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This is to certify that the

dissertation entitled

TRANSPORT 0F VOLATILE ORGANIC COMPOUNDS
IN THE UNSATURATED ZONE

presented by

MUNJ ED A. MARAQA

has been accepted towards fulfillment
of the requirements for '

Ph. D. degreein CIVIL AND ENVIRONMENTAL
ENGINEERING

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Major professor

 

 

 

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MS U i: an Affirmative Action/Equal Opportunity Institution 0- 12771

 

 

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TRANSPORT OF DISSOLVED VOLATILE ORGANIC COMPOUNDS

IN THE UNSATURATED ZONE

by

Munjed A. Maraqa

A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY
Department of Civil and Environmental Engineering

1995

ABSTRACT

TRANSPORT OF DISSOLVED VOLATILE ORGANIC COMPOUNDS
IN THE UNSATURATED ZONE

by
Munjed A. Maraqa

The main objective of this research was to explore the impact of individual
transport mechanisms on the average velocity and extent of spreading of dissolved
volatile organic compounds (V OCs) in the subsurface. Soil organic matter, pore-water
velocity, and level of saturation were selected as the primary variables for investigation.
Two nonionic organic compounds were employed: dimethylphthalate, as a nonvolatile
compound, and benzene, as a volatile one. Tritium was also used and was verified to act

as an ideal tracer.

Sorption and volatilization affect the transport speed of VOCs dissolved in the
aqueous phase. This study showed that sorption-related retardation coefficients for the
two nonionic organic compounds, as estimated from batch sorption isotherms and the
properties of the soil matrix, were higher than their column-determined counterparts. The
extent of deviation between the two techniques was independent of the organic carbon
content of the soil. Although not specifically investigated experimentally, it was
speculated that differences between the results of the two techniques were likely to result

from either mixing differences or differences in particle spacing in the two systems.

It was also found that sorption-related retardation coefficients determined under
dynamic flow conditions when the soil was partially saturated were higher than the values
determined at full saturation. The increase in retardation was proportional to the decrease

in saturation. When the retardation coefficients were normalized to the same solid/water
ratio, the values under the two flow conditions were similar for comparable pore-water
velocities. This suggested that sorption-related retardation coefficients under unsaturated
conditions can be estimated using a single value of the sorption distribution coefficient
and assuming that the sorption capacity of the solids is unaltered by desaturation. The
impact of volatilization on retardation of benzene was not significant under the conditions
employed in this study. It was shown mathematically that this effect could be significant

for higher volatility compounds and for low organic carbon soils.

The effects of dispersion in the liquid phase, diffusive transport in the air phase,
and transport nonequilibrium on the extent of spreading of dissolved VOCs were also
investigated. This study showed that the dispersivities of partially saturated soils were 2-3
times higher than the values obtained under saturated conditions. At low levels of
saturation, however, spreading of benzene caused by dispersion in the liquid phase
became negligible compared to that caused by diffusion in the air phase. Commonly
accepted empirical relations overestimated the effective diffusion coefficient in the air

phase.

This study revealed that there was no physical nonequilibrium, created by slow
diffusion in and out of immobile water regions, during transport of solutes through
partially saturated soils. However, sorption-related nonequilibrium during transport of
nonionic organic compounds, under both saturated and unsaturated flow conditions,
should be considered. The impact of changes in soil organic matter, pore-water velocity,
and saturation on the extent of sorption nonequilibrium was investigated. The results
showed that a 3-fold increase in soil organic matter slightly changed the extent of
sorption nonequilibrium. It was also found that the mass transfer coefficient of nonionic
organic compounds between equilibrium— and nonequilibrium-type sorption sites is
dependent on the pore-water velocity, but not on soil organic matter. Changes in

saturation did not appear to influence the values of the nonequilibrium parameters.

To my mother

iv

ACKNOWLEDGMENTS

I would first like to thank my major advisor Dr. Thomas C. Voice for his
encouragement and support throughout the program. My greatest appreciation also to the
other members of my committee: Dr. Roger Wallace and Dr. Susan Masten of the
Department of Civil and Environmental Engineering; and Dr. Raymond Kunze of the

Department of Crop and Soil Sciences.

Special recognition go to: Dr. Mackenzie Davis; Dr. Simon Davies; Dr. David
Wiggert; and Dr. Craig Criddle of the Department of Civil and Environmental Engineering
and Dr. Paul Laconto of the Hazardous Substance Research Center at MSU for their extra
support and encouragement. I am also grateful to: Dr. P. S. C. Rao, University of Florida,
Gainsville; Dr. John Gierke, Michigan Technological University; and Dr. Arthur Corey,
Colorado State University for their valuable comments.

I gratefully acknowledge the National Institute of Environmental Health Sciences
for exclusively funding this work, and the Department of Civil and Environmental
Engineering for the teaching assistantship I obtained in the first semester at MSU. Thanks
are also due the secretarial personnel at the Department of Civil and Environmental
Engineering office and the Research Complex for making things easier. Sincere thanks, in
this regard, must go to Linda Steinman and Brenda Minott.

My life at MSU was more enjoyable with: J .J . Yao; Herr Soeryantono; Reza
Rakhshandehroo; James Grant; Jamie Gellner; Blake Key; Xianda Zhao; Mike Witt;
Myung Chang; Nancy I-Iyden; Mike Annable; George Zalidis; Lizette Chevalier; Mark
Dixon; Bill Brunner; Fred Degroot; Hung Nguyen; Mara Hollinbeck; Chien-Chun Shih;
I-yuang Hsu; Brad Upham; and my coffee-mate Yanlyang Pan.

This work was made possible by the support, love, and encouragement of my

family, especially my wonderful mother.

TABLE OF CONTENTS

 

LIST OF TABLES ............................................................................................ ix
LIST OF FIGURES ............................................................................................ x
CHAPTER 1 OBJECTIVES AND REVIEW ................................................. 1
1.1 Introduction .................................................................................................... 1
1.2 Research objectives ......................................................................................... 5
1.3 Review of dispersion processes ....................................................................... 6
1.3.1 Theory of dispersion ....................................................................................... 6
1.3.2 Modeling dispersion under saturated- unsaturated conditions ......................... 7
1.3.2.1 Dispersion under saturated conditions ......................................... 8
1.3.2.2 Dispersion under unsaturated conditions ................................... 13
1.3.3 Comments on dispersion in the unsaturated zone ......................................... 14
1.4 Review of sorption processes for NOCs ........................................................ 14
1.4.1 Mechanisms of sorption of NOCs ................................................................. 15
1.4.2 Effect of moisture content on sorption of NOCs .......................................... 17
1.4.3 Modeling sorption in soil aquifers ................................................................. 20
1.4.4 Comments on modeling sorption in soil aquifers .......................................... 23
1.5 Review of volatilization and air phase transport processes ............................. 25
1.5.1 Volatilization of VOCs -- ...... -- - _26
lSZTransportofVOCsmthcarrphase .............................................................. 29
1H53DispersionarrdretardationofVOCsunderunsaturatedconditions .............. 30‘
1.6 Validity of local equilibrium assumption ........................................................ 32
1.7 Summary ...................................................................................................... 34
1.8 Literature cited ............................................................................................. 36

CHAPTER 2 EFFECT OF WATER SATURATION ON
DISPERSIVITY AND IMMOBILE WATER
IN SANDY SOIL COLUMNS - _ - - ...... 43

 

2.1 Introduction .................................................................................................. 43

2.2 Materials and methods .................................................................................. 47
2.3 Results and discussion .................................................................................. 52
2.3.1 Role of chemical interaction .......................................................................... 53
2.3.2 Role of physical nonequilibrium .................................................................... 55
2.3.4 Dispersivity under saturated-unsaturated flow conditions ............................. 64
2.4 Summary and conclusions ............................................................................. 67
2.5 References .................................................................................................... 69

CHAPTER 3 COMPARISON BETWEEN RETARDATION
COEFFICIENTS OF NONIONIC ORGANIC
COMPOUNDS DETERMINED BY BATCH

 

AND COLUMN TECHNIQUES- . - _ 71

3.1 Introduction .................................................................................................. 71
3.2 Experimental procedure ................................................................................ 74
3.3 Data analysis ................................................................................................. 76
3.4 Results and discussion .................................................................................. 79
3.4.1 Batch sorption experiments ........................................................................... 79
3.4.2 Saturated cohimn experiments ...................................................................... 85
3.4.3 Batch/column retardation coefficients ........................................................... 91

3.5 Summary and conclusions ............................................................................. 94
3.6 References .................................................................................................... 96

CHAPTER 4 RETARDATION OF NONIONIC ORGANIC
COMPOUNDS UNDER UNSATURATED

 

FLOW CONDITIONS - 99

4.1 Introduction .................................................................................................. 99
4.2 Materials and methods ................................................................................ 102
4.3 Data analysis ............................................................................................... 102
4.4 Results and discussion ................................................................................ 107
4.4.1 Efiect of saturation on retardation .............................................................. 107

4.4.2 Eflect of volatilization on retardation .......................................................... 111

viii

4.4.3 Difl'usive transport in the air phase .............................................................. 117
4.4.4 Practical implications .................................................................................. 120
4.5 Conclusions ................................................................................................ 120
4.6 References .................................................................................................. 122

CHAPTER 5 SORPTION NONEQUILIBRIUM DURING
TRANSPORT OF NONIONIC ORGANIC
COMPOUNDS THROUGH SOIL COLUMNS:
EFFECT OF SOIL ORGANIC MATTER, PORE-

WATER VELOCITY AND SATURATION ........................ 123

5.1 Introduction ................................................................................................ 123
5.2 Materials and methods ................................................................................ 126
5.3 Data analysis ............................................................................................... 127
5.4 Results and discussion ................................................................................ 132
5.4.1 Impact of SOM on sorption nonequilibrium ............................................... 132
5.4.2 Impact of pore-water velocity on sorption nonequilibrium ......................... 138

5. 4. 3 Impact of saturation on sorption nonequilibrium ........................................ 142

5.5 Summary and conclusions .................................................................................... 146
5.6 References .................................................................................................. 148

CHAPTER 6 DISSERTATION SUMMARY AND
RECOMMENDATIONS - - 150

 

6.1 Dissertation summary ................................................................................. 150

6.2 Recommendations ....................................................................................... 153

LIST OF TABLES

Table 2.1 Review of some experimental investigations of dispersion in

unsaturated soil columns under steady-state flow conditions ............... 44
Table 2.2 Properties of packed soils .................................................................... 48
Table 2.3 Retardation of tritium in saturated short columns ................................. 5 3

Table 2.4 Experimental conditions and dispersion coefficients for the
saturated flow experiments ................................................................. 56

Table 2.5 Experimental conditions and the results of fitting the AD and

MIM models to the unsaturated flow experiments ............................... 57
Table 2-6 Linear regression results between D and V0 ......................................... 62
Table 3.1 Properties of packed columns .............................................................. 74
Table 3.2 Some properties of the used organic chemicals .................................... 75
Table 3.3 Results of the linear and Freundlich type models .................................. 84
Table 3.4 Retardation coefficients based on batch results using

the linearized sorption coefficient ........................................................ 84
Table 3.5 Retardation coefficients determined from BTCs using

first moment analysis and curve fitting technique ................................. 88
Table 4.1 Experimental conditions and values of R for DMP

under unsaturated conditions ............................................................ 104
Table 4.2 Values of R for benzene under unsaturated conditions ....................... 105

Table 5.1 Results of fitting the AD model to benzene and DMP
using independently determined dispersion coefficient ....................... 129

Table 5 .2 Results of fitting the nonequilibrium model to the
saturated experiments using dispersion coefficient
determined from tritium BTCs .......................................................... 130

Table 5.3 Results of fitting the nonequilibrium model to DMP
unsaturated experiments using dispersion coefficient
determined from tritium BTCs .......................................................... 131

LIST OF FIGURES

Figure 1.1 Schematic conceptualization of possible VOC transport
and transfer mechanisms under unsaturated conditions ......................... 2

Figure 1.2 Impact of transport and transfer processes on VOC
movement in unsaturated soil columns ................................................. 4

Figure 2.1 Schematic diagram of the unsaturated soil column with the
sample collection device .................................................................... 49

Figure 2.2 Water distribution along the depth of a Metea soil column at
a negative pressure of 55 mbar .......................................................... 51

Figure 2.3 Selected BTCs from the pulse input saturated flow experiments.
Dots are experimental data, and solid lines are simulations with the
AD model using parameter values listed in Table 2.4 ......................... 59

Figure 2.4 Selected BTCs of the unsaturated experiments. Dots are
experimental data, solid lines are simulations with the AD model
(without retardation) and dashed lines are simulation with MIM

model. Simulation parameter values are as listed in Table 2.5 ............. 60
Figure 2.5 Dispersion coefficient for the three soils under saturated (closed

symbols) and unsaturated (open symbols) conditions ......................... 61
Figure 2.6 Dispersivity of three sandy soils at various levels of saturation ............ 66

Figure 3.1 Retardation factors determined from column BTCs:
(a) R=T @ ClCo=0.5, (b) the area above the BTC, and
(c) the mean of BTC .......................................................................... 77

Figure 3.2 Batch rate study of benzene (triangles) and DMP (circles).
Open symbols for blank tubes ............................................................ 80

Figure 3.3 Batch sorption isotherm for DMP (circles) and benzene
(triangles) after a 3-day (open symbols) and a 14—day
(closed symbols) mixing period .......................................................... 83

Figure 3.4 Sorption isotherm of DMP (circles) and benzene
(triangles). Closed symbols for S/W ratio =1/ 1.5 and
open ones for S/W ratio=1/6.5 .......................................................... 86

 

 

 

Figure 3.5 Retardation coefficients as influenced by pore-water velocity
and hydraulic residence time for DMP on Oakville A soil. Closed
symbols for short column and open ones for long column .................. 90

Figure 3.6 Comparison between batch/column sorption distribution
coefficients for aquifer materials with different organic carbon
content. Circles for DMP and uiangles for benzene ........................... 92

Figure 4.1 BTC of DMP on Oakville A subject to the conditions
of experiment USA3 ........................................................................ 106

Figure 4.2 Retardation coefficients for DMP on Oakville A soil under
saturated (closed symbols) and unsaturated (open symbols)
flow conditions ................................................................................ 109

Figure 4.3 Percentage increase in R for DMP as a functiOn of saturation ........... 110

Figure 4.4 Retardation of DMP under saturated (closed symbols) and
unsaturated (open symbols) conditions ............................................ 112

Figure 4.5 Percentage increase in R for benzene as a function of saturation.
Solid line is the linear fit for DMP data of Figure 4.3 ....................... 114

Figure 4.6 Theoretical estimation of the impact of volatilization on
retardation of selected VOCs ............................................................ 115

Figure 4.7 Retardation of benzene under saturated (closed symbols) and
unsaturated (open symbols) conditions ............................................ 116

Figure 4.8 BTCs of benzene and tritium (a and b, respectively) at various
levels of saturation subject to the conditions indicated, and for
benzene at various saturated velocities (c) ....................................... 118

Figure 4.9 Error in the effective dispersion coefficient of benzene under
unsaturated conditions ..................................................................... 119

Figure 5.1 Selected BTCs of benzene (triangles) and DMP (circles).
Dashed lines are simulations using the equilibrium model and
solid lines are simulations using the nonequilibrium model ............... 133

Figure 5.2 Effect of SOM on transport of benzene (triangles) and
DMP (circles) .................................................................................. 134

xii

Figure 5.3 BTCs of benzene (triangles) and DMP (circles) as single (open
symbols)- and dual (closed symbols)-injected into the
soil columns .................................................................................... 136

Figure 5.4 Effect of pore velocity on transport of benzene (triangles) and
DMP (circles) ................................................................................. 139

Figure 5.5 Relationship between mass transfer coefficient and pore-water
velocity, circles for Oakville A, diamonds for Pipestone and
triangles for Oakville B soil, open symbols for DMP and
closed ones for benzene ................................................................... 141

Figure 5.6 Selected BTCs of DMP under unsaturated conditions, open
and closed circles symbols are data of experiment USA2 and
USA4 with saturation of 78 and 52%, respectively. Lines are
simulations using the nonequilibrium model ................................... 143

Figure 5.7 Relationship between normalized fraction of instantaneous
sorption sites and retardation coefficients, circles for
Oakville A, diamonds for Pipestone and triangles for
Oakville B soil, open symbols are for unsaturated experiments
and closed ones for saturated experiments ....................................... 144

Figure 5.8 Relationship between mass transfer coefficient and pore-water
velocity, circles for Oakville A, diamonds for Pipestone and
triangles for Oakville B soil, open symbols are for unsaturated
experiments and closed ones for saturated experiments .................... 145

CHAPTER 1

OBJECTIVES AND REVIEW

1.1 Introduction

Dissolved volatile organic chemicals (V OCs) present in the subsurface are of concern
because of their potential to produce adverse health efi‘ects. Currently, many of the accepted
remediation strategies depend primarily on extensive water extraction or soil excavation These
may be inefficient and costly remedies. Identification of efficient, costcfiective approaches,
however, depend on a thorough understanding of the fundamental mechanisms that control the
transport and fate of these contaminants.

Subsurface transport mechanisms can be divided into two categories: those that leave
the structure of a chemical unchanged, and those that transform the chemical into one or
several products. The first category of processes includes transport and mixing within a given
phase as well as transfer processes between difierent phases. Alterations ofthe structure ofa
compound may occur by chemical, photochemical, or biological transformation reactions. This
study focuses on the first category of processes. It is not intended, by doing so, to undermine
the impact the second category of processes may have on the ultimate fate of VOCs.

figure l-la exemplifies aregionwithin theunsaturated zonethatiscontarninated by
aVOC. AsshownschematicallyinFrgure1-1b,threedistinctpbases(solid,water,andair)are
presentmrdermrsaturatedconditions.Inthisfigure,itisalsoconceptualizedthatafractionof
the water phase is relatively immobile. Ifa VOC is present in the flowing fraction of the water
phase,tbeVOCissubjectedto advectionarrddispersionwithirrthatfiactionlnaddition,the
compoundmayuansfertodreotherphasesmrdtodrehnmobilewaterfiacuon Transferofthe
compound from the water phase (mobile or immobile) to the solid phase is referred to as

 

(a)

 

 

 

 

 

     

.-;;:+:-:~‘ '--:a;.r.-.-. .

   
   

    
 
 
   

'Z'Z: ' ,4”!
4/ ..I/

z;
':/

(b)

Figure 1-1. Schematic conceptualization of possible VOC transport and transfer
mechanisms under rmsaturated conditions

3

sorption, while that from the water phase to the air phase is volatilization. The volatilized part
might be subjected to the same transport mechanisms as the one in the mobile liquid phase.
Yet, the effect on the fate of the chemical might be totally different.

The impact of some of the above mentioned mechanisms on the transport of a VOC is
presented in Figure 1-2. Advection is the mechanism by which chemicals are transported by the
bulk motion of the flowing phase. As illustrated in Figure l-2a, a nomeactive chemical present
in the water phase moves at an average velocity equal to the average pore-water velocity. Due
to hydrodynamic dispersion, however, part of the chemical plume migrates slightly faster, while
part moves slightly slower than the average water velocity as shown in Figure 1-2b.
Hydrodynamic dispersion is caused by two processes: mechanical mixing during fluid
advection and molecular diffusion driven by concentration gradients.

The effect of sorption is demonstrated in Figure l-2c. Sorption reduces the
average velocity of the solutes with respect to that of the water molecules. The
importance of sorption in retarding the transport of organic chemicals has led some
investigators to suggest modification of soil materials as a means to reduce the migration
of solute plumes (Boyd er al., 1988; Lee et al., 1989). Sorption may also have an effect
on many natural transformation processes. Microorganisms, for example, are thought to
be unable to assimilate and transform sorbed molecules compared to those in soil solution
(Orgam er al.,l985). Chemical reactions may also be affected by sorption (Macalady and
Wolfe, 1985).

Intheabsenceofairflow,volatilizationof VOCsresultsinanincreaseinVOC
retardation as part of the dissolved VOC in the water phase partitions into the air phase.
Theoretically, the increase in retardation is a function of Henry’s constant and air saturation
DiffusivefianspofihrtheairphasedoesnotafiectretardationbutresultsinanincreaseinVOC
spreading. Figure l-2d shows the impact of volatilization and air phase diffusion VOC

transport.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Co * C A INPUT
so“
column
A: t
C A OUTPUT
Advection (a)
+ > r
Dispersion C A
(b)
+
a t
Sorption C A
(C)
+
: t
Volatilization CA
and
diffusion in the (d)
air phase
> t

 

 

 

Figure 1-2 Impact of transport and transfer processes on VOC movement
in unsaturated soil columns

Transfer processes of a VOC between difierent phases are commonly described as
being in equilibrium. The use of this approach is applicable if the transfer time is much smaller
than the mean residence time. The validity of this assumption under certain conditions is
questionable. The impact of nonequilibrium in any of the transfer processes (ie. sorption
nonequilibrium, volatilization nonequilibrium , slow mass transfer into immobile water) is an
enhanced spreading of the chemical and, therefore, an apparent increase in dispersion.

The main focus of this research is to explore the effect of some transport mechanisms
on the mobility of VOCs in the unsaturated zone. The effect of sorption, advective-d'npersive
transportintheliquid phase, anddifiusive transportintheairphasewillbeconsidered. Soil
organic matter content and the degree of water saturation are chosen as the principle
parameters ofinterest in this study. It is intended in this chapter to provide the reader with an
overall review of the literature related to dispersion, sorption, volatilization, and difl'usive
transport in the subsurface environment Subsequent chapters report the results of experimental
researchdesignedto increaseourunderstandirrg ofVOC transportinthevadosezone. The
specific objectives of this research are as presented below.

1.2 Research objectives

Thisstudywas subdivided into fourmainareasofresearch. Theresultsofeachareaare
presentedinaseparatechapter. Eachchapteriswrittento essentiallystandaloneandisinthe
process ofbeirrg published

Thefirstareaofresearch (Chapter2)wasdesignedto investigatethedispersive
behavior of nonaggregated soils under unsaturated-flow conditions as compared to the
conditions whenthesoilisfullysaturated. Insodoing, abetterunderstanding ofthe
appropriate conceptual representation of the geometry of the unsaturated pore vohrrne would
be gained Our approach was to isolate any induced dispersion due to chemical nonequilibrium

of the solute with the solid matrix or solute exchange between mobile and immobile water
upon desaturation.

The second and third areas of research were designed to address the impact of organic
matter and level of saturation on the ultimate sorption capacity of soil aquifers. In the second
phase (Chapter 3), the discrepancy between batch- and column-determined retardation
coemcients were investigated. It is also intended to determine if the extent of discrepancy is

related to soil organic matter content.

The primary objective of the third phase (Chapter 4) was to determine the role of
water saturation on the retardation of nonionic organic compounds (NOCs). To our
knowledge, this study is the first to explore the impact of soil moisture content on the
retardationcoeflicientunderdynamic conditiom. Theinfluenceofdifi‘usive transportintheair
phase on the movement of VOCs was also addressed.

The final area ofresearch (Chapter 5) was designed to determine, on a quantitative
basis, the impact of soil organic matter and water saturation on the degree of sorption
nonequilibrium of dissolved nonionic organic compounds (NOCs). The influence of changes in
pore-water velocity on sorption nonequilibrium was also investigated.

1.3 Review of dispersion prom

1.3.1 Theory of dispersion

Hydrodynamic dispersioninporous mediarefersto thespreading ofastreamor
discrete vohrrne of contaminants as it flows through the subsurface. For example, if a set of
particles is injected into porous media through which groundwater is flowing, the par-ticks will
spreadlongitudinallyinthedirection offlow (longitudinaldispersion) andtransverselyinthe
other direction (transverse dispersion).

Hydrodynamic dispersion is primarily caused by two mechanisms: mechanical
dispersion and molecular diffusion. Mechanical dispersion on a microscopic scale is caused by
three mechanisms (Freeze and Cherry, 1979): (1) deviation of velocity in individual pore
channels from the average groundwater velocity, (2) diversion of flow paths around individual
pore channels which results in variations in the average velocity among diflerent pore channels,
and (3) dispersive processes related to the tortuosity, branching and interfingering of pore
channels. The first mechanism is usually referred to as dynamic and the other two as kinematic
( Sahirni and Imdakm, 1988). Molecular diffusion, on the other hand, occurs due to natural
thermal motion of dissolved constituents. Qualitatively, mechanical dispersion and molecular
diffusion are analogous but the causes and the magnitude of their impacts vary. In fact, most of
the time, one of the two mechanisms predominates. As reported by Shackelford (1991),
diffusive mass transport is dominant at seepage velocities of 5 0.005 m/yr.

On a macroscopic scale, it is believed that hydrodynamic dispersion is caused by the
presence of large-scale heterogeneity within the subsurface (Anderson, 1979; Anderson, 1984).
Anderson (1979) reported values of hydrodynamic dispersion coeflicients under field
conditions that are 1000-10000 times larger than values reported in the laboratory. Moreover,
theonlydispersionthatcanbemeasuredinthelabisthatwhichisobservableatthe
macroscopic scale. It is assumed that this macroscopic dispersion is a result of the microscopic
processes previously described (Freeze and Cherry, 1979). In practice, the dispersion
coeflicient is used as an empirical parameter that includes all of the solute spreading
mohanisms that are not accounted for in the transport model.

1.3.2 Modeling dkpers’on under saturated-unsaturated conditions:

Detennmisficmrdsmchastizbavebeenusedtodescribesohrteuansponmfln
subsurface.Amodelisregardedasstochasficifanyofflrevariablesmitsmathematkzal
expressionaredescribedbyaprobabilitydistributionAmodelistermeddeterministicifallthe
variables are viewed as free from random variations. Stochastic models use variable velocity
and dispersion coefficient. The reasoning behind the development of these models is the wide

variability of soil properties in the field. Stochastic models are not reviewed in this chapter.
Readers who are interested in the use of statistical approaches to characterize dispersion in
porous media may refer to the work by Bear (1969), Greenkorn (1970), Scheidegger (1974),
Sahimi er al. (1983, 1986), and Sahimi and Irndakrn (1988).

Deterministic models assume that Darcy's Law applies, ie. all water particles move at
the same velocity through the media Because this assumption negbcts microscopic variations
in fluid velocity, a transport component analogous to Fick's First Law is introduced to account
for dispersion. The justification for the use of this type is given by Taylor ( see Frcher er al.,
1979) in his study of laminar flow through pipes. Therefore, deterministic models use a
constant dispersion coeflicient to describe area-averaged solute movement.

The following section reviews the various forms of the dispersion coefficient reported
to describe miscible displacement, and the flow and transport of contaminants in the saturated-
unsaturated zones. The factors affecting dispersion in porous media are also discussed.

1.3.2.1 Immersion under saturated conditions

Dispersion under saturated flow conditions has been modeled in two forms, namely.
the advectionodispersion (AD) model, and mobile-immobile water (MIM) models.

AD Model:

Several investigators have concluded (Perkins and Johnston, 1963), or tactically
assumd (Brigham er al., 1961; Greenkorn, 1970) that dispersion in porous media is Frckian
ie., that the transport of a nonreactive solute can be described as:

9—t=9D——-v— (1.1)

where, 0 is the volumetric water content, C is the concentration, t is the travel time, D is the
hydrodynamic dispersion coeflicient, v is the seepage velocity and x is the distance.

Brigham er a1. (1961) studied the impacts of particle size, pack/core lengths and
diameter, and phase velocity on dispersion using packs of glass beads and cores of sandstone.
The authors found that dispersion in the sandstone cores was always higher than that in the
packs of glass beads. This was thought to be due to pore-level heterogeneity in the sandstone
cores. Moreover, dispersion was found to be independent of the sample length (samples of
length z 1-8 m) and diameter, except those of very small diameter where wall effects were

important.

Perkins and Johnston (1963) reviewed various forms of the dispersion coefficient
which were derived previously. The report presented the efiects of particle size distribution,
fluid density ratio, and turbulence on dispersion. According to Perkins and Johnston (1963),
dispersion increases for soils with lower uniformity coefficients (well graded) and with
nonuniforrnity of particle shape. Dispersion also increases when the displacing fluid is denser
than the displaced one.

Greenkom (1970) characterized dispersion in porous media which were composed of
glass beads of several different sizes. The dispersion coeflicient for homogeneous and linearly
heterogeneous media was found to be of the form:

D = a v: (1.2)
where, aandb amemphicalconsmntsdratdecreaseudthdreadecreasemdrebeaddimneter.
For heterogeneous media, Greenkom (1970) found that increases in the permeability of the
media increased dispersion and that the dispersion coeflicient is a function of the slope of the
particle size distribution curve.

Charlaix er al. (1987) depicted the efiects of porosity on dispersion They found that
the hydrodynamic correlation length, dispersivity, which is a function of the pore size, was
higher in consolidated media than that in unconsolidated ones. Gupta and Greenkom (1974),
found that dispersivity increases approximately linearly with an increase in clay content

10

MM Models:

Breakthrough curves (BTCs) predicted by the AD Model are nearly symmetrical.
However, several experimental studies on aggregated soils under saturated flow conditions
have shown strongly nonsigmoid and asymmetrical concentration distributions ( for example,
see van Genuchten and Wierenga, 1976, 1977; Nkedi-Kizza er al., 1983; Hutzler et al., 1986).
This has lead to the development of the MIM models, which are also referred to as transport

nonequilibrium models.

While the AD Model assumes that all the water participates in the flow and solute
transport, the MIM models assume that a fraction ofthe water is relatively immobile and,
therefore, does not participate in the flow. The immobile water fraction, however, afiects solute
transport as some mass ofthe solute diffuses into and out ofthe immobile water fraction The
mathematical formulation of the MIM models is usually written as ( Coats and Smith, 1964):

ac ac a’c a
9 "+9 4:9 D -—"'--e v C- (1.3)

 

 

where, the subscripts m and im refer to the mobile and immobile water fiaction, respectively,
D... and v... are the hydrodynamic dispersion coeflicient and average pore-water velocity of the
mobile water, respectively. Other parameters are as previously defined.

To complete the model formulation another equation is used to describe the transfer of
the sohrte between the mobile and immobile water regions. Two different approaches have
been proposed: (1) a mass transfer approach and (2) a difillsion approach In the Mass Transfer
Model, a first-order kinetic transfer equation has been proposed as ( Coats and Smith, 1964):

ehigfwwrch) (1.4)

where, or is the mass transfer coefficient between the two water regions and other parameters
K , as previously defined Coats and Smith (1964) performed experiments on consolidated and

11

where, on is the mss transfer coeficient between the two water regions and other parameters
as previously defired. Coats and Smith (1964) performed experiments on consolidated and
unconsolidated core samples and found that the MIM model with a first—order mass transfer
coefficient is more accurate than the AD model The authors calculated the dispersion

coefficient using the following formulation:

odeo
D=050dpva; 2< D <50 (1.5)

O

 

where, d” is the average particle size and o is proportional to the degree of heterogeneity of
the porous media. Coats and Smith ( 1964) warned against directly applying the dispersion
coefficients determined by Eq.(1.5) to field studies due to possible scaling effects. According to
Coats and Smith (1964), the effects of rate limitation ill mass transfer between mobile and
immobile water regions under field conditions could be negligible due to greater lengths and
lower velocities than those observed in the laboratory experiments.

In the Diffusion Models, the geometry of the aggregate is specified and Eck's Law is
then used to describe the concentration distribution within the specified geometry. For spherical
aggregate geometry, the immobile vohlme-averaged concentration (C5...) is defined as (van
Genuchten and Cleary, 1979; Rao et al., 1980a: Crittenden er al., 1986):

3
cm = 7} Cg dr (1.6)
5 o

where, {is the aggregate radius, r is the radial coordinate, and C; is the local aqueous
concentration inside the aggregate, which is determined using Fick's Law as follows:

_§_D D§_12.%p29§§) ; OSrSE, (1.7)

where, D; is the effective pore diffusion coefficient in the immobile phase.

Athirdapproachthathasbeenutilized todescribethetransport ofsolutesirrsoils
containing an immobile water region is the Efiective (Apparent) Dispersion Model. This

12

approach assumes that local equilibrium between mobile and immobile regions may
satisfactorily describe solute transport. The effects of difi'usive mass transfer and hydrodynamic
dispersion coefficient are combined to obtain an efiective dispersion coeflicient ( Day) that can
be used in the classical AD model This approach is actually based upon the fact that
nonequilibrium causes the spreading of the front of BTC which results in a higher dispersion

coefficient.

Day has been expressed ill different forms. Passioura ( 1971) presented a form of D4

for nonreactive solutes in a system of spherical aggregates:

1_ 2 2
e

where, D is the hydrodynamic dispersion coefi’icient, DC is the molecular diffusion coeflicient ill
porous spheres, (fis the radius ofsphere andois the porosity ofthe system. Otherforms ofqu
have been given by De Smedt and Wierenga (1984) and Parker and Valocchi (1986).

Def: D+

The applicability of the effective dispersion concept requires that mean residence times
be large enough to mitigate differential gradients between mobile and immobile regions (Parker
and Valocchi, 1986). Rao et al. (1980b) found that the limiting condition on Eq. (1.8) is:

W >03 (1.9)
:2 v.

where L is the length.

As mentioned earlier the mobile-immobile water models has been utilized to describe
sohrte transport in aggregated media. However, Schulin er al. (1991) presented data for
saturated experiments with aggregate packing that was adequately described by the advection-
dispersion model combined with an equilibrium ion-exchange isotherm. Schulin er al. (1991)
used the mobile-immobile water model and found no significant improvement in data fitting
over the AD model.

13

1.3.2.2 Dispersion under umaturated conditions:

Most of the deterministic models used to describe solute transport under unsaturated
flow conditions are based upon models previously developed for saturated conditions. The AD
model (Smiles et al., 1981; Bond er al., 1982; Bond, 1986; Schulin er al., 1987; Seyfrmd and
Rao, 1987; James and Robin, 1986), the MIM model with first-order mass transfer coefficient
(van Genuchten and Wierenga, 1977; Guadet et al., 1977; De Smedt and Wierenga, 1984;
Bond and Wierenga, 1990), and the MIM model with specified pore geometry (Gierke er al.,
1990) have been used for simulating unsaturated miscible displacement experiments.

AlthoughtheuseoftheMIMmodels undersaturatedcasesisusuallyassociatedwith
aggregated media, the models have been used under unsaturated conditions for nonaggregated
media ( De Smedt er al., 1986; Bond and Wierenga, 1990). Bond and Wierenga, 1990
indicated that the suitability of using the AD model for unsaturated nonaggregated porous
media depends on the applied flow conditions. They presented steady and unsteady unsaturated
miscible displacement experiments and found that the AD Model satisfactorily described
unsteady flow experiments but a MIM model is needed to account for the tailing in the BTCs
of the steady flow experiments. Several investigators, however, presented data for
nonaggregated porous media under steady unsaturated flow conditions which were
successfullydescribedbytheADmodel ThispointisreviewedinmoredetailinChapterZ.

There have been several derivation to describe dispersion in unsaturated soils. The

formula developed by Bear ( 1969):
D=avz+Dc (1.10)

has been used and found satisfactory by some investigators. For example, Kirda er al. ( 1973)
found that D could be modeled with a = 0.545 and b =1.355 for v2 0.01 cm/min, Yale and
Gardner (1978) found that a = 0.216 and b = 1.0 for 0.01<v, <0.28 cm/min, Biggar and
Nielsen ( 1976) used a = 2.93 and b = 1.11. Eq. (1.10) was used by others (Schulin er al.,
1987; De Smdt and Wierenga, 1984) to model dispersion using the MIM model provided that

14

only the mobile fraction of water is responsible for solute dispersion. De Smedt and Wierenga
(1984) found that the AD model could be used to describe unsaturated BTCs if dispersion
coefficients of about 20 times larger than those for comparable saturated experiments were
used. The use of such an approach is similar to the use of the effective dispersion model, since
both hydrodynamic dispersion and difiusional exchange between the mobile and immobile

water fractions are lumped into one parameter.

1.3.3 Comments on dispersion in the umaturated zone:

Dispersion ill porous media has been characterized by a number of researchers from
different disciplines but the general form is still ambiguous. The primary reason for this is the
inability to include the effects of phase saturation on dispersion In addition, a more
confounding and persistent problem is correlating the laboratory-scale with the field-scale
studieswherethediscrepanciesarisedueto thefactthatthemovement ofwaterthrough
unsaturated zone is three-dimensional and not one-dimensiona1(see, for example, Gelhar et al.,
1985), and the existence of large scale heterogeneity ill the field.

Several forms of the dispersion coeficient, however, have been derived but were case
specific. Dispersion has also been characterized using statistical mechanics, but these
derivationsstillneed to berigorouslyverifiedusing laboratoryandfielddata. Thus, therestill
lacks a unique formulation for the dispersion coeflicient in the unsaturated zone.

1.4 Review of sorption processes for NOCs

Most existing models that deal with the sorption of dissolved organic compounds
in the saturated zone assume that sorption can be described by the use of a partitioning
coefficient determined by experiments on the basis of batch studies. Linear, equilibrium
submodels are usually used for modeling purposes. This may be adequate under certain
conditions, but usually it is used to simplify model analysis and to reduce the required
computation time. In contrast, kinetic approaches requires quantitative treatment of the

15

microscopic transport steps and detailed specification of the geometry of the solid phase
(Rubin, 1983). Although such detailed knowledge is impossible for aquifer materials

(V alocchi, 1985), an adequate understanding of sorption kinetics is necessary to develop
efficient processes to destroy, immobilize, or separate organic pollutants from the soil

matrix.

The conceptual formulation of the various models that deal with the transport of
dissolved organic contaminants through the subsurface are reviewed in the following
sections. Before doing so, a brief idea about the nature of the sorptive interaction of

NOCs is given below.
1.4.1 Mechanisms of sorption of NOCs:

There are two schools of thought on the nature of the sorptive interaction of
N OCs. One assumes that sorption occurs by hydrophobic partitioning between soil
solution and soil organic matter (see for example, Chiou, 1989). The other (Mingelgrin
and Gerstl, 1983), however, regards this mechanism as unproved and that the evidence is
insufficient to exclude surface adsorption. Chiou (1989) has outlined the arguments that
support the partitioning mechanism. These include the ability to model the sorption of
organic solutes at high relative concentration using linear isotherms, the noncompetitive
nature of the interaction of binary solutes, the observed low heats of sorption, and the fact
that the interaction of organics with soil is similar to partitioning of the chemicals into
organic solvents. Recently, Murphy et al. (1990) investigated the sorpitivity of carbazole,
dibenzothiophene and anthracine on hematite and kaolinite coated with natural humic
substances up to a mass percent carbon of 0.5% and found nonlinear sorption isotherms.
They concluded that the actual physio-chemical mechanism is adsorption onto the surface
of the organic carbon phase rather than partitioning into the organic phase.

The tendency of N OCs to partition onto the soil phase has been usually modeled
using a linear equilibrium model as:

16

q = K D C, (1.11)

where, q is the amount of sorbate per unit mass of sorbent, Kp is the distribution
coefficient and C, is the equilibrium concentration of sorbate in the aqueous phase.
Contaminant transport can also be expressed on an organic carbon basis as ( Karickhoff et
al., 1979):

Koc=Ko/foc (1-12)
where, foe is the fraction of sorbent as organic carbon and K0, quantifies the degree of
hydrophobicity of the compound. Several investigators have developed empirical
relationships to estimate the K“ value based on the octanol-water partition coefficient
(Km) or the water solubility of an NOC (see schwarzenbach et al., 1993). The K” value of
a given NOC may vary over an order of magnitude for different soils. Such variations may
be attributed in part to compositional differences in the soils organic matter (Mingelgrin
and Gestl, 1983; Garbarini and Lion, 1986). For example, Garbarini and Lion (1986), in
examining the capacity of selected components of soil organic matter to sorb
trichloroethylene and toluene, observed that the use of a sorbent oxygen content as well as
its carbon content yields a more accurate prediction of K0, than relationships that rely
solely on the organic matter content of the sorbent. The authors warned, however, against
directly applying the relationships they determined to soil with low organic carbon content
due to the possible influence of the mineral matrix. For low-organic carbon mineral
systems, investigations have shown that Kac-Km relationships (where K,c is calculated by
assuming no mineral contribution to sorption) tend to deteriorate below an foe of 0.001
(Schwarzenbach and Westall, 1981 ; Mackay et al., 1985). This suggests that mineral
surfaces contribute (under certain conditions) to the sorption of NOCs. Karickhoff (1984),
in reviewing sorption of organic pollutants in aquatic systems, proposed a multiple
sorptive model in which sorption onto mineral surfaces and partitioning into soil organic
matter contribute to the sorption of NOCs. Mineral contribution to sorption, as discussed
by Karickhoff (1984), tends to occur with high sorbate polarity and/or low organic carbon
content of the sorbate, especially with coincident high clay content.

17

The value of K0,. has also been shown to be influenced by the nature of the mineral-
organic association (Garbarini and Lion, 1986; Murphy et al., 1990). Murphy et al. (1990)
observed that a given humic substance exhibited a different sorptivity for the tested
compounds on the different humic substances-coated mineral surfaces. They attributed this
to the effect of the mineral surface on the interfacial configuration of the humic substances
by either altering the size of the hydrophobic domains on the humic molecule or the

accessibility of these domains to the tested organic compounds.

Sorption linearity appears to depend also on the concentration of an NOC in the
aqueous phase. At low aqueous phase concentration, sorption isotherms are reasonably
linear. Karickhoff (1981) attributed this to the independence of the fugacity coefficient
upon concentration. At high NOC concentration, nonlinear isotherms have been noticed
(Rao and Davidson, 1979; Means er al. 1980; Schwarzenbach and Westall, 1981). Means
et al. (1979, 1980) found that the use of Freundlich sorption model gives more accurate
fitting of polycyclic aromatic hydrocarbons isotherms. The Freundlich model is usually
given as:

q=KD C," (1.13)
where, n is a constant (#1). N onlinearity affects the shape of solute BTC (Brusseau and
Rao, 1989). For n >1, breakthrough front will be spreading and elution front will be self-
sharpening. The effect, however, will be opposite for n <1. The effect of the latter may
mask the effect of nonequilibrium, since nonequilibrium tends to spread the front of BTC.

1.4.2 Effect of moisture content on sorption of NOCs:

Most of the work dealing with the sorption of NOCs was conducted under
conditions where the solid surface is fully covered by water. Little is known about the
impact of changes in water coverage on the ultimate sorption of hydrophobic organic
compounds. The results presented by Spencer and Claith (1970) and those of Chiou and
Shoup (1985) showed that under very dry conditions the adsorbed concentration of
hydrophobic organic compounds would be higher than that obtained with the water phase

18

present. Chiou and Shoup (1985) also found that if the water content is increased such
that it is greater than what is required to provide solid surface coverage, then sorption is
independent on further increase in water content. The above findings, however, are in
contrast with the findings of Peterson er al. (1988) for the sorption of trichloroethylene

(T CE) on a porous aluminum oxide surface coated with humic acids. Peterson et al.
(1988) observed a nonlinear increase of TCE sorption coefficient over the examined
moisture contents (the high end of which corresponds to 2.4 monolayers of water). They
attributed the increase in K4 to either the possibility of the existence of very small fractions
of dry sites or that moist solid surface, which is completely covered with water, has a

sorptive binding strength greater than that when all the pore space is saturated with water.

Experimental observation of vapor phase sorption of N OCs on dry soils and clays
have shown that these materials have a sizable capacity to absorb organic vapors, which is
strongly related to the absorbent external surface area as determined by the Brunauer-
Emmett-Teller (BET) Model (Call, 1957; Chiou and Shoup, 1985; Pennell er al., 1992a).
The observed sorption isotherms were highly nonlinear and corresponds to type-II BET
which is characteristic of vapor condensation to form multilayer adsorbates (Chiou and
Shoup, 1985; Pennell er al., 1992a). It has also been found that sorption is primarily due
to mineral adsorption to solid surface rather than partitioning into soil organic matter
(Pennell er al., 1992a). For the case where the mineral surface is totally covered by
organic matter, linear sorption isotherms have been found (Peterson er al., 1988). This
would suggest that under such conditions of complete coverage of the mineral surface by
the organic matter phase, partitioning into soil organic matter is the controlling factor. In
addition, vapor phase sorption on dry clays have been found to be influenced by
exchangeable cation species (Jurinak, 1957; Pennell er al., 1992b) and cation exchange
capacity (Pennell er al., 1992b). Such variation in the sorption uptake was attributed to
variation in BET surface areas. However, Pennell er al. (1992b) observed higher sorption
of p-xylene on Ca-, Na-, and Li-Kaolinite than what would be accounted for based on
BET surface area. They suggested the possibility of having specific interactions between

p-xylene and exchangeable cations.

l9

Sorption isotherms of water vapor by dry soils has also been shown to be nonlinear
and of the BET-type, but with higher sorption capacity than organic vapors (Chiou and
Shoup, 1985; Pennell er al., 1992b). The high sorption capacity of water can be explained
based on the strong polar interactions with polar minerals (Chiou et al., 1983). Pennell er
al. (1992b) concluded that sorption of water on Ca- and Na-kaolinite is related to the
hydration energy of exchangeable cations. It would be expected, therefore, that water
effectively competes with N OCs for mineral adsorption sites. This has been noticed by
many investigators (Spencer and Claith, 1970; Chiou and Shoup, 1985 ; Peterson et al.,
1988; Pennell et al., 1992a; 1992b). Chiou and Shoup (1985) noticed that in addition of
the dramatically reduced sorption capacities of benzene, m-dichlorobenzene, and
trichlorobenzene in the presence of water vapor, the isotherms for organic vapor at
relative humidity (RH) of 50% or more are practically linear. Moreover, at RH of 90% the
sorption capacities fall into a range close to those found in aqueous systems. Nonlinear
BET isotherms, however, have been reported by Shonnard er al. (1993) for the sorption
of benzene and dichloromethane at RH of 25% and 33%, and by Pennell et al. (1992a) for
the sorption of p-xylene at RH of 67% and 90%. On the other hand, Pennell er al. (1992b)
noticed small reduction in p-xylene with increasing RH. The authors attributed the
continuation of sorption of p-xylene in the presence of water to the possible existence of a

considerable fraction of surface sites not covered by water.

Although the effect of moisture content on the sorption of NOCs is well
established, the specific mechanisms responsible for the sorption at RHs above what is
required to provide surface coverage by at least a monolayer of water remain unclear. Call
(1957), for example, studied the effect of RH on the sorption of ethylenedibromide on
several soils and clay minerals. Call (1957) suggested that sorption on wet soils is
attributed to dissolution in sorbed water films and adsorption at the gas-liquid interface. In
contrast, Chiou and Shoup (1985) postulated that hydrated soils behave as a dual sorbent
in which the mineral surface acts as a conventional solid adsorbent and the organic matter

as a partition medium. Pennell er al. (1992a) , however, demonstrated that mechanisms in

20

addition to what have been proposed by Chiou and Shoup ( 1985) must be considered to
account for vapor sorption of p-xylene in the unsaturated zone. They concluded that a
multimechanistic approach should be utilized for such purposes which include: " a)
adsorption on mineral surface, b) partitioning into the soil organic matter, c) dissolution

into sorbed water films, and d) adsorption on the gas-liquid interface".

Little is known about the effect of soil moisture content on the sorption of NOCs
under dynamic conditions. The findings of Chiou and Shoup (1985) and those of Peterson
er al. (1988), although in conflict with each other, do not incorporate the impact of
changes in vertical velocity associated with changes ill soil water content. Soil water
content and velocity are positively correlated. A decrease in vertical velocity will retard
the downward transport of the chemical. However, a decrease in water content increases
the fraction of air-filled pores, resulting in creation of additional dead-end pores which rely
on diffusion process to attain equilibrium with the displacing solution (Gupta et al. 1973).

1.4.3 Modeling sorption in soil aquifers:

The one—dimensional equation describing solute transport through a homogeneous

soil column, under steady-state conditions, is given as:

8C paq 32C 8C
— -- = - 1.14
at * eat a; "°az ( )

where, q is the concentration in the solid phase, and other parameters are as defined

previously.

Prior to solving Eq. (1.14), a submodel was required to describe the sorption rate.
For a linear equilibrium sorption reaction, Eq. (1.14) in a nondirnensional, scaled form
reduces to

ac D azc ac

87:353-8—2 (1.15)

21

R=l+£§l (1.16)

where C is the normalized solute concentration, L is the length of the column, T is the

normalized time = v0 0 t/L, and R is the retardation coefficient.

The existing equilibrium transport models, however, have been less than
satisfactory for simulating solute transport under several conditions (van Genuchten and
Wierenga, 1977; Gaudet et a1, 1977 ; Gupta et al., 1973; Krupp and Elrick, 1968). The
observed asymmetry and tailing of BTCs using soil columns has been attributed to slow
solute sorption reaction or slow mass transfer with respect to advective flow of the pore-

water. Nonequilibrium submodels are presented in the following sections.

Two general types of models have been developed to simulate sorption kinetics; 1)
sorption-related models and 2) transport-related models (Brusseau er al.,l989). The
sorption-related models result either from chemical nonequilibrium or intrasorbent
diffusion. Transport-related models, also referred to as physical nonequilibrium models,
assume the existence of mobile and immobile water regions with solute transfer between
the two water regions. These models have been discussed in detail in section (1.3.2.1).
Sorption-related models are discussed in the following section.

Chemical nonequilibrium models:

All the chemical nonequilibrium models assume that the sorption reaction is the
rate-limiting process. The derivations of these models ignore the existence of mobile-
immobile water regions and assume that all the water contributes to chemical transport.
The difference among the chemical nonequilibrium models is in the nature of the sorption
rate a sorbate undergoes. In the one-site first-order model, all the soil sites are assumed to
be kinetically controlled. The equation that describes the rate of sorption is given as (van
Genuchten et al. 1974):

 

22

9.4 _ 9 n
at _ kfpc qu (1.17)

where, k, and k, are the forward and reverse rate coefficients, respectively. This
mathematical formulation implies that sorptive exchange is limited by only one of many
important processes including binding by single class of sorbing site. It was found that this
model does not fit experimental data well (Wu and Gschwend, 1986), especially at high
pore-water velocity (van Genuchten, 1974, Pignatello, 1989).

Kinetic sorption data always shows a rapid initial uptake followed by a slow
approach to equilibrium (Wu and Gschwend, 1986; van Genuchten and Wierenga, 1976;
Khan, 1973). This finding has been utilized in developing the two-site chemical
nonequilibrium models. In these models, sorption on one of the sites is assruned to be
instantaneous, while sorption on the other site is kinetically controlled (Cameron and
Klute, 1977). The mathematical formulation of the sorption rates are (Brusseau and
Rao,1989):

aq, _ 8C

_at _ FKD—at (1.18)
3
% =1 Y[(1-F)KDC ’ qzl (1°19)

where, F is the fraction of the instantaneous sorption sites, 7 is a first-order rate constant
and q) and q; are the amount sorbed on the instantaneous and kinetically controlled
sorption sites. The model was found to be more successful than the one-site model in
fitting column BTC data (Wu and Gschwend, 1986; Cameron and Klute, 1977).
Unfortunately, the model retains three fitting parameters (7, Kp, F) which cannot be
estimated by independent means. In addition, the model was found inadequate to describe
the BTC of 2,4—dimethylammonium salt and atrazine (Rao et al., 1979).

23

Intrasorbent diffusion:

Intrasorbent diffusion involves the diffusive mass transfer of sorbate within the
matrix of the sorbent. This can be separated into two classes; intraorganic matter diffusion
(IOMD) and intramineral diffusion (Brusseau and Rao, 1989;1Brusseau et al., 1939).
Given that organic matter is the predominant sorbent for HOCs, intramineral diffusion is

not likely to be important (Brusseau et al., 1989; Wu and Gschwend, 1986).

The conceptualization upon which the IOMD model is based requires that soil
organic matter has a three dimensional structure, and that diffusion within the organic
matter matrix is the rate-limiting process. Evidence of the last requirement has been given
by Brusseau er al. (1991), Bouchard et al. (1988) and Nkedi-Kizza et al. (1989).

The mathematical formulation of an IOMD model is similar to the formulation of
the Transport-nonequilibrium models, discussed in section 1.3.2.1, except that all the

water present is considered mobile.
1.4.4 Comments on modeling sorption in soil aquifers

Brusseau and Rao (1989) and Brusseau et al. (1991) discussed the appropriateness
of using chemical nonequilibrium models for the transport of N OCs. They stated that "the
assumption of two significant types of sorption sites may not be viable," and that the
nature of the hydrophobic reaction "results in hydrophobic sorption being a rapid
process". Furthermore, experimental evidence of physical, not chemical, contribution to
nonequilibrium is given by Wu and Gshwend, 1986: The lack of temperature dependence
was interpreted as evidence that a physical process was being manifested; the dependence
of sorption rate on particle size is consistent with a diffusive mechanism. The effect of
diffusion into the organic matter in causing nonequilibrium is also experimentally
supported by Bouchard et al. (1988).

24

Significant differences exist between different model hypotheses for the transport
and transfer processes of organic chemicals in the soil. Because of the number of
parameters associated with each model, verification of specific process hypothesis has
been confounded. Usually, complex models with many parameters can achieve good
agreement with experimental observations if parameters are adjusted to the data.
However, this agreement does not constitute a test of the model hypotheses, but merely
demonstrates the versatility of the model to describe outflow shapes or soil profiles.
Nkedi-Kizza et al. (1984) showed, for example, that the mobile-immobile water model
and the chemical nonequilibrium model with two different types of sorption sites had the
same mathematical form. Thus, their optimum fit to any single concentration-time or
concentration-depth record will be identical, even though they have been built on
physically distinct hypotheses. It is imperative, therefore, to devise independent means of
measuring the model parameters by a method other than simultaneous curve-fitting with
other parameters. Efforts in this regard are very limited and are restricted to porous media
with well defined su'ucture ( Rao et al., 1980).

The assumption that a single process is responsible for the observed
nonequilibrium results in a lumped kinetic term for systems where nonequilibrium is
affected by more than one process. This limitation has recently led to the development of
other transport models which account for more than a single nonequilibrium process (see
Brusseau et al., 1989). The main limitation of these models is still the large number of
transport parameters that, in most of the cases, cannot be determined independently.

One of the transport parameters related to sorption is the retardation coefficient
This parameter is either determined using batch or column technique. However, results
reported using the two techniques for modeling sorption under saturated conditions are
ambiguous. This has been discussed in more details in Chapter 3. Studies regarding
retardation under unsaturated conditions are very limited. As discussed earlier, Previous
work focus on determination of changes in distribution (partitioning) coefficient with

changes in moisture content under static conditions. It is not straightforward, however, to

25

determine how the distribution coefficient changes with saturation under dynamic
conditions. The difficulty arise due to the fact that under dynamic conditions R (not Kp )
is the parameter that can be determined from an unsaturated column study. To obtain Kp
from the value of R one needs to know the value of the solid/water ratio, i.e. p/0 at that
level of saturation. The value of 0 can be determined gravirnetrically, the amount of solid
that participated in the sorption process could be different from that when the column was
fully saturated. Determination and changes of R with saturation is the primary topic of
Chapter 4 of this study.

1.5 Review of volatilization and air phase transport processes

The earliest model of VOC transport in the unsaturated zone was developed by
Jury er al. (1983, 1984a, b, c). The model incorporates the effects of volatilization,
leaching, and degradation to describe the major loss pathways of pesticides. The model
which assumes linear reaction and equilibrium conditions, was intended for use as a
screening tool to assess behavior under prototype conditions rather than to make precise
predictions under specific circumstances. Baehr (1987) and Mendoza and McAlary (1990)
provided numerical solutions for transport of organic vapors in the unsaturated zone.
Their model does not incorporate water mobility and assume instantaneous and
equilibrium conditions. Gierke er al. (1990) developed a one-dimensional transport model
to simulate the transport of VOCs in unsaturated soil columns. The model takes into
consideration advective-dispersive transport in both liquid and gas phase and accounts for
sorption. The model, however, has not been experimentally validated using a sorptive
medium. Moreover, independently determined gas dispersion coefficient and Henry's
constant were altered in the description of the column data. This emphasizes the need for a
better understanding of the role of volatilization and transport in the air phase as a
function of saturation. The following sections review volatilization and transport of VOCs
in the air phase. Section 1.5.3 addresses the impact of volatilization and diffusive uansport
in the air phase on retardation and dispersion of VOCs.

26

1.5.1 Volatilization of VOCs

The importance of volatilization of VOCs and vapor transport in the subsurface
has only recently been appreciated. Wilson et al. (1981) presented the results of a
laboratory investigation of the transport of organic pollutants in soil columns. By
infiltrating organic solutions in unsaturated columns, they found that 30 to 90% of the

organic mass was lost to volatilization during percolation.

The partitioning between dissolved and vapor phases for an organic compound is
generally described through the equilibrium relation known as Henry's law. Henry's law
states that the partial pressure of a compound above the water phase, P,- is proportional to
the mole fraction of the compound in the water phase, X:

P, = k,,x (1.20)
where kg is Henry's constant. Henry's law is obeyed very well for sparingly soluble,
noneloectrolyte compounds assuming an ideal gas phase ( Noggle, 1985). Using the ideal
gas law:

PiV = chT (1.21)
where Vis the volume of the air phase, n is the number of moles of the compound, RC is
the universal gas constant, and T is the temperature. Eq. (1.20) may now be expressed in
the dimensionless form:
G = K ”C (1.22)
where G is the concentration in the air phase, C is the concentration in the liquid-phase
and K” is the dimensionless form of the Henry's constant (= kg /RC 1).

In almost all models describing vapor and dissolved phases, Henry's law is assumed
to apply at all times, i.e. the phases are assumed to be in equilibrium, and the relationship
is assumed to apply over the entire concentration range. Thus, Henry's constant may be
calculated from two properties of organic compounds: its vapor pressure and solubility in
water. The first expresses the equilibrium relationship between a solid or liquid compound

and its gaseous concentration, and the second expresses that between the compound and

27

its concentration in water. If a compound is both at equilibrium with the gas phase and the
water phase, then the respective concentrations in the gas and water phases must be at
equilibrium, and thus the ratio of these respective concentrations should yield the Henry's
law constant

K, = Gm /C,,,, (1.23)
where the subscript sat refers to the saturated state of the phase. Since both vapor
concentration and solubility are temperature dependent, K” is a function of temperature. In
general, Ky increases by a factor of two to three for each 10 °C rise in temperature.
However, for an isothermal simulation, solution concentration in the two phases are
assumed to be proportional and one of them may be eliminated from the transport

equations using Eq.(1.23)

Although virtually all models representing these two phases assume the equilibrium
form of Henry's law (Jury and Ghodrati, 1989), it is probable that a mass transfer
limitation occurs in the transfer from the bulk water to the water-air interface, across the
interface, or from the interface into the bulk air. Gierke er al. (1990) concluded from
model comparisons to experimental observations of trichloroethene transport with water
flow through unsaturated soil columns that the rate of mass transfer across the air-water is
fast. Similar conclusion was also reached by Gierke er al. (1992) for their toluene vapor
transport experiments through unsaturated soil columns. The level of saturation that has
been measured in the work of Gierke er al. (1990, 1992) was less than 64%. Jury and
Ghodrati (1989) indicated, however, that air-water mass transfer may be limited at
relatively high soil water contents.

The rates of transfer from the bulk water to the interface and from the interface to
the bulk air are generally considered much slower than the rate across the interface itself
(McCarty, 1983). Under this condition, the interfacial concentration in the water Cr... is in
equilibrium with the interfacial concentration in the air G... and thus

K” =0,“ ICm (1.24)

28

Mass transfer parameters between the water and the air phases have not been
studied in unsaturated soils. Several studies, however, have been conducted in the field of
air stripping and packed-tower operations. McCarty (1983) reviewed the removal of
organic substances from water by air stripping and showed that the overall mass transfer

coefficient of the compound, 01,, from water to air takes the form:
1 l 1

 

(1.25)

where out is the liquid transfer coefficient, and out8 is the gas transfer coefficient. The above
equation shows that the overall mass transfer rate depends on the rate of transfer from the
bulk water to the air-water interface and the rate of transfer from the interface to the bulk
air. Eq. (1.25) also illustrates that mass transfer will be liquid-phase controlled for
compounds with very large Ky since the last term in the equation becomes negligible, but
will be gas-phase controlled for very small K”. For intermediate values of K” , mass

transfer will be gas- as well as liquid-phase controlled

The other parameter that needs to be determined is related to the area of contact of
the phases, the geometry of the phase interfaces, and the distribution of the phases within
the pores. Application of the theories that has been developed to predict mass transfer
rates across interface boundaries were limited, in this regard, to very simple systems
(Pfannkuch, 1984). In view of the difficulties in characterizing interface mass transfer
processes in porous media ill terms of fundamental parameters, a simplified approach is
usually used. A first-order expressions in which the mass transfer driving force is
proportional to the difference between the concentration in the two phases is employed.
The proportionality constant is an overall mass transfer coefficient reflecting the
contribution of the geometry of the soil and the distribution of the phases in the pores.
Gierke er al. (1990), for example, used the following form to describe mass transfer of
VOCs between air and water

a 39m, an [i-C] (1.26)

29

This equation is similar to Eq. (1.4) used to describe mass transfer between the mobile and
immobile water regions. Gierke er al. (1990) used a correlation developed by Turek and

Lange (1981) for trickle bed reactors to estimate the value of 01,- am .

1.5.2 Transport of VOCs in the air phase

VOC dissolved in the water phase will volatilize and migrate through the gas phase
in the unsaturated zone by both diffusive and advective processes. It is common in
modeling miscible transport of VOCs in the vadose zone to assume a static gas phase.
Pinder and Abriola (1986) questioned the validity of neglecting gas phase advection in
modeling the transport of highly volatile organics in the vadose zone. Kell (1987)
investigating the transport of pentane in dry laboratory sand columns, noted significant
advective transport Kreamer er al. (1988) suggested, however, that vapor-phase
advection is small and can be neglected unless air pumping is present or unless there is a

rapidly fluctuating water table.

Advection in the air phase may also be caused by density gradients arising from the
high vapor pressure and molecular weights of some organic liquids. Abriola (1989)
reviewed modeling multiphase transport of organic chemicals in porous media, and
warned against not incorporating convection (density effect) of the air phase in modeling
VOC transport in the vadose zone. Density-driven gas flow models were developed by
Falta er al. (1989) and Mondoza and Frind (1990). Density variations with gas
composition were found to have a significant impact on dense vapor (relative vapor

density > 1.2) transport in soils with permeability greater than 10'" m2.

In the absence of vapor pressure and high density gradients, gaseous diffusion is
expected to be the major mechanism for vapor transport Diffusive processes may include
ordinary diffusion, thermal diffusion, and counter diffusion resulting from evaporation of
soil water (Weeks er al., 1982). Among all, ordinary gaseous diffusion is the mechanism of

30

greatest importance in the unsaturated zone (Weeks et al., 1982). This mechanism is a

result of a concentration gradient within the unsaturated region.

As coefficients of molecular diffusion in the gas phase are four to five orders of
magnitude compared to those of diffusion in the liquid phase, ordinary gaseous diffusion
may be a significant transport mechanism for VOCs in the unsaturated zone. Weeks et al.
(1982) detected significant downward diffusion of fluorocarbons into the unsaturated
zone. Mendoza and McAlary (1990) predicted that a TCE vapor plume in a permeable
sandy material will spread tens of meters in the unsaturated zone within a few months by
molecular diffusion and possibly by density-driven advection. Gierke er al. (1990)
concluded that vapor diffusion is an important transport mechanism for TCE in sand with
average pore-water velocities less than 0.43 cm/day. Therefore, volatilization and
subsequent gas phase transport and gas-water partitioning, under certain transport
conditions, may result in increased water phase contamination in both saturated and

unsaturated zones.
1.5.3 Dispersion and retardation of VOCs under unsaturated conditions

Conservation of mass of a nondegradable VOC through homogeneous porous
medium is expressed as:
a

atmwc + 9,0 + p q) + A-[Jw + 1a]: 0 (1.27)

where, J... and Ja are water and air flux, respectively. All other symbols are as defined
previously. If equilibrium conditions are valid to describe mass partitioning between air,
water, and solid phases, then G and q can be written in terms of C as shown in Eq (1.22)

and Eq. (1.11), respectively.

Under the assumption that ordinary diffusion is the prevailing transport mechanism

in the air phase, then water and air flux may be expressed as:

31

J... = 0,,voC - 0,,DAC (1.28)
and
Jo = -D. AG (1.29)
where, D, is the effective diffusion coefficient in the air phase. Terms in Eq.(1.28) are
identified earlier. For nonreactive vapors in moist soils, Millington and Quirk (1961)
showed that D, can be calculated from the free-air diffusion coefficient (D,"") using the
following relationships:

D, = 9,1.DZ" (1.30)

/3
,=92_
a 2

¢

(1.31)

Sallam er al. (1984) indicated that Eq.(1.31) is an approximate representation.
They found that a coefficient of 2.1 rather than 7/3 provided better agreement with
experimental data. Neilsen er al. (1984) pointed out that significant differences in
estimated diffusion coefficients occur depending on the assumed model. They present a
pore distribution model to estimate the diffusion coefficient of radon. Peterson er al.
(1988) found that the gaseous diffusion coefficient predicted empirically by Eqs. (1.30)
and (1.31) can be in error by as much as 400%.

Eq.(1.27) can be written in terms of air phase concentration, liquid phase
concentration (Baehr, 1987), or total concentration (Jury er al., 1983). Baehr (1987)
considered stagnant liquid phase, and Jury et al. (1983) neglected hydrodynamic
dispersion. In terms of liquid phase concentration, Eq.(1.27) may be written as:

 

 

9.10. p K» ac Kw. a’C ac
I —— -—- = D - .— 1.32
(+e.+e.)8t (+0.)?lx’ vax ()
2
8C 1 a C 8C (1.33)

E = 'EHDefirlfi - 120$]

where, D47 is an overall effective dispersion coefficient Since dispersion affects only the

spreading of the BTC but not the mean of the curve, then R is a measure of retardation.

32

Retardation and diffusive transport of VOCs in the air phase at various levels of saturation

are discussed in more detail in Chapter 4.

1.6 Validity of local equilibrium assumption

Several studies have addressed the problem of developing criteria for the
applicability of local equilibrium assumption (LEA) (V alocchi, 1985; Parker and Valocchi,
1986; Jennings and Kirkner; 1984; Bahr and Rubin, 1987). Jennings and Kirkner (1984)
used Damkohler I number (D.), which is the ratio of an average transit time to reaction
time, in a study of multicomponent transport affected by surface reactions and solution
phase complexing. They concluded that LEA is applicable when the smallest D. exceeds
100, and reasonable approximation can be achieved when D. exceeds 10. However, the
authors cautioned that the smallest D. criteria is applicable to the boundary conditions they
used and modification of the criteria may be needed for other boundary conditions.
Valocchi (1985) argued that the use of Damkohler numbers as criteria may not be
sufficient as other parameters may influence the validity of LEA

Valocchi (1985) and Parker and Valocchi (1986) used the first, second and third
temporal moments to evaluate the impact of nonequilibrium upon solute transport and
assess the differences between nonequilibrium and equilibrium models. In the temporal
moment method, developed by Aris (1958), the first three moments correspond to the
mean, degree of spreading and degree of asymmetry of the BTC, respectively. Valocchi
(1985) and Parker and Valocchi (1986) examined several nonequilibrium models of a
solute that undergoes linear sorption reaction. Fractional deviations in the second and
third central moments of the BTCs for equilibrium and nonequilibrium models have been
used to quantify the applicability of LEA '

Valocchi (1985) compared the behavior of two physical and chemical
nonequilibrium models to that of a local equilibrium model. The derived moments indicate
that nonequilibrium does not affect the mean breakthrough of a solute (all models have the

33

same first temporal moment). However, expressions of the second and third moments
illustrate the enhanced spreading and asymmetry created by nonequilibrium conditions.
The criteria used by Valocchi (1985) for assessing the deviation from nonequilibrium is

given by the E parameter defined as:

E=-£"———"'— (1.34)

where, U,,, and U,, are the nonequilibrium and corresponding equilibrium moments.

When E parameter = 0, solution to nonequilibrium and equilibrium models will be exactly

The most benefit of using the temporal moment method is that evaluation of
transport models can be made without knowledge of the analytical or numerical solution
to the transport models. A major limitation of the use of the method, however, is that its
dependency upon Laplace transformation makes its applicability restricted to linear

problems.

Bahr and Rubin (1987) developed a method termed SKIT, separation of the
kinetically influenced term, to identify the term or terms responsible for departure from
local equilibrium. The authors proposed four steps to develop a SKIT equation: (1) write
the system of mass balance equations describing the transport problem, (2) obtain
substitution expression for the sorbed species, (3) differentiate the expressions obtained in
step 2, and (4) substitute the differentiated expressions into the original mass balance
equation. Note that step 2 needs to be modified in case of compounds that undergo
volatilimtion. Once developed, the SKIT equation will be a sum of an equilibrium
equation and one or more kinetically influenced terms, as shown in the following
nondimensional equation developed by Bahr and Rubin ( 1987):
F \ 1

ac a’c ac 1 1 ac 1 a’c ac
ar az az p, H .1 ar paz az

D02)

 

 

 

 

 

 

34

where, Pp is equal to the sum of two Damkohler numbers ( D“ and Du). Eq. (1.37) shows
that the kinetically influenced term is a product of (lle) and a differential facter. Bahr and
Rubin (1987) proposed using Pp as a criterion for quantifying the validity of using LEA.
To quantify the departure of a nonequilibrium model from local equilibrium a parameter a

is proposed which is defined as:

c = -q— (1.36)
Qeq

When q = q,, solution to nonequilibrium and equilibrium models will be exactly similar.
A major limitation of the use of the SKIT method is that kinetic data are necessary to
make a feasible prediction of the departure from LEA. Another limitation is that it can not
be applied to all transport models.

1.7 Summary

Several transport and transfer mechanisms may affect the movement of dissolved
VOCs ill the unsaturated zone including, advection and dispersion ill the water phase, sorption,
volatilization, and advection and dispersion ill the air phase.

Dispersioninporousmediahas beencharacterizedbyanumberofresearchelsfi’om
difierent disciplines but the general form is still ambiguous. The primary reason for this is the
inability to inchlde the effects of phase saturation on dispersion. A more confounding and
persistent problem is correlating laboratory-scale with field-scale studies where the
discrepanciesarisedueto thefactthatthemovementofwaterthroughunsaturatedzoneis
three-dimensional and not one-dimensional and the existence of large scale heterogeneities in
the field.

One of the transport parameters related to sorption is the retardation coefficient
This parameter is determined using either a batch or column technique. Reports vary as to
the relationship between the results obtained by the two techniques. In addition,
extrapolation of the results of either technique to describe retardation under unsaturated

35

conditions are yet to be verified. Determination of the impact of water content on the
sorption distribution coefficient was limited to static-type experiments and at levels of
saturation that do not contribute to flow. Little is known about the effect of soil moisture

content on the sorption of N OCs under dynamic conditions.

Several factors are potential causes for nonequilibrium during VOC transport in
the unsaturated zone including: slow diffusion between mobile and immobile water
regions, slow chemical reaction, s_1_qw diffusion into the matrix of soil organic matter, or
slow partitioning into or from the air phase. Tremendous efforts have been expended in
deve10ping nonequilibrium transport models which assume one or more of the above
factors as the rate-limiting process. Unfortunately, verification of specific process
hypotheses has been confounded. Adequate understanding of the cause and reasonable
quantification of the extent of nonequilibrium is necessary to develop efficient processes to

destroy, immobilize, or separate organic pollutants from the soil matrix.

In the absence of vapor pressure and high density gradients, volatilization may
enhance retardation of VOCs and gaseous diffusion is expected to be the major
mechanism for vapor transport. As coefficients of molecular diffusion in the gas phase are
four to five orders of magnitude higher than those in the liquid phase, ordinary gaseous
diffusion may be of significant importance.

36

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Mendoza, C. A., and Frind, E. O., 1990. Advective-dispersive transport of dense organic
vapors in the unsaturated zone, 1, Model development, Water Resour. Res., 26:
379-387.

Mingelgrin, U. and Gerstl, Z. J ., 1983. Reevaluation of partitioning as a mechanism of
nonionic chemicals adsorption in soils, J. Environ. Qual, 12: 1-1 1.

Murphy, E. M., Zachara, J. M. and Smith, S. C., 1990. Influence of mineral-bond hurnic
substances on the sorption of hydrophobic organic compounds, Environ. Sci.
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Nielsen, K. K., Rogers, V. C. and Gee, G. W., 1984. Diffusion of radon through soils: A
pore distribution model, Soil Sci. Soc. Am J. 48:482-487.

Nkedi-Kizza, P., Biggar, J. W., van Genuchten, M. Th., Wierenga, P. J ., Selim, H. M.,
Davidson, J. M. and Nielsen, D. R. 1983. Modeling tritium and chloride 36
transport through an aggregated oxisol. Water Resour. Res., 19:691-700.

Nkedi-Kizza, P., Biggar, J. W., van Genuchten, M. Th., Wierenga, P. J ., Davison, J. M.,
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Nkedi-Kizza, P., Brusseau, M. L. Rao, P. S. C. and Hornsby, A. G., 1989.

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Noggle, J., 1985. Physical chemistry, Little, Brown, Boston, Mass.

Orgam, A.V., Jessup, R. E., Ou, L. T. and Rao, P. S. C., 1985. Effects of sorption on
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Environ. Microbiol, 49:582-587.

40

Parker, J. C., and Valocchi, A. J., 1986. Constraints on the validity of equilibrium and
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399-407.

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Pennell, K. D., Rhue, R. D. Rao, P. S. C. and Johnston, C. T., 1992a. Vapor-phase
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Toronto Press.

41

Schulin, R., Papritz, A., Fluhler, H. and Selim, H. M., 1991. Parameter estimation for
simulating binary homovalent cation transport in aggregated soils at variable ionic
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1444.

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Pub. Co., NY, 1979, 349.

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porous media: Experimental evaluation with tritium. Soil Sci. Soc. Am. J ., 41:
272-278.

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in sorbing porous media: 111. Experimental evaluation with 2,4,5-T, Soil Sci Soc.
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southern high plains of Texas, Water Resour. Res. 18:1365- 1378.

42

Wilson, J. T., Enfield, C. G., Dunlap, W. J ., Crosby, R. L., Foster, D. A., and Baskin, L.
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Yale, D. F. and Gardner, W. R., 1978. Longitudinal and transverse dispersion coefficients
in unsaturated plainfield sand. Water Resour. Res., 14: 582-588.

CHAPTER 2

EFFECT OF WATER SATURATION ON DISPERSIVITY AND INIMOBILE
WATER IN SANDY SOIL COLUMNS

2.1 Introduction

The normalized one-dirnensional advection-dispersion (AD) equation describing
solute transport through a homogeneous soil column, under steady-state conditions, is
given by Eqs. (1.15) and (1.16), in which D is the hydrodynamic dispersion coefficient
which has commonly been expressed by Eq. (1.10). The first term on the RHS of Eq.
(1.10) is referred to as mechanical dispersion. This is primarily caused by two mechanisms;
one kinematic and the other dynamic ( Sahimi et al., 1983). The kinematic mechanism
results from a variation in the length of streamlines that traverse the length of the column.
The dynamic mechanism results from a variation in the speed of fluid movement from one
streamline to the next Longitudinal spreading of solutes in porous media may also be
caused by the existence of nonequilibrium processes during solute transport. This
spreading should not be incorporated into the dispersion coefficient if this coefficient is to
be referred to as the hydrodynamic dispersion coefficient

Two unsettled issues have been reported for experiments conducted under steady-
state, unsaturated conditions: the fust regarding the shape of BTCs and the second
regarding differences in the dispersive behavior compared to the case when the porous
media is saturated. Table 2.1 summarize the results of some of these experiments. The two

issues are discussed below in more detail.

43

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45

Some experiments under unsaturated flow conditions have shown nonsigmoid and
asymmetrical concentration distributions (van Genuchten and Wierenga, 1976, 1977;
Nkedi-Kizza et al., 1983; De Smedt and Wierenga, 1979, 1984, 1986; Bond and
Wierenga, 1990). Such observations are inconsistent with the use of the simple AD model
and led to the development of other transport models that use one of the following
approaches: (1) models that incorporate a diffusive interchange of solute between mobile
and immobile zones of specified geometry (van Genuchten et al., 1984), (ii) models that
incorporate a first-order mass transfer of solute between mobile and immobile water
regions (Deans, 1963; Coats and Smith, 1964; van Genuchten and Wierenga, 1976), and
(iii) an AD model with a modified (lumped) dispersion coefficient (Baker, 1977). The use
of approach (1) requires detailed knowledge of the geometry of the porous media.
Approach (ii) is simpler and provides simulations similar to those obtained using the .
diffusion based models ( Parker and Valocchi, 1986). The system of normalized equations
describing approach (ii) for a linear, equilibrium sorption is ( van Genuchten and

Wierenga, 1976):

 

 

 

ac do n azc ac
IR m l_ R int = m m _ m
13 ar H B) ar rum az2 az (2,)
(l-B)Raci"' =0)(Cm-Cim)
37 (2.2)

where Cm and C i," are the average relative concentrations in the mobile and immobile
water regions, respectively. R is as defined before, Dm and vom are the dispersion
coefficient and average pore-water velocity of the mobile water, respectively. B is a .
dimensionless partition variable and (1)18 the normalized mass transfer coefficient. [3 and (o

are defined as:
B:(6m+prD)/(9+pKD) (2.3)
(I): (XL/Vomem (24)

46

where 0", is the volumetric water content of the mobile region, f is the fraction of sorption
sites in the mobile region and or is the average mass transfer coefficient between the mobile
and immobile water regions. When R: 1 (i.e. Kn is zero), 13 reduces to the fraction of
mobile water (i.e. Bn/B). Evidence of the existence of stagnant (immobile) water regions
was clear for some investigators (Krupp and Elrick, 1968; Gupta et al., 1973; De Smedt
and Wierenga, 1979; De Smedt and Wierenga, 1984; Bond and Wierenga, 1990; and
others). Other researchers have shown the suitability of using the AD model without
considering the existence of an immobile region (Biggar and Nielsen, 1976; Yale and
Gardner, 1978; James and Rubin, 1986; Schulin et al., 1987; Seyfried and Rao, 1987).
James and Rubin (1986), for example, were able to describe chloride transport through
unsaturated sand columns using an AD model that included anion exclusion. Their support
for the existence of anion exclusion is the difference in the shape of saturated BTCs of

chloride from those of tritium.

The other unsettled issue is the change in the mechanical dispersion when the soil
is desaturated. Application of the capillary tube model of Aris (1956) would predict that
for the same average pore-water velocity the dynamic part of mechanical dispersion will
be reduced as the media is desaturated. This is because the possible range of pore sizes is
reduced as the larger pores are emptied. Experimental results reported by James and
Rubin ( 1986) are in agreement with this analysis. However, results reported by Yale and
Gardner (197 8); De Smedt and Wierenga (1979, 1986); in addition to those (not listed in
Table 2.1) of Biggar and Nielsen (1976) and De Smedt and Wierenga (1984) have shown
an increase in dispersion for partially saturated media as compared to the fully saturated
case. De Smedt and Wierenga (1984) assumed that hydrodynamic dispersion retains the
same value, at a given pore-water velocity, regardless whether the media is saturated or
unsaturated. They attributed the increase in dispersion of their unsaturated experiments to

the existence of a physical nonequilibrium situation created by solute exchange between

47

mobile and immobile water regions. Yale and Gardner ( 1978), however, reported
symmetrical BTCs with what appears to be higher mechanical dispersion under
unsaturated conditions. Yale and Gardner ( 1978) speculated that this occurred because of

a wider variation in the pore-water velocity distribution when the soil is desaturated.

The purpose of this chapter is to investigate the dispersive behavior of non-
aggregated soils under unsaturated flow conditions as compared to when the soils are fully
saturated. In so doing, a better understanding of the appropriate conceptual representation
of the geometry of the unsaturated pore volume will be gained. Our approach is to isolate,
if it exists, any induced dispersion due to chemical nonequilibrium of the solute with the
solid matrix or due to solute exchange between mobile and immobile water regions. This
will then allow quantifications of changes in mechanical dispersion as the media is
desaturated. We will expand the work of Yale and Gardner (1978) to natural soils and that
of James and Rubin (1986) to a tracer that does not undergo anion exclusion. The
unsaturated experiments will be conducted over a range of saturations using three soils

having similar grain size distributions.

2.2 Materials and methods

Soil from the A and B horizons of Oakville sand (mixed, mesic Typic
Udipsamments) and from the B horizon of a Pipestone sand (mixed, mesic Entic
Haplaquods) were used in the experiments described below. Soil samples were air-dried
and ground to pass through a 0.85-mm sieve. Samples were characterized for pH, cation-
exchange capacity (CEC), organic matter, and particle size (see Table 2.2). Sample pH
was determined on a 1:1 sample-water suspension (Eckert, 1988), CEC was determined
by a method outlined by Wamcke et al. (1980), organic matter content was determined

using the wet digestion technique (Schulte, 1988), and particle size distribution was

48

determined by the hydrometer method. The differences in the pH values arnon g the three
soils are considered very slight. Variations in the CEC might be due to variations in the
organic matter content. Similar grain size distributions were also found among the sand
fractions of the three soils (not shown in Table 2.2). About 53% of each soil sample was

found to have a medium size (250-500 um), 30% within the fine sand range, and 12%

within the coarse range.

Table 2.2. Properties of Packed Soils.

 

soil pH CEC organic sand silt clay 0 p K
meg/1mg carbon 91. % % so an’lem’ yom’ anlhr

Oakville A 6.8 5.9 2.25 94.5 3.5 2.0 0.408 1.587 33.62
Pipestone 5.7 4.2 1.57 95.0 3.1 1.9 0.383 1.636 37.16
Oakville B 6.0 1.8 0.70 94.5 4.0 1.5 0.353 1.587 39.46

The soil columns were constructed of glass cylinders ( 5.45 cm ID x 30.2 cm long)
with Teflon end-plates. A porous stainless-steel plate (Soil Measurement Systems,
Tucson, AZ) that functions as a capillary barrier was attached to the outflow end of each
column. The columns could be operated in either a saturated or an unsaturated mode.
Tensiometers (Soil Measurement Systems, Tucson, AZ) were used to measure soil-
water suction at one-third and two-thirds the column length. This was necessary to
establish a unit hydraulic gradient for the unsaturated experiments. The aqueous phase was
applied to the top of the column using a precision constant flow pump (Harvard Apparatus
Inc., South N atick, MA). A modified column setup of the one reported by Annable et al.
(1993) has been used in this study as shown in Figure 2.1. '

A sample from each soil was uniformly packed in a soil column. All the soil

columns were initially evacuated and then wet from the bottom very slowly with 0.01 N

49

 

      

Inflow From Fort Open During
Syringe Pump l Desalination
Teflon Cap
- ’ 1:1 1' '
Plexiglass Collar II
__ 0‘ i I
l I l I Teflon O-Fiing
Septum — - ;
. 1/4' Glass Wafls

 

Tensiometer

 

'L

 

 

 

 

 

 

 

 

 

Figure 2.1 Schematic diagram of the unsaturated soil column with the
sample collection device

50

CaC12 solution until they were completely saturated. The soil columns were weighed to
determine the saturated moisture content (0). Saturated hydraulic conductivity (K) was
determined using the constant head method. Column bulk density (p), 0, and K values are
listed in Table 2.2. Flow of a 0.01 N CaC12 solution was established at different velocities
less than or equal to K by adjusting the delivery rate from the syringe pump for the
saturated experiments or the applied suction and delivery rate to obtain a unit hydraulic
gradient for the unsaturated flow experiments. In the later case, water content or degree of

saturation was determined by column weight

To verify that a uniform saturation had been established along the depth of the soil
columns, Metea soil (83% sand, 11% silt, 6% clay), classified as loamy, mixed, mesic
Arenic Hapludalfs, was packed in a 30.2 cm column, and unit hydraulic gradients were
established at several degrees of saturation. The column was then sacrificed to measure
the water content distribution along the length of the column. The water content
distribution was compared with the mean value determined by difference between the
weight of the column at that saturation and the dry weight of the column. This is presented
in Figure 2.2 for a saturation of 43.2%. Some variations in actual water distribution along
the length of the column can be seen in the figure. The upper part of the column is drier
than the lower part This might be due in part to a 5 mbar higher suction detected in the
upper tensiometer compared to the lower one, or due to redistribution of the water along
the length of the column between the time the flow stopped and the time the column was
segmented. The largest detected difference from the average was 4%. In all the
unsaturated experiments conducted for the soils listed in Table 2.2 except for the first
unsaturated experiment of each soil, the difference in the tensiometers readings never
exceeds 3 mbar. At an applied suction pressure of 7 mbar at the pressure plate for the first

unsaturated experiment of each soil, no negative pressure was detected in the

51

 

 

 

 

 

 

30 “r .I
assumed
actual . distribution
25 “ distribution \ /
o
m .._
E
5 e
5'
e
g 15 --
'5
=
'2 10 r-
5 ..
O
0 r l l l
0 5 10 15 Z)
Moisture content,%

 

Figure 2.2 Water distribution along the depth of a Metea soil column at
a negative pressure of 55 mbar

 

52

tensiometers. It is assumed, therefore, that a uniform moisture content was established

along the depth of the column for the conducted unsaturated experiments.

Tritiated water was injected either in the form of a pulse input for a fixed period of
time or as a step increase that was maintained until the effluent concentration reached the
input concentration. A fraction collector was used to collect effluent samples for the step-
increase studies, which were only used for saturated flow. In the pulse input experiments,
effluent samples were collected using clean glass syringes attached to the outlet of the
column as shown in Figure 2.1. Effluent samples were analyzedfor tritium by liquid
scintillation counting. At the end of each experiment, the columns were displaced by a
tracer-free calcium chloride solution, until the effluents were free from any detectable

amount of tracer.

Retardation coefficients (R) for tritiated water were determined by measuring the
area above the BTC for a smp input (Nkedi-Kizza er al., 1987). Short columns (5.45 cm
ID x 10.2 cm long) packed with either Oakville B soil or Oakville A soil were employed
Injected tritium concentration was identical to the one used in the long column
experiments. Experiments were conducted at four different saturated flow rates that cover

the range of flow rates used for the saturated-unsaturated long column experiments.

2.3 Results and discussion

To determine the dispersive behavior of a porous media, any induced spreading as
a result of chemical or physical nonequilibrium has to be isolated. Chemical nonequilibrium
is caused by slow solute interaction with all or some specific sites of the solid matrix
Physical nonequilibrium, however, results from slow solute diffusion in and out of

relativley stagnant water regions. This might be created by the nature of the structure of

53

the media, i.e. aggregated vs. nonaggregated, or the flow conditions, i.e. saturated vs.
unsaturated. The following section focuses on the interaction of tritium with the solid
matrix. This is necessary to determine R, which is one of the transport parameters that
needs to be used in Eqs. (1.15), (1.16), and (2.1). The value ofR will determine if
verification of the existence of chemical nonequilibrium is necessary. The second section
focuses on data analysis using two models: one assumes that the system is operating under
physical equilibrium and the other accounts for the presence of physical nonequilibrium.
The last section compares the values of hydrodynamic dispersion coefficient under

unsaturated conditions to that under saturated ones.

2.3.1 Role of chemical interaction

R values are usually determined by either batch or column experiments. Since
tritium is commonly thought to function as an ideal tracer (W ierenga and van Genuchten,
1989), the batch equilibration method may not be sensitive enough to measure small
values of K D ( van Genuchten and Wierenga, 1977). Under these circumastances, the use

of soil column technique becomes preferable over batch experiments.

Table 2.3. Retardation of tritium in saturated short columns

 

 

 

Oakville B Oakville A
Vn (CID/111') R Vn (cm/hr) R
17.267 0.999 17.257 1.045
5.180 0.982 5.177 0.999
2.302 0.993 2.283 1.087

0.575 0.976 0.571 1.001

54

Table 2.3 shows the values of R measured in this study for tritium at a range of
average flow velocities similar to the range used in the saturated and unsaturated
experiments; all values are very close to 1.0. These results are consistent with the findings
of Wierenga and van Genuchten (1989). Values different from 1.0 have been reported by
some investigators, however. Seyfried and Rao (1987), for example, found that R for
tritium is 1.10-1.18 for column experiments. Sorption of tritium is thought to be due to
isotopic exchange with crystallatic hydroxyls of clay particles (W ierenga et al., 1975; van
Genuchten and Wierenga, 1977). Nkeddi-Kizza et al. (1983) and Schulin et al. (1987),
after fitting the AD model with D and R as unknowns to tritium data, noticed some
dependency of R on flow velocity, with lower R values at higher velocities. Schulin et al.
(1987) attributed their higher than previously reported values of KD , i.e. 0.025 cm3/g for
less than 2mm dia. soil fraction, to a possible small error in determining 0. R values
reported by Nkeddi-Kizza et al. (1983) ranged between 0.626 and 1.33. Values less than
1.0 are thought to be an indication of the existence of a "physical nonequilibrium" situation

between the mobile and immobile water regions ( Nkeddi-Kizza et al., 1983).

For the soils under investigation, and within the range of flow velocities employed
there was no evidence of either a positive or negative retardation of tritium to the soil
matrix. Since retardation is not a function of column length (W ierenga and van Genuchten,
1989), a value of R=1.0 was used in fitting the BTCs generated from the long column
experiments to the AD and MIM models. Since R=1, any nonequilibrium present during
tritium transport through the soil columns cannot be attributed to slow chemical

interaction.

55

2.3.2 Role of physical nonequilibrium

BTCs for the saturated-unsaturated experiments were analyzed first using the AD
model which assumes that the system is under physical equilibrium. The unsaurated BTCs
were then analyzed using the MIM to determine parameter values for the immobile water

fraction and mass transfer coefficient

The AD model: Tritiated water was injected through saturated soil columns at flow
velocities ranging from approximately the magnitude of the saturated hydraulic
conductivity (s 37 cm/hr) to about 0.2 cm/hr. The conditions for these experiments are
listed in Table 2.4. Generated BTCs were analyzed to determine D using the nonlinear
least squares inversion program CXTFIT of Parker and van Genuchten (1984) with R=1
and voand T. are as given in Table 2.4. D values are accompanied by their 95% confidence
limits. Similarly the AD model was fit to the unsaturated experimental data. Values of D
along with the conditions of the unsaturated experiments are listed in Table 2.5. Values in
parenthesis represent 95% confidence limits as estimated by CXTFIT. A typical BTC for
each soil column is shown in Figure 2.3 for the saturated experiments and in Figure 2.4 for
the unsaturated ones. For comparison of dispersion under saturated and that under
unsaturated flow conditions it is useful to employ the same range of pore-water velocities.
Therefore, the first saturated experiment of each soil, i.e. SBl, SP1, and 8A1 is not
included in the discussion of this chapter since the average pore-water velocities of these

experiments ( > 30 cm/hr) are beyond the range of the unsaturated flow velocities.

The values of D obtained using the AD model for the saturated and unsaturated
experiments are plotted versus the average pore-water velocity for each soil as shown in

Figure 2.5. Small air saturations as noticed in experiments USBl, USPl, and USAl

Table 2.4. Experimental conditions and dispersion coefficients for the saturated

flow experiments

56

 

 

 

 

 

Experiment Tracer v0, Normalized D,
Application cm/hr Pulse Time, To cmzlhr
Oakville B
SB 1 pulse 36.47 2.186 180401804
8B2 step increase 14.76 - 8.0221240
SB3 pulse 7.29 2.20 3.275i2.05
SB4 step increase 1.84 - 0.668:l:0.22
SBS step increase 0.99 - 0.289:1:0.06
SB6 pulse 0.73 2. 17 0.203:l:0.1 1
8B7 step increase 0.25 - 011410.01
Pipestone
SP1 pulse 33.60 2.08 l8.780:|:7.l7
SP2 step increase 13.62 - 859211.79
SP3 pulse 6.72 2.09 2.900:l:0.34
SP4 step increase 1.70 - 0.687i0.10
SP5 step increase 0.91 - 0.2332120.08
SP6 pulse 0.67 2.05 0.159:l:0.07
SP7 step increase 0.23 - 0.1272004
Oakville A
SAl pulse 3 1.55 1.95 20. 870:1:3.45
8A2 step increase 12.79 - 9.440:l:O.99
8A3 pulse 6.30 1.96 5.37 1:1:2. 14
SA4 step increase 1.60 - 0.846:l:0.09
SA5 step increase 0.85 - 0.382i0.11
SA6 pulse 0.62 1.91 0.2201007
SA7 step increase 0.21 - 0.138:1:0.03

 

57

Table 2.5. Experimental conditions and the results of fitting the AD and MIM models to
the unsaturated flow experiments

 

 

 

 

 

Exp. v0, T, 3% AD Model MIM model
cm/llr D, SSE D, p a) SSE
cm2/hr cmzlhr
USBl 18.738 2.16 95.6 8.53 0.16 8.05 0.98 0.0023 0.160
($2.89) ($2.65) ($0.08) ($0.238)
USBZ 9.180 2.56 71.0 9.17 0.09 7.85 ‘ 0.923 0 0.004
($2.78) ($0.54) ($0.006) NA
USB3 2.735 1.69 50.6 2.53 0.09 2.09 0.937 0 0.005
($0.55) ($0.1 l) ($0.004) NA
USB4 1.014 2.21 47.8 1.32 0.20 0.71 0.897 0 0.006
($0.43) (10.05) ($0.005) NA
USP] 17.496 2.12 96.0 11.63 0.11 11.84 1.0 0.00012 0.100
($2.35) ($2.42) NA ($6.326)
USP2 8.397 2.42 72.0 14.24 0.05 14.42 1.0 0.0009 0.042
($2.91) ($2.70) NA ($3.223)
USP3 2.562 1.64 55.4 2.81 0.11 2.80 1.0 0.0012 0.102
($0.62) ($1.75) NA ($4.37)
USP4 1.026 2.30 43.6 0.66 0.35 0.67 1.0 215370 0.329
($0.33) ($0.34) NA NA
USAl 16.506 1.94 95.5 11.98 0.13 12.16 1.0 0.0042 0.112
($3.62) ($2.86) NA ($4.627)
USA2 7.272 2.08 78.0 1 1.22 0.01 10.73 0.983 0 0.010
($1. 12) ($0.99) ($0.009) NA
USA3 2.155 1.38 58.5 3.75 0.03 3.80 1.0 0.0063 0.029
($0.38) ($0.37) NA ($2.833)
USA4 0.806 1.80 52.2 0.76 0.01 0.76 1.0 1947 0.011
($0.06) ($0.06) NA NA

 

58

(S)95%) do not appear to cause a change in the dispersivity of the media as shown in
Figure 2.5. De Smedt and Wierenga (1984) observed that porous media at 90% saturation
or above have identical dispersive behavior to fully saturated ones. Figure 2.5 shows,
however, that for any saturation (S) S the saturation of U82 experiments, the dispersion
coefficient is higher than its value if the media is saturated. This behavior has been noticed
by other investigators as previously shown in Table 2.1. When a linear regression of the
form D=av0 is used to fit the saturated data and the unsaturated data for saturation less
than or equal to that which corresponds to US2 experiments, we found that the ratio
amm/a,“It a 1.9-2.8. The results of the regression are presented in Table 2.6 along with the

r2 of the regression given in parenthesis.

This ratio is much lower than the ones reported by De Smedt and Wierenga (1979
and 1984). Their ratios were 20 and 73, respectively. The higher ratios were attributed to
the existence of a physical nonequilibrium situation created by the presence of immobile
water regions under unsaturated conditions, while all the water is considered mobile for
the saturated cases. Therefore, part of the increase in D is caused by this nonequilibrium
situation. Their evidence for the presence of an immobile water region, as shown also by
Bond and Wierenga (1990), is the tailing and asymmetry of the BTCs. The extent of
tailing and asymmetry has been shown to be a function of, among other parameters, the
average pore-water velocity. Our BTCs, as shown in Figure 2.4, appear to be symmetrical
with no noticeable tailing. This indicates that dead end pores either do not exist or do not
play a significant role in causing physical nonequilibrium in the transport of tritium.
Therefore, non-equilibrium considerations cannot be used to explain the higher D values in

this study. The MIM model was used, however, to confirm this observation.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Q
U
Pore volumesJ
8A1
23:
6 8
Pore volumes!
536
Q
U
Pore volume”
SP3

 

 

 

Figure 2.3 Selected BTCs from the pulse input saturated flow
experiments. Dots are experimental data, and solid lines are
simulations with the AD model using parameter values listed
in Table 2.4

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Q
U
Pore volumes. T
USA4
Q
U
0 l 2 3 4 5 6
[1333 Pore vokmes, 'I'
1.2 -
1 i
8 08 ~-
\ 0.6 "'
U 0.4 ~-
0.2 -r
0 l l l I
O l 2 3 4 5 6
mpg Pore volumes. T

 

 

Figure 2.4 Selected BTCs of the unsaturated experiments.
Dots are experimental data, solid lines are simulations with
AD model and dashed lines are simulation with MIM model.
Simulation parameter values are as listed in Table 2.5

bl

 

 

 

 

 

 

 

 

 

 

 

 

 

J
I: 10 -_
§E 6 --
= 'E 4 ‘“ o
.2 0 a
Z’. 2 +0
g- 0 J!" % % l :
'° 0 5 10 15 20
pore-water velocity, cm/lu'
OakvilleB
J
g 15 “r A
a 4
§ 5 ‘0 1' A
3 E 5 --
I: a a
fi- 0 w : : l :
"’ o 5 lO 15 20
pore-waterveloclty,cmlhr
Pipepstone
J
5 15 “r
E n 13
£3 10 -- -
3‘5 5 -- .
E D
3» o a : l : :
'° 0 5 10 15 20
pore-water velocity,cmlbr
OakvilleA

 

 

Figure 2.5 Dispersion coefficient for the three soils
under saturated (closed symbols) and unsaturated
(Open symbols) conditions

62

The MIM model: Numerical experiments using CXTFIT to determine MIM parameters
for data generated with the MIM model under conditions similar to those observed in our
lab experiments showed parameter value errors of about 4% due to inaccuracies in the

numerical integration. The relative error (STOPER) in subroutine ROMB (which handles

Table 2.6. Linear regression results between D and v0

 

 

Dispersivity (cm)

Soil Saturated Unsaturated
Oakville B 0.531(O.99) O.996(O.99)
Pipestone O.588(O.97) 1.630(O.97)
Oakville A O.754(0.99) 1.552(099)

 

the required numerical integration) of CXTFIT was reduced to 5* 10‘7 instead of the
reported value of 5"‘10‘5 and the number of iterations was adjusted so that convergence
was achieved to improve this situation. Parameter value errors of less than 0.16% were
then obtained. Several initial values of B and a) were tried to obtain the values listed in
Table 2.5. Selection of the shown optimized values was based on the lowest value of sum
of square errors (SSE) without violations of physical reality. The following constraints
have been imposed on the optimized values to avoid violations of physical reality: D 2 0, to
2 O, and 05 551.0.

The MIM model was fit to the unsaturated experimental data Values of D, B, and
(o are listed in Table 2.5. Values in parenthesis represent 95% confidence limits as
estimated by CXTFIT. When the optimized B is greater than 1.0 or a) is 0 or large, no

confidence interval is estimated.

63

Fitting the MIM model to the Pipestone and Oakville A data did not result in a
significantly better representation of the experimental results as can be seen from the SSE
values. The optimized B for all the unsaturated experiments of Pipestone and Oakville A
soils were greater than 1.0 but less than 1.018, except for USA2 which was 0.983. Values
greater than 1.0 have been replaced by 1.0. This should not alter the values of SSQ, since
the way CXTFIT estimates SSE for any B 21 is, in fact, based on B =1. With B=1, the
value of D predicted using the MIM model should be identical to the value predicted using
the AD model. Therefore, the added complexity of the MINI model is not necessary to

explain tritium movement in these two soils.

Use of the MIM model for Oakville B soil shows a value of B that ranges between
089-093 with high certainty as noticed in the confidence intervals listed in Table 2.5.
Error propagation methods were used to estimate the uncertainty in the calculated values
of v0 . This has been found to be around 1.4%. Therefore, the 10% immobile water
fraction noticed for Oakville B soil cannot be explained based on experimental error in
determining average pore-water velocity. De Smedt and Wierenga (1984) and Schulin er
al. (1987) found that about 85% of the water content in their experiments is mobile. Bond
and Wierenga (1990) found 96% to be mobile. It can also be seen in Table 2.5 that B is
independent of the degree of saturation and the average pore-water velocity. This was also
noticed by De Smedt and Wierenga (1984), Schulin et al. (1987) and Bond and Wierenga
(1990). In earlier studies (Bond and Wierenga, 1990, for example) use of the MIM model
was justified because the small, non zero values of a) required to achieve better fit produce
a mass transfer effect that is evidenced in the tailing and asymmetry of the data. The values
of a) as estimated by CXTFIT for the unsaturated experiments on Oakville B soil were
found to be 0. For (0:0, there is no mass transfer from the mobile to the immobile water
region and any immobile water present is isolated from the flowing fraction. This is an

equilibrium situation in which the MIM model reduces to:

64

B_m= _.__..._
aT Lvm 322 32 (2.5)

O

This equation is similar to the AD equation, with the exception that the BTC will be
shifted to the left for B<1. It is expected, therefore, that the predicted BTCs will exhibit no
tailing and the use of the MIM model becomes unnecessary. However, The use of the AD
model without accounting for B will influence the value of D predicted, since the
optimization scheme used to estimate model parameters is such that it will force the model
simulation to go through the data points as much as possible. Owing to the inadequacy of
the AD model to describe the experimental data in this case, the model simulation will, as
a matter of necessity, yield higher D values in order to shift the ETC to the left. This of
course, will be associated with a higher degree of uncertainty in D and a higher SSE value
compared to the ones obtained using the MINI model as can be seen in Table 2.5.

Suggesting a need for a 2-parameter model to describe the generated data.
2.3.3 Dispersivity under saturated-unsaturated flow conditions

After isolating the effect of nonequilibrium on dispersion, De Smedt and Wierenga
(1986) found that the dispersivity for the unsaturated media is about 7 times higher than
that when the media is saturated. Yale and Gardner (197 8) also noticed what seems to be
a more dispersive unsaturated media The above findings and ours are in conflict with the
expectation deduced from the capillary tube model for unsaturated media, i.e. less
dispersion due to narrowing the range of pore sizes available to flow. A possibility for this
contradiction is that the conceptualization upon which the capillary tube model was built

upon might be successful in describing the contribution of the dynamic mechanism of

65

dispersion, it neglects, however, the contribution of the kinematic mechanism as part of

mechanical dispersion. It is well to consider this point further.

As the media is desaturated, changes in orientation of flow paths will occur. The
effect of such changes is a more tortuous, irregular pore sequences that are not oriented in
the principal direction of flow (Corey et al., 1963). This will increase the contribution of
the kinematic mechanism to dispersion. A capillary tube model that treats a porous media
as a bundle of capillary tubes that do not intersect each other cannot account for such an
increase. A more appropriate model, from this point of view, is one that involves a random
network of connected pores. Sahimi and Imdakm (1988) gave an explanation of dispersion
in unsaturated media using random walk and percolation theories. To model the
distribution of immiscible fluid, the authors used the concepts of random percolations.
They predicted that, for the case where thin films of the wetting phase that coat the
surface of the nonwetting phase are taken into account, hydrodynamic dispersion increases
with desaturation until a saturation of z 0.4, after which it decreases and becomes very
small at saturation close to 0. We presented in Figure 2.6 the dispersivity values as a
function of wetting phase saturation for the three soils used. As previously indicated, the
dispersivity of the media at saturation of about 95% is similar to that of the fully saturated
case. The model of Sahimi and Imdakm (1988) shows, however, an immediate increase in
dispersivity as saturation is reduced. With the limited number of data points available for
saturation of < 95 %, it seems that there is an increase followed by a decrease in
dispersivity as saturation decreases. This is consistent with the numerical observations of
Sahimi and Imdakm (1988). More experimental data are needed, however, to draw a firm

conclusion.

The contradiction between our findings and those of James and Rubin (1986) is

hard to explain, but may be attributed to differences in the experimental procedure. James

 

 

 

0.5 -- zoom“ ‘ ‘

0.4 .. .W .
OWE

dlsporslvlty, cm

 

 

 

 

saturation %

 

 

Figure 2.6 Dispersivity of three nonaggregated soils at various levels
of saturation

67

and Rubin (1986) evaluated the dispersion coefficient for the unsaturated experiments by
determining chloride concenuation along the soil profile at an average soil length of 15
cm. Their evaluation of dispersion coefficient for the saturated experiments was based on
collecting effluent samples from a 10-cm length column. According to James and Rubin
(1986), apparatus induced dispersion has been accounted for. Differences between their
results and ours are possibily due to differences in the column length and flow rates used.
Corey et al. (1963), for example, found that dispersion for unsaturated soil increases as
the column length increases. The same finding was also noticed for their saturated
experiments at high flow rates, but not at low rates. Meanwhile, it has been demonstrated
that at short distances the dispersion coefficient rises sharply for saturated media, but the
rate of increase falls off rapidly (Han et al., 1985). Yet, it is not known how the rate of
increase changes under unsaturated conditions. A study that investigates the dispersive
behaviour of both saturated and unsaturated soil at different column lengths using the
same tracer and same technique of sampling would be helpful answering the above

question.

2.4 Summary and Conclusiom

Two conflicting issues have been reported for the transport of nonsorbing tracers
through nonaggregated media under steady, unsaturated conditions: the first is whether
there is physical nonequilibrium created by slow solute diffusion into relatively stagnant
water regions, the second is whether the dispersivity increases, remains the same, or

decreases as the media is desaturated.

68

In this study, we investigated the dispersive behavior of three nonaggregated sandy
soils using an ideal tracer over a range of saturation and found that the dispersivity of
unsaturated soil is about 1.9-2.8 times higher than when the soil is fully or nearly
saturated. This behavior contradicts the expectation deduced from the capillary tube
model which treats the porous medium as bundles of tubes that do not intersect each
other. It suggests, however, that a model which accounts for intersection of capillary tubes

”—7.1% '1" “J" ’17
could represent the geometry of the unsaturated pore volume more appropriately. We '1’ M. at:

I II. 4: (v0 \

m... u‘ ..- s

 

 

speculated that the increase in dispersivity under unsaturated conditions is a result of an

increase in the tortuous path length.

We also concluded that there was no evidence of mass transfer limitation in the
transport of tritium through the media For two of the soils used in this study, there was
no evidence of immobile water regions. There is a possibility, as noticed for the third soil,
for some immobile water that is totally isolated from the flowing fraction and did not

produce physical nonequilibrium in the system.

69

2.5 References

Annable, M. D., Wallace, R. B., Hyden, N. J. and Voice, T. C., 1993. Reduction of
gasoline components leaching potential by soil venting. J. Contam. Hydrol.,
12: 15 l-170.

Aris, R., 1956. On the dispersion of a solute in a fluid flowing through a tube. Proc. Roy.
Soc. A235:67-??.

Baker, L. E., 1977. Effects of dispersion and dead-end pore volume in miscible
flooding. Soc. Pet. Eng. J., 219-227.

Bear, J ., 1969. Hydrodynamic dispersion in Flow Through Porous Media, edited by R. J.
M. DeWiest, Academy, N.Y., 530 pp.

Biggar, J. W. and Nielsen, D. R., 1976. Spatial variability of the leaching characteristics
of a field soil. Water Resour. Res., 12:78-84.

Bond, W. J. and Wierenga, P. J., 1990. Immobile water during solute transport in
unsaturated sand columns. Water Resour. Res., 26:2475-2481.

Coats, K. H. and Smith, B. D., 1964. Dead—end pore volume and dispersion in porous
media. Soc. Pet. Eng. J., 4:73-84.

Corey, J. C., Nielsen, D. R. and Biggar, J. W., 1963. Miscible displacement in saturated
and unsaturated sandstone. Soil Sci. Soc. Am. Proc., 27:258-262.

De Smedt, F. and Wierenga, P. J ., 1979. A generalized solution for solute flow in soils
with mobile and immobile water. Water Resour. Res., 15:1137-1141.

De Smedt, F. and Wierenga, P. J., 1984. Solute transfer through columns of glass beads.
Water Resour. Res., 20, 225-232.

De Smedt, F., Wauters, F. and Sevilla, J ., 1986. Study of tracer movement through
unsaturated sand. J. Hydrology, 85:169-181.

Deans, H. A., 1963. A mathematical model for dispersion in the direction of flow in
porous media. Trans. AIME, 225: 49-52.

Eckert, D. J ., 1988. Recommended Chemical Soil Test Procedure for the Central Region,
North Central Regional Pub. # 221, North Dakota State University, Fargo, North
Dakota, pp. 6-8.

Freeze, R. A. and Cherry, J. A., 1979. Groundwater, Pentic-Hall Inc., Englewood Cliffs,

N.J., 604 pp.

Gupta, R. K., Millington, R. J. and Klute, A., 1973. Hydrodynamic dispersion in
unsaturated porous medial. concentration distribution during dispersion. J. Ind.
Soc. Soil Sci., 21:1-7.

Han, N-W, Bhakta, J. and Carbonell, R. 6., 1985. Longitudinal and lateral dispersion in
packed beds: Effect of column length and particle size distribution. AICHE J. 31:
277-288.

James, RV. and Rubin, J., 1986. Transport of chloride ion in a water-unsaturated soil
exhibiting anion exclusion. Soil Sci. Soc. Am. J., 50:1142-1149.

Kirda, C., Nielsen, D. R.and Biggar, J. W., 1973. Simultaneous transport of chloride and
water during infiltration. Soil Sci. Soc. Am. Proc., 37:339-345.

Krupp, H. K. and Elrick, D. E., 1968. Miscible displacement in an unsaturated glass
beads medium. Water Resour. Res., 4:809-815.

70

Nkedi-Kizza, P., Biggar, J. W., van Genuchten, M. Th., Wierenga, P. J., Selim, H. M.,
Davidson, I. M. and Nielsen, D. R. 1983. Modeling tritium and chloride 36
transport through an aggregated oxisol. Water Resour. Res., 19:691-700.

Nkedi-Kizza, P., Rao, P. S. C. and Hornsby, A. G., 1987. The influence of organic
cosolvents on leaching of hydrophobic organic chemicals through soil. Environ.
Sci. Technol., 21:1107-1111.

Parker, J. C., and Valocchi, A. J., 1986. Constraints on the validity of equilibrium and
first-order kinetic transport models in structured soils. Water Resour. Res., 22:
399-407.

Parker, J .C., and van Genuchten, M. Th., 1984. Determining transport parameters from
laboratory and field tracer experiments, Bull. 84-3, Va Agric. Exp. Stn.,
Blacksburg.

Sahimi, M., Davis, H. T. and Scriven, L. E., 1983. Dispersion in disordered porous
media. Chem. Eng. Commun. 23, 329-341.

Sahimi, M. and Irndakm, A. 0., 1988. The effect of morphological disorder on
hydrodynamic dispersion in flow through porous media. J. Phys. A: Math. Gen.,
21: 3833-3870.

Schulin, R., Wierenga, P. J ., Fluhler, H. and Leuenberger, J., 1987. Solute transport
through a stony soil. Soil Sci. Soc. Am. J., 51: 36-42.

Schulte, E. E., 1988. Recommended Chemical Soil Test Procedure for the Central Region,
North Central Regional Pub. # 221, North Dakota State Universtiy, Fargo, North
Dakota, pp. 29-32.

Seyfried, M. S. and Rao, P. S. C., 1987. Solute transport in undisturbed columns of an

aggregated tropical soil: Preferential flow effects. Soil Sci. Soc. Am. J., 51:1434-
1444.

van Genuchten, M. Th. and Wierenga, P. J., 1976. Mass transfer studies in sorbing
porous media. I. Analytical solutions. Soil Sci. Soc. Am. J ., 40: 473-480.

van Genuchten, M. Th. and Wierenga, P. J ., 1977. Mass transfer studies in sorbing
porous media: Experimental evaluation with tritium. Soil Sci. Soc. Am. J ., 41:
272-27 8.

van Genuchten, M. Th., Tang, D. H. and Guennelon, R., 1984. Some exact solutions for
solute transport through soils containing large cylindrical macropores. Water Resour.
Res., 20:335-346.

Wamcke, D. D., Robertson, L. S., and Mokrna, D. L., 1980. Agron. Abst., Am. Soc.
Agron., pp 147.

Wierenga, P. J., van Genuchten, M. Th, and Boyle, F. W., 1975. Transfer of boron and
tritiated water through sandstone. J. Environ. Qual., 4:83-87.

Wierenga, P. J. and van Genuchten, M. Th., 1989. Solute transport through small and

large soil columns. Ground Water 27: 35-42.

Yale, D. F. and Gardner, W. R, 197 8. Longitudinal and transverse dispersion coefficients

in unsaturated plainfield sand. Water Resour. Res., 14: 582—588.

CHAPTER 3

COMPARISON BETWEEN RETARDATION COEFFICIENTS OF
NONIONIC ORGANIC COMPOUNDS DETERMINED
BY BATCH AND COLUMN TECHNIQUES

3.1 Introduction

It is generally believed that the primary sorption mechanism for dissolved nonionic
organic compounds (N OCs) is hydrophobic partitioning to the soil organic matter matrix
and that the ultimate extent of sorption is a function of the degree of hydrophobicity of the
compound and the fraction of organic matter on the soil (Chiou, 1989). Investigators,
however, found that for low-carbon soils (< 0.1%), the relationship between sorption
capacity and soil organic carbon content tends to deteriorate and that the contribution of
mineral surfaces to sorption of N OCs should be considered (Schwarzenback and Westall,
1981; Karickhoff, 1984; Mackay et al. 1985).

The impact of sorption is to reduce the average velocity of the contaminant
relative to that of water. The normalized 1-D advection-dipersion equation describing
transport of NOCs through a homogeneous soil column, under steady-state conditions is
usually written as:

2
Realises (3,1,

a1 P ax2 ax
where C is the normalized concentration, T is the dimensionless time = v.tlL, v.is the
average pore-water velocity, t is the time, L is the length of the column, X is the
normalized length = x/L, x is the length, P is the Peclet number = vJ/D, D is the
hydrodynamic dispersion coefficient, and R is the retardation coefficient defined as:

71

72

R=1+£eI£’-’— (3.2)

in which p is the bulk density, [(0 is the linear distribution coefficient and 0 is the

volumetric water content.

Proper determination of R can have a significant impact on managing and
preventing groundwater contamination. In the laboratory, retardation coefficients are
customarily determined by either batch or packed column experiments. The advantages
and disadvantages of the column and batch approaches have been discussed by Kool et al.
(1989) and Jackson et al. (1984). Reports vary as to the relationship between values of R
determined by the two techniques; good agreement (MacIntyre et al., 1992; Nkedi-Kizza
et al., 1987; Lee et al., 1988), slight differences (Bouchard et al., 1988; Celorie et al.,
1989), and high deviations (up to 100%) (MacIntyre and Stauffer, 1988; Lion et al., 1990;
Bilkert and Rao 1985) have all been reported.

Similarity of R's in the work of MacIntyre et al. (1992) between the two methods
was attributed to relatively rapid kinetics and linear nature of the sorption isotherms.
Bilkert and Rao (1985) noted that the high discrepancy between the two values may be a
consequence of failure to reach local equilibrium in the column. While, the independence
of KD on velocity in the work of MacIntyre and Stauffer (1988) did not allow them to
attribute this to nonequilibrium, neither were they able to resolve the cause. The degree of
sorption nonequilibrium of NOCs has been shown to increase with the increase in soil
organic matter content (Bouchard et al., 1988). Therefore, if failure to attain equilibrium
is the cause of discrepancy between batch and column coefficients, then the deviations

between the two methods will increase with increases in soil organic matter.

Several other factors have been offered to explain disagreement between batch-
and column-determined retardation coefficients including: loss of sorbent particles through
column end retainers, column flow variations, column flow channeling (MacIntyre et al.

1992), mixing differences between the two methods (Schweich et al. 1983), reductions in

73

soil particle spacing (Celorie et al., 1989), differences in soil/water (S/W) ratio between
batch and column experiments(Lion et al., 1990), and the use of undisturbed columns and
homogenized soil samples if spatial variability in sorption occur along the depth of the
column (Chrysikopoulos et al. 1990).

The above factors can be categorized into two groups: sorption-related factors
including sorption nonequilibrium, nonlinearity, and nonsingularity, and sorption-
nonrelated factors. If discrepancy between the two methods is caused by sorption-
nonrelated factors, the use of one of the techniques may become inappropriate. For
example, if the discrepancy is a result of differences in the SM ratio, mixing differences,
particle spacing, or homogenized batch samples, then the assumption that batch-
determined parameters can be applied to dynamic systems will not be valid. On the other
hand, if the discrepancy is caused by loss of sorbent particles through the column end
retainer, column flow variations, or column flow channeling, then the use of a column
technique for determination of sorption coefficients becomes questionable. Prior to
answering such questions, identification whether the discrepancy is sorption-related or

sorption-nonrelated becomes essential.

The purpose of this paper is to compare batch and column retardation coefficients
and to assess the impact of the possible factors that are previously reported to cause
discrepancy between the results of the two techniques. No literature was found that
considered the impact of changes in soil organic matter on the degree of discrepancy
between batch- and column-determined retardation coefficients. If the discrepancy is
sorption-related, then the extent of deviation between retardation coefficients determined
by the two techniques will be dependent on the amount of soil organic carbon. In this
study, three aquifer materials of similar texture but different organic matter are utilized
Earlier studies focused on comparing the results of the two techniques using aquifer
materials of low organic carbon content. Discrepancy between the two methods may not
be noticeable on these materials. The aquifer materials employed in this study have
relatively medium to high organic carbon.

74

3.2 Experimental Procedure

The same soils described in Chapter 2 are employed in this phase of study. The
properties of the long soil-columns are presented in Table 3.1. Two nonionic organic
compounds have been chosen: Benzene and dimethylphthalate (DMP). Both benzene and
DMP were obtained from Aldrich Chemical Co. in pure forms (99+%). l‘C—labeled
benzene mixed with cold benzene was used in all the experiments and was analyzed by
liquid scintillation counting. DMP was analyzed by a Gilson HPLC using 50% water/50%
acetonitrille as the mobile phase.

Table 3.1. Properties of packed columns

 

 

 

 

Soil Organic p 0
carbon (%) g/cm3 cm’lcm3
Oakville A 2.25 1.587 0.408
Pipestone 1.57 1.636 0.383
Oakville B 0.70 1.587 0.383

 

Table 3.2 shows some of the properties of the two compounds. Reported
experimental and calculated values of octanol/water partition coefficient (K...) for benzene
did not exhibit a wide range. It is not clear why the values for DMP vary significantly.
Values in the upper range are usually the ones calculated based on established empirical
relations (see Veith et al., 1978). The ones in the lower range are commonly the ones that
have been determined experimentally (Leyder and Boulanger, 1983). We determined the
K... for the two compounds using a method similar to the one reported by Chiou et al.
(197 9). The only difference between their method and the method we utilized is the phase
in which the compounds are initially dissolved. We found that the value for benzene is
consistent with the one previously reported and that for DMP is close to the one reported

in the lower range and it depends on the initial concentration in the aqueous solution.

75

Table 3.2. Some properties of the used organic chemicals

 

 

 

Compound Molecular Solubility log K0,. Du,” x105
Weight @ 20°C, rug/l cm’ls

Benzene 78 1780‘" 2.13 ‘b’ 1.1

DMP 194 1744‘” 6000“” 1.53“) -2.1 l m 0.78

 

‘" Verschueren, 1983.
m Veith et al., 1978. K0,, is the octanol/water partition coefficient
‘°’ McCarty, 1983. D. is the molecular diffusion coefficient in the water phase.

“” Callahan et al. (1979)-
(e) Leyder and Boulanger (1983).

Sorption experiments were conducted using both batch and saturated-flow
experiments. The experimental conditions for the saturated experiments, sample
collection, and column size and material were the same as the one reported in Chapter 1.
Among the saturated experiments, only pulse type experiments were conducted. The
column experiments were conducted at several flow rates. Both benzene and DMP were
originally dissolved into 0.01N C3C12 deaired, deionized water before injection into the
columns. Initial concentration of the compounds was =30 mg/l (< 2.5% solubility limit).
To inhibit biodegradation, 0.05 % sodium azide was dissolved in the prepared water
solution. This concentration of inhibitor was recommended by Russell and McDuffie
(1986) for DMP. The effectiveness of the biocide was verified by a recovery of 95% of the
compounds when a mass balance was performed for the saturated experiment with the
lowest flow rate. No adsorption, relative to tritium, of the two compounds to the column
material was noticed when a saturated experiment using a lO—cm long column filled with
clean glass beads was conducted. N o evidence of hydrolysis of DMP was detected as
DMP and phthalic acid, which has a different retention time in the HPLC method, were
monitored in the effluent samples.

Batch experiments included kinetic studies and equilibrium isotherms. A l4-day
sorption rate study was conducted to estimate the time required to achieve equilibrium for
each sorbent/sorbate combination. In addition, 3-day and 14-day sorption isotherms were
performed to evaluate potential differences resulting from the slightly asymptotic behavior

76

observed in the rate studies. In the batch experiments a fixed S/W ratio of 1/1.5 g/ml was
used. 15 g soil was added first to 25-ml Corex centrifuge tubes (volume when full ~ 28
ml) . For the rate experiments, ~22.5 m1 of 0.01N CaClz deaired deionized water
containing 0.05% sodium azide and 30 mg/l benzene and DMP was added to each tube.
The isotherms were set-up similarly, except that the initial concentration was varied over a
range from about 5 mg/l to approximately 7% of solubility. After being filled with these
solutions, the tubes were immediately capped with Teflon-lined screw caps and tumbled
end over end for the desired period of time. Phase separation was accomplished by
centrifugation 4000 rpm for 30 minutes. Aqueous samples collected using glass syringes
were then analyzed for benzene and DMP concentration. The amount sorbed by soil was
determined by difference. Blank tubes were tested to verify that no sorption to the tube
material occurred. The exact amounts of soil, organic compound-free water solution and
organic compound solution added to each tube were determined by difference in tube
weight between subsequent steps. In addition, a l4-day sorption isotherm of benzene and
DMP on Oakville A soil with a W ratio of ll6.5 was also conducted to evaluate whether
the solid/solution ratio affected sorption in this system.

3.3 Data analysis

Retardation coefficients for benzene and DMP on the three aquifer materials have
been determined by batch and column techniques. In the batch technique, a sorption
isotherm is constructed and the slope of the isotherm along with the properties of the soil
aquifer, i.e. p and 6, are utilized to estimate R. In the column technique, a dimensionless
breakthrough curve (BTC) of the chemical is used to determine R using: (1) the number of
pore volumes at which C=0.5Co, (2) the area above the curve for a step input, or (3) the
mean (first moment) of the BTC for a pulse input. The three cases are schematically
shown in Figure 3.1 a, b, and c, respectively. Other column techniques that have been used
for the determination of R are reviewed by Jacobson et al. (1984).

77

 

 

 

 

 

 

 

 

 

 

 

C/Co”
(a)
0.5
A, T
R
C/CO R= area
(b)
:T
C/CoA
input
(e)
; l
3 5 rr

 

R

Figure 3.1 Retardation factors determined from column BTCs:
(a) R=T @C/Co=0.5, (b) the area above the BTC, and
(c) the mean of BTC.

78

Retardation coefficients computed by the above three column methods will be
identical for symmetric BTCs (Bouchard et al., 1988). For asymmetric BTCs , retardation
factor determination using C=0.5Co are inappropriate ( Nkedi-Kizza et al., 1987;
Bouchard et al., 1988). Asymmetry of BTC is caused by solute nonequilibrium which may
either be transport- or sorption-related or both. Transport-related nonequilibrium is due to
slow solute diffusion in an out of "immobile" water regions. Sorption-related
nonequilibrium may be due to slow chemical reaction or slow diffusive transport within
the sorbent or the intraparticle pores. For more details about nonequilibium transport
models, the reader is referred to the excellent review by Brusseau and Rao (1989).

Retardation coefficients were determined for Oakville B and Oakville A soils using
two column lengths ( 10.4 and 30.2 cm) and different pore-water velocities. Those for
Pipestone soil were determined using only the 30.2-cm long column. For the short
column, a step increase in the concentration has been used and the experiment was
terminated when the relative concentration of the effluent solution reached ~1.0.
Retardation coefficients were then evaluated by measuring the area above the BTCs. For
the long columns, a pulse input of approximately 2 pore volumes has been injected. The
columns were then flushed with compound-free solution. Retardation coefficients were
then determined using two methods: (1) the mean of BTC, (Valocchi, 1985):

Tc.— a

R= ° -o.sr,,

Crfl'
0

(3.3)

 

where T, is the number of pore volumes of benzene/DMP-solution injected, and (2) a
curve fitting technique using the nonlinear, least squares optimization program CXTFIT of
Parker and van Genuchten (1984) subject to the modification employed in Chapter 1. In
the curve fitting technique, BTCs were analyzed using a bicontinuum model that assumes
instantaneous sorption for some portion of the porous media and is rate-limited for the
remainder. The governing nondimensional equations describing the bicontinuum

nonequilibrium model have been presented elsewhere (see, for example, Brusseau, 1992;

79

Bnrsseau et al., 1991). Input parameter values for D are the same as the ones determined

for tritium for the same experimental conditions of this study (see Chapter 1).

3.4 Results and discussion

Several factors have been tested for possible effect of causing discrepancy between
batch and column retardation coefficients including sorption nonequilibrium, sorption
nonlinearity, sorption nonsingularity, S/W ratio, column channeling, and column residence
time. The impact and direction these factors may have on obtaining different retardation
factors from the two techniques along with experimental findings regarding their effects on
the retardation of benzene and DMP are discussed below. Batch experiments are utilized
to investigate the effect of batch nonequilibrium, sorption nonlinearity, and SM ratio.
Column experiments are employed to determine the effect of column nonequilibrium, flow
channeling, sorption nonsingularity, and column residence time. Comparison between
values of retardation coefficients obtained by the two techniques are discussed in the last
part of this section.

3.4.1 Batch sorption experiments
Rate study:

Sorption distribution coefficients are generally determined by mixing a certain
amount of soil with an aqueous solution containing the targeted compounds. If the mixing
time was not enough for the compound in the solution to reach equilibrium with that on
the solid phase, then the distribution coefficient would be underestimated. This will result
in a higher retardation coefficients using a column technique compared to those from a

batch sorption isotherm.

The results of a batch rate study for benzene and DMP on Oakville A and Oakville
B soils are presented in Figure 3.2. The figure shows a rapid sorption rate at initial times

 

 

 

 

 

 

 

 

5 1.2
1? 1;--0 a --------- a ------- 6
A a
E; 0.8 a I. g . .
g5 0.5--
o 3 0.4 -~
° 0.2--
§ 0 : + 1: :
°‘ 0 1(1) 200 300 400
TlmoJus
II B
5 1.2
E I - a--. ......... a ....... o
0.8
g '- 5 A A
g% 0-6 ' o o . :
o ’ 0.4
g 0.2
o o. : . 4. :
°‘ 0 too 200 300 400
mam
OakvmeAJ

 

 

Figure 3.2 Batch rate study of Benzene (triangles) and DMP
(circles). Open symbols for blank tubes.

81

and a much slower rate at later times. Similar behavior has been noticed by other
researchers (Wu and Gschwend, 1986; Brusseau et al., 1989). The figure also shows that
at early times benzene and DMP are sorbed to the same extent and start to deviate (DMP
being sorbed more) at later times. Benzene reached apparent equilibrium after
approximately 40 hrs while it appeared that DMP continued to sorb over the entire mixing
period. The slow continued sorption of DMP resulted in a greater total amount of this
compound being taken up by the soil. This contradicts the expectation based on the Kow
values of the two compounds, i.e. higher or at least equivalent sorption of benzene, and
suggests the possibility of another bonding mechanism, besides partitioning. Seip et al.
(1986) also noticed higher retardation of DMP than benzene. They attributed this to the
possible formation of hydrogen bonds between the oxygen atoms of DMP and the
hydrogen atoms on the soil surface. Another possible mechanism is the formation of
phthalate/soil organic matter complexes (Autian, 1973). Slow sorption of DMP may then
be attributed to chemical nonequilibrium caused by the non-partitioning mechanism(s).

Sorption nonlinearity

The retardation coefficient defined by Eq. (3.1) is based on linear sorption
behavior. Linearity is commonly observed at low aqueous concentrations, however, at
high concentrations, nonlinear isotherms have been reported (Means et al., 1980;
Schwarzenbach and Westall, 1981). Means et al. (1980) used a Freundlich sorption model
to describe the isotherms of polycyclic aromatic compounds. The Freundlich model is
given as:

q= kC" (3.4)
where q is the amount sorbed at equilibrium with the aqueous concentration C, k and n are
constants. A modified form of Eq. (3.2) results when the Freundlich model is used:

R= 1+ brig-CH (3.5)

The implication of Eq. (3.5) is that retardation coefficients determined for a nonlinearly I
sorbed compound assuming a linear sorption isotherm will differ from those determined

82

from a column BTC. The difference (higher or lower) depends on the value of n (less than

1 or greater than 1) and the injected solution concentration.

In this study sorption isotherms were determined for two different mixing times: 3
days and 14 days. The results using Oakville A and Oakville B soils are shown in Figure
3.3. For the 3-day sorption isotherm the two compounds are similarly sorbed on the low
organic matter content soil, but deviate from each other on the high organic matter soil,
with DMP showing slightly higher sorption than benzene. As noticed in the rate study,
deviation between the two compounds becomes more clear at late times. This is also
obvious for the 14-day isotherm. Figure 3.3 also shows that benzene reached equilibrium
much earlier than DMP, since the 3—day and 14-day isotherms for benzene are identical.

The l4-day sorption isotherm data for the two compounds were fit to a linear
sorption model with zero intercept The values of the linear distribution coefficient (K0 )
for the three soils and the associated correlation coefficient (r2) are listed in Table 3.3.
Although sorption linearity for the two compounds seems to be an appropriate
assumption, the data were also fit to the Freundlich model.. The values of k and n for the
nonlinear model are also shown in Table 3.3. The F-test was used to determine if a benefit
is gained in selecting the nonlinear model over the linear one. The results of the F-test, as
shown in Table 3.3, indicated some benefit in each case at the 95% confidence limit from
fitting the isotherms data to the nonlinear model. '

To determine retardation coefficients based on the batch sorption data, the
nonlinear parameters have been utilized to obtain a linearized coefficient using the
following equation ( van Genuchten et al. 1977):

TKWC dC= 310w» dC (3.6)
0 o

This requires that the areas under the isotherms over the range 0-30 mg/l for both the
linearized and the nonlinear equations be the same. The value of 30 mg/l is selected

because it is the concentration of injection fluid into the columns. Values of R estimated

 

 

l
l

l
I

L

1-

Amount sorbed. ug/g
o 5 8 8 8 8 8

 

 

 

 

 

 

 

7’ e
e a
.1- . 6 ’0
a
man» A g i i i
0 20 40 60 80 it!)
, Final aqueous concentration. mgll
OakvilleB
60 -.
9 e
9 5° " 0 °
. 40 .- a
g a
9 3° " . 5
¢— 0
C m "‘ . O A
3 l
o M
E to «@3‘
0 i i t i l
0 20 40 60 80 im
, Final aqueous concentration. mgll
OakvilleA

 

 

 

Frgure 3.3 Batch sorption isotherm of DMP (circles) and
benzene (triangles) after a 3-day (open symbols) and al4-day
(closed symbols) mixing period

84

Table 3.3. Results of the linear and Freundlich type models

 

 

 

 

 

 

 

Soil Compound K D r1 SSE It It SSE F F ,5;
Oakville B benzene 0.194 0.955 4.25 0.405 0.803 0.52 57.1 5.31
DMP 0.303 0.967 6.87 0.579 0.825 0.77 63.1 5.31
Pipestone benzene 0.518 0.966 13.8 0.695 0.866 7.24 7.25 5.31
DMP 0.559 0.947 37.8 1.172 0.808 10.53 20.7 5.31
Oakville A benzene 0.666 0.996 4.57 0.832 0.939 1.67 13.9 5.31
DMP 1.554 0.987 35.02 2.119 0.906 16.82 9.31 5.31

 

SSE is the sum of square errors

using K m . p and 0 of the soil columns are listed in Table 3.4. In using the linear
sorption coefficients instead of the linearized coefficients, it is estimated that the maximum

error in R is about 12.0% for DMP on Pipestone and the average error is about 6%.

Table 3.4. Retardation coefficients based on batch
results using the linearized sorption coefficient

 

 

 

 

 

 

 

 

Soil Compound K “nears! R

Oakville B benzene 0.229 2.03
DMP 0.350 2.57
Pipestone benzene 0.474 3.03
DMP 0.674 3.88
Oakville A benzene 0.697 3.71
DMP 1.615 7.28

SIW ratio

Some investigators have suggested that the sorption distribution coefficient is
dependent upon the SIW ratio used in the isotherm experiment, and possibly in the field as
well (O'Conner and Connolly, 1980; Voice et al., 1983; Di Toro, 1985). These
investigators have all reported that K0 decreases with increasing solid concentration. The
SIW in a soil column is about 4g/ml. This is much higher than those commonly utilized in
batch experiments. The impact of this phenomenon on R would result in a lower
retardation in columns when compared to those determined by batch techniques.

85

If such an effect is present and applicable to the system under study, one would
need to employ a SIW ratio in batch studies similar to that found in a column in order to
use the batch test for estimation of column retardation factors. This is difficult to
accomplish, however, due to problems with phase separation at such high solids
concentrations. To determine whether a solids concentration effect is operative for the
solutes selected in this study, additional l4-day isotherms were conducted for both
benzene and DMP at a SIW ratio of 1y6.5ml and the Oakville A soil. These isotherms
were compared to the corresponding isotherms with a SIW ratio of 1g/1.5 ml as shown in
Figure 3.4. This data indicate that the SIW ratio does not effect the isotherm results for
the two ratios used. This is also consistent with the findings of Lion et al. (1990) for

phenanthrene using two SIW ratios (1:1 and =- 1:5 g/g).

3.4.2 Saturated column experiments

Column flow channeling

Flow channeling refers to the restriction of flow to some channels in the column,
i.e. other available channels are much less conductive. Unless accounted for, flow
channeling results in a shift to the left of a BTC, and therefore, a lower value of R. The
presence of a flow channeling can be detected with the use of an ideal tracer for which R
equals to 1.0. Values less than 1.0 are an indication of an inappropriate estimation of
pore-water velocity based on the assumption that all the pores participate in the flow.
Nkedi-Kizza et al. ( 1983) reported values of R for tritium, which is commonly thought to
function as an ideal tracer, that are less than 1.0. They attributed that to the existence of a
physical nonequilibrium created by the presence of mobile and immobile water regions.

Solution injected into the columns contained tritium in addition to benzene and
DMP. Tritium data was analyzed and reported in Chapter 1. We found that the values of R
ranged between 0.97 6- 1 .087. We concluded that there is no evidence of existence of

immobile water in the columns. Therefore, any discrepancy between batch- and column-

 

 

 

OUT 0
0 db
55° --
~m-_ o A
s . -
530" AA
$13-1 ?‘A
$10" I”
0 i i i i i
0 20 40 60 80 lm

Final aqueous concentration. mg/l

 

 

 

Figure 3.4 Sorption isotherm of DMP (circles) and benzene
(triangles). Closed symbols for SIW ratio =1/ 1.5 and open
ones for SIW ratio: l/6.5

87

determined retardation coefficients must be attributed to other factor(s) but flow

channeling.
Residence time in the column

Effect of hydraulic residence time in the column on the value of retardation
coefficient for benzene and DMP has been investigated. Hydraulic residence time is a
function of pore-water velocity and column length. The impact of the two parameters on

R is presented below.

Values of R estimated by moment analysis (R mm) and those by curve fitting (R,,)
for the long column experiments are reported in Table 3.5. Values in parenthesis are the
95% confidence limits as estimated by CXTFIT. Table 3.5 shows that the values of R
determined using moment analysis are lower than the corresponding values determined by
curve fitting. In addition, the values of R determined by moment analysis appear to
increase with the reduction in pore-water velocity. The values of R determined by curve
fitting, except for those of DMP on Oakville A soil, are not, however. Several
investigators reported a leftward shift of BTC as the velocity increases or an apparent
velocity dependence (inverse relation) of R (van Genuchten et al. , 1974; Schwarzenbach
and Westall, 1981; Bouchard et al., 1988) which is generally regarded as a result of
nonequilibrium in the column. Brusseau et al. (1991) and Brusseau and Rao (1989)
argued that the velocity dependent R is an artifact and that the first temporal moment is
independent of the extent of nonequilibrium in the system. Therefore, the true value of R is
independent of velocity, and the dependency of R determined using moment analysis is, in
actuality, an artifact. There are several conditions, however, under which the use of
temporal moment analysis may not yield the true value of R: ( 1) extreme nonequilibrium
(Bnrsseau et al., 1991), (2) experimental artifacts such as insufficient collection of effluent
samples from soil column in a manner that not all the mass injected is accounted for, and

(3) analytical limitations where it is difficult to accurately determine the contribution of

88

peak tailing which is marginally greater than the analytical baseline (Lion et al., 1990).

Each of the above conditions would result in underestimation of the column retardation.

For all the experiments on Oakville B soil, effluent samples were collected until the
concentration of the compounds reached its detection limit and a mass balance was
verified. Yet, differences between the two determined values of R exist. Hence,
discrepancy cannot be due to failure to account for all the mass injected. On the other
hand, inspection of Table 3.5 indicates that existence of extreme nonequilibrium is likely to
be the cause of the discrepancy, since the deviation between the values of R determined by
the two methods narrows down as the velocity decreases. This is expected since the extent

of nonequilibrium will be less at lower velocities.

Table 3.5. Retardation coefficients determined from BTCs using first moment analysis

 

 

and curve fitting technique
Benzene DMP
Exp. v. T. D. R.,... R... Rm... R.
cm/hr cm’lhr

 

SAl 31.55 1.95 20.87 2.14 2.46 (2110.14) 2.32 2.95 (10.16)
SA2 6.3 1.96 5.37 2.16 2.78 (10.84) 2.83 3.28 ($0.25)
SA3 0.62 1.91 0.22 2.27 2.73 (10.17) 3.35 4.03 ($0.19)
SP1 33.6 2.08 18.78 2.23 2.76 (10.34) 2.2 2.83 (10.29)
SP2 6.72 2.09 2.90 2.27 2.74 (10.19) 2.33 2.92 ($0.21)
SP3 0.67 2.05 0.16 2.41 2.75 (10.14) 2.68 2.77 (10.06)
SBl 36.47 2.18 18.04 1.37 1.64 ($0.18) 1.50 1.85 (10.17)
SB2 7.29 2.20 3.27 1.36 1.62 (10.16) 1.51 1.70 (10.06)
SB3 2.17 2.17 0.20 1.52 1.65 (10.03) 1.71 1.73 (10.04)

Velocity dependent R for sorption of DMP on Oakville A soil, even with the use of
a model that incorporates the effects of nonequilibrium, may signify the existence of an
additional sorption process that is observable when relatively slow velocities are used.
Alternatively, the observed increase in retardation at lower velocity could be due to
inadequacy of the used nonequilibrium model to describe the effect of velocity on the
BTCs. Schwarzenbach and Westall '(1981) observed a similar trend and suggested the use

89

of a continuous distribution of mass transfer coefficients. The different values of mass
transfer coefficients for the case where sorption rate-limitation is due to diffusive
transport, as interpreted by Schwarzenbach and Westall (1981), would correspond to
different diffusion path lengths.

Sorption nonsingularity

Discrepancy between batch- and column-determined retardation coefficients may
result due to improperly interpreting column data. For example, if the applied boundary
conditions did not permit the effluent relative concentration to reach 1.0 due to relatively
small pulse size or extensive tailing, then retardation coefficients are either determined
using the number of pore volumes at ClCo=0.5 or temporal moment analysis. Constraints
on using the former method has been discussed. The later method considers both sorption
and desorption paths. If sorption nonsingularity exists, then retardation coefficients from
batch technique, where only sorption path is usually considered, will be different from
their column counterparts (assuming other factors to be ineffective). N onsingularity has
been noticed in the work of van Genuchten et al. (1977) for 2,4,5-T. van Genuchten et al.
(1977) found that the linearized KD desorption > [(0 adsorption. If this is the behavior for
DMP and benzene, then one would expect higher retardation based on temporal moment
analysis of a pulse input compared to the ones estimated from the area above the BTC.

Retardation coefficients for DMP on Oakville A soil for the two column lengths
are presented in Figure 3.5a. The values for the long column experiments are those
determined by temporal moment analysis and the values for the short column are the ones
determined from the area above the curve. Figure 3.5a shows that the values for the short
column are higher than those for the long column at comparable pore-water velocity.
There is a possibility that the behavior noticed in Figure 3.5a is due to different column
lengths used rather than sorption nonsingularity. To investigate this point, the values of R
determined using number of pore volumes at ClCo=0.5 for the two columns are

compared. The results are presented in Figure 3.5b and indicated that the values of R for

 

 

 

 

5

*5 3.5 'B

eo— O .o

5 2 5 -- . o

E 15 --

a

g 0.5 i j 5 g
(0) average pore-water velocity,cm/hr

 

 

 

 

 

 

 

 

E’ 3 5

.9 G E

§ R 2.5 . .0 . O

.5 8 15 ~-

‘6 B

U 0.5 4

:2 9 J i i l :

.9 (5 i0 20 30 40
(b) Pore-water velocity. cm/hr

.3 3.5 T . 0

9 e

“E 2.5 30

9

g 1.5 1*-

5

E 05 i 1 § § 1'

0 10 20 30 40 50

(c) Residence time in the column. hr

 

 

Figure 3.5 Retardation factors as influenced by pore-water
velocity and hydraulic residence time for DMP on Oakville A
soil. Closed symbols for short column and open ones for long
column.

91

the long column are still higher than those for the short ones. Therefore, the difference in
R cannot be attributed to sorption nonsingularity. Brusseau (1992) also observed that
sorption of 1,4—dichlorobenzene, tetrachloroethene, p-xylene and naphthalene on three
aquifer materials is not affected by nonsingulatrity. The other possibility is a dependency
of R on the column length. To explore this, values of R shown in Figure 3.5a are plotted
Vs. the residence time as illustrated in Figure 3.5c. Clearly, there is no difference between

the values of R for the two column lengths at the same residence time.

3.4.3 Batch/column retardation coefficients

The main purpose of this study is to compare between batch-determined
retardation coefficient and those determined using column BTCs. We will compare
between distribution coefficients listed in Table 3.4, where sorption nonlinearity has been
accounted for, with those corresponding to the values of R determined from curve fitting
for the column experiment (Table 3.5). The reason for comparing between distribution
rather than retardation coefficients is to exclude the effect of different bulk density and
moisture content among the columns. The values of R from the column were averaged for
each sorbate-sorbent combination, except that for DMP on Oakville A soil where the
value at the lowest flow rate was considered. This reduces the impact of hydraulic
residence time on R and allows closer comparison with the batch-determined values for

DMP on Oakville A soil.

Figure 3.6 shows the percentage difference in Kw...“ for the two compounds
using the three soils. In the figure Kb and Kc refer to batch- and column-determined
linearized disuibution coefficients, respectively. Figure 3.6 reveals that even after
accounting for sorption nonlinearity and hydraulic residence time there is still a difference
between batch and column distribution coefficients. The one determined from the batch
are higher by an average of 46% for benzene and 90% for DMP than those from the
column. Also, the difference in the deviations between the two compounds is similar

(about 40%), and is independent of the amount of soil organic matter.

 

 

 

 

1m --
m f.
80 ‘r 2 ='
be. E g g
’3 __ g 9 o
is 6° . a .
g (S:
A 40 "’ ‘ . ‘
55
20 “ A
0 i 1 1 1 Jr
0 0.5 1 1.5 2 2.5

soil organic carbon.%

 

 

Figure 3.6 Comparison between batch/column sorption distribution
coefficients for aquifer materials with different organic carbon content.
Circles for DMP and triangles for benzene.

93

Figure 3.6 also shows that for the soil with intermediate carbon content, the
difference between the distribution coefficients is lower than that for the soils with low and
high organic matter. For the latter soils, the difference is identical for each compound;
61% for benzene and 107% for DMP. This makes it difficult to draw any conclusion
regarding whether then; is a trend in changes in distribution coefficients with changes in
soil organic carbon. However, similar differences in deviations between the two

compounds using the low and high organic matter soils suggests an independence on soil

organic matter.

Among the other possible factors that cause discrepancy between batch- and
column-determined retardation coefficients which are not investigated here are: loss of
sorbent particles through column end retainer (MacIntyre et al., 1992) and effective
accessibility to sorption sites in batch as compared to column (Schweich et al., 1983;
Celorie et al., 1989). Loss of soil material from the column will have an impact if either
loss of particles occur or the aqueous solution is a good extractor of the soil organic
matter. Water solution are not good extractor of soil organic matter (Hayes, 1985). On
the other hand, loss of soil particles from the column is highly unlikely given the direction
in which the column experiments were conducted; starting with the one that has the .
highest flow rate and ending with the one that has the lowest. In this direction, one would
expect a decrease in R with the decrease in pore velocity if the sorbent is lost during the

experiments. Our results do not show this to be the case.

Although not proven experimentally, mixing differences between the two
techniques becomes a potential explanation for this discrepancy. It is possible that mixing
in a batch tube either created sorption sites that are not accessible during transport
through the soil column (Schweich et al., 1983) due to soil abrasion, or reduction in soil
particle spacing results in less surface area which is accessible by solute for sorption
(Celorie et al., 1989). Experimental confirmation of the above factor is needed. A soil
column can be equilibrated with a certain aqueous concentration, then soil samples from

the column are mixed in batch tubes with aqueous solution in which the concentration of

94

the compound is equal to equilibrium concentration of the aqueous phase in the column. A
decrease in the aqueous-phase concenuation after mixing would be an indication of further
sorption due possible sorption sites that are inaccessible during column transport. Further
investigation to elucidate whether the cause of this discrepancy is soil abrasion or a result
of reducing particle spacing is needed. We propose applying the same mechanical forces
used for batch mixing to the intended-to-be-used soil samples prior to packing in the soil
column. Similarities in batch- and column-determined retardation coefficients would
indicate that the originally noticed discrepancy is due to mixing differences. If discrepancy
still exists, then the cause will be due to reducing particle spacing. Had this been the case,
accurate determination of retardation factors in the laboratory would necessitate
subjecting soil packed columns to similar confining pressures as those present in the field.
Indeed, experiments where column-determined retardation factors as a function of
confining pressure may serve as a direct verification if particle spacing is the cause of
discrepancy between retardation coefficients obtained by batch and column techniques.

3.5 Summary and conclusion:

The impact of previously reported factors that cause discrepancy between batch-
and column-determined retardation coefficients have been assessed. Batch and column
experiments on three sandy aquifer materials of 0.7, 1.57, and 2.25% organic carbon
content have been conducted. Variations in soil organic matter allows determination
whether the discrepancy is sorption-related or not. Batch-determined retardation
coefficients for benzene and DMP are higher than their column-determined counterparts.
Sorption nonequilibrium, SIW ratio, sorption nonsingularity, and column flow channeling
are not the cause of this discrepancy. Sorption nonlinearity has a minor impact. Column
hydraulic residence time has a significant impact on the value of retardation coefficient for
DMP using the high organic matter soil but not on the other sorbate-sorbent

combinations.

95

After accounting for sorption nonlinearity and considering the value of R at the
lowest velocity when residence time was a factor, batch-deterruined distribution
coefficients were 16-107% higher than column-determined values. The extent of deviation
between the two values was independent of the amount of soil organic matter. This
discrepancy may be attributed to mixing differences between the two techniques. Further

investigation is proposed to resolve this issue.

96

3.6 References

Autian, J ., 1973. Toxicity and health threats of phthalic esters: Review of the literature,
Environ. Health Perspect, 4: 3-26.

Bilkert, J. N. and Rao, P. S. C., 1985. Sorption and leaching of three non-fumigant
nematicides in soils, J. Environ. Sci. Health, part B 20:1-26.

Bouchard, D. C., Wood, A. L., Campell, M. L., Nkedi-Kizza, P., and Rao, P. S. C., 1988.
Sorption nonequilibrium during solute transport, J. Cont. Hydrol, 2:209-223.

Brusseau, M. L., 1992. N onequilibrium transport of organic chemicals: The impact of
pore-water velocity, J. Contam. Hydrol, 9:353-368.

Brusseau, M. L., and Rao, P. SC, 1989. Sorption nonideality during organic contaminant
transport in porous media. CRC Crit. Rev. Environ. Control, 19: 33-99.

Brusseau, M. L., Larsen, T. and Christensen, T. H., 1991. Rate-limited sorption and
nonequilibrium transport of organic chemicals in low carbon aquifer materials,
Water Resour. Res., 27:1137-1145.

Callahan, M. A., Slimak, M. W., Gable, N. W., May, I. P., Fowler, C. F., Freed, J. R.,
Jennings, P., Durfee, R. L., Whitemore, F. C., Maestri, B., Maybe, W. R., Holt, B.
R., and Gould, C., 1979. Water-related environmental fate of 129 priority
pollutants, National Technical Information Service, US EPA Report-440/4-79-
029,1160p.

Celorie J. A., Woods, S. L., Vinson, T. S., and Istok, J. D., 1989. A comparison of
sorption equilibrium distribution coefficients using batch and centrifugation
methods, J. Environ. Qual., 18:307-313.

Chiou, C. T., Freed, V. H., Schmedding, D. W. and Kohnert, R. L., 1977. Partition
coefficient and bioaccumulation of selected organic chemicals, ES&T, 11: 475-
478.

Chiou, C.T., 1989. In Reaction and Movement of Organic Chemicals in Soils, B. I.
Sawheny and K. Brown (eds.), Soil Sci. Soc. Am. Special Publication #22,
Madison, WI, pp. 1-29

Chrysikopoulos C. V., Kitanidis, P. K., and Roberts, P. V., 1990. Analysis of one-
dimensional solute transport through porous media with spatially variable
retardation factor, Water Resour. Res., 26:437-446.

Di Toro, D. M., 1985. A particle interaction model of reversible organic chemicals
sorption, Chemosphere, 14: 1503-1538.

Hayes, M. H. B., 1985. Extraction of humic substances from soil, In Humic substances in
soil, sediment, and water: Geochemistry, isolation, and characterization, edited
by GR. Aiken, D. N. McKnight, R. C. Warshaw and P. MacCarthy, John Wiley
and Sons, N. Y., pp 329-362.

Jackson D. R, Garrett, B. C., and Bishop,T. A., 1984. Comparison of batch and column
methods for assessing the leachability of hazardous waste, Environ. Sci. Technol.,
18:666-673.

Jacobson J., Frenz, J ., and Horvath, C., 1984. Measurement of adsorption isotherm by
liquid chromatography, J. Chromatography, 316:53-68.

Kool J. B., Parker, J. C., and Zelany, L. W., 1989. On the estimation of cation exchange
parameters from column displacement experiments, Soil Sci. Soc. Am. J ., 53:
1347-1355.

97

Lee, L. S., Rao, P. S. C., Brusseau, M. L. and ngada, R. A., 1988. Nonequilibrium
Sorption of organic contaminants during flow through columns of aquifer
materials, Environ. Toxicol. Chem., 7:779-793.

Leyder, F. and Boulanger, P., 1983. Ultraviolet adsorption, aqueous solubility, and
octanol-water partition for several phthalates, Bull. Environm. Contam. Toxicol.,
30: 152-157.

MacIntyre W. G., Stauffer, T. B., and Antworth, C. P., 1991. A comparison of sorption
coefficients determined by batch, column, and box methods on a low organic
carbon aquifer material, Ground Water, 29:908-913.

McCarty, P. L., 1983. Removal of organic substances from water by air stripping, In
Control of organic substances in water and wastewater, Berger, B. B. (editor),
EPA-600/8-83-011, Office of Research and Development, US. Environmental
Protection Agency, Washington, DC. 20460, pp. 119.

Means, J. C., Wood, S. G., Hassett, J. J., and Banwart, W. L., 1980. Sorption of
polynuclear aromatic hydrocarbons by sediments and soils, Environ. Sci. Technol.
14: 1524-1531.

Nkedi-Kizza P., Rao, P. S. C., and Hornsby, A. G., 1987. Influence of organic cosolvent
on leaching of hydrophobic organic chemicals through soils, Environ. Sci.
Technol., 21:1107-1111.

O'Connor, D. J. and Connolly, J. P., 1980. The effect of concentration of adsorbing solids
on the partition coefficient, Water Research, 14: 1517-1523.

Parker, J .C., and van Genuchten, M. Th., 1984. Determining transport parameters from
laboratory and field tracer experiments, Bull. 84-3, Va. Agric. Exp. Stn.,
Blacksburg.

Russell D. J. and McDuffie B., 1986. Chemodynarnic properties of phthalate esters:
Partitioning and soil migration, Chemosphere, 15:1003-1021.

Schwarzenbach, R. P., and Westall, J ., 1981. Transport of nonpolar organic compounds
from surface water to groundwater. Laboratory sorption studies, Environ. Sci.
Technol., 15: 1360-1367.

Schweich, D., Sardin M., and Guedent, J. -P., 1983. Measurement of a cation exchange
isotherm from elution curves obtained in a soil column: Preliminary results, Soil
Sci. Soc. Am. J ., 47:32-37.

Seip H. M., Alstad, J., Carlberg, G. E., Martinsen, K., and Skaane, R., 1986.
Measurement of mobility of organic compounds in soils, The Science of the Total
Environment, 50:87- 101.

Valocchi A. J ., Validity of local equilibrium assumption for modeling solute transport
through homogeneous soils, Water Resour. Res., 1985, 21, 808-820.

van Genuchten M. Th., Davidson, J. M., and Wierenga, P. J ., 1974. An evaluation of
kinetic and equilibrium equations for the prediction of pesticide movement through
porous media, Soil Sci. Soc. Am. J ., 38:29-36.

van Genuchten, M. Th., Wierenga, P. J ., and O'connor, G. A., 1977. Mass uansfer studies
in sorbing porous media: III. Experimental evaluation with 2,4,5-T, Soil Sci. Soc.
Am. J., 41:278-284.

Veith, G. D., Austin, N. M., and Morris, R. T., 1978. A rapid method for estimating LogP
for Organic chemicals, Water Res., 13:43-47.

98

Verchueren, K., 1983. Handbook of environmental data on organic chemicals, 2nd
edition, Van N ostrand Reinhold Company Inc.

Voice, T. C., Rice, C. P., and Weber, W. J. Jr., 1983. Effects of solids concentration on
the sorptive partitioning of hydrophobic pollutants in aquatic systems, Environ.
Sci. Technol., 14:513-518.

Wu, S. C., and Gschwend, P. M., 1986. Sorption kinetics of hydrophobic organic
compounds to natural sediments and soils. Environ. Sci. Technol., 20: 717-725.

CHAPTER 4

RETARDATION OF NONIONIC ORGANIC COMPOUNDS UNDER
UNSATURATED FLOW CONDITIONS

4.1 Introduction

The retardation coefficient (R) represents the average speed of contaminant
transport in subsurface environment relative to that of groundwater. This parameter is

usually expressed as:

P Kn
9w

where, K0 is the linear sorption distribution coefficient, p is the soil bulk density, and 9.. is

 

R=1 + (4.1)

the volumetric water content Retardation coefficients can be estimated using a value of
K0 determined in a batch experiment and a knowledge of the bulk properties of the
aquifer. This approach has been widely used for contaminant transport under saturated
conditions, although recent evidence suggests that batch distribution coefficients may not
translate directly to dynamic conditions (see Chapter 3). This approach has also been used
for unsaturated conditions, however, there is no consensus on the effect of water content
on R.

We can identify three potential causes for deviation of the value of R from that
determined when the soil is fully saturated. First, the value of KD determined using a
traditional sorption isotherm or saturated soil columns might be different from that when
the soil is partially saturated. It is still unclear how the sorptive capacity of the soil changes
above a moisture content which corresponds to a surface coverage. Chiou and Shoup
(1985) found that, beyond a monolayer of water coverage, sorption will maintain a level
which is independent on further increase in water content. The above findings, however,

are in contrast with the findings of Peterson et al. (1988) for the sorption of

100

trichloroethylene (TCE) on a porous aluminum oxide surface coated with humic acids.
Peterson et al. (1988) observed a TCE sorption coefficient of about 2 and 3 orders of
magnitude higher than that found under fully saturated conditions at water surface
coverage that corresponds to 1.6 and 2.4 monolayers of water, respectively. They
attributed the increasefin KD to either the possibility of existence of very small fractions of
dry sites or that moist surfaces, which is completely covered with water, have a sorptive

binding strength greater than that when all the pore space is saturated with water.

The specific mechanisms responsible for the sorption of organic compounds at
relative humilities above what is required to provide surface coverage by at least one
monolayer of water remain unclear. Call (1957) suggested that sorption of
ethylenedibromide on wet soils is attributed to dissolution in sorbed water films and
adsorption at the gas-liquid interface. In contrast, Chiou and Shoup (1985) postulated that
hydrated soils behave as a dual sorbent in which the mineral surface acts as a conventional
solid adsorbent and the organic matter as a partition medium. Ong and Lion (1991)
concluded that that sorption of TCE vapor at field capacity can be accounted for by
dissolution of the compound in the water bound to the soil surface and partitioning into
the soil organic matter. Pennell et al. (1992) suggested a multimechanistic approach to
account for vapor sorption of p-xylene in the unsaturated zone that includes: adsorption
on mineral surfaces, partitioning into the soil organic matter, dissolution into sorbed water

films, and adsorption on the gas-liquid interface.

The second potential cause for deviation is that most of the work dealing with
sorption of N OCs in the unsaturated zone was conducted under static conditions (batch
experiments) and at saturation that corresponds to or below field capacity. Little is known
about the effect of soil moisture content on sorption of N OCs under dynamic conditions.
Under these conditions, it is the value of R (not K., ) that can directly be determined from
a column BTC. Determination of K0 using the measured value of R requires knowledge of
the ratio (pie...) at that saturation. This ratio defines the ratio of the amount of solid that
actively participated in the sorption process to the volume of flowing water present within

101

a unit volume of the aquifer. Although it is straightforward to determine the value of this
ratio under saturated conditions, it is not known how this ratio is altered upon
desaturation. As the soil is desaturated, the larger pores are known to be emptied first. An
element which contains these pores would have lower density than one which contains
only smaller pores. The impact of this is a higher solid/water ratio within a volume
containing the small pores, and consequently a greater amount of contaminant sorption.
This is based on the assumption that sorption is restricted to solid grains constructing the
pore channels that contains the flowing water. It is possible that solid grains constructing

other pore channels would also act as sorbents.

A third possible cause must be considered for volatile N OCs which can partition
into the air phase under unsaturated conditions. Assuming no advective air movement, and
equilibrium sorption and volatilization, the 1-D transport equation of dissolved VOCs in
terms of liquid-phase concentration can be written as (Baehr, 1987):

 

 

M11. 9 K” 29'. - KHDefiZC LC.
(1 + 0w + )a: _ (0+ 0w ’a 2 - Voax (4.2)
ac 1 32C ac
— = — — - — 4.
8t RHDeflrlaxz v0 3x] ( 3)

where, D3” is an overall effective dispersion coefficient D is the hydrodynamic dispersion
coefficient D. is the effective diffusion coefficient in the air phase, 0. is volumetric air
content, 0,. is volumetric moisture content, and R is a measure of retardation. The
contribution of volatilization to retardation depends, therefore, on the volumetric air

content (9.) and Henry's coefficient (K.,).

The objective of this study was to investigate the role of saturation on the
retardation of NOCs. Miscible displacement experiments on packed soil columns were
performed. To our knowledge, this study is the first to report the effect of saturation on

102

retardation under dynamic conditions. A volatile and a nonvolatile organic compound
were employed. The nonvolatile compound was used to determine the impact of changes
in KD and the ratio (pie...) on changes in R. Inclusion of the volatile compound then
allowed evaluation of the impact of volatilization on retardation. Three soils with different

organic matter content were utilized.

4.2 Materials and methods

Three natural nonaggragated soils were employed in this study. The soils have
similar textures but the organic carbon content on these soils varied: 0.7% for Oakville B,
1.57% for Pipestone, and 2.25% for Oakville A soil. Other properties of the soils used can
be seen in Table 2.2. Dirnethylphthalate (DMP) was chosen as a nonvolatile organic
compound and benzene as a volatile one. “C-labelled benzene was analyzed by liquid
scintillation counting, and DMP was analyzed by HPLC. Some of the physical properties
of the two compounds were described previously (Table 3.2).

Pulse-type miscible displacement experiments were conducted at four levels of
saturation. Uniform saturation along the length of the packed soil columns was achieved
by adjusting the flow rate and the applied suction at the bottom of the column such that
equal tensiometer readings at 1/3 and 2/3 the depth of the column were achieved. A pulse
input of 1.38-2.56 pore volumes containing benzene and DMP at a concentration of
approximately 30 mg/l was injected. The columns were then flushed with compound-free
groundwater. The experimental conditions, characteristics of the injected solution, column
setup, and sample collection were the same as the one reported in Chapter 2. The

experimental conditions are also listed in Table 4.1.

4.3 Data analysis

Retardation coefficients for DMP and benzene at each level of saturation were
determined using (1) first temporal moment analysis (V alocchi, 1985):

103

(4.4)

 

— 05 To

CJI'
0

where, C is the normalized effluent concentration, Tis the pore volume, and T, is the
number of pore volume of solution containing tracers that was injected into the column,
and (2) a curve fitting technique using the nonlinear, least squares optimization program
CXT'FTT of Parker and van Genuchten (1984) subject to the modification employed in
Chapter 2. In the curve fitting technique, BTCs were analyzed using a bicontinuum model
that assumes instantaneous sorption for some portion of the porous media and rate-limited
sorption for the remainder. The governing nondimensional equations describing the
bicontinuum nonequilibrium model have been presented elsewhere (see, for example,
Brusseau, 1992; Brusseau et al., 1991). Input parameter values for D are the same as
those determined for tritium, as reported in Chapter 2, for the same experimental
conditions employed in this study. In the case of benzene, the value of D, R, the fraction of
instantaneous sorption sites (B), and the Damkohler number (to) were determined by curve
fitting for all the experiments except those with saturation> 95%. For the experiments ~
with saturation > 95%, D of tritium was utilized, and the other three parameters were
determined by curve fitting. This was done since the contribution of diffusive transport in
the air phase above that saturation, as will be shown latter, can be neglected.

The value of R determined by the above two approaches and the amount of
compound recovered are listed in Table 4.1 for DMP and Table 4.2 for benzene. The
amount of tracer recovered is estimated by dividing the area under the BTC by the number
of pore volumes injected (T.,). It is obvious that the amount of tracer recovered decreases
with an increase in soil organic matter content. This could be due to not collecting effluent
samples over longer period of time. Although the experiments were terminated when the
concentration in the effluent was 5 0.06 C, , some of the tracer was not accounted for

because of the long tailing noticed in the BTle of benzene and DMP on Pipestone and

104

Oakville A soils. Extensive tailing could be due to slow diffusion out of the sorbent An
example of this behavior is presented in Figure 4.1. To evaluate the effect of tailing the

Table 4.1 Experimental conditions and values of R for DMP under unsaturated conditions

 

 

 

 

 

 

 

Exp. V., S, T. D‘ mobile R R Recovery

cm/hr % for 3H water" 1st fit

an’Ihr moment

Oakville B
USBl 18.74 95.6 2.16 8.05 0.98 1.36 1.55 0.99
USB2 9.18 71.0 2.56 7.85 0.92 1.59 1.57 0.99
USB3 2.73 50.6 1.69 2.09 0.94 1.98 2.21 0.94
USB4 1.01 47.8 2.21 0.71 0.90 2.46 2.88 0.94
Pipestone
USPl 17.50 96.0 2.12 11.84 _ 2.12 2.64 0.91
USP2 8.40 72.0 2.42 14.42 _ 2.71 3.36 0.90
USP3 2.56 55.4 1.64 2.80 _ 4.07 4.55 0.89
USP4 1.03 43.6 2.30 0.67 _ 5.34 5.86 0.93
Oakville A
USAl 16.51 95.5 1.94 12.16 _ 2.32 2.83 0.89
USA2 2.27 78.0 2.08 10.73 _ 2.55 3.38 0.87
USA3 2.16 58.5 1.38 3.80 _ 4.19 5.46 0.85
USA4 0.81 52.2 1.80 0.76 = 5.40 7.29 0.82
"‘ As reported in Table 2.6

curve was extended to C/Co = 0 using the slope of the last three data points. The area
under the extended portion is equivalent to 11.37% of the mass of the compound. This
compares favorably with the 15% of the mass that was not accounted for by only
considering the main portion of the pulse (recovery of DMP for experiment USA3 was
85% in Table 4.1). The impact of not accounting for this mass would be a reduction in the
value of R determined by moment analysis. For the above example, an 11% increase in R
results when the extended portion is considered. Therefore, the values of R determined by
moment analysis would be slightly higher if the total mass is accounted for. It is not
surprising, therefore, to see that the retardation coefficients determined by curve fitting are
higher than those determined by moment analysis. Other factors that would lead to

105

erroneous R determined by moment analysis have been discussed in Chapter 3. Hence, the

values of R determined by curve fitting were used in all subsequent analyses.

Table 4.2 Values of R for benzene under unsaturated conditions

 

 

 

 

 

 

Exp. Recovery R R Dd," D.“ (Eq.3)
1st fit (ml/hr anzlhr
moment
Oakville B
USBl 0.93 1.36 1.63 (8.05) 8.051
USB2 0.95 1.59 1.58 11.40 9.05
USB3 0.94 2.05 2.07 13.14 32.69
USB4 0.90 2.37 2.94 16.44 44.36
Pipestone
USPl 0.89 2.22 2.87 (11.84) 1 1..841
USP2 0.93 2.81 3.33 6.54 16.066
USP3 0.94 3.97 4.10 8.23 19.85
USP4 0.88 4.43 5.64 8.88 76.67
Oakville A
USAl 0.91 2.08 2.57 (12.16) 12.161
USA2 0.90 2.35 3.14 6.40 11.32
USA3 0. 89 3.45 4.53 5.28 15.43
USA4 0.87 3.99 5 .34 7.10 26.98
*Values as determined by curve fitting. Values in parenthesis are those
of tritium reported in Table 2.6

To account for the immobile water detected in columns packed with Oakville B
soil as noticed in Chapter 2, retardation coefficients were normalized relative to those of
tritium by dividing the value of R by the percentage of mobile water. In the discussion that
follows, the normalized retardation coefficients are used and are still denoted as R.

In the unsaturated experiments, the moisture content and flow velocity are
coupled. In order to be able to identify the effect of saturation on R, knowledge of the
impact of flow velocity, if it exists, is essential. Several investigators reported a leftward
shift of BTCs as the velocity increased or an apparent velocity dependence (inverse

106

 

 

 

 

 

] input
0.8 --
o 0.6 -.
Q
U 0.4 T
0.2 ~-
0 -P o O%\ i
o T° 5 10 15

 

 

 

Figure 4.1 BTC of DMP on Oakville A subject to the
conditions of experiment USA3.

107

relation) of R (van Genuchten et al., 1974; Schwarzenbach and Westall, 1981; Bouchard
et al., 1988). In Chapter 3, we determined retardation coefficients for benzene and DMP
using the same soil columns utilized in this study with a range of average pore-water
velocity that covers the range of pore-water velocity of the experifnents reported here. We
found that R is not a frinction of velocity for the different sorbate-sorbent combinations
except for the combination of DMP on Oakville A soil. The values of R at various pore-
water velocities under saturated conditions as reported in Chapter 3 were adopted in this

study.
4.4 Results and discussion

Three factors may cause deviations between R determined when the soil is fully
saturated and those when the soil is partially saturated: (1) changes in the value of K9, (2)
changes in the solid/water ratio, and (3) volatilization into the air phase. DMP, a
nonvolatile NOC, was used to assess the impact of the first two factors, and benzene was
employed to investigate the role of volatilization on retardation. The data for DMP are
discussed in the following section and those for benzene are presented in the subsequent

one.
4.4.1 Effect of saturation on retardation

Table 4.1 shows that the values of R determined by curve fitting increase with
reductions in Saturation. The sarrre trend was not noticed, except for DMP on Oakville A
soil, under saturated conditions. For DMP on Oakville A, the values of R determined
under saturated and unsaturated conditions as a function of pore-water velocity are
plotted in Figure 4.2. The figure shows that the increase in R as the soil is desaturated is
higher than would be expected as an effect of velocity, especially at low saturation.

The percentage increase in R over that expected for saturated conditions is plotted
against saturation in Figure 4.3. Values of R under saturated conditions were estimated by

108

linear interpolation for the same pore-water velocity. It can be seen that a decrease in
saturation caused an increase in retardation, up to approximately 100% increase at the
lowest saturation (40%). A linear function was used to fit the data in Figure 4.3 excluding
those of US1, since the saturation for these experiments was higher than 95%. The best fit

was found to be:

M =—2.8lS(%)+212.7 S S 74%

sat
= 0 S > 74% (4'5)

 

with a correlation coefficient of 0.8. The line intersects the x-axis at a saturation of 0.74.
We assumed that there was no increase in R above that saturation. The above relationship
(Eq.(4.5)) is presented as a solid line in Figure 4.3. It is interesting to note that the data
from all three soils is reasonably well represented by this relationship, suggesting that
changes in R with saturation are not related to the organic matter content

Unfortunately, the use of packed soil columns does not directly allow
distinguishingiftheincreaseinRisduetoanincreaseinKDoranincreaseinthe
solid/water ratio upon desaturation. When desaturated, the solid/water ratio may fall
within two limits. The lower limit is equivalent to the one used when the soil is saturated.
This means that the reduction in the moisture content is accompanied by similar reduction
in the amount of soil that actively participates in the sorption process. In this case, the
ratio (pie...) where 0,... is the saturated water content maintains the same value. As we
discussed in the introduction section, one would expect a solid/water ratio which is higher
than its value under saturated conditions even if sorption is restricted to those solid walls
constructing the active pores. Therefore, the assumption upon which the lower limit is
established could be considered conservative. The upper limit would be to assume that all
the solids in the column are active as sorbents, regardless of saturation. In this case, the
reduction in saturation is not accompanied with a reduction in the amount of sorbent, and

the solid/water ratio would be (plSOm). One might visualize that under this assumption

 

109

 

 

 

3 _-
o
6 __
o
m
4 «- e
d) o .
2 i l i i l
0 10 20 30 40
pore-water velocity

 

 

Figure 4.2 Retardation coefficients of DMP on Oakville A
soil under staurated (closed symbols) and unsaturated (open
symbols) flow conditions.

110

 

 

 

 

x Oakville B
D e Pipestone
s - OakvilleA
x
.5
0
a
8
.5
1 ‘ l
80 100

 

 

 

 

Figure 4.3 Percentage increase in R for DMP as a function
of saturation.

111

the solid grains constructing the empty pore channels have a stagnant water film which is
connected to the mobile water in the small pores. Accessibility of the compound to the
grains in the large pores occurs through diffusion of the compound from the mobile water

into the stagnant water covering these grains.

If it is assumed that sorption under unsaturated conditions is restricted to solid
walls constructing the water-filled pores, and that the average bulk density of an element
surrounding these pores does not deviate from that of the whole soil column, then the
increase in R should be a result of an increase in KO. However, if the average bulk density
of the element surrounding the water-filled pores was higher than that of the soil column,
or the solid grains constructing the large pores are active sorbents, then the above
conclusion might not be valid unless the increase in R was higher than what would be
expected based on full participation of all solid grains in the sorption process. Let us
consider the case where all the solid grains actively participate in sorption, i.e. the upper
limit of solid/water ratio. In order to compare between K., under saturated and unsaturated
conditions, the data needs to be normalized to the same solid/water ratio. For convenient
comparison, we plotted (R-1)S as a function of velocity as shown in Figure 4.4. The figure
shows that the values for the unsaturated experiments are very close to the ones when the
soil is saturated. For all the unsaturated experiments, the values are less than or equal to
the saturated values, except at the lowest saturation where the values for the unsaturated
case are slightly higher than the saturated ones. Therefore, if the assumption of full
participation of all the solids in the sorption process is valid, one cannot then attribute the

increase in R under unsaturated conditions to an increase in the value of K0.

4.4.2 Effect of volatilization on retardation

The values of R for benzene determined by curve fitting are compared to the
average values of R under saturated conditions. The percentage increase in R as a function

of saturation is presented Figure 4.5. As was found for DMP, the deviations between the

112

 

 

 

 

 

 

 

 

 

 

 

:1 2
2 1 .
' O 00 O
O l 0 2O 30 40
Oakville B pore-water velocity
V:
2 2 ‘FO .0 o .
0 10 20 30 40
Prpestone' pore-water velocity
5? 3
A O
2 2J7 -. . .
0 10 20 30 40
033va A pore-water velocity

 

 

 

Figure 4.4 Retardation of DMP under staurated

(closed symbols) and unsaturated (open symbols)
conditions.

113

saturated and unsaturated values increase with decreases in saturation. Again, the increase
in R appears to be independent of the soil organic matter content. Unlike DMP, part of the
increase in R for benzene, as depicted by Eq. (4.2), is due to partitioning into the air

phase.

Also shown in Figure 4.5 (solid line) is the relationship developed above for DMP
(Eq. 4.5). Most of the data (excluding that at 95% saturation) were either on or above the
line. This is because Eq.(4.5) does not account for an increase in R due to volatilization.
The impact of volatilization on retardation, in this case, is not great. This is because of the
low value of K., and relatively high organic matter content of the soils. As depicted by Eq.
(4.2), the contribution of volatilization to the overall retardation, for a given compound
and at a certain saturation, will be constant for different soils. However, the percentage
increase in R is dependent on the value of pKD IO , and therefore, is dependent on the soil
organic matter. To see this, the impact of volatilization on retardation is estimated for
three VOCs: benzene, ethylbenzene, and cyclohexane on a nonsorbing (pKD/O =0) and a
sorbing (pKD/O =2) aquifer materials with the use of Eq.(4.2) and is presented in Figure
4.6. The three compounds were selected because of their different K” values. The value of
K., is 0.19 for benzene, 0.37 for ethylbenzene and 6.8 for cyclohexane (Corapcioglu and
Baehr, 1987). As shown in Figure 4.6, the percentage increase in R is a function of K.,, 0.
and the extent of sorption. For compounds with relatively high K., the impact of
volatilization on retardation, as presented in Figure 4.6, becomes significant

When normalized to the saturated solid/water ratio, the retardation coefficient or
specifically the parameter (R-1)S, of the unsaturated experiments coincides with the values
determined for the saturated experiments, except at low saturation (Figure 4.7) where the
values are slightly higher when the soil is partially saturated. This could be due to higher
impact of volatilization on retardation at low saturation.

114

 

 

 

 

e° x Oakville B
M. O PIDGS‘I’ODO
S - Oakville A
i
.5 _
a—
80 l 00

 

 

 

 

Figure 4.5 Percentage increase in R for benzene as a

function of saturation. Solid line is the linear fit for DMP
data of Figure 4.3.

115

 

100 -~ ‘.

60:
40"” \\
20"“- \\\~

% increase R
/

80 -— \

 

 

0.4 0.6 0.8

, saturation
R sorptron=0

 

‘ ‘ ~
0 L I jig-a
I i

 

 

iOO -— ‘,
80 ‘- —benzene \
60 -- ----cyclobexane \.

— — -ethlbenzene \
40 "" y \s

20 -=

% increase R

~
‘

‘-
‘—
~—

 

 

R sorption=3

 

0 l 1 site-- —:
0.4 0.5 0.6 0.7 0.8 0.9

 

Figure 4.6 Theoretical estimation of the impact of

volatilization on retardation of selected VOCs.

 

116

 

 

 

 

 

 

 

 

 

 

S? 2
a; 1 A AA A A
O l O 20 30 4O
Oakville B pore-water velocity
4:": 2 #A AA A A
5., 1
0 l 0 2O 30 40
Pipestone pore-water velocity
.53: f M A A
5
O 10 20 30 4O
Oakville A pore-water velocity

 

 

Figure 4.7 Retardation of benzene under staurated
(closed symbols) and unsaturated (open)
conditions.

 

117

4.4.3 Diffusive transport in the air phase

Although an investigation of the impact of diffusive transport in the air phase was
not the purpose of the work presented herein, the results are amenable to some discussion
of this topic. Figure 4.8 shows BTCs of benzene and tritium under saturated and
unsaturated conditions. BTCs of benzene exhibit higher dispersion as the saturation
decreases (Figure 4.8a). The increase in dispersion is not due to changes in velocity as
shown in Figure 4.8c. In fact a decrease in velocity should reduce dispersion, and on a
normalized scale the BTCs should have the same Peclet number. The changes in the slope
of BTC with desaturation is not detected by tritium, either ( Figure 4.8b). Therefore, the
increase in the slope of the BTCs can be attributed to diffusive transport in the air phase.
Recall from Eq. (4.2) that volatilization has an impact on both dispersion and retardation.
The increase in dispersion coefficient is a function of effective diffusion coefficient in the

air phase (D.).

For nonreactive vapors in moist soils, Millington and Quirk (1961) showed that D.
can be calculated from the free-air diffusion coefficient (1):") using the following

relationships:
D. = 9.1.Df' (4.6)
97/3
1. = :12— (4.7)

For benzene, D" , as estimated by the Hirschfelder-Bird-Spotz equation (W elty et al.,
1984) is 310 cm’lhr. Eqs. (4.6) and (4.7) can now be used to determine the value of D. at
different levels of saturation. Adding the value of hydrodynamic dispersion coefficient
determined from tritium BTCs, the value of the effective hydrodynamic coefficient (D4)
of Eq.(4.2) can be determined. The estimated values of Day and those determined from
curve fitting are presented in Table 4.2. Excluding USl experiments, values of D4;
generally increases with the decrease in saturation. This is expected since the conuibution
of diffusive transport becomes dominant at lower saturation and the effect of

hydrodynamic dispersion coefficient in the liquid phase becomes negligible as the velocity

118

 

C/Co

 

 

 

 

 

 

 

 

 

    
 
   

 

0 036.5 cm/hr
9 0.5 O 7.3 cm/hr
0 a 0.7 cm/hr

0 .
0 5 10
T

 

 

 

Figure 4.8 BTCs of benzene and tritium (a and b,
respectively) at various levels of saturation subject to the
experimental conditions indicated, and of benzene at
various saturated velocities (c).

 

 

119

 

 

 

a 800 " XOakvilleB

'g 700 7’ .Pipestone

g A 900 " —OakvilleA

=6 53 500 --

.3 g 400 ~-

g g 300 -- _

o o __ _

.S 8 200 X X o

8 100 n- ..

,5 0 i x i :

60 80 100

Saturation (%)

 

Figure 4.9 Error in the effective dispersion coefficient of
benzene under unsaturated conditions.

 

120

decreases. Table 4.2 also shows that the values of Day estimated using the above
relationships (Eqs. (4.6) and (4.7)) are higher than the corresponding values found in this
study. Figure 4.9 shows that the percentage error could be as high as 700%, with an
average value of about 200%. The figure also shows that the error increases at lower
saturation. Peterson et al. (1988) found that the gaseous diffusion coefficient predicted
empirically can be in error by as much as 400%. They attributed that to the uncertainty
associated with the empirical relationships (Eqs. (4.6) and (4.7)) and the Hirschfelder-
Bird-Spotz equation. Gierke et al. (1990) found a similar error and needed to reduce the
predicted gas dispersion coefficient for TCE by a factor of 10 in order to be able to

describe their column data.
4.4.4 Practical implications

The practical implications of the above findings is that retardation under
unsaturated conditions can be predicted based on a single value of K0. There are two
alternatives. First one could use the same solid/water ratio as determined for saturated
conditions. In this case R.,... = R... . Second, one could assume that the amount of solid
sorbent remains the same, and therefore, R.,... = {( R... -1)/S}+1. The later approach
would result in a higher retardation upon desaturation. In this study, most of the data
collected is in agreement with the later approach. The assumption that retardation is not
function of saturation, however, is more conservative since it does not underestimate the
average Speed of the compound. The second approach can be employed for volatile
chemicals given that the contribution of volatilization to retardation is not great (< 10%).
If the impact of volatilization is high, its contribution to R could become important
especially for low organic carbon aquifers.

4.5 Conclusiom

Three factors could result in deviation of R under unsaturated flow conditions
from those when the soil is fully saturated: (1) changes in the value of K0, (2) changes in

121

the solid/water ratio, and (3) volatilization into the air phase. In this Study we determined
R for benzene and DMP under dynamic conditions using packed soil columns over a
saturation that varies from 43-100%. The values of R for the two compounds under
unsaturated conditions were compared to the one determined in Chapter 3 when the soil

was saturated.

Retardation coefficients under unsaturated conditions are generally higher than
those when the soil is saturated. The deviations were found to decrease with increasing
saturation. A single equation was found to adequately describe the relationship between
the amount of the deviation and saturation for three soils with different organic carbon
contents. Determination of R for a nonvolatile organic compound using packed soil
columns does not allow for directly distinguishing if the increase in R is due to an increase
in K. or an increase in the solid/water ratio upon desaturation. Our data revealed that
retardation factors under unsaturated conditions, when normalized to the saturated
solid/water ratio, would be very close to the upper limit of solid/water ratio. We could not
conclude therefore, thath changes as the media is desaturated. For practical purposes,
the distinction as to whether the increase is due to changes in K., or changes in solid/water

ratio may not be necessary.

The effect of volatilization on retardation for the case studied is not as significant
as the other two factors. Volatilization will have a significant impact on retardation for
compounds with higher K., values and in aquifers with low organic matter content Further
work in this regard is needed. Diffusive transport in the air phase has a significant impact
on dispersion. The value of the effective diffusion coefficient in the air phase has been
found to be about 2 times lower than the values determined based on previously developed

empirical relations.

122

4.6 References

Baehr, A. L., 1987. Selective transport of hydrocarbons in the unsaturated zone due to
aqueous and vapor phase partitioning, Water Resour. Res., 23:1926-1938.

Bouchard, D. C., Wood, A. L., Campell, M. L., Nkedi-Kizza, P., and Rao, P. S. C., 1988.
Sorption nonequilibrium during solute transport J. Cont. Hydrol, 2:209:223.

Brusseau, M. L., 1992. N onequilibrium transport of organic chemicals: The impact of
pore-water velocity, J. Contam. Hydrol, 9:353-368.

Brusseau, M. L., Larsen, T. and Christensen, T. H., 1991. Rate-limited sorption and
nonequilibrium transport of organic chemicals in low carbon aquifer materials,
Water Resour. Res., 27:1137-1 145.

Call, F., 1957. The mechanism of sorption of ethelynedibromide on moist soils, J. Sci.
Food, Agric., 8:630—639.

Chiou, C. T., and Shoup, T. D., 1985. Soil sorption of organic vapors and effects of
humidity on sorptive mechanism and capacity, Environ. Sci. Technol., 19:1196-
1200.

Corapcioglu, M. Y., and Baehr, A. L., 1987. A compositional multiphase model for
groundwater contamination by petroleum products, 1. Theoretical considerations,
Water Resour. Res., 23:191-200.

Gierke, J. S., Hutzler, N. J. and Crittenden, J. C., 1990. Modeling the movement of
volatile organic chemicals in columns of unsaturated soil, Water Resour. Res.,
27:1529-1547.

Millington, R. J ., and Quirk, J. P., 1961. Permeability of porous solids, Trans. Faraday
Soc., 57:1200-1207.

Ong, S. K and Lion, L. W., 1991. Effects of soil properties and moisture on the sorption
of trichloroethylene vapor, Water Res., 25:29-36.

Parker, J.C., and van Genuchten, M. Th., 1984. Determining transport parameters from
laboratory and field tracer experiments, Bull. 84—3, Va. Agric. Exp. Stn.,
Blacksburg.

Pennell, K. D., Rhue, R. D. Rao, P. S. C. and Johnston, C. T., 1992. Vapor-phase
sorption of p-xylene and water on soils and clay minerals, Environ. Sci. Technol.,
26:756-763.

Peterson, M. 8., Lion, L. W. and Shoemaker, C. A., 1988. Influence of vapor-phase
sorption and diffusion on the fate of uichloroethylene in an unsaturated aquifer
systems, Environ. Sci. Technol., 22:571-578.

Schwarzenbach, R. P., and Westall, J ., 1981. Transport of nonpolar organic compounds
from surface water to groundwater. laboratory sorption studies, Environ. Sci.
Technol., 15: 1360-1367.

Valocchi A. J., Validity of local equilibrium assumption for modeling solute transport
through homogeneous soils, Water Resour. Res., 1985, 21, 808-820.

van Genuchten, M. Th., Davidson, J. M., and Wierenga, P. J ., 1974. An evaluation of
kinetic and equilibrium equations for the prediction of pesticide movement
through porous media. Soil Sci. Soc. Am. J., 38:29-35.

Welty, J. R., Wicks, C. E., and Wilson, R. E., 1984. Fundamentals of momentum, heat
and mass transfer. Wiley, NY, 3rd ed., 803 pp.

CHAPTER 5

SORPTION NONEQUILIBRIUM DURING TRANSPORT OF NONIONIC
ORGANIC COMPOUNDS THROUGH SOIL COLUMNS: EFFECT OF SOIL
ORGANIC MATTER, PORE-WATER VELOCITY, AND SATURATION

5.1 Introduction

Equilibrium approaches are usually used to model sorption of dissolved nonionic
organic compounds (N OCs) in the subsurface. This is consistent with the generally
accepted view of the process by which N OCs are sorbed by natural sorbents, i.e.
partitioning to sorbent organic matter. While this approach may be adequate under certain
conditions, it is usually used to simplify model analysis and to reduce the required
computation time. In contrast kinetic approaches require quantitative treatment of the
microscopic transport steps and detailed specification of the geometry of the solid phase.
Although such detailed knowledge is impossible for aquifer materials (V alocchi, 1985), an
adequate understanding of sorption kinetics is necessary to develop efficient processes to
destroy, immobilize, or separate organic pollutants from the soil matrix.

Two general types of models have been developed to simulate sorption kinetics of
organic compounds: chemical nonequilibrium models and diffusive mass transfer models.
Chemical nonequilibrig models assume that the sorption reaction is the rate-limited

 

 

process. The two-site chemical nonequilibrium models, for example, assume two parallel
sorption domains: sorption on one of the domains is instantaneous, while sorption on the
other is kinetically controlled (Cameron and Klute, 1977). The conceptualization upon
which the diffusive mass transfer models was developed, however, requires that the rate
limiting process is physical rather than chemical. Two types of models have been
developed in this regard: intraparticle diffusion (Ball and Roberts, 1991) and intraorganic

123

124

matter diffusion models. These models assume that the two classes of sites are arranged in

series rather than in parallel and that sorption on these sites is always at equilibrium.

Brusseau and Rao (1989) and Brusseau et al. (1991b) discussed the
appropriateness of using chemical nonequilibrium models for the transport of NOCs. They
stated that the assumption of two types of sorption sites with one being rate-limited is not
viable, and that the nature of hydrophobic reaction results in hydrophobic sorption being a
rapid process. Experimental evidence of physical, not chemical, contribution to
nonequilibrium is given by Wu and Gshwend (1986): the lack of temperature dependence
was interpreted as evidence that a physical process was being manifested; the dependence
of sorption on particle Size is consistent with a diffusive mechanism. Moreover, Bnrsseau
er al. (1991b) concluded that their experimental results were explained well using the
intraorganic matter diffusion model, but could not be explained using the inuaparticle
diffusion model. Evidence supporting the existence of intraorganic matter diffusion,
although indirect has also been presented by other investigators ( Nkedi-Kizza et al.,
1989; Bouchard et al., 1988).

It is not surprising, therefore, that soil organic matter (SOM) has evolved as an
important parameter that affects sorption nonequilibrium of N OCs. Qualitative assessment
of the effect of SOM on the degree of nonequilibrium has been reported (Bouchard et al.,
1988). No study has been found that quantitatively compares the extent of sorption
nonequilibrium for natural aquifer materials that have different organic matter but the same
texture. The rate of approach to equilibrium has been shown to be influenced by the
particle size (Wu and Gshwend, 1986; Ball and Roberts, 1991). It is our first objective to
quantitatively evaluate changes in the degree of sorption nonequilibrium as the SOM
changes. To avoid differences in the extent of nonequilibrium associated with different
particle size, aquifer materials selected for this study have similar grain size distributions.

The degree of nonequilibrium is usually quantified by the Damkohler number
(Jennings and Kirkner, 1984; Valocchi, 1985; Bahr and Rubin, 1987). The Damkohler

125

number, which is the ratio of hydraulic residence time to characteristic sorption time, is
inversely proportional to pore-water velocity. However, the validity of this direct
relationship between pore-water velocity and Damkohler number is dependent on the
invariance of other parameters that define the Damkohler number with pore-water
velocity. Apparent variations of the rate "constant", which is directly related to the
Damkohler number, with the time of experiment has been reported (van Genuchten et al,
1974; Brusseau et al, 1991a; Brusseau, 1992). Dependence of the rate "constant" on the
time of the experiment may have significant impact on the appropriateness of the
developed criteria that are used to validate local equilibrium assumptions. Hence, it would
have an impact on the validity of directly translating lab-determined parameters to field
scenarios. An investigation of the potential existence of a functional relationship between
pore-water velocity and nonequilibrium parameters including the rate constant is the

second objective of this study.

The third objective is to determine the effect of saturation on sorption
nonequilibrium of NOCs. Several investigators reported an increase in the extent of
nonequilibrium as the porous media is desaturated (van Genuchten and Wierenga, 1976,
1977; Nkedi-Kizza et al., 1983; De Smedt and Wierenga, 1979, 1984, 1986; Bond and
Wierenga, 1990, among others). In their studies, nonequilibrium was attributed to slow
solute diffusion into and out of immobile water regions. Therefore, nonequilibrium was
associated, in their case, with the existence of immobile water regions which affect the
transport of both ideal tracers as well as solutes that sorb. N 0 study has been reported
regarding the potential impact of saturation on sorption-related nonequilibrium. In Chapter
4 of this study, we reported an increase in retardation of two NOCs upon desaturation.
We, indirectly, attributed this increase to an increase in the solid/water ratio when the soil
is desaturated and argued that accessibility of the compound to the grains in the emptied
large pores occurs through diffusion from the water-filled pores into a stagnant water
covering these grains. Hence, there is a possibility of a higher degree of nonequilibrium in
the transport of N OCs in unsaturated soils as compared to that when the soil is saturated.
To evaluate the effect of saturation on sorption nonequilibrium, we compared between the

126

values of the nonequilibrium parameters determined for two N OCs under both saturated

and unsaturated conditions.

5.2 Materials and methods

Three soils were employed in this study. These soils were selected because of their
different organic matter contents and similar textures. The organic carbon content of the
Oakville A, Pipestone, and Oakville B soils is 2.25, 1.57, and 0.70%, respectively. Other
physical properties are shown Table 2.2. Two NOCs were chosen: benzene and
dimethylphthalate (DMP). “C-labeled benzene was analyzed by liquid scintillation
counting. DMP was analyzed by high pressure liquid chromatography. The physical
properties of the two compounds were described in Table 3.2 and the references cited

therein.

Pulse-type miscible displacement experiments using 5.45 i.d. x 30.2 cm glass
columns under both saturated and unsaturated flow conditions were conducted. For the
saturated-flow experiments, three different flow rates were employed. The unsaturated
experiments were conducted at four levels of uniform saturation. The two compounds
were dissolved in a 0.01 N calcium chloride deionized, deaired water solution. Unless
otherwise indicated, the two compounds were injected simultaneously into the column via
a syringe pump using glass syringes. Effluent samples were collected using glass syringes
attached to the outlet of the column and were analyzed shortly after collection. At the end
of the experiment the columns were displaced by an organic compound-free calcium
chloride solution until the effluents were almost free from any amount of NOCs. The
experimental conditions applied in this study were exactly the same as the ones reported in
Chapter 2.

127

5.3 Data analysis

Generated BT‘CS of benzene and DMP were analyzed to determine the optimized
parameter values, and their confidence intervals using the nonlinear least squares inversion
program CXTFIT of Parker and van Genuchten (1984). The program was slightly
modified, as described in Chapter 2, to achieve better accuracy in the numerical
integration. The BTCs were analyzed using both equilibrium and nonequilibrium approach.

For a linear sorption reaction, the equilibrium model in a nondimensional, scaled

form is given as:

2
1049.229 (5,,
31 P 322 32
where,
C = c/ ca (533)
Z = z/ L (5.2b)
r = v0: / L (5.2c)
P = voL/ D (5.2d)
R =1+—"I§D (5.2e)

and where c is solute concentration, c. is solute concentration in the influent solution, 2 is
distance, L is column length, t is time, Tis number of pore volumes, v, is average pore-
water velocity, D is hydrodynamic dispersion coefficient P is the Peclet number, p is bulk
density, 0 is moisture content K0 is distribution coefficient and R is the retardation
coefficient The values of R for benzene and DMP along with the sum of square errors
(SSE) are shown in Table 5.1. Input parameter values for V., T. and D used in the
simulation are also listed in the table. Values of D used are those determined from tritium
BTCs under the same experimental conditions (Table 2.4).

128

Although significant differences exist between the conceptualization of sorption-
related nonequilibrium models, they are mathematically equivalent for the case of linear
sorption (Nkedi-Kizza et al., 1989). This mathematical formulation in a normalized form is

given as:
1.3.9.2 ___ 122E _ ac
4"“ 1”” ar p 322 az ‘53)
(I- B)R— 8Q_T2 =m(C- Q2) (5.4)
where,
_ 0+ FpKD
B — —0+ 9K1) (5.5a)
1 42
=-——— 5.5b
Q2 (1- F) KD Co ( )
w=%(l-B)R (5.5c)

0
and where q; is sorbed concentration in the rate-limited domain, B and mare the
parameters that specify the degree of nonequilibrium in the system. The values of R, B,
and a) for benzene and DMP were determined using the input parameter values listed in
Table 5.1. The optimized values along with their 95% confidence limits and the SSE
values are listed in Table 5.2.

The nonequilibrium model was also used to analyze the data of DMP under
unsaturated conditions. Input parameter values for v., T. and D are listed in Table 5 .3. The
values of D are those for tritium under the same experimental conditions (Table 2.6). The
optimized parameter values for R, B and a) and their confidence intervals are also reported
in Table 5.3.

129

Table 5.1 Results of fitting the AD model to benzene and DMP using
independently determined dispersion coefficient

 

 

 

 

 

Exp. Tracer v. T. Dfor 3H R SSE
cm/hr on’mr

Oakville A

SAl Benzene 31.55 1.95 20.88 l.98(:l:0.05) 0.214
DMP 2. 14(:1:0.08) 0.635

SA3 Benzene 6.30 1.96 5.37 2.05 (10.07) 0.354
DMP 2.50(i0.05) 0.980

SA6 Benzene 0.62 1.91 0.222 2.19(:l:0.08) 0.445
DMP 2.86(:l:0.07) 1.405

Pipestone

SP1 Benzene 33.60 2.08 18.78 2.09(:t0.08) 0.185
DMP l.95(:t0.08) 0.419

SP3 Benzene 6.72 2.09 2.88 2.15(:l:0.06) 0.432
DMP 2. l4(:l:0.10) 1.060

SP6 Benzene 0.67 2.05 0.156 2.32(:1:0.08) 0.377
DMP 2.55(:l:0.10) 0.702

Oakville B

SBl Benzene 36.47 2.18 18.04 1.36(10.06) 0.540
DMP 1.41(:l:0.04) 0.368

SB3 Benzene 7.29 2.20 3.27 l.43(:l:0.03) 0.250
DMP l.54(:t.0.05) 0.350

SB6 Benzene 0.73 2.17 0.204 l.44(:t0.05) 0.260
DMP 1.52(:l:0.04) 0.310

 

 

130

Table 5.2 Results of fitting the nonequilibrium model to the saturated experiments
using dispersion coefficient determined from tritium BTCs.

 

 

 

 

 

Experiment Tracer R B a) SSE F k,1lhr
Oakville A
8A] Benzene 2.45(i0.13) 0.787(10007) 0265010051) 0.018 0.64 0.534
DMP 2.95(i0.l6) 0.642(10032) 0528010068) 0.012 0.46 0.526
SA3 Benzene 2.78(i0.84) 0.693(10.193) 0.204(10079) 0.104 0.52 0.050
DMP 3.28(.t0.25) 0.639(10033) 0.718(10168) 0.048 0.48 0.127
SA6 Benzene 2.73(:l;0. 17) 0.755(i0.038) 0.383(i0.072) 0.03 0.61 0.011
DMP 4.03(10.l9) 0.5 83(i0.023) 0.977(i0.1 17) 0.015 0.45 0.012
Pipestone
SP1 Benzene 2.76(i0.34) 0.733(:l:0.083) 0.220(10048) 0.027 0.58 0.334
DMP 2.83(:l:0.29) 0.640(zt0.050) 0.381(zt0.064) 0.033 0.44 0.419
SP3 Benzene 2.74(:t:0. l9) 0.750(:l:0.040) 0.302(i0.056) 0.028 0.61 - 0.099
DMP 2.92(r:o.21) 0.660(10030) 0.610(i0.130) 0.059 0.48 0.138
SP6 Benzene 2.75(:t0.14) 0.797(i0.037) 0.342(10072) 0.029 0.68 - 0.014
DMP 2.77(:l:0.06) 0.740(10020) l.170(:l:0.320) 0.022 0.59 0.036
Oakville B
881 Benzene 1.64(10.02) 0.750(10050) 0.130(10020) 0.184 0.62 0.544
DMP 1.85(:t0.17) 0.756(10034) 0.176(zt0.032) 0.049 0.47 0.474
SB3 Benzene l.6l(:l:0.15) 0.894(zt0.079) 0.161(10.155) 0.164 0.72 0.229
DMP 1.70(:l:0.06) 0.820(i0.024) 0.259(10045) 0.049 0.56 0.206
SB6 Benzene l.65(:l:0.03) 0.708(10058) 0.225(10037) 0.026 0.67 0.026
DMP l .73(i0.04) 0.796(i0.016) 0.570(i0.170) 0.016 0.52 0.039

 

Table 5.3 Results of fitting the nonequilibrium model to DMP unsaturated

131

experiments using dispersion coefficient determined from tritium BTCs.

 

 

 

 

Exp. V0 To S D(’H) R B 0) SSE F k
cm/hr £96) crn‘lhr llhr
USA] 16.51 1.94 95.5 12.16 2.83 0.66 0.60 0.017 0.475 0.344
10.13 10.02 10.09
USA2 7.272 2.08 78.0 10.73 3.38 0.61 0.60 0.009 0.452 0.112
10.18 10.02 10.08
USA3 2.156 1.38 58.5 3.800 5.46 0.45 1.60 0.002 0.330 0.038
10.13 10.01 10.09
USA4 0.806 1.80 52.2 0.757 7.29 0.37 2.24 0.011 0.274 0.013
10.33 10.02 10.24
USPl 17.50 2.12 96.0 11.84 2.64 0.73 0.28 0.033 0.561 0.231
10.25 10.06 10.06
USP2 8.397 2.42 72.0 14.42 3.36 0.69 0.45 0.014 0.559 0.121
10.20 10.04 10.09
USP3 2.562 1.64 55.4 2.797 4.55 0.57 1.91 0.009 0.447 0.084
10.12 10.02 10.28
USP4 1.026 2.30 43.6 0.665 5.86 0.55 2.01 0.006 0.457 0.026
10.12 10.02 10.24
USBl 18.74 2.16 95.6 8.052 1.55 0.84 0.19 0.074 0.564 0.479
10.08 10.08 10.09
USB2 9.180 2.56 71.0 7.853 1.57 0.86 0.24 0.011 0.655 0.309
10.04 10.02 10.09
USB3 2.735 1.69 50.6 2.089 2.21 0.71 0.49 0.016 0.502 0.066
10.09 10.02 10.08
USB4 1.014 2.21 47.8 0.705 2.88 0.67 0.27 0.022 0.52 0.009
10.28 10.06 1.0.04

 

132

5.4 Results and Discussion

Examples of simulations using the predicted parameter values of Table 5.1 for the
equilibrium model and of Table 5.2 for the nonequilibrium model are shown in Figure 5.1.
The dashed and solid lines were fitted to the measured points using the equilibrium and
nonequilibrium models, respectively. The optimized simulation for the nonequilibrium
model closely match the experimental results, while obvious deviations between optimized
simulation for the equilibrium model and the data points can been seen. Comparison of the
corresponding SSE values listed in Table 5 .1 and 5 .2 reveals that the nonequilibrium
model performed better, in all cases, than the equilibrium approach. The difference in
performance appears to increase as the SOM increases, i.e. higher differences in the SSE
values for the equilibrium and nonequilibrium model using Oakville A, than for Pipestone,
than for Oakville B soil. This is consistent with the findings of Bouchard et al. (1988) and
of Brusseau er al. (1991a) who suggested higher deviations between the equilibrium and

nonequilibrium approach as the value of retardation coefficient increases.

Table 5 .1 and 5 .2 show that the values of R predicted using the nonequilibrium
model are higher than those predicted using the equilibrium model. Moreover, the values
of R predicted by the equilibrium model appear to increase with the increase in flow rate.
Those predicted by the nonequilibrium model do not have the same trend, except for DMP
on Oakville A soil. Dependence of R on the flow rate, as discussed by Brusseau et al.,
(1991a), is generally regarded as an indication of sorption- related nonequilibrium. The
use of an equilibrium model, therefore, may not lead to the true value of R.

5.4.1 Impact of SOM on sorption nonequilibrium

BTCs of DMP and benzene on the three selected soils at the lowest conducted
flow rate are shown in Figure 5.2. It is noticed in the figure that the retardation of DMP
increases, as the BTC is shifted to the right, with the increase in SOM. This is not the case
however, for benzene. Although the curves using Pipestone and Oakville A soils are

 

 

133

 

SA]

ClCo
CICo

   

 

 

 

 

 

CICo

 

 

 

 

 

 

 

 

Figure 5.1 Selected BTCs of benzene (uiangles) and DMP (circles). Dashed lines
are simulations using the equilibrium model and solid lines are simulations using

the nonequilibrium model.

 

 

134

 

 

 

 

 

 

 

 

 

1 7’ em“, .OokviIeA
0.8 .- 0° 030% oPlpostone
o -, 0 OOakvmoB
2 0.6 o °’$%
U 04 "’ O 6. %“
0.2 -- o 0.. °¢bxo
o +ch % ma, 9 ° 9.
0 2 4 6 8
T
1 1—
a“ AOakvleA
0-3 "’ $5 . AW
8 0.6 -- a 4‘ a‘.‘ ‘°°"""'°
U 0.4 -- A f
A A
0.2 -- ‘ AA ‘
0 «M ”5%
O 2 4 6 8
.1

 

Figure 5.2 Effect of SOM on transport of benzene
(triangles) and DMP (circles).

 

 

135

shifted to the right of that using Oakville B, it is surprising to see that Pipestone causes
retardation to benzene as much or even a little more than with the Oakville A soil. Batch
sorption coefficients of the two compounds (see Table 2.3) follow a consistent trend with
SOM (i.e. the coefficient increases with the increase in SOM). The physical properties (p
and 0 ) of the packed columns of Pipestone and Oakville A are not significantly different
from each other to cause an impact on the values of retardation of benzene in the column.
We investigated the behavior of the two compounds when injected simultaneously and
separately into the soil columns. There was no evidence of sorption competition as can be
seen clearly in Figure 5 .3. It is possible that there was not enough time for benzene to
diffuse into the interior portion of the SOM on Oakville A. DMP, however, showed
increased retardation with the increase in SOM. This should not contradict the above
possible explanation offered for benzene if one adopted the possibility of another sorption
mechanism for DMP such that the inaccessibility of DMP to partition on the interior layers
of the SOM on Oakville A did not significantly alter the retardation factor as was the ease

with benzene.

The values of B listed in Table 5 .2 are dependent on the SOM. The average value
of B for benzene on Oakville A, Pipestone, and Oakville B soils is 0.745, 0.76, and 0. 87,
respectively, and that for DMP is 0.62, 0.68, and 0.79, respectively. Table 5 .2 also shows
that at a certain flow rate, the value of B for benzene is higher than that for DMP. Since B
is defined as the fraction of retardation caused by instantaneous sorption, a compound
with a higher value of B means that the compound is easier to access or faster to react

with the sorption sites.

If nonequilibrium is caused by diffusion rather than slow reaction, then one would
expect an increase in the extent of nonequilibrium for a compound with low diffusion
coefficient and with the increase in the thickness of the organic coating on the mineral
surface. The above findings agree with this picture. If nonequilibrium, however, is caused
by slow reaction with SOM, then one has to assume that SOM is stratified in a manner

that the reaction on the sorption sites closer to the exterior surface is faster than that on

136

 

 

 

 

 

 

 

 

O
0.8 --
8 0.6 ~—
6 0.4 .- a
02 -- a"
o —r—J 1r . :
o l 2 3 4
Pipestone I
l T ‘
0.3 4 {9°
8 0.6 -- I
B 0.4 4-
02 -H-
o : i . 1
o l 2 3 4
Oakville A T

 

 

Figure 5.3 BTCs of benzene (triangles) and DMP
(circles) as single (open symbols)- and dual (closed
symbols)«injected into the soil columns.

 

137

the interior sites of the matrix of organic matter. In fact, the opposite has been proposed
by Bouchard et al., (1988) to explain the increase in the degree of sorption nonequilibrium
as the soil organic matter increases. They suggested that the more polar soil organic
carbon moieties are oriented toward the aqueous phase, leaving more hydrophobic regions
less accessible to organic solutes within the matrix of organic carbon. Therefore, one may
conclude that nonequilibrium, for the case presented here, is caused by slow diffusion.
Unfortunately, the values of B cannot assist in differentiating whether this slow diffusion

of tracer is within the matrix of SOM or within the intraparticle pores.

The values of F calculated from the values of B using Eq. (5.5a) are also listed in
Table 5 .2. One might assume that observations made regarding B would apply to F, as
well. This is, indeed, true; the average value of F for benzene on Oakville A, Pipestone
and Oakville B soil is 0.59, 0.62, and 0.67, respectively, while that for DMP is 0.46, 0.50,
and 0.51, respectively. This variation in F, however, among the different soils is not as
significant as the variation in the amount of SOM itself. For example, a 3-fold increase in
soil organic matter between Oakville B and Oakville A soils caused less than a 15%
reduction in the value of F. This raises a question regarding the arrangement of SOM on
the mineral surfaces. If the soil carbon was uniformly spread over the sand surface, it
would form a film that varies linearly in its thickness with variation in the amount of
carbon available, assuming that the density of the organic matter remains the same for the
three soils. Based on this type of arrangement of organic carbon, higher variations in F are
expected using the aquifer materials utilized in this study. Since this is not the case, the
above picture regarding the arrangement of soil organic matter may not be valid. Electron
microscopic examination of the arrangement of SOM revealed that SOM exists as patches
or porous blobs (Schnitzer, 197 8). If one were to adopt this picture, then the number of
organic matter ”blobs" associated with the soil that has the high organic matter content
will be higher. The fraction of accessible sorption sites, however, remains almost

0011818111,

138

Inspection of Table 5 .2 also reveals that the value of k, for the same flow rate,
does not change with changes in SOM. This supports the above argument regarding the
arrangement of SOM on the solid surface. To see this, diffusion into SOM is usually
expressed as (Brusseau er al., 1991b):

c D p

where c is the shape factor, D, is the diffusion coefficient into polymers, I is the
characteristic diffusion length. If one were to assume that the three aquifer materials have
the same c, and that D, for a given compound is constant, then one would expect k to be
function of F and 1. Variations in F among the soils utilized in this study, as shown before,
are very slight. Therefore, similar k values are an indication of similar diffusion path
lengths. Hence, the SOM on the three aquifers would have similar thicknesses, but more

organic matter "blobs" are associated with the soil that has higher organic matter.

5.4.2 Impact of pore-water velocity on sorption nonequilibrium

BTCs of benzene and DMP for different pore-water velocities are presented in
Figure 5 .4. The BTCs do not seem to be influenced by flow rate, except for DMP on
Oakville A soil. A shift to right with the reduction in flow rate for DMP on Oakville A has
resulted, as discussed in Chapter 4, in variations in the value of retardation coefficient. We
attributed the velocity dependence observed in R to the possibility of the existence of an
additional sorption process that is observable when relatively slow velocities are used. The
impact of pore-water velocity on the nonequilibrium parameters B and (o is the subject of

the remainder of this section.

Table 5 .2 shows that the values of B are independent of pore-water velocity.
Hence, the value of F should be independent of velocity. Table 5.2 shows, in fact, that
there is no functional relationship between F and pore-water velocity for the two
compounds using the three soils. The F factor would likely be a function of velocity for a

139

 

 

 

 
  

  

 

 
 
  

 

 

 

 

 

 

 

 

 

 

 

  

‘ ‘31.55¢m/hr 0'8 T 031.55cmlht
0'8 A 630”“ 0.6 w o aaoem/ru
8 0.6 A 0‘62 CW"! 8 00.62 cmltv
\ \ 0 4 1"
U 0.4 U
C
0 0 1 ‘ TL : . '
0 2 6 8 0 4 6 8
T
Oakville A Oakville A
I A 33.60 em/hr I O 33.60 cm/hr
8 0 6 A 0.67 cmlht 9 0.6 O 067 cm!”
x 9 2
O U 0.4
0.2
0 T I 2H
0 4 6 8
T
Pipestone Pipestone
l I
A 36.47 cmlht 036.47 cm!"
0.8 ‘ 7.29 an,” 0-3 o 729 emlhr
8 0 6 a 0.73 mm 0 0.6 a 0.73 art/hr
-.. 2
U U 0.4
0.2
0
0 4 6 8
Oakville B Oakville B

 

 

 

Figure 5 .4 Effect of pore velocity on transport of benzene (triangles) and DMP

(circles).

 

140

chemical nonequilibrium process involving a continuous distribution of reaction times
(Schwarzenbach and Westall, 1981). On the contrary, F should be fairly independent of
velocity for nonequilibrium caused by slow diffusion (Brusseau et al., 1991a). Therefore,
the independence of F on velocity is suggestive that sorption nonequilibrium is due to
slow diffusion. Again, the F factor does not allow distinguishing if slow diffusion is within

the matrix of SOM or within intraparticle pores.

Values of a), as indicated by Eq. (5.50), are expected to be velocity dependent. The
values of k, the mass transfer coefficient, are not expected to be, however. The values of k
for the two compounds using the three aquifer materials are presented in Figure 5.5 as a
function of pore-water velocity. The figure shows dependence of k on pore-water velocity.
This is inconsistent with a constant mass transfer coefficient of the compound that would '
describe all the experiments on the same soil. van Genuchten et al. ( 1974) noticed
dependence of the first-order reaction constant of picloram on flow velocity. van
Genuchten er al. (1974) hypothesized that at high flow velocity the residence time of the
herbicide in the column is too short to allow diffusion to all sorption sites. They argued
that not all the sorption sites actively participate in sorption at high flow rate. Brusseau et
al. (1991a) also noticed a time-scale effect on k. Brusseau et al. ( 1991a) compared their k
values with those of Ball and Roberts (1991), Roberts et al. (1989) and Lee et al. (1988)
and noticed that smaller “rate constants" are associated with longer experimental times.
The dependence of k on pore-water velocity in the above studies was attributed to changes
in KO. The same reason can be used here to explain variation of k with velocity for DMP
on Oakville A, since K0 , in this case, changes with velocity. However, for all the other
sorbate-sorbent combinations there was no dependence of KD (or R) on pore-water

velocity. Therefore, a different explanation should be offered for the noticed functionality.

The dependence of k on pore-water velocity could be a result of a time-scale
effect, where the value of the "rate constant" is dependent on the length of time of the
experiment but the actual sorption process is not altered. Therefore, the dependence of k,

not [(9, on pore-water velocity is a result of the mass transfer coefficient being a time-

l4]

 

 

0.6 T
0.5 " ‘

I

l

0.3 -
0.2 1
0.1 ‘

0“»

mass transfer coefficient, llhr

 

l J J
I l I

5 15 25 35 45
pore-water velocity, cm/hr

‘
qu-

 

Figure 5 .5 Relationship between mass transfer coefficient
and pore-water velocity, circles for Oakville A, diamonds
for Pipestone and triangles for Oakville B soil, open
symbols for DMP and closed ones for benzene.

 

142

averaged parameter. Brusseau (1992) noticed similar dependence of k on pore-water
velocity. The author argued that the dependence of k on pore-water velocity could be a
result of variation of the diffusion coefficient or the characteristic diffusion length or both
with the time of experiment. Schwarzenbach and Westall (1981) proposed using a
continuous distribution, not a single value, of k to be able to describe the effect of flow
velocity on transport of chemicals affected by sorption nonequilibrium. As indicated by
Schwarzenbach and Westall (1981), the different k values would correspond to different
diffusion path length. Hutzler er al. (1986), indeed, used different values of l to describe

BTCs generated at different flow rates.

5.4.3 Impact of saturation on sorption nonequilibrium

Parameters values for all the unsaturated experiments are reported in Table 5.3.
Values for F and k are estimated using Eqs. (5.5a) and (5.5c), respectively, along with the
values of R and v, listed in the table. An example of the simulations produced by the
nonequilibrium model at two levels of saturation using Oakville A soil is shown in Figure
5.6. The figure shows that the nonequilibrium model was able to provide a good
description of the generated BTCs. Changes in R with the decrease in saturation, as
noticed in Table 5 .3, have been discussed in Chapter 4 and were attributed to changes in
the solid/water ratio upon desaturation. The following discussion will focus on the values

of the nonequilibrium parameters B and a) of Table 5 .3.

Saturation and pore-water velocity are coupled. Therefore, to assess the impact of
saturation on sorption nonequilibrium, the effect of pore-water velocity should be isolated.
To do so, a comparison between nonequilibrium parameter values determined under
saturated conditions with those determined when the soil is partially saturated will be
performed. Table 5 .3 shows that the values of B decrease as saturation is reduced. As
indicated earlier, this should not be due to a decrease in velocity, since we accepted the
fact that nonequilibrium is due to a diffusion limitations rather than slow chemical

reaction. Therefore, changes in B could be due to changes in saturation. However, changes

143

 

 

 

d-

 

15

 

 

 

Figure 5 .6 Selected BTCs of DMP under unsaturated
conditions.0pen and closed circles are data of experiment
USA2 and USA4 with saturation of 78 and 52%,
respectivley. Lines are simulations using the nonequilibrium
modeL

 

144

 

 

 

 

 

Figure 5.7 Relationship between normalized fraction of
instantanuous sorption sites and retardation coefficient,
circles for Oakville A, diamond for Pipestone and triangles
for Oakville B soil, open symbols are for unsaturated
experiments and closed ones for saturated experiments

145

 

0.6 T
0.5 + '
0.4 .- °
0.3 -~ A

0.2 4- 4

$6

0.] ‘-

o h} : i a
0

10 Z) 30 40
pore-water velocity, cmlhr

mass transfer coefficienLl/hr
o

 

db

 

 

 

Figure 5.8 Relationship between mass transfer coefficient
and pore-water velocity, circles for Oakville A, diamond for
Pipestone and triangles for Oakville B soil, open symbols are
for unsaturated experiments and closed ones for saturated
experiments

146

in B are also associated, as shown in Table 5.3, with an increase in R. In order to
determine if changes in B are due to changes in R or changes in saturation, the values of B
for the unsaturated experiments are compared to those for the saturated ones. This is
presented in Figure 5.7. The figure shows that the values of B for the saturated
experiments are not different from those for the unsaturated experiments at comparable
retardation coefficients. Hence, the variations in B are indeed due to variations in R and
the decrease in saturation did not directly affect the fraction of instantaneous sorption
sites. Similar conclusions can be reached if one compares the values of F with pore-water

velocity.

For the saturated-flow experiments, the mass transfer coefficient, k, was found to
be dependent on pore-water velocity. Therefore, the values of k determined under
unsaturated-flow conditions are expected to vary with velocity (saturation).The impact of
saturation on k was investigated by comparing the values of k for both saturated and
unsaturated experiments at the same pore-water velocity. The values plotted in Figure 5.8
show that the values of k under unsaturated conditions compare well with those
determined when the soil is saturated. Therefore, there is no evidence of change in k with

changes in saturation.

5.5 Summary and conclusions

Values of transport nonequilibrium parameters determined from analysis of BTCs
of two NOCs were utilized to assess the impact of SOM, pore-water velocity and level of
saturation on the extent of sorption nonequilibrium. Three aquifer materials with relatively
high organic carbon content were used in this study.

The assumption of local equilibrium during transport of N OCs was not valid even
at low pore-water velocity. The two NOCs exhibit sorption nonequilibrium which appears
to be of diffusive nature rather than a result of slow reaction rates. Our results do not

147

allow one to conclude whether slow diffusion occurs within the matrix of organic matter

or within the intraparticle pores.

A 3-fold increase in SOM was accompanied only by a slight increase in the extent
of sorption nonequilibrium. This is suggestive that SOM is not uniformly distributed over

the mineral surfaces, and is consistent with electron microscopic observations reported by

others.

Diffusion mass transfer coefficients vary proportionally with pore-water velocity.
Hence, established criteria for the validation of the local equilibrium approach, which is
built on the assumption of a constant diffusion mass transfer coefficient, need to be
evaluated. The use of previously developed criteria may be problematic in extrapolating
lab-obtained parameters to field scenarios when modeling transport of organic chemicals

in the subsurface.

It has been reported by other investigators that physical nonequilibrium, created by
the existence of slow solute diffusion into an out of immobile water regions, may develop
during transport of solutes in partially saturated soils. Previous work using the same
aquifer materials concluded that physical nonequilibrium does not exist. This work also

showed that there was no impact of saturation on sorption nonequilibrium.

148

5.6 References

Bahr, J. M. and Rubin, J., 1987. Direct comparison of kinetic and local equilibrium
formulations for solute transport affected by surface reactions, Water Resour.
Res., 23:438-452.

Ball, W. P. and Roberts, P. V., 1991. Long-term sorption of haloginated organic
chemicals by aquifer material. 2. Intraparticle diffusion, Environ. Sci. Technol. 25:
1237-1249.

Bond, W. J. and Wierenga, P. J ., 1990. Immobile water during solute transport in
unsaturated sand columns. Water Resour. Res., 26:2475-2481.

Bouchard, D. C., Wood, A L., Campell, M. L., Nkedi-Kizza, P., and Rao, P. S. C., 1988.
Sorption nonequilibrium during solute transport, J. Cont. Hydrol., 2: 209-223.

Brusseau, M. L., 1992. N onequilibrium transport of organic chemicals: The impact of
pore-water velocity, J. Cont. Hydrol., 9:353-368.

Brusseau, M. L., Larsen, T., and Christensen, T. H., 1991a. Rate-limited sorption and
nonequilibrium transport of organic chemicals in low organic carbon aquifer
materials, Water Resour. Res., 27:1137-1145.

Brusseau, M. L., R. E. Jessup, and P. S. C. Rao, 1991b. Nonequilibrium sorption of
organic chemicals: Elucidation of rate-limiting processes, Environ. Sci. Technol.,
25: 134- 142.

Brusseau, N. L. and Rao, P. S. C., 1989. Sorption nonideality during organic contaminant
transport in porous media, Critical Rev. Environ. Control, 19:33-99.

Cameron, D. A. and Klute, A., 1977. Convective-dispersive solute transport with a
combined equilibrium and kinetic adsorption model. Water Resour. Res., 13:183-
188.

De Smedt, F. and Wierenga, P. J ., 1979. A generalized solution for solute flow in soils
with mobile and immobile water. Water Resour. Res., 15:1137-1141.

De Smedt, F. and Wierenga, P. J ., 1984. Solute transfer through columns of glass beads.
Water Resour. Res., 20, 225-232.

De Smedt, P., Wauters, F. and Sevilla, J ., 1986. Study of tracer movement through
unsaturated sand. J. Hydrology, 85: 169-181.

Hutzler, N. C., Crittenden, J. C., Gierke, J. S., and Johnson, A. S., 1986. Transport of
organic compounds with saturated groundwater flows: Experimental results,
Water Resour. Res., 22:285-295.

Jennings, A. A. and Kirkner, M., 1984. Instantaneous equilibrium approximation
analysis, J. Hydraul. Eng. Div. ASCE, 110:1700-1716.

Lee, L. S., Rao, P. S. C., Brusseau, M. L., and 0gwada, R. A., 1988. Nonequilibrium
sorption of organic contaminants during flow through columns of aquifer
materials, Environ. Toxicol. Chem., 7 :779-793.

Nkedi-Kizza, P., Biggar, J. W., van Genuchten, M. Th., Wierenga, P. J ., Selim, H. M.,

Davidson, J. M. and Nielsen, D. R. 1983. Modeling tritium and chloride 36 transport
through an aggregated oxisol. Water Resour. Res., 19:691-700.

149

Nkedi-Kizza, P., Brusseau, M. L. Rao, P. S. C. and Hornsby, A. G., 1989.

N onequilibrium sorption during displacement of hydrophobic organic chemicals
and “Ca through soil columns with aqueous and mixed solvents. Environ. Sci.
Technol., 23:814-820.

Parker, T. C. and van Genuchten, M. Th., 1984. Determining transport parameters from
laboratory and field tracer experiments, Bull. 84-3, Va Agric. Exp. Stn.,
Blacksburg.

Roberts, P. V., Semprini, L., Hopkins, G. D., Grbic-Galic, D., McCarty, P. L., and
Reinhard, M., 1989. In—situ aquifer restoration of chlorinated aliphatics by
methanotrophic bacteria, EPA Publ. EPA-600/J-89-125, U.S. Environ. Prot.
Agency, Washington, D. C.

Schnitzer, M., 1978. Humic substances: Chemistry and reactions. In: M. Schnitzer and
S. U. Khan (editors), Soil organic matter. Elsevier, New York, NY, pp 1-64.

Schwarzenbach, R. P., and Westall, J., 1981. Transport of nonpolar organic compounds
from surface water to groundwater: Laboratory sorption studies, Environ. Sci.
Technol., 15:1360-1367.

Valocchi A. J ., 1985. Validity of the local equilibrium assumption for modeling sorbing
solute transport through homogeneous soils, Water Resour. Res., 21:808-820.

van Genuchten, M. Th. and Wierenga, P. J ., 1976. Mass transfer studies in sorbing
porous media. 1. Analytical solutions. Soil Sci. Soc. Am. J ., 40: 473-480.

van Genuchten, M. Th, Davidson, J. M. and Wierenga, P. J ., 1974. An evaluation of
kinetic and equilibrium equations for the prediction of pesticide movement
through porous media. Soil Sci. Soc. Am J., 38:29-35.

van Genuchten, M. Th., Wierenga, P. J. and O'Conner, G. A, 1977. Mass transfer studies
in sorbing porous media: Experimental evaluation with tritium. Soil Sci. Soc. Am.
J., 41: 272-278.

Wu, S. C. and Gschwend, P. M., 1986. Sorption kinetics of hydrophobic organic
compounds to natural sediments and soils. Environ. Sci. Technol., 20:717-725.

' CHAPTER6

DISSERTATION SUMMARY AND RECOMMENDATIONS

6.1 Dissertation summary

The overall objective of this study was to gain a better understanding of the
transport of dissolved VOCs in the unsaturated zone. This study focused on transport
mechanisms that affect the mean velocity of contaminant movement and the extent of
spreading from the mean. An in-depth review of the literature related to these mechanisms
has been presented in Chapter 1. The four chapters that follow contain the results of the
experimental and analytical investigations. Each of these chapters can stand alone and are
currently in the process of being published. This section is a general summary of Chapter 2
through Chapter 5. However, readers interested in a more detailed summary of a
particular chapter are directed to the summary section at the end of that chapter.

Three nonaggregated sandy soil samples were utilized in this study. The soils
varied in their organic carbon content but had similar grain size distribution. Three tracers,
i.e. tritium, benzene and dimethylphthalate were used. The use of tritium served as an ideal
tracer, that of dirnethyphthalate as a nonvolatile organic compound, and that of benzene as
a volatile organic compound. Soil columns were designed to operate in either a saturated
or an unsaturated modes. The columns were also designed to eliminate air advection when
the soil was partially saturated. Saturated flow experiments were conducted at three
different pore-water velocities. Unsaturated experiments were performed under a unit
hydraulic gradient to assure uniform water distribution along the depth of the column.

Aqueous effluent samples were collected using glass syringes in a manner that avoided

150

151

losses by volatilization. The samples were analyzed for tracer concentration shortly after

collection.

Several studies have been conducted to examine the dispersive behavior of
unsaturated media. In reviewing these studies, two unsettled issues were identified: the
first is whether there is transport nonequilibrium created by slow solute diffusion into
relatively stagnant water regions, and the second relates to changes in the dispersivity of
the media when desaturated. The existence of transport nonequilibrium developed as a
result of desaturation, enhances solute spreading. Hence, its impact, if not properly
isolated, appears as increased dispersion. The objective of Chapter 2 was to investigate the
impact of saturation on the dispersivity of natural, nonaggregated porous media. Results
of this phase indicated that there was no physical nonequilibrium during transport of
uitium through the porous media utilized. Results also showed that the dispersivity under
unsaturated conditions was higher than the value determined for the saturated
experiments. These results suggest that a model which accounts for intersection of
capillary tubes could be more appropriate to represent the geometry of the unsaturated
pore volume than the simple bundle-of—capillary tubes model.

Chapter 3 and 4 of this study were directed towards quantifying the average
velocity of dissolved organic contaminants relative to that of water. Retardation of
dissolved ( in water) VOCs in the subsurface occurs due to partitioning into other phases.
Under saturated conditions, sorption into the soil matrix will be the cause of retardation.
In the unsaturated zone, both sorption and volatilization will influence the average speed
of dissolved VOCs. In Chapter 3 a comparison was made between values of retardation
coefficients determined by two commonly used techniques: batch and saturawd column
experiments. Results of this phase showed that batch-determined retardation coefficients
are higher than their column-determined counterparts. Several factors have been
previously reported to cause discrepancy between the results of the two techniques. These
factors are either sorption-related ( i.e. nonequilibrium, nonlinearity, nonsingularity) or
sorption-nonrelated. Our results showed that the extent of deviation in the values of

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retardation between the two techniques was independent of the amount of soil organic
matter. Hence, sorption-related factors were probably not the cause of this disparity.
Although not proven experimentally, mixing differences between the two techniques

becomes a potential explanation.

Chapter 4 was the first to report the effect of saturation on retardation of a volatile
and a nonvolatile organic compounds under dynamic conditions. Previous work, in this
regard, was limited to static (batch) type experiments and for saturation that does not
contribute to aqueous flow. Retardation coefficients determined under unsaturated flow
conditions were compared to those when the soil was fully saturated. This phase showed
that retardation coefficients for unsaturated soils are higher than the values determined
when the soil is saturated, and that the deviations in retardation are generally higher as the
saturation is reduced. It was also found that there was no functional relationship between
the extent of deviations in the values of retardation coefficient and the amount of soil
organic matter. The impact of volatilization on retardation of benzene under unsanrrated
conditions was not significant. This phase demonstrated through theoretical
considerations, however, that the impact of volatilization on retardation for VOCs with
high volatility and for aquifers with low carbon content is significant.

Besides volatilization, two factors may cause an increase in retardation under
unsaturated conditions as compared to when the soil is saturated. The first is an increase in
the value of sorption distribution coefficient and the second is an increase in the
solid/water ratio. Our data revealed that retardation factors under unsaturated conditions,
when normalized to the saturated solid/water ratio, would be very similar. We were not
able to conclude that the distribution coefficient changes as the media is desaturated. For
practical purposes, a distinction whether the increase in retardation is due to changes in
distribution coefficient or changes in solid/water ratio may not be necessary. A distinction
is important, however, from a mechanistic standpoint.

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Investigation of the impact of soil organic matter, pore-water velocity and level of
saturation on the extent of sorption nonequilibrium was the main focus of Chapter 5.
Results in this chapter showed that the assumption of local equilibrium during transport of
organic chemicals through packed soil columns was not valid even at low pore-water
velocity. In addition, sorption nonequilibrium of the utilized nonionic organic compounds
appeared to be of a diffusive nature rather than a chemical kinetic limitation. However, the
extent of sorption nonequilibrium was not significantly enhanced by increasing the amount
of soil organic matter. This suggests that soil organic matter is not uniformly distributed

over the mineral surfaces, which is consistent with electron microscopic observations

reported by others.

The results of Chapter 5 also showed that the diffusion mass transfer coefficient
varies proportionally with pore-water velocity, and that the common assumption of a
constant mass transfer coefficient is questionable. This may have serious implications on
the validity of previously established criteria for validation of local equilibrium approaches,
and may have implications on extrapolating lab-obtained parameters to field scenarios. By
comparing the values of the nonequilibrium parameters determined under unsaturated
conditions with those determined for the saturated case, it was found that desaturation

does not have an impact on sorption nonequilibrium of the employed organic compounds.

6.2 Recommendations

The following includes directions for future research based on the present study:-
0 Investigate the dispersive behavior of saturated-unsaturated soil for different column
lengths using the same tracer and same technique of sampling.
0 Provide a data base to verify the derived stochastic models that characterize dispersion
in porous media.
0 Design and conduct laboratory experiments to investigate the effect of mixing

. differences and particle spacing on sorption in a batch and column systems.

154

Experimentally investigate the impact of volatilization on retardation for VOCs with
different Henry's constants using low carbon aquifer materials

Establish relationship(s) for better prediction of effective diffusion coefficients in the
air phase.

Elucidate the reason for the dependence of nonequilibrium mass transfer coefficient on
average pore-water velocity.

Determine whether sorption nonequilibrium of nonionic organic compounds is due to

intrasorbent or intraparticle diffusion limitations.

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