analysis of benzene transport in twoüdimensional aquifer model

HYDROLOGICAL PROCESSESHydrol. Process. 19, 2481–2489 (2005)Published online 14 March 2005 in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/hyp.5683

Analysis of benzene transport in a two-dimensionalaquifer model

Jae-Woo Choi,1 Heon-Cheol Ha,2 Song-Bae Kim3 and Dong-Ju Kim1*1 Department of Earth and Environmental Sciences, Korea University, Seoul 136-701, Korea

2 PO Box 66-1, Capital Defence Commander, Eun-Pyeong Ku, Seoul 122-600, Korea3 School of Biological Resources and Materials Engineering, Seoul National University, Seoul 151-742, Korea

Abstract:

In this study, the fate and transport of aqueous benzene was investigated in a laboratory-scale homogeneous aquiferby conducting a two-dimensional plume test. Benzene solution was introduced as a pulse type along the width of theaquifer model through a recharge zone situated at the upper-left part of the model and followed by a steady state flow.Solution samples were collected at various locations on the front side of the model to capture two-dimensional plumesat discrete time intervals. The benzene plumes showed a moderate retardation relative to chloride plumes observedfrom the previous study conducted for the same aquifer model. The retardation factor was obtained from the ratio oftravel distances of benzene peaks to chloride peaks from the injection point, computed using a line integral method.Mass recovery of aqueous benzene revealed that there was a significant reduction of benzene mass, indicating theoccurrence of volatilization and/or irreversible sorption during transport. Thus, retardation along with volatilizationand/or irreversible sorption may be important processes affecting the fate and transport of aqueous benzene in theaquifer model. Copyright 2005 John Wiley & Sons, Ltd.

KEY WORDS plume test; benzene; retardation; irreversible sorption; volatilization; aquifer model

INTRODUCTION

In a subsurface environment, the characterization of fate and transport of contaminants is essential forremediation practices. Sorption plays a prominent role in the fate and transport of contaminants in soilsand groundwater, resulting in retardation and reduction of contaminant concentration through reversibleand irreversible sorption respectively. Many researchers have investigated the reversible sorption of organiccontaminants in porous media and determined the sorption-related parameters, such as retardation factor,using various laboratory and field methods (Roberts et al., 1986; Mehran et al., 1987; MacIntyre et al., 1991;Priddle and Jackson, 1991; Rogers, 1992; Benker et al., 1998).

In parallel with the reversible sorption, irreversible sorption affects also the fate and transport of organiccontaminants in a subsurface environment. Several researchers have observed the irreversible sorption oforganic compounds in soils using laboratory batch and column experiments (Yong et al., 1985; Burgos et al.,1996; McGroddy et al., 1996; Kan et al., 1997, 1998; Broholm et al., 1999). In addition to the irreversiblesorption, volatilization may also contribute to the fate of organic contaminants, especially for aromatichydrocarbon compounds, during transport through the subsurface (Chiang et al., 1989; Lahvis et al., 1999).

Very recently, Baek et al. (2003) reported the occurrence of irreversible benzene sorption in sandy aquifermaterials, and Kim et al. (2004) determined laboratory-scale dispersivities from two-dimensional KCl plumedata obtained from the same aquifer model. Hence, following the previous study of Kim et al. (2004), wefurther investigated the fate and transport of aqueous benzene by conducting a two-dimensional plume test

* Correspondence to: Dong-Ju Kim, Department of Earth & Environmental Sciences, Faculty of Science, Korea University, Anam Dong5-1, Sungbuk Ku, Seoul, 136-701 Republic of Korea. E-mail: [email protected]

Received 22 October 2003Copyright 2005 John Wiley & Sons, Ltd. Accepted 26 May 2004

2482 J.-W. CHOI ET AL.

in the same aquifer model. Based on the benzene plumes, retardation and other possible processes suchas volatilization and irreversible sorption were also studied through mass recovery and two-dimensionalmodelling of benzene transport.

MATERIALS AND METHODS

Two-dimensional plume test

A plume test was performed in the same two-dimensional aquifer model as described by Kim et al. (2004)using aqueous benzene as a reactive tracer and aquifer materials. The aquifer model was constructed withpolycarbonate materials in dimensions of 110 cm (L) ð 25 cm (W) ð 71 cm (H). The model was partitionedinto two parts: a 100 cm long aquifer on the left, and a 10 cm long water storage reservoir on the right. Thepossibility of aqueous benzene mass sorption onto the polycarbonate was examined by a separate experimentin which concentrations of benzene solutions in two different containers made of glass and polycarbonatewere measured at regular time intervals. The loss of benzene mass via sorption was only 4Ð0% and 5Ð0% forboth containers respectively at 16 h, indicating that sorption of aqueous benzene onto the polycarbonate wallsof the aquifer model can safely be neglected during the plume test.

In the tracer experiment, a steady state flow condition was imposed in the aquifer by applying a constant flux(28 ml min�1) of distilled water using a peristaltic pump. Once the steady state flow condition was reached,a benzene solution of 1 L (1500 mg l�1) was injected into the aquifer for 37Ð5 min using the recharge andtracer injection system while the top of the injection system was covered to prevent the volatilization ofaqueous benzene. During the injection of tracer, the flow of distilled water was interrupted and followed bythe continuous application of distilled water at the previous recharge rate. In order to prevent diffusion anddispersion across the width of the aquifer model, tracer solutions were applied for the entire width (25 cm) atthe upper left side of the model through an acrylic reservoir of dimensions 4 cm (L) ð 25 cm (W) ð 5 cm (H)with 75 recharge outlets.

Samples were collected from the inner part located at 5 cm from the aquifer wall, corresponding to eachsampling port on the front side of the aquifer model, in order to increase the detection efficiency at 4, 9,16 and 22 h after the tracer injection. Benzene concentration was analysed using a high performance liquidchromatograph (HPLC, Young Lin Co., Seoul, Korea) equipped with a fluorescence detector (M720), M925pump, Rheodyne injector and C18 column (150 ð 4Ð6 mm2; Phenomenex, USA).

Simulation of benzene transport

A two-dimensional equation (McDonald and Harbaugh, 1988) describing groundwater flow in an unconfinedaquifer is given by:

Kxx∂2h

∂x2 C Kzz∂2h

∂z2 D Ss∂h

∂t�1�

where h is the hydraulic head (L), Kxx, Kzz are the permeability (LT�1) of aquifer materials in x and zcoordinates, and Ss is the specific storage coefficient (L�1). The advective–dispersive transport equation(Zheng, 1992) for a reactive solute in a saturated flow regime showing retardation and decay, such as anyloss from irreversible sorption (Baek et al., 2003) and/or volatilization, can be written as:

R∂C

∂tD ∂

∂xi

(Dij

∂C

∂xj

)� ∂

∂xi�viC� � �C �2�

where xi is the spatial coordinate (x, z), R is the retardation factor, C is the solute concentration, Dij is thehydrodynamic dispersion coefficient tensor (L2T�1), vi is the average linear flow velocity (LT�1), and � is

Copyright 2005 John Wiley & Sons, Ltd. Hydrol. Process. 19, 2481–2489 (2005)

ANALYSIS OF BENZENE TRANSPORT IN A TWO-DIMENSIONAL AQUIFER MODEL 2483

the first-order decay rate coefficient (T�1) representing any losses such as volatilization and/or irreversiblesorption. Assuming that molecular diffusion is negligible, the dispersion tensor, Dij, may be expressed as:

Dxx D ˛Lv2

x

jvj C ˛Tv2

z

jvjDxz D Dzx D �˛L � ˛T�

vxvz

jvj �3�

Dzz D ˛Lv2

z

jvj C ˛Tv2

x

jvjwhere ˛L and ˛T are the longitudinal and transverse dispersivities (L), respectively, vx, vz are the componentsof the velocity vector, and jvj D �v2

x C v2z �1/2.

Model simulation was performed using Equations (1) and (2) to examine the effect of the retardation factoron the benzene plume movement under the given aquifer conditions. The flow and transport parameters usedin the simulation are given in Table I. The longitudinal (˛L) and transverse (˛T) dispersivities were adoptedfrom Kim et al. (2004), who conducted a chloride plume test for the same aquifer model. The flow domainwas divided into 28 rows and 50 columns (1400 cells) with uniform grid size of 2 cm in each dimension. Noflow boundary condition was imposed along the bottom and left sides of the aquifer, while a free seepage(h D 0) condition was applied to the right boundary (Kim et al., 2004).

Estimation of retardation factor and mass recovery

The benzene retardation factor (R) can be estimated by comparing the travel distance of the chloride peakfrom the injection point to that of the benzene peak. The travel distances of the chloride and benzene peakscan be calculated using the following line integral equation:

L D∫ x

0

√1 C �f0�x��2dx �4�

R D Lc

Lr�5�

where L is the travel distance, x is the location of the peak concentration point in a horizontal direction,f�x� D ae�bx C c is the function that can be determined by selecting the appropriate a, b and c to bestdescribe the travel track of tracers between the injection and peak concentration points, and Lc and Lr are thetravel distances of conservative and reactive tracers, respectively. The solution of Equation (4) was obtainedusing Maple V software (Waterloo Maple, Inc., 1998).

The mass recovery of benzene solution was determined from the calculation of observed versus injectedmass using a method of planar area calculations described in Surfer 7 User’s Guide (Golden Software, Inc.,1999).

Table I. Flow and transport parameters used in the simulation

Parameter Value

Horizontal hydraulic conductivity, Kxx 1Ð61 cm min�1

Vertical hydraulic conductivity, Kzz 1Ð61 cm min�1

Porosity, n 0Ð40Dry bulk density, �d 1Ð66 g cm�3

Longitudinal dispersivity, ˛L 0Ð2 cmTransverse dispersivity, ˛T 0Ð04 cmFirst-order decay rate coefficient, � 0Ð08 h�1



RESULTS AND DISCUSSION

Benzene plume movement

The observed benzene plumes at 4, 9, 16 and 22 h after tracer injection are presented in Figure 1. Thebenzene plume shows a banded shape propagating from the upper-left corner to the lower-right corner of theaquifer model. As the benzene plume travels down the flow path, the peak concentration of the plume decreasesrapidly, as illustrated in Figure 2. At 4 h after tracer injection, the plume peak concentration is positionedhorizontally at 20 cm and vertically at 18 cm away from the injection point, with a peak concentration of280 mg l�1. It is remarkable that the peak concentration decreased down to 19% of the input concentration(1500 mg l�1) at 4 h after injection, indicating a significant reduction of the aqueous benzene in the aquifer.At 22 h after injection, the plume peak position is horizontally at 76 cm and vertically at 28 cm away fromthe injection point, and a peak concentration of 61 mg l�1, equal to 4% of the input concentration, wasobserved.

The mass recoveries of benzene at 4, 9, 16 and 22 h are determined to be 65%, 51%, 43% and 39%,respectively. The reduction of the mass recovery during the transport of the aqueous benzene through theaquifer can be explained by the fact that other processes rather than retardation govern the fate of aqueousbenzene. From the inspection of Equation (2), it can be explained that the parameter responsible for thereduction of mass recovery should be the first-order decay rate constant (�), representing the reduction ordecay of the aqueous benzene mass.

During contaminant transport in the subsurface, major processes responsible for the contaminant massreduction would be biodegradation, radioactive decay, volatilization and irreversible sorption. In our study,the sandy materials were autoclaved before being packed into the aquifer model, and thus the possibility ofbenzene mass reduction owing to biodegradation was eliminated. In addition, the mass reduction of benzene byradioactive decay can be counted out since benzene is not a radioactive compound. However, the possibilityof aqueous benzene mass reduction by volatilization and/or irreversible sorption cannot be excluded. Forinstance, the benzene mass applied to the aquifer can be removed from the aqueous phase by volatilizationnear the water table during transport through the unconfined aquifer model. Mass reduction of hydrocarboncompounds by volatilization was also reported by Chiang et al. (1989) and Lahvis et al. (1999), who observedvolatilization along with biodegradation of BTX compounds in a shallow aquifer and at gasoline spill sites,respectively. Recently, mass reduction by irreversible sorption was also reported by Baek et al. (2003), whoinvestigated the irreversible sorption of benzene using a column approach, showing that a significant amountof the added benzene was not desorbed from the same sandy material. Thus, volatilization coupled withirreversible sorption can be major processes affecting the fate of aqueous benzene during transport throughthe aquifer materials. Unfortunately, the amount of benzene mass loss by each process could not be analysedthrough the experimental method used in this study.

Retardation of benzene plume

The extent of the benzene plume retardation can be investigated by comparison of the observed benzeneand chloride plumes. In Figure 3, the benzene plumes at 9 and 16 h after tracer injection are shown togetherwith the corresponding chloride plumes observed for the same sandy aquifer model from the previous studyof Kim et al. (2004). It clearly demonstrates that the chloride plume (solid line) travelled further than thebenzene plume (shaded contour) at the same observation time, indicating that the benzene plume was retardedcompared to the chloride plume.



-80 -80

-80

0

-80

Depth below water table (cm)

-16

-24

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-40

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4 hr


-16

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-40

-48

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-16

-24

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-40

-48

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16 h

r

9 hr

22 h

r


-16

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Dis

tanc

e fr

om s

ide

of ta

nk (c

m)

1020

3040

5060

7080

9010

00

Dis

tanc

e fr

om s

ide

of ta

nk (c

m)

1020

3040

5060

7080

9010

0

Figu

re1.

The

obse

rved

benz

ene

plum

es(u

nit

ofis

olin

e:m

gl�1

)at

4,9,

16an

d22

haf

ter

trac

erin

ject

ion



0

-8

0

Dep

th b

elow

wat

er ta

ble

(cm

)

-16

-24

-32

-40

-48

-5610 20 30 40 50 60 70 80 90

Distance from side of tank (cm)100

4 hr (280 mg/L)

9 hr (110 mg/L)

16 hr (84 mg/L)

22 hr (61 mg/L)

Figure 2. The location of the benzene plume peak concentrations during transport through the unconfined aquifer model

In case of 9 h after tracer injection (Figure 3a), the function, f(x), for chloride is f�x� D 44Ð0e�0Ð014x � 44Ð0with corresponding travel distance of 48Ð5 cm, while for benzene, f�x� D 37Ð0e�0Ð030x � 37Ð0 with a traveldistance of 45Ð1 cm. Therefore, from Equation (5), R at 9 h after tracer injection was 1Ð10. In the samemanner, R at 16 h (Figure 3b) was found to be 1Ð20. These values are considerably different from the resultsof Priddle and Jackson (1991), who reported from a laboratory column experiment that benzene was retarded14Ð3 times relative to a conservative tracer. However, they were slightly overestimated compared to theresults of Baek et al. (2003), who found that no benzene retardation occurred during transport through sandyaquifer materials. Despite the same aquifer materials being used in the two laboratory aquifer model tests, thediscrepancy between the results from this study and Baek et al. (2003) can be attributed to the effect of flowvelocity on the benzene retardation. In this study, the flow velocity observed during the plume test was about30 times lower than that used in the previous column study conducted by Baek et al. (2003). Thus, due tothe fast flow in the column study of Baek et al. (2003), neither reversible sorption nor retardation of aqueousbenzene could be observed. It is noted that the R value increases slightly with time or travel distances. Thisconforms to the findings of Roberts et al. (1986), who reported that the retardation factors of organic solutessuch as tetrachloroethylene, dichlorobenzene and carbon tetrachloride increased over time during the fieldobservation at the Borden site, Ontario, Canada.

Effect of retardation on benzene transport

The simulation result at 22 h after tracer injection is presented in Figure 4. The simulated benzene plumehas a banded shape, which accords well with the observed one. The benzene plume movement is rathersensitive to the variation of R in terms of the peak concentration and the plume size. When R D 1Ð0, the peakconcentration of 36 mg l�1 was located at 81 cm away from the injection point, and the plume covered alarge area of the flow domain. As the value of R increased, the travel distance of the peak concentration andthe plume size decreased while the peak concentration increased. In case of R D 2Ð0, the peak concentrationwas 80 mg l�1 and located at 53 cm away from the injection point. At R D 5Ð0, the peak concentration was143 mg l�1 and situated at 32 cm away from the injection point. This indicates that the extent of benzeneplume attenuation is also considerably affected by retardation.



0 10 30 40 50 60 70 80 90 100Distance from side of tank (cm)

-56

-48

-40

-40

-32

-24

-16

-8

0

Dep

th b

elow

wat

er ta

ble

(cm

)

-56

-48

-32

-24

-16

-8

0

Dep

th b

elow

wat

er ta

ble

(cm

)

(b)

(a)

20

Figure 3. The comparison of the observed benzene plume (shaded contour) with the chloride plume observed by Kim et al. (2004) (solidline) (unit of isoline: mg l�1): (a) 9 h; (b) 16 h after tracer injection

CONCLUSIONS

The fate and transport of aqueous benzene in the unconfined sandy aquifer was investigated by conductinga two-dimensional plume test in a physical aquifer model. The benzene plume showed a slight retardationrelative to that of chloride, with a retardation factor ranging from 1Ð10 to 1Ð20, which increased over traveltime or distance. The benzene mass recovery revealed that the prominent reduction of aqueous benzene massoccurs during transport through the aquifer due to volatilization and/or irreversible sorption. Therefore, itis concluded that both reversible and irreversible sorption, that cause retardation and mass reduction, alongwith volatilization, were associated with the fate and transport of aqueous benzene in the aquifer. Furtherstudy should focus on the effect of pore water velocity on the retardation of reactive contaminants, since the



0-56

-48

-40

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-24

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-8

0

Dep

th b

elow

wat

er ta

ble

(cm

)

R = 5.0 R = 2.0 R = 1.0

10 20 30 40 50 60 70 80 90 100

Distance from side of tank (cm)

Figure 4. The effect of retardation factor (R) on the movement of the simulated benzene plume at 22 h after tracer injection (unit of isoline:mg l�1)

retardation factor of benzene showed an increasing tendency with a decrease of flow velocity through theaquifer materials.

ACKNOWLEDGEMENTS

The authors acknowledge that this study was supported by KOSEF (ABRL project no. R14-2002-049-01002-0(2002)).

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analysis of benzene transport in twoüdimensional aquifer model