migration of saline solutions in variably saturated porous media

www.elsevier.com/locate/jconhyd

Journal of Contaminant Hydrology 72 (2004) 109–133

Migration of saline solutions in variably saturated

porous media

Noam Weisbroda,*, Michael R. Niemetb, Mark L. Rockholdc,Thomas McGinnisd, John S. Selkerd

aDepartment of Environmental Hydrology and Microbiology, Institute for Water Sciences and Technologies,

Jacob Blaustein Institutes for Desert Research, Ben-Gurion University of the Negev,

Sede Boquer Campus 84990, IsraelbCH2M HILL, Corvallis, OR 97330, USA

cPacific Northwest National Laboratory, Richland, WA 99352, USAdDepartment of Bioengineering, Oregon State University, Corvallis, OR 97331, USA

Received 12 November 2002; received in revised form 1 October 2003; accepted 31 October 2003

Abstract

Migration of concentrated NaNO3 solutions in homogeneous packs of pre-wetted silica sands was

investigated using a light transmission system. Solutions of 5 molal NaNO3 were found to migrate

downward 24–62% faster than pure water, in an unstable, fingered manner. This behavior was

attributed primarily to a surface tension induced, non-zero apparent contact angle between the

imbibing and the resident fluids. For saline solutions of similar surface tension to that of pure water

(achieved by the addition of 2% methanol), the migration rates and plume shapes were comparable to

that of water, demonstrating that density was not the primary source of the observed differences in

migration patterns. At depths where resident saturation increased above residual, the migration

process appeared to occur via film flow with slight changes in saturation ( < 4%), rather than in a

series of abrupt jumps, as observed at shallower depths. A method for contact angle scaling was used

to illustrate the effects of non-zero contact angles on capillary pressure–saturation curves.

D 2003 Elsevier B.V. All rights reserved.

Keywords: Interfacial tension; Contact angle; Saltwater; Moisture content; Film flow; Capillary forces

1. Introduction

Highly concentrated solutions of electrolytes are rare in natural environments; it is

uncommon for concentrations resulting from agrochemicals and other contaminants to

0169-7722/$ - see front matter D 2003 Elsevier B.V. All rights reserved.

doi:10.1016/j.jconhyd.2003.10.013

* Corresponding author. Tel.: +972-8-6596903; fax: +972-8-6596909.

E-mail address: [email protected] (N. Weisbrod).

N. Weisbrod et al. / Journal of Contaminant Hydrology 72 (2004) 109–133110

exceed 0.5 mol/l. An extreme case exists at the Hanford Nuclear Reservation, in southeast

Washington State, where more than 4 million liters of highly saline solutions have leaked

from radioactive waste storage tanks over the last 50 years. These caustic solutions are

typically extremely saline (>5 mol/l) and have migrated into the underlying vadose zone.

They have been identified in the local groundwater system, at a depth of roughly 60 m

below the ground surface in some areas (GJPO, 1996). Although this represents an

extreme case, migration of highly saline solutions is also likely to be of concern at selected

landfills, industrial complexes and other waste facilities. This paper explores experimen-

tally and conceptually the processes that control the initial disposition of such highly

concentrated solutions as they penetrate unsaturated porous media.

Several factors should be taken into account when considering migration of highly

saline solutions in the vadose zone: (1) the density, viscosity and surface tension of the

infiltrating solution; (2) the effective contact angle between the advancing saline solution

and the interface with which it is wetting; (3) gradients in vapor pressure between the salty

plume and the surrounding pore-water (Weisbrod et al., 2003); (4) dispersion and

diffusion; and (5) the potential release of colloidal particles from the solid surfaces due

to the rise and fall of the local ionic strength (e.g., Blume et al., 2002).

Surface tension is an important parameter affecting flow in unsaturated porous media.

Past studies have focused on compounds that tend to reduce surface tension. For example,

dissolved organic compounds reduce the surface tension at gas–liquid interfaces and have

a significant affect on unsaturated flow (Dicarlo et al., 2000; Smith and Gillham, 1994,

1999). Selker and Schroth (1998) found that the effective contact angle of liquid entering

dry sand was far from zero and that hydrodynamic scaling based on fluid viscosity, surface

tension and density are not sufficient to account for the effect of liquid–air interfacial

tension. Very little work has been devoted to the study of the mechanisms that control

migration of high surface tension (saline) solutions. Ouyang and Zheng (1999) considered

saline solutions in model systems; however, surface tension and contact angle were

neglected. Only the impact of solution density was investigated and was found to have a

negligible effect on transport of aldicarb (relatively low solubility), but a significant effect

on transport of acephate (relatively high solubility).

This paper focuses on the relative rates of migration of highly saline solutions as

influenced primarily by factors (1) and (2) above, which are the most immediate, short

time processes. Some very interesting longer time frame issues are explored in Weisbrod et

al. (2003). In this paper, the migration patterns of various infiltrating solutions are

compared for four sand textures. Hypotheses and mechanisms for the observed phenom-

ena are then discussed.

2. Capillary pressure in unsaturated porous media

For primary wetting into previously dry porous media, the interface between liquid and

a pore, in a pore of mean radius r, requires that at equilibrium:

pc ¼ pg � pl ¼2ðrsg � rlsÞ

rð1Þ

N. Weisbrod et al. / Journal of Contaminant Hydrology 72 (2004) 109–133 111

where pc is the change in pressure across the gas–liquid interface, pg is the pressure in

the gas phase, pl is the pressure in the liquid phase, rsg is the interfacial tension of the

solid–gas interface and rls is the interfacial tension of the liquid–solid interface. For

most systems, the interfacial tensions, rsg and rls, cannot be measured accurately.

Therefore, it is typically sought to express Eq. (1) in terms of readily available

parameters. In most gas– liquid–solid capillary systems, these parameters are the

liquid–gas interfacial tension and the contact angle between the liquid–gas interface

and the solid.

Young’s equation states that for contact between a liquid–gas interface and rigid solid

at equilibrium

rsg ¼ rls þ rlgcosc ð2Þ

where rlg is the interfacial tension between the liquid and the gas phases and c is the

contact angle of the liquid–gas interface with the solid. Combining Eqs. (1) and (2)

yields:

pc ¼ pg � pl ¼2rlgcosc

rð3Þ

For a given pore size, the capillary pressure depends on the interfacial tension between

the liquid–gas interface, the density of the fluid and the contact angle. If rlg and c are

known, rsg and rlg can be evaluated numerically using an equation of state approach

(Spelt et al., 1992).

The interfacial tension between the liquid and the gas phases, rlg, increases with

electrolyte concentration. The magnitude of this change depends on the type and

concentration of salt (Lide, 1991). Increases in the ionic strength of an imbibing

solution may also increase the contact angle. The magnitude of such changes depends

on the liquid properties and the wettability of the solid surface (e.g., Butkus and Grasso,

1998). Selker and Schroth (1998) found that the apparent contact angle also might vary

as a function of migration rate and can be non-zero even for pure water. Recent work by

Hassanizadeh et al. (2002) indicates that dynamic effects in capillary pressure–

saturation relationships may also have a significant impact on unsaturated flow. Such

dynamic effects could be accentuated for saline solutions infiltrating into water-wet

porous media. These dynamic effects may be due, in part, to dynamic changes in the

effective contact angle during the migration process. Although both liquid–gas

interfacial tension and contact angle generally increase with the electrolyte concentra-

tion, the relationships between these changes are largely unknown. The determination of

contact angles on soil surfaces is known to be problematic (Drelich et al., 1996;

Morrow, 1975). Furthermore, the relationship between apparent contact angle and

capillary pressure (interfacial curvature) at pore walls has been shown to be non-

constant or hysteretic (Philip, 1971).


3. Materials and methods

3.1. Experimental setup

A light transmission system was used to quantify liquid content within 2D flow cells in

space and time. The light transmission system consisted of three primary components:

chamber, light source and detector (Fig. 1a). The media-containing portion of the light

transmission system, referred to as the chamber, consisted of two 1.27-cm-thick� 50.0-

Fig. 1. (a) Major optical components of the light transmission system and (b) exploded and assembled views of

the light transmission chamber.


cm-wide� 65.0-cm-high glass panels separated by a 1.0-cm-thick U-shaped aluminum

spacer. The glass sheets were sealed to the spacer by 4.8-mm diameter rubber O-ring stock

contained within continuous channels machined on both faces of the spacer. A drain-port

through the bottom of the spacer allowed exchange of fluid within the system. A 1.0-cm-

thick acrylic manifold topped with 200-mesh stainless steel wire screen provided the lower

media boundary. The chamber components were compressed together within a rubber-

lined aluminum frame. The resulting inner chamber thickness was 1.0 cm (Fig. 1b). All

aluminum parts were anodized black to avoid reflections.

The light source, to which the chamber was mounted, consisted of eight fluorescent

tubes (Philips F17T8/TL835, 61 cm) within a black sheet metal enclosure. The detection

system utilized a thermoelectrically cooled 14-bit gray-scale digital CCD camera (ISI

Systems, Santa Barbara, CA) with a Kodak KAF0400 (768� 512 pixel) scientific grade

CCD array. The distance from the chamber to the camera lens (Nikon, 50 mm, F1.4-16)

was 4 m. All images were obtained through a 620-nm center-wavelength, 10-nm band-

pass, filter (OrielR 53930, Stratford, CT) installed in the camera’s internal filter wheel. In

all cases, the lens aperture setting was F4 and exposure times varied from 0.8 to 1.8 s

depending on media type. With this system geometry, each pixel on an image represented

1 mm2 of chamber surface area.

The media used was AccusandR (Unimin, Le Sueur, MN); well-defined, homogenous,

translucent silica sands in 12/20, 20/30, 30/40 and 40/50 grades. Major physical and

mineralogical properties of the sands are summarized in Table 1. A more-detailed

description of the AccusandR properties can be found in Schroth et al. (1996). Preparation

of the sand consisted of rinsing with deionized water 8–10 times, until no turbidity was

observed in the supernatant. Next, the sand was dried in an oven at 45 jC for 48 h. No

other chemical treatments were performed to remove colloidal materials and oxides from

the sand grains.

Five solutions were used for the migration experiments. These solutions are

identified as: (A) 5 molal NaNO3; (B) 5 molal NaNO3 with 2% methanol by

volume; (C) distilled, deionized, water (NANOpureR 04751, Barnstead Thermolyne);

(D) 2 molal NaNO3; and (E) 0.75 molal NaNO3. Note that the NaNO3 was chosen

due to its high concentrations in the Hanford radioactive wastes. The molal

concentrations represent moles of salt per kilogram of water. The physical properties

Table 1

Accusand and packed chamber properties

12/20 20/30 30/40 40/50

Particle diameter, d50 (mm)a 1.105 0.713 0.532 0.359

Uniformity coefficient (d60/d10)a 1.231 1.130 1.207 1.200

Particle density (g/cm3)a 2.665 2.664 2.665 2.663

Total Fe (g/kg)a 9.31 7.64 7.65 5.58

Ks (cm/min)a 30.19 10.02 8.94 4.33

Porosity 0.342 0.335 0.337 0.340

Capillary fringe depth (height)b 47.5 (7.5) 41.5 (13.5) 37 (18.0) 32 (23.0)

zf (cm) 44 37 29 22

a From Schroth et al. (1996).b cm above zero pressure level.

Table 2

Solution properties

Solution Composition Density

(g/cm3)

Viscosity

(cp)

Fluid mobility

ratio

Surface tension

(mN/m)

A 5 molal NaNO3 1.247 1.314 0.96 80.54

B 5 molal NaNO3 + 2%

methanol

1.199 1.034 1.17 70.28

C Pure water 0.993 1.001 1.00 72.8

D 2 molal NaNO3 1.095 1.117 0.99 75.19

E 0.75 molal NaNO3 1.037 1.036 1.01 73.69


of the solutions and a summary of the experimental details are given in Tables 2 and

3, respectively. Viscosity (GilmontR low shear falling ball viscometer), density and

surface tension (pendent drop technique on a KrussR Automated Goniometer DSA

10) were measured for each of the solutions (ThetaDyne, Charlotte, NC). Although

the solution properties were measured prior to interaction with the AccusandR, the

low organic content of the sand (b1%) suggest that no significant variation in those

properties are likely to occur. The addition of nitrate to the solutions raised the

surface tension and viscosity of the solution by promoting hydrogen-bonding strength.

This was offset by the addition of Methanol (surface tension of 25 mN/m) to solution

B to reduce the surface tension. The addition of 2% methanol (by volume) to a 5

molal NaNO3 solution lowered the surface tension to approximately that of pure

water, while only slightly lowering viscosity and density (Table 2).

The relative mobilities of different fluids can be estimated from ratios of kinematic

viscosities, (q‘/l‘)/(qw/lw), where q is the fluid density, l is the dynamic viscosity, and the

subscripts ‘ and w denote the fluid of interest (e.g., NaNO3 solution) and pure water,

respectively (Table 2). The relative mobility of the 5 molal NaNO3 solution is 0.96, which

indicates that this solution is actually less mobile than pure water, in spite of its higher

density, due to its much higher viscosity. The relative mobility of the NaNO3 solution

containing 2% methanol is 1.17, which indicates that this solution is the most mobile of

those tested. It should be noted, however, that these estimates of relative mobility do not

consider surface tension, wettability, or contact angle effects, which are discussed in more

detail with the experimental results.

Table 3

List of experiments reported, indicating the sand, pre-wetting solution and solutions applied, as well as the

number of images taken and the light transmission calibration parameter

Exp. no. Sand grade Pre-wetteda Left plume Center plume Right plume Number of frames Ires/Is

1 12/20 C A C B 77 0.336

2 20/30 C A C B 66 0.230

3 30/40 C A B C 52 0.141

4 40/50 C A C B 48 0.098

5 30/40 C A D E 60 0.154

6 40/50 A A C B 57 0.075

7 30/40 C A None B 78 0.135

a See solution properties in Table 2.


3.2. Experimental procedure

The salient experimental conditions of seven experiments (Experiments 1–7) are

summarized in Table 3. To insure reproducibility, three additional experiments were

carried out as repetitions of Experiments 2–4. These results were consistent with the first

experiments and are not discussed for reasons of brevity.

In all experiments, the chamber was prepared and packed with a single sand grade as

described in Niemet and Selker (2001) and Weisbrod et al. (2002). The pore space was

purged with at least 10 pore volumes of CO2 gas, slowly delivered through the lower port.

Next, distilled water (solution C) was delivered through the same port at f 20 ml/min

until the media was saturated, with the exception of Experiment 7, in which solution Awas

used for the wetting process. To ensure complete saturation and removal of dissolved CO2,

four additional pore volumes of water were passed through the sand. The porosity of each

pack (Table 1) was determined based on the volume of fluid required to saturate the sand,

the mass of sand and the overall internal volume of the chamber. Images were taken prior

to and following saturation in all experiments, which were termed the ‘‘dry’’ and

‘‘saturated’’ images, respectively. After saturation, the chamber was allowed to slowly

drain ( < 10 ml/min) for 24 h, with the zero-pressure level held at the height of the

manifold’s upper surface. Following drainage the outflow pipe was closed in all experi-

ments, excluding Experiment 7. The vertical extent of saturated media (capillary fringe

height) ranged from 7.5 to 23 cm above the manifold surface, depending upon sand grade

(Table 1).

Typically, three evenly spaced 5-ml solution applications (Table 2) were dripped at a

rate of 1 ml/min onto the surface of the sand. In Experiment 7, only two solutions were

used (Table 3). An image was taken immediately after application, followed by imaging at

10-min intervals for the first 3 h after the injection, at 1-h intervals from 3 to 24 h after the

injection, at 2-h intervals from 24 to 48 h after the injection and at 3-h intervals from 48 to

72 h after the injection. In some of the experiments, additional images were taken after 72

h. The total number of images ranged from 48 to 78 per experiment (Table 3).

3.3. Image processing and data analysis

Post-experiment image processing to determine liquid saturation from the raw data

images was performed using the method of Niemet and Selker (2001). After removing the

bias and dark signals from the images, the relative degree of light transmission, I/Is, was

computed on a pixel-by-pixel basis, where I represents the transmission image of interest

and Is represents the saturated image. The log-scaled relative degree of light transmission,

X, was then determined as

X ¼ lnI

Is

� ��ln

Ires

Is

� �ð4Þ

where, Ires/Is is the average relative light transmission at residual saturation (Sres),

determined for each experiment from the image immediately prior to application of the


infiltrating solutions (Table 3). The effective saturation, Seff, was computed from a fourth-

order polynomial approximation, unique to each of the sands,

Seff ¼ aX4 � bX3 þ cX2 � dX þ 1 ð5Þ

where a, b, c and d are polynomial coefficients and Seff is the saturation scaled between

residual and complete saturation (Seff = 0 at Sres and Seff = 1 at S = 1). Eq. (5) implicitly

accounts for the effect of the pore size distribution on drainage. The apparent liquid

saturation, S, was then determined by

S ¼ Seff ð1� SresÞ þ Sres ð6Þ

All of the parameters needed to compute S from the above equations are shown in Table 4.

To best distinguish the infiltrating plumes, DS images were computed by differencing

between each saturation image and the saturation image immediately prior to the solution

applications (S0).

DS ¼ S � S0 ð7Þ

The processed images provide a pixel-by-pixel spatial distribution of the changes

in apparent saturation. The resulting DS maps were produced using a 16-band custom

color palette. Changes in apparent saturation from 0% to 32% are shown, with each

band representing a 2% change. The color scale proceeds from violet (least change)

to red (greatest change), with black reserved for the 0–2% interval. For each

experiment, there exists typical DS variability, from image to image, for pixels at

which there is no change in apparent saturation. This variability is a function of

saturation and grain size and is the composite effect of numerous sources of noise

inherent to the system. Hence, for each experiment, there is a minimum change in

apparent saturation for which a true change cannot be distinguished from a random

variation at a pixel (termed DSmin). We found the standard deviation of the pixels in

the earliest DS image for each experiment, for which there was no change, to be

equal to about 0.005, for all sands. The DSmin value was chosen to be four times the

standard deviation, or 2% saturation, for all of the experiments. All image processing

was performed using Transform 3.4 (Fortner Software LLC).

Table 4

Selected properties of the AccusandsR required for determination of liquid saturation from light transmission

(from Niemet and Selker, 2001)

Sand Sresa a b c d

12/20 0.034 0.87 1.45 1.00 1.42

20/30 0.046 0.57 0.94 0.64 1.27

30/40 0.052 0.26 0.39 0.29 1.16

40/50 0.057 0.19 0.24 0.19 1.14

a From Schroth et al. (1996).


Wetting front depth is defined here as the location of the tip of the plume where

DSzDSmin. To better distinguish the wetting front contours, two smoothing passes were

performed on the DS images. In each smoothing pass, every pixel was averaged with its

eight nearest neighbors. Incremental wetting front velocities, vi, were calculated from the

vertical distance traveled by the wetting front over the time between consecutive images:

vi ¼zi � zi�1

ti � ti�1

ð8Þ

These velocities describe the dynamic behavior of the plumes as they evolve and provide

information about the flow process within a restricted depth interval for the conditions at

that time.

It should be noted that high concentrations of salts increase the index of refraction of the

liquid and consequently affect the saturation values measured using the light transmission

method. As the index of refraction of the liquid increases, it approaches that of the

translucent sand particles, resulting in less interfacial losses as the light passes between

solid and liquid phases (Niemet and Selker, 2001). The result will be a net increase in

transmitted light provided that the media is close to saturation. However, an increase in the

index of refraction of the liquid will create a greater differential between the index of

refraction of the gaseous phase and increase the interfacial losses between the liquid and

gaseous phases. Hence, relative to pure water, an increase in the index of refraction can be

expected to produce an increase in transmitted light when the media is nearly saturated and a

decrease in transmitted light when the media is near residual saturation. The magnitude of

the change in light transmission for a given salt depends on both the salt concentration and

the degree of liquid saturation and cannot be accurately corrected for at this time. While this

will affect apparent saturation values predicted from light transmission and would be of

concern if precise mass balances were required, it does not significantly affect the

delineation of the plumes.

4. Results

4.1. Residually saturated zone

Images showing the changes in apparent saturation (DS) following application of the

solutions are shown in Figs. 2–5, for sand grades 12/20 (Experiment 1), 20/30

(Experiment 2), 30/40 (Experiment 3) and 40/50 (Experiment 4), respectively. The first

image (time = 0) was taken immediately after the solution application was completed. The

infiltrating fluids in these experiments were A, C and B, from left to right (except

Experiment 3, Tables 2 and 3). The resident fluid was distilled water, C. Wetting front

depth as a function of time for these four experiments is presented in Fig. 6. From Figs. 2–

6, it is clear that, in all four experiments, solution A migrated downward faster than B and

B faster than C. Modification of the application location (A, B, C—from left to right), as

demonstrated in Experiment 3 (Fig. 4), had no influence on the relative migration rates,

showing that packing variations across the width of the chamber were negligible.

Fig. 2. Three frames from Experiment 1. Solutions A, C and B (left to right, respectively) were applied to 12/20

sand pre-wetted with pure water C. Time from end of application is noted above each frame. The pseudo-

colorized images describe the apparent changes in saturation (DS) with respect to before solutions were applied.


Since the imaging time sequence was similar for all the experiments, the incremental

wetting front velocities can be directly compared at a given time, from the slopes of the

curves on Fig. 6 (note the data triplets at each time). Also, velocities can be compared at




Arrow denotes the secondary plume.




Arrow denotes the secondary plume. Note that fluid from plume A developed a flow path along the left side of the

chamber.

Fig. 4. Three frames from Experiment 3. Solutions A, B and C (left to right, respectively) were applied to 30/40



Arrow denotes the secondary plume.



unique depths by fitting a continuous function through the data. Comparing velocities

between sand grades is complicated by two main factors. First, the depth in the chambers

available for unsaturated migration is less for the finer sands than for the coarser grades. This

is evident in the characteristic curves (saturation vs. depth) of each of the sands, shown in

Fig. 7. Finer sands have higher native water contents with depth. Time-based comparison

between sand grades can be problematic since the solutions penetrate deeper into the coarser

sands in much less time than in the fine sands; note the time sequences of Figs. 2–5.

Perhaps the best region for the relative comparison of wetting front velocities is within the

upper region of the chambers where the sand was at residual saturation, corresponding to the

first 20 cm of depth in all sands. In the 12/20 sand, the wetting fronts had traveled nearly 20

cm by the time the 5-min injection period was completed. Hence, for comparison in this

region, the wetting front depths and corresponding velocities between the first (immediately

following injection) and second images (10 min after first image) are compared. In all cases,

the velocities during this interval represent the maximum measured velocities of all wetting

Fig. 6. Wetting front depth of solutions A, B and C for Experiments 1 (12/20), 2 (20/30), 3 (30/40) and 4 (40/50),

(a) to (d), respectively. Capillary fringe depth prior to the experiment is noted (as CF, above the solid line) as well

as the transition depth where the secondary finger developed (zf, dashed line).

0.0 0.2 0.4 0.6 0.8 1.0

50

40

30

20

10

0

Saturation

Dep

th,

cm

zf,20/30

44

37

29

22

outflow manifold depth = 55 cm

zf,12/20

zf,30/40

zf,40/50

12/20 20/30 30/40 40/50

Fig. 7. Characteristic curves of the four sand grades as calculated from the image immediately prior to

the application of the solutions. Each depth measurement represents the average of all pixels within the

given row. The transition depth between residual and funicular water content, zf, is noted for each sand

grade.


fronts, vmax, the values of which are shown in Table 5. Note that vmax is a specific case of vi(Eq. (8)) where the time increment is between the first and the second images.

The trend in vmax indicates that the impact of surface tension on the velocity was

greater in the finer sand. In the 12/20 sand (coarse), solution A moved about 25%

Table 5

Local velocities (cm/min) above and below zf and maximum velocities

Sand grade Exp. 1

12/20

Exp. 2

20/30

Exp. 3

30/40

Exp. 4

40/50

Exp. 5

30/40

Exp. 6

40/50

Exp. 7

30/40

vi (depth, cm) of

A above zf

0.15 (40) 0.07 (29) 0.06 (20) 0.06 (30) 0.06 (28)

vi (depth, cm) of

A below zf

1.2 (42) 0.17 (32) 0.16 (24) 0.19 (34) 0.15 (33)

vmax of A 2.02 1.18 0.45 0.26 0.54 0.23 0.54

vmax of B 1.62 0.87 0.37 0.20 0.25 0.43

vmax of C 1.04 0.73 0.34 0.22 0.27

vmax of D 0.48

vmax of E 0.42


faster than solution B, but both migrated more than 50% faster than solution C (Figs.

2 and 6a, Table 5). Therefore, it seems that both higher solution density and higher

surface tension led to the higher migration rate of the solutions. In the 20/30 sand,

solution A migrated about 36% faster than B and about 62% faster than C (Figs. 3

and 6b, Table 5). In the 30/40 and 40/50 sand grades, solution A migrated about

27% and 24%, faster than B and C, respectively, which moved at similar rates

despite their different densities (Figs. 4, 5 and 6c,d, Table 5). In the 40/50 sand, the

velocity of B was slightly lower than C, despite the significantly higher density of B.

It should be noted, however, that the velocities were generally very low in these sand

grades. Therefore, over the 10-min interval for which vmax was calculated, the

solutions migrated a very small distance. The overall travel time through the residual

water content zone (see Fig. 7) of solution A is more than a factor of three less than

that of solutions B and C in the 30/40 and 40/50 sands.

In Figs. 2–5, it is evident that significantly greater apparent changes in saturation

were observed for the saline plumes relative to the pure water plumes for each of the

sands. For 12/20 sand (Fig. 2), where the three plumes are distinctly separated at

early time, the total predicted volumetric changes in the saline plumes exceed the

pure water plume by up to 50%. This phenomenon is likely the result of the higher

indices of refraction of the saline solutions relative to pure water, as discussed

previously. Therefore, it should be recognized for the saline plumes that the apparent

changes in saturation are not representative of actual changes in saturation and should

be used only as an indication of relative plume displacement.

4.2. Zone with saturations above residual

In all sand grades except 12/20, a ‘‘secondary finger’’ developed at the tip of the

wetting front of solution A (Figs. 3–6), at a point slightly above the capillary fringe.

This occurrence is marked by a narrowing of the plume width and an increase in the

local velocity (Table 5). Due to the 1-h delay between images at this point in the

experiment, the exact depth and time of the velocity increase could not be

determined. Development of the secondary finger appears to correspond to the depth

where transition between residual pendular water and water in the funicular state

occurred. We use the symbol zf to refer to the depth at which the rapid transition

from residual to funicular water occurs (Fig. 7). This also corresponds to the depth

where the secondary finger formation was initiated.

It should be noted that the DS values within the secondary finger were less than

4%, which is only slightly above the DSmin. In contrast, the DS values within the

wetting front of the primary plume were greater than 10%. Therefore, it is likely that

different mechanisms controlled the flow in the primary vs. secondary finger. The

low DS values below zf suggest that flow may have occurred via this zone before the

secondary finger was actually observed, corresponding to regions where DS <DSmin.

Fluid accumulation on top of the capillary fringe before the secondary finger was

observed to reach this depth supports this hypothesis. No secondary fingers were

observed for solutions B or C in the four experiments. They apparently did not reach

the critical depth, zf, required for this to occur (Fig. 6).


4.3. Impact of salt concentration, resident fluid and merging plumes

In Experiment 5, solutions A, D and E were applied to 30/40 sand. The downward

migration rate increased with salinity (Fig. 8a, Table 5). Values of vmax were 0.54, 0.48 and

0.42 cm/min for solutions A, D and E, respectively. It should be noted, however, that,

since density and surface tension increase in parallel, the impact of elevated density versus

elevated surface tension on the migration rate could not be determined from this

experiment. For example, vmax of A was 12.5% higher than D, similar to the difference

in their density. On the other hand, vmax of D was 14% higher than E, while the difference

in their density was only 5%. As in the previous experiment with 30/40 sand (Experiment

3), a secondary finger was observed for solution A at a depth of f 30 cm.

In Experiment 6, solutions A, B and C were applied to 40/50 sand that was pre-wetted

with solution A rather than with C. Solution A migrated downward 8% slower than B and

15% slower than C (Fig. 8b, Table 5), despite the higher density of A. This is contrary to

the results of Experiments 1 to 4, where the wetting front of A advanced downward faster

than both B and C.

In Experiment 7, only two solutions, A and B, were introduced into 30/40 sand. This

experiment was performed to evaluate the significance of the plumes merging, which

occurred to varying extents in all the previous experiments in which three infiltrating

solutions were used simultaneously. Merging of the advancing plumes could have

potentially impacted the salt concentration within the plumes and affected the migration

rates. In Experiment 7, however, the relatively large distance between the plumes (22 vs.

11 cm) served to eliminate any possible merging of plumes (Fig. 9). The outflow port was

also kept open throughout this experiment (constant zero pressure boundary) and therefore

no accumulation of fluids on the capillary fringe was observed. A similar migration pattern

and differences in vmax were observed for solutions A and B in this experiment, and the

three-solutions applied to the 30/40 sand in Experiment 3 (22% and 25%, respectively,

Fig. 8. (a) Wetting front depths of solutions A, D and E (Table 2) applied to 30/40 sand pre-wetted with C; and (b)

solutions A, B and C applied to 40/50 sand pre-wetted with A rather than C, as in all other experiments. Capillary

fringe and zf are noted here as in Fig. 7.

Fig. 9. Three frames from Experiment 7. Solutions A (left) and B (right) were applied to 30/40 sand pre-wetted

with pure water C. Time from end of application is noted above each frame. The pseudo-colorized images

describe the apparent changes in saturation (DS) with respect to before solutions were applied. Arrow denotes the

secondary plume.


Table 5), suggesting that the merging between the plumes that occurred in Experiment 3

had no significant influence on the observed migration rates.

5. Discussion

5.1. Wetting front velocity and plume shape

Provided that the application rate is significantly below the saturated hydraulic

conductivity of a given porous media, the gravitational and capillary forces acting on

the advancing solution dictate the geometry of the infiltrating plume (Selker and Schroth,

1998). On this basis, the slight differences in viscosities would not be expected to

significantly affect the plume dimensions since vmax was at least an order of magnitude

below the saturated hydraulic conductivity in all experiments (Tables 1 and 5). The

gravitational force is constant for a solution with a given density (regardless of sand

grade), while capillary forces generally increase with decreasing pore size (Eq. (3)). The

consistently higher wetting front velocities of solution A relative to B, and the similar

velocities of solutions B and C in the finer sand grades, indicate that density played a

relatively minor role in all experiments and an insignificant role in the finer sands. In the

40/50 sand, solution B migrated slightly slower than C despite its 20% higher density

(Experiment 4, Fig. 5). The surface tension of solution B was only 3.5% lower than C,

which further supports that large differences in density were relatively unimportant in the

fine sand. Differences in migration rates that cannot be directly attributed to differences in


fluid mobility (Table 2) are presumably a result of surface tension and contact angle

effects.

The plume widths are difficult to quantify since they evolve in time, are convoluted in

shape, and the fingers merged at later time in the finer sands. Qualitatively, from Figs. 2–5

and 9, it is apparent that a narrower finger was formed by the higher surface tension

solution (A) relative to the lower surface tension solutions (B and C), especially for the

finer sands. This suggests that the lateral transport of A was restricted when C was the

resident fluid. Since capillarity promotes spreading of the infiltrating phase into the porous

media, one might expect the higher surface tension fluids to spread more laterally than the

relatively lower surface tension liquids (given zero contact angle and equal density).

However, our results show that the increased surface tension of the advancing fluid

actually resulted in reduced lateral spreading, while vertical wetting front velocity

increased. These results suggest that the effective contact angles were non-zero.

The broad, bulbous plumes observed for solutions B and C are consistent with the

results of Diment and Watson (1985) and Glass et al. (1989) for water introduced from

point sources into sand that was initially at residual water content. On the other hand, the

more sharply defined and narrow shapes of the solution A plumes, are similar to those

observed in numerous experiments and simulations where solutions were applied to water-

repellent or dry soils (Bauters et al., 2000; Nieber et al., 2000).

In natural soils, which are rarely dry at depth, the occurrence of fingering is still under

debate (e.g., Glass and Nicholl, 1996). Also, many coarsely textured natural soils have

laterally dominant micro-layering within single strata, and cross bedding with contrasting

texture, both due to turbulent and unstable depositional processes. The results presented

here suggest that fingering can be enhanced in pre-wetted media when the imbibing

solution has elevated surface tension. Moreover, water vapor diffusion from the surround-

ing low water content environment into the saline solution, may further promote plume

transport (Xu and Preuss, 2001; Weisbrod et al., 2000, 2003). As noted in those papers,

water vapor diffusion is likely to be a very important long-term mechanism leading to

continued migration of saline plumes. Water vapor diffusion is not of significant

importance at the time scales considered in the work presented here, but is discussed in

detail by Weisbrod et al. (2003).

When the sand was pre-wetted with high-salinity solution, A (Experiment 6, Fig. 8), it

was observed that the pure water, with lowest density and lowest surface tension, migrated

most quickly, while the methanol solution plume was more rapid than the pure saline

solution. However, the velocities were all within 15%. The lower surface tension imbibing

solutions appear to have mixed with the higher surface tension resident solution more

aggressively. Unlike the issue of contact angle, this process is not amenable to a simple

force-balance analysis to estimate the expected magnitude of the effect. It is not clear how

these processes would effect movement at actual sites, since uniform contamination with a

saline solution seems an unlikely description of initial conditions.

5.2. Surface tension and apparent contact angle

Lowering the surface tension of a fluid by heating or adding surfactants makes it a

better ‘‘wetting agent’’, improving its ability to enter porous media. Conversely, increasing


the surface tension (by adding salts) results in more cohesive forces within the fluid

molecules at the surface, giving rise to an energetic obstacle to imbibition in water-wetted

media. This latter situation corresponds to the case when the advancing fluid was the

saline solution (A) and the low surface tension was the resident one (C), as well as the

initial entry of saline solution in a pristine subsurface environment.

While the classical equations for capillary pressure, Eqs. (1)–(3), explain the hydro-

static or equilibrium condition of a single fluid in dry media or a media pre-wetted with the

same fluid (where the contact angle is assumed to be close to zero), they may be

insufficient for systems pre-wetted with a different fluid. In a system where the resident

and advancing solutions have distinct surface energies, the forces at the interfaces between

solutions may be different from those found entirely within either the resident or

advancing fluids, and the effective contact angle is likely to be non-zero under certain

conditions.

Three force balance conceptualizations at the contact point between an advancing and

resident fluid are shown in Fig. 10: (a) the resident and the advancing fluids are the same

(A into A or C into C). The fluids and surface energies are equal and a zero contact angle

(c= 0) is expected at the contact point between fluids; (b) the advancing fluid has a lower

surface tension than the resident fluid (C into A). Here, the contact angle is also expected

to be zero; however, the fluids will not establish a mechanically stable condition until full

mixing has occurred. Prior to equilibrium, the net force is into the surrounding medium,

which may assist in spreading; and (c) the advancing solution has a higher surface tension

than the resident fluid (A into C). A non-zero gas–liquid contact angle is required for the

advancing solution to maintain mechanical equilibrium at the interface between the fluids.

Given the surface tension values of A and C (Table 2), balance of force in the direction of

wetting requires that the contact angle for A into C is equal to 25.3j (Eq. (2)). Using the

Washburn approach (Washburn, 1921) combined with the Green and Ampt Model (Green

and Ampt, 1911), McGinnis (2001) calculated the dynamic contact angle of solutions A

and C while imbibing into columns packed with 40/50 AccusandR pre-wetted with C. It

was found that while a contact angle of f 2j was calculated for C imbibing into C,

f 21j was calculated for A imbibing into C, which corresponds well with the predictions

from Eq. (2).

In all three cases depicted in Fig. 10, it was assumed that the thin film of resident fluid

is absorbed by the advancing fluid and immediately mixed. Since the total volume of water

in all the thin films is low, the solution behind the contact point is representative of the

initial advancing fluid composition until enough resident fluid has been incorporated to

achieve significant dilution. Furthermore, all interfacial forces between the liquid and solid

phases were assumed to be equal and opposite about the contact point. Some degree of

mixing is likely to occur about the contact point between the advancing and the resident

fluids, effectively changing the local contact angle in the zone of mixing. However, the

effective contact angle is expected to remain unchanged in the bulk of the advancing fluid

(Fig. 10c). The extent of the mixing zone is dynamic and is expected to increase over time

until complete mixing between fluids is achieved; at which point, the contact angle will be

zero. In addition to mechanical dispersion and diffusion, another mechanism that can

contribute to mixing between the advancing and resident fluids is the Marangoni effect

(Adamson and Gast, 1997), where micro-scale (sub-pore scale) turbulence may manifest

Fig. 10. Young’s force balance diagram at the contact point between an imbibing fluid and a resident fluid with

various surface tension pairs. The imbibing solution enters from the left and the arrow heads indicate the direction

of force. The fluids A and C from our experiments are indicated by subscripts. (a) Same fluid (either A or C) or

fluids are completely mixed; (b) C imbibes into A; (c) A imbibes into C. A contact angle of 25.3j is assumed

when A is the advancing and C is the residual fluid. The expected miscible mixing zone at the diffusive interface

between liquids is illustrated.


into macroscopic mixing. This effect could not be quantitatively determined in this

research. However, the leading-edge dilution between the advancing and resident fluids is

likely to preclude a significant Marangoni effect at depth. Further research is needed to

quantitatively determine the importance of the contact angle effect versus the Marangoni

effect under various conditions.

The effect of a non-zero contact angle on imbibition is not obvious. Scaling the

pressure–saturation curve for imbibition of C into C to represent the imbibition of A

into C violates standard scaling theory due to lack of geometric similarity as a result

of the non-zero contact angle (Miller and Miller, 1956). Alternative formulations for

scaling due to contact angle have been presented, all of which consider the effect of


contact angle on pendular water (Melrose, 1965; Demond and Roberts, 1991;

Frankenfield and Selker, 1994). All of these methods scale the pressure–saturation

curve downward; i.e. yield a lower capillary pressure than would result from scaling

by contact angle alone.

Using Eqs. 22–27 of Rockhold et al. (2002), pc and Seff were tabulated for both

zero and non-zero contact angles over a range of pendular ring sizes from

0VuV 45j, at 0.1j increments. Effective saturation was converted to degree of

saturation by Eq. (6). Contact angle scaling factors, pc(a)/pc(0) were then determined

as a function of saturation; shown in Fig. 11 for contact angles of 10j, 25.3j and

45j. The scaling factors for capillary pressures at corresponding saturations were

computed by linear interpolation between discrete data pairs. Interestingly, since the

relative capillary pressures are controlled by the geometry of single pendular rings,

the scaling factor is independent of porosity.

The effect of contact angle scaling on the pressure–saturation curve for 40/50 sand

is depicted in Fig. 12. The primary drainage curve for C (pure water), taken from

Experiment 4, is shown as the thin solid line. Relative to C, the primary drainage

curve for A scales only by the different surface tension (Table 2) as dictated by Eq.

(3), shown as the thick solid line. These two cases correspond to capillary pressure–

saturation curves for porous media that have been rewetted by the same fluid,

assuming no gas entrapment. The scaled characteristic curve where A is the

Fig. 11. The scaling factor as a function of saturation for three different contact angles as calculated using Eqs.

(22)– (27) in Rockhold et al. (2002).

Fig. 12. Pressure–saturation relations corresponding to the main drainage and primary wetting curves for the 40/

50 sand, with no air-entrapment during rewetting. For pure water and salt water (A and C, respectively),

differences between the two curves reflect the change due to surface tension assuming zero contact angles.

Imbibition of A into C was calculated using the scaling function depicted in Fig. 11 with c = 25.3j. Note that thescaling function varies with saturation and is only applicable before the pendular rings merge with one another in

transition to a funicular water stage.


advancing fluid and C is the resident fluid is shown as the thick dashed line. The

contact angle scaling applies only to low water contents such that the pendular rings

do not coalesce with adjacent solid surfaces or other pendular rings. In Fig. 11,

contact angle scaling was applied up to a value of u = 45j corresponding to a

saturation where the pendular rings would begin to overlap for a simple cubic

packing of spherical particles. The figure illustrates that the capillary forces acting on

solution A advancing into a media pre-wetted with C are less than the other cases,

which is supportive of the observed behavior in the migration experiments. In other

words, the interface between the two solutions acts effectively as a separate phase for

a short period of time; the resulting effective contact angle between the imbibing and

resident solutions follows its own pressure–saturation relationship. It should be noted

that dilution due to mixing between the advancing and receding solutions as well as

diffusion will cause concentrations to vary near the hydrodynamic wetting front.

Therefore, the sharp wetting front assumed in Fig. 10 is a simplification. These

effects will introduce additional complexities in the interaction between the advancing

and receding solutions.


5.3. Secondary plume and film flow

Secondary plumes were observed for most plumes of solution A at zf (Figs. 3–6 and 9,

see arrows). This event was associated with a narrowing of the finger width and an

increased rate of downward movement (Figs. 6b–d and 8a, see arrows). A similar sudden

acceleration was observed for finger movement from an air-dry soil into an underlying

moist soil by Liu et al. (1994). Finger velocity increased and finger width decreased upon

contact with the moist soil.

In our experiments, the wetting process above zf took place by way of a classical

capillary transport from empty to full pores (series of Haines jumps), while below this

depth the movement followed film flow along grain surfaces without the noticeable filling

of pores. In the media with water held in a pendular state, the DS within the imbibing

plume was always above 10%, while below zf the DS was between 2% and 4%; this

suggests that the migration mechanism changed dramatically once the plumes reached a

region where the film thickness was sufficient to conduct the flow. Slight changes in fluid

film thickness may have been responsible for the minor increases in DS below zf. Fluid

accumulated on top of the capillary fringe before the visible (DS>DSmin) secondary finger

developed (Figs. 3–5), indicating that fluid also migrated to the capillary fringe through

changes in saturation less than DSmin. Film flow has been suggested as a mechanism for

flow in unsaturated porous media (Lu et al., 1994a,b) and along fracture surfaces (Or and

Tuller, 2000; Tokunaga and Wan, 1997; Tokunaga et al., 2000). Our observations imply

that film flow played an important role in the downward migration of fluid in unsaturated

porous media above residual water content.

6. Summary and conclusions

Laboratory experiments demonstrated that high surface tension solutions penetrating

into homogenous pre-wetted unsaturated porous media significantly enhanced vertical

fingered flow. It appears that differences in surface tension between the infiltrating and

resident fluids, and consequently the contact angle, had the greatest impact on wetting

front velocity and geometry. Our assumption is that the gradient in surface energy at the

interface between the resident fluid (coating the particles) and the advancing fluid

prevented a zero contact angle from forming between the fluids over the relatively short

period of contact during migration. The magnitude of the resulting contact angle was

estimated from the relative surface tension with the understanding that the contact angle is

effective across a zone of mixing. Although pure water and saline solutions are typically

considered completely miscible fluids, our results suggest that the mixing process is not

spontaneous. The micro-scale processes at the interface are not completely understood. It

should be noted, however, that direct measurements of contact angles at the interface of the

migrating saline solution and the residual pore water is impossible at this time and

therefore the proposed mechanism cannot be proven directly. Therefore, the possibility

that other mechanisms could underlie the observed phenomena cannot be eliminated.

Once the infiltrating solutions reached the depth where resident saturation increased

above residual levels, zf, a visible secondary plume developed at the tip of the plume


and the local wetting front velocity increased. The secondary plumes appeared to

migrate via film flow rather than isolated pore filling. The accumulation of fluid on top

of the capillary fringe without visible contact with the fingertip suggested that film

flow occurred through very small changes in water content, below the detection limits

of our system (DS < 2%). Further research is needed to quantify the impact of surface

tension in different salt solutions and various concentrations as well as to better

understand the practical implications of the observed film flow. Also, possible methods

to measure the resulting contact angle between solutions need to be investigated.

Beyond scientific interest, the observed phenomena appear to be influential where

infiltrating solutions have high surface tension and should ultimately be incorporated in

predictive models.

Acknowledgements

We would like to thank Anderson Ward and Maria Dragila for the many constructive

discussions provided during the preparation of this manuscript. Thanks to Joan Sandeno

for her editorial assistance. The insightful reviews of Emil Frind and Karsten Preuss were

appreciated and helped to improve the paper. This work was funded by the Department of

Energy under contract number DE-FG07-98ER14925.

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