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dissertation entitled

MODELING DESORPTION KINETIVS IN SOIL COLUMNS

presented by

IRFAN ASLAM

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MODELING DESORPT ION KINETICS IN SOILS COLUMNS

By

Irfan Aslam

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

2006

ABSTRACT
MODELING DESORPTION KINETICS IN SOILS COLUMNS
By

Irfan Aslam

The inﬂuence of desorption resistance on desorption kinetics exhibited by sorbed
organic contaminants was investigated due to its importance in remediation.
Experimental and mathematical tools were used to evaluate the effect of partial
reversibility of the sorption process. Kinetic parameters in batch and column experiments
were compared to assess the relative importance of differential sorption and desorption.
Three natural sandy soils, which included two surface soils and one of an aquifer origin,
were selected as natural sorbents. Naphthalene was used as a representative hydrophobic
organic compound (HOC) due to its higher solubility and lower hydrophobicity
compared to other 16 polycyclic aromatic hydrocarbons (PAHs) included in EPA’S list of
priority pollutants. A series of batch and column experiments using different techniques

were conducted with equilibration time as a primary variable.

This study provides an improved understanding of desorption kinetics in batch and
column systems. The results support the hypothesis for the existence of three desorption
regimes in columns for a soil-contaminant combination, given that the same
observational regimes exist in batch systems. The results also indicate that packing the
aggregate material in soil columns limits desorption as a result of an increase in diffusion
path lengths, which causes a greater fraction of the soil matrix to behave in a rate-limited

mode.

The experimental evidence also suggests that a small fraction of contaminant
becomes desorption resistant immediately on contact with the solid phase. An increase in
the soil-contaminant contact time results in a signiﬁcant shift of contaminant from the
rate-limited domain to the desorption-resistant domain. However, the effect of contact
time on desorption rate coefﬁcients, which describe desorption from the rate-limited

domain, is not signiﬁcant.

Application of mathematical models to describe desorption in batch and column
systems conﬁrmed the importance of representing observational regimes with a
compatible mathematical description for improved predictions and highlights the need for
models based on time-independent parameters. This study also reveals that an increase in
the number of ﬁtting parameters other than the minimum required to represent the

observational regimes is not justiﬁed.

DEDICATION

To my family

iv

ACKNOWLEDGEMENTS

I want to convey my thanks to my advisors Dr. Thomas C. Voice and Dr. Mantha S.
Phanikumar for the guidance and support they provided throughout my research. I also

convey my gratitude to my committee members Dr. Roger Wallace and Dr. David Long.

I am also grateful to National University of Science and Technology (NU ST)
Pakistan for creating a joint programme with MSU for graduate studies, which enabled

me to achieve my goal of graduate education in the United States.

I feel obliged to mention here about my ﬁ‘iend Shaukat Alvi and his family. We have
enjoyed their love and company since our ﬁrst day at MSU. I personally have always

drawn inspiration form Shaukat in difﬁcult times during my research.

It is also fair to mention the name Of my colleagues Chris Saffron, Shawn
McElmurry, with whom I could discuss my research problems and get a meaningful

critique and ideas to work on.

TABLE OF CONTENTS

LIST OF TABLES ................................................................................. viii
LIST OF FIGURES .................................................................................. x
LIST OF APPENDICES .......................................................................... xiii
CHAPTER 1. INTRODUCTION AND OBJECTIVES ....................................... 1
Introduction ....................................................................................... 1
Research objectives .............................................................................. 3
References ....................... . .................................................................. 5
CHAPTER 2. LITERATURE REVIEW ......................................................... 6
Review of sorption process ..................................................................... 6
Sorption mechanisms .......................................................................... 7
Effect Of dissolved organic matter (DOM) on sorption ................................... 9
Modeling sorption kinetics in batch systems ................................................. 10
Modeling desorption kinetics in batch systems .............................................. 10
Chemical site models ........................................................................ 11
Kinetic models ............................................................................... 12
Distributed-rate models ..................................................................... 13

Pore diffusion models ....................................................................... 14
Sorption/desorption in contaminant transport models ...................................... 15
Equilibrium transport in porous media ................................................... 15
Non- equilibrium transport in porous media ............................................. 17
Transport-related nonequilibrium .................................................... 17

A diffusion based interpretation of physical nonequilibrium ..................... 19
Sorption-related nonequilibrium ..................................................... 21
Comparison of equilibrium and nonequilibrium approaches .......................... 22
Comparison of physical and chemical nonequilibrium approaches ................... 22
Multiple-process induced non-equilibrium ............................................... 24
Irreversible sorption in transport models .................................................. 25
Statistical models ................................................................................ 26
Temporal and spatial moments ............................................................ 26
Statistical models used in chromatography .............................................. 28
Focus of studies in contaminant transport .................................................... 29
Retardation ................................................................................. 29
Dispersion .................................................................................. 32

Mass transfer ............................................................................... 33

Effect of nonlinear sorption ........................................................... 34

Review of experimental techniques ............................................................ 34

vi

Summary .......................................................................................... 36
References ......................................................................................... 37

CHAPTER 3. DESORPTION KINETICS OF NAPHTHALENE IN BATCH AND

COLUMN EXPERIMENTS ..................................................................... 44
Abstract .......................................................................................... 44
Introduction ...................................................................................... 45
Material and methods ........................................................................... 48
Analysis .......................................................................................... 54
Results and discussion .......................................................................... 61
Conclusions ...................................................................................... 79
References ....................................................................................... 8 1

CHAPTER 4. EFFECTS OF AGING ON DESORPTION KINETICS IN SOIL

COLUMNS .......................................................................................... 84
Abstract .......................................................................................... 84
Introduction ...................................................................................... 85
Material and methods ........................................................................... 88
Analysis .......................................................................................... 90
Results and discussion .......................................................................... 91
Conclusions ..................................................................................... 1 16
References ....................................................................................... 1 17

CHAPTER 5. EFFECTS OF PORE-WATER VELOCITY ON SORPTION

NONEQUILIBRIUM ............................................................................ 119
Abstract ......................................................................................... 119
Introduction .................................................................................... 121
Material and methods ......................................................................... 124
Analysis ......................................................................................... 128
Results and discussion ........................................................................ 134
Conclusions .................................................................................... 162
References ...................................................................................... 164

CHAPTER 6. DISSERTATION SUMMARY AND CONCLUSIONS .................. 167
Dissertation summary ........................................................................ 167
Recommendations ............................................................................. 171

vii

Table 3-1

Table 3-2

Table 3-3

Table 3-4

Table 3-5

Table 3-6

Table 4-1

Table 4-2

Table 4-3

Table 4-4

Table 4-5

Table 5-1

Table 5-2

Table 5-3

LIST OF TABLES

Characteristics of soils and packed columns .................................. 49

Fractions of equilibrium, rate-limited and non-desorption sites and the
desorption rate coefﬁcients for batch desorption of naphthalene estimated
by ﬁtting the three-site model .................................................... 63

Retardation factors and dispersion coefﬁcients estimated using the
equilibrium model ................................................................ 66

Desorbable, water-extractable and solvent-extractable naphthalene mass
for each soil in column desorption experiments .............................. 69

Comparison of batch and column sorption distribution coefﬁcients ....... 7O

Parameters for the two-site and the three-site models in column desorption
experiments .......................................................................... 72

Details of the soil mass and the liquid-phase volumes used for the
isotherm and series-dilution desorption experiments ......................... 89

Summary of column conditions and the calculated column distribution
coefﬁcients at 3 days, 2 months and 5 months aging time ................. 102

Parameters of the two-site and the three-site models for Kalkaska-A in
column desorption experiments ................................................ 111

Parameters of the two-site and the three-site models for SPCF in column
desorption experiments ......................................................... 112

Parameters of the two-site and the three-site models for Plume-A sand in
column desorption experiments ................................................ 113

Properties of packed soil columns ............................................. 124
Dimensionless parameters for the two-site and the three-site models ..... 133

Retardation factors and the dispersion coefﬁcients with 95% conﬁdence
intervals ............................................................................ 137

viii

Table 5-4

Table 5-5

Table 5-6

Table 5-7

Column Peclet numbers and mass fractions for the three soils at different
velocities ........................................................................... 140

Estimated parameters for Kalkaska-A using the two-site and the three-site
models ............................................................................ 141

Estimated parameters for SPCF using the two-site and the three-site
models ............................................................................. 143

Estimated parameters for Plume-A sand using the two-site and the three-
site models ........................................................................ 145

ix

Figure 3-1
Figure 3-2

Figure 3-3

Figure 3-4

Figure 3-5

Figure 3-6

Figure 3-7

Figure 3-8

Figure 3-9

Figure 4-1

Figure 4-2

Figure 4-3

Figure 4-4

LIST OF FIGURES

Experimental setup for column desorption .................................... 52
Three-day sorption isotherms of naphthalene ................................. 61

Best ﬁts of the three-site model to the observed naphthalene desorption
data in batch experiments ......................................................... 64

Best ﬁts of the equilibrium model to tritiated water BTCs at 0.1
mL/min .............................................................................. 67

Naphthalene desorption from soil columns in three soils .................... 68

Model best ﬁts for the two-site and the three-site models to the observed
naphthalene desorption data in soil columns ................................... 73

Model best ﬁts of the two-site and the three-site models to the observed
naphthalene desorption data in soil columns showing the cumulative mass
desorbed ............................................................................. 74

Schematic showing an increase in difﬁrsion path lengths as a result of
packing in soil columns ........................................................... 78

Comparison of batch and column parameters obtained by nonlinear
regression using the three-site model ........................................... 79

Sorption isotherms for the three soils. Squares, circles and diamonds
represent 3-day, 2-month and 5-month equilibration period
respectively ........................................................................ 93

Series-dilution desorption in Kalkaska-A for different equilibration
periods. The solid lines represent the sorption phase and the dashed lines
represent the desorption isotherms .............................................. 96

Series-dilution desorption in SPCF for different equilibration periods. The
solid lines represent the sorption phase while the dashed lines represent
the desorption isotherms .......................................................... 97

Series-dilution desorption in Plume-A sand for different equilibration
periods. The solid lines represent the sorption phase while the dashed lines
represent the desorption isotherms .............................................. 98

Figure 4-5

Figure 4-6

Figure 4-7
Figure 4-8

Figure 4-9

Figure 4-10

Figure 5-1

Figure 5-2

Figure 5-3

Figure 5-4

Figure 5-5

Figure 5-6

Figure 5-7

Change in the non-desorbable concentration (Sud) and the fraction of non-
desorption sites (fnd) with an increase in aging period ........................ 99

Cumulative naphthalene desorption from the soil columns at an aging time
of 3 days, 2 months and 5 months. A summary of desorbable, water-
extractable and solvent-extractable naphthalene mass from each column
desorption experiment is also shown .......................................... 104

Best ﬁts of the two-site and the three-site models for Kalkaska-A ....... 107
Best ﬁts of the two-site and the three-site models for SPCF ............... 108
Best ﬁts of the two-site and the three-site models for Plume-A sand. . ..109

Changes in the fractions of equilibrium, rate-limited and non-desorption
sites and the desorption rate coefﬁcients with aging ....................... 115

Experimental setup for pulse-type experiments with naphthalene and
tritiated water .................................................................... 127

Box model representations of four variations of the three-site model
..................................................................................... 132

Three-day sorption isotherms for naphthalene ............................... 134

Tritiated water BTCs for Kalkaska-A. Circles represent the experimental
data and solid lines are simulations using the equilibrium
model ............................................................................... 138

Tritiated water BTCS for SPCF. Circles represent the experimental data
and solid lines are simulations using the equilibrium
model ............................................................................... 138

Tritiated water BTCS for Plume-A sand. Circles represent the
experimental data and solid lines are simulations using the equilibrium
model .............................................................................. 139

Best ﬁts of the two-site and the three-site models to the observed
naphthalene breakthrough data for Kalkaska-A ............................. 150

xi

Figure 5-8
Figure 5-9

Figure 5-10

Figure 5-11

Best ﬁts of the two-site and the three-site models to the observed

naphthalene breakthrough data for SPCF ..................................... 151
Best ﬁts of the two-site and the three-site models to the observed

naphthalene breakthrough data for Plume-A sand .......................... 152
The effect of SOM on transport of naphthalene ............................ 156
The effect of pore-water velocity on transport of naphthalene ............ 161

xii

LIST OF APPENDICES

Table A-1 Details of the independently measured and estimated parameters for the
two-site and the three-site models in column desorption
experiments ....................................................................... 173

xiii

CHAPTER 1
INTRODUCTION AND OBJECTIVES

1.1 Introduction

A variety of anthropogenic activities worldwide are responsible for the leaching
of organic chemicals into the soil, which are cause for concern and are the focus of
remediation efforts. In the past, the fate and transport of these chemicals in the subsurface
environment has been extensively researched. These studies range in scope from
analyzing the behavior of chemicals in simple lab-scale batch systems to ﬁeld-scale
remediation designs employing state-of-the—art technologies.

Contaminants are typically retarded relative to water during subsurface transport.
A continuous sampling of contaminants often shows skewed breakthrough curves (BTCs)
with pronounced tailing. This non-ideal behavior is attributed to the presence of
nonequilibrium that may be sorption-related or transport-related. Batch and column
studies are normally conducted either concurrently or in isolation to develop an
understanding of processes governing the fate and transport of contaminants. The
knowledge gained through these studies is useful for protection of ground water resources
or in designing remediation strategies for contaminated sites.

Traditionally, the soil matrix to which the contaminants sorb, is believed to be
comprised of two different domains i.e., an equilibrium domain and a kinetic/rate-limited
domain. Sorption and desorption behavior of organic contaminants in soils has been
characterized based on this dual domain conceptualization for a wide range of soil-
contaminant combinations. The soils include low organic-carbon aquifer materials as

well as high organic-carbon surface soils while the contaminants include organic as well

as inorganic chemicals. Recent research, however, provides evidence for the existence of
a third domain, commonly referred to as the non-desorption or desorption-resistant
domain (Connaughten et al., 1993; Park, 2000; Park et al., 2003; Park et al., 2001). It is
generally believed that the fraction of the contaminant sorbed to non-desorption domain
either does not desorb at all or desorbs at a very slow rate, which is insigniﬁcant
compared to the time scales of most lab studies. These batch studies have focused on
quantifying the desorption-resistant fraction of the soil matrix and desorption rates.

Desorption resistance, however, has not received due attention in saturated
column studies, which represent an environment closer to subsurface ﬂow in the
saturated zone. In fact, there are only a limited number of studies that have systematically
tried to address this aspect. A comprehensive understanding of desorption-resistance in
transport studies is important from a remediation perspective. The focus of remediation
efforts is also shifting towards in-situ bio-remediation, which is believed to be a cost
effective method with a potential to completely mineralize organic chemicals.
Traditionally, bioremediation efforts have been based on the assumption that a
contaminant can be degraded biologically in the liquid-phase only. Recently, evidence of
sorbed-phase biodegradation has been obtained in some studies (Guerin and Boyd, 1992)
and further research in this area is underway. It is therefore essential to explore

desorption-resistance in ﬂow-through systems.

1.2 Research Objectives

The overall objective of this research was to study the effect of irreversible
sorption on contaminant transport under saturated conditions in natural soils. In order to
do a systematic evaluation, we set forth three main objectives. Experiments were
speciﬁcally designed to address each of these objectives. A brief description is provided
in the following paragraphs. The details of the experimental design and methods of
analysis to address each objective have been documented in a separate chapter in this
dissertation.

The ﬁrst speciﬁc objective (Chapter 3) was to verify, experimentally, the
existence of three desorption regimes i.e., an instantaneous regime, a rate-limited regime
and a very slow regime (irreversible relative to the experimental time scale) in the
column experiments. This was achieved by designing rate studies in batch and column
systems coupled with solvent extractions at the end of desorption to quantify the non-
desorbable contaminant mass. Based on the experimental observations in batch and
column systems, the existing dual-domain mathematical model for contaminant transport
(Van Genuchten and Wagenet, 1989) was modiﬁed to account for irreversible sorption by
incorporating a non-desorption domain. Naphthalene desorption from soil columns was
analyzed using the existing two-site model and the proposed three-site model.
Conclusions about difference in batch and column systems could also be drawn based on
the comparison of desorption in batch and column systems and using a three-regime
model for both systems.

The second objective (Chapter 4) was to evaluate the effects of soil-contaminant

contact time, commonly referred to as “aging”, on desorption in batch and column

systems. The experiments were conducted employing differentially-aged soils and to
evaluate the effect of soil-contaminant contact time on desorption in batch and column
systems.

The third objective (chapter 5) was to study the effects of column residence time
on sorption nonequilibrium because of its analogy to soil-contaminant contact time i.e.,
aging. In this study, column experiments were conducted over a range of pore-water
velocities resulting in different soil-contaminant contact time. For data analysis, a variety
of mathematical formulations were employed to model the observed breakthrough
curves. This evaluation made it possible to ascertain the best mathematical approach to
describe the combined sorption/desorption behavior in soil columns for organic
contaminants, which are likely to exhibit signiﬁcant desorption resistance. The developed
model can prove to be an effective tool in evaluating the effect of irreversible sorption on
natural attenuation of organic contaminants with a prior knowledge of kinetic parameters.

Chapter 6 is a summary of the complete work with important conclusions and

recommendations for future research pertaining to desorption in soil columns.

1.3 References

Connaughten, D.F., Stedinger, J .R., Lion, L.W. and Schuler, ML, 1993. Description of
time-varying desorption kinetics: Release of naphthalene from contaminated soils.
Environmental Science & Technology, 27(12): 2397-2403.

Guerin, W.F. and Boyd, S.A., 1992. Differential bioavailability of soil-sorbed
naphthalene to 2 bacterial species. Applied and Environmental Microbiology,
58(4): 1142-1152.

Park, J .H., 2000. Bioavailability of sorbed organic contaminants. Ph.D. Thesis, Michigan
State University, East Lansing, 155 pp.

Park, J.H., Feng, Y.C., J i, P.S., Voice, T.C. and Boyd, S.A., 2003. Assessment of
bioavailability of soil-sorbed atrazine. Applied and Environmental Microbiology,
69(6): 3288-3298.

Park, J.H., Zhao, X.D. and Voice, T.C., 2001. Biodegradation of non-desorbable
naphthalene in soils. Environmental Science & Technology, 35(13): 2734-2740.

Van Genuchten, MT and Wagenet, R.J., 1989. Two-site/two-region models for pesticide
transport and degradation: Theoretical development and analytical solutions. Soil
Science Society of America Journal, 53(5): 1303-1310.

CHAPTER 2
LITERATURE REVIEW

2.1 Review of sorption process

The word sorption carries the meaning of a chemical’s association with the solid
phase and encompasses both adsorption onto a two-dimensional surface or absorption
into a three-dimensional matrix (Schawarzenbach et al., 1993). The sorption distribution

coefﬁcient K d is usually measured by developing sorption isotherms, which involve

mixing a certain amount of soil with an aqueous solution containing the target compound.
The isotherms are typically linear at low aqueous concentrations, but have been reported
to exhibit nonlinearity at high concentrations (Means et al., 1980; Schawarzenbach and
Westall, 1981). The linearity of partitioning coefﬁcients in hydrophobic organic

compounds (HOCs) at low concentrations is assumed to be due to constant activity
coefficients in sufﬁciently dilute systems, which have been proposed as < 10'5 M

(Karichoff et al., 1983) and equal to 10‘3 M (Chiou et al., 1979). Other than aqueous
concentrations, the factors that are known to affect partitioning include soil-to-water ratio

and mixing conditions. Decrease in K d with an increase in soil-to-water ratio has also

been reported. Voice et a1. (1983) reported that rapid mixing in batch results in

substantial soil abrasion and can create active sorption sites, while Maraqa et a1. (1998)

argued that mixing conditions do not inﬂuence the ultimate sorptive capacity of the soil.
The Freundlich and the Langmuir models are normally used to describe

nonlinearity in sorption isotherms. The Freundlich model is based on the assmnption that

the number of sorption sites is large relative to the number of contaminant molecules and
is mathematically described by:

S = K FC" (2-1)

where S is the solid-phase concentration (pg/Kg), C is the aqueous concentration (pg/L),

K1.- is the Freundlich coefﬁcient (mL/g) and n is the exponent that describes nonlinearity.

In the Langmuir model, sorption increases linearly with increasing aqueous concentration
at lower concentrations; however, the sorbed-phase concentration approaches a constant
value at higher concentrations due to a limited number of sorption sites in the soil matrix.
The mathematical form of the Langmuir model is:

_ KLbC

— 2-2
1+KLC ( )

where K L is the Langmuir coefﬁcient (mL/ g) and b is the maximum sorbed-phase

concentration (pg/Kg).

2.1.1 Sorption mechanisms

Two distinct mechanisms are widely accepted to explain sorption i.e., adsorption
onto a two-dimensional mineral surface or hydrophobic partitioning to soil organic matter
(SOM) (Mingelgrin and Gerstl, 1983). Predominance of either of these mechanisms is
believed to depend on the conditions existing in the system. Sorption to the mineral
surfaces is typically considered to be a surface phenomenon, which is nonlinear and
competitive in nature (Chiou et al., 1979). It is also considered as a charge-driven
phenomenon that depends on the charge of the mineral surface, which can be either
positively or negatively charged depending on the solution composition and pH. The
surface charge affects the sorption of polar and ionic organic chemicals (Laird and

Fleming, 1999).

In natural soils, the main sorbent for nonionic organic chemicals is the naturally
occurring organic matter, which is conceptualized as a mesh of macromolecules with
physico-chemical properties similar to that of a polymer (Altfelder, 2000). Sorption of
chemicals to SOM is known to follow a partitioning that is linear and non-competitive
(Chiou et al., 1979). The organic-rich domains provide a thermodynamically favorable
environment for non-polar organic compounds compared to water, such that in the
presence of an organic matrix, the organic solutes will be driven from the aqueous phase
and concentrate in the organic phase (Chiou et al., 1979; Chiou and Schmedding, 1983).
The driving force for sorption is the hydrophobic effect resulting in a free energy gain
during diffusion from water to the sorbent. Weber and Huang (1996) proposed two
domains within SOM with different physico-chemical properties i.e., an outer “rubbery”
domain, which exhibits linear sorption, and an inner “glassy” domain with a nonlinear
sorption. Two distinct stages of sorption due to SOM heterogeneity have also been
postulated (Pignatello, 1998; Pignatello and Xing, 1996) i.e., a fast stage with an
equilibration time of hours and a slow stage extending to weeks, months or years. For a
dominant organic partitioning, the sorption distribution coefﬁcient is usually normalized
by the fraction of organic carbon.

Kd = focKoc (2'3)

where K 0c is the organic carbon partitioning coefﬁcient and foe is the mass fraction of the
organic carbon. K DC has been successfully correlated with other solute properties, most
notably with octanol-water partitioning coefﬁcient (Kow) , which is a quantitative

measure for the degree of hydrophobicity of the solute in question. The correlation of

K 0c and K W is given by:

Log(Koc) = ALOg(Kow) + B (2’4)

where A and B are the empirical regression coefﬁcients. A compilation of these

regressions from relevant literature has been reported by Ball (1989). K ac values are

sometimes normalized by the fraction of organic carbon in SOM using the relation:

Kom = ocfoc/ am (2'5)

where Kom is the organic matter partitioning coefﬁcient and foe / om is the Motion of

organic carbon in SOM. Chiou (1989) proposed the following relation to estimate the

contaminant solubility in SOM (Sam) if K am and water solubility (SW) are known:

Sam = KamSw (2-6)

2.1.2 Effect of dissolved organic matter (DOM) on sorption

Dissolved organic matter is present in most surface waters and contains up to 90%
of the humic substances. A change in DOM concentration is likely to cause
reorganization in the macromolecular structure of dissolved humic substances, which is
probably responsible for the alteration of their association capacity with HOCs (Akkanen
and Kukkonen, 2003). The quality and variations of DOM can affect desorption and
subsequently biodegradation. Plaehn et al. (1999) studied the impact of DOM on
desorption and mineralization rates of naphthalene using DOM extracted from high
organic soils as well as prepared from commercially available fulvic acid reference
standards. The authors found that neither the partitioning of naphthalene nor the
desorption rate was affected by the presence of DOM. They caution however, that
although not apparent in their data, the effects of DOM on the mechanisms of desorption

and biodegradation may be important for other contaminant-soil-organism combinations.

2.2 Modeling sorption kinetics in batch systems

Sorption has been typically modeled as biphasic. In a dual-domain
conceptualization, the sorbent is assumed to consist of two separate domains i.e., an
equilibrium domain and a rate-limited domain. In the equilibrium domain, the sorption is
fast compared to the duration of experiment. Therefore the assumption of equilibrium is
considered valid. The mass transfer between the aqueous phase and the rate-limited
domain is driven by the concentration gradient. Mathematically, the solid-phase

concentration in the two domains is represented by:

Seq = fqudC (2'7)
%=a[(l-f )K C—S ] (28)
at eq d neq -

where C is the concentration in the liquid-phase (pg/L), Seq and Sneq are the sorbed-phase

concentrations (pg/Kg) in the equilibrium domain and rate-limited domains respectively,

feq is the fraction of sorption sites that undergo instantaneous sorption and a is the

. . -1 . . . . . . . .
sorption rate coefﬁment (hour ). Replacmg the equlllbrlum distnbutlon coefﬁc1ent

K d with a Freundlich distribution coefﬁcient K F or the Langmuir coefﬁcient K L with

necessary mathematical adjustments accounts for the effects of nonlinear sorption.

2.3 Modeling desorption kinetics in batch systems

Desorption is kinetically controlled by either release from surface sorption sites or
by diffusion through the sorbent to water (Van Noort et al., 2003). A variety of
mathematical models have been proposed to describe desorption based on different
conceptualizations of the desorption process. These models include chemical site models

i.e., the two-site model (Rao et al., 1979; Van Genuchten and Wagenet, 1989) and the

10

three-site model (Park, 2000; Park et al., 2001; Park et al., 2002), two and three-
parameter pore diffusion models (Johnson etal., 2001), three-parameter kinetic model
(Cornelissen et al., 1998a; Comelissen et al., 1998b), ﬁve-parameter kinetic model
(Cornelissen et al., 1998a; Comelissen etal., 1997), gamma-distribution model
(Connaughten et al., 1993) and hybrid gamma model (Ahn et al., 1999). Each of these

models is brieﬂy described in the following paragraphs.

2.3.1 Chemical site models

A two-site desorption model for the batch systems assumes that soil matrix has two
types of desorption sites i.e., equilibrium and nonequilibrium/rate-limited sites. Equations
27 and 2-8 describe desorption based on a two-site conceptualization. In a three-site
desorption model (Park, 2000), the soil matrix has three types of desorption sites i.e.,
equilibrium, nonequilibrium/rate-limited and nondesorption sites. The equilibrium and
nondesorption partitioning in the model are described by:

Seq = fqudCdes (2'9)

Sud = fnd Kd Ce(sorp) (2‘10)

while the release from the rate-limited sites follows the ﬁrst-order expression:

 

dS e
dntq =a[fnqudCdes _Sneq:| (2'11)
where Seq , Sneq and Sud are the sorbed-phase concentrations in equilibrium, rate-limited

and nondesorption sites respectively, Cdes is the liquid-phase concentration in the

desorption assay, C450,” is the liquid-phase concentration at sorption equilibrium,
feq, fneq and fnd are the equilibrium, rate-limited/kinetic and nondesorption site fractions

and a is the ﬁrst order desorption rate coefﬁcient for the rate-limited sites. In the two- and

11

the three—site models, the solute exchange between the aqueous and solid phases is

described by a driving force formulation based on the linear distribution coefﬁcient K d .

2.3.2 Kinetic models

The kinetic models viz., three- and ﬁve-parameter kinetic models use only kinetic
rate coefﬁcients to describe desorption from each domain. A three-parameter kinetic
model assumes that the soil matrix is divided into two domains i.e., a rapid desorption
domain that exhibits rapid desorption and a slow desorption domain, for which, the
desorption occurs at slower rates compared to the rapid domain. The mathematical

formulation of the three-parameter kinetic model is as follows:

 

 

dS

d; = —a,s, (2-12)
dS

dts : “asSs (2-13)
ST = S, + S, (2-14)
ﬂ+ﬁ=1 (2w)

A ﬁve-parameter kinetic model accounts for very slow desorption and is based on

following set of equations:

 

937’ = -arS, (2-16)
dS
Titi- = —aSSS (2-17)
dS

drs = “avsSvs (2‘18)
ST =Sr+Ss +Svs (2-19)
fr+fs+fvs=1 (2'20)

12

In the kinetic models, S is the sorbed-phase concentration (pg/Kg), a is a desorption

. -l . . .
rate coefﬁcrent (hour ) and f represents the domarn srze. The subscnpts r, s and vs
denote rapid, slow and very slow desorption.

2.3.3 Distributed-rate models

A gamma-distribution model assumes the entire soil matrix divided into a series of
compartments. Associated with each compartment is a different desorption rate
coefﬁcient that follows the gamma distribution. The time rate of change in sorbed-phase

concentration is described by:

 

00 91—] a -ﬂki
151: j_k,(s,.—KdC)k' ‘3 dk, (2-21)
dt 0 ma)

where k is the desorption rate coefﬁcient for the i th compartment, 0: and ﬂ are the two

parameters the for gamma distribution and l" is the gamma ﬁmction. Similar to the
chemical two—site model, the hybrid gamma-distribution model assumes the soil matrix is
comprised of two domains, i.e., an equilibrium domain and a rate-limited domain. The
rate-limited domain is modeled in the same manner as the gamma-distribution model
while the equilibrium domain is treated similar to that of the chemical two-site model.
The following set of equations is used to represent desorption in a hybrid gamma-

distribution model:

 

Seq = fqudC (2-22)

dS °° .a-1 a waki

ﬂ = 1-1.,(5, «do "I '6 e .11., (2-23)
dt 0 F(a)

ST = Seq + Sneq (2'24)

13

 

2.3.4 Pore diffusion models

One, two and three-parameter pore diffusion models are also based on a
conceptualization of one, two and three domains respectively. However, the desorption
from the rate-limited domain is described by using a formulation based on Fick’s law
which accounts for a speciﬁc geometry of the porous medium. For spherical geometry,

the equations for the three-parameter pore diffusion model are:

2
asneq = D a 5,8,, + Z asneq (2-25)
at arz r 61’
ST = Seq + Sneq + Sud (2-26)

where D is the pore diffusion coefﬁcient (cm2/hour) and r is the radial distance (cm).

Some of these models (i.e., the chemical three-site model, the three-parameter pore
diffusion model and the ﬁve-pararneter kinetic model) explicitly account for the non-
desorbable fraction. There are advantages and disadvantages to each of these models and
it is difﬁcult to designate any model as the best. Ahn et a1. (1999) applied the two-
site/two-region model and the gamma—distribution model to describe naphthalene
desorption and found that the two-site model failed to capture the slow desorption while
the garnma- distribution model was unable to describe the initial rapid release. Similarly,
Culver et a1. (1997) pointed out that the performance of the two-site model was very

sensitive to the value of K d , while the performance of distributed-rate models was robust

over a wide range of partitioning coefﬁcients. Saffron (2005) applied nine different
models to previously reported naphthalene and atrazine desorption data and concluded

that overall the three-regime models better describe the desorption of the two

14

contaminants than the two-regime models do. Johnson et a1. (2001) also reached a similar

conclusion while testing six models to describe phenanthrene desorption.

2.4 Sorption/desorption in contaminant transport models

F low through porous media has been investigated by conducting column studies,
which have been useful in characterizing the processes affecting the fate and transport of
contaminants. These processes include dispersion, diffusion, sorption, ion-exchange etc.
Many conceptualizations of the porous media and the corresponding mathematical
formulations exist e. g., the capillary tube model, the cell model and statistical models.
However it has always been simpliﬁed in a manner so as to treat all these processes at a
macroscopic scale rather than microscopic due to computational limitations and

mathematical complexities.

2.4.1 Equilibrium transport in porous media

An example of the simpliﬁcations mentioned above is the convection-dispersion
equation (CDE). For ﬂow through a non-aggregated homogeneous porous medium under

saturated conditions, the transport of a solute is described by:

2
6t 0 at 6x2 6x
where C is the solute concentration in liquid phase (pg/L), S is the concentration in

sorbed phase (pg/Kg), D is the hydrodynamic dispersion coefﬁcient (cm2/lrr), p is the

. . 3 . . 3 3 .
sorl densrty (g/cm ), 915 the saturated porosrty (cm /cm ), v rs the average pore-water

velocity (cm/hr), x is distance along the direction of ﬂow (cm), and t is time (hr). The

CDE is referred to as the equilibrium model if the condition of local equilibrium is

15

assumed between the two phases. In that case, the governing equation for the solute

transport becomes:

ac 62C ac
R— = D—— _. 2-28
at 6x2 v 6x ( )

where R =1+ %. The equilibrium model is based on the local equilibrium assumption

(LEA), which considers the sorption rates to be faster compared to other processes such
as advection and dispersion. The equation representing the solute transport is simpliﬁed
with this assumption, as only the mobile pore water needs to be explicitly considered and
the sorbed-phase concentration can be deﬁned in terms of the aqueous concentration at
each spatial location in the porous medium (Ball, 1989). If the LEA is valid, the
breakthrough curves for column experiments employing the nonionic organic
contaminants, which are hydrophobic, should exhibit symmetrical BTCs. On the
contrary, the observed BTCs in most lab and ﬁeld studies exhibit asymmetry and tailing.
This provided a motivation for the researchers to hypothesize and test alternative
mechanisms responsible for asymmetrical behavior and to lay down the criteria for the
validity of the LEA.

A measure of the relative importance of kinetic to equilibrium processes is the
Damkohler number, which is deﬁned as the ratio of the transport and reaction time scales.
The Damkohler number has traditionally been used to assess the validity of the LEA. It
has been shown that LEA is generally valid when the Damkohler number is greater than
100 (Valocchi, 1985) and is considered to be a fair approximation when its value is
greater than 10 (Brusseau and Rao, 1989a). In most cases however, the condition is not

met, which warrants the use of a nonequilibrium model rather than relying on the LEA-

16

based equilibrium model. Brusseau et al. (1991b) found via sensitivity analysis of a
bicontinum model that the leftward shiﬁ of the BTC is minimal when the Darnkohler
number is in the range of approximately 4 or greater, and hence the nonequilibrium
should have a minimal effect on the determination of the retardation factor (R) when
these conditions are met. In a separate study by Maraqa et a1. (1999) the LEA was found

to be invalid at a very low pore-water velocity of 0.7 cm/hr.

2.4.2 Nonequilibrium transport in porous media

Nonequilibrium in contaminant transport through a porous medium is viewed to
exist due to processes that are either sorption-related or transport-related. Transport-
related nonequilibrium (also referred to as physical nonequilibrium) is assumed to exist
due to entrapment of a fraction of the mobile phase in the pores that are isolated from the
main ﬂow, while sorption-related nonequilibrium is due to sorptive interactions of the
solute with a dual-property matrix, in which the sorption is instantaneous for one ﬁ'action
while it is rate-limited for the other.

2.4.2.1 Transport-related nonequilibrium

Transport-related nonequilibrium results ﬁ'om slow solute diffusion into and out of
relatively stagnant water regions, which might be created by the nature of the porous
matrix e.g., a higher degree of aggregation or a level of saturation that is less than fully
saturated. Under these conditions, the total water content is assumed to be distributed
between two regions i.e., a mobile region and an immobile region (Coats and Smith,
1964; Van Genuchten and Wierenga, 1976). The solute transfer between the mobile water
region (instantaneous sorption domain) and the immobile water region (rate-limited

sorption domain) can be described by Fick’s law if the geometry of the porous medium

17

can be speciﬁed. But as the models based on geometry are difﬁcult to apply in the ﬁeld,
the solute transfer between the mobile and immobile water regions have been mostly
described using ﬁrst order rate expressions. The model based on this conceptualization of
a transport-related nonequilibrium is also referred to as the two-region nonequilibrium
model or mobile-immobile model (MIM). The mathematical formulation of the MIM

(Van Genuchten and Wierenga, 197 6) is given as:

2
(9,, + prd)a_;m_ = amp," %"L -JW ng—m-amm — Cm.) (2-29)
x
6C-
[6.... +(1—f)pKd]—a;—’"=a(Cm -C.-...) (2-30)

where the subscripts m and im refer to the mobile and immobile liquid regions

respectively, J W = v6 = vmﬂm is the volumetric ﬂux density (cm/hr), f represents the
fraction of sorption sites that equilibrate with the liquid phase in the mobile region and a

. . -1 .
rs the ﬁrst order mass transfer coefﬁcrent (hr ) governrng the rate of solute exchange

between the mobile and immobile liquid regions. Here 6 = 6m + 49,-," . Normalized

equations for the two-region nonequilibrium model for a linear sorption case are:

lei/1-16% acl

————————a) c —c 231
BT P6Z2 6Z (1 2) ( )
(l-m-a—Ciwm-Cz) (2.32)
6T
where
0993. C2=£m,z=i. T=3‘-,P=M=-‘i
Co Co L L Dm D

R=l+pKd,ﬂ=6m+prd and =E£
9 6+pKd V0

where C1 and C2 are the normalized average relative concentrations in the mobile and
immobile water regions respectively. P is the Peclet number for the mobile zone, Dm is

the dispersion coefﬁcient in the mobile zone and a) is the dimensionless mass transfer
coefﬁcient between the mobile and immobile water regions. The models based on the
concept of physical nonequilibrium are sometimes referred to as diffusive mass transfer
models as they describe the rate-limiting sorption process as a physical rather than a
chemical process (Maraqa, 1995).

Three different mathematical treatments of the solute transfer between the mobile
and immobile regions in the porous medium exist (Brusseau, 1989) i.e., (1) by using
Fick’s law (2) by use of ﬁrst order mass transfer expression and (3) by using a lumped
dispersion coefﬁcient that includes the hydrodynamic dispersion as well as axial
diffusion. Physical nonequilibrium is believed to affect the transport of both sorptive as
well as non-sorptive solutes. In most of the current transport-related nonequilibrium
models, sorption kinetics have been simulated using a formulation that assumes a
constant mass-transfer coefﬁcient, one that is independent of pore-water velocity
(Maraqa et al., 1999).

2.4.2.2 A diffusion based interpretation of physical nonequilibrium

Two diffusive mass transfer models are the intra-particle diffusion model (Ball and
Roberts, 1991) and the intra-organic matter diffusion model. Retarded intra-particle
difﬁrsion involves diffusion of solutes through pores contained in micro porous particles,
with retardation occurring by instantaneous sorption to the walls. Intra-organic matter
diffusion involves diffusion within the matrix of the organic carbon components of the

solid phase (Brusseau et al., 1991a).

19

Diffusion of the solute from the mobile region to the immobile region takes place
in a series of steps, which include diffusion from the bulk solution to the boundary-layer,
ﬁlm diffusion and intra-aggregate diffusion (any of which could be rate-limiting). Intra-
aggregate diffusion may occur either by pore diffusion or surface diffusion or both. As
these two processes act in parallel, the faster of the two will be the predominant transport
mechanism and therefore will control the transfer rate (Brusseau, 1989). Although the
dominance of surface diffusion has been found in activated carbon (F ettig and
Sontheimer, 1987), the same is not believed to hold for soil/aquifer systems due to less
tortuosity as compared to the activated carbon. The choice of the model incorporating
surface diffusion or pore diffusion is only important for nonlinear isotherms, as identical
BTCs are expected in both cases for linear isotherms (Weber and Chakravorti, 1974). The
relative importance of each of these processes is often quantiﬁed through the Biot
number, which is the ratio of the ﬁlm transfer rate to the intra-aggregate transfer rate.
Generally, the intra-aggregate diffusion is considered as the rate-limiting step during
sorption (Brusseau and Rao, 1989b).

Spherical geometry is commonly applied for describing the immobile phase and is
applicable when the ﬂow surrounds the spherical aggregates or sorbents containing
immobile water. For spherical geometries, the average aqueous concentration in the
immobile phase is described by:

a
c,,,, (x,t) = 33- erC(r,x,t)dr (2-33)
‘1 o

where a is the radius of the immobile zone, r is the radial distance from the center of the
immobile region and C is the aqueous concentration of solute within the pore at position r

,time t and distance x.

20

2.4.2.3 Sorption-related nonequilibrium

Sorption-related nonequilibrium is caused by slow solute interaction with all or
some speciﬁc sorption sites of the solid matrix. Sorption nonequilibrium models assume
that the sorption reaction is the rate-limiting process (Cameron and Klute, 1977). In a
two-site nonequilibrium model, the adsorption sites are sub-divided into two categories
i.e., equilibrium sites and rate-limited sites (Van Genuchten and Wagenet, 1989). For

steady ﬂow in a homogeneous soil, the transport of a linearly- adsorbed solute is given

by:

D—-v————[(1—feq)ch-S,,,q] (2-34)

1+fequd ac” azc ac ap
a a: 5x2 ax a

as”,

 

= a[(1—f,q)ch—s,,,q] (2-35)

. . . . -1 . .
where a rs the ﬁrst-order kinetic rate coefﬁcrent (hr ), f eq IS the fraction of exchange

sites that are always at equilibrium, the subscripts eq and neq refer to the equilibrium and

rate-limited/kinetic sorption sites respectively. Employing the dimensionless parameters,

the two-site model reduces to the following dimensionless form:

 

R————-——a) C —C 2-36
'BafPazzaz (12) ()
6C
(l-ﬂ)R—2=w(C1-C2) (2-37)
6T
where:
S
C1=£, C2: neq , Z=£, T=Xt—,and R=1+pKd
C0 (1— feq)KdC0 L 9

6+ K __
P=E,ﬂ= feqp d andwzw
D 6+,0Kd V

 

21

Subscripts 1 and 2 refer to the equilibrium sites and rate-limited sites respectively, ,6 is

the dimensionless partitioning coefﬁcient and a) is the dimensionless mass transfer

coefﬁcient.

2.4.3 Comparison of equilibrium and nonequilibrium approaches

In most studies involving transport in soil columns, the focus has been to prove
either the existence of transport-related or sorption related nonequilibrium. Each of these
cases has arguments to support their respective cases. In general, the nonequilibrium
models describe the transport of reactive solutes better than the equilibrium models. This
limits the reliability of the LEA approach except for the ideal transport cases involving
conservative solutes. For example, Maraqa et a]. (1999) used two non-ionic organic
compounds (NOCs) i.e., benzene and dimethylpthalate (DMP), to study the effects of
residence time and degree of water saturation on sorption nonequilibrium parameters, and
observed that nonequilibrium model simulations closely matched the experimental
results, while deviations between the equilibrium model simulations and the data points

were signiﬁcant.

2.4.4 Comparison of physical and chemical nonequilibrium approaches

Prior to studying the effects of sorption on the BTCs of reactive contaminants
through a porous medium, the existence of the type of nonequilibrium (i.e., physical or
sorption-related) must be established. It is relatively easy to interpret the results under the
assumptions of a physical nonequilibrium but if the sorption-related nonequilibrium
exists concurrently, isolating the effects of both is not trivial.

The immobile water fractions have been mostly associated with unsaturated

conditions and aggregated media; therefore, most applications of the physical

22

nonequilibrium model have been in studies involving unsaturated ﬂow conditions or in
those utilizing aggregated media. In spite of the fact that evidences of immobile water
fraction were found in these studies, the possibility of sorptive interactions could not be
ruled out. For example Kamra et a1. (2001) conducted displacement studies on the
leaching of bromide and two pesticides (atrazine and isoproturon) under unsaturated
steady ﬂow conditions employing aggregated soils in 24 small undisturbed soil columns
(5.7 cm in diameter and 10 cm long). Each soil sample differed in soil structure and
organic carbon content. They inferred from the estimated parameters of the
nonequilibrium model that 5 —12% of water at one site, and 12% at the other site was
immobile during displacement in non-preferential ﬂow columns. The corresponding
values for preferential ﬂow columns of the two sites ranged between 25% to 51%
determined by curve ﬁtting with CXTFIT and 24% to 72% by the moment method,
suggesting the role of certain mechanisms other than immobile water to be responsible
for higher degrees of nonequilibrium. Several other studies e. g., (Bouchard et al., 1988;
Brusseau et al., 1991a; Kamra et al., 2001; Lee et al., 1988; Maraqa etal., 1997; Maraqa
et al., 1998) were not conclusive in ruling out the role of sorptive interactions as a cause
of nonequilibrium. Maraqa et a1. (1999) demonstrated that nonequilibrium conditions

resulted from slow sorptive interactions but not due to the slow diffusion into and out of

 

immobile water regions thereby conﬁrming the presence of a sorption-related
nonequilibrium rather than a physical one. Majority of studies involving organic
contaminants have preferred the use of sorption-related nonequilibrium models. The use
of the MIM model in these studies has been limited to ruling out the possibility of

existence of the immobile water fractions.

23

 

2.4.5 Multiple-process induced nonequilibrium

The inherent weakness in assuming a single process as being responsible for
nonequilibrium has also been realized which results in a lumped kinetic term for a system
being affected by more than one rate-limiting process. The effects of concurrent multiple
processes contributing towards nonequilibrium have also been investigated. The multi-
process nonequilibrium model (MPNE) (Brusseau, 1989; Brusseau, 1991) was
formulated to simulate solute transport in a porous medium where transport-related as
well as sorption-related non-idealities were operative. In the MPNE model, the authors
used a dual-porosity approach to represent physical non-ideality and a dual-domain
approach for sorption non-ideality. The four dimensionless equations for the MPNE

model are:

1.

ac,

R
0] 6T

 

+k3<CZ -SZ)+w(CZ —C;) =—a—-—— (2-38)

ac;

Rm 6,. +k.?(C;-S;)=(CZ—CZ) (2-39)

 

as;

0 t it
an 6T = kn (Cn - Sn) (2-40)

 

*

as,
ar

 

R02 =k2<CZ -SZ> (240

t . . . . * . . .
where C rs the drmensronless aqueous concentration, S rs the drmensronless sorbed-

phase concentration, R is the retardation factor, k0 is the dimensionless Damkohler
number, subscripts a and n represent the advective and non-advective domains and the
subscripts 1 and 2 represent the instantaneous and rate-limited sorption sites respectively.
More details on the equation formulation and description of dimensionless variables can

be found in (Hu and Brusseau, 1996). The global retardation factor R is given by:

24

R =Ral +1?“2 +1?"1 +an =1+§Kd (2-42)

(Hu and Brusseau, 1996) investigated the transport of rate-limited sorbing solutes
in a saturated, aggregated porous medium with an objective to isolate the effects of
physical non-ideality and sorption non-ideality and to study the synergistic effects of
multiple non-idealities on contaminant transport. The experimental procedures to test the
multi-process non-ideality approach involved creating three separate systems i.e., with
physical non-ideality (porous spheres), with sorption non-ideality (homogeneously
packed soil columns) and with physical and sorption non-ideality (columns packed with a
mixture of soil and porous spheres). The analysis involved independent determination of
parameters from the physical and sorption non-ideality experiments and using these in the
MPNE model in a predictive mode. The authors suggested that the MPNE model
adequately described the processes controlling the transport of rate-limited sorbing
solutes in an aggregated system. In another study, Johnson et a1. (2003) used the MPNE
model to determine the relative contributions of physical hetero geneity-related processes
and nonlinear/rate-limited sorption-desorption of TCE in undisturbed cores. The authors
were able to successfully describe the breakthrough curves using MPNE model.

Application of the MPNE model requires a large number of ﬁtting parameters.
Although, the use of the model in lab-scale studies is possible, its use under ﬁeld

conditions in a real predictive sense is limited.

2.4.6 Irreversible sorption in transport models

The observations of irreversible sorption date back to the seventies, however, it has
seldom been incorporated in transport models. It is only recently that some studies have

focused on desorption-resistance in transport models. For example, Prata et a1. (2003)

25

conducted batch and column experiments to study the sorption-desorption behavior of
atrazine, with a focus on irreversible sorption. The results indicated that approximately
90% of atrazine desorbed in batch while in columns, desorption was only 53-65%. They
attributed this increase in non-desorbable fraction in columns to an increased contact
time, which contributed to a higher physical diffusion of atrazine in the humic
substances. Mathematically, irreversible sorption is described as a ﬁrst-order process.
This approach will work only for systems in which there is no physical decay and
irreversible sorption is the only sink. In the presence of a concurrent physical
degradation/decay, the ﬁrst order degradation rate coefﬁcient will account for the lumped

effects of irreversible sorption and decay/degradation.

2.5 Statistical models

Statistical models generally employed include the temporal and spatial moments,
the exponentially modiﬁed gaussian equation (EMG), the bi-exponentially modiﬁed
gaussian equation (BEMG) and the nonlinear chromatography equation (N LC). Most
applications of statistical models have been in the ﬁeld of chromatography. The ﬁrst two

models, being the most widely used, are discussed in the subsequent paragraphs.

2.5.1 Temporal and spatial moments '

Temporal moment analysis is a powerful method that may be utilized to evaluate
various aspects of solute transport (Brusseau, 1989). Traditionally, these have been used
in chemical engineering, soil sciences, hydrology and environmental engineering.
Statistical moments are classical ﬁmctions that are used to describe the distribution of any
data set with no assumptions about their functional form (Howerton et al., 2003).

Temporal moments may be used to evaluate the impact of nonequilibrium on solute

26

transport and to assess the differences between equilibrium and nonequilibrium models
(Brusseau, 1989). One limitation however is, that moments can only be used for analysis
and cannot be used in a predictive mode. A comparison of the temporal evolution of
observed moments with the derived moments helps in deciding, if an equilibrium model
is suited to describe the BTC or use of a nonequilibrium model is necessary. The
observed temporal moments are calculated based on time-concentration data. The zeroth,
ﬁrst, second, third and fourth moments represent the mass, time of the center of mass,
variance or degree of spreading, skewness or degree of asymmetry and kurtosis or a

measure of degree of ﬂatness of the peak respectively. These are deﬁned by the following

 

 

set of equations.
M0 = fcma: (2-43)
ItC(t)
= 2-44
1 I C (t) ( )
_ I(t-M1)" cma: (2-45)
" - [cmdt

where the subscripts denote the moment numbers.

Analytical solutions exist in literature for temporal and spatial moments for
advection-dispersion equation and its variations. These analytical solutions are equated to
the observed moments for estimating the parameters. Srivastava et a1. (2004) presented
the analytical solutions for temporal moments for the MPNE model incorporating the
rate-limited sorption, ﬁrst-order mass transfer and ﬁrst-order transformation with an
objective to study the effects of rate coefficients on the observed moments. The authors
found that in the presence of transformation reactions, rate coefﬁcients are not monotonic

functions of the temporal moments.

27

The analytical solutions for the spatial moments have also been derived for a multi-
process nonequilibrium case by Srivastava et a1. (2002). The authors argue that the spatial
heterogeneity of material properties can be satisfactorily accounted for by using an
increasing macro-dispersivity function however, they also suggest that these analysis can
be only used as a preliminary assessment tool for ascertaining the relative importance of
various processes under consideration. They emphasize that spatial moments are obtained
for the solute present in the solution phase and do not represent the entire solute in porous
medium. The temporal moments have more practical value in column experiments, as it
is more convenient to obtain the breakthrough curves rather than spatial solute
distribution in columns. Even if spatial distribution of solute in columns is obtained, a
limited number of data points donot offer the possibility of an analysis based on spatial
moments. The effect of number of data points on the temporal moments has been
investigated by Howerton et a1. (2003). Another limitation of moment-based analysis is
that precise analytical expressions have to be derived for the speciﬁc model employed to

analyze the effect of different processes on the associated rate coefﬁcients.

2.5.2 Statistical models used in chromatography

The most widely used equation in chromatography is the exponentially modiﬁed
gaussian equation (EMG), which is a convolution of a gaussian and an exponential

ﬁrnction (Howerton et al., 2003) and is of the form:

2 _ _
C(t) = Eéexp [i7 JET—t] [wk/{.3 — 5;)4' 1] (2-46)

where A is the area, ’6 is the retention time of the gaussian component, a is the standard

 

deviation of the gaussian component (a quantitative measure of the zone broadening

28

arising from symmetrical processes such as diffusion, dispersion and mass transfer) and
r is the standard deviation of the exponential component (parameter quantifying the zone
broadening from asymmetrical processes (Howerton and McGufﬁn, 2004). BEMG and
NLC are similar statistical models (not described here) used in chromatography.
Howerton and McGufﬁn (2004) used these three statistical models to study the
thermodynamic and kinetic behavior of a series of four-ringed PAHs with varying
degrees of annelation and found that neither NLC nor BEMG provided a better

description of zone proﬁles than EMG.

2.6 Focus of studies in contaminant transport

Numerous studies have been conducted involving nonequilibrium contaminant
transport, which focused on different aspects. These aspects include but are not limited to
retardation, dispersion, effects of nonlinear sorption, and mass transfer. A brief review of

each of these aspects is presented in the following paragraphs.

2.6.1 Retardation

The retardation coefﬁcient R represents the average speed of contaminant in the
porous medium relative to that of aqueous phase. For a conservative tracer, values of R
less than unity indicate the existence of transport-related nonequilibrium between the
mobile and immobile water regions (Nkedikizza et al., 1983). Controversies do exist
regarding the appropriateness of determining R in batch or column experiments. R can be

calculated with knowledge of K d obtained through batch isotherms. Methods to calculate
R using column data include: (1) the number of pore volumes eluted when C / C0 = 0.5 (2)

the area between the elution curve and the step input curve (Nkedikizza et al., 1987) (3)

the ﬁrst moment of the BTC for a pulse type input (Valocchi, 1985) and (4) by curve-

29

ﬁtting the equilibrium model to the observed BTC. Retardation coefﬁcients computed by
the above four methods will be identical for symmetric BTCs. For asymmetric BTCs,
determination of R by the ﬁrst method may be inappropriate (Nkedikizza et al., 1987).
The second method cannot be used, if the applied boundary conditions did not permit the
relative efﬂuent concentration to reach unity. In column experiments, slow desorption
rates compared with sorption result in a pronounced tailing in the BTCs. For pulse-type
input, the column experiment is terminated when the quantiﬁcation limit of the target
compound is reached. In such a case, the BTCs may lack much of the tail data, although
most of the solute has actually been recovered. Sorption parameters estimated by inverse
modeling of column data are therefore subject not only to random errors but also to errors
caused by the necessity to use a truncated data set.

Maraqa et a1. (1998) utilized batch and column techniques to determine R for
benzene and dimethylpthalate (DMP) and found that R values calculated using the batch
data were consistently overestimated for the two compounds. Although, the author
successfully ruled out previously reported causes of this discrepancy (i.e., sorption non-
singularity, sorption nonequilibrium, presence of immobile water regions in the column,
reduction in particle spacing in the columns) it still remained unclear, why the values of R
determined by these two techniques were different. Altfelder et al. (2001) also used DMP
to examine the compatibility of batch and column techniques for determining R. They
estimated the sorption parameters by ﬁtting a linear and a nonlinear model to 3-day and
14-day isotherms. The authors conclude that a major part of the apparent difference could
be related to the analytical difﬁculties in determining the extensive tailing of the observed

BTCs and recommend that batch technique is preferred over columns for determining the

30

retardation coefﬁcients. Kamra et a1. (2001) analyzed the BTCs of bromide under
unsaturated steady state conditions in undisturbed soil columns using the equilibrium and
the MIM model. They compared R values estimated using these models with those
estimated by temporal moment analysis and concluded that the values of R did not differ
signiﬁcantly for the equilibrium model. They also report that the BTCs were better
reproduced by the curve ﬁtting than by moment method. In their case, although the
moment method failed to capture the peak concentrations, it described the tail of BTCs

better than the curve ﬁtting approach. Nevertheless, for an ideal tracer like Tritium, the

batch equilibration may not be sensitive enough to measure small values of K d (Van

Genuchten and Wierenga, 1976). For such a case, the column technique still remains
preferable over the batch experiments.

To further explore the reasons for differences between the values of sorption
distribution coefﬁcient determined by batch and column techniques, Maraqa (2001)
employed a circulation-through column in addition to the batch and miscible
displacement experiments. The author used dimethylpthalate (DMP), diethylphathalate
(DEP) and dipropylylphathalate (DPP) as contaminants and two natural soil samples with

0.36 % and 1.48 % organic carbon. Their K d values determined from batch were higher
than the column K d values but were comparable with those determined by circulation-

through columns. The author attributed the discrepancy between the batch and miscible
displacement technique to a leftward shiﬁ of the BTCs after ruling out some of the
factors originally viewed as a cause for this deviation; however, the identiﬁcation of the

exact cause still remained obscure.

31

R has also been found in some cases to be velocity-dependent, which may indicate
the presence of an additional physical or chemical process currently not included in the
nonequilibrium models, but becomes apparent only at relatively large spatial or time
scales. Dependence of R on the ﬂow rate is generally regarded as an indication of
sorption-related nonequilibrium (Brusseau and Reid, 1991), in which case, R determined
with the equilibrium model may not provide a good measure of actual retardation

(Maraqa et al., 1999).

2.6.2 Dispersion

Hydrodynamic dispersion coefﬁcient (D) is the sum of mechanical dispersion (Dh)

and effective diffusion coefﬁcient (De).

D = 1),, + De (2-47)
1),, = 2v" (2-48)
1), = Dwrw (249)

where rw is the tortuosity factor, A is the dispersivity and n is an empirical constant whose

value typically ranges between 1 and 1.2 (Freeze and Cherry, 1979). The tortuosity factor
is assumed to account for the shape and length of the molecular path and depends on
water content but not on velocity (Nielsen et al., 1986). The signiﬁcance of molecular

diffusion can be assessed with particle Peclet number i.e., P = vd /De where d is the mean

soil particle diameter. At higher P, the dispersion coefﬁcient exhibits a linear increase
with pore water velocity for non-aggregated sands or glass beads (Bear, 1972).
Mechanical dispersion occurs, because water ﬂow varies in magnitude and direction in
soil pores as a result of meandering through the complex pore structure (Perfect et al.,

2002). Mechanical dispersion is primarily caused by two mechanisms, i.e., kinematic and

32

dynamic (Sahimi et al., 1983). The kinematic mechanism results ﬁom variation in length
of the streamlines that traverse the length of the column while, the dynamic mechanism
results from a variation in the speed of the ﬂuid movement from one streamline to the
next. Longitudinal spreading of solute in a porous medium may also be caused by the
existence of nonequilibrium processes. This spreading should not be incorporated into the
dispersion coefﬁcient if it is to be referred to as hydrodynamic dispersion coefﬁcient

(Maraqa et al., 1997).

2.6.3 Mass transfer

Dependence of mass-transfer coefﬁcient on pore-water velocity has already been
reported in the literature by many investigators e. g., (Brusseau, 1992; Brusseau and Reid,
1991; Van Genuchten et al., 1977). Maraqa et al. (1999) report that, (l) sorption
nonequilibrium appeared to be of a diffusive nature rather than due to a slow chemical
reaction, (2) mass-transfer coefﬁcients varied proportionally with pore-water velocity and
(3) variations in the degree of water saturation had no impact on the value of the sorption
mass-transfer coefﬁcient other than what would be expected due to changes in the
residence time. A strong correlation between the mass-transfer coefﬁcient and residence
time (LR/v) is also viewed to exist and may continue to decrease in a consistent way at
large residence times. Maraqa et al. (1999) were able to overcome the inconsistencies in
the column lengths in the previously reported data by regressing the log (co) on the
values of log (LR/v) where a) is the dimensionless mass transfer coefﬁcient They were
able to explain 92% of the observed variations in log (co) but suggested that factors in
addition to the residence time will be required to clarify the unexplained variations in log

a) values.

33

2.6.4 Effect of nonlinear sorption

Nonlinear sorption affects the shape of BTCs and may also mask the effects of
nonequilibrium. A value of the Freundlich exponent less than unity (i.e., n < 1) sharpens
the breakthrough front and spreads the elution front while the opposite is true for n >1.
These effects of nonlinearity complicate the assessment of solute dispersion by BTC
analysis (Brusseau, 1989). Linearization of the nonlinear isotherm is an option in the
absence of analytical solutions as advocated by Brusseau (1989). The effects of nonlinear
sorption on other aspects of transport have also been studied. For example, Brusseau
(1995) studied the effect of nonlinear sorption on contaminant transport in the presence
of rate-limited sorption and ﬁrst-order transformation, to investigate the coupled effect of
these two processes. Mathematically, it was achieved by incorporating the Freundlich
partitioning coefﬁcient in the chemical two-site model. An important conclusion drawn
from this theoretical analysis is that a model based on linear sorption cannot provide an
accurate simulation of the transformation and transport of nonlinearly sorbing solutes
when the Freundlich exponent is less than ~ 0.9. The author suggested that the relative
impact of nonlinear sorption on the solute transport is mediated by the magnitude of

transformation.

2.7 Review of experimental techniques

In soil sciences the frequently used term of “miscible displacement” involves
generating a breakthrough curve by injecting the solute of interest at a desired
concentration until the relative concentration at the outlet is unity (i.e., C / Co =1). The

displacement of a non-reactive tracer is also carried out under identical conditions in

order to determine the dispersive properties of the medium and the retardation of the

34

solute. Injecting a pulse of a ﬁnite duration and collecting efﬂuent samples at the outlet to
generate a complete time series for the entire residence time of the solute has also been
resorted to in column studies. A sequential tracer experiment of J aynes et al. (1995) was
an attempt for in situ measurement of MIM parameters by Oliver and Smettem (2003).
Most of such studies rely on employing a single conservative tracer. Recently, multiple
tracer approach has been used by Fesch et al. (1998) to achieve independent information
on the hydrodynamic properties of the columns and the relative importance of different
sorbents, if more than one sorbent is present. It is also helpful in determining the
accessibility and distribution of these sorbents on the pore scale. Tracer tests using
multiple tracers with different diffusivities can also be used to help elucidate the relative
contribution of diffusion-mediated mass transfer to solute transport. For a system, that is
inﬂuenced by diffusional mass transfer process, it is expected that the solute with larger
diffusion coefﬁcient would be closer to the condition of equilibrium at a given time than
the solute with a smaller diffusion coefﬁcient (Nelson et al., 2003).

The ﬂow interruption technique has also been used in many studies e.g.,
(Brusseau et al., 1989; Fesch et al., 1998; Fortin et al., 1997; Hu and Brusseau, 1996;
Johnson et al., 2003). Flow interruption has been used to differentiate between dispersion
and nonequilibrium effects and is based on the assumption that, during the periods of
ﬂow interruption, the solute transport proceeds only by diffusion. Changes in the aqueous
concentration with increasing periods of ﬂow interruption can be used to identify and

quantify processes such as diffusion (Brusseau et al., 1989).

35

2.8 Summary

Multiple processes e. g., sorption, volatilization, and decay etc., affect the transport
of reactive organic contaminants in the subsurface environment. A single process can be
studied in the lab by designing experiments, which eliminates the possibility of existence
of the non-desirable processes from the system. This approach helps in understanding the
mechanisms controlling the process and can lead to the development of mechanistic
models, which can be used to investigate the inﬂuence of an individual mechanism on the
overall contaminant behavior. Sorption has been identiﬁed as a process with a signiﬁcant
inﬂuence on the fate and transport of hydrophobic organic compounds in subsurface.
Treatment of sorption in transport models has traditionally been based on a bimodal
approach, which is based on an equilibrium transfer and a rate-limited transfer of the
contaminant between the solid and liquid phases. Evidence of desorption
resistance/irreversible sorption inﬂuencing the desorption behavior in batch systems
exists but its effects have not been evaluated in ﬂow-through systems. The presence of a
desorption-resistant fraction in the ﬂow-through systems can have a signiﬁcant effect on
the transport of organic contaminants. It is likely to inﬂuence the nonequilibrium
parameters as well as the natural attenuation of the contaminant in the ﬁeld transport.

Hydrodynamic conditions exert major inﬂuence on the behavior of organic
contaminants in transport through porous media. Velocity and residence time are viewed
to affect the mass transfer rates, however, the inﬂuence of these variable on the extent of
desorption-resistant fraction of the organic contaminants is unknown. Adequate
understanding of these effects is essential in order to develop efﬁcient remediation

designs.

36

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Weber, T.W. and Chakravorti, R.K., 1974. Pore and solids diffusion models for ﬁxed-bed
adsorbers. American Institute of Chemical Engineers journal, 20(2): 228-238.

Weber, W.J. and Huang, W., 1996. A distributed reactivity model for sorption by soils
and sediments. 4. Intraparticle heterogeneity and phase-distribution relationships

under non-equilibrium conditions. Environmental Science & Technology, 30(3):
881 -88 8.

43

CHAPTER 3

DESORPTION KINETICS OF NAPHTHALENE IN BATCH AND COLUMN
EXPERIMENTS

Abstract

Differences in the desorption behavior of naphthalene in batch and column systems
were investigated using three sandy soils containing different organic matter content.
Soil-naphthalene equilibration for both systems was done in batch for three days to
ensure identical conditions during the sorption phase. In addition, three-day sorption
isotherms were also conducted on all soils. Solvent extraction with methanol was
performed at the end of desorption to account for non-desorbable naphthalene. Kinetic
parameters were estimated using nonlinear regression with the two-site and the three-site
model. Tritiated water was used to obtain independent estimates of dispersion. Sorption
isotherms were linear and consistent with respective organic matter content for all soils.
A signiﬁcant amount of naphthalene could be recovered by methanol extraction in'all
soils after desorption from soil columns, which suggests that the traditional approach of
assuming the solid matrix comprising of only two domains (i.e., an equilibrium domain
and a rate-limited domain) is questionable. In all soils, the three-site model incorporating
a non-desorption domain described desorption better than the two-site model. The results
also provide evidence that longer diffusion path lengths due to packing in columns limit
the ability of the contaminant to diffuse into the bulk solution resulting in a greater

number of sorption sites to behave as rate-limited sites.

44

3.1 Introduction

Three regimes of behavior i.e., fast, slow and very slow are known to exist in
batch desorption rate studies involving an equilibration period of 2 to 15 days (Ahn et al.,
1999; Connaughten et al., 1993; Park, 2000; Park et al., 2003; Park et al., 2001). Rates of
desorption associated with the release of hydrophobic organic compounds (HOCs) from
soils and sediments are at least biphasic, with an initial rapid sorption phase that occurs
over a few hours or days, followed by an extremely slow desorption that can take months
or years to reach the end point (Johnson et al., 2001). Very slow desorption is sometimes
referred to as non-desorption (Park et al., 2001), desorption-resistant or irreversible
sorption (Kan et al., 1997). Although “true” sorption equilibrium may take a very long
time to reach, formation of a desorption-resistant fraction within 24 hours (Sharer et al.,
2003a; Sharer et al., 2003b) to 3 days (Park et al., 2003) has been observed in batch

studies.

Numerous mathematical models exist in the literature that describe desorption in
batch systems. These can be categorized based on the different conceptualizations e. g.,
chemical site models, kinetic models, distributed-rate models and pore diffusion models.
The assumption in chemical site models is that the rate-limited sorption/desorption is
chemically controlled and a rate-limited sorption/desorption reaction explains the
behavior of organic compounds from the soil matrices (Brusseau and Rao, 1989). The
chemical two-site and three-site models (Park, 2000) are based on a mathematical
formulation that uses a driving force formulation based on the linear distribution

coefﬁcient [(4. Kinetic models i.e., the three-parameter kinetic model (Cornelissen et al.,

45

1998a) and the ﬁve-parameter kinetic model (Cornelissen et al., 1998b) represent two and
three regimes of desorption behavior by characterizing these as rapid, slow and very slow
processes. These models are based on kinetic rate formulations that are independent of

K d . The distributed-rate models include a gamma-distribution model (Connaughten et

al., 1993) and a hybrid gamma-distribution model (Ahn et al., 1999). In these models, the
soil matrix is assumed to contain a series of compartments and desorption from each of

these compartments is described by a unique desorption rate coefﬁcient. In addition, one,
two and three-parameter pore diffusion models are based on Fick’s law and describe one,

two and three desorption regimes respectively.

All of these models are mathematical approximations of desorption behavior in
batch systems incorporating one, two or three-regimes of behavior. In a recent study
(Saffron, 2005), it was shown by a comparison of nine different models applied to the
desorption data for four soils and two contaminants that three-regime models describe the
observed desorption behavior better than the two-regime models. The conclusion drawn
from this study was based on the “Akaike information criterion” (AIC) (Burnham and
Anderson, 1998). AIC is a statistical tool to decide if increasing the number of model
parameters to improve the description of observed data is justiﬁed. The experimental
limitations however, limit our ability to draw a distinction between different categories of

models if these models are based on equivalent regime description.

In the past, with the exception of a few studies e.g., (Ahn et al., 1999; Prata et al.,
2003), ﬂow-through systems have been typically modeled following the dual-domain
approach. For contaminant-soil combinations, if three regimes of behavior are observed

in batch systems, there is a high probability that these regimes will also exist in the ﬂow-

46

through systems. In such cases, the adequacy of the dual-domain model becomes
questionable. A mathematical description of these regimes, that is compatible with
observations, is essential to accurately describe the transport of contaminants in ﬂow-

through systems.

In this study, our objective is to experimentally verify, the presence and extent of
the third desorption regime (i.e., non-desorption) in ﬂow-through systems. We also

evaluate the differences in kinetic parameters between batch and column systems.

47

3.2 Materials and methods

Solute. Unlabeled and 14C-naphthalene with uniformly labeled carbons, procured from

Sigma Aldrich Co., was utilized as a representative HOC for batch and column
desorption experiments due to its suitability compared with other 16 PAHs in the EPA’s

list for priority pollutants. The solubility of naphthalene in water is approximately 31.6

mg/L at 25 C and its Kow is about 2300.

Sorbents. Three natural soils i.e., Kalkaska-A, SPCF and an aquifer sand from the
Plume-A site Schoolcraft, MI (Dybas et al., 2002) hereafter referred to as Plume-A sand,
containing different amounts of soil organic matter (SOM) were used for this study.
Mechanical characteristics and SOM of these soils are presented in Table 3-1. These soils
represent two different classes in terms of their origin. Kalkaska-A and SPCF are surface
soils while Plume-A sand is of aquifer origin obtained from approximately 60 feet below
surface. Soil samples were passed through U.S series sieve No. 20 (> 850 microns) to

remove larger components after air drying and were irradiated in 20 mL glass vials by y-
irradiation (60Co source) at a dosage of 5 Mrad at Radiation Science & Engineering

Center (RSEC), Pennsylvania State University. Sealed vials were stored at room
temperature and were opened immediately before use. Sterility of soil was veriﬁed once

by plating and no colonies were observed after 3 days.

Spiking solutions. The spiking solutions were prepared by mixing unlabeled and 14C-

naphthalene in methanol. The spiking solution for the isotherms (4925 mg/L total

naphthalene concentration) contained an activity of 2281 dpm/uL and 0.0984% 14C-

naphthalene. The spiking solution for rate and transport studies (4939.1 mg/L total

48

naphthalene concentration) contained approximately 2% l4C—naphthalene and an activity

of 52092 dprn/ptL

Table 3-1: Characteristics of soils and packed columns

 

 

Soil (33:13; Sand,“ Silt”! Clay,“ Densigy Pogosity;
(%) (%) (%) (°/°) (g/ cm ) (cm /cm )
Kalkaska-A 3.9 91 7.7 1.7 0.572 :t .045 0.413 :1: 0.025
SPCF 1.9 78 17 5 1.385 :h 0.009 0.436 :1: 0.016
Plume-A sand ND 97.6 0 2.4 1.811 :1: 0.016 0.354 :1: 0.016

 

*Analysis done at the Plant and Soil Sciences laboratory, Michigan State University
Sorption isotherms. Three-day sorption isotherms were conducted in 5 mL vials with
Teﬂon caps. Soil-to-water ratios were carefully selected to achieve an equal mass
distribution at the end of equilibration period. The aliquots of sterile soil (i.e., 0.348 :I:
0.028 g of Kalkaska-A, 0.844 :1: 0.095 g of SPCF, and 2.64 :1: 0.0283 g of Plume-A sand)
were used in triplicate for the isotherms. Liquid phase volume used for these three soils
was 4.589 i 0.034 mL, 4.179 at 0.022 mL and 2.464 :t 0.028 mL respectively. The vials
were spiked with naphthalene to achieve an initial liquid-phase concentration between 0.5
mg/L to 31 mg/L. Maximum volume of the spiking solution did not exceed 30 p.L and
minimum activity in the liquid phase at the end of equilibration period was always greater
than 200 dpm/mL in all samples except one sample of Kalkaska-A, which contained an
activity of 120 demL. Vials were tumbled end-over-end in dark at 6 rpm for 72 hours.
At the end of mixing period, these vials were centrifuged at 1163 x g for 5 minutes for

solids separation. The supernatant was sampled and analyzed for naphthalene by liquid

49

scintillation counting (LSC) and selected samples were veriﬁed by high performance
liquid chromatography (HPLC) using a reverse phase C-18 column with a mobile phase
consisting of 80% aceonitrile and 20% acidiﬁed water at a ﬂow rate of 1.3 mL/min.
Naphthalene was detected by UV absorption at a wavelength of 220 nm.

Batch desorption. Desorption rate studies in batch were conducted in 25 mL centrifuge
vials with mininert valves equipped with Teﬂon liners. The vials were autoclaved for 30

minutes and oven-dried for 24 hours prior to use. Soil slurries were prepared in these

vials in triplicate by mixing an aliquot of sterile soil with CaC12 (0.01M) prepared in

deionized water. Soil mass used was 1.0 g :1: 0.002 g for Kalkaska-A, 4.603 g i 0.02 g for
SPCF, and 15.004 :t 0.00045 g for Plume-A sand and the liquid-phase volume used was
28.165 1 0.0034 mL for Kalkaska-A, 27.996 i 0.001 mL for SPCF, and 22.999 :1:
0.0015mL for Plume-A sand. These soil slurries were spiked with naphthalene to achieve
an initial liquid-phase concentration of 1500 ug/L. After spiking, vials were tumbled end-
over-end in dark for 72 hours, centrifuged at 1076 x g for 10 minutes and the supernatant
was analyzed by LSC. Sorbed-phase concentration was calculated by difference. After

completion of sorption step, the remaining liquid was decanted to the extent possible,

vials were topped up with naphthalene free CaClz and were tumbled again at 6 rpm as

described earlier. A periodic sampling of the supernatant at 0.5,1,2,3,4,6,12,24,36,48 and
72 hours was done to monitor the liquid-phase concentration over time. At the end of 72
hours of sampling, vials were once again decanted and methanol extraction was

performed to determine the concentration of non-desorbable naphthalene.

An independent test to verify the extraction efﬁciency of methanol was also
conducted on separate batch samples for a three-day equilibration period (initial liquid-

50

phase concentration between 1-5 mg/L). Methanol was found to be 100 :t 5% efﬁcient in
recovering sorbed naphthalene. This test also conﬁrmed that calculation of sorbed-phase

concentration by difference in the sorption isotherms was appropriate.

Column desorption. Column desorption studies were performed using stainless steel
columns (15 cm length and 1.1 cm i.d.), with reducing unions at both ends ﬁtted with 25-
micrometer frits, to prevent loss of ﬁne particles (Figure 3-1). The column ﬁttings

included stainless steel tubing 1/ 16 inches outer diameter (id 1.27 mm) and Teﬂon

valves. The columns and ﬁttings were autoclaved for 30 minutes at 120 0C and were

dried at 105 0C for 24 hours prior to use. Soil-naphthalene equilibration was done in 50

mL Corex centrifuge vials with mininert valves containing Teﬂon liners. Soil slurry was

prepared by mixing a known mass of each soil with 0.01m CaClz and spiking each vial

so as to achieve an initial liquid-phase concentration of 5 mg/L. The vials were then
tumbled end-over-end in dark for three days. At the end of equilibration period, the vials
were centrifuged at 1076 x g for 10 minutes and the liquid phase was analyzed for

naphthalene by LSC and HPLC.

Columns were packed with pre-equilibrated wet soil. Approximately 2 mL of the
liquid phase was initially poured in the column and the wet soil was transferred using a
spatula accompanied by gentle tapping of the column surface with a steel rod, so that soil
could settle at bottom. Scooping of the soil continued until the column was ﬁlled with

wet soil and the liquid phase initially poured in, could overﬂow.

51

 

cataract 5:38 com 953. geoﬁtoaxm ”Tm 053m

5:883 5:200

    

8.88% .2302 _ Q- 582.8 29:3

.222. __ow
8:89.58 63m

53958 855 -© - -
8.7.5: :8 82.2 :8.

éa. _
8335.
5:38 ..

=8

     
   

52

 

The columns were then capped and desorption was initiated by injecting 0.01 M

CaClz at a constant ﬂow rate of 0.1 mL/min using a syringe pump. Samples were

collected over time using a fraction collector in glass tubes pre-ﬁlled with scintillation
ﬂuid. Sample so collected could settle at the bottom of scintillation cocktail preventing
the loss due to volatilization. These samples were then transferred to scintillation vials
and analyzed for naphthalene by LSC. Desorption from soil columns continued until the
activity in the liquid phase was less than 200 dpm/mL. Columns were then removed and

soil was pushed out using a stainless steel rod in pre-weighed 50 mL Corex centrifuge

vials. These vials were ﬁlled with CaClz to the top and were tumbled at 6 rpm for 24

hours, centrifuged at 1076 x g for 10 minutes and the liquid phase was analyzed for
naphthalene, which represented water-extractable fraction. After two to three successive
water extractions, solvent extraction was performed using methanol to measure the non-

desorbable naphthalene.

To measure the density and porosity of each soil, four separate columns were wet-
packed with naphthalene-free soil using the method described above for the spiked soil
and were weighed before and after packing. The soil was then pushed out of columns in
pre-weighed glass beakers that were oven-dried and re-weighed. Density and porosity for
each soil was determined gravimetrically and is reported in Table 3-1. Each soil was also
characterized for retardation and dispersion by employing identical soil columns for
tritiated water breakthrough. Approximately, two pore volumes of tritiated water with an

activity of 28000-31000 DPM/mL were injected and the efﬂuent was sampled every ﬁve

minutes. The activity of 3H20 was analyzed by LSC.

53

3.3 Analysis

Mathematical models. In a three-site batch desorption model, the soil matrix is assumed
to comprise of three types of desorption sites i.e., equilibrium sites, rate-limited sites and

non-desorption sites (Park, 2000). The equilibrium and non-desorption partitioning in this
model are described by:

S... =f..K..C... (34>

Snd = fndeCeq (3'2)

while the release from the rate-limited sites follows the ﬁrst-order expression:

 

dS
gteq = a [fnqud Cdes " Sneq] (3'3)
where Seq , Sneq and Sm] are the sorbed-phase concentrations (rig/Kg) in equilibrium, rate-

limited and non-desorption sites respectively, Cdes is the liquid-phase concentration

(pg/L) in the desorption assay, Ceq is the liquid-phase concentration (pg/L) at sorption

equilibrium; feq , fneq and fnd are the equilibrium, rate-limited and non-desorption site
. . . . -1 . . .

fractions, a IS the ﬁrst order desorption rate coefﬁcrent (hr ) for the rate-lrmrted srtes

and K; is the linear sorption distribution coefﬁcient. For a linear sorption case, K d in the

batch systems is given by:

S
K d = “1 (3-4)

Ceq

 

For desorption from a soil column, K d can be calculated by (Zhao and Voice, 2000):

_ (M, — Pvc0)1ooo
msoiICO

 

Kd (3-5)

54

where M e is the contaminant mass calculated from the efﬂuent desorption curves (11g),
mm” is the soil mass in column (g) and CO is the average liquid-phase concentration in
soil column prior to desorption (pg/L) and R, is the volume of liquid phase (equal to one

pore volume) in the column at the start of desorption (mL). Solute transport through a

porous medium is typically based on the advection-dispersion equation:

2
a: 0 at 5x2 6x
where C is liquid-phase concentration (ug/ L), S is sorbed-phase concentration (pg/Kg), v

is average linear pore-water velocity (cm/hr), D is hydrodynamic dispersion coefﬁcient
(cmZ/hr), x is the distance along principal direction of ﬂow (cm) and t is time (hr).
Equation 3-6 is referred to as the equilibrium model, if the condition of local equilibrium

is assumed between the liquid phase and sorbed phase. The dimensionless form of the

equilibrium model is:

—————— ‘ 3-7
6T P522 az ( )
where
C,_£,Z=:,T=v_t,,.=1 112,ng

c, L L a D

In lab and ﬁeld studies, the asymmetry in the observed breakthrough curves (BTCs) is
believed to be a result of a slower desorption rate compared to sorption. The most widely
used model to describe these rate limitations is the two-site model (Selim et al., 1977;
Van Genuchten and Wagenet, 1989) in which, the solid matrix is divided into two

domains i.e., an equilibrium domain comprising of instantaneous sorption/desorption

55

sites and a rate-limited domain comprising of sorption sites for which sorption/desorption
is rate-limited. For a homogeneous soil, the governing equations for a linearly adsorbed

solute are:

f PKd ac a2c ac a
+__eq__ —=D—-V———p[(1—feq)KdC_Sneq] (3'8)

1
( 0 at 6x2 6x 61

6S",
f-aﬂl—feqwdC—Sneq] (3-9)

where Sneq is solid-phase concentration in the rate-limited domain (rig/Kg), a is the ﬁrst

order kinetic rate coefﬁcient (hr'l) governing the rate of solute exchange between liquid

phase and solid matrix in rate-limited domain and feq is fraction of exchange sites that

are at equilibrium. Using the dimensionless parameters, the two-site model reduces to

following form:

 

 

——————a) C -C 3-10
6T PaZZ 62 (1 2) ( )
6C
(1—ﬂ1R—l=w(CI-Cz) (3—11)
6T
where:
C Sneq 6+fequd “(l-16)RL
C1:—’ C2 = , = , 0):—
Co (l-feq)KdCo 6+pKd v

Subscripts I and 2 refer to the equilibrium and rate-limited sites respectively, ,6 is the

dimensionless partitioning coefﬁcient and a) is the dimensionless mass transfer
coefﬁcient. The parameters R, T, P and Z are the same as described for Equation 3-7.

Some studies have utilized a ﬁrst order degradation rate coefﬁcient to mimic non-

56

desorption e.g., (Prata et al., 2003), however, in the presence of degradation, mass
disappearance due to irreversible sorption has to be separated from that due to
degradation/decay. This can be achieved by incorporating a non-desorption site fraction

( fnd) in the soil matrix (Figure 5-2). The governing equations for the three-site model

then become:

fequd ac azc ac a_1p

 

 

( 6 ) at 6x2 Vex —[( ”feq fnd) d —neq] (3‘12)
_a_3__,0 —fndeC
6S
anteq =al[(1_feq-fnd)KdC—Sneq] (3'13)
62’" = asfndeC (3-14)

The dimensionless equations for the three-site model for the ﬂow-through systems are:

ﬂlR—=————-0)1(C1—C2)-w3C1 (3-15)

 

 

6C
R(I—ﬂ1—ﬂ2/R)a—;-=ar(q—Cz) (3—16)
6C3
—= C 3-17
.52 6T a’31 ( )
where:
S
C1=—C—', C2: neq C3 =___Snd
Co (1‘ feq— fnd>KdCo fndeCo
9+f pKd K _aLR al-
= ‘3" .ﬂ2=”f—"———" ‘1 —‘— ———(I 131“ 132/R) a>3=-——- 3 A
9+pKd 9

Desorption from soil columns ﬁlled with wet pre-equilibrated soil represents only the

desorption phase. The three-site model equations have to be modiﬁed to represent this

57

special case by eliminating the term that represents solute ﬂux from the liquid phase to

the non-desorption sites. The governing equations for this special case are:

feqPKd ac azc ac ap
__ _1_

 

 

(1+ 6 at _D¥—v3;— 0 [(l—feq-fndde-Sneq] (3-18)
55"“ = 1— — K c-s -
at “I“ feq fnd) d neq] (3 19)

and the dimensionless equations for the three-site model representing column desorption

become:

AR—-—————-—-wl(C1 -C2) (3-20)

R(1‘ﬂ1-ﬂz/R)§a%.2-=0)1(C1‘C2) (3-21)

Solution technique. The solution of the advection dominated transport problems
generated by simple ﬁnite-difference and ﬁnite element methods typically contain
spurious oscillations and/or numerical diffusion near steep concentration gradients
(Fischer et al., 1979). In addition, there are additional truncation errors in solving
transient problems that arise from approximating the time derivative term (Croucher and
O'Sullivan, 1998). Hi gher-order accurate schemes (greater than second-order) guarantee
much better convergence towards grid-independence along with better wave number
resolution (Demuren et al., 2001). For this study, the governing three-site model
equations, with initial and boundary conditions, were solved using a high-resolution
numerical scheme. The spatial derivatives were approximated using a fourth-order
compact scheme with spectral like resolution (Lele, 1992) and a fourth-order Runge-
Kutta scheme was used for temporal differencing. Higher accuracy was achieved by

implicitly solving the fourth-order compact relations for the ﬁrst and second derivatives

58

of the concentrations, which form a system of equations solvable by tri-diagonal matrix
solvers (Phanikumar and Hyndman, 2003). The well-known Thomas algorithm (Roache,
1998) was used to solve the system of equations resulting in a tri-diagonal matrix form. A

uniform grid of 301 points was used for all model runs.

Parameter estimation. Parameters for the batch desorption (i.e., a , feq and fneq ) were
estimated by nonlinear regression of the three-site model for batch systems (Equations 3-
1 to 3-3). Column desorption data were analyzed to determine the optimized parameter
values using nonlinear regression with two-site model and three-site model for the ﬂow-

through systems. Parameters for the two-site model (,B and (0) were estimated using the
K d values obtained from batch isotherms and those calculated from the column
desorption. A nonlinear least squares inversion program CXTFIT (Toride et al., 1999)

was used for estimating these parameters. Parameters for the three-site model (161,132 and

so) were estimated using variable-metric methods (also called sequential quadratic
programming, SQP) as implemented in MATLAB. A script was developed in MATLAB
to run the FORTRAN code based on the dimensionless equations of the three-site model

and to minimize the following objective function:
It 2

F(¢)=Z[C(¢). —C.b.] (3—22)

i=1

in which ¢ is the parameter set [,Blﬂzfo] , Cabs is the vector of observed concentrations,

C (915) is a vector of the predicted model concentrations for the sampling times. The SQP

algorithm converged to a minimum in approximately 500-1000 iterations with a relative

tolerance of 10-5. The details of measured, estimated and calculated parameters for

59

column desorption using two-site and three-site model are tabulated in Table A-1 in

Appendix-A.

60

3.4 Results and discussion

Isotherms. Sorption of naphthalene was linear in all the three soils (Figure 3-2).
Distribution coefﬁcients calculated using linear regression were 9.22 mL/g for Kalkaska-

A, 5.82 mL/g for SPCF and 1.46 mL/g for Plume-A sand respectively. The K d values for

all soils are consistent with their respective SOM i.e., 1.9 % and 3.9 % and < 0.03% for
Kalkaska-A, SPCF and Plume-A sand respectively. Our value for SPCF is comparable
with the previously reported value of 4.26 mL/ g (Park et al., 2001) but is different for
Kalkaska-A (i.e., 25.6 mL/g). The reason for this difference was attributed to a different
batch of soil collected from the same location but at a different time of the year, which is

likely to alter SOM.

10‘

 

 

U U I I I U I '1
D Kalkaska-A
0 SPCF
O Plume-A sand

 

 

 

a
O
a

 

Sorbed concentration (pg/Kg)
8

2

1o _ I I I IIIIIl I I I I IIIIl I I I I IIIIi

1o2 , 1,03 _ 10‘ 10’
mm concentration (pg/L)

Figure 3-2: Three-day sorption isotherms of naphthalene

61

Batch desorption. In batch desorption rate studies, an equilibrium regime and a non-
desorption regime could be observed in all soils, however, the rate-limited regime was
relatively insigniﬁcant in SPCF (Figure 3-3). This indicates that the release of
naphthalene occurred faster in SPCF than in Kalkaska-A. Parameters for the three-site
model (Table 3-2) indicate that the site fractions for Kalkaska-A and Plume-A sand were
remarkably similar. These two soils are similar in their mechanical characteristics but
different in SOM and origin. Out of the two surface soils, the soil with low SOM (i.e.,
SPCF) displayed larger fractions of equilibrium sites (i.e., 0.63 compared with 0.29) and
lower fraction of non-desorption sites (i.e., 0.35 against 0.59) compared with Kalkaska-
A. The fraction of rate-limited sites for Kalkaska-A and SPCF was 0.12 and 0.02
respectively. Desorption rate coefﬁcient for Kalkaska-A was signiﬁcantly lower than that
of SPCF indicating a slower desorption. These observations are contrary to what has been
observed by Park et al. (2001), who reported that the estimated non-desorption site
fractions obtained by a nonlinear regression based on a chemical three-site model were
remarkably similar, in spite of the soils bearing different organic content. Park et al.

(2003) reported a systematic increase in the fraction of equilibrium (0.20 to 0.73) sites,

desorption rate coefﬁcients (0.002 to 0.0029 min'l) and the linear distribution coefﬁcient

K d with an increase in the organic carbon (1.29% to 38.3%). They also report a narrow

range of rate-limited sites (i.e., 0.14 to 0.17) for their soils excluding the K-
montrnorillonite and Housten. However, no conspicuous trend was observable for the
fraction of non-desorption sites and the authors donot offer any explanation in this regard.
Sharer et al. (2003b) suggested the presence of a speciﬁc physical or chemical sorption

interaction rather than slow diffusion based on a rapid formation of a desorption-resistant

62

fraction (i.e., 0.17-0.27) within 24 hours. This could probably be explained by the
behavior of the soil with almost no organic matter content (i.e., Plume-A sand), for which
the fraction of non-desorption sites was the highest. The preferred sorption mechanism
for HOCs is partitioning to organic matter; however, immediate formation of non-
desorbable naphthalene suggests that some fraction of naphthalene mass interacts with
active mineral surface sites. It also hints at the possibility that these two processes occur
simultaneously. The equilibrium and rate-limited site fractions in Plume-A sand were 25
% and 15% respectively while the desorption rate coefﬁcient was approximately 5 times
lower than that of Kalkaska-A and approximately 28 times lower than SPCF. This
indicates a dominant surface adsorption mechanism rather than SOM partitioning in

Plume-A sand that appears to follow comparatively slower kinetics.

Table 3-2: Fractions of equilibrium, rate-limited and non-desorption sites and the
desorption rate coefﬁcients for batch desorption of naphthalene estimated by ﬁtting the
three-site model

 

 

 

Desorption 2
Soil Site fractions rate R
coefﬁcient
feq fneq fnd a (hr—1)
Kalkaska-A 0.29 0.12 0.59 0.364 0.955
SPCF 0.63 0.02 0.35 2.163 -
Plume-A sand 0.25 0.15 0.60 0.077 0.983

 

63

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1m I I 1 V 1 j

O expdata
.Kalkaska-A _ mm," 1
80- .
c 60 ' ‘
e . 1

I ‘

g 40 I I E.

g; a=0.36418.3e-006/l'r
O feq=0.2912.5e-006 '
20 . fneq=0.12:l:2.66-006 .
R2=0.9556 ,

o J I I I I I

o 10 20 30 4o 50 60

Time (hours)

10c . . . .

SPCF - m...
' — regression ‘
80- .
A b - i d

a: Fa—H—ﬁ '

c 60- .

c a=2.16t0.0235h
*é. ' rml = 0.63 1 0.00078 ‘
«:1; 40' fmq=0.023t0.00081 ‘
0 L 12%-0.0071 ‘
2o» .
t 1

0 4I g I I I

 

 

0 10 20 30 40 5O 60

 

 

 

 

 

Time (hows)
100 . . r . .
.Plume-A sand L 33%; .
80 - .
60 ' 1

 
   
 

A
O

a=0.077:t2.766-005/ﬂ'
feq=02612.63e-005 .

r =0.15: 3.86 e-OOS ,
neq

R2=0.983

Desorption (%)

8

 

 

O I I I I; I I

0 1o 20 30 4o 50 60
Tune (hous)

 

Figure 3—3: Best ﬁts of the three-site model to the observed naphthalene desorption data
in batch experiments

64

Analysis of tracer data. In column desorption experiments, it is important to rule out
the possibility of a physical process being the cause of rate limitations (e.g., entrapment
of water into relatively stagnant zones). In addition, the dispersive properties of the
medium must be determined. To rule out the possibility of a physical process responsible
for rate-limited desorption, the equilibrium model was ﬁtted to tritiated water BTCs
(Figure 3-4) using the nonlinear least squares inversion program CXTFIT (Toride et al.,
1999) and the retardation coefﬁcients were determined. Values of R less than unity
indicate that all the pores do not participate in ﬂow (Maraqa et al., 1998). Values of R
less than unity for tritiated water have been reported (Nkedikizza et al., 1983) and have
been attributed to transport-related nonequilibrium created by the presence of mobile and
immobile water regions. In our data, no evidence of a transport-related nonequilibrium
was found in any of the soils. The retardation factors for Kalkaska-A and Plume-A sand
were not different than unity (Table 3-3). For SPCF, the estimated R was signiﬁcantly
greater than unity. Values greater than unity for tritiated water have been reported. For
example, Seyfried and Rao (1987) reported R for tritiated water between 1.10-1.18 for
their columns. We also observed a velocity-dependent R for SPCF (i.e., 1.083 to 1.282) in
our experiments conducted at four different velocities ranging between 3.16 — 15.79
cm/hour in a separate study (all data not reported here). We attribute this to the isotopic
exchange of tritiated water with crystallatic hydroxyls of clay particles as proposed by
Van Genuchten and Wierenga (1977). We note that SPCF has a clay content of 5 %,
which is slightly higher than the other two soils. Based on the analysis of retardation, the
dispersion coefﬁcients for Kalkaska-A and Plume-A sand were estimated using the

e(luilibrium model in CXTFIT with a value of R ﬁxed to unity. Due to a signiﬁcant

65

 

velocity-dependent R in SPCF, the dispersion coefﬁcient was estimated by using R=1.083
estimated in ﬁrst step. These estimated dispersion coefﬁcients were used in all the

subsequent model applications to calculate Peclet numbers.

Table 3-3: Retardation factors and dispersion coefﬁcients estimated using the equilibrium
model

 

 

Soil Velocity Retardation factor Dispersion czoefﬁcient
(cm/hr) R D (cm A“)

Kalkaska-A 18.34 0.970 (0961-0980) 5.66 (4.56-6.77)

SPCF 15.80 1.083 (1078-1088) 1.67 (1.47-1.86)

Plume-A Sand 17.18 0.995 (0986-1003) 12.33 (11.30-13.36)

Note: The values in parentheses represent lower and upper bounds based on 95% conﬁdence intervals

66

 

 

_KalkaTska-A r 3; ﬁrﬁmm

 

 

1.2

 

olc0

 

 

 

 

 

 

 

 

 

Clc0

 

 

  
    
  
   

    

l l

 

 

2 3
Pore volunes
I I I l
0 Ex .data
12 _Plume-A sand _ “Em... m...

 

 

 

C/Co

0.4

0.2

    

 

 

L L
1 2 3
Pore volumes

Figure 3-4: Best ﬁts of the equilibrium model to tritiated water BTCs at 0.1 lemin

67

Column desorption. Desorption of naphthalene from soil columns continued for
approximately 65 to 70 pore volumes for Kalkaska-A and SPCF while for plume-A sand
it took approximately 30 pore volumes. The desorption curves from the columns for the
three soils exhibited different shapes (Figure 3-5) but were consistent with what would be
expected based on the organic matter partitioning for the two surface soils (i.e., Kalkaska-

A and SPCF) and with that of surface adsorption for Plume-A sand.

 

 

<> Plume A and
El SPCF
O Kalhdta-A "

   

 

 

 

C/Co

 

 

 

Time (minutes)
Figure 3-5: Naphthalene desorption from soil columns in the three soils

The degree of sorption nonequilibrium in non-ionic organic compounds (N OCs)
has been shown to increase with an increase in SOM (Bouchard, 1998). In soil with a
higher SOM (i.e., Kalkaska—A), the methanol extractable mass was higher compared to
SPCF (Table 3-4). A higher mass elution in column desorption for SPCF compared with
Kalkaska—A (i.e., 88.01 % compared with 65.41%) when almost equal number of pore

volumes have eluted, indicates comparatively slower desorption for Kalkaska-A soil than

68

SPCF. Methanol extractable mass at the end of column desorption was also greater for
Kalkaska-A than SPCF (i.e., 23.59% compared to 8.26%) suggesting a strong correlation

between SOM and desorption-resistance.

Table 3-4: Desorbable, water-extractable and solvent-extractable naphthalene mass for
each soil in column desorption experiments

 

 

Mass from Mass from Mass from
Soil column batch water methanol Recovery
desorptron extraction extraction
(%) (%) (%) (%)
Kalkaska-A 64.51 1 1 .90 23.59 70.4
SPCF 88.01 3.72 8.26 60.7
Plume-A sand 41.50 13.92 44.59 86.6

 

Sorption distribution coefﬁcient K d is a fundamental parameter in some of the
mathematical models that use a driving force formulation of the form (Kd C-Sneq) to
describe desorption in batch and column systems. K d values derived from batch isotherms

can be used in transport models in the absence of sorption nonlinearity and non-
singularity. In our case, isotherms for all three soils were linear over the concentration
range employed; therefore, modifying the governing transport equations to incorporate
the effects of nonlinear isotherms in transport models was not considered essential.
However, in all three soils, an evidence of sorption non—singularity existed as conﬁrmed
by solvent-extractable naphthalene in all batch and column experiments. It was, therefore,

essential to investigate which K d value is appropriate to use in the transport model. As an
initial step, a comparison was made between the isotherm K d and the column desorption
K d for each soil. The column desorption K d was calculated with Equation 3-5 using the

desorbable mass calculated by integrating the time-concentration data from the column

69

 

desorption. Sorption non—singularity affects the value of K d in column desorption

experiments, because a signiﬁcant fraction of contaminant mass is unaccounted for. This

is evident from the values listed in Table 3-5. Column K d values calculated using
Equation 3-5 were 15-55 % lower than the isotherm K d values when only the naphthalene
mass desorbing from soil columns was used. The column desorption K d values for
Kalkaska-A and SPCF become comparable with the batch isotherm K d values, once the

total mass is accounted for. We note that the total naphthalene mass includes the mass
desorbed from soil column, the mass recovered by water extraction that follows column

desorption and the mass recovered by methanol extraction.

Table 3-5: Comparison of batch and column sorption distribution coefﬁcients

 

 

 

 

Batch K d Column desorption K d
. From Using Using Using desorbable,
$011 isotherm desorbable desorbable water-extractable
mass and water- and solvent-
extractable extractable mass
mass
Kalkaska-A 9.22 6.45 7.69 10.14
SPCF 5.82 4.93 5.55 5.65
Plume-A sand 1.46 0.65 0.93 1.83

 

In our experiments, we were able to establish that the conditions of physical
equilibrium exist in the system, as the equilibrium model was able to describe tritiated
water BTCs for all three soils. Therefore, we analyzed the column desorption data under
an assumption of sorption-related nonequilibrium. Retardation factor R is model a
parameter that needs to be assigned correctly for estimating other parameters in

equilibrium or nonequilibrium models. In columns, conventional methods to estimate R

70

include (1) number of pore volumes eluted at which C/Co equal 0.5 (2) area above the
curve for a step input and (3) the mean (ﬁrst moment) for a pulse input. For columns,
wet-ﬁlled with pre-equilibrated soil, none of these methods is suitable to use. In the
absence of an ability to estimate R by any of these three methods, one of the available
options is estimation of R by curve ﬁtting. However, due to non-desorption, R estimated
by curve ﬁtting is underestimated, as was the case for all three soils. The R values
estimated by curve ﬁtting with two-site model were 28.18 ($0.47) for Kalkaska-A, 16.40

(i026) for SPCF and 4.306 (i0.307) for Plume-A sand. These R values result in

K d values of 7.14, 4.85 and 0.65 for the three soils respectively and are signiﬁcantly

lower than isotherm K d or column desorption K d values.

In nonequilibrium models that are based on either a two-domain or a three-
domain conceptualization, the driving force controlling the mass ﬂux from liquid phase
to solid phase and vise versa is represented by the term (KdC-Sneq). This representation is

inadequate, if K d values are calculated based on the mass eluting form the column only
and water-extractable and solvent-extractable mass is neglected. We calculated R for

naphthalene in two different ways; (1) using the isotherm Kd and (2) using the column

desorption K d that was calculated from the total naphthalene mass (i.e., desorbable mass

+ water-extractable mass + solvent—extractable mass), both being physically measured

parameters. In our model applications, R and hence K d was not estimated as a ﬁtting

parameters.

71

 

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72

 

.-

I I I d m
KalkaSka‘A -3.- 3316861116 K d (Isotmrm)

2-site with Kd (oolum) h

 

 

1 " --..

 

_ 3-sitethth(ootum)

 

 

 

 

 

 

Pore volunes

SPCF 0 exp.data

,,,,, 25118 with K d asottrerrn)
-..- 2-site with K d (oolum)
_ 3-site with K d (oolum)

I

 

 

 

 

 

C/Co

 

 

 

 

Pore volunes

 

ﬁum‘e—A sand 0 8.6.8.6

o ..... 2-srte wrth K a (rsothemr)

. --.- 2-site with K d (601mm)
_ 3-site with Kd (oolum)

 

 

 

0/c0

 

 

 

 

 

Figure 3-6: Model best ﬁts for the two-site and the three-site models to the observed
naphthalene desorption data in soil columns

73

 

' ' r ‘ .data‘ I
Kal kaska-A ”3, ﬁts with Kd asothamt)
- 2-sib with K a (001mm)
_ 3-sib with Kd (ooum)

 

 

 

 

 

 

 

 

0 10 2O 30 40 50 60 70

 

 

    

 

 

 

 

 

 

 

 

 

Pore voltmes
o exudate ' SPCF
,,,,, 2-sita with Kd (isotherm)
1 -.-- 2-sibwltth(cohm) ....----—-:-:.::':. .
_ 3-sita with Kd (comm) 39-33:: ......
081- "
0
g 0.6
04-
02
10 20 30 4o 50 so
Pore volunes
' ' 'o .826 ‘
Plume-A sand _____ 331681th (bottom)
1- ..-- 2-sita witth(oolu'm) ..
_ 3-sitawith K d (coltmn)
0.8» .

 

 

 

 

3L

0 5 10 15
Pore volume

30

Figure 3-7: Model best ﬁts of the two-site and the three-site models to the observed
naphthalene desorption data in soil columns showing the cumulative mass desorbed

74

Comparison of mathematical models. The two-site model with an R based on isotherm

K d poorly described the observed time-concentration data (Figure 3-6) as is evident
from the relatively low values of correlation coefﬁcient (i.e., R2 between 095-097).
However, the inability of the two-site model to describe naphthalene desorption is not
due to the use of isotherm K d to calculate R, because the isotherm K d and column

desorption K d for the three soils do not differ signiﬁcantly. The two-site model does not

account for the residual contaminant mass due to non-desorption and results in a greater-
than-actual mass elution. This is evident for all soils in cumulative mass desorption plots
(Figure 3-7) and is more pronounced for SPCF, which desorbs faster compared to the
other two soils. Both applications of two-site model (i.e., with isotherm and column

desorption K d ) result in almost identical desorption curves. This supports the hypothesis
that absence of a third domain rather than the difference in batch and column K d is the
reason for the relatively inferior description of the desorption data with the two-site
model. But we caution here that our column K d values should not be compared with the
column K d in miscible displacement experiments, in which case, the sorption equilibrium

is achieved by injecting the solute of interest until the inﬂuent and the effluent
concentrations are equal. In our case, we equilibrated soil with naphthalene in batch for

column desorption as well, therefore, drawing a similarity between the column K d in our

experiments and that in the conventional miscible displacement experiments is not

appropriate. The naphthalene desorption in columns could be best described by the

proposed three-site model (R2 = 0.995 for all soils).

75

The degree of nonequilibrium in a solid matrix exhibiting rate-limited mass
transfer depends on the size of rate-limited domain as well as the mass transfer rate
between the liquid phase and rate-limited domain. Only a slight variation exists in the
fraction of equilibrium, rate-limited and non-desorption sites, estimated using the three-
site model, for Kalkaska-A and SPCF while for Plume-A sand the variation is signiﬁcant.

Another notable difference is a three-times lower desorption rate coefﬁcient (a) for

Kalkaska-A compared with SPCF (i.e., 0.0588 hr.1 compared with 0.1806 hr-l). A lower

a is consistent with the higher SOM content in Kalkaska-A as compared to SPCF.

Plume-A sand exhibited the maximum desorption resistance (i.e., fnd = 0.62) which, we

attribute to a different sorption mechanism in the absence of SOM. The fraction of rate-

limited domain was much smaller (i.e., fneq = 0.24) compared to what was observed in
organic soils.

Comparison of batch and column parameters. A comparison between the batch and
column parameters was also done to assess the suitability of use of batch parameters in
transport models. For a given soil, the batch and column-derived parameters are expected
to be similar, if identical conditions for equilibration exist in sorption phase and the
desorption parameters are estimated using mathematical models based on similar
conceptualization of the porous medium. The results from our experiments were,
however, to the contrary. For all three soils, the fraction of equilibrium sites was higher in
batch and fraction of rate-limited sites was consistently lower in columns. This can
probably be explained based on the limited ability of the contaminant molecules to access
bulk liquid in columns as compared to batch. In a well-mixed batch environment, the

onset of desorption results in instantaneous desorption from all of the equilibrium sites as

76

 

the desorption process is not physically hindered. On the other hand, the packing in soil
columns results in longer-than-normal diffusion path lengths, which a contaminant
molecule needs to traverse in order to diffuse to the bulk solution (Figure 3-8). An
evidence of sorption to equilibrium or rate-limited sites is provided by the naphthalene
mass extracted in water-extraction step in column desorption experiments. Another

possible explanation for the differences in the equilibrium and rate-limited site fractions

is that high feq values in batch could be due to an abrupt change of concentration gradient

when the vials are decanted at the end of sorption process and desorption is started by
adding a known volume of contaminant free liquid which is approximately 3-20 times
greater than the volume of soil in the vial. In the column experiments it is not practical to
achieve this difference due to the packed nature of the soil matrix. Desorption in columns
is started by resuming the ﬂow with a contaminant-free liquid and the exposure of soil

matrix to the liquid is not instantaneous, as is the case in batch systems.

77

 

Column

Batch

Diffusion path

Film surrounding the
particle

Surface sites

Sorption sites lowted
in pores

   

 

 

 

Figure 3-8: Schematic showing an increase in diffusion path lengths as a result of packing
in soil columns

The fraction of non-desorption sites was higher in batch for the two surface soils
i.e., Kalkaska-A and SPCF while it was almost similar for plume-A sand (Figure 3-9). It
is difﬁcult to explain the differences in the non-desorption site ﬁ‘actions for the two soils

and the similar fnd values for one soil. A similar explanation can be offered for the higher

desorption rate coefﬁcients in batch than in column for the two surface soils as was the
case for equilibrium sites and rate-limited sites, but again, it is difﬁcult to justify the
opposite trend in Plume-A sand, in which case, the desorption rate coefﬁcient values
were higher in column compared to batch. In general, due to differences in the
environments between the two systems, it is viewed that it is not appropriate to use the
batch parameters in transport models even if these have been estimated using the same

mathematical formulations based on similar conceptualizations.

78

 

1
E uilibruim sites f No 'libri it t - Batch
0.. q (ea) n-equr umses(neq) BColunn

0.0 1
0:4 i lb

02*

   

o.
Non-desorptiom sites (ind) Desorption rate coefficient a. (hr'1)
0.81 2 ..

 

 

 

 

Kalkaska-A SPCF Plume-A sand Kalkaska-A SPCF PIumo-A sand

Figure 3-9: Comparison of batch and column parameters obtained by nonlinear
regression using the three-site model

3.5 Conclusions

Based on our results we conclude that the traditional approach of viewing the solid matrix
consisting of an equilibrium domain and a rate-limited domain is questionable and that
incorporating a non-desorption domain in transport models enhances the predictive
ability of the models. We also conclude that inadequate representation of the

observational regimes rather than the difference in K d is the reason for the inferior

description of desorption by the two-site model. This is supported by minor differences in

batch and column K d values. We also conclude that batch parameters other than K d are

not comparable with their column counterparts even if these have been estimated by

application of mathematical models based on the same conceptualization. We found that

79

 

in soil columns, a higher degree of rate limitations is expected due to a greater fraction of

the soil matrix behaving in rate-limited mode.

80

3.6 References

Ahn, I.S., Lion, L.W. and Shuler, M.L., 1999. Validation of a hybrid "two-site gamma"
model for naphthalene desorption kinetics. Environmental Science & Technology,
33(18): 3241-3248.

Bouchard, DC, 1998. Sorption kinetics of PAHs in methanol-water systems. Journal of
Contaminant Hydrology, 34(1-2): 107-120.

Brusseau, ML. and Rao, P.S.C., 1989. Sorption non-ideality during organic contaminant
transport in porous media. Critical Reviews in Environmental Control, 19(1): 33-
99.

Bumharn, K.P. and Anderson, DR, 1998. Model selection and inference. Springer-
Verlag, New York City, 353 pp.

Connaughten, D.F., Stedinger, J.R., Lion, L.W. and Schuler, M.L., 1993. Description of
time-varying desorption kinetics: Release of naphthalene from contaminated soils.
Environmental Science & Technology, 27( 12): 2397-2403.

Comelissen, G., Rigterink, H., Ferdinandy, M.M.A. and Van Noort, P.C.M., 1998a.
Rapidly desorbing fractions of PAHs in contaminated sediments as a predictor of

the extent of bioremediation. Environmental Science & Technology, 32(7): 966-
970.

Comelissen, G., Van Noort, P.C.M. and Govers, H.A.J., 1998b. Mechanism of slow
desorption of organic compounds from sediments: A study using model sorbents.
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Croucher, AB. and O'Sullivan, M.J., 1998. Numerical methods for contaminant transport
in rivers and estuaries. Computers & Fluids, 27(8): 861-878.

Demuren, A.O., Wilson, RV. and Carpenter, M., 2001. Higher-order compact schemes
for numerical simulation of incompressible ﬂows, part 1: Theoretical
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Dybas, M.J. et al., 2002. Development, operation, and long-term performance of a full-
scale biocurtain utilizing bioaugrnentation. Environmental Science & Technology,
36(16): 3635-3644.

Fischer, B.H., List, E.J., Koh, R.C.Y., Imberger, J. and Brooks, NH, 1979. Mixing in
inland and coastal waters. Academic Press Inc., New York.

Johnson, M., Keinath, T. and Weber, W.J., 2001. A distributed reactivity model for
sorption by soils and sediments. 14. Characterization and modeling of

phenanthrene desorption rates. Environmental Science & Technology, 35(8):
2734-2740.

81

Kan, A.T., Fu, G., Hunter, M.A. and Tomson, M.B., 1997. Irreversible adsorption of
naphthalene and tetrachlorobiphenyl to Lula and surrogate sediments.
Environmental Science & Technology, 3 1(8): 21 76-21 85.

Lele, S.K., 1992. Compact ﬁnite difference schemes with spectral-like resolution. Journal
of Computational Physics, 103: 16-42.

Maraqa, M.A., Zhao, X., Wallace, RB. and Voice, T.C., 1998. Retardation coefﬁcients
of nonionic organic compounds determined by batch and column techniques. Soil
Science Society of America Journal, 62(1): 142-152.

Nkedikizza, P. et al., 1983. Modeling tritium and chloride-36 transport through an
aggregated oxisol. Water Resources Research, 19(3): 691-700.

Park, J .H., 2000. Bioavailability of sorbed organic contaminants. Ph.D. Thesis, Michigan
State University, East Lansing, 155 pp.

Park, J .H., Feng, Y.C., Ji, P.S., Voice, T.C. and Boyd, S.A., 2003. Assessment of
bioavailability of soil-sorbed atrazine. Applied and Environmental Microbiology,
69(6): 3288-3298.

Park, J .H., Zhao, X.D. and Voice, T.C., 2001. Biodegradation of non-desorbable
naphthalene in soils. Environmental Science & Technology, 35(13): 2734—2740.

Phanikumar, MS. and Hyndman, D.W., 2003. Interactions between sorption and
biodegradation: Exploring bioavailability and pulsed nutrient injection efﬁciency.
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Prata, F., Lavorenti, A., Jan, V., Burauel, P. and Vereecken, H., 2003. Miscible
displacement, sorption and desorption of atrazine in a Brazilian oxisol. Vadose
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Roache, P.J., 1998. Fundamentals of computational ﬂuid dynamics. Herrnosa Publishers,
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Saffron, C., 2005. Plant-enhanced remediation of naphthalene. Ph.D. Thesis, Michigan
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Selim, H.M., Davidson, J .M. and Rao, P.S.C., 1977. Transport of reactive solutes through
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Seyfried, MS. and Rao, P.S.C., 1987. Solute transport in undisturbed columns of an
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Sharer, M., Park, J .H., Voice, T.C. and Boyd, S.A., 2003a. Aging effects on the sorption-
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82

 

Sharer, M., Park, J .H., Voice, T.C. and Boyd, S.A., 2003b. Time dependence of
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Toride, N., Leij, R]. and Van Genuchten, M.T., 1999. The CXTFIT code for estimating
transport parameters from laboratory or ﬁeld tracer experiments. 137, US Salinity
Laboratory, Riverside, California.

Van Genuchten, M.T. and Wagenet, R.J., 1989. Two-site/two-region models for pesticide
transport and degradation: Theoretical development and analytical solutions. Soil
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83

CHAPTER 4
EFFECTS OF AGING ON DESORPTION KINETICS IN SOIL COLUMNS

Abstract

A study was conducted to explore the effects of aging on desorption kinetics in
saturated soil columns. Sorption isotherms, batch series-dilution desorption and column
desorption experiments were conducted with naphthalene on three sandy soils with
different organic content involving different equilibration periods. Each soil was
characterized for dispersion and retardation using tritiated water. Increased soil-
naphthalene contact time resulted in an increase in the total naphthalene distribution to
sorbed phase in all soils. A signiﬁcant increase in the non-desorbable (solvent-
extractable) naphthalene due to an increase in the equilibration period was evident in
batch as well as column desorption. This increase in non-desorbable naphthalene was

accompanied by a corresponding decrease in the desorbable naphthalene.

Nonlinear regression of the column desorption data with the conventional two-site
model and the three-site model indicate that data are difﬁcult to reconcile using the two-
site model. The three-site model, which incorporates non-desorption sites, described
naphthalene desorption better than the two-site model in all nine cases (i.e., three soils at
three aging periods). We conclude from parameters of the three-site model, that aging
results in a shift of contaminant from nonequilibrium domain to non-desorption domain,
while the effect of aging on the size of equilibrium domain and desorption rate

coefﬁcients is minimal.

84

4.1 Introduction

Soil-contaminant contact time, commonly referred to as aging, is an important
variable inﬂuencing different aspects of the sorption and the desorption process. These
aspects include the extent of sorption, isotherm linearity, the distribution of the
contaminant in equilibrium, nonequilibrium and non-desorption compartments, the rate
of release from the solid matrix and the reversibility of the sorption process. The effect of
aging on the extent of sorption is well known, as the equilibrium sorption distribution
coefﬁcient (K d ) has been shown to increase with an increase in the contact time. For
example, (Xing and Pignatello, 1996) evaluated the sorption isotherms for
dichlorobenzene and dichlorophenol over periods of 1 and 30 days and found that the
sorption coefﬁcient, K F , increased 1.3 times for dichlorobenzene and 2.7 times for
dichlorophenol. Similar observations exist for other organic compounds in studies
involving the aging effects on sorption/desorption kinetics e.g., (Sharer et al., 2003a;
Sharer et al., 2003b). The increase in K d , however, has been reported to be compound-
speciﬁc and not necessarily related to aging. For example, (Sharer et al., 2003a) reported
a signiﬁcant increase for 2,4 D over a 14 month period, a decrease in K d for atrazine over

a 30 day period, and no change for chlorobenzene. The effect of aging on the isotherm
linearity produced mixed results with some supporting an increase in non-linearity e.g.,
(Weber and Huang, 1996; Xing and Pi gnatello, 1996) with aging while others found no

signiﬁcant effect e. g., (Sharer et al., 2003a; Sharer et al., 2003b).

Three aspects are important with reference to desorption viz., (1) how quickly a

fraction of contaminant becomes desorption-resistant (2) how the size of the desorption-

85

resistant fraction of the matrix changes over time and (3) how the rate of desorption ﬁ'om
rate-limited compartment changes over time. Formation of a desorption-resistant ﬁaction
has been observed over equilibration times of 24 hours (Kan et al., 1997; Park et al.,
2003; Park et al., 2001). An increase in the desorption-resistant ﬁaction with an increase
in soil-contaminant contact time has also been reported e. g., (Johnson et al., 2001;
Pignatello, 1990b; Sharer et al., 2003a; Sharer et al., 2003b). (Pignatello, 1990a) studied
the slowly reversible or the non-labile fraction of non-polar halogenated hydrocarbons on
soils and observed that non-labile ﬁaction increased nonlinearly with the incubation time
and applied concentration. (Sharer et al., 2003b) studied the effects of aging on
desorption kinetics in lab-controlled environment on chlorobenzene (CB) using four soils
ranging in OC from 0.69% to 13.4%. The authors found that 17-27% of non-desorbable
fraction was observable aﬁer only 24 hours and increased to 28-45% after 14 months of
aging. Observations for a slower desorption in aged soils compared to freshly
contaminated soils also exist. Aging is also believed to affect the desorption rates for the
non-equilibrium compartment. For example, (McCall and Agin, 1985) observed a
decrease in the desorption rate coefﬁcient with aging. Similar ﬁndings exist in the work
of (Carmichael et al., 1997) who found an order of a magnitude difference between the
desorption rates of fresh and ﬁeld weathered PAHs. Sharer et a1. (2003 a) found that aging
appeared to affect the desorption rates of chlorobenzene, ethylene dibromide and atrazine

but did not affect 2,4 D.

Most of the studies referred aimed at exploring the effects of aging on desorption
kinetics of short and long-term aged soils in batch systems. Despite the signiﬁcant

implications of aging on desorption, there are very few long-term laboratory studies, that

86

have focused on analyzing the inﬂuence of aging on desorption parameters in soil
columns. In this study, we conducted column desorption experiments with short and
long-term aged soils. Our approach was to ensure identical conditions for sorption in
batch except the equilibration time so that we could explicitly measure the kinetic
desorption parameters for differentially-aged soils. By employing sorbents with different

organic content, we also aimed at evaluating the role of SOM in the desorption process.

87

4.2 Materials and methods

Solute and sorbents. Unlabeled and 14C-naphthalene with uniformly labeled carbons

procured from Sigma Aldrich Co. was utilized as a representative HOC for the batch and
column desorption experiments. Three sandy soils i.e., Kalkaska-A, SPCF and an aquifer
sand from the Plume-A site, Schoolcraft, MI (hereafter referred to as Plume-A sand)
containing different organic matter content were used for the study. The methods of pre-
treatment for these sorbents, their mechanical characteristics and the respective organic
matter content have been reported in Chapter 3.

Sorption isotherms. Three-day, 2-month and 5-month sorption isotherms were
conducted on three soils. The protocol for the three-day isotherms has been discussed in
detail in Chapter 3. The same protocol was adhered to for 2-month and 5-month
isotherms. Soil mass and liquid-phase volume used for the batch isotherms for each soil
are presented in Table 4-2.

Series-dilution desorption in batch. The series-dilution desorption experiments were
performed on all three soils at differential equilibration periods ranging from 10 minutes
to 12 days to monitor a change in the non-desorbable concentration. Triplicate soil

slurries were prepared in 5 mL vials with mininert valves equipped with Teﬂon liners. An
aliquot of sterile soil was mixed with CaC12(0.01M) prepared in deionized water. The
details of soil mass and liquid-phase volume for each soil are presented in Table 4-2. The
resulting soil-to-water ratios were 0.075. 0.214 and 0.712 for Kalkaska-A, SPCF and
Plume-A sand respectively. The soil slurries so prepared were spiked with 4 uL of

naphthalene spiking solution resulting in an initial liquid-phase concentration of 381 5 :1:

63.9 rig/L for Kalkaska-A, 4183.68 :1: 99.8 [Lg/L for SPCF and 4986.05 :h 208.35 rig/L for

88

Plume-A sand respectively. After spiking, the vials were tumbled end-over-end in dark
for different equilibration periods between 10 minutes and 12 days. At the end of
respective equilibration periods, the vials were centrifuged at 1163 x g for 5 minutes and
the supernatant was analyzed by liquid scintillation counting (LSC). The sorbed-phase
concentration was calculated by difference. On completion of the sorption step, the

remaining liquid-phase was decanted to the extent possible. Vials were reﬁlled with

naphthalene-free CaClz, tumbled at 6 rpm for 18-24 hours and the liquid-phase was

analyzed again for naphthalene after centrifugation. Approximately, 4-6 successive
dilutions were done in each case except for the sorption time of 10 minutes; in which
case, the low radioactivity after two consecutive dilutions did not warrant further
dilutions.

Table 4-1: Details of the soil mass and the liquid-phase volumes used for the isotherms
and series-dilution desorption experiments

 

 

 

 

Batch isotherms Series-dilution desorption
Soil Soil mass Liquid volume Soil mass Liquid volume
(8) (1111-) (8) (mL)
Kalkaska-A 0.348 i 0.028 4.589 i 0.034 0.342 :1: 0.0216 4.512 :1: 0.074
SPCF 0.844 :1: 0.095 4.179 :1: 0.022 0.889 t 0.027 4.1514 i 0.099
:3?“ 2.64 :t 0.0283 2.464 d: 0.028 2.487 i 0.032 3.490 :1: 0.146

 

Column desorption. A detailed description of the method used for column desorption
experiments involving an equilibration period of three-days has been presented in

Chapter 3. The same procedure was adopted for column desorption studies for the

89

equilibration period of 2 months and 5 months. The dispersive properties of the three

soils were also determined using tritiated water as discussed in Chapter 3.

Independent tests to verify the extraction efﬁciency of methanol after 3 days and
5 months were also carried out on separate batch samples by spiking the soil with an
initial liquid-phase concentration between 1-5 mg/L. Methanol was found to be 100 :t 5%
efﬁcient in recovering sorbed naphthalene for the three soils after 3 days of equilibration.
However, after 5 months of equilibration period, methanol could recover 80.9 i 2.71% of
naphthalene for Kalkaska-A, 76.1 i 4.34% for SPCF and 77.0 i 2.46% for Plume-A sand

respectively.

4.3 Analysis

In this study, the desorption of naphthalene from soil columns for the three different
aging periods (i.e., three days, two months and ﬁve months) was analyzed using the two-
site and the three-site models. The three-site model assumes that (1) the solid matrix can
be divided into equilibrium, nonequilibrium and non-desorption sites (2) the equilibrium
sites achieve an instantaneous equilibrium with the aqueous phase that can be described
by a linear distribution coefﬁcient (3) the release from the non-equilibrium sites is
described by the concentration gradient between the two phases and (4) the release from
the non-desorption sites (designated as irreversible sorption) is insigniﬁcant during the
experimental time scales. The dimensional and dimensionless equations for these models,
the solution technique and the parameter estimation technique have been described in

detail in chapter 3. The two-site model was used with two different parameters i.e., (1)

90

with isotherm K d and (2) with column desorption K d . The three-site model was used with

column desorption K d only.

4.4 Results and discussion

Aging isotherms. The slope of the sorption isotherms was calculated by using linear
regression from the plots of the amount of naphthalene sorbed (rig/Kg) versus the
concentration in aqueous phase (rig/L). This corresponds to the sorption distribution
coefﬁcient K d . Sorption of naphthalene was linear for all three soils for all aging periods.
K d calculated using linear regression was 9.22 mL/ g for Kalkaska-A, 5.82 mL/g for
SPCF and 1.46 mI/g for Plume-A sand respectively based on a three-day isotherm
(Figure 4-1). There appears to be a considerable effect of aging on sorption capacity of
naphthalene for all the three soils. A comparison of K d values for the three aging periods
provides evidence that an apparent equilibrium appears to have been reached quickly on
all three soils, however, the “true” equilibrium takes a much longer time and the tested
period of aging (5 months) may not be sufﬁcient to reach the true equilibrium state, for
surface soils containing SOM. The K d values at different aging periods for naphthalene
indicate a rapid initial sorption phase followed by a slow and continuous uptake. One
notable difference is for the Plume-A sand, for which K d increased by almost 100% from

3 days to 2 months but showed no increase thereafter. This contradicts the ﬁndings of
(Loehr and Webster, 1996) but is consistent with the ﬁndings of (Xing and Pignatello,
1996) who observed that largest relative increase in sorption coefﬁcient (K p) for
dichlorophenol occurred for a mineral soil (0C 1.74%) rather than the soil with OC as
high as 54.1%. In several other studies also, an increase in the extent of sorption as a

91

 

consequence of aging has been found e.g., (Sharer et al., 2003a; Sharer et al., 2003b;

Xing and Pi gnatello, 1996)

92

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

10 . . ....., . ......., . .......
3 E Kalkaska-A f
x - .
3 5’ y=922x I
51°? '5
.L: i :
g 'l
- 4
C
810‘:- 'E
E : i
o
to ’ ° 1
3
10 I I IIIIIII I I IILIIII I I IIIIII
2 3 4 5
10 .10. o 10
Ltqurd oomerrtration(pg/L)
10° . ......, 4 Wm... . . ”m:
a E SPCF 3
¥ P 1
3 . .
5‘05? '5
“a : :
§ : :
8 . .
C
810‘? 1‘
E ; :
a) . .
3
10 I LILI_.LIII I I IIIIIII I I IIIIII
102 . 1t)3 .10‘ 105
LiqudconoentrattonmglL)
10‘b . . . . . . . . . . . .u
t Plume-Asand 1
A ' =2.89
g1 ; y=2.88x y x j
g F d
z - i
o
'5 . l
g
8‘3103- -
8 : :
E I I
c?) - l
I I I I III I I I I I I II
. . 103 . 10‘
Liqud concentration (pg/L)

Figure 4-1: Sorption isotherms for the three soils. Squares, circles and diamonds
represent 3-day, 2-month and 5-month equilibration period respectively

93

Series-dilution desorption. In series-dilution desorption experiments, an increase in the
sorbed naphthalene with an increase in the sorption period is evident for all soils (Figure
4-2 to Figure 4-4). The slope of sorption line increased from 4.41 to 10.64 for Kalkaska-
A corresponding to an increase in the sorption equilibration period from 10 minutes to 12
days. A similar trend is evident for SPCF and Plume-A sand, in which case, the increase

in slope is 4.30 to 9.07 and 0.28 to 2.0 respectively. The K d values based on the three-day

sorption isotherms for the three soils also lie within this range. Desorption isotherms
donot coincide with sorption data in all cases providing an evidence of hysteresis. The
non-desorbable naphthalene concentration was calculated by the intercept of the
desorption isotherms and was found to be 1196 rig/Kg for Kalkaska-A, 779.68 1.1ng for
SPCF and 447.9 rig/Kg for plume-A sand respectively for the least sorption time of 10
minutes.

A change in the slope of the desorption isotherms with an increase in soil-naphthalene
contact time is also apparent in all three soils. The sorption and desorption lines appear to
converge at lower equilibration periods and start to diverge at longer equilibration
periods. This divergence is a result of an increase in the intercept, which identiﬁes the

non-desorbable naphthalene concentration (Sud) . A consistent increase in the non-

desorbable concentration can be observed for all three soils (Figure 4-5). This is
consistent with previous studies e.g., (Carmichael et al., 1997; Connaughten et al., 1993;
Farrell and Reinhard, 1994; Grathwohl and Reinhard, 1993; Harmon and Roberts, 1994;
Pignatello, 1990a; Pignatello, 1990b; Pignatello et al., 1993; Wu and Gschwend, 1986).
Although, the extent of desorption as affected by aging in these studies has been different

in laboratory-spiked and ﬁeld-contaminated samples, the phenomena has been noted in

94

both. Carmichael et al. (1997) in their sequential desorption experiments found that 15-

14
30% of C-phenanthrene and 15-40% of 14C-Chrysene had become non-labile over a

contact period of 85 days.
The rate of increase in the non-desorbable concentration (Sud) appeared to be fast for

equilibration periods up to three days and tends to slow down at later periods. Non-

desorbable fraction of the soil matrix (fnd) , was calculated for each series-dilution

experiment by the relation Snd /ST . A signiﬁcant fraction of the soil matrix appeared to

behave as non-desorption sites i.e., 0.095 for Kalkaska-A, 0.081 for SPCF and 0.38 for
plume-A sand. The increase in the non-desorption site fractions revealed a consistent but
nonlinear trend over time for all three soils (Figure 4-5). For a differential equilibration
time spanning over 12 days, the ranges of fnd displayed by Kalkaska-A, SPCF and
Plume-A sand were 0.095-0.33, 0.081-0.25 and 0.38-0.55 respectively. It is to be noted

that the range of fnd for Plume-A sand with no SOM is the highest among the three soils.

95

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. ' ' jD— Kalkaska-A
Change "1 3nd —o— SPCF
8000 - —<>— Plume-A sand -
I
s? 6000 - -
a I
3-
I
E 4000 - -
(I) I . O
2000 - I . o t -
a, 9’ 9 .
O i i t t :
Change in f nd
0.8 - ..
0.6 - -
o
0. , . -
. . ___—/I 4‘)
0.2 ‘9’ la ‘
5‘5/
0 l l L l l
0 50 100 150 200 250 300

Time (hours)

Figure 4-5: Change in the non-desorbable concentration (Sud) and the fraction of non-
desorption sites (fnd ) with an increase in aging period

99

Column desorption. A systematic reduction in the liquid-phase concentration and a
corresponding increase in the sorbed-phase concentration with an increase in the aging
time from three days to ﬁve months occurred during the sorption phase for column

desorption (Ceq values in Table 4-2). This reduction is consistent with the observation of

an increase in the sorptive uptake for each soil in sorption isotherms. It is to be noted that
Plume-A sand did not exhibit an increase in the uptake for the period from 2 months to
ﬁve months as the liquid-phase concentration decreased form 3 days to 2 months but a
slight increase is noted thereaﬁer. A similar trend is observed in our aging isotherms for

Plume-A sand.

Cim-t in Table 4-2 represents the initial liquid-phase concentration at the start of column
desorption (i.e., the mean of ﬁrst three samples from column desorption). The process of
column packing using pro-equilibrated wet soil spanned over an average time of 20
minutes, exposing the soil slurry to air and causing volatilization of naphthalene. A lower
Cm, at the start of column desorption than the corresponding Ceq values is due to

volatilization that occurred during the process of column packing. The CW, in column
desorption was lower than corresponding Ceq values in all cases with the exception of one
i.e., Kalkaska-A at three-day equilibration period, where a higher CW, at the start of
column desorption than Ceq value was noted. For the three-day equilibration period, bulk

of naphthalene is considered to be reversibly sorbed and a loss of naphthalene due to
volatilization might induce desorption from sorbed-phase prior to the start of column

desorption.

100

 

f

Desorption of naphthalene in Kalkaska-A and SPCF continued for approximately
70 to 80 pore volumes, while for plume-A sand it occurred over approximately 35 to 40
pore volumes for all aging periods. The desorption curves from the soil columns

exhibited different shapes for the three soils (Figure 4- 7). Column K d values were

calculated using Equation 3-5 (Chapter 3) for all desorption experiments and compared

with the isotherm K d values for the corresponding aging times. Our results conﬁrm a

previously drawn conclusion based on comparison of the three-day batch and column

desorption experiments that the reason for the normally lower K d values reported in

literature might be due to differences in solute accessibility in batch and column
environments. Furthermore, we calculated the desorption K d values based on the three
different mass fractions. The column K d values in Table 4-2 represent those calculated by
accounting for the naphthalene mass desorbed from columns, the mass recovered by
water extraction at the end of a column desorption and the mass recovered by solvent
extractions. In our experiments, the difference between the batch and column K d ranged
between 2.61% to 24.21% for all nine cases compared. This highlights that, if a common
method of equilibration employed for both batch and column studies, the

resulting K d values for a soil-contaminant combinations are likely to be comparable.

Aging had a signiﬁcant effect on the reversibility of sorption process as noted by
the differences in the desorbable naphthalene (i.e., mass of naphthalene desorbed ﬁ'om
the soil columns plus mass extracted by water extractions at the end of column
desorption) and non-desorbable naphthalene for all three soils. For Kalkaska—A, the

desorbable naphthalene mass decreased from 76.41% to 49.74% with a corresponding

101

increase in the non-desorbable mass from 23.59% to 50.26% over a period of 5 months,
while for SPCF, the desorbable mass decreased from 91.73% to 68.56% with a
corresponding increase in the non-desorbable mass from 8.26% to 31.44% (Figure 4-6).
For Plume-A sand, a similar increase is noted in the non-desorbable mass form 44.59% to

64.31%.

Table 4-2: Summary of column conditions and the calculated column distribution
coefﬁcients at 3 days, 2 months and 5 months aging time

 

c o o I j
Liquid-phase Liquld-phase Column
concentration at the concentration at desorption

 

 

 

 

end of sorption the start of distribution
. equilibration in column coefﬁcient Recovery
801] batch desorption
Ceq Cm: Kd (column)
(us/L) (rig/L) (mL/g) (%)

Kalkaska-A (3 days) 318.8 354.7 10.14 70.70
Kalkaska—A (2 months) 228.9 190.0 13.46 62.74
Kalkaska-A (5 months) 197.6 182.2 12.49 58.79
SPCF (3 days) 604.6 550.3 5.65 60.71
SPCF (2 months) 513.5 460.2 9.02 84.89
SPCF (5 months) 448.0 448.0 8.63 88.38
Plume-A (3 days) 1548.6 1198.8 1.81 86.64
Plume-A (2 months) 1201.2 1003.3 2.48 76.99
Plume-A (5 months) 1288.7 908.1 2.86 83.24

 

*

Calculated using equation (3-5) in Chapter 3

Out of the two surface soils, the desorbable naphthalene mass was consistently lower by
21-28% for Kalkaska-A than for SPCF and the non-desorbable mass was consistently

higher by 15-20% for all aging times. The water-extractable mass fraction was also

102

higher for Kalkaska-A compared with SPCF for all aging periods, although the difference
between the two is not as signiﬁcant as is the case for the desorbable and non-desorbable
mass ﬁ'actions. The effect of variation in SOM and hence the distribution of naphthalene
to the organic phase rather than pore diffusion is apparently supported by these consistent
differences in the naphthalene mass distribution of the two soils. Another notable
difference consistent with the variation in isotherm K d values over time is the behavior of
Plume-A sand with almost no SOM. Compared with Kalkaska-A and SPCF, the least

amount of mass was desorbable for Plume-A sand (28.34% to 41.5%).

103

 

 

 

(:1me
D 5months

 

|- 3days

 

 

 

 

JDDJ

 

 

 

 

 

 

 

 

Cummulative mass desorption (%)

 

 

 

 

 

 

 

 

 

 

0 1000 2000 3000 4000 oesomaue Water sum
. extractable extractaje
Time (mmutes)

Figure 4-6: Cumulative naphthalene desorption from the soil columns at an aging time of
3 days, 2 months and 5 months. A summary of desorbable, water-extractable and solvent-
extractable naphthalene mass from each column desorption experiment is also shown

104

Model comparisons. In applying the mathematical models to column desorption data,
we minimized the number of estimated parameters by supplying independently
determined dispersion coefﬁcients obtained through independent tracer tests involving
tritiated water and the sorption distribution coefﬁcients for each soil. Our ﬁrst goal was to

isolate a difference, if any existed, between the model outputs obtained by K d values

determined through batch isotherms and those determined from the column desorption

data. The two-site model was not able to describe desorption from soil columns with

U

isotherm K d as well as the column K d and resulted in a hi gher-than-actual naphthalene
mass elution for all nine cases (Figure 4-7 to Figure 4-9). Owing to minor differences in

the isotherm K d values and the colmnn K d values, the description of desorption data with

the two-site model for both cases was not signiﬁcantly different. With isotherm K d , the

R2 values ranged between 0.83-0.95 for Kalkaska-A, 0.92-0.97 for SPCF and 0.97-0.98

for Plume-A sand respectively. A reduction in the R2 values is also observed for all soils

with an increase in aging time, although, it is more pronounced in high organic soil (i.e.,
Kalkaska—A), comparatively less pronounced in SPCF and almost insigniﬁcant in Plume-
A sand. The deterioration in the two-site model ﬁts for Kalkaska-A at an aging period of
5 months is expected due to a greater deviation between the isotherm and the

column K d values.

All applications of the three-site model were also based on measured

column K d values. The three-site model described naphthalene desorption from soil

columns better than the two-site model for all nine cases (Figure 4-7 to Figure 4-9). The

105

R2 values for all nine cases (i.e., three soils at three aging times) ranged between 0.98-

0.99. We conclude based on the comparison of the two-site and three-site model best ﬁts,
that an inadequate representation of the observational regimes rather than differences in
K d values, is the reason for a less accurate description of the naphthalene desorption in

soil columns. Therefore, in the subsequent analysis, we base our analysis on the

parameters of the three-site model only.

106

 

V I I I l 1'

 

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3 days ”:3“ 3gb with K a (isotherm)
1.. 2—sitewimKd(ookm)

_ 3-site with Kd (ooium)

l

 

 

 

olco

 

 

 

 

 

 

Clo0

 

 

 

 

Pore volunes

 

5 months

Cloo

 

 

 

 

Pore volunee

Figure 4-7: Best ﬁts of the two-site and the three-site models for Kalkaska—A

107

 

 

 

 

 

 

 

 

 

 

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0/c0

 

 

 

 

Pore volunes

Figure 4-8: Best ﬁts of the two-site and the three-site models for SPCF

108

 

 

 

 

 

 

 

 

 

 

' ' ’ .data '
3 days -3., signs with K d (isotiietm)
1 » _,__ 2-sitewith K d (ooum) -
_ 3-sitewith Kd(mll.rm)
0.0»
O
9 0.6-
U
0.4i
0.2»
00
Pore volu'nes
2 months

C/Co

 

 

 

 

 

Pore volumes

 

I 5 months .

oic0

 

 

 

 

0 5 10 15 20 25 30
Pore voltmes

Figure 4-9: Best ﬁts of the two-site and the three-site models for Plume-A sand

109

The parameter estimation described earlier in chapter 3 was done using the non-
dimensional equations. The fractions of equilibrium/rate-limited/non-desorption sites ’and

desorption rate coefﬁcients were calculated based on the estimated parameters ﬂ1,,62 and
a). The effect of aging was neither signiﬁcant nor systematic on the fraction of

equilibrium site ( feq) in all three soils, which displayed a narrow range i.e., 0025-0043

for Kalkaska-A, 0054-0094 for SPCF and 0.089-0.14 for Plume-A sand. On the

contrary, the decrease in nonequilibrium site fractions (A fneq ) with a corresponding

increase in the non-desorption sites (A fnd ) was evident in all soils. For example,
Kalkaska-A showed A fneq of 0.345 and 0.03 with a correspondingA fnd of 0.32 and 0.03,

for a period of 2 and 5 months. This is in agreement with some previous batch studies
e.g., (Pignatello, 1990b; Sharer et al., 2003a). Similar correspondence was observed in
the estimated site fractions for other two soils overtime, however, this change is not
consistent for the three soils studied. For example, in Kalkaska-A, the change is more
than 90% in the ﬁrst two months while for SPCF and Plume-A sand, the change in

nonequilibrium sites (A fneq ) and the corresponding change in non-desorption sites

(A fnd) is almost equal. These results explain the resistance to desorption exhibited by

contaminants in long-term contaminated soils and support the hypothesis that increased
soil-contaminant contact time is likely to limit desorption due to an increased probability

for contaminant molecules to “diffuse” deeper into intra-aggregate micro-pores.

110

 

 

 

 

 

 

 

 

 

 

 

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A comparison of desorption rate coefﬁcient (a ) estimated using the three-site model also
reveals that unlike the change in the size of the rate-limited and non-desorption domains,
the change in desorption rate coefﬁcients is not signiﬁcant. This coefﬁcient decreased
systematically with aging for SPCF while the minor variations in case of Kalkaska-A and
Plume-A sand would not render it to be statistically different. The variations in a
observed for Kalkaska-A and Plume-A sand was not systematic either (Figure 4-10).
Aging appeared to affect the size of the rate-limited compartment more than desorption
rates. These ﬁndings are, to some extent, in conﬂict with those of Sharer et al. (2003b)
who found a decrease in the desorption rate coefﬁcient for chlorobenzene, ethylene
dibromide and atrazine but no change for 2.4.D. Similar observations exist in other
studies e.g., (Carmichael et al., 1997; Johnson et al., 2001; McCall and Agin, 1985) about
a slight reduction in desorption rate coefﬁcients for some cases, while no change in
others. For example, (Johnson et al., 2001) found that the desorption rate coefﬁcient for
slowly desorbing fractions decreased by a factor of 2 with increased aging for a humic
topsoil but remained unaffected for an aging time beyond three months for a shale. In the
light of these results as well as ﬁndings of some previous studies, it can be said that the
effect of aging on the desorption rates is likely to be a function of compound-sorbent-
aging period combination and cannot be generalized based on a limited set of

observations.

114

 

 

 

 

 

 

 

 

 

 

 

Kal Plane-A sand

Figure 4-10: Changes in the fractions of equilibrium, rate-limited and non-desorption
sites and the desorption rate coefﬁcients with aging

115

 

4.5 Conclusions

The results from this study provide evidence that partitioning of HOCs to the solid phase
is a time-dependent process and the extent of sorption is likely to increase with soil
contact time. Contrary to some previous ﬁndings, aging did not cause a reduction in the
isotherm linearity; however, a signiﬁcant effect of aging was noted on the distribution of
contaminant in various compartments in the solid matrix. A signiﬁcant amount of
naphthalene was rendered non-desorbable over a very short equilibration time suggesting
that the formation of a desorption-resistant fraction could be instantaneous for some
matrix-contaminant combinations. This highlights the presence of a speciﬁc physical or
chemical interaction as suggested by (Sharer et al., 2003b).

We also conclude based on the comparison of the two-site and the three-site models, that
for contaminants exhibiting signiﬁcant non-desorption, a compatible mathematical model
results in a better description and the data are difﬁcult to reconcile with the dual domain
approach. We also suggest that, our aging conceptual model, in which, a shift of
contaminant from nonequilibrium domain to non-desorption domain occurs over time is
consistent with our observations and explains the resistance to desorption exhibited by

contaminants over long-term contact times.

116

4.6 References

Carmichael, L.M., Christman, RF. and Pfaender, F.K., 1997. Desorption and
mineralization kinetics of phenanthrene and chrysene in contaminated soils.
Environmental Science & Technology, 31: 126-132.

Connaughten, D.F., Stedinger, J .R., Lion, L.W. and Schuler, M.L., 1993. Description of
time-varying desorption kinetics: Release of naphthalene from contaminated soils.
Environmental Science & Technology, 27(12): 2397-2403.

Farrell, J. and Reinhard, M., 1994. Desorption of halogenated organics from model
solids, sediments, and soil under unsaturated conditions .2. Kinetics.
Environmental Science & Technology, 28(1): 63-72.

Grathwohl, P. and Reinhard, M., 1993. Desorption of trichloroethylene in aquifer
material - Rate limitation at the grain scale. Environmental Science &
Technology, 27(12): 2360-2366.

Harmon, T.C. and Roberts, P.V., 1994. The effect of equilibration time on desorption rate
measurements with chlorinated alkenes and aquifer particles. Environmental
Progress, 13: 1-8.

Johnson, M., Keinath, T. and Weber, W.J., 2001. A distributed reactivity model for
sorption by soils and sediments. 14. Characterization and modeling of

phenanthrene desorption rates. Environmental Science & Technology, 35(8):
2734-2740.

Kan, A.T., Fu, G., Hunter, M.A. and Tomson, M.B., 1997. Irreversible adsorption of
naphthalene and tetrachlorobiphenyl to Lula and surrogate sediments.
Environmental Science & Technology, 31(8): 2176-2185.

Loehr, RC. and Webster, M., 1996. Behavior of fresh vs. aged chemicals in soils. Journal
of Soil Contamination(5): 361-383.

McCall, P.J. and Agin, G.L., 1985. Desorption kinetics of picloram as affected by
residence time in the soil. Environmental Toxicology and Chemistry, 4: 37-44.

Park, J .H., Feng, Y.C., J i, P.S., Voice, T.C. and Boyd, S.A., 2003. Assessment of
bioavailability of soil-sorbed atrazine. Applied and Environmental Microbiology,
69(6): 3288-3298.

Park, J .H., Zhao, X.D. and Voice, T.C., 2001. Biodegradation of non-desorbable
naphthalene in soils. Environmental Science & Technology, 35(13): 2734-2740.

Pignatello, J .J ., 1990a. Slowly reversible sorption of aliphatic halocarbons in soils .2.
Mechanistic aspects. Environmental Toxicology and Chemistry, 9(9): 1117-1126.

117

Pignatello, J .J ., 1990b. Slowly reversible sorption of aliphatic halocarbons in soils. 1.
Formation of residual fractions. Environmental Toxicology and Chemistry, 9:
1 107-1 1 15.

Pignatello, J .J ., Ferrandino, F .J . and Huang, L.Q., 1993. Elution of Aged and Freshly
Added Herbicides from a Soil. Environmental Science & Technology, 27(8):
1563-1571.

Sharer, M., Park, J .H., Voice, T.C. and Boyd, S.A., 2003a. Aging effects on the sorption-
desorption characteristics of anthropogenic organic compounds in soil. Journal of
Environmental Quality, 32(4): 1385-1392.

Sharer, M., Park, J .H., Voice, T.C. and Boyd, S.A., 2003b. Time dependence of
chlorobenzene sorption/desorption by soils. Soil Science Society of America
Journal, 67(6): 1740-1745.

Weber, W.J. and Huang, W., 1996. A distributed reactivity model for sorption by soils
and sediments. 4. Intraparticle heterogeneity and phase-distribution relationships

under non-equilibrium conditions. Environmental Science & Technology, 30(3):
881-888.

Wu, SC. and Gschwend, P.M., 1986. Sorption kinetics of hydrophobic organic
compounds to natural sediments and soils. Environmental Science & Technology,
20(7): 717-725.

Xing, B. and Pi gnatello, J .J ., 1996. Time-dependent isotherm shape of organic

compounds in soil organic matter: Implications for sorption mechanism.
Environmental Toxicology and Chemistry, 15: 1282-1288.

118

CHAPTER 5
EFFECTS OF PORE-WATER VELOCITY ON SORPTION NONEQUILIBRIUM
Abstract

The contaminant residence time in ﬂow-through soil columns is considered
analogous to the equilibration time or “aging” in batch and is controlled by the varying
pore-water velocity. Because of this analogy, we evaluated the effect of pore-water
velocity on desorption-resistance and sorption non-equilibrium of naphthalene using
three natural sorbents (i.e., two surface soils and one of an aquifer origin). Each soil was

characterized for retardation and dispersion at four different velocities by injecting a

pulse of approximately two pore volumes of tritiated water (3H20). Dispersion

coefﬁcients were estimated by curve ﬁtting the equilibrium model to the observed BTCs.
Pulse injections for naphthalene were conducted at three pore-water velocities ranging
between 7-36 cm/hr and solvent extractions were performed after each column desorption

to measure the amount of non-desorbable naphthalene mass.

Nonequilibrium was evident in the breakthrough curves for all soils, although the
degree of asymmetry and nonequilibrium was different in each case. Similarly, non-
desorption was also evident in all soils, as evidenced by solvent-extractable naphthalene
at the end of column desorption. For the two surface soils, an increase in the non-
desorbable naphthalene mass with a decrease in pore-water velocity could not be
established, as velocity varied over a narrow range (14.80-16.3% for Kalkaska-A and
3.54-5.83% for SPCF). On the contrary, a signiﬁcant increase in the non-desorbable
naphthalene mass (6.33% to 18.31 %) with a reduction in pore-water velocity was

evident in case of Plume-A sand.

119

The observed time-concentration data for naphthalene was analyzed using the
two-site model and four different formulations of the three-site model. In general, the
three-site model describes naphthalene breakthrough better than the two-site model for all
nine cases (i.e. three soils at three different pore-water velocities). An interesting ﬁnding
in our work is that all four formulations of the three-site model resulted in identical ﬁts to
observed naphthalene breakthrough curves. This suggests that an increase in the number
of model parameters to improve the description of observed sorption/desorption behavior
is not justiﬁed in this case. However, an analysis of the estimated parameters suggests
that a mathematical formulation that accounts for a shift of contaminant from the
equilibrium domain to the non-desorption domain and formulated with time- independent

parameters, is preferred over the driving force formulations based on the linear

distribution coefﬁcient K d .

120

5.1 Introduction

Processes governing the fate and transport of organic contaminants have been
investigated in the past to develop a better understanding of the mechanisms involved.
Slow desorption compared to sorption greatly affects the shape of the breakthrough
curves in lab and ﬁeld studies. Sorption is typically known to follow biphasic behavior
while good evidence for the three desorption regimes has been found in a number of
batch studies. These three regimes include a fast regime, a slow regime and a very
slow/non-desorption regime. In recent batch studies, formation of a desorption-resistant
fraction within 24 hours (Sharer et al., 2003a; Sharer et al., 2003b) to 3 days (Park et al.,
2003) has also been observed. The extent of sorption, distribution of contaminant to
different domains, the extent of desorption as well as desorption rates are believed to be

greatly affected by soil-contaminant contact time.

Batch experiments to study the sorption-desorption behavior in laboratory
normally utilize the equilibrium concept, in which desorption is induced after sorption
equilibrium or at least an “apparent equilibrium” between the solute in aqueous phase and
solid phase has been achieved. The column studies are normally conducted to apply these
ﬁndings to the ﬂow-through systems. These involve either the miscible displacement
technique or pulse-type injections. In miscible displacement, an “apparent equilibrium” is
achieved by injecting the solute of interest long enough so that the efﬂuent concentration
equals the inﬂuent concentration prior to cutting off the solute injection. The pulse-type
experiments on the other hand, represent a case, where the “apparent equilibrium” is
dependent on the duration of injected solute pulse. For shorter pulse duration, the

“apparent equilibrium” is not reached and a condition of nonequilibrium is viewed to

121

exist between the sorptive and desorptive ﬂuxes. For such cases, the description of the

solute behavior using model formulations that are based on equilibrium partitioning

coefﬁcient are questionable. Equilibrium sorption distribution coefﬁcient (K d ) may

increase 1.3 to 10 times between short and long-term soil contact times and sorption
isotherms may become non-linear with increased contact time (Xing and Pignatello,
1996). Similar observations exist for the variations in domain size as a result of an
increased contact time. For example, an increase in the desorption-resistant fraction with
an increase in soil-contaminant contact time has been reported e.g., (Pignatello, 1990b;
Sharer et al., 2003a; Sharer et al., 2003b). In such a case, the mathematical formulations

that are based on time independent parameters may be more appropriate to use.

A variety of mathematical models, based on different conceptualizations of the
porous medium, have been used to describe desorption in batch systems. These models
include chemical site models i.e., two-site model (Rao et al., 1979; Van Genuchten and
Wagenet, 1989) and the three-site model (Park, 2000; Park et al., 2001; Park et al., 2002),
two and three-parameter pore diffusion models (Johnson et al., 2001), three-parameter
kinetic model (Cornelissen et al., 1998a; Comelissen et al., 1998b), ﬁve-parameter
kinetic model (Cornelissen et al., 1998a; Comelissen et al., 1997), gamma-distribution
model (Connaughten et al., 1993) and hybrid gamma-distribution model (Ahn et al.,

1999).

Most applications of these models have been limited to batch systems. On the contrary,
with the exception of a few studies e.g., (Ahn et al., 1999; Prata et al., 2003),
Transport of organic contaminants through porous media has typically been modeled

following the dual domain approach that neglects the desorption-resistant domain.

122

For this work, we have utilized pore-water velocity as a variable to control the
soil-naphthalene contact time and study its effects on the extent of non-desorption and
nonequilibrium. In the process, we compared different mathematical models for the ﬂow-
through systems based on the three regimes of behavior. These formulations utilize the
equilibrium distribution coefﬁcient and the kinetic rate coefﬁcients to describe the solute

ﬂux between the aqueous phase and the solid phase.

123

5.2 Materials and methods
Solute and geosorbents. The three soils described in Chapter 3 were employed in this

phase of study. The properties of dry packed soil columns are summarized in Table 5-1.

For this study also, unlabeled and 14C-naphthalene with uniformly labeled carbons,

(procured from Sigma Aldrich Co.) was used as a representative hydrophobic organic
compound (HOC). The method of pretreatment and sterilization for the soils has been

described in Chapter 3. The same method was followed for this phase of the study.

Table 5-1: Properties of the packed soil columns

 

 

ﬂOrganic . .
Soil content Densrty Porosrty
(%) (g/cm3) (cm3/cm3)
Kalkaska-A 3.9 1.540 :1: 0.024 0.384 :1: 0.013
SPCF 1.9 1.405 :1: 0.010 0.423 a: 0.006

Plume-A sand ND 1.650 t 0.016 0.354 d: 0.016

*
Analyzed at the Plant and Soil Sciences Laboratory in Michigan State University

Sorption isotherms. Three-day sorption isotherms were performed on each soil to

determine sorption distribution coefﬁcient (K d ) for each soil. The protocols for the

isotherms have been described in Chapter 3. Independent tests of extraction efﬁciency of
the solvent (i.e., methanol) were also carried out on separate batch samples involving an
equilibration period of three days. The method was reliable as 100 :1: 5 % of naphthalene
could be recovered.

Step increase-decrease column experiments with naphthalene. Column studies were

conducted using stainless steel columns (15 cm length and 1.1 cm i.d.) with reducing

124

unions at both ends ﬁtted with 25-micrometer frits to prevent the loss of ﬁne particles
(Figure 5-2). The column ﬁttings included stainless steel tubing 1/16 inches outer

diameter (id 1.27 mm) and Teﬂon valves. The columns and ﬁttings were autoclaved for

30 minutes at 120 0C and were oven-dried at 105 0C for 24 hours prior to use. The

columns were dry-packed for each experiment and ﬂushed with approximately 4-6 pore

volumes of C02 to replace the air in soil pores prior to saturation. These columns were

then saturated from the bottom by injecting approximately 8-10 pore volumes of CaClz.

After saturation, the columns were removed for the system, capped and weighed to
determine the saturated water content. Column densities and porosities are summarized in
Table 5-1. A pulse of approximately 2 pore volumes of the aqueous phase containing
naphthalene was injected and efﬂuent samples were collected over time in 10 mL glass
tubes containing scintillation ﬂuid to minimize volatilization losses. The sampling
continued until the activity in the collected samples was lower than approximately 200
dpm/mL. The soil columns were then taken off and the soil was pushed out in pre-
weighed vials. These vials were capped aﬁer topping up with methanol and were tumbled
end-over-end at 6 rpm for 24 hours. Phase separation was achieved by centrifugation at
1076 x g for 15 minutes and the liquid phase was analyzed for naphthalene by liquid
scintillation counting (LSC).

To characterize each soil for dispersion, identical soil columns were prepared using the

same procedure as outlined in the previous section. Approximately two pore volumes of

Tritiated water (BHZO) with an activity of 28000-31000 dpm/mL was injected and the

125

1..

 

 

 

efﬂuent was sampled every ﬁve minutes. Activity of 3H20 was determined by LSC.

These tracer tests were performed over a range of pore-water velocities for each soil.

126

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127

5.3 Analysis

Mathematical models. For the ﬂow-through systems, the most widely used model is the
two-site model (Van Genuchten and Wagenet, 1989) in which the available sorption sites
in a solid matrix are divided into equilibrium sites and nonequilibrium/rate-limited sites.

For steady ﬂow in a homogeneous soil, the governing equations for a linearly sorbed

 

solute are:
fequd ac 62C ac ap
(1+T)E=D?_va-—0—Kl—feq)KdC—Sneq] (5'1)
BSneq
at = a[(1— feq)KdC—S,,eq] (5-2)

where C is the aqueous concentration (pg/L), S is the sorbed-phase concentration (pg/kg),

v is the pore-water velocity (cm/hr), D is the hydrodynamic dispersion coefﬁcient

(cmz/hr), x is the distance along the principal direction of ﬂow (cm) and t is the time

(hr), a is the ﬁrst order kinetic rate coefﬁcient (hrl) for solute exchange between the

aqueous phase and nonequilibrium sites. Employing the dimensionless parameters
summarized in Table 5-2, the two-site model reduces to the following dimensionless

form:

ﬂiRgf-FEf-Ei-qu—Cz) (5-3)
(1-ﬂi)R§§%=wl(C1-C2) (5-4)

Subscripts I and 2 refer to the equilibrium sites and the rate-limited sites

respectively, ,61 is the dimensionless partitioning coefﬁcient and (01 is the dimensionless

mass transfer coefﬁcient. In the presence of a signiﬁcant amount of the contaminant

128

irreversibly sorbing to solid matrix however, use of the two-site model is questionable
and a model based on the conceptualization of three-domains in a solid matrix may be a
more appropriate description of the observed behavior. For the three-site model, the

governing equations are:

 

 

feqPKd 6C 62C 6C alp a3p
(1+——H_)—6t— = DEXT-vE-Tlﬂ-feq ’fnd)KdC_Sneq]‘7fndeC (5'5)
6S
anteq = al[(l ‘feq ‘fnd )KdC’Sneq] (5'6)
623d = a3fndeC (5-7)

The dimensionless equations for this formulation are:

R————-—- C -C - C 5-8
6C2
R(l'ﬂl-ﬂz/R)3F=04(C1'C2) (5'9)
6C3
—= C 5-10
.32 6T ‘03 1 ( )

In this model conceptualization (hereaﬁer referred to as Model 1), the solute ﬂux between
the aqueous phase and the nonequilibrium domain is represented by a driving force
formulation based on the linear distribution coefﬁcient K d and a single rate coefﬁcient (21
GTigure 5-2). For soils exhibiting a comparatively higher degree of nonequilibrium (i.e.,
extensive tailing) due to a greater difference between the sorption and the desorption rate,
a single rate coefﬁcient to represent the solute ﬂux between the two phases may be
inadequate. In that case, it is appropriate to represent both ﬂuxes with two separate rate
coefﬁcients and the resulting governing equations for the three-site model (hereafter

referred to as Model 2) become:

129

 

fequ a azc ac _a_1__p

 

 

(1+ ——)%t_=D gj—V_ 6x —(1 feq fnd)KdC+
a—‘gp Sneq ai _fndeC

628‘] = 01(1-feq "fnd)KdC "azsneq

623d =a3fndeC

The dimensionless equations for this case become:

6C
R(1-,31 ‘ﬂz ”01372: wicl "0’2C2

8C3
’626 -— ‘ -0)3C1

One of the limitations of the K d -based formulations (i.e., the two-site model, Model 1

(5-11)

(5-12)

(5-13)

(5-14)
(5-15)

(5-16)

and Model 2) is the time scale dependence of K d . The time-independence in these

formulations can be achieved by replacing K d with K eq (i.e., the distribution coefﬁcient

for the equilibrium domain) and utilizing kinetic rate coefﬁcients to describe the solute
exchange between the aqueous phase and nonequilibriurn/non-desorption domain. In this

formulation, sorption/desorption is instantaneous for the equilibrium compartment with

equal rates and is rate-limited for the nonequilibrium compartment, as is the case in

Model 1 and Model 2, but is kinetically controlled. The governing equations for this case

(Model 3) are:
ac azc ac a
(1+Keq%)3(t£=D-gx—2——v__ 2__E.Sneq— —a1C—a3C
as
ﬂzﬂéc-a25neq
a: p

130

(5.17)

(5.18)

65nd 6:36
— = —C 5-19
at p ( )
The dimensionless equations for Model 3 are represented by:
ac1 1 azc1 ac1
—=———-—— C + C — C 5-20
6C2
—— = C - C 5-21
6T 0’1 1 (02 2 ( )
6C3
= C 5-22
6T ‘03 1 ( )

Models 1,2 and 3 treat sorption to the nonequilibrium/rate-limited sites and non-

 

desorption sites as simultaneous and are based on the assumption that each solid phase
particle is in direct contact with liquid phase. The evidence in certain aging experiments
is, however, to the contrary, which reveal a shift of contaminant from the nonequilibrium

domain to the non-desorption domain. For such a case, the governing equations become

 

 

(Model 4):
ac azc ac a
(1+/reg %)—a;.=DEx7-v3x—-a,C+—;ﬂsneq (5-23)
as a 6
g" = 1:7 C—azSneq -a3s,,d (5-24)
if = “ZQC (5-25)

and the dimensionless equations for Model 4 are:

——_—————— c + c 5-26
6T P 622 El (01 l (02 2 ( )
ac2
a7 = «AC1 -w2C2 -w3C2 (5'27)
533 = aacz (5-28)

131

Solution technique and parameter estimation. The dimensionless equations for all

model formulations were solved using a hi gh-resolution numerical scheme. The spatial

derivatives were approximated using a fourth-order compact scheme with spectral-like

resolution (Lele, 1992). A fourth-order Runge-Kutta scheme was used for temporal

differencing. Parameters for two-site model were estimated using the non-linear least

squares inversion program CXTFIT (Toride et al., 1999). Parameters for all formulations
of the three-site model were estimated using sequential quadratic programming (SQP) as
implemented in MATLAB. The solution technique and the parameter estimation methods

have been described in detail in Chapter 3. The same methods were utilized for parameter

estimation in this study.

 

 

 

 

 

 

 

 

 

 

 

 

Model 1
Liquid phase (C)
Seq = fqudC al a3
[I l 4 i
H v I v
EQ- Domain Non-Eq. Non-des
(f...) Domain (fm) Domain (fm)
Model 3
Liquid phase (C)
S.q = KoqC CZ1 a2 a3
11 I 4 1
H l v
Eq. Domain Non-Eq. Non-des
(foq) Domain (fm) Domain (fad)

 

 

 

 

 

 

 

 

 

 

 

 

 

Model 2
Liquid phase (C)
seq = fqudC a, a2 (13
4| 1 4 I
I} f l v
Eq. Domain Non-Eq. Non-des
(f...) Domain (rm) Domain (f...)
Model 4
Liquid phase (C)
S = C a
.. K... II a2
ll 4
11 j I ___, a.
Eq. Domain Non-Eq. Non-des
(foq) Domain (fm) Domain (fad)

 

Figure 5-2: Box model representations of four variations of the three-site model

132

 

 

Table 5-2: Dimensionless parameters for the two-site and the three-site models

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Para- Two-site Three-site model formulations
meter model _
Model 1 Model 2 Model 3&4
C 3 _C_ 3 2
‘ c0 c0 c0 CO
C Sneq Sneq Sneq S neq pb
2 (l—feq)KdC0 (l-feq_fnd)KdCO (l—feq—fnd)KdC0 6C0
C NOt Snd Snd Snd pl)
3 app‘wab‘e fndeCo fndxdco 9C0
K PbKd PbK
PbKd MEL—i l+—— 9"
R l + T 9 9 1 + 9
19 + K 19 + K 6 + K
,6] feq pb d feq pb d feq pb d Not applicable
9+PbKd 9+PbKd 9+PbKd
Not bende bende -
,62 applicable 6 19 Not apphcable
(10-3)“; “1(1‘ﬂl‘ﬂ2/R)LR “1(1‘ﬂl“ﬂ2/R)LR alL
‘01 —— v v _
v v
a}; Not Not applicable 02 (1 — ’61 - .32 /R)LR a_2L_
applicable V v
Not (131-132 “31032 33!;
(03 applicable v v v
P :1; a :2 a
D D D D
T vt r: v_t :1
L L L L
Z x 5. 1 3:
L L L L

 

133

 

5.4 Results and discussion

Sorption isotherms. Sorption of naphthalene was linear for all the three soils (Figures 5-

3). K d values were 9.22 mL/ g for Kalkaska-A, 5.82 mL/g for SPCF and 1.46 mL/g for
Plume-A sand respectively. The K d values in our experiments are consistent with the

organic content of the three soils i.e., 1.9 % and 3.9 % and < 0.03% respectively.

 

 

 

 

  

 

 

 

 

’- I I 7 I I IIII j T7 T_IT f ﬂ WI:
C D Kalkaska-A 3
a * 0 SPCF sagnc —
x 5 O Plume-A sand ‘
\
or 10 g- L:
3 E 1
c . s-sazc i
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o . _
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1 1 1 1 L1111 L 1 1 1 11 111 1 1 1 L1 11
10 2 3 4 5

.5
O

10 , 1,0 . 10
LlQUld ooncentratron(pg/L)

Figure 5-3: Three-day sorption isotherms for naphthalene

Analysis of tritiated water BTCs. The choice of the nonequilibrium model i.e., mobile-
immobile model (MIM) or sorption-related nonequilibrium model is normally made
based on the results of independent tracer studies that employ a conservative tracer and
are conducted under experimental conditions similar to those employed for the solute of

interest. Fitting the observed tritiated water breakthrough curves to the equilibrium model

134

and determining the retardation coefﬁcient is a means to conﬁrm the presence/absence of
immobile water. Inappropriate estimation of pore-water velocity is indicated by values of
R less than unity, which is based on the assumption that all the pores do not participate in
ﬂow (Maraqa et al., 1998). Values of R less than unity for tritiated water have been
reported (Nkedikizza et al., 1983) and attributed to the transport-related nonequilibrium
created by the presence of immobile water regions. In our experiments, we estimated R
using the non-linear least squares inversion program CXTFIT (Toride et al., 1999) by
ﬁtting the equilibrium model to the observed tritiated water BTCs (Figure 5-4 to 5-6). In
our data, no evidence of immobile water was found, as the estimated values of R for
Kalkaska-A and Plume-A sand at four different velocities were found to be not different
than unity (Table 5-3). For SPCF, R was signiﬁcantly greater than unity. Values of R
greater than unity for tritiated water have been reported. For example Seyfried and Rao
(1987) reported a value of R for tritiated water between l.10-1.18 for their columns. We
also observed a velocity-dependent R for SPCF (i.e., 1.083 to 1.282) for a velocity range
of 3.16 — 15.79 cm/hour and we attribute this to the isotopic exchange of tritium with
crystallatic hydroxyls of clay particles as proposed by Van Genuchten and Wierenga,
(1977). Note that the SPCF contains clay content of 5 %, which is comparatively higher
than the other two soils.

Based on our analysis of retardation, the dispersion coefﬁcients for Kalkaska-A and
Plume—A sand were estimated using the equilibrium model with a value of R ﬁxed at
unity. Due to a signiﬁcant velocity-dependent R for SPCF, dispersion coefﬁcient for
SPCF was estimated by using the values of R estimated in step 1. These estimated

dispersion coefﬁcients were used in all the nonequilibrium model applications and were

135

not estimated by curve ﬁtting. Dispersion coefﬁcients so obtained for the three soils were
consistent with their respective mechanical characteristics. For Plume-A sand (97.6%

sand), Kalkaska-A (91% sand) and SPCF (78% sand), the dispersion coefﬁcient ranged

between 1.494-12.336 cmZ/hr, 1.493-5.666 cmz/hr and 0.423-1.672 cmZ/hr respectively.

. . . . . . 2
Disperswn coefﬁcrents also correlated well With the pore-water veloc1ty WIth R values

of 0.974, 0.916 and 0.981 for Plume-A sand, Kalkaska-A and SPCF respectively.

136

Table 5-3: Retardation factors and the dispersion coefﬁcients with 95% conﬁdence
intervals

 

 

 

 

 

 

 

 

 

 

, Normalized Retardation Dispersion Correlation
Soil Velocrty pulse time, factor coefﬁcient D coefﬁcient
(cm/hr) T R 2 2
(cm /hr) R
18.34 2.10 0.9704 5.6664 0.994
(:1: 0.10) (:1 1.1052)
12.84 2.00 0.9896 4.9734 0.996
(d: 0.011) (t 0.7152)
KalkaSka'A 9.17 2.01 0.9782 4.014 0.984
(:h 0.022) (:1: 1.098)
3.67 2.53 1.006 1.4934 0.992
(:1: 0.014) (a: 0.261)
15.79 2.00 1.083 1.6728 0.998
(4. 0.005) ($01968)
11.06 1.84 1.139 1.0662 0.997
(:t 0.007) (i0.1602)
SPCF 7.90 2.00 1.182 0.78 0.997
$0.005) (20.090)
3.16 1.99 1.282 0.4236 0.958
(10.030) (20.201)
17.18 2.00 0.9945 12.336 0.998
(:1: 0.009) (a: 1.032)
12.03 2.00 1.008 7.626 0.995
Plume-A (:1: 0.012) (:1: 0.846)
sand 8.59 2.00 1.007 6.69 0.994
(a; 0.014) (:1: 0.870)
3.44 1.97 1.021 1.494 0.982
4:1: 0.019) (:t 0.4026)

 

 

 

 

137

 

 

 

 

C/c0

 

 

 

 

 

 

Pore volumes

Figure 5-4: Tritiated water BTCs for Kalkaska-A. Circles represent the experimental data
and solid lines are simulations using the equilibrium model

1.5

 

 

 

 

C/Co

 

 

 

 

 

Pore volumes

Figure 5-5: Tritiated water BTCs for SPCF. Circles represent the experimental data and
solid lines are simulations using the equilibrium model

138

 

 

 

 

 

 

 

 

 

Pore volumes

Figure 5-6: Tritiated water BTCs for Plume-A sand. Circles represent the experimental
data and solid lines are simulations using the equilibrium model

Analysis of naphthalene BTCs. Mass balance calculations for naphthalene show a
recovery range between 73-97% for all the pulse-type experiments with one exception of
SPCF at a velocity of 14.9 cm/hr, which appears to be an experimental artifact. For the
two surface soils, i.e., Kalkaska-A and SPCF, the non-desorbable naphthalene mass was
unaffected by pore-water velocity i.e., 14.80-16.30 % for Kalkaska-A and 3.54-5.83 %
for SPCF (Table 5-4). However, an increase in non-desorbable naphthalene for Plume-A
sand (i.e., 6.33-18.31%) with a decrease in pore-water velocity (35.9 - 8.7 cm/hr) was

evident in our data.

139

Table 5-4: Column Peclet numbers and mass fractions for the three soils at different
velocities

 

C-- Peclet Desorbable Non-
mzt

 

 

 

. Velocity Recovery
S011 Number m
.1. .7.
33.82 13.843 48.3 83.7 16.3 86.26
Kalkaska-A 16.62 14.952 44.0 84.81 15.19 85.74
7.91 11.49 37.3 85.20 14.80 73.96
29.39 15.13 149.6 96.46 3.54 96.40
SPCF 14.94 20.00 147.0 95.27 4.73 101.52
7.55 11.87 141.8 94.17 5.83 78.43
35.92 14.83 20.4 93.67 6.33 88.39
Plume-A sand 17.01 14.69 21.1 91.54 8.46 81.45
8.68 8.062 22.4 81.69 18.31 93.80

 

 

The observed BTCs of naphthalene were analyzed using nonequilibrium models only
(i.e., the two-site model and four variations of the three-site model). Optimized
parameters for the two-site model were estimated under two different scenarios (1)

parameter ,6] and 601 were estimated with a ﬁxed R based on isotherm K d (designated as
Risothem ) and (2) R was also estimated as a ﬁtting parameter (designated as R 18,) in

addition to ,61 and (01. For all applications of the two-site and the three-site model, the

dispersion coefﬁcients estimated from the tritiated water BTCs were used. The optimized
parameters with 95% conﬁdence intervals and the correlation coefﬁcients are listed in

Table 5-5 to Table 5 7.

140

 

 

 

 

 

 

 

 

 

 

 

 

 

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146

Model comparisons

Comparison of R2 values listed in Tables 5-5 to 5-7 reveals that the two-site model with a

retardation factor based on the isotherm K d performed poorly in all cases compared to

other model formulations. The model failed to converge to a solution in case of SPCF at a

velocity of 29.4 cm/hour. The model performance appears to increase with a decrease in

SOM as R2 values ranged between 0.54 to 0.89 for Kalkaska-A, 0.87 to 0.96 for SPCF

and a constant value of 0.98 for plume-A sand respectively. In the second application of

the two-site model, in which, we estimated R in addition to ,61 and a), , a signiﬁcant

improvement in the model performance was observed for Kalkaska-A with R2 values

ranging between 0.90-0.96. For the other two soils, the model ﬁts improved compared to

the preceding case, however, the resulting K d values (i.e., 10.22-16.24 for Kalkaska—A
and 6.75-6.87 for SPCF) are signiﬁcantly higher than the respective isotherm K d which is

not expected as the batch environment is more conducive for partitioning to sorbed phase

than the columns.

Mathematical formulations based on the three-site model described naphthalene BTCs
better than the two-site model in general, as is evident by a comparison of the respective
correlation coefﬁcients. An important feature of the model ﬁts using different
formulations of the three-site model was identical BTCs by all four formulations (i.e.,
Model 1,2,3&4) for all nine cases (i.e., three soils and three velocities). The identical ﬁts

with Model 1 and Model 2 also support the idea that an increase in number of parameters

147

other than those necessary to describe the observational regimes does not result in an

improved description of the observed behavior.

Different formulations of the three-site model stated earlier are based on two
different conceptualizations of mass transfer mechanism between the sorbed phase and
the aqueous phase. In Models land 2, the solute ﬂux between the sorbed and aqueous
phases is described by a driving force formulation based on linear distribution coefﬁcient.
Models 3 and 4, on the other hand, treat sorption and desorption purely based on kinetics
and the solute ﬂux between the two phases is mathematically described by the kinetic rate
coefﬁcients for each domain. The choice of the appropriate model to describe the
naphthalene transport in soil columns requires a little more than merely a comparison of
goodness of ﬁt or the correlation coefﬁcients. Due to the fact, that Model 2 with an extra
rate coefﬁcient, resulted in BTCs that were identical to Model 1, it was not considered for

further analysis.

A comparison of Model 1 and Model 3 was done to explore the appropriateness

of the two different classes of models. In Model 1, the parameter K d and the fractions of
the solid matrix (i.e., feq , fneq and fnd) are time-dependent. The dependence of K d on

contact time is well established in our data as well as other sorption studies. In a separate
study involving desorption experiments with aged soils, we also found an evidence of the

dependence of the domain size on the soil-contaminant contact time. Another limitation

in K d -based models is the interdependence of the parameters in the dimensionless form

of the governing equations that results in a higher parameter uncertainty. Models 3 and 4,

which are based on time-independent parameters are free from these limitations. The

148

 

retardation factor R in Model 3 is based on K eq (i.e., the partitioning coefﬁcient for

equilibrium compartment) and not K d . Furthermore, the domain size in these models is

arbitrary and the solute ﬂux between the aqueous phase and each solid phase domain is
kinetically controlled. We did an analysis of sensitivity to initial parameter values for
Models 1 and 3 and found that the parameter uncertainty in Model 1 was as high as 136%

compared to less than 5% in Model 3.

The evidence, in aging experiments (data not reported here) suggests however, that soil-
contaminant contact time affects the size of nonequilibrium and non-desorption domains
only and the size of equilibrium domain remains more or less unaffected. This in mind, it
is fair to assume that nonequilibrium compartment and non-desorption compartments are
arranged in series rather than in parallel. Model 4 is a representation of this arrangement
of compartments in the solid matrix. Therefore, we contend that Model 4 is a conceptual

3-site model that includes the effects of aging and provides a superior description of

pulse-type injection experiments in soil columns.

149

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152

Effect of SOM on sorption nonequilibrium

Figure 5-10 represents the observed BTCs of naphthalene in the three soils at three

different ﬂow rates. A shiﬁ of the BTC to the right is evident at all ﬂow rates indicating

an enhanced retardation with an increase in the SOM. A direct correlation of K d with

SOM is well established for HOCs. In our experiments also, we observed an increase in

K d with an increase in SOM (Figure 5-3). The retardation factors calculated on the basis
of isotherm K d values correlate to SOM with an R2 of 0.994. If R values are obtained by

curve ﬁtting in columns, these should also correlate with SOM as the column properties
do not differ signiﬁcantly in terms of density and porosity (Table 5-1). The average

values for R for Kalkaska-A, SPCF and plume-A sand were 36.03, 25.03 and 4.64
respectively using Model l, which correlates wellwith SOM (R2 = 0.963). Our ﬁndings
are also consistent with those of (Maraqa, 1995) who found an increase in R for Benzene
and DMP in soils with different SOM.

Nonequilibrium is generally considered to exit if the BTCs exhibit a non-
gaussian/asyrnmetric shape. The asymmetrical nature of BTCs is an evidence of a rate-
limited mass transfer in a fraction of the soil matrix. Since ,6, is deﬁned as the ﬁaction of
retardation caused by instantaneous sorption sites, a higher value of ,6] means that either

the sorption sites are more readily accessible or it is easier for the compound to
access/react with the sorption sites (Maraqa, 1995). No difference was observed

in ,61 values for Kalkaska-A and SPCF. The ,61 values for Kalkaska-A ranged between

0.56-0.65 while for SPCF the range was 0.56-0.61 suggesting no correlation with SOM.

153

 

Plume-A sand with the least amount of organic content showed ,61 values between 0.40
and 0.45. The variation in the values of ,6] in the three soils is not as signiﬁcant as the

differences in SOM. This was also not true for plume-A sand that showed lower

,6] values and resultantly lesser number of instantaneous sorption sites. A similar trend

was also observed by Maraqa (1995) who reported that the instantaneous sorption sites
were not well correlated with SOM, although in the author’s case, the three soils
employed differed in SOM but were similar in texture and origin (i.e., all soils were
aquifer material).

Inspection of Tables 5-5 to 5-7 indicates that for all model applications of the three-site
model (except Model 1 which is based on a net mass transfer rate coefﬁcient), values of

a1 and a2 for Kalkaska-A are lower than those of SPCF for a given ﬂow rate. This

suggests a strong correlation between SOM and the degree of nonequilibrium. In
general, the sorption and desorption rate coefﬁcients for SPCF are 2.5-4 times higher
than Kalkaska—A, with almost double SOM as compared to SPCF. This is consistent with
the results from our batch sorption/desorption rate studies and those of Park (2000) but
contradicts the ﬁndings of Maraqa (1995) who reported no change in desorption rate
coefﬁcients of benzene and DMP in soils with different SOM. This may be due to a
difference in the origin of soils. In our work, Kalkaska-A and SPCF are surface soils
while those used by Maraqa (1995) are all of an aquifer origin. It is also important to note

the differences in 613 values that are higher for Kalkaska-A than SPCF indicating a faster

rate of mass transfer to the non-desorption compartment. Mass transfer coefﬁcient values
for Plume—A sand fall between the values of SPCF and Kalkaska-A, which although, is

difﬁcult to explain based on SOM correlation alone, it is an indication that in aquifer

154

material, the predominant sorption mechanism may be other than partitioning to SOM.

This aspect however, requires further investigation.

155

 

 

Concentration (pg/L)

 

 

 

I I ' I o Plum-Am
0.2ml/m1n , SPCF

1 11111

 

 

 

1

11111111 1 1 1111111

1

  

 

 

 

1 ‘ i .. 1 1
100 500 1M 1500 2WD 2500 3000 3500
T1me(mindes)
1043 T l . l l
in 0.1 ml/mln .

 

 
  
 

 

 

 

   

3
3
c: 1
3 :
E .
1:
§ 3 '5
3 u 3
r '1
Q l
10‘ 1 1 1 1
0 1 2000 3000 4000 5000 6000
Tume(minutes)
10‘: 1 I 1 l :
:13 0.05 ml/min ;
.. 1» :
d 3 O
310E 1.
E . f
'a _ .
g 1 1,. .
§ 102. I. ' .. ':
O : ' 2 :
0 1- 3
1 1 1 1

 

 

 

4000 6000 8000 10000 12000
Time (minutes)

Figure 5-10: The effect of SOM on transport of naphthalene

156

 

 

Effect of pore-water velocity on nonequilibrium
Observed BTCs of naphthalene at three different pore-water velocities are presented in
Figure 5-11. A reduction in the peak concentration was observed for Kalkaska-A and

plume-A sand at the lowest ﬂow rate, while for SPCF no signiﬁcant change in the peak

concentrations is apparent. Based on its dimensionless form, the parameter A in the two-

site and the three-site models is independent of pore-water velocity, therefore, should be

velocity invariant. As a result the ﬁ'action of equilibrium sites ( feq) and rate-limited sites

( fneq ) should also be independent of velocity. Several investigators have reported

conﬂicting results with regard to a correlation of the fraction of the rate-limited sites with
velocity. For example, Kookana et al. (1993) suggested a correlation between the rate-
limited site fractions and velocity. On the contrary, Brusseau et al. (1991) and Maraqa et
al. (1999) found no correlation between both entities in their work. Schawarzenbach and
Westall (1981) suggest that the fraction of rate-limited sites is likely to be a function of
velocity due to a difference in the sorption reaction time if the nonequilibrium due to a

predominant chemical interaction exists. The dependence of K d on soil-contaminant

contact time, in our data and many other studies, supports the assertion of

Schawarzenbach and Westall (1981). K d is likely to increase with an increase in the
residence time at low pore-water velocities, will affect the magnitude of ,6. and hence
feq. However, in another study involving desorption experiments with differentially

aged soils (data not reported here), we found that an increase in soil-naphthalene contact
time affects the distribution of naphthalene in nonequilibrium and non-desorption

domains and that the ﬁaction of equilibrium sites ( qu) remains more or less unaffected.

157

Inspection of Tables 5-5 to 5-7 reveals that the estimated feq values for Kalkaska-A,

SPCF and plume-A sand (estimated using Model 1) vary slightly with pore-water
velocity but fail to reveal a consistent trend. The fraction of contaminant mass partitioned
to rate-limited and non-desorption compartments, however, is likely to be time-dependent
and is likely to increase at low velocities as a result of a longer residence time as
supported in many studies. For example, Connaughten et al. (1993) argue that an increase
in the exposure time would increase the contaminant mass in the rate-limited
compartment. Similarly, Lee et al. (2002) reported that the efﬂuent breakthrough curves
at low pore-water velocities had a greater degree of nonequilibrium. With evidences from
previous studies and our data ﬁ'om desorption experiments involving differentially aged
soils, lack of a consistent trend in the fraction of nonequilibrium and non-desorption sites
with a change in pore-water velocity, is counter intuitive. A probable cause might be the
range of velocities employed resulting in the residence times, that are insigniﬁcant
compared to the soil contact time needed to cause an observable variation in the

distribution of contaminant in different domains.

The presence of a third site fraction (i.e., a non-desorbable fraction) will result in

a reduction in feq , f neq or both and subsequently the lower ,6 values. Some researchers

have also found an evidence of a ﬁnite-sized desorption-resistant domain. For example,
Kan et al. (1997) conducted batch adsorption-desorption experiments on natural and
surrogate sediments involving multiple adsorption-desorption steps, and concluded a
ﬁnite compartment size for the irreversible fraction on natural sediments as well as
surrogate solids. The authors also concluded that the amount in irreversibly sorbed

compartment increased linearly with the number of adsorption steps until its maximum

158

 

capacity is reached, after which, it becomes reversible. If that is true, then the size of
irreversible compartment will depend on the contact time, which is function of pore-

water velocity.

An increase in the degree of nonequilibrium with an increase in the exposure time
also suggests that a fraction of the rate-limited compartment turns into a desorption-
resistant compartment. This is explained by the presence of residual amounts of
naphthalene in the ﬁeld samples used in some studies even 6-8 months after their removal
ﬁ'om the source (Connaughten et al., 1993). There is also evidence that desorption is
much slower in aged soils as compared to freshly contaminated soils. For example,
Pignatello (1990a) studied the slowly reversible or non-labile fraction of non-polar

halogenated hydrocarbons on soils and observed that the non-labile fraction increased

non-linearly with incubation time and applied concentration. The functional form of ml in

the two-site and the three-site model suggests its dependence on pore-water velocity,

however, the net desorption rate coefﬁcient a1 is independent of the velocity. The same is

also true for al, a2 and 513 in all variations of the three-site model. A strong correlation
exists for all rate coefﬁcients in our experiments with the pore-water velocity in all
formulations of the three-site model. Although, inconsistent with expectations of a
constant rate coefﬁcient being able to explain the BTCs at all velocities, an increase in
the rate coefﬁcients with an increase in the pore-water velocity have previously been
noted in some studies e. g., (Ball and Roberts, 1991; Brusseau et al., 1991; Maraqa, 1995).
This dependence of a is viewed to be caused by an increase in the K d in ﬁrst two cases,
however Maraqa (1995) related this to a time-averaged nature of the mass transfer
coefﬁcient. In our case, the dependence of K d on the pore-water velocity is not

159

 

 

established i.e., the estimated retardation factor R doesnot exhibit any consistent increase

with a decrease in pore-water velocity.

160

 

0.08 .

 

 

 

 

I ' I ' '

o 33.0 cmlh
1. KalkaSKa'A 0 10.0 mm; -

. A 7.9 cmlhr
0.00 L .
- f0, .
9° 0 04 - y _,

o 3

0.02 '-

    

 

 

1 1
20 40 60 80 100 120 140

 

 

 

 

 

Pore volume
0.16 . . , 4
SP CF 0 29.4 ethr
0 O 14.9 cmlhr -
A 7.6 cmlhr
0.12 ~ x -

C/C0

0.08- .1
- .‘ X .
0...- 5 _
:.

 

 

 

 

 

20 4o 00 00 100
Pore volume
0'8 ' ' ' 009mm
0 . f
Plume-A sand . 17.0“”...
: g A 0.7 emu"
0.0 - 0, -
c, 5
9 0.4- A d
o

 

 

 

16 20 26
Pore volume

Figure 5-1 1: The effect of pore-water velocity on transport of naphthalene

161

 

5.5 Conclusions

Based on the experimental evidence, we conclude that the extent of irreversible sorption
is unaffected by the pore-water velocity. Out of the two surface soils, the soil with a high
SOM had a higher percentage of non-desorbable naphthalene mass (i.e., 14.80-16.3% for
Kalkaska-A compared to 3.54-5.83% for SPCF). However, the non-desorbable mass in
both soils was unaffected by the pore-water velocity. For Plume-A sand, the non-
desorbable naphthalene mass appeared to increase with a reduction in pore-water
velocity. The variation in pore—water velocity did not affect the different fractions of soil
matrix (i.e., equilibrium, rate-limited and non-desorption fraction) and the parameters a)
for the range of pore-water velocities employed in this study. The same may not,
however, be true for extremely low pore-water velocities resulting in residence times that
are orders of magnitude higher. SOM, on the other hand, had a more pronounced effect,
as the wvalues for Kalkaska—A (1 .168-1 .574) were consistently lower than those for

SPCF (1.753-2.538) for all BTCs.

Our results also indicate that, the three-site model better describes the breakthrough
of naphthalene than the two-site model for all nine cases (i.e., three soils at three different
velocities). However, all variants of the three-site model resulted in identical ﬁts to the
observed naphthalene BTCs, which indicates, that an increase in the number of model
parameters to enhance the description of the observed BTCs is not justiﬁed. We also
suggest that a mathematical formulation that accounts for a shift of the contaminant from

the equilibrium domain to the non—desorption domain and utilizes time-independent

162

 

 

parameters, may be preferred over formulations based on the linear sorption distribution

coefﬁcient.

163

 

 

5.6 References

Ahn, I.S., Lion, L.W. and Shuler, M.L., 1999. Validation of a hybrid "two-site gamma"
model for naphthalene desorption kinetics. Environmental Science & Technology,
33(18): 3241-3248.

Ball, WP. and Roberts, P.V., 1991. Long-term sorption of halogenated organic chemicals
by aquifer material .2. Intra—particle diffusion. Environmental Science &
Technology, 25(7): 1237-1249.

Brusseau, M.L., Larsen, T. and Christensen, TH, 1991. Rate-limited sorption and
nonequilibrium transport of organic chemicals in low organic-carbon aquifer
materials. Water Resources Research, 27(6): 1137-1145.

Connaughten, D.F., Stedinger, J .R., Lion, L.W. and Schuler, M.L., 1993. Description of
time-varying desorption kinetics: Release of naphthalene from contaminated soils.
Environmental Science & Technology, 27(12): 2397-2403.

Comelissen, G., Rigterink, H., Ferdinandy, M.M.A. and Van Noort, P.C.M., 1998a.
Rapidly desorbing fractions of PAHs in contaminated sediments as a predictor of

the extent of bioremediation. Environmental Science & Technology, 32(7): 966-
970.

Comelissen, G., Van Noort, P.C.M. and Govers, H.A.J., 1998b. Mechanism of slow
desorption of organic compounds from sediments: A study using model sorbents.
Environmental Science & Technology, 32(20): 3124-3131.

Comelissen, G., Van Noort, P.C.M., Parsons, J .R. and Govers, H.A.J., 1997. Temperature
dependence of slow adsorption and desorption kinetics of organic compounds in
sediments. Environmental Science & Technology, 31(2): 454-460.

Johnson, M., Keinath, T. and Weber, W.J., 2001. A distributed reactivity model for
sorption by soils and sediments. 14. Characterization and modeling of
phenanthrene desorption rates. Environmental Science & Technology, 35(8):
2734—2740.

Kan, A.T., Fu, G., Hunter, M.A. and Tomson, M.B., 1997. Irreversible adsorption of
naphthalene and tetrachlorobiphenyl to Lula and surrogate sediments.
Environmental Science & Technology, 31(8): 2176-2185.

Kookana, R.S., Schuller, RD. and Aylmore, L.A.G., 1993. Simulation of simazine
transport through soil columns using time-dependent sorption data measured
under flow conditions. Journal of Contaminant Hydrology, 14(2): 93-115.

Lee, J .H., Hundal, L.S., Horton, R. and Thompson, M.L., 2002. Sorption and transport
behavior of naphthalene in an aggregated soil. Journal of Environmental Quality,
31(5): 1716-1721.

164

 

Lele, S.K., 1992. Compact ﬁnite difference schemes with spectral-like resolution. Journal
of Computational Physics, 103: 16-42.

Maraqa, M.A., 1995. Transport of dissolved volatile organic compounds in the
unsaturated zone. Ph.D. Thesis, Michigan State University, East Lansing, 154 pp.

Maraqa, M.A., Wallace, RB. and Voice, T.C., 1999. Effects of residence time and degree
of water saturation on sorption nonequilibrium parameters. Journal of
Contaminant Hydrology, 36(1-2): 53-72.

Maraqa, M.A., Zhao, X., Wallace, RB. and Voice, T.C., 1998. Retardation coefﬁcients
of nonionic organic compounds determined by batch and column techniques. Soil
Science Society of America Journal, 62(1): 142-152.

Nkedikizza, P. et al., 1983. Modeling tritium and chloride-36 transport through an
aggregated oxisol. Water Resources Research, 19(3): 691-700.

Park, J .H., 2000. Bioavailability of sorbed organic contaminants. Ph.D. Thesis, Michigan
State University, East Lansing, 155 pp.

Park, J .H., Feng, Y.C., Ji, P.S., Voice, T.C. and Boyd, S.A., 2003. Assessment of
bioavailability of soil-sorbed atrazine. Applied and Environmental Microbiology,
69(6): 3288-3298.

Park, J .H., Zhao, X.D. and Voice, T.C., 2001. Biodegradation of non-desorbable
naphthalene in soils. Environmental Science & Technology, 35(13): 2734-2740.

Park, J .H., Zhao, X.D. and Voice, T.C., 2002. Development of a kinetic basis for
bioavailability of sorbed naphthalene in soil slurries. Water Research, 36(6):
1620-1628.

Pi gnatello, J .J ., 1990a. Slowly reversible sorption of aliphatic halocarbons in soils .2.
Mechanistic aspects. Environmental Toxicology and Chemistry, 9(9): 1117-1126.

Pi gnatello, J .J ., 1990b. Slowly reversible sorption of aliphatic halocarbons in soils. 1.
Formation of residual fractions. Environmental Toxicology and Chemistry, 9:
1107-1115.

Prata, F ., Lavorenti, A., Jan, V., Burauel, P. and Vereecken, H., 2003. Miscible
displacement, sorption and desorption of atrazine in a Brazilian oxisol. Vadose
Zone Journal, 2: 728-738.

Rao, P.S.C., Davidson, J .M., Jessup, RE. and Selim, H.M., 1979. Evaluation of
conceptual models for describing nonequilibrium adsorption-desorption of

pesticides during steady flow in soils. Soil Science Society of America Journal,
43(1): 22-28.

165

Schawarzenbach, RP. and Westall, J ., 1981. Transport of non-polar organic compounds

from surface water to groundwater. Laboratory sorption studies. Environmental
Science & Technology, 15(11): 1360-1367.

Seyfried, MS. and Rao, P.S.C., 1987. Solute transport in undisturbed columns of an
aggregated tropical soil - Preferential ﬂow effects. Soil Science Society of
America Journal, 51(6): 1434-1444.

Sharer, M., Park, J .H., Voice, T.C. and Boyd, S.A., 2003a. Aging effects on the sorption-
desorption characteristics of anthropogenic organic compounds in soil. Journal of
Environmental Quality, 32(4): 1385-1392.

Sharer, M., Park, J .H., Voice, T.C. and Boyd, S.A., 2003b. Time dependence of
chlorobenzene sorption/desorption by soils. Soil Science Society of America
Journal, 67(6): 1740-1745.

Toride, N., Leij, F.1- and Van Genuchten, M.T., 1999. The CXTF IT code for estimating
transport parameters from laboratory or ﬁeld tracer experiments. 137, US Salinity
Laboratory, Riverside, California. ,

Van Genuchten, M.T. and Wagenet, R.J., 1989. Two-site/two-region models for pesticide
transport and degradation: Theoretical development and analytical solutions. Soil
Science Society of America Journal, 53(5): 1303-1310.

Van Genuchten, M.T. and Wierenga, P.J., 1977. Mass transfer studies in sorbing porous
media .2. Experimental evaluation with tritium (JHZO). Soil Science Society of
America Journal, 41(2): 272-278.

Xing, B. and Pi gnatello, J .J ., 1996. Time-dependent isotherm shape of organic

compounds in soil organic matter: Implications for sorption mechanism.
Environmental Toxicology and Chemistry, 15: 1282-1288.

166

CHAPTER 6
DISSERTATION SUMMARY AND CONCLUSIONS

6.1 Dissertation summary

The objective of this research was to evaluate the importance of desorption
resistance in modeling desorption in soil columns which mimic subsurface systems.
Understanding the inﬂuence of desorption resistance on desorption kinetics and sorption
nonequilibrium is important for decision making in remediation. We selected naphthalene
as a representative HOC because it is included in EPA’s list of 16 priority PAHs, has a
high solubility, relatively moderate hydrophobicity and has been used by our research
group for bioavailability and phytoremediation studies in the past. Two surface soils with
different organic matter content and an aquifer sand with almost no organic content were

used as natural sorbents.

The ﬁrst objective focused at evaluating the differences in desorption kinetics in
batch and column systems. Our approach was based on the hypothesis, that if three
regimes of desorption behavior are observed in batch for a soil-contaminant combination,
the same should be observable in column desorption. We completed the sorption phase
(three days) in batch for both types of experiments to ensure identical conditions and
period of equilibration. This approach allowed an assessment that is free from those
discrepancies which normally exist between batch and column systems due to a non-
identical sorption environment. Batch and column desorption experiments were
augmented with the three-day sorption isotherms to determine the sorptive capacity of
each soil for the same period. In addition, the analysis of tritiated water breakthrough

curves with equilibrium model not only allowed an independent assessment of the

167

dispersive properties of each soil, but also enabled us to establish the conditions of
physical equilibrium. As a result, we could conclude that the rate limitations were due to
sorptive interaction of naphthalene with the soil matrix and not due to the entrapment of a

ﬁaction of water in the dead-end pores.

Based on experimental evidence of solvent extractable naphthalene in batch and
columns, we analyzed the naphthalene desorption in columns using the existing two-site
model and a proposed three-site model. The three-site model that is based on the
conceptualization of the soil matrix comprising three types of sorption sites rather than
two, could successfully describe naphthalene desorption from the soil columns. A lack of
non-desorption sites in the soil matrix in the two-site model resulted in greater-than-
actual mass elution. This makes the traditional approach of assuming the solid matrix
comprising of only two types of sorption sites questionable. A comparison of kinetic
parameters for batch and columns also provided evidence that longer difﬁision path
lengths due to packing of aggregate particles in soil columns limit the ability of the
contaminant to diffuse to the bulk solution. This results in a greater fraction of soil matrix

to behave as rate-limited sites in columns than those in the batch systems.

The second objective was aimed at evaluating the effects of soil-contaminant
contact time on the extent of irreversible sorption and desorption kinetics. Contact time is
known to have a considerable inﬂuence on the sorptive capacity of the sorbents,
distribution of contaminant in equilibrium, non-equilibrium and non-desorption
compartments and desorption rates in batch studies. The same, however, has not been
systematically addressed in column studies. We followed an approach, in which, the

column desorption experiments conducted under identical conditions (except the period

168

of equilibration in sorption phase) revealed the inﬂuence of contact time on the extent of
non-desorption and desorption kinetics. Results of these experiments were substantiated
by 2-month and 5-month sorption isotherms and serial dilution desorption experiments

involving differential equilibration period (i.e., between 10 minutes to 12 days).

Sorption isotherms revealed an increase in the distribution of naphthalene to the
sorbed phase for the two organic soils. Maximum increase in sorptive capacity was,
however, noted for the aquifer sand that showed a 100% increase from 3 days to 2
months and no increase thereafter. Another notable ﬁnding was a considerable increase in
solvent extractable naphthalene over time, with a corresponding decrease in the

desorbable naphthalene, for all three soils.

Based on our results we conclude that partitioning of HOCs to solid phase is a
time-dependent process and is likely to increase with soil contact times as we witness an
increase in the sorbed-phase concentration for all soils with an increase in contact time.
We also conclude, based on the comparison of the two-site and the three-site models, that
for contaminants exhibiting signiﬁcant non-desorption, a three-site model results in a
better description and the data are difﬁcult to reconcile with the dual domain approach.
We also suggest that our aging conceptual model that accounts for a shift of contaminant
from nonequilibrium domain to non-desorption domain is consistent with our
observations and explains the resistance to desorption exhibited by contaminants over

long-term contact times.

The third objective was aimed at exploring the impact of pore-water velocity on
the extent of non-desorption and sorption nonequilibrium. Pore-water velocity in column

experiments is a variable that is inversely related to column residence time, which in turn

169

 

is analogous to soil-contaminant contact time or “aging”. We approached this objective
by conducting pulse-type column experiments in the three soils at different pore-water
velocities ranging between 7-35 cm/hour. Tracer tests with tritiated water allowed an
independent characterization of each soil for dispersion that resulted in a reduction in the

number of ﬁtting parameters.

Theoretically, an increased soil-naphthalene contact time as a result of low pore-
water velocity should increase the distribution of contaminant to the non-desorption
domain, which we veriﬁed by solvent extractions in batch and column desorption studies.
The same was however, not apparent in our pulse-type experiments, as the naphthalene
mass extracted at the end of the column experiments failed to show a variation with the
pore-water velocity for the two organic soils. Furthermore, only a slight variation for
Plume-A sand was observed. The velocity range employed provided a column residence
time ranging between 7-68 hours for Kalkaska-A, 10-41 hours for SPCF and from 3-14
hours for the plume-A sand. Due to our inability to achieve longer residence times by
further reducing the velocity, we refrain from drawing conclusions about the invariance
of non-desorbable naphthalene with a change in pore-water velocity and hence the
residence time, as it is not supported by other experiments in batch involving a similar

range of equilibration times.

The observed time-concentration data for naphthalene was analyzed using a two-
site model and four variations of the three-site model. Two of these were based on the
driving force formulation using the linear distribution coefﬁcient while the other two
utilized kinetic rate coefﬁcients. Our results indicate that, the three-site model better

describes the breakthrough of naphthalene than the two-site model for all nine cases (i.e.,

170

three soils at three different velocities). However, all formulations based on the three-site

model resulted in identical ﬁts to the observed naphthalene BTCs, which indicates that

increase in the number of model parameters to enhance the description of the observed

BTCs is not justiﬁed. We also suggest that a formulation that accounts for the shift of

contaminant from equilibrium domain to non-desorption domain and utilizes time-

independent parameters may be preferred over the K, based formulations.

6.2 Recommendations

Our recommendations for future research based on the present study are as

follows:

No conclusive evidence so far exists for a correlation between the non-desorption
fraction of soil matrix and the chemical characteristics of the contaminant or
mechanical and compositional properties of the soil. In order to be able to develop
such correlations, systematic studies are required to build a comprehensive database

for the non-desorption of PAHs.

An evidence of change in the domain size with an increase in the contact time and
instantaneous mass distribution to the non-desorption domain in addition to
equilibrium domain, has been found in many studies. Current experimental methods
employed in sorption rate studies donot allow a differentiation in mass distribution to
each of these compartments. A ﬁrst order mass transfer does not adequately describe
the exact nature of non-linear increase in the size of the non-desorption domain.
Carefully planned batch experiments that allow realistic comparisons of the
differences in mass transfer in batch and column environments are needed to separate

these effects.

171

Employing a volatile compound like naphthalene involves mass balance problems
and data is sometimes difﬁcult to reconcile inspite of strong expectations.
Development of online detection methods, in which, the concentration of the eluting
solute could be monitored would solve the mass balance problems. Current online
detection methods, which normally rely on ﬂuorescence measurements, are not
appropriate for the soils that are high in organic content due to the possibility of

interferences.

172

Table A-1: Details of the independently measured and estimated parameters for the two-
site and the three-site models in column desorption experiments

 

 

 

Parameter Two-site model Three-site model
Batch sorption . . .
distribution coefﬁcient Measured by conducting independent isotherm on the three
K d (isotherm) 80115

 

Column distribution

K d (column) calculated by using the relation

 

coefﬁcient K d (column) K d = M2
msoilCO
Calculated using the relation Calculated using the relation
K . .
Retardation factor (R ) R = 1+ p—g‘j— wrth K; R = 1+ p—Igd-wrth Kd

(isotherm) and Kd (column)

 

(column)

 

Peclet number (Pe)

Calculated using the relation Pe = XDIJ

The dispersion coefﬁcient D was independently estimated
by ﬁtting the equilibrium model (Equation 3-7) to tritiated

water breakthrough.

 

 

Estimated by ﬁtting the two-

 

 

Estimated by ﬁtting the

 

 

ﬂ or ,6] site model (Equation 3-10 & three-site model (Equation
3'1 1) ‘0 “sew“ , _ 3-20 & 3-21) to observed
naphthalene desorptron usrng naphthalene desorption
a) 0rd); CXTFIT code using sequential quadratic
ro ammin S P
,62 Not applicable p gr g ( Q )
Fraction of equilibrium , , 0 + feq pK d
sites ( feq) Calculated usrng the relation ,6 or ,6] = W
F . Calculated using the relation
ractron of non- N 1' bl f K
desorption sites ( fnd) 0t app 1ca e ,62 = '0—"5—‘1

 

Fraction of
nonequilibrium sites

(In... 1

Calculated using the relation
feq '1' fneq = 1

Calculated using the relation
feq +fneq +fnd :1

 

 

Desorption rate
coefﬁcients (a or al)

 

Calculated using the relation
0) = a(1— ,81)LR
v

 

Calculated using the relation

w=-“—‘L3(I-ﬂl—&)
v R

 

173