insight into the relative importance of individual model parameters within a complex system. Modelevaluation not only assists in understanding where weaknesses in the modeling results may lie, but it also assists withdata interpretation, and provides guidance for further model
modifications and future experimental designs.

2. Methods
2.1. Experiments and Experimental Data
[7] Pang et al. [2005] conducted a series of column
experiments using various concentrations of bacteria to

W12S10study Cd transport in the presence of Bacillus subtilis spores
or E. coli vegetative cells under saturated conditions. A
column (18 cm long, 10 cm in internal diameter) was
uniformly packed with coarse gravel aquifer material (meandiameter d50 = 16.69 mm, uniformity d60/d10 = 53) with abulk density of 1.9 g/cm3 and effective porosity of 0.27. The
mean flow rate applied was 32.4 (±0.4) mL/min. A solution
containing Cd (approximately 4 mg/L) and bromide (Br)(approximately 2 mg/L), at a fixed pH value (pH = 7.0, 7.5 or
7.7 for different experiments), was first injected for about
five pore volumes. B. subtilis spores or E. coli wereintroduced to the column together with Cd and Br for further
3.4 pore volumes. Subsequently, the column was flushedwith solution-free fresh water. The experiments were conducted at room temperature (20°C ± 1) over 3 – 4 hours. Total
effluent Cd concentrations, and in some experiments dissolved Cd concentrations, were analyzed. In all experiments,
untreated groundwater extracted from alluvial gravel aquifers was used as the background electrolyte. The bacteria
were washed with saline solution, and the solution was
diluted with untreated groundwater to the required concentration before an experiment was conducted. Detailed
experimental information is given by Pang et al. [2005].
[8] Figures 1 and 2 demonstrate that when bacterial
concentrations were sufficiently high, with the introductionof either B. subtilis spores or E. coli, there were simultaneous steep rises and flat plateaus of Cd concentrations(Figures 1b, 1c, 2b and 2c), indicating that Cd was cotransported with these bacteria. In contrast, this feature was not
displayed in Cd breakthrough curves (BTCs) when bacteria
concentrations were low (Figures 1a and 2a). Both Figures 1
and 2 also show a relatively fast arrival, often before one
pore volume, of both Br and Cd. While Br BTCs displayeda sharp rise in concentrations after the early arrival, Cd
concentrations increased only gradually, indicating kinetically controlled adsorption to the aquifer material. Similarly,
a gradual decrease of Cd concentrations after the maximum
peak or plateau indicates kinetically controlled desorption of
Cd from the aquifer material.
[9] Pang et al. [2005] also examined the kinetics of Cd
adsorption onto B. subtilis spores or E. coli in batch
experiments that were conducted in the absence of aquifer
media. Bacterial solutions spiked with known masses of Cd,
held in 40 mL screw top glass vials, were gently stirred
continuously for three hours at room temperature (20°C ± 1).
Bacteria-free controls with Cd only were also prepared toestimate Cd precipitation and adsorption onto the experimental apparatus. Total and dissolved Cd concentrations
were analyzed. To be consistent with the column experiments, untreated groundwater was used as the backgroundelectrolyte and the bacteria used were washed with saline
solution before dilution. The kinetics of Cd sorption to thebacteria is illustrated in Figure 3. While there was a sharp
decrease of dissolved Cd concentrations in the solution with
B. subtilis spores, only a small decrease of dissolved Cd
concentrations was observed in the solution with E. coli.
While Cd concentrations in the solution with E. coli reacheda semiequilibrium state relatively quickly, sorption of Cd to
B. subtilis spores continued for longer than three hours.
2.2. Modeling[10] Although many complex processes (e.g., transientvariably saturated water flow, irreversible straining and

2 of 13W12S10PANG AND ŠIMŮNEK: BACTERIA-FACILITATED Cd TRANSPORT IN GRAVEL COLUMNSW12S102.2.1. Bacteria Transport[11] Bacteria transport was described using the advection-dispersion equation coupled with the first-orderattachment-detachment kinetics [e.g., Hornberger et al.,
1992; McCaulou et al., 1994]:
@qc Cc@Sc@@Cc@qc Cc
qc Dc
þr
¼

@x
@t
@t
@x
@x

ð1Þ

@Sc
¼ qc kac Cc  rkdc Sc
@t

ð2Þ

r

where Cc is the bacteria concentration in the aqueous phase[cfu L3] (cfu is colony-forming unit, a unit indicating thenumber of microorganisms present in a water sample); qc is

Figure 1. Cd and Br transport in the presence of B. subtilis
spores in the column experiments of Pang et al. [2005](a) B. subtilis C0 = 9  104 cfu/mL, pH = 7.0. (b) B. subtilis
C0 = 7  105 cfu/mL, pH = 7.7. (c) B. subtilis C0 = 5.6 
107 cfu/mL, pH = 7.0. B. subtilis spores were introduced
after about 5 pore volumes injection of Cd and Br.
nonlinear blocking, air-water interface) are considered in theoriginal HYDRUS CFM [Šimůnek et al., 2006], only thesimpler version of the model was needed for the relatively
simple experimental system described above, which
involved steady state, fully saturated flow conditions.
Straining of the bacteria was considered to be negligible
because the size of the largest bacteria (6 mm) was only
0.04% of the media grain diameter (16.69 mm), which iswell below the 0.5% threshold for straining [Bradford et al.,2004]. Inactivation of bacteria and precipitation of Cd werealso considered insignificant given the short durations ofexperiments. Thus we have focused our attention on the
kinetic behavior of Cd adsorption to bacteria and aquifer
media. To describe the experimental system, the HYDRUS
CFM was simplified to consider exchange processes
between liquid, solid, and colloid phases using linear
exchange models, which is given below.

Figure 2. Cd and Br transport in the presence of E. coli inthe column experiments of Pang et al. [2005]. (a) E. coli
C0 = 5  103 cfu/mL, pH = 7.5. (b) E. coli C0 = 1.6  105
cfu/mL, pH = 7.0. (c) E. coli C0 = 3.7  107 cfu/mL, pH =7.0. E. coli were introduced after about 5 pore volumes
injection of Cd and Br.

3 of 13W12S10PANG AND ŠIMŮNEK: BACTERIA-FACILITATED Cd TRANSPORT IN GRAVEL COLUMNSW12S10Figure 3. Results of kinetic batch study on Cd sorption to suspended bacteria. Circles are observed
data, and lines are model predictions using the kinetic sorption model.
the water content accessible to bacteria [L3L3]; Sc is thebacteria concentration attached to the aquifer media[cfu M1]; Dc is the dispersion coefficient for bacteria[L2T1]; r is the bulk density of the aquifer material[ML3]; kac and kdc are the first-order rate coefficients forbacteria attachment and detachment [T1], respectively; qc
is the water flux density for bacteria moving only in pores
from which they are not excluded [LT1]; t is the time [T];and x is the distance from the inlet [L].
[12] In comparison to solutes that are thought to travel
through all pores, colloids often travel only throughinterconnected larger pores, with a smaller pore network.
As a result of size exclusion, the aquifer pore network
accessible to colloids may have smaller water content,
smaller dispersion, and greater pore water velocity. The
water flux density for bacteria, qc, can be calculated fromthe ratio of the relative hydraulic conductivity of the entire
pore space (Krw) to the relative hydraulic conductivity of thebacteria accessible pores (Krc), and the water flux density
qw [LT1] as follows
qc ¼ qw

Krc
Krw

ð3Þ

2.2.2.1. Cd Sorbed to the Solid Phase[14] Solute sorption to the aquifer material is describedusing the two-site sorption concept that assumes that the
total sorption, S, can be divided into the kinetic andinstantaneous sorption as follows:r

where C is the dissolved Cd concentration [ML3]; Se andSk are Cd concentrations sorbed instantaneously andkinetically, respectively, to the aquifer media [MM1],
Smc and Sic are Cd concentrations sorbed to the suspended
mobile bacteria and to the deposited immobile bacteria[M cfu1], respectively; q is the total water content [L3L3];
D is the dispersion coefficient [L2T1]. Note that we usedthe entire water content, dispersion and water flux for
Cd. Interactions between different contaminant pools inequation (4) are further expressed by a number of massbalance equations, which are given below.

@Sk¼ w½ð1  f ÞKd C  Sk @t

ð6Þwhere w is the first-order rate constant [T1] and f is thefraction of exchange sites assumed to be in equilibrium withthe solution phase (dimensionless). We have assumed thatsorption Se on the instantaneous sites is a linear process, i.e.,
Se = fKdC.
2.2.2.2. Cd Sorbed to Mobile and Immobile Bacteria[15]@qc Cc Smc @@Cc@qc Cc Smc
qc Smc Dc¼
þ qy m kamc C
@x
@t
@x
@x
 qc kdmc Cc Smc  qc kac Cc Smc þ rkdc Sc Sic

r

ð4Þ

ð5Þ

and

2.2.2. Bacteria-Facilitated Cd Transport[13 ] Transport of Cd interacting with bacteria wasdescribed by the following equation@qC@Se@Sk @qc Cc Smc@Sc Sic
þr
þr
þ
þr
@t
@t
@t
@t
 @t



@
@C
@qw C @@Cc
@qc Cc SmcqDþqc Smc Dc
¼
@x
@x
@x
@x
@x
@x

S ¼ Se þ Sk

ð7Þ@Sc Sic¼ qy im kaic C  rkdic Sc Sic þ qc kac Cc Smc  rkdc Sc Sic ð8Þ@twhere kamc and kdmc are the rate coefficients for Cd sorption
to and desorption from mobile bacteria [T1], respectively;
kaic and kdic are the rate coefficients for Cd sorption to anddesorption from immobile bacteria [T1], respectively; andparameters y m and y im are dimensionless variables that
adjust the sorption rate to the changing number of mobile
and immobile colloids present, respectively [Šimůnek et al.,2006]. Values of y m and y im increase from zero when there
are no bacteria present to one when the number of bacteria
is the same as the number (reference number) of bacteria forwhich kamc and kaic were determined. They can be larger
than one if the number of bacteria is larger than thisreference number. The numerical solution of the above
equations has been implemented into the HYDRUS-1D
CFM. Detailed information is given by Šimůnek et al.
[2006].

4 of 13W12S10PANG AND ŠIMŮNEK: BACTERIA-FACILITATED Cd TRANSPORT IN GRAVEL COLUMNS

Figure 4. Observed (circles) and simulated (lines) Br
concentrations using the equilibrium model. Cd +B. subtilis experiments: (a) C0 = 9  104 cfu/mL,
pH = 7.0 (experiment a); (b) C0 = 7  105 cfu/mL, pH =7.7 (experiment b); (c) C0 = 5.6  107 cfu/mL, pH =7.0 (experiment c). Cd + E. coli experiments: (d) C0 = 5 
10 3 cfu/mL, pH = 7.5 (experiment a); (e) C 0 =1.6  105 cfu/mL, pH = 7.0 (experiment b); (f) C0 =3.7  107 cfu/mL, pH = 7.0 (experiment c).
2.2.3. Inverse Modeling2.2.3.1. Batch Experimental Data
[16] Data from batch experiments carried out in theabsence of aquifer material were used to derive the kinetics
of Cd sorption to the mobile bacteria (kamc and kdmc) as thebacteria used in the batch experiments were suspended insolution. Experimental data were analyzed using anequation adopted from Schijven and Hassanizadeh [2000]:C
kdmc þ kamc exp½ðkamc þ kdmc Þt ¼
C0
kamc þ kdmc

ð9Þ

in which Co is the initial Cd concentration [ML3].
Equation (9) was fitted to the concentration versus timedata, with an aid of the least squares method using theSolver Optimizing Function that is implemented in Excel.
To measure the quality of model fit, the sum of squared
residuals (SSRs) and R-square (r2) were calculated using
standard statistic formula. The fitted curves are given in
Figure 3.
2.2.3.2. Column Experimental Data[17] BTCs of the conservative solute tracer Br were first
analyzed to derive Krw and D using the internal HYDRUS-1D
optimization routine. Model-simulated and observed Br

W12S10concentrations are compared in Figure 4. Bacteria BTCs
were then analyzed to estimate flow and transport properties
for bacteria using the attachment and detachment model andthe internal HYDRUS-1D optimization routine. In the
preliminary analysis of bacteria data, Krc, Dc, kac, and kdc
parameters were estimated independently from Br results.
However, the apparent optimized Dc values were generally
significantly larger than the D values estimated from Br.
Since these large Dc values were considered to be an artifact
and a reflection of large variations in the bacteria data, in thefurther analyses we neglected possible velocity enhancement of bacteria and further simulated bacteria BTCs using
the same conductivity and dispersion derived from Br while
optimizing only kac and kdc. Because of the relatively small
size of bacteria in comparison with the pore network ofcoarse aquifer material, the flow paths of bacteria and Br
will likely be similar, resulting in the same values of meanpore velocities and dispersivities. We consider that the error
in using same dispersion for bacteria and Br is relatively
smaller than that using dispersion estimated from the erratic
bacteria data that contains significant variations. Muchsmaller standard errors for the model results were obtained
when assuming this simplification of the system.
[18] Finally, Cd BTCs were simulated using the bacteriafacilitated Cd transport model. The Krw, D, kamc, kdmc, kac,and kdc coefficients obtained from the analyses of the Br andbacteria BTCs and batch experiments were held constant in
the simulations of bacteria-facilitated Cd transport. In addition to reducing the number of optimized parameters, theuse of independently determined kamc and kdmc values wasneeded. This is because the Cd sorption rates to mobile andimmobile bacteria are highly correlated (r2 > 0.92) andmodel results would contain very high level of uncertainty ifthey were both optimized, as indicated by the results ofsome preliminary optimizations. Model simulations werefirst carried out to optimize the five model parameterscharacterizing the sorption to immobile bacteria (kaic andkdic) and instantaneous and kinetic sorption to the aquifer
material (w, Kd, and f). The PEST optimization package of
Doherty et al. [1994] was used for the inverse parameter
optimization. An equal weight was allocated during the
optimizations to both the total and dissolved Cd concentrations observed in the effluent. As the results of optimizations constantly yielded f = 0.01 and kdic = 0.00, thesevalues were subsequently fixed. Further optimizations werecarried out with fewer parameters, which significantly
reduced the standard errors of the model estimations.
Experimental data that did not show a significant bacteriafacilitated Cd transport were simulated by setting kaic, kdic,
kamc, and kdmc equal to zero in the model, while Kd, w and fwere optimized. To measure the quality of model fit, SSRs,
standard error coefficient (SE), and r2 were calculated.
2.2.4. Sensitivity Analysis of Model Parameters[19] To evaluate the impact of model input parameters on
the model’s output (the total and dissolved Cd in theeffluent), a sensitivity analysis was undertaken. We focusedon parameters that describe three-phase interactions. The
following nine parameters, which characterize Cd sorption/
desorption to/from mobile/immobile bacteria (kamc, kdmc,
kaic, kdic), Cd sorption to aquifer material (f, Kd, w), andbacteria attachment/detachment to/from the aquifer material(kac, kdc), were selected for the sensitivity analysis. Cali-

5 of 13W12S10PANG AND ŠIMŮNEK: BACTERIA-FACILITATED Cd TRANSPORT IN GRAVEL COLUMNSW12S10

Table 1. Rate Coefficients of Cd Adsorption/Desorption to/From the Suspended Bacteria Derived From the Kinetic
Batch Study in the Absence of Aquifer Media
Experimental Condition
ExperimentB. subtilis
E. coli

Bacteria Co,
cfu/mL7

9.9  10
1.9  108

Optimized Results

Cd Co,
mg/mL

pH

kamc,
h1

kdmc,
h1

Reversibility
kdmc/kamc

r2

SSRs

0.50
0.50

7.0 – 7.5
6.9 – 7.4

2.30
0.16

1.28
1.74

0.56
10.8

0.96
0.95

0.02
0.00

brated simulations were used as the baseline for comparisonof the test results, with the aid of SSRs. One parameter wastested at a time while all other parameters were fixed at thecalculated values. Possible ranges of parameter values were
evaluated in the analysis.

3. Results and Discussion
3.1. Model Description of Experimental Data
[20] Table 1 lists the rate coefficients of Cd adsorption/
desorption to/from the suspended mobile bacteria optimized
applying the kinetic sorption model (equation (9)) tothe data from the kinetic batch study. The kinetic sorption
model appears to fit well (r 2 = 0.95 – 0.96, SSRs =0.00 – 0.02) with the observed batch experimental data
(Figure 3). The results show that the fraction of Cd sorbed
onto B. subtilis spores is much greater than onto E. coli
(Figure 3), and that the Cd sorption rate to the spores ismore than one order of magnitude greater than the Cd
sorption rate to E. coli (Table 1). The greater sorption of
Cd onto B. subtilis spores than onto E. coli was also observed in the column data. As shown in Figures 1 and 2,
the difference between the total and dissolved Cd effluent
concentrations is significant for Cd cotransport with
B. subtilis spores but insignificant for Cd cotransport with
E. coli. Pang et al. [2005] explained this difference using
the fundamentally different structural and chemical properties of cell walls of gram-positive bacteria (B. subtilis) andgram-negative bacteria (E. coli). Unlike gram-positive bacteria, the surface of the gram-negative bacterial cell could
produce outer membrane vesicles. It is thought that thesesoluble secretion products might have chelated Cd insolution and competed with the bacterial surface for theavailable Cd, thereby reducing the observed degree ofadsorption onto the E. coli cells. For a more detailed
description, please refer to Pang et al. [2005]. The possible
chelation of Cd by E. coli is also supported by the fact thatthe rate of Cd desorption from E. coli is one order ofmagnitude greater than its sorption rate (Table 1). Althoughsorption of Cd onto B. subtilis spores is also reversible,
sorption rate is faster than the desorption rate (Table 1). Our
observation of the reversible sorption of Cd onto theselected bacteria is consistent with findings made by others.
Cd sorption was found to be fully reversible onto both B.
subtilis [Fowle and Fein, 2000] and E. coli [Yee and Fein,2001] in batch studies.
[21] Although the two bacterial species react very differently with Cd, their attachment/detachment behavior to/from the aquifer media is similar, as indicated by the kac
and kdc values optimized using the attachment/detachment
model (Table 2). Attachment of both B. subtilis and E. coli
to the aquifer media is reversible during the short time frameof the experiments, with the attachment rate generally muchgreater than the detachment rate. There seems to be no clear
pattern in kac and kdc values with changes in bacterial
concentrations and pH values. However, the optimized kacvalues are in a narrow interval varying by only a factor oftwo (with one exception) with small SE values (Table 2).
Figure 5 shows that the first-order kinetic attachment/
detachment model fits generally well with the observed
bacteria concentrations (r2 = 0.71 – 0.94, SSRs = 0.11 –0.59), except for the erratic experimental data at low
E. coli input concentration (r2 = 0.54, SSRs = 0.98).

Figure 5. Observed (circles) and simulated (dashed lines)
bacterial concentrations using the attachment-detachment
model. Bacteria were introduced after about 5 pore volumes
injection of Cd and Br. B. subtilis: (a) C0 = 9  104 cfu/mL,
pH = 7.0 (experiment a); (b) C0 = 7  105 cfu/mL,
pH = 7.7 (experiment b); (c) C0 = 5.6  107 cfu/mL, pH =7.0 (experiment c). E. coli: (d) C0 = 5  103 cfu/mL,
pH = 7.5 (experiment a); (e) C0 = 1.6  105 cfu/mL, pH =7.0 (experiment b); (f) C 0 = 3.7  10 7 cfu/mL,
pH = 7.0 (experiment c).

6 of 13

PANG AND ŠIMŮNEK: BACTERIA-FACILITATED Cd TRANSPORT IN GRAVEL COLUMNSW12S10

W12S10

Table 2. Rate Coefficients of Bacteria Attachment/Detachment to/From the Aquifer Media Optimized Using the
Attachment/Detachment Modelkac, h1

Fixed From Br Data

kdc, h1ExperimentBacteria, cfu/mL

pH

Krw, cm/hr

ax,a cm

Value

SE

Value

SE

r2

SSRs

Cd + B. subtilis (experiment a)
Cd + B. subtilis (experiment b)
Cd + B. subtilis (experiment c)
Cd + E. coli (experiment a)
Cd + E. coli (experiment b)
Cd + E. coli (experiment c)

9.0  104
7.0  105
5.6  107
5.0  103
1.6  105
3.7  107

7.0
7.7
7.0
7.5
7.0
7.0

27.19
16.71
25.99
25.08
26.18
28.38

1.35
0.90
1.50
1.31
1.50
1.50

1.02
1.96
1.29
3.11
1.33
1.86

0.28
0.26
0.74
0.80
0.48
0.43

0.43
0.00
0.10
0.36
0.42
0.07

0.49
0.19
0.82
0.44
0.63
0.01

0.92
0.83
0.71
0.54
0.90
0.94

0.14
0.27
0.59
0.98
0.19
0.11

a

Dispersivity.

[22 ] Table 3 gives parameters optimized using thecolloid-facilitated solute transport model. Model-simulated
and observed concentrations of Cd, including both total anddissolved effluent concentrations, are compared in Figures 6
and 7. The excellent agreement between the optimized
and measured BTCs suggests that the newly developed
HYDRUS CFM is capable of simulating bacteria-facilitatedmetal transport for the experimental problem tested herein
and that exchange processes between liquid, solid, andcolloid phases can be adequately described using linear
exchange models.
[23] The interaction of Cd with the aquifer media is
described by parameters w, f and Kd. Table 3 shows thatw and f values are similar in experiments with E. coli and B.
subtilis spores and change little between experiments. Thisfinding indicates that the Cd sorption rate to the aquifer
media and the fraction of the kinetic sites are not affected by
the presence of bacteria. The optimized f value is consistently close to zero, suggesting that Cd transport is a kinetic
process. The Kd values do not show any particular pattern,reflecting variations of experimental conditions and uncertainty of model simulations. It is expected that similar to
w and f, Kd values should not be affected by the presence orabsence of bacteria as attached bacteria would not havecovered enough of the soil surface to significantly change
its sorption characteristics.
[24] Bacteria-facilitated Cd transport is described by therate coefficients of Cd adsorption and desorption to unattached and attached bacteria (kamc, kdmc, kaic, kdic). As
mentioned previously, we have determined kamc and kdmc
using the batch experimental data, and estimated kaic andkdic using the column experimental data. We have thus
assumed that rates of kamc and kdmc are the same in boththe batch and column systems. Results of kamc and kdmc
have been discussed previously, here we only discuss theresults of kaic and kdic. During preliminary optimizations,the kdic value constantly approached zero, which suggeststhat the sorption of Cd onto deposited bacteria is essentiallyirreversible.
[25] The kaic value for Figures 6c and 6d is significantly
greater than that for Figure 6b (Table 3), inferring a greater
Cd adsorption onto deposited bacteria in Figures 6c and 6d.
This may explain the more pronounced tailing in Figures 6c
and 6d, in comparison with Figure 6b, as bacteria deposited
to the solid matrix would act as additional sorption sites. The
kaic values for Figures 7b –7e are similar (Table 3), which isin agreement with the similar degree of Cd BTC tailings. The
greater kaic value for Figures 6c and 6d than for Figure 6b isthought to be due to an increase in the input concentration of
B. subtilis spores providing more bacterial sorption sites for
Cd. In contrast, the kaic value for Figures 7d and 7e is smaller
than for Figures 7b and 7c (Table 3) with an increasein E. coli concentration, again suggesting chelation of Cd
by E. coli. However, the standard error of kaic estimation forE. coli in Figures 7b and 7c is quite large (Table 3), thus theresults contain a high level of uncertainty.
[26] Unlike the approach used by others [Tsezos and Bell,1989; Corapcioglu and Kim, 1995] who assumed the sameadsorption or desorption rate coefficients of a contaminant
for both unattached and deposited bacteria, we assumed
different rates for deposited and unattached bacteria due to anumber of reasons: (1) Although unattached and deposited
cells of a particular strain of bacteria have similar surface
characteristics [Corapcioglu and Kim, 1995], the surface
areas of deposited cells are relatively less exposed tosorption for the contaminant. (2) Nutritional state andactivity of deposited and unattached bacteria may be different. Deposited bacteria might be better fed from nutrientson aquifer grain surfaces and thus may be more active
metabolically for acquiring contaminants. (3) Deposited

Table 3. Transport Parameters Derived From Cd BTCs Using the Colloid-Facilitated Solute Transport Modela
Kd, g/mLw, h1kaic, h1f

Experiment

Value

SE

Value

SE

Value

SE

Value

SE

Cd + B. subtilis (experiment a)
Cd + B. subtilis (experiment b)
Cd + B. subtilis (experiment c)
Cd + E. coli (experiment a)
Cd + E. coli (experiment b)
Cd + E. coli (experiment c)

5.58
2.29
5.00
2.72
6.59
4.00

0.22
0.43
0.06
0.09
0.06
0.12

0.28
0.25
0.45
0.36
0.33
0.34

0.01
0.04
0.01
0.01
0.01
0.00

18.71
46.52
20.08
16.71

5.31
6.36
9.31
4.88

0.03
0.01
0.01
0.01
0.01
0.01

0.00
0.00
-

r2
0.91
0.93
0.78
0.87

SSRs
0.08
0.16
0.02
0.10
0.01
0.16

a
Here kamc and kdmc were fixed at values determined from the batch experimental data. A zero kdic value was fixed, as suggested fromthe result of preliminary optimizations.

7 of 13W12S10PANG AND ŠIMŮNEK: BACTERIA-FACILITATED Cd TRANSPORT IN GRAVEL COLUMNS

Figure 6. Observed (circles) and simulated (lines) Cd
concentrations using the colloid-facilitated solute transportmodel for the Cd + B. subtilis spores experiments. (a) C0 =9  104 cfu/mL, pH = 7.0 (experiment a). (b) C0 = 7 
105 cfu/mL, pH = 7.7 (experiment b). (c and d) C0 = 5.6 
107 cfu/mL, pH = 7.0 (experiment c).
bacteria cells might be surrounded by a matrix of extracellular polymers (EPS), produced by other bacterial species
that naturally occur in the aquifer media. Researchers haveshown that cells produce EPS to ‘‘glue’’ themselves tomineral surfaces [Jucker et al., 1997, 1998; McWhirter etal., 2002]. Bacterial EPS occur naturally in subsurface
media and have well-documented metal-binding properties[Czajka et al., 1997; Jensen-Spaulding et al., 2004]. In
contrast, unattached cells might lack EPS. (4) The chemistry
in the biofilm at the mineral-water interface might bedifferent than of the bulk water phase. Using microelectrodes to construct profiles of pH and oxygen through abiofilm at the micron scale, Haack and Warren [2003] havefound a significant difference in pH and dissolved oxygen
within the biofilm compared to the overlying solution.
[27] Different sorption rates to unattached and depositedbacteria seem to be evident from our inverse analyses ofexperimental data. In comparison with Cd sorption rates tounattached bacteria (kamc in Table 1), Cd sorption rates toattached bacteria are significantly greater (kaic in Table 3).
However, there is a large uncertainty associated with the kaic
estimations since the amount of bacteria attached to thesolid phase at any particular time is very small compared to
the number of bacteria in the solution (Figure 5). Therefore
Cd sorption to immobile bacteria is much less significant.
Since sorption to the aquifer material and the mobile
bacteria dominate the Cd sorption process, estimated sorption coefficients to immobile bacteria are highly uncertain.
Fortunately results of the sensitivity analysis (next section)
have shown that the effect of parameters kaic and kdic onmodel results is relatively insignificant compared to Kd andkamc. This would offset some drawback associated withmodel uncertainty on kaic.
[28] Nevertheless, if kaic is indeed greater than kamc, themost relevant explanation is the possible effects of indigenous EPS and biofilm already on the mineral surfaces,
created by native microbes. It is also possible that theW12S10degree of separation of aggregates of bacteria (‘‘declumping’’) differs between unattached and deposited bacteria,
which in turn affects the extent and kinetics of their binding
to Cd. We consider that the effects of change in the
nutritional state of the bacteria and biofilms produced by
the introduced bacteria were minimal during the short
experimental durations.
[29] Although ultimately up to seven parameters (Krw, D,
kac, kdc, w, Kd, and kaic) were fitted to experimental data, theparameter values were not fitted simultaneously, but sequentially to different sets of data. Since the dispersion andconductivity values were fitted to the Br BTC, these twoparameters should be relatively well defined. Bacteria
attachment, kac, and detachment, kdc, coefficients were thenfitted to the bacteria BTC and thus should be similarly welldefined. Finally, three Cd sorption parameters characterizing Cd sorption to the solid phase (w and Kd) and toimmobile bacteria (kaic) were evaluated. Note that the
information about the solid phase sorption parameters is
contained mainly in the first part of the BTC with thegradual increase in effluent Cd concentrations that is also
not affected by the presence of bacteria. Thus with the
exception of the kaic parameter, other parameters should be
defined reasonably well.

Figure 7. Observed (circles) and simulated (lines) Cd
concentrations using the colloid-facilitated solute transportmodel for the Cd + E. coli experiments. (a) C0 = 5 
103 cfu/mL, pH = 7.5 (experiment a). (b and c) C0 =1.6  105 cfu/mL, pH = 7.0 (experiment b). (d and e) C0 =3.7  107 cfu/mL, pH = 7.0 (experiment c).

8 of 13W12S10PANG AND ŠIMŮNEK: BACTERIA-FACILITATED Cd TRANSPORT IN GRAVEL COLUMNS

Figure 8. Effects of various reaction parameters on the total Cd concentrations in the effluent.

9 of 13

W12S10W12S10PANG AND ŠIMŮNEK: BACTERIA-FACILITATED Cd TRANSPORT IN GRAVEL COLUMNS

3.2. Sensitivity of Model Results to Selected
Parameters[30] Using Cd BTC of Figures 6c and 6d as an example,
the effects of various parameters that describe three-phaseinteractions are shown in Figure 8 for the total Cd in theeffluent (includes both dissolved Cd and Cd sorbed tomobile bacteria) and in Figure 9 for the dissolved Cd. The
thickest dark line, which is the final calibrated simulation,
serves as a baseline for comparison of the test results. The
calibrated parameter values, their additional values used in
the sensitivity analysis (Table 4) and SSRs of simulated
results against the calibrated values are listed in Table 4.
Results of the calibrated simulations are used as the basis
for calculating SSRs in the sensitivity analysis in order tohave the same number of data points at a similar timeinterval, while the measured data are more limited and at
irregular time intervals. The possible range of parametervalues is covered by the calibrated parameter values andadditional values tested.
[31] Cd BTCs can be divided into three distinguish parts
depending on the inflow of bacteria and solutes into thecolumn (section 2.1): in step 1, only Cd and Br were addedat the influent; in step 2, Cd, Br and bacteria were added
simultaneously; in step 3 the column was flushed withfreshwater without Cd, Br, or bacteria. On the basis of
Figures 8 and 9, the following results are summarized anddiscussed.
[32] 1. As kamc increases, total Cd in the effluent increases
significantly in step 2 but decreases slightly in step 3,
whereas dissolved Cd decreases at all times. This suggeststhat bacteria-facilitated Cd transport, as a result of faster
adsorption of Cd onto mobile bacteria, prompts a more
rapid leaching of total Cd from the system while reducing
dissolved Cd concentrations. Consequently, a high kamc
results in less Cd staying in the system after bacteria areflushed out.
[33] 2. Higher kdmc decreases the total Cd and increases
the dissolved Cd during step 2, but has almost no effect oneither total or dissolved Cd during step 3. This indicates that
the Cd desorption rate from mobile bacteria only effects Cd
concentrations during bacteria-facilitated transport and has
no effect on Cd after the bacteria are flushed out.
[34] 3. Higher kaic decreases both the total and dissolved
Cd in the effluent at all times.
[35] 4. Higher kdic increases both total and dissolved Cd
at all times.
[36] 5. As kac increases, both the total and dissolved Cd
decreases at all times. In contrast, as kdc increases, both thetotal and dissolved Cd increases at all times. This is because
higher bacteria attachment to the aquifer material would
increase immobile bacteria mass, which in turn enhances
sorption of Cd on immobile bacteria. On the other hand,higher bacteria detachment would increase mobile bacteria
mass, which then promotes more Cd adsorbed onto mobile
bacteria and consequently its leaching out from the system.
[37] 6. As f increases, the front of the total and dissolved
Cd BTC becomes delayed and the peak of BTC is reduced.
The f parameter divides the sorption sites between equilibrium and kinetic sites. While equilibrium sorption (larger f )leads to retardation of solutes, kinetic sorption leads to a
gradual increase of effluent concentrations.

W12S10[38] 7. An increase in Kd or w would reduce the total anddissolved Cd at all times, especially in steps 1 and 2, thus
Cd BTC flattened. While the Kd parameter increases theequilibrium sorption (thus leads to retardation of solutes),
the product of Kd and w is proportional to the sorption rateon kinetic sites, which increases sorbed concentrations andreduces dissolved concentrations.
[39] The above section summarizes the effects of various
parameters describing Cd-bacteria interaction (points 1 –4),
bacteria-aquifer media interaction (point 5), and Cd-aquiferinteraction (points 6 –7). Our points 1 and 2 are consistent
with results of the sensitivity analysis by Corapcioglu andJiang [1993], who used their own colloid-facilitated contaminant transport model. They also reported that theincreased sorption rate of a contaminant to mobile colloids
will increase the total solute flux, whereas an increase in
the desorption rate of a contaminant from mobile colloids
will decrease the total solute flux. Similar to point 7,
Corapcioglu and Kim [1995] also reported that as Kd
increases, the contaminant BTC flattens out. Our point 5
on the reverse effect of kac on solute concentration is also
consistent with result of Corapcioglu and Kim [1995].
[40] The relative sensitivity of the above reaction parameters on model results could be measured by the percentagechange (plus for increase and minus for decrease) in thepeak Cd concentration when increasing a parameter value
by tenfold. The sequence of parameters with regard to theireffect on the total Cd in the effluent is as follows: Kd(68%) > w (66%) > kac (29%) > kamc (+22%) > kdc(+18%) > f (+15%) > kdmc (5%) > kdic (+3%) > kaic
(1%). The order of parameters with regard to their effect on
the dissolved Cd is as follows: w (79%) > f (5%) > kamc
(0.43%) > kdmc (+0.06%). Changes in other parameters(Kd, kac, kdc, kdic, kaic) have smaller or no effect on thepeak dissolved Cd concentration. These general trends
are also reflected in the SSRs values of the sensitivity
analysis (Table 4), although SSRs do not provide a directcomparison.
[41] The above sensitivity analysis demonstrates that thebacteria-facilitated Cd transport is most sensitive to Kd, w,
kac, kamc, kdc and f. This suggests that for the experimental
system discussed here, parameters describing Cd sorption/
desorption to/from the aquifer material, bacteria attachment/
detachment to/from aquifer material, and Cd sorption tomobile bacteria are the most critical parameters for theaccuracy of model predications. This suggests that Cd
sorption/desorption to/from the aquifer material, bacteria
attachment/detachment to/from aquifer material, and Cd
sorption to mobile bacteria are the most important processes
that occur in our experimental system. Model results are
relatively less sensitive to parameters kdmc, kaic and kdic.

4. Conclusion[42] The HYDRUS colloid-facilitated solute transportmodel, simplified to consider exchange processes between
liquid, solid, and colloid phases using linear exchange
models, was successfully used to describe column experimental data involving Cd transport facilitated by B. subtilis
spores and E. coli in saturated gravels. The model described
the observed total and dissolved Cd concentrations in theeffluent reasonably well.

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W12S10PANG AND ŠIMŮNEK: BACTERIA-FACILITATED Cd TRANSPORT IN GRAVEL COLUMNSW12S10Figure 9. Effects of various reaction parameters on the dissolved Cd concentrations in the effluent.

[43] The model results suggest that the rates of Cd
sorption or desorption not only differ between different
bacterial species, but they also differ between unattachedand deposited bacteria. Although the Cd sorption rate tounattached bacteria was one order of magnitude greater forB. subtilis spores than for E. coli, the sorption rates of Cd todeposited spores and deposited E. coli did not show
a significant difference. The modeling results suggest a

11 of 13

PANG AND ŠIMŮNEK: BACTERIA-FACILITATED Cd TRANSPORT IN GRAVEL COLUMNSW12S10

W12S10

Table 4. Parameter Values Used in the Sensitivity Analysis and Sum of Squared Residuals in Comparison With
Calibrated Values
Test Values
Parameter

Units

Calibrated Value

kamc
kdmc
kaic
kdic

h1
h1
h1
h1

2.30
1.28
46.5
0.00

kac
kdc

h1
h1

1.29
0.10

f
Kd
w

g/mL
h1

0.01
5.00
0.45

Test 1

Test 2

SSRs - Total
Effluent Cd

SSRs - Dissolved
Cd

Test 1

Test 2

Test 1

Test 2

0.27
0.03
0.55
0.01

12.5
0.03
0.49
0.29

0.04
0.01
0.82
0.02

1.56
0.01
0.73
0.47

Bacteria-Aquifer Media Interaction
0.23
2.30
0.64
0.00
1.30
0.14

0.25
1.59

0.46
0.01

0.13
0.26

8.03
11.7
6.66

0.83
92.7
78.6

6.75
8.21
5.64

Cd-Bacteria Interaction
0.23
46.5
0.00
0.13
0.23
2.30
0.13
1.28

Cd-Aquifer Media Interaction
0.10
1.00
0.50
50.0
0.04
4.46

reversible sorption of Cd onto unattached bacteria and an
irreversible sorption of Cd onto deposited bacteria for both
species. The rate of Cd desorption from unattached E. coli
was one order of magnitude greater than its sorption rate,
which was probably caused by chelation of Cd by the outermembrane vesicles secreted by E. coli.
[44] Although the two bacterial species reacted very
differently to Cd, their attachment/detachment characteristics to/from the aquifer media were similar, and these
did not appear to be affected by their interactions with Cd.
The attachment of both bacterial species to the aquifer
media was reversible, and, in general, the attachment rate
was much higher than the detachment rate. It also appears
that Cd interactions with the aquifer media were not affectedby the presence or absence of bacteria, possibly because thedeposited bacteria did not cover enough of the soil surface
to significantly change its sorption characteristics for theexperiments discussed here. Although for the experiments
discussed here bacteria-aquifer media interactions do notseem to be affected by Cd and Cd-aquifer media interactions, the results of model simulations suggest that bacterial
attachment/detachment to aquifer media plays a very important role in the degree of bacteria-facilitated Cd transport
as these activities significantly affect the number of mobile/immobile colloids available for Cd sorption onto them andthus alter the mobility of Cd.
[45] Compared to other optimized parameters, the rates
for Cd sorption to both unattached and deposited bacteria
exhibit the greatest standard errors. Although the use of
independently estimated rates for Cd sorption/desorption to/from unattached bacteria from a batch study significantly
narrowed the standard errors, the uncertainty of the optimized sorption rate to deposited bacteria remained quite
high. Results of the sensitivity analysis indicated that theeffect of the Cd sorption rate on the unattached bacteria on
model results was significantly greater than its sorption rate
to deposited bacteria. We have inferred some possible
reasons for differences in the rate coefficients and our model
results seem to support them.
[46] The model evaluation results provided some guidance for the design of future experiments. The model results
are very sensitive to the parameters describing solute-solid

0.90
97.2
82.6

interaction (Kd, w, and f); colloid-solid interaction (kac andkdc) and solute mobile colloid interaction (kamc). Therefore
future work should focus on accurately determining theseparameters. As model-optimized kamc values are highly
uncertain, it is recommended that this parameter be
estimated from batch experiments that closely mimic thephysical and biochemical conditions of the system ofinterest. In particular, the design of batch and column
experiments need to ensure the use of the same pH andconcentrations of colloids and contaminants as a slightchange in these conditions may result in a significant
change in the experimental results [Pang et al., 2005].
Future work is also needed to closely examine the characteristics of unattached and deposited colloids, and to independently determine individual effects of different factors,
including surface areas, charge, activity, EPS, chemistryof the biofilms and bulk water.
[47] Acknowledgments. We thank Chris Daughney of Institute ofGeological and Nuclear Sciences Ltd. (New Zealand) for his valuable
discussion comments on metal-bacteria interactions. This study was fundedby the Foundation for Research, Science and Technology (New Zealand)
under contract number CO3X0203 and in part by the Terrestrial Sciences
Program of the Army Research Office (Terrestrial Processes and Landscape
Dynamics and Terrestrial System Modeling and Model Integration).

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


L. Pang, Institute of Environmental Science and Research Ltd., PO Box
29181, Christchurch, New Zealand. (liping.pang@esr.cri.nz)
J. Šimůnek, Department of Environmental Sciences, University ofCalifornia, Riverside, CA 92521, USA.

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