Lumping Analysis for Sorption of Neutral Organic
Compounds in Mixtures to Simulated Aquifer Sorbents
Jin Chul Joo1; Charles D. Shackelford, M.ASCE2; and Kenneth F. Reardon3
Abstract: The concept of using lumping analysis to reduce the complexity associated with the sorption of 12 neutral organic compounds
(NOCs) comprising complex mixtures to simulated aquifer sorbents was evaluated. The sorbates covered a wide range of octanol–water
partitioning coefficients, K ow (i.e., 0:24 ≤ log K ow ≤ 4:23), and the sorbents included different types of mineral surfaces and humic acid–
mineral complexes with different fractions of organic carbon, f oc (i.e., 0:006% ≤ f oc ≤ 0:221%). Both a priori lumping criteria (i.e., the
aqueous activity coefficient at saturation γsat
w , and the organic carbon partitioning coefficient, K oc ) and experimentally derived lumping criteria
(i.e., Freundlich sorption parameters) were evaluated as potential lumping criteria. The results indicated that the sorption behavior of the
12 NOCs contained in mixtures could be approximated reasonably well by lumping them into a fewer number of pseudocompounds (four
to six) with similar sorption behaviors based on Freundlich sorption parameters, and that both γsat
w and K oc could be used as viable a priori
lumping criteria. However, the number and compositions of the pseudocompounds were a complex function of the hydrophobicity (i.e., γsat
w
and K oc ) of the NOCs and varied as a function of the type of mineral surface (e.g., uncoated, α-FeOOH-coated, and Al2 O3 -coated sands) and
the f oc of the sorbent. DOI: 10.1061/(ASCE)EE.1943-7870.0000498. © 2012 American Society of Civil Engineers.
CE Database subject headings: Organic carbon; Organic compounds; Organic matter; Pollutants; Soil pollution; Sorption; Subsurface
environment.
Author keywords: Lumping analysis; Mixtures; Neutral organic compounds; Pseudocompounds; Simulated aquifer sorbent; Sorption.
Introduction
Natural geosorbents are comprised of different structural and
physicochemical components that are known to interact differently
with neutral organic compounds (NOCs) in terms of binding energies and the rates of associated sorption and desorption (Karickhoff
1984; Weber et al. 1992; Xing et al. 1996; Luthy et al. 1997; Chiou
and Kile 1998; Allen-King et al. 2002; Pignatello et al. 2006;
Chefetz and Xing 2009). These different components of geosorbents include amorphous versus condensed soil organic matter
(SOM) with different aliphatic and aromatic moieties and highsurface-area carbonaceous materials, macroporous versus mesoporous and microporous mineral matrices, and interlayer surfaces of
swelling clays. In addition, distinct sorption reactivities for NOCs
result, in part, from the fractionation and variations in the structural
and chemical properties of SOM and the mineral surface blockage
by SOM in SOM–mineral complexes (Karickhoff 1984; Feng et al.
2006; Joo et al. 2008a). Thus, the overall sorption of NOCs by
natural geosorbents is affected by the sum of the contributions
1
Senior Researcher, Korea Institute of Construction Technology, 2311,
Daehwa-Dong, Ilsanseo-Gu, Goyang-Si, Gyeonggi-Do, 411-712, Republic
of Korea; formerly, Graduate student, Colorado State Univ., Fort Collins,
CO 80523-1372.
2
Professor, Dept. of Civil and Environmental Engineering, 1372
Campus Delivery, Colorado State Univ., Fort Collins, CO 80523-1372
(corresponding author). E-mail: [email protected]
3
Professor, Dept. of Chemical and Biological Engineering, 1370
Campus Delivery, Colorado State Univ., Fort Collins, CO 80523-1370.
Note. This manuscript was submitted on June 3, 2010; approved on
September 19, 2011; published online on September 21, 2011. Discussion
period open until October 1, 2012; separate discussions must be submitted
for individual papers. This paper is part of the Journal of Environmental
Engineering, Vol. 138, No. 5, May 1, 2012. ©ASCE, ISSN 0733-9372/
2012/5-552–561/$25.00.
of several active components in heterogeneously combined
geosorbents.
The majority of the research that focuses on contaminant sorption of NOCs to geosorbents has been conducted using singlesorbate systems to reveal sorption mechanisms for each component
and to reconcile models for heterogeneous geosorbents. However,
subsurface contamination typically involves mixtures of compounds (e.g., fuel hydrocarbons, chlorinated solvents, pesticides,
and landfill leachates). Although the entire system of differential
equations with interaction parameters describing the migration
of the individual NOCs contained in mixtures can be solved simultaneously in space and time, such a detailed analysis becomes increasingly more complicated and less computationally efficient as
the number of compounds contained in the mixtures increases.
A potentially more practical alternative to such a detailed analysis is the so-called “lumping analysis,” whereby a greater number of
individual components in a system (e.g., chemical species, variables, and reactions) are grouped into a fewer number of pseudocomponents (e.g., pseudocompounds and pseudoreactions) that
approximates the behavior of the system, such that the overall
complexity of the system is reduced. Such lumping analyses
have been applied widely in the oil refining industry to provide
tractable approximations to stoichiometry and kinetics of complex hydrocarbon mixtures (Jaffe et al. 2005). Lumping analyses
have also been applied in describing multicomponent adsorption
of organic compound mixtures to granular activated carbon
(Calligaris and Tien 1982), sorption of heavy metals to humic substances (Yu et al. 1996), biodegradation reactions in wastewater
treatment (Li et al. 1996), toxicology of organic compound mixtures (Dennison et al. 2004), partitioning of secondary organic
aerosol mixtures (Bian and Bowman 2005), and regulation of protein synthesis (Maria 2006).
On the basis of the aforementioned applications of lumping
analyses to various complex systems, the concept of using lumping
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analysis to describe the sorption behavior of NOCs contained in
mixtures to low-surface-area, coarse-grained aquifer materials
coated with humic acid (HA) was evaluated in this study. This
evaluation was based on answering the following questions:
(1) What are the primary grouping criteria that determine the
pseudocompounds?
(2) How are the number and compositions of pseudocompounds
determined?
(3) How are the number and compositions of pseudocompounds
affected by mixture compositions and heterogeneous subsurface environments?
(4) How are the relevant sorption parameters of pseudocompound
assigned?
(5) Can the sorption parameters for a pseudocompound be estimated a priori from the sorption parameters of the individual
sorbates comprising the pseudocompound?
In an attempt to answer these questions, the specific objectives
of this study were to evaluate the potential use of lumping analysis
for describing the sorption behavior of NOCs contained in mixtures
to various types of aquifer sorbents, to evaluate the influence of
different types of mineral surfaces and HA–mineral complexes with
different organic carbon content (f oc ) on the number and compositions of any resulting pseudocompounds, and to develop both
experimental and theoretical lumping schemes converting mixtures
of NOCs into a fewer number of pseudocompounds for various
types of aquifer sorbents. To achieve these objectives, the sorption
behaviors of 12 NOCs covering a wide range of properties were
evaluated using batch equilibrium sorption tests (BESTs) and a
variety of simulated aquifer sorbents under abiotic conditions.
ionization detector (FID). The qualitative identifications and quantitative determination of each sorbate are described in Joo (2007).
To reduce the uncertainty originating from both measurement and
systematic errors, the precision, accuracy, and method detection
limits were evaluated before each analysis.
Batch Sorption Methodology
The detailed procedures for performing the batch equilibrium sorption tests are described by Joo et al. (2008a). The stock solutions of
the NOC mixtures with different initial concentrations were diluted
at concentrations ranging over three orders of magnitude (see Joo
2007). All of the BESTs for each sorbent and each NOC both
individually and within mixtures were performed in triplicate at
a minimum.
Sorption Model
The Freundlich sorption model was used to describe and interpret
all sorption isotherm data as follows:
C s ¼ K f C ne
ð1Þ
where C s (μmol∕kg) and C e (μmol∕L) = equilibrium solid-phase
and aqueous-phase concentrations, respectively; the parameter
K f [ðμmol∕kgÞ∕ðμmol∕LÞn ] = Freundlich unit sorption capacity;
and n (dimensionless) = joint measure of the relative magnitude
and diversity of sorption energies (Weber et al. 1992). The sorption
parameters for NOCs to various sorbents were obtained by nonlinear regression using TableCurve 2-D v. 5.01 (SYSTAT Software).
Lumping Analysis
Materials and Methods
Simulated Aquifer Sorbents
The detailed preparation procedures and characterization of
HA-coated sands and metal (hydr)oxide-coated sands have been
described by Joo et al. (2008a, b). Overall, four different types
of simulated aquifer sorbents were used in this study: uncoated
sand, α-FeOOH-coated sand (FES), Al2 O3 -coated sand (ALS),
and HA-coated sand with different f oc (HAS). The physicochemical properties of the simulated aquifer sorbents are summarized in
Joo et al. (2008a, b).
Mixtures of Neutral Organic Compounds
The mixtures of NOCs evaluated in this study were selected on the
basis of both detection frequency in contaminated groundwater and a
priority list of hazardous substances [Agency for Toxic Substances
and Disease Registry (ATSDR)]. The NOCs were comprised of 12
compounds, six of which were considered to be polar (hydrophilic),
with polar functional groups (i.e., oxygen atom), and six of which
were considered to be nonpolar (hydrophobic), with no polar functional groups. The six polar compounds included acetone (ACE),
2-butanone (2-BUT), 2-hexanone (2-HEX), phenol (PHE), p-cresol
(p-CRE), and 2,4-dimethyl phenol (2,4-DMP). The six nonpolar
compounds included benzene (BZ), toluene (TOL), m-xylene
(m-XYL), chlorobenzene (CB), 1,4-dichlorobenzene (1,4-DCB),
and 1,2,4-trichlorobenzene (1,2,4-TCB). The selected physicochemical properties of the 12 NOCs are summarized in Joo (2007).
Analytical Method
The concentration of each sorbate contained in mixtures was measured using gas chromatography (GC) (HP 5890 II; HewlettPackard) with a mass selective detector (MSD) and a flame
Cluster analysis was adopted in this study for the lumping analysis. Cluster analysis is a technique for grouping individual or multiple objects into clusters, such that objects in the same cluster tend
to be more similar to each other than to objects in different clusters
(Hair et al. 1998). A schematic diagram illustrating the lumping
procedures for sorption of the NOCs contained in mixtures to simulated aquifer sorbents is shown in Fig. 1.
To assess the similarity among the 12 NOCs considered in this
study with respect to their sorption behaviors, sorption parameters
(i.e., K f and n) for each NOC contained in mixtures were plotted as
the primary grouping criteria. The similarity in the sorption behaviors among the 12 NOCs was measured according to the Euclidean
distance between each pair of sorption parameters for the NOCs
[i.e., after standardizing the sorption parameters for the 12 NOCs
to possess equal weight with respect to distance measurement
(see Joo 2007)]. The standardization of each sorption parameter
was performed with the STANDARD (STD) option in PROC
CLUSTER (SAS 9.1, SAS Institute) before cluster analysis began.
After the Euclidean distance between the NOCs was determined,
the most appropriate clustering algorithm to maximize the differences between clusters relative to the variation within the clusters
was determined. In this regard, preliminary results suggested that
Ward’s method (Ward 1963) provided the most accurate solutions
among the cluster algorithms. Ward’s method was performed by
specifying METHOD ¼ WARD in PROC CLUSTER.
Although several criteria and guidelines have been suggested to
provide a single cluster solution, no standard or objective selection
procedure exists (Hair et al. 1998). Generally, the cluster procedure
should be terminated when the increase in error by lumping exceeds a specific threshold value. The methods for determining an
appropriate number of clusters were based on values of statistical
parameters, including the semipartial R2 (SPRS), cubic clustering
criterion (CCC), pseudo F (PSF), and pseudo t 2 (PST2). The SPRS
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Fig. 1. Flow chart illustrating the lumping procedure for the sorption of neutral organic compounds in complex mixtures to simulated aquifer sorbents
represents the decrease in the proportion of variance as a result
of joining two clusters to form the current cluster, whereas the
CCC approximates the expected R2 under the uniform null
hypothesis. The PSF measures the separation among all the clusters
at the current level, whereas the PST2 measures the separation between the two clusters most recently joined (Milligan and Cooper
1985). In this study, a consensus between the PSF and PST2
statistics was used as the indicator of the proper number of clusters
(i.e., local peaks of the PSF combined with a small value of PST2
and a larger PST2 for the next cluster lumping). The PSF and PST2
statistics were readily obtained from the PSEUDO option in
PROC CLUSTER.
Considering the overall uncertainties originating from the sorption data in terms of measurement error and Freundlich sorption
parameters in terms of model fitting, cluster analysis also was
performed with 20% of sorption parameters (i.e., K f and n)
for each NOC contained in mixtures to ensure that the cluster analysis was not affected by the uncertainties. After evaluating all possible clusters, the best number of clusters and cluster components
was determined on the basis of statistics criteria and thermodynamic sorption background (e.g., enthalpy and entropy changes
companying sorption) because sorption of NOCs generally occurs
as the result of two types of thermodynamic forces (i.e., enthalpyrelated and entropy-related forces). Enthalpy-related forces relate
to the molecular-scale interactions associated with sorption
(e.g., van der Waals forces, hydrogen bonding, ligand exchange,
and dipole–dipole interactions), whereas entropy-related forces
represent the increasing disorder resulting from the disappearance
of the highly structured solvation envelope around the NOCs in the
aqueous phase.
Results and Discussion
Sorption to Hydrophilic Mineral Surfaces
Hierarchical Cluster Analysis
As illustrated in Fig. 2, the semipartial R2 values (proportions of
variance by lumping two clusters) increased slightly as the number
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pseudocompounds, as based on the semipartial R2 values, were appropriate for the hydrophilic mineral surfaces. Furthermore, the
same cluster results were obtained using 20% of sorption parameters in all cases, indicating that the cluster analysis was not
affected by the overall uncertainties originating from both sorption
data and model fitting. Consequently, four pseudocompounds
could be used to approximate the sorption behavior of the 12 individual NOCs contained in mixtures to the hydrophilic mineral
surfaces evaluated in this study.
Effects of Mixture Compositions and Type of Mineral
Surfaces
As summarized in Joo (2007), the effects of mixture compositions
and type of mineral surfaces on the sorption of nonpolar NOCs to
hydrophilic mineral surfaces were negligible. In contrast, the compositions of the pseudocompounds for polar NOCs were inconsistent among the individual tests, although none of the polar NOCs
contained in mixtures were associated with nonpolar NOCs within
the same pseudocompound. For example, PHE and 2-HEX were
lumped together into pseudocompound C in Tests 1 and 3, whereas
PHE and 2-HEX were lumped together or separately into pseudocompound C or D in other tests, depending on mixture compositions and type of mineral surfaces. These inconsistent lumping
schemes suggest that the effects of mixture compositions and type
of mineral surfaces on the sorption of polar NOCs to hydrophilic
mineral surfaces are significant.
The complex mixture and sorbent effects for the sorption of
polar NOCs to hydrophilic mineral surfaces can be attributed to
the mutual competition for hydrophilic specific sorption sites, such
as H-bonding (Chiou and Kile 1998). In this scenario, the change
in sorption behavior for a given polar NOC likely was a result of
the existence of other polar NOCs contained in mixtures. The presence and magnitude of mutual competition among polar NOCs
were also subject to variation, depending on the mixture compositions (i.e., concentration and polarity of polar NOCs) and the type
of mineral surfaces (i.e., specific volume of vicinal water region
and availability of hydrophilic specific sorption sites). Thus, these
inconsistent lumping schemes for the polar NOCs reflect inaccurate
lumping systems.
Fig. 2. Dendrogram for the sorption of 12 NOCs in mixtures: (a) to
uncoated sand; (b) to α-FeOOH-coated sand; and (c) to Al2 O3 -coated
sand
of clusters was reduced to four, whereas a relatively large increase
occurred when the number of clusters was reduced from four to
three. Thus, the sorption behavior of the 12 NOCs contained in
mixtures could be described without incurring significant error
by four pseudocompounds for the three hydrophilic mineral
surfaces.
Also, the behavior of the PSF and PST2 in the appropriate number of clusters is illustrated in Joo (2007). A clear consensus between the PSF and PST2 statistics confirmed that the same four
Evaluation of the Potential for a Priori Lumping Criterion
Although the sorption of NOCs to hydrophilic mineral surfaces
can be affected by factors other than the hydrophobicity of the
NOCs in an aqueous solution, the free energy of the sorption of
nonpolar NOCs to hydrophilic mineral surfaces has been shown
to be inversely related to the free energy of the aqueous dissolution
of nonpolar NOCs (Mader et al. 1997). Accordingly, compositions
of pseudocompounds are shown as a function of the logarithm of
the aqueous activity coefficient at saturation, log γsat
w , for each
NOC in Fig. 3.
As shown in Fig. 3, the sorption behavior of the 12 individual
NOCs contained in mixtures to hydrophilic mineral surfaces can be
sat
lumped based on log γsat
w . This result indicates that γw can be used
as a possible a priori lumping criterion for the sorption of NOC
mixtures to hydrophilic mineral surfaces, although the relative contributions of different forces (i.e., hydrophobic versus hydrophilic)
to the overall sorption may differ for different mixture compositions
and types of mineral surfaces.
Effectiveness of Pseudocompound Sorption to Hydrophilic
Mineral Surfaces
After the compositions of the pseudocompounds were identified, the
effectiveness of the pseudocompounds for describing the sorption
behavior of the component compounds was evaluated. The evaluation included preparing pseudocompounds by dissolving only
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Logarithm of Aqueous Activity Coefficient, log γwsat
PS A
PS B
PS C
The resulting sorption of each component compound in each pseudocompound was compared to the 95% confidence intervals for the
associated best-fit Freundlich sorption model based on the sorption
of the pseudocompound, as illustrated in Fig. 4 for uncoated sand
[see Joo (2007) for results involving FES and ALS].
For all hydrophilic mineral surfaces, the sorption isotherms of
pseudocompounds A and B, which were comprised of only nonpolar NOCs, described the sorption behaviors of component compounds better than those of both pseudocompounds C and D, which
were comprised of only polar NOCs. Each pseudocompound also
exhibited substantially different sorption behavior in both sorption
capacity (K f ) and nonlinearity (n).
For example, pseudocompound A exhibited more sorption
capacity (i.e., 0:194 ≤ K f ≤ 0:246) and linearity (i.e., 0:981 ≤
n ≤ 1:02), whereas pseudocompound D exhibited less sorption
capacity (i.e., 0:086 ≤ K f ≤ 0:191) and nonlinearity (i.e., 0:627 ≤
n ≤ 0:708). The values of K f and n for all pseudocompounds were
within the ranges of those for the respective component compounds
(Joo 2007). These results indicate that each pseudocompound
was comprised of component compounds with similar sorption
capacities and nonlinearity. Consequently, the sorption behavior
of the 12 NOCs contained in mixtures to hydrophilic mineral surfaces was approximated reasonably well by a fewer number of
pseudocompounds.
PS D
6
1,2,4-TCB
1,4-DCB
m-XYL
CB
TOL
BZ
2,4-DMP
p -CRE
2-HEX
PHE
2-BUT
5
4
3
2
ACE
1
0
α −FeOOH
Uncoated
Al O
2 3
Type of Hydrophilic Mineral Surface
Fig. 3. Effect of the type of hydrophilic mineral surface on the number
and compositions of pseudocompounds as a function of the logarithm
of the aqueous activity coefficient at saturation
the component compounds belonging to those pseudocompounds
(at various concentrations). Sorption tests then were conducted using
the prepared pseudocompounds with each hydrophilic mineral surface. On the basis of the lumping analysis for species grouping, the
aqueous-phase and solid-phase concentrations of the pseudocompounds were calculated by the summation of the aqueous-phase
and solid-phase molar concentrations of the respective component
compounds at equilibrium in each batch bottle, respectively.
Pseudocompound Sorption Estimated from Single-Sorbate
Component Sorption
The Freundlich sorption parameters for the pseudocompounds
identified thus far were based on regressions of the summations
of the aqueous-phase and solid-phase molar concentrations of
40
15
10
30
PS B
CB
m-XYL
TOL
BZ
s
20
PS A
1,2,4-TCB
1,4-DCB
Amount Sorbed, C (µmol/kg)
s
Amount Sorbed, C (µmol/kg)
25
C =0.246C
s
1.00
e
2
(r =0.983)
5
20
C =0.243C
s
2
(r =0.984)
10
(b) Pseudocompound B
(a) Pseudocompound A
0
0
0
20
40
60
80
100
Equilibrium Concentration, C (µmol/L)
e
PS D
2-BUT
ACE
3
4
2
e
s
0.708
e
2
2
1
(d) Pseudocompound D
(c) Pseudocompound C
0
50
100
150
200
Equilibrium Concentration, C (µmol/L)
C =0.086C
(r =0.969)
s
Amount Sorbed, C (µmol/kg)
s
Amount Sorbed, C (µmol/kg)
4
PS C
0.851
2,4-DMP Cs=0.081Ce
p-CRE
2
(r =0.984)
PHE
2-HEX
6
0
0
50
100
150
200
Equilibrium Concentration, C (µmol/L)
e
10
8
0.956
e
0
0
20
40
60
80
100
Equilibrium Concentration, C (µmol/L)
e
Fig. 4. Sorption isotherms of individual pseudocompounds and respective component compounds for uncoated sand; dashed lines denote the
corresponding 95% confidence intervals for the associated best-fit Freundlich sorption model for the pseudocompounds
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the respective component compounds at equilibrium. However, an
alternative approach is to assign the Freundlich sorption parameters
of the pseudocompounds by using aqueous mole fraction-weighted
averages of single-sorbate Freundlich sorption parameters of
the component compounds belonging to each pseudocompound
(Calligaris and Tien 1982), that is, without conducting sorption
tests with each pseudocompound. Thus, the feasibility of this alternative approach was evaluated by comparing the Freundlich
sorption parameters on the basis of regression with those estimated
from aqueous mole fraction-weighted averages of single-sorbate
Freundlich sorption parameters of the component compounds.
The results of this comparison are summarized in Table 1 for uncoated sand [see Joo (2007) for results involving FES and ALS].
The comparison resulted in less than 8% difference in the
Freundlich sorption parameters for pseudocompounds A and B
to hydrophilic mineral surfaces, whereas the difference for pseudocompounds C and D ranged from 1.3 to 47%. This approach was
therefore not as applicable in the case of the pseudocompounds
comprised of only polar NOCs as it was for the pseudocompounds comprised of only nonpolar NOCs. This conclusion
is consistent with the presence of mutual competition among the
similar polar NOCs for hydrophilic specific sorption sites, such that
both sorption capacity and nonlinearity for the polar NOCs in
single-sorbate systems to the hydrophilic mineral surfaces were altered by the presence and the quantity of other polar NOCs within
the pseudocompounds.
Sorption to Humic Acid–Mineral Complexes
Hierarchical Cluster Analysis
The semipartial R2 values increased slightly until there were
four, five, and six clusters for HAS1 (f oc ¼ 0:051%), HAS2
(f oc ¼ 0:119%), and HAS3 (f oc ¼ 0:221%), respectively, followed
by a relatively large increase in the semipartial R2 for subsequent
numbers of clusters, as shown in Fig. 5. A clear consensus between
the PSF and PST2 statistics also indicated that four, five, or
six pseudocompounds were appropriate for HAS with different
f oc (Joo 2007). Furthermore, the same cluster results were obtained
using 20% of sorption parameters in all cases, suggesting that the
overall uncertainties originating from both sorption data and model
fitting do not need be considered in the lumping analysis. Thus,
the sorption behaviors of the 12 individual NOCs contained in
mixtures could be described more conveniently in the sorption
behaviors of four, five, and six pseudocompounds for HAS1,
HAS2, and HAS3, respectively.
Effects of Mixture Compositions and Fraction of Organic
Carbon (f oc )
Whereas the effect of mixture compositions on the sorption of nonpolar NOCs to each HAS was negligible, the effect as a result of the
fraction of organic carbon on the sorption of nonpolar NOCs was
significant (see Joo 2007). Because hydrophobic sorption of nonpolar NOCs to macromolecular HA is promoted by the reduced
entropy of the water comprising the solvation envelope around
the nonpolar NOCs (Karickhoff 1984; Allen-King et al. 2002), hydrophobic sorption increases as the NOCs become more hydrophobic and the f oc of the HAS increases. As a result, the compositions
of the pseudocompounds for the nonpolar NOCs was a complex
function of the hydrophobicity of NOCs and the f oc of HAS.
Although none of the polar NOCs were associated with nonpolar NOCs within the same pseudocompounds, the compositions
of the pseudocompounds for polar NOCs were inconsistent among
the individual tests involving HAS1 (Joo 2007). For example, PHE
in HAS1 was lumped into pseudocompound C in Tests 1, 3, and 5,
whereas PHE was lumped into pseudocompound D in other
tests, depending on the mixture compositions. These inconsistent
Table 1. Freundlich Sorption Parameters (K f and n) for Pseudocompounds versus Those Estimated from Single-Sorbate Component Compounds for
Uncoated Sands
Freundlich sorption parameters
Pseudocompounda
Pseudocompound
A
B
C
D
Individual
compound
components
K f ;ss
nss
K f ;p
np
K f ;p
np
K f ;p
np
K f ;ss ∕K f ;p
nss ∕np
1,2,4-TCB
1,4-DCB
Average
CB
m-XYL
TOL
BZ
Average
2,4-DMP
p-CRE
PHE
2-HEX
Average
2-BUT
ACE
Average
0.263
0.245
0.254
0.222
0.325
0.262
0.241
0.263
0.102
0.095
0.081
0.092
0.093
0.077
0.129
0.103
0.979
0.967
0.973
0.951
0.935
0.968
0.939
0.948
0.853
0.763
0.739
0.810
0.786
0.714
0.662
0.688
0.246
1.00
0.297
1.06
0.195
0.945
1.03
0.973
0.243
0.956
0.300
1.02
0.186
0.893
1.08
0.992
0.081
0.851
0.106
0.912
0.056
0.790
1.14
0.929
0.086
0.708
0.117
0.781
0.055
0.636
1.20
0.972
Single-sorbate
b
Actual values
Upper limit valuesc
Lower limit valuesd
Ratiose
a
Aqueous concentration ranges at equilibrium: 0:1μmol∕L ≤ Ce ≤ 200μmol∕L.
Aqueous concentration ranges at equilibrium: 0:1μmol∕L ≤ C e ≤ 150μmol∕L.
Upper limit of Freundlich sorption parameters based on the 95% confidence interval.
d
Lower limit of Freundlich sorption parameters based on the 95% confidence interval.
e
Based on average values for single sorbates and actual values for pseudocompounds.
b
c
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was therefore dependent on the mixture compositions (i.e., concentration and polarity of NOCs) and the types of sorbent (i.e., availability of hydrophilic specific sorption sites). Similar to the
hydrophilic mineral surfaces, complex mixture and sorbent effects
in the sorption of polar NOCs contained in mixtures to HA-mineral
complexes yielded approximately lumpable systems.
Logarithm of Organic Carbon Partitioning Coefficient, log Koc
Evaluation of the Potential for a Priori Lumping Criterion
Although the sorption of NOCs to HAS can be promoted by several
mechanisms, including both absorption (partitioning) and adsorption to HA domains and onto hydrophilic mineral surfaces, the
partitioning of NOCs contained in mixtures to HAS becomes an
increasingly dominating contribution to overall sorption when a
sufficient number of competing NOCs are present (Xing et al.
1996). Additionally, linear partitioning of NOCs to macromolecular HA, whereby the distribution coefficient (K d ) is equal to the
product of f oc and the organic carbon partitioning coefficient,
K oc (i.e., K d ¼ f oc K oc ), has been shown to be a major component
of sorption for sorbents with f oc > 0:1% (Karickhoff 1984;
Allen-King et al. 2002; Joo et al. 2008a). Accordingly, the compositions of the pseudocompounds based on different f oc values are
shown as a function of the logarithm of K oc for each NOC in Fig. 6.
As shown in Fig. 6, the sorption behavior of the 12 individual
NOCs contained in mixtures to HAS with different f oc can be
lumped on the basis of log K oc . As the f oc of HAS increased,
the NOCs with higher log K oc (≥ 1:96) became more distinguishable than those with lower log K oc (≤ 1:87) as a result of the greater
dependency of sorption on f oc with increasing K oc . In contrast, the
NOCs with lower values of log K oc (≤ 1:87) were not separated
into different pseudocompounds because of the lesser dependency
of sorption on f oc . Therefore, similar to γsat
w for sorption to hydrophilic mineral surfaces, K oc can be used as the possible a priori
lumping criterion for the sorption of NOC mixtures to HAS with
different f oc , although the relative contributions of different forces
(i.e., absorption versus adsorption to HA domains and adsorption
onto hydrophilic mineral surfaces) to the overall sorption may differ for different mixture compositions and f oc values of the sorbent.
Fig. 5. Dendrogram for the sorption of 12 NOCs contained in mixtures
to HA-coated sands: (a) HAS1 (f oc ¼ 0:051%); (b) HAS2 (f oc ¼
0:119%); and (c) HAS3 (f oc ¼ 0:221%)
lumping schemes suggest that the effect of mixture compositions
on the sorption of polar NOCs to HAS1 was not negligible. The
complex mixture effect for the sorption of PHE to HAS1 with lower
f oc values (i.e., 0.051%) can be attributed to mutual competition for
hydrophilic specific sorption sites of both mineral surfaces and HA.
In contrast, the compositions of the pseudocompounds for polar
NOCs to HAS2 and HAS3 were identical, regardless of the mixture
compositions and the f oc of the HAS (Joo 2007). The presence and
magnitude of competitive effects among the various polar NOCs
PS A
PS B
PS C
PS D
PS E
PS F
4
1,2,4-TCB
1,4-DCB
m-XYL
CB
TOL
BZ
2,4-DMP
p-CRE
2-HEX
PHE
2-BUT
ACE
3
2
1
0
-1
0
0.05
0.1
0.15
0.2
Fraction of Organic Carbon, f (%)
0.25
oc
Fig. 6. Effect of the fraction of organic carbon on the number and compositions of pseudocompounds as a function of the logarithm of the
organic carbon partitioning coefficient
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Effectiveness of Pseudocompound Sorption to Humic–Acid
Mineral Complexes
In the same manner as previously described for the hydrophilic
mineral surfaces, the compositions of the pseudocompounds were
identified, and sorption tests were conducted using the prepared
pseudocompounds with each HAS with different f oc . The resulting
sorption of each component compound in each pseudocompound
was compared to the 95% confidence intervals for the associated
best-fit Freundlich sorption model based on the sorption of the
pseudocompound, as illustrated in Fig. 7 for HAS3.
For each of the HAS, the sorption isotherms for the pseudocompounds comprised of only nonpolar NOCs described the sorption
behaviors of the individual compounds better than those of the
pseudocompounds comprised of only polar NOCs. The sorption
behavior of each pseudocompound was clearly distinct in both
sorption capacity (K f ) and nonlinearity (n). The values of K f
and n for all pseudocompounds were also within the ranges of
those for respective component compounds (Joo 2007). These results indicate that each pseudocompound contained component
compounds with relatively similar sorption capacities and nonlinearity. As a result, lumping by species grouping was feasible
for describing the sorption behaviors of the 12 NOCs contained
in mixtures to the low-surface-area, coarse-grained aquifer materials coated with HA.
Pseudocompound Sorption Estimated from Single-Sorbate
Component Sorption
The comparison of the Freundlich sorption parameters on the basis
of regression with those estimated from aqueous mole fractionweighted averages of single-sorbate component compounds
resulted in less than 12% difference in the Freundlich sorption
parameters for pseudocompounds comprised of nonpolar NOCs,
40
PS B
1,4-DCB
Amount Sorbed, C (µmol/kg)
PS A
1,2,4-TCB
30
s
60
s
Amount Sorbed, C (µmol/kg)
80
40
C =3.96C
s
20
0.929
e
2
(r =0.997)
20
C =1.53C
s
2
(r =0.994)
10
(a) Pseudocompound A
0
(b) Pseudocompound B
0
0
10
20
Equilibrium Concentration, C (µ mol/L)
e
20
s
40
Amount Sorbed, C (µmol/kg)
25
PS C
m-XYL
CB
s
Amount Sorbed, C (µmol/kg)
0
10
20
30
Equilibrium Concentration, C (µmol/L)
e
60
C =0.899C
20
s
0.928
e
2
(r =0.991)
PS D
TOL
BZ
15
10
C =0.346C
s
(r =0.987)
5
(d) Pseudocompound D
0
0
20
40
60
80
Equilibrium Concentration, C (µmol/L)
e
8
PS F
2-BUT
ACE
6
s
Amount Sorbed, C (µmol/kg)
PS E
2,4-DMP
p-CRE
PHE
2-HEX
s
Amount Sorbed, C (µmol/kg)
0
20
40
60
80
Equilibrium Concentration, C (µmol/L)
e
40
30
0.978
e
2
(c) Pseudocompound C
0
0.957
e
20
C =0.368C
s
10
0.857
e
2
(r =0.994)
4
C =0.208C
s
2
0
50
100
150
200
Equilibrium Concentration, C (µmol/L)
e
(r =0.995)
(f) Pseudocompound F
(e) Pseudocompound E
0
0.749
e
2
0
0
20
40
60
80
100
Equilibrium Concentration, C (µmol/L)
e
Fig. 7. Sorption isotherms of individual pseudocompounds and respective component compounds for HA-coated sand (HAS3; f oc ¼ 0:221%);
dashed lines denote the corresponding 95% confidence intervals for the associated best-fit Freundlich sorption model for the pseudocompounds
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Table 2. Freundlich Sorption Parameters (K f and n) for Pseudocompounds versus Those Estimated from Single-Sorbate Component Compounds for
HA-Coated Sand (HAS1; f oc ¼ 0:051%)
Freundlich sorption parameters
Pseudocompounda
Pseudocompound
A
B
C
D
Individual
compound
components
K f ;ss
nss
K f ;p
np
K f ;p
np
K f ;p
np
K f ;ss ∕K f ;p
nss
1,2,4-TCB
Average
DCB
CB
m-XYL
TOL
BZ
Average
2,4-DMP
p-CRE
PHE
2-HEX
Average
2-BUT
ACE
Average
0.958
0.958
0.363
0.266
0.295
0.264
0.268
0.291
0.174
0.075
0.093
0.061
0.101
0.138
0.165
0.152
1.01
1.01
1.06
0.979
1.01
0.981
0.948
0.996
0.797
0.813
0.766
0.812
0.797
0.578
0.610
0.594
0.932
0.997
1.04
1.06
0.822
0.933
1.03
1.01
0.330
0.964
0.388
1.02
0.272
0.908
0.882
1.03
0.069
0.872
0.085
0.963
0.053
0.781
1.46
0.914
0.142
0.661
0.199
0.777
0.085
0.545
1.07
0.898
Single-sorbate
b
Upper limit valuesc
Actual values
Lower limit valuesd
Ratiose
a
Aqueous concentration ranges at equilibrium: 0:1μmol∕L ≤ Ce ≤ 200μmol∕L.
Aqueous concentration ranges at equilibrium: 0:1μmol∕L ≤ C e ≤ 150μmol∕L.
c
Upper limit of Freundlich sorption parameters based on the 95% confidence interval.
d
Lower limit of Freundlich sorption parameters based on the 95% confidence interval.
e
Based on average values for single sorbates and actual values for pseudocompounds.
b
as summarized in Table 2 for HAS1 [see Joo (2007) for results
involving HAS2 and HAS3].
However, the difference for the pseudocompounds comprised
of polar NOCs ranged from 2.4 to 51%. In contrast to pseudocompounds comprised of nonpolar NOCs, the Freundlich sorption
parameters of pseudocompounds comprised of polar NOCs were
not accurately represented by using aqueous mole fractionweighted averages of single-sorbate Freundlich sorption parameters of component compounds. Because both sorption capacity
(K f ) and nonlinearity (n) for polar NOCs in single-sorbate systems
to HAS were altered by the presence and the quantity of other polar
NOCs within the pseudocompounds, sorption of polar NOCs contained in mixtures to HAS was affected to a greater extent by the
variation in concentrations and compositions of the NOCs contained in mixtures. Consequently, the assignment of the Freundlich
sorption parameters of pseudocompounds using aqueous mole
fraction-weighted averages of single-sorbate Freundlich sorption
parameters of component compounds led to inaccuracy in the sorption prediction for the polar NOCs.
create pseudocompounds with Freundlich sorption parameters
that were simply estimated from the aqueous mole fractionweighted averages of the single-sorbate Freundlich sorption parameters for the component compounds was successful for some
mixtures. However, the number and compositions of pseudocompounds were found to be a complex function of the hydrophobicity (i.e., γsat
w and K oc ) of the NOCs and varied as a function of
the type of mineral surfaces (e.g., uncoated, α-FeOOH-coated,
and Al2 O3 -coated) and the f oc for sorbent. Considering that
the lumping analysis for the sorption of complex mixtures to
heterogeneously combined geosorbents represents a compromise
between simplicity and accuracy, further study is warranted to determine the optimum number and compositions of pseudocompounds for certain mixtures by using both structure-oriented
lumping (e.g., organic molecules represented as vectors of structural increments) and stochastic optimization solution techniques
(e.g., the tabu search algorithm).
Conclusions
Financial support for this study was provided by the Science to
Achieve Results (STAR) Program U.S. Environmental Protection
Agency (EPA) (STAR R-82935501-0). The opinions expressed
in this paper are solely those of the authors and are not necessarily
consistent with the policies or opinions of the EPA.
The concept of using lumping analysis to reduce the complexity
associated with the sorption of 12 neutral organic compounds
(NOCs) comprising complex mixtures to simulated aquifer sorbents was evaluated using experimentally derived lumping criteria
(i.e., Freundlich sorption parameters) and a priori lumping
criteria (γsat
w and K oc ). The lumping results indicated that the sorption of 12 NOCs could be approximated reasonably well by a
fewer number of pseudocompounds (four to six) by species grouping based on Freundlich sorption parameters. Also, the use of a
priori lumping criteria (γsat
w and K oc ) for the individual NOCs to
Acknowledgments
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