Transport in Porous Media 18: 283-302.1995.
@ 1995 Kluwer Academic Publishers. Printed in the Netherlands.

283

Experimental Investigation of Solute Transport inLarge, Homogeneous and Heterogeneous,
Saturated Soil Columns
K. HUANG, N. TORIDE, and M. TH. VAN GENUCHTEN
U.S. Salinity Laboratory, USDA, ARS 4500 Glenwood Drive Riverside, CA 92501, U.S.A.
(Received: 25 June 1993; in final form: 5 May 1994)
Abstract. Laboratory tracer experiments were conducted to investigate solute transport in 12.5-m
long, horizontally placed soil columns during steady saturated water flow. Two columns having
cross-sectional areas of 10 x IOcm’ were used: a uniformly packed homogeneous sandy column
and a heterogeneous column containing layered, mixed, and lenticular formations of various shapes
and sizes. The heterogeneous soil column gradually changed, on average, from coarse-textured at
one end to fine-textured at the other end. NaCl breakthrough curves (BTC’s) in the columns were
measured with electrical conductivity probes inserted at 50- or 100-cm intervals. Observed BTC’s in
the homogeneous sandy column were relatively smooth and sigmoidal (S-shaped), while those in theheterogeneous column were very irregular, nonsigmoidal, and exhibited extensive tailing. Effective
average pore-water velocities (tr,rr) and dispersion coefficients (&r) were estimated simultaneously
by tilting an analytical solution of the convection-dispersionequation to the observed BTC’s. Velocity
variations in the heterogeneousmedium were found to be much larger than those in the homogeneous
sand. Values of the dispersivity, (Y = Derr/ecrrr for the homogeneous sandy column ranged from
0.1 to 5.0cm, while those for the heterogeneous column were as high as 200cm. The dispcrsivity
for transport in both columns increased with travel distance or travel time, thus exhibiting scaledependency. The heterogeneous soil column also showed the effects of preferential flow. i.e., somelocations in the column showed earlier solute breakthrough than several locations closer to the inlet
boundary. Spatial fluctuations in the dispersivity could bc explained qualitatively by the particular
makeup of the heterogeneities in the column.
Key words: Solute transport experiments, heterogeneous media, dispersion, scale-depcndcncy.

1. Introduction
Solute transport in soil and groundwater is affected by a large number of physical, chemical and microbial processes and media properties. Ignoring microbial
processes and assuming equilibrium interactions between solutes in the liquid andsolid phases, transport during one-dimensional steady water flow in a uniform
medium is generally described with the convection-dispersion equation (CDE) as
followsdC
PCoc
Rdt=D8r2-vz,
where C is the volume-averaged solution concentration (M/L3), t is time (T), x
is distance (L), v = Q/E is the average pore-water velocity (L/T) in which q is

K. HUANG CT AL.

284

the Darcian fluid llux density (L/T)) and c is the effective porosily ( L3/L3), R is aretardation factor accounting for linear equilibrium sorption or exchange (dimen-

sionless), and D is the dispersion coefficient (L*/T).
Assuming negligible diffusion, the ratio of the dispersion coefficient to thepore-water velocity is given by the dispcrsivity, cr:
D

cy=V

(2)

The dispersivity reflects the scale of mechanical mixing caused by variations in

the local fluid velocity around its mean value. The value of cy has traditionallybeen considered a characterisitc of the entire medium (Bear, 1972), usually in t h eorder of 0.1 to 2 cm for repacked homogeneous soil columns (Fried, 1975; Freeze
and Cherry, 1979). These results are in contrast to those from field experiments
which indicate that CY for natural geologic media can be o n e or several orders ofmagnilude higher than lhose determined using disturbed laboratory soil c o l u m n s(Fried, 1975; Anderson, 1979; Pickens and Grisak, 1981a; Molz et al., 1983; Gelhar
et al., 1992). Moreover, results from field studies suggest that the dispersivity may
increase with travel time, travel distance, and/or measurement scale (Pickens andGrisak, 198 I a; Molz et al., 1986; Huyakorn et al., 1986). This scale-dependencyof the dispersivity is considered to be a consequence of the heterogeneous natureof the geological materials (e.g. Pickens and Grisak, 1981 b; Molz et a l . , 1983;
Sudicky, 1986; Moltyaner and Killey, 1988).
The problem of scale-dependent dispersion has been the subject of numerous
theoretical and a selected few experimental studies. Theoretical studies by Gelhar
et a l . (1979), Smith and Schwartz (1980), Dagan (1982, 1984), Poley (1988),
and Neuman (1990), among olhcrs, have demonstrated the significant effects ofvariations in hydraulic properties on dispersive mixing. These studies suggest thatthe dispersivity of a heterogeneous aquifer at first grows more or less linearlywith the solute residence time and/or travel distance as the mixing scale increases,
but eventually may approach a constant asymptotic value. The approach lo au

asymptotic dispersivity may be very slow and involve relatively long travel times
or distances (Dagan, 1984; Sudicky, 1986).
As a complement to the above theoretical studies, several large-scale field
experiments have been carried out to investigate solute transport behavior in naturalaquifers (Freyberg, 1986; Sudicky, 1986; Moltyaner and Killey, 1988; Garabcdianet al., 1991; Boggs et al., 1992; Jensen et al., 1993). These studies have provided
considerable insight into the transport process as affected by both small- andlarge-scale variations in the hydraulic properties. Unfortunately, large-scale field
experiments are very costly, time-consuming, and relatively difficult to execute.
As opposed to carefully controlled laboratory tracer studies such experiments also
involve a large number of uncertainties which are difficult to control or quantify,
including those arising from the natural heterogeneity of the aquifer material, as
well as human activities.

EXPERIMENTAL INVESTIGATION OF SOLUTE TRANSPORT

285

An obvious advantage of laboratory tracer studies is that the experimental conditions can be much better controlled and monitored. Many of the early laboratory
displacement studies, especially those in soil physics (e.g., Nielsen and Biggar,
1961; Elrick et al., 1966) involved relatively short columns (generally less than50cm) using both disturbed and undisturbed soils. More recently, tracer experiments have been carried out to study transport in much larger columns or lysimeters
filled with a variety of soil of geologic materials, including layered or otherwise
stratified formations, as w e l l as soil slabs containing lenses of distinctly different
permeabilitics, a l l designed to simulate various heterogeneous conditions at spatial
scales of up to about 2 to 3 m (e.g., Sudicky et al., 1985; Refsgaard, 1986, Silliman
et al., 1987; Schincariol and Schwartz, 1990). Most of these experiments wereused to study convective transport and dispersion parallel to layering as generally
occurs in saturated groundwater systems. For example, in flow tank experiments
designed to also study density-dependent fl ow, Schincariol and Schwartz (1990)
found that more dispersion occured in a lenticular medium than in both homogeneous and layered systems. By contrast, Khan and Jury (1990) studied transport inboth repacked and undisturbed vertical soil colutnns of lengths up to 87 cm. They
found a significant linear increase in the dispersivity, (Y, with length of the undisturbed colutnns, but no clear evidence that cr related to the measurement scale of
the repacked columns. Vertical solute transport in much larger (6-m long) repacked
homogeneous and horizontally layered soil columns was studied by Wierenga andvan Genuchten (1989) and Porro et al. (1993), respectively. Their studies showedthat some preferential flow occurred in the homogeneous columns, and that dispersivities were greater in the uniform column (3.5 cm) than in the layered column(1.2cm).
The purpose of this paper is to present experimental results of solute transport
throught 12.5-m long homogeneous and heterogeneous soil columns. The length
dimensions were chosen such that different heterogeneous formations could be
included in the columns, and to allow for a scale-dependent dispersion process
to develop as much as possible. Three tracer experiments were conducted during
steady saturated water flow: (1) transport of a NaCl solution into a homogeneous
sandy column, (2) transport into a heterogeneous column containing a variety oflayered, mixed, and lenticular soil formations of various shapes and sizes, andpacked such that the particle size changed on average from very coarse at one end
to very fine at the other end, and (3) leaching of solute from the same heterogeneouscolumn, but with flow now in the opposite direction, i.e, from the fine-textured tothe coarse-textured side. Effective average pore-water velocities and dispersion
coefficients were estimated by fitting analytical solutions of equation (1) to thebreakthrough curves observed at regular intervals along the horizontally placedcolumns.

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K. HUANG ET AL.

2. Experimental
2.1. COLUMN PREPARATIONThe experiments were conducted using 12.5-m long c o l u m n s constructed with 0.5cm thick plexiglass plates. The columns had internal dimensions of 10 cm in widthand 10cm in height. Two soil columns were prepared, a homogeneous c o l u m npacked as uniformly as possible with a medium-textured sand, and a heterogeneouscolumn. The heterogeneous column was filled with a wide range of soil materials
including clay, fine-, medium- and coarse-textured sands, gravel, and pebbles of 1
to 2cm in diameter, as well as various mixtures of these materials. Several lenses
and layers of different shapes and sizes were rather arbitrarily embedded in thisheterogeneous column to ensure a relatively high degree of heterogeneity. The
soil materials used in both columns were taken from the deposits of a mountain
river; they were clean, well-sorted, and contained negligible organic matter. Figure
1 shows a schematic of the experimental setup, including a cross-section of theheterogeneous soil. Notice that, on average, the particle size of the heterogeueouscolumn decreased gradually from very coarse at the inflow end (the M-hand sidein Figure 1) to relatively fine at the outlet (right-hand side). The porosity of eachmaterial was estimated indirectly from measurements of the particle density andthe dry soil bulk density using standard methods (Klute, 1986). The porosity, IL,
was approximately 0.45 for the clay, and about 0.33 for the other materials. In
order to ensure tightly compacted soil cohnnns, the soils were first slightly wetted
and carefully mixed before packing. The cohnnns were subsequently packed layer
by layer in increments of 1 to 2cm. During packing, piezometers were installed
laterally at 50-cm intervals in the center of both columns, while electrodes were
installed at 50-cm intervals in the homogeneous column and 100-cm intervals in
the heterogeneous column (Figure lc).
After packing, but before closing the columns at the top, the horizontally-placedcolumns were slowly saturated from the bottom up for three days and then allowed
to drain through holes in the bottom plexiglass plate. The wetting and drying cycle
promoted further compaction of the soil. Following drainage, a clay paste of about
1 cm thickness was placed on the surface of the packed columns to serve as theupper aquitard (the bottom plexiglass plate served as the lower aquitard). The
columns were subsequently covered tightly by a plexiglass plate. To keep close
contact between the plexiglass plate and the top clay layer, the inside surface ofthe top plate was made rough by gluing small pieces of gravel on the surface. A
series of braces were installed next to prevent the columns from swelling during
the transport experiments. Finally, a high-quality silicon sealant was applied along
the plexiglass joints to avoid leakage, while small l-cm long influent and effluent
reservoirs were connected to both ends of the soil cohnnns. The reservoirs wereseparated from the soil columns by plexiglass screens, coarse-textured sand and anylon mesh. The packed columns thus obtaiucd simulated confined aquifers withthicknesses of approximately 9 cm.

EXPERIMENTAL INVESTIGATION OF SOLUTE TRANSPORT

287

2.2. TRANSPORT EXPERIMENTS
Before starting the transport experiments, the columns were saturated slowly fromthe bottom using deaired tap water. Entrapped air in the columns was removed byapplying a slightly negative pressure at each piezometer. A steady saturated flow
field was established in the columns by imposing constant positive pressure heads
at the inlet and outlet positions using Mariotte bottles and constant head levelapparatus, respectively (Figure 1). Deaircd tap water was continuously applied
for about one week to remove as much remaining entrapped air as possible. We
assumed that steady-state water flow was reached when fluctuations in the observed
drainage rates and piczometer readings became negligible.
Table I summarizes the hydraulic conditions for the three experiments. Althoughsteady flow conditions were established before the transport experiments, the flow
rates at the outlets continued to decrease slowly during the tracer studies. For
example, the flow rate decreased from 12.09 to 11.25 cm/hr during the first 24 hrs of
the transport experiment in the homogeneous sandy column,. The flow rates listed inTable I hence are averages of the measured drainage rates during the experiments.
The continued small changes in flow rates were likely due lo slight changes inthe soil hydraulic properties because of pore clogging by fine soil particles, andperhaps also because of changes in the concentration and/or ionic composition of
the soil solution (Nielsen et al., 1986). The following three tracer experiments werecarried out after steady-state flow were established: (1) a tracer injection (transport)
experiment in the homogeneous sandy soil column by replacing inflowing tap waterwith a NaCl solution of concentration Co = 6 g/L, (2) a tracer injection experimentin the heterogeneous column by applying the 6 g/L NaCl solution at the coarse end(the left-hand side of Figure 1 b), and (3) a leaching experiment in which the initialsaline (6 g/L) fluid introduced during the injection experiment was replaced withdeaired tap water applied at the fine-textured end of the heterogeneous column(the right-hand side of Figure lb). The leaching experiment was started after
continuously application 6 g/L NaCl solution for 4 days when the entire column
reached a more-or-less uniform initial concentration, C;.
Breakthrough curves (BTC’s) were estimated from electrical conductance readings using a calibrated relationship between the specific concentration of a NaClsolution and the corresponding electrical conductance. The electrical conductance
was measured be means of electrical conductivity probes inserted laterally into thecenter of the columns at 50- and lOO-cm intervals in the homogeneous and heterogeneous columns, respectively. The platinum-blackened 5-mm diameter electrodes
with cell constants of either 0.9 or 1.1 l/cm were isolated from the surrounding
saturated soil by means of screened copper tubes (Figure lc). The clcctrical conductivity of the deaired tap water solution (equivalent to a 0. I54 g/L NaCl solution)
was considered negligible in the BTC data analysis.
The transport experiment in the homogeneous column was conducted in March,
1991, at a temperature 17 f2 “C. The injection and leaching experiments in the

EXPERIMENTAL INVESTIGATION OF SOLUTE TRANSPORT

289

TABLE I. Summary of hydraulic gradient (J), flow rate (q), porosity (n),ensemble average of the fitted pore-waler velocity (ii), and effective porosi-ty (c)
Experiment

Tracer injection inhomogeneous sandycolumnTracer injection inheterogeneous column(coarse + fine)
Leaching fromheterogeneous columnJqcmhr-’

n
-

0
cmhr-

c
-

0.0539

11.51

0.33

34.7

0.332

0.0488

14.33

0.37

61.6

0.233

0.0205

4.93

0.37

20.7

0.238

(fine + coarse)

heterogeneous column were carried out in May 1991, at average temperatures of

22 and 30 OC, respectively. The measured BTC’s for the homogeneous columns areshown in Figure 2, while those for the heterogeneous soil are presented in Figures 3
and 4 for the tracer injection and leaching experiments, respectively. The figures
show relative concentrations obtained by dividing observed concentrations by theconcentration (Co) of the applied tracer solutions or, in the case of leaching, by the
initial concentration (Ci).

3. Data Analysis
Assuming solute transport in a small-scale homogeneous medium, the dispersion
coefficient, D, can be readily determined by fitting appropriate analytical solutions of the CDE, equation (l), to the experimental data (e.g., Fried, 1975; Sauty,1980). More sophisticated approaches, such as the stochastic-analytic approachesof Dagan (1982) and Gelhar and Axness (1983), may be needed to determine theeffective flow and transport parameters of heterogeneous media using information
about the geostatistical properties of the hydraulic properties. Such information is
impractical to obtain for most or all field-scale transport problems (Sudicky andHuyakorn, 1991). In our study we also had no detailed information about the spatial distribution of the hydraulic conductivity and porosity, since only breakthroughcurves and steady Darcian flow rates, q, were measured.
In order to evaluate large-scale transport behavior without having detailed information of the hydraulic property distributions inside the columns, we applied, as

in the stochastic approach, a macroscopic mean transport equation with effective parameters. The macroscopic convection-dispersion equation with effective

290

K. HUANG ET AL.

7.5 8.5 9.5 10.5 ] 1.5 m,o0

x=1,0 2.0

3.0

4.0_

LO_ 6.Q

7.0

8.,0 9..0

5

10

15

20

25

30

10.0 Il..0 12.0 r

35

40

d

Time, t (hr)Fig. 2. Observed breakthrough curves for the tracer injection experiment in the homogeneous
sandy soil column.

constant parameters for tracer transport in a heterogeneous medium is given by(Moltyaner and KilIey, 1988; Jensen et al., 1993).

(3)
where (C) is the vertical mean concentration, while the subscript eff denotes aneffective parameter. Our approach here implies that the measured EC concentrations represent mean values as averaged over the relatively small (0.01 m2)
cross-sectional area of the columns. When the parameters of the mean transport
equation, (3), are determined from a breakthrough curve al a certain location, x,
they are affected by all of the flow and transport processes between the inlet position and that particular location. Therefore, the estimated effective parameters will
represent average values pertaining to the applicable travel distance (between 0 andx) and measurement time period. The spatial distribution of the resulting effective

EXPERIMENTAL INVESTIGATION OF SOLUTE TRANSPORT

291

Fig, 3. Observed breakthrough curves for the tracer injection experiment in the heterogeneous
soil column in which waler flowed from the coarse-textured end to the fine-textured end.
eo x- 0.5 m
1.5
ee
2.6
3.5
4.5
6.5
6.5
7.5
0.5

0-e

DfJ
IwJl
ma
bb
A--A
*-A

1....,....,..‘.,..‘.,.“‘,‘...,“.’,”..,..”,.’.~

IO

20

JO

40

50

60

70

60

90

100

110

Time, t (hr)Fig. 4. Obscrvcd breakthrough curves for the leaching experiment in the heterogeneous soilcolumn in which water flowed from the fine-textured end to the coarse-textured end.

parameters should in an approximate manner reflect the macroscopic lransport
properties of the heterogeneous medium.
Effective average pore-water velocities, v,rr, and dispersion coefficients, U,m,were estimated from the observed BTC’s in Figures 2, 3 and 4 using the nonlinear
least-squares parameter optimization code CXTFIT of Parker and van Genuchten(1984). This code was used to fit the analytical solution of the macroscopic CDE
for a flux-type inlet boundary condition, a uniform initial condition and a uniform
semi-infinite system, to the experimental data. The code enables one to fit V,K and292

K. HUANG ET AL.

L&m, simultaneously to the measured BTC data. We assumed negligible retardationof the NaCl tracer in the columns, i.e. R = 1 in (1) and I& = 1 in (3), since the soils
involved mostly coarse-&lured materials relatively free of organic matter. Oncev,~ and D,n were estimated from the BTC at a particular location, the apparent
dispersivity, (Y, was calculated using an equation similar to (2). Table II summarizes
the simultaneously fitted pore-water velocities and dispersion coefficients. The
coefficient of determination, r2, in this table reflects the goodness-of-fit (Spiegel,
1992, p. 263) as follows(4)
where the subscripts obs and est denote observed and estimated values, respeclively, the bar indicates a mean value, and where N is the number of observed
concentration data at a particular observation point.
4. Results and Discussion
The observed solute breakthrough data for the transport experiment in the homogeneous column (Figure 2) show relatively regular, sigmoidal (S-shaped) distributions at most measuring points. These distributions are consistent with CDE type
BTC’s usually observed for carefully packed, relatively short homogeneous soilcolumns.
The BTC’s for the injection experiment in the heterogeneous c o l u m n are shownin Figure 3. As compared to those for the homogeneous column, the observed
concentrations are much more irregular (less smooth) and exhibit nonsigmoidal
distributions. The BTC’s in many cases also do not reach the inlet concentration
within the experimental time period because of extensive tailing. The BTC’s inFigure 4 for the leaching experiment, starting from the opposite (i.e., fine-texlured)side of the heterogeneous column, show very similar features, i.e., irregular distributions with considerable tailing. One notable difference between Figures 3
and 4 is the lack of tailing in the BTC’s near the inlet position in Figure 3 (thecoarse-textured side), and the more pronounced tailing in the BTC’s near the inlet
position in Figure 4 (now the fine-textured side). This feature reflects the moreheterogeneous nature of the soil near the outlet as depicted in Figure 1, and therelatively homogeneous makeup near the inlet (recall that the flow direction in
the leaching experiments is opposite from that in the injection experiment). The
BTC’s in Figures 3 and 4 exhibit increased tailing and spreading as the transport
experiments progressed in time and distance.
Figure 5 shows plots of the fitted effective average pore-water velocity versus
distance for each of the three transport experiments. In the figure, V,N represents
the ensemble average of lhe fitted velocities derived from all measured BTC’s
during a particular experiment. We emphasize again that the use of an effective
pore-water velocities, vea, assumes that the medium between the inlet and theEXPERIMENTAL INVESTIGATION OF SOLUTE TRANSPORT293

TABLE II. Estimated effective average pore-water velocities, ucn, dispersion coefficients, L),[r, andcoefficients of determination, r*, for the three transport experiments
Distance,

Tracer injection in

Tracer injection in

Leaching f r o m

cm

homogeneous

heterogeueous column

heterogeneous

sandy column(coarse -+ fine)column(fine -+ coarse)wf
cm Iir-’LI err

hr-’

ciii*

r2

wf

-

cm hr-’

50

34.92

3.1

0.983

100

35.76

3.3

0.985

150
200

36.54

5.6

0.985

3G.48

8.0

0.992

250

35.92

14.1

0.995

300

36.08

18.6

0.994

u ell

hr-’

cm*

r*

VCll

-

cm ix-

67.1

185

0.984

67.7

867

0.937

63.2

807

0.950

350

35.83

20.2

0.996

64.6

1444

0.909

400

35.76

27.1

0.996

62.7

1405

0.929

69.4

1394

0.936

450

35.42

31.5

0.997

500

35.28

39.3

0.998

550

35.56

48.3

0.997

600

39.14

52.6

0.997

650

34.24

73.7

0.990

700

34.00

77.0

750
800

34.15
33.83

68.8

5075

0.920

0.993

49.7

11180

0.984

104.8
122.2

0.992
0.997

66.3

10860

0.956

60.1

6084

0.97s

54.1

5800

0.980

53.8

7174

0.983

53.2

6297

0.963

850

33.1 I

128.8

0.998

900

34.19

108.3

0.998

950

33.70

122.1

0.998

1000

33.44

139.3

0.993

1050

33.50

139.8

0.998

1100

33.03

120.0

0.99s

1150

33.20

162.5

0.996

I200

33.63

165.6

0.992

1250

u dr
ciii*

rz
Iir-’

-

16.3

482

0.953

8.2

751

0.927

19.3

4743

0.980

24.1

2348

0.972

25.5

1676

0.970

22.3

3338

0.960

29.0

6793

0.926

20.7

4683

0.968

20.9

3865

0.970

20.9

3852

0.970

20.8

3693

0.950

20.9

3293

0.943

20.2

3780

0.940

observation point is homogeneous so that the macroscopic transport equation (3)can be invoked. Still, the fitted Vem should be different from one point to anothersince the nonhomogeneities in the columns change with the transport distance ormeasurement scale. Notice that VeK for the homogeneous sandy c o l u m n is almost
constant with distance. This is not surprising since the sand used for this column
had a relatively uniform particle size, whereas also considerable care was laker1 lo
pack lhe column as homogeneously as possible. Table II lists the siulultaneously
deterrnined values of Vem and Deg. We also estimated the dispersion coelficient foreach I3TC by assunling a fixed value for the pore-water velocity as calculated frontv = q/n in whicl! q is lhe nleasured Darcian llux (Table I) and 11 the porosily (0.33)

294

K. HUANG E T AL.

A?.--*_**__*--A.

_. l .

y_&.*,’

,*’

‘,

.,
,

\*
*

,’

,h.

,#’
\\ ‘ ‘
‘, ,’h’V.,, = 61 .6 cm/hr

..

k

‘.

..

*-----A---__*

.
l -

_-

I

0

/II)----- I --._

,r=\B.,, = 34.7 cm/t1r-C-*-4--.__~_-*-4-~--.-_*__*-O..-‘(C-~-~-~--o--~-~_*_~--~.

\ .\

‘d’

#’

,’

-a*’

,’

.y

‘. \

******___*******)*.

V.,, = 20.7 cm/k‘b_____ )____._____“..___.____
Transport In homogeneous column
Transport In heterogeneous column
Leaching In heterogeneous column

I

,

,

I

I

I

200

400

600

600

1000

1200

Distance, x (cm)Fig. 5. Fitted effective pore-water velocity versus distance for the three transport experiments.
The parameter ~~1 represents the ensemble average velocity.

of the homogeneous column. The fitted dispersion coefficients thus obtained forthis column (results not further shown here) were found to be very close to thoselisted in Table II for the simultaneous fit.
Contrary to the homogeneous column, values of ‘u,~ for the tracer injection andleaching experiments in the heterogeneous column varied quite dramatically with
distance. The results in Figure 5 show a slowly increasing or decreasing trend with
distance, depending on whether flow took place from the coarse-tcxlurcd (left) side
to the line-textured (right) side in Figure lb, or vice versa. Although the fitted v,rfvalues represent average flow velocities from the inlet position lo the measurement
location, some dramatic variations are apparent along the column. These variations
in ven can be related directly lo lhe heterogeneities embedded in lhe columns. For
example, the significant changes in the flow velocity at approximately x = 1.5
and 6.45 m for the leaching experiment (see Figures 1 b and 5; lhc coordinate
in Figure lb runs now from right to left) must have been a consequence of thelocally very heterogeneous nature of the medium. The relatively coarse backgroundmaterial in these two parts of the column contained several clay lenses and othermixtures with widely different hydraulic propcrtics. The resulting heterogeneous
makeup of the medium causes the flow regime to become two- or three-dimensional,
with concomitant variations in 21,fl.

EXPERIMENTAL INVESTIGATION OF SOLUTE TRANSPORT295

The effects of heterogeneity on the transport process can also bc demonstrated
by considering the effective porosity given by 6 = Q/v,~, where q is the imposedwater flux, and 4~ is thc ensemble average of fitted pore-water velocities estimated frotn the BTC’s at all tneasuring points (see Table II). Table I summarizes
the calculated effective porosities for the three tracer experiments. As mentioned
before, t h e measured porosity n of the individual soils used in the experiments
was approxitnately 0.45 for the clay, attd 0.33 for most of the other soil materials,
including the sand used for tltc homogeneous column. Given these values and theamounts of each soil type used in the two columns, we estimate the average n to beabout 0.33 for the homogeneous sandy soil column, and 0.37 for the heterogeneous
soil colutnn. Tlte effective porosity (c = 0.33) was the same as the independently measured value of the porosity, n, for the homogeneous column. In contrast,
the calculated effective porosities for the heterogeneous column (c was 0.233 and0.238 for the injection and leaching experiments, respectively) were much smallern = 0.37) for the heterogeneous column. The reduced
that the estintated porosity (neffective porosity for the heterogeneous column was probably caused by mixing
of soil materials of significantly different particle sizes during packing, cloggingof large pores by relative small particles, and the likely presence of relatively
immobile water in low-permeability clay lenses.
Figure 6 contpares typical observed and fitted breakthrough curves for the threetransport experiments. The agreement between the observed and fitted curves forthe homogeneous column (Figure 6a) was excellent for all BTC’s, with most r2
values exceeding 0.99 as indicated in Table II. The excellent description of thedata indicates the general applicability of the CDE equation to transport in thehomogeneous column. By comparison, relatively poor description of the observed
BTC’s were obtained for the heterogeneous column (Figures 6b, c), except inFigure 6b at relatively short travel distances (x <3 m). The descriptions were especially poor at later times when tailing was most pronounced. The discrepancies
between the observed and fitted BTC’s for the heterogeneous column are an obvious consequence of textural heterogeneities both along and perpendicular to themacroscopic flow direction. These heterogeneities combine to produce preferential
flow and related ‘physical nonequilibrium effects as discussed by van Genuchten
and Cleary (1979) attd Brusseau et al. (1989). among others. Physical nonequilibrium is often modeled using a dual-porosity (or two-region) approaclt in which themedium is partitioned into distinct mobile and immobile (stagnant or non-moving)liquid regions (e.g., Coats and Smith, 1964; van Genuchten and Cleary, 1979). The
effects of physical nonequilibrium are cumulative during transport and can lead toconsiderable tailing as t h e transport process proceeds in time and space.
As discussed before, most of the breakthrough curves for the homogeneous
colutnn ltad signtoidal shapes. However, several BTC’s in the homogeneous column
also sltowed sonte effects of preferential flow. Figure 7a presents the measured
BTC’s between x = 7.5 and 9.0m. Notice that the BTC’s at x = 8.5 m and 9.0 m
are very close and even crossed each otltcr at approximately t = 30 hr. This fact

K. HUANG ET AL.

Distance, x (cm)Fig. 8. Calculated dispersivilies as estimated from the filled effective dispersion coefficientsand velocities for the homogeneous sandy soil column.

implies the presence of some preferential flow between x = 8.5 and 9.0 m. Similar
observations of preferential flow in large uniformly packed soil columns were also
made by Porro et al. (1993). in their case for vertical transport. These results show
that, in practice, it is very difficult to achieve complete homogeneity when packing
relatively large soil columns. For the same reason it is also difficult to imagine
the existence of a truly homogeneous aquifer formed in the field by natural forces.
Hence, the term ‘homogeneous aquifer’ as commonly used in hydrogeoiogicalstudies does not necessarily imply a uniform transport process consistent with suchclassical theories as the CDE model.
Much more irregular breakthrough curves were obtained for the heterogeneouscolumn. Figures 7b and 7c present several cases where the observed BTC’s atdifferent locations cross each other. For example, Figure 7b pertaining to theinjection scenario shows that the concentrations at x = 7.0 m were always lower
than those at x = 8.0 m, and also lower than those at x = 9.0 m for t > 17 hr. For theleaching experiment (Figure 7c), the concentrations at x = 4.5 m decreased much
faster than those at x =2.5 and 1.5 m for t > 15 hr. Note also that the BTC at x =1.5 m in Figure 7c at first increased before decreasing in response to the imposedleaching process. The above irregularities and tailing phenomena are a result of
the nonuniform velocity distribution caused by the heterogeneous nature of themedium, i.e., the presence of clay lenses and various types of sand, silt and clay
mixtures in different parts of the column. We also note here that the EC-measured
concentrations represent only small sampling volumes in the column; hence, theobserved BTC may not accurately reflect average concentrations, (C), over eachcross-section as presumed in the data analysis based on equation (3). This failure of
the EC measurements lo represent average concentration undoubtedly contributed
to the irregular distributions observed for the heterogeneous column.
Figure 8 shows a plot of the apparent dispersivity, (Y, versus distance in thehomogeneous sandy column. Values of (Y range from 0.1 to 5.0 cm. These values
are the same or slightly higher than dispersivities usually observed for transport in299

EXPERIMENTAL INVESTIGATION OF SOLUTE TRANSPORT
250l-v-

200
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3
CJ

150

Pt
.:
‘E

100

E.
.r
n

50,
,*4-m4

b,

0

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5

,

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200

,.

400

.

:

,

600

.

,

800

Distance. x (cm)

.

,

64

1000

I

.#.I.,.,. j

I

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200

400

600

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1000

1200

Distance, x(cm)Fig. 9. Calculated dispersivities as estimated from the fitted effective dispersion coefficientsand velocities for the injection (a) and leaching (b) experiments in the hclcrogcncous soilcolumn.

relatively small, homogeneous laboratory soil columns. Notice that the dispersivity
increased with the measurement scale, especially between x = 6 and 8 m where
we previously noted the presence of some preferential flow. The marked increasein (Y near x = 7 m suggests that preferential flow may play an important partin the development of a scale-dependent dispersion process. An increase in thedispersivity with the measurement scale during transport in a large unsaturated,uniformly packed soil column (6.0 m deep by 0.95 m diameter) was also found by
Porro et al. (1993). The dispersivity in their study increased from 2.2 cm at a depthof 82 cm to 7.8 cm at 400 cm.
In marked contrast to the homogeneous column, the dispersivities for the heterogeneous column were much higher and fluctuated greatly, ranging between 3
and 130cm for the injection experiment (Figure 9a), and between 20 and 200cm
for the leaching experiment (Figure 9b). The dispersivities for both experiments
also exhibit scale-dependency as was the case for the sandy column. The fluctuations in cy as shown in Figure 9 appear to be the result of the particular makeup of
the heterogeneities in the column. For example, (Y increases significantly when theheterogeneities appear in the form of nearly horizontal lenses more or less parallelto the flow direction. Solute spreading in those instances is enhanced because ofincomplete lateral solute mixing over the entire cross-sectional area of the column(Jury and Fluhler, 1992). On the other hand, the presence of layers perpendicular
to the flow direction, or of relatively homogeneous parts in an otherwise heterogeneous column, has a decreasing effect on cr (e.g., compare Figures 1 b and 9a at
x = 9 m). This last feature is consistent with observations by Parker and Albrecht(1987) and Porro et al. (1993) that layering perpendicular to the transport direction
may actually decrease apparent dispersion (or even lead to sharpening of a solute
BTC). Finally, we note from Figures 9a, b that, at the same travel distance, thedispersivity for the leaching experiment (starting from fine-textured end of the300

K. HUANG ET AL.

heterogeneous column) is generally higher than (Y for the injection experiment(starting from the coarse-textured end). While some effect of the flow direction
on the dispersivity is apparent and intuitively logical, the results in Figure 9 do
not relate in an obvious manner with the physical makeup of the heterogeneouscolumn (Figure 1 b) to permit more definite statements.
5. Conclusions
Tracer experiments were conducted in 12.5-m long homogeneous and heterogeneous saturated soil columns during steady confined flow. Three experiments werecarried out: (1) transport of a NaCl solution into a homogeneous sandy column,(2) transport into a hclcrogcneous column containing a variety of materials whose
particle size, on average decreased from very coarse at the inlet position lo veryfine at the outlet position, and (3) leaching of solute from the same heterogeneouscolumn, but with flow now in the opposite direction. Effective average pore-waler
velocities and dispersion coefficients were determined simultaneously by fitting
the macroscopic CDE to breakthrough curves observed at regular intervals along
the horizontally placed columns.
The observed BTC’s for the homogeneous sandy column were relatively smoothand sigmoidal, although a few curves showed some tailing and/or crossing of
BTC’s, thus indicating the presence of some preferential flow in the homogeneouscolumn. Excellent agreement was obtained between the observed and fitted CDE
curves for this column. The dispersivity of the homogeneous c o l u m n increased
with the measurement scale from 0.1 to 0.5 cm, whereas the average pore-watervelocity was essentially constant throughout the column. These results suggest thatsome preferential flow and scale-dependent dispersion are likely to occur in mostgroundwater systems, even if seemingly homogeneous.
As opposed to the homogeneous column, BTC’s for the heterogeneous column
were more irregular, nonsigmoidal, and exhibited extensive tailing and crossing ofdifferent curves. The observed BTC’s for this column were in most cases poorly
described with the CDE model. Fitted effective average pore-waler velocities varied rather erratically with distance, while the dispersivities (varying between 3 andabout 200 cm) were much higher than those for the homogeneous sandy column.
Dispersivities for the tracer injection and leaching experiments in the heterogeneous column also exhibited a scale-dependency, similarly as for transport in the
sandy column. Estimated dispersivities for especially the heterogeneous column
were found to be much higher than those commonly obtained for relatively shortlaboratory soil columns. Spatial variations in the dispcrsivity could be explained
qualitatively by the particular makeup of the heterogeneities in the column. For
example, the dispersivity generally increased with distance in regions where lhesand layers and clay lenses were situated approximately parallel to the flow direction, but decreased (leading to BTC front sharpening) in regions where the layers
were mostly perpendicular to the flow direction.

EXPERIMENTAL INVESTIGATION OF SOLUTE TRANSPORT

301

Acknowledgements
This work was supported in part by the National Science Foundation of China
under grant NSFC-0488012, 1989. The assistance in the experimental work by
Zhen-Guang Huang and Si-Hong Liu of the Department of Geology and Mining
Engineering, Fuzhou University, China is sincerely appreciated.

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