use of geostatistical models in dnapl source zone architecture and dissolution profiles assessment...

THEMATIC ISSUE

Use of geostatistical models in DNAPL source zone architectureand dissolution profiles assessment in spatially variable aquifer

Aksara Putthividhya • Suwit Rodphai

Received: 17 July 2013 / Accepted: 31 July 2013 / Published online: 21 August 2013

� Springer-Verlag Berlin Heidelberg 2013

Abstract Following the accidental subsurface release of

dense nonaqueous phase liquids (DNAPLs), spatial vari-

ability of physical and chemical soil/contaminant proper-

ties can exert a controlling influence on infiltration

pathways and organic entrapment. DNAPL spreading,

fingering, and pooling typically result in source zones

characterized by irregular contaminated regions with

complex boundaries. Spatial variability in aquifer proper-

ties also influences subsequent DNAPL dissolution and

aqueous transport dynamics. An increasing number of

studies have investigated the effects of subsurface hetero-

geneity on the fate of DNAPL; however, previous work

was limited to the examination of the behavior of single-

component DNAPL in systems with simple and well-

defined aqueous and solid surface chemistry. From a

DNAPL remediation point of view, such an idealized

assumption will bring a large discrepancy between the

designs based on the model simulation and the reality. The

research undertaken in this study seeks to stochastically

explore the influence of spatially variable porous media on

DNAPL entrapment and dissolution profiles in the satu-

rated groundwater aquifer. A 3D, multicomponent, multi-

phase, compositional model, UTCHEM, was used to

simulate natural gradient water flooding processes in spa-

tially variable soils. Porosity was assumed to be uniform or

simulated using sequential Gaussian simulation (SGS) and

sequential indicator simulation (SIS). Soil permeability

was treated as a spatially random variable and modeled

independently of porosity, and a geostatistical method was

used to generate random distributions of soil permeability

using SGS and SIS (derived from measured grain size

distribution curves). Equally possible 3D ensembles of

aquifer realizations with spatially variable permeability

accounting of physical heterogeneity could be generated.

Tetrachloroethene (PCE) was selected as a DNAPL rep-

resentative as it was frequently discovered at many con-

taminated groundwater sites worldwide, including

Thailand. The randomly generated permeability fields were

incorporated into UTCHEM to simulate DNAPL source

zone architecture under 96-L hypothetical PCE spill in

heterogeneous media and stochastic analysis was con-

ducted based on the simulated results. Simulations revealed

considerable variations in the predicted PCE source zone

architecture with a similar degree of heterogeneity, and

complex initial PCE source zone distribution profoundly

affected PCE recovery time in heterogeneous media when

subject to natural gradient water flush. The necessary time

to lower PCE concentrations below Thai groundwater

quality standard ranged from 39 years to more than

55 years, suggesting that spatial variability of subsurface

formation significantly affected the dissolution behavior of

entrapped PCE. The temporal distributions of PCE satu-

ration were significantly altered owing to natural gradient

water flush. Therefore, soil heterogeneity is a critical factor

to design strategies for characterization and remediation of

DNAPL contaminated sites. The systematic and compre-

hensive design algorithm developed and described herein

perhaps serves as a template for application at other

DNAPL sites in Thailand.

Keywords DNAPL � PCE � Heterogeneity �Groundwater contamination � Geostatistics

A. Putthividhya (&) � S. Rodphai

Department of Water Resources Engineering, Faculty of

Engineering, Chulalongkorn University, Bangkok 10330,

Thailand

e-mail: [email protected]

123

Environ Earth Sci (2013) 70:1983–1991

DOI 10.1007/s12665-013-2713-4

Introduction

Dense nonaqueous phase liquids (DNAPLs) such as chlori-

nated solvents, PCB, oils, and creosotes, are groundwater

contaminants commonly encountered throughout the world,

including Thailand, as a result of their association with dry

cleaning, metal degreasing, manufactured gas production,

and wood preservation operations. Because DNAPLs are

denser than water, they are able to migrate through the

vadose or saturated zones under gravitational and capillary

forces and can become entrapped as residual source zone in

the subsurface environment. The presence of residual

DNAPL ganglia or pools within a formation is difficult to

detect yet can create a persistent dissolved contaminant

source, not readily amenable to effective remediation by

traditional pump-and-treat technologies. Nonuniformity and

heterogeneity in soil properties and DNAPL compositions

contribute to further spreading and irregular distributions of

entrapped DNAPL. DNAPL source zone architecture as well

as the variance and spatial correlation of the aquifer per-

meability field can strongly influence remedial performance

and mass flux. In most contaminated groundwater aquifer

remediation efforts, however, it is not economically feasible

or operationally practical to fully characterize the 3D dis-

tribution of physical and/or chemical parameters required to

predict groundwater flow and contaminant transport with

certainty, even in the most homogeneous aquifers.

The motivation for this research stemmed from the need

to better understand the consequences of aquifer hetero-

geneities in the context of a common hazardous waste spill

situation where limited site characterization data are

available, but comprehensive data that would lead to a

convincing and definitive decisions, such as the choice of

alternative geostatistical algorithms use to simulate the

distribution of aquifer properties are difficult to evaluate a

priori. The purpose of this study is to assess the influence of

aquifer physical heterogeneity on predicted DNAPL source

zone architecture for a hypothetical spill in a saturated

aquifer. For this, stochastic algorithms were applied to

model porosity and permeability distributions indepen-

dently within a single glacial depositional unit for which a

3D array of sediment particle size distributions are

repacked porosity measurements which were available

from Lemke et al. (2004). Subsequent transfer of multiple

stochastic realizations to numerical flow and transport

simulators permitted Monte Carlo evaluation of uncertainty

by computing DNAPL distribution statistics for equally

possible 3D ensembles of realizations generated using the

chosen geostatistical simulation algorithms. The flow and

entrapment behavior of a two-phase model used to generate

DNAPL source zones of varying configurations, following

a simulated single DNAPL release in a saturated aquifer,

were generated.

Materials and methods

Aquifer and DNAPL source zone characterization

The aquifer chosen as a study area is located in Oscoda,

Michigan, USA, at the site of a former dry cleaning

facility. The aquifer is composed of relatively homoge-

neous glacial outwash sands and is underlain by a thick

clay layer approximately 8 m below the ground surface. A

suspected DNAPL source zone was identified beneath the

building in an unconfined aquifer where a PCE plume

emanates and discharges into Lake Huron approximately

200 m down gradient (Drummond et al. 2000). Lemke

et al. (2004) obtained grain size distributions (GSDs) of the

aquifer materials based on 167 samples collected from 12

vertical and inclined cores (Fig. 1). Also, the arithmetic

mean porosity value of 0.36, measured in a subset of 162

repacked samples, was reported. Isotropic K (hydraulic

conductivity) values for all samples were estimated from

normalized GSDs using the Kozeny–Carman (K–C)

equation (Bear 1972):

K ¼ qwg

lw

k ¼ qwg

lw

d2m

180

/3

1� /ð Þ2

" #ð1Þ

dm is a representative grain size. Lemke et al. (2004)

reported the estimated K values were nonuniform, ranging

from 1 to 48 m/d. Constant fluid density and viscosity for

water at 15 �C were assumed. Good agreement between

measured and estimated K values was achieved assuming

value of 0.36 and using the normalized d10 value as the

representative grain size.

The next step involved five individual soil classifications

based on KMEANS clustering of the 167 measured grain

size distributions following the approach of Schad (1993)

(Figs. 1, 2).

Alternative geostatistical simulation approaches

Two classes of geostatistical simulation algorithms, para-

metric (SGS) and non-parametric (SIS) (Deutsch and

Journel 1998), were employed to generate 3D nonuniform

/ and K fields. Implementation of the sequential principle

under the Gaussian model is referred to as a SGS. SGS is

very fast and straightforward because the modeling of

Gaussian grain size cumulative distribution function (cdfs)

at each location requires the solution of only the (co)kri-

ging system at the location. SIS, on the other hand, is

considered the most widely used non-Gaussian simulation

technique. The indicator is employed to model the

sequence of conditional cdfs from which simulated values

are drawn. The indicator approach, unlike SGS, allows one

to account for class-specific patterns of spatial continuity

1984 Environ Earth Sci (2013) 70:1983–1991

123

Normalized distributions for 167 measured sand samples

0

10

20

30

40

50

60

70

80

90

100

850 600 425 300 212 150 106 75 53 38

Grain Size (um)

Per

cen

t F

iner

Th

anWeight average grain size distribution cdfs for five

KMEANS clustering of normalized cdfs

0

10

20

30

40

50

60

70

80

90

100

850 500 355 250 180 125 90 63 45 0

Grain Size (um)

Per

cen

t F

iner

by

Wei

gh

t

Class 1

Class 2

Class 3

Class 4

Class 5

soil class identified based on (a) (b)

Fig. 1 Grain Size Cumulative Distribution Function (cdf) plots:

a Normalized distributions for 167 measured sand samples; dark line

represents the 167 samples average (Lemke et al. 2004); b Newly

developed weighted average grain size distribution for five soil

classes identified based on KMEANS clustering of normalized cdfs

0

5

10

15

20

25

0.29 0.30 0.31 0.32 0.33 0.34 0.35 0.36 0.37 0.38 0.39

Porosity

Fre

qu

ency

0

5

10

15

20

25

30

1 5 9 13 17 21 25 29 33 37 41 45

K(m/d)

0.28

0.3

0.32

0.34

0.36

0.38

0.4

0 10 20 30 40 50 60

Fre

qu

ency

K(m/d)

Po

rosi

ty

(a)

(b) (c)

Fig. 2 Porosity and Hydraulic Conductivity Data: a Histogram of

measured porosity values for repacked samples; b Histogram of

K values estimated directly from measured grain size distribution d10

values using the Kozeny–Carman Relationship (Eq. 1) with a uniform

porosity of 0.36; c Cross plot of / and K values for 167 core samples.

Scattering suggests a weak correlation between variables. The R2

value for a linear regression is 0.09

Table 1 Alternative spatial

variability modelsStochastic Description Min/mean/max Standard deviation

SGS Sequential gaussian simulation 0.75/17.39/47.62 7.31

SIS Sequential indicator simulation 4.88/17.32/32.81 6.57

Environ Earth Sci (2013) 70:1983–1991 1985

123

through different indicator semivariogram models. Another

advantage of indicator-based simulation techniques is the

flexibility to corporate the information coded under the

format of local prior probability (Goovaerts 1999). Each

simulation method can generate multiple equally probable

realizations of nonuniform heterogeneous aquifer proper-

ties, each honoring the properties’ statistical spatial struc-

ture and probability distribution (Srivastava 1994).

Spatial variability of / and K

Two stochastic algorithms were used to model the 3D

spatial distribution of k (Table 1). Both sets of stochastic

K distribution were generated over a 10 9 15 9 8 m grid

centered on the suspected DNAPL source zone at the site.

Fifty realizations were simulated in each set using

10 9 15 9 80 cm grid increment, commensurate with

scale of support for grain size distribution measurement.

In the first set of stochastic realizations, SGS was used.

Simulated d10 grain size distribution values were

subsequently converted to K using K–C relationship (based

on Eq. 1). Experimental semivariograms for d10 values

(Fig. 3) were fit to a zonal anisotropy model with a nugget

effect of 0.35 estimated from both vertical and horizontal

semivariograms, and a spherical semivariogram model as

shown in Eq. 2:

c hð Þ ¼ c � 1:5h

a

� �� 0:5

h

a

� �3 !

if h� a

c hð Þ ¼ c if h� a

ð2Þ

c(h) is the semivariogram value for a lag distance, h; c is a

positive contribution to the variance, and a is the direction-

dependent range (Table 2).

The results in Fig. 3 are normalized to the variance to

generate a sill of 1.0. V exp is vertical experimental; Hexp is

horizontal experimental; Vmod is vertical modeled; Hmod is

horizontal modeled.

Experimental vertical and horizontal semivariograms for

porosity measurements (Fig. 4) were fit with a zonal

anisotropy model, including a nugget effect of 0.45 esti-

mated from the vertical, horizontal semivariogram and an

exponential semivariogram model:

cðhÞ ¼ c � 1:0� exp � 3h

a

� �� ð3Þ

c(h) is the semivariogram value for a lag distance, h; c is a

positive contribution to the variance, and a is the direction-

dependent range (Table 2). The plot in Fig. 4 is normalized

to the variance to generate a sill of 1.0.

Fig. 3 Experimental and modeled normal score semivariograms for measured grain size distribution based on d10 data

Table 2 Variogram parameters for SGS geostatistical modeling of

porosity and representative grain diameter

Model Orientation Nugget Variance Range

(m)

Integral

scale (m)

SGS porosity Horizontal 0.45 1.10 5.00 1.67

SGS porosity Vertical 0.45 0.96 3.50 1.16

SGS d10 Horizontal 0.35 1.12 6.00 2.00

SGS d10 Vertical 0.35 1.00 2.30 0.76


123

Geostatistical ensemble sets

Four ensemble sets (shown in Table 3) were generated to

investigate the influence of aquifer physical heterogeneity

on DNAPL infiltration. The first ensemble, namely the

reference set, assumed uniform porosity of 0.36 and gen-

erated K by SGS from 3D distributions of d10 values using

K–C relationship. Three additional simulation sets (i.e., Set

1, Set 2, and Set 3) were simultaneously created to explore

any possible differences that could occur in the aquifer

structure, and DNAPL distributions accounted for vari-

ability in porosity and permeability under saturated aquifer

conditions.

Sets 1 and 2 (composed of 50 realizations) were iden-

tical based on the spatial distribution of d10 generated by

SIS algorithm; d10 values were randomly assigned from the

histogram corresponding to each of the five indicator

classes. Instead of assuming uniform porosity like Set 1,

the porosity was created by employing SGS algorithm in

Set 2. K and k values were calculated as a function of both

simulated porosity and d10 values at each grid node.

Realizations in Set 3 diverged from those in Sets 1 and 2 as

the porosity was simulated using SIS algorithm from the

histogram corresponding to each of the five indicator

classes.

Simulated DNAPL release

A release of PCE (i.e., DNAPL representative used in this

study) was simulated using UTCHEM in 2D profiles

extracted from 3D geostatistical realizations (as described

in the last section). In each realization, 96 L of PCE was

released over an area of 0.3 m2 from the top layer of the

domain, at a constant flux of 2,400 mL/day for the period

of 400 days. An additional 330 days were simultaneously

simulated to allow for organic liquid infiltration and

redistribution without further release of PCE into the sys-

tem. All constant pressure and saturated boundaries along

the domain sides and no-flow condition at the bottom

Fig. 4 Experimental and modeled normal score semivariograms for measured porosity data

Table 3 Variable treatment of

porosity (/) and intrinsic

permeability (k) parameters

among the four alternative

simulation sets

Set Reference set Set 1 Set 2 Set 3

Porosity (/) Uniform Uniform Random (SGS) Random (SIS)

k SGS k = f(d10) SIS k = f(d10) SIS k = f(d10,/) SIS k = f(d10,/)

Realizations 50 50 50 50

Table 4 UTCHEM simulation input parameters

Variable Water PCE

Density kg/m3 999.032 1623.0

Viscosity (kg/m s) 0.001139 0.00089

Compressibility (1/Pa) 4.4 9 10-10 0


123

boundary were assumed. This infiltration rate employed in

the simulations was assured to not result in any significant

pooling of PCE across the lateral as well as the vertical

profile boundaries. Table 4 shows a list of UTCHEM

simulation input parameters.

Results and discussions

Aquifer parameter distributions

Generated K and porosity values from the two geostatisti-

cal models were compared. Figures 5 and 6 depict aquifer

property distributions for 3D and extracted 2D represen-

tative profiles, respectively, from each of the four simula-

tion sets. The results in Figs. 5 and 6 demonstrated that

simulated / in Sets 2 and 3 varied significantly, perhaps

contributed to the nugget effect (i.e., 0.40 for SGS and

0.012–0.224 in SIS). Stratification in the / profile using

SIS algorithm was observed while a strong random com-

ponent of / was evidenced from SGS algorithm. This

might also be contributed to the large nugget effect of 0.40

in the case of SGS simulation.

With a high degree of stratification observed in the

indicator class simulations (Set 3; Figs. 5, 6), profiles of d10

generated in the same way (i.e., Sets 1, 2, and 3) were

totally diverged from those generated directly using SGS

(i.e., reference set) as demonstrated in Figs. 5 and 6. Lemke

et al. (2004) employed six individual indicator classes and

reported that the d10 profiles generated based on six indi-

vidual indicator classes were visually similar to those gen-

erated directly using SGS. This discrepancy was perhaps

because dividing the porous media into six classes resulted

in the decomposition of the essentially monomodal non-

uniform d10 pdf into subsidiary distributions with smaller

overlapping probability distribution ranges associated with

individual classes, resulting in a more spatial randomization

of d10 values of each subsidiary set, compared to only five

individual indicator classes used in this work.

The uniform / assumption (i.e., reference set and Set 1)

resulted in a direct correlation between d10 and K values in

Figs. 5 and 6. Independent simulation of a variable

porosity field was expected to contribute to greater spatial

disorder within K fields estimated using K–C equation in

Sets 2 and 3 in Figs. 5 and 6. Again, a higher degree of

stratification of K fields was evidenced in Set 3 resulted

from SIS algorithm employed to generate both d10 and /compared to the representative simulation in Set 2 where a

strong random component of / was evidenced from SGS

algorithm.

The variations in aquifer architecture among the four

alternative geostatistical simulation approaches

Fig. 5 Comparison of aquifer

parameter 3D geostatistical

simulations


123

demonstrated in this work suggested that the choice

between SGS and SIS might be of a serious concern for

characterizing aquifer parameter spatial variability as well

as the predicted waste infiltration in a statistically

homogeneous (i.e., physically heterogeneous) but nonuni-

form sand aquifer.

Simulated DNAPL distributions

Ensemble statistics for PCE saturation, vertical infiltration,

and lateral spreading are presented in Table 5 for all sim-

ulation sets. Figure 7 illustrates simulated PCE saturation

for four representative realizations from each of the four

sets. PCE saturation was scaled from 0.0008 to 0.2295 to

enhance the depiction of low saturation variability. Maxi-

mum PCE saturations ranged from 0.0007 to 0.23

(Table 5). Reference set simulations exhibited a smaller

variance in maximum PCE saturation, an overall decrease

in vertical penetration (z), and a decreased degree of lateral

spreading (x). Set 3 simulations, on the other hand, dem-

onstrated a high variance in maximum PCE saturations, an

overall decrease in vertical penetration, and an increased

degree of lateral spreading among the four sets as depicted

in Fig. 7. This observation was consistent with the lesser

degree of stratification in K field of the reference set before

the PCE spill was simulated. Analysis of the high

Fig. 6 Comparison of aquifer

parameter distributions in

representative 2D profiles

extracted from 3D geostatistical

simulation

Table 5 Ensemble statistics for PCE distribution metrics

Property Set Minimum Mean Max Standard

deviation

Concentration (VF) Ra 0.0026 0.0833 0.2295 0.0552

Concentration (VF) 1 0.0013 0.0786 0.2063 0.0474



zm Ra 0.35 2.51 4.55 0.97

zm 1 0.55 2.25 3.65 0.85

zm 2 0.95 2.17 3.55 0.84

zm 3 0.95 2.13 3.65 0.85

xm Ra 2.33 – 7.67 0.79

xm 1 2.33 – 8.33 0.72

xm 2 2.33 – 9.00 0.71

xm 3 2.33 – 8.33 0.72

a Refers to the reference set and VF refer to the volume faction unit


123

saturation cells in the reference set output files suggested

that apparent pooling in these simulations was caused by

entry pressure contrast as well as the contrast in k values.

Figure 8a–c demonstrated the PCE source zone archi-

tecture obtained from simulation Sets 1, 2, and 3 employ-

ing the similar SIS algorithm based on the properties listed

Fig. 7 Representative PCE saturation distributions for each simulation set

Fig. 8 Representative DNAPL

saturation distributions in the

same set


123

in Table 3. Figure 8a–c looked quite similar based on

visualization alone. A box plot was employed as a tool to

statistically analyze any possible variations in PCE

entrapment characteristics among the three simulations.

The results indicated that the PCE source zone distributions

obtained from Sets 1 and 3 based on simulated k using SIS

algorithm seemed to possess a normal distribution. On the

other hand, PCE source zone distribution obtained from Set

2 obviously skewed to the left, suggesting significant PCE

pooling occurred somewhere in the numerical domain

during the spill.

From four sets of simulations (i.e., 200 realizations

total), the maximum PCE infiltration depth ranged from 3.5

to 4.5 m while the lateral spreading (assume the mid-point

injection) ranged from 2.33 to 9.00 m from left to right of

the injection point. The maximum time to lower the con-

taminant concentrations below Thai groundwater quality

standard obtained from this work ranged from 42 to

55 years, suggesting that the heterogeneity of surface

chemistry significantly influenced dissolution behavior of

entrapped DNAPLs.

Conclusions

This study examined the influenced of stochastic model of

spatially variable hydraulic conductivity on predicted

infiltration of PCE in nonuniform aquifer porous matrix.

This ability of stochastic simulation to create realizations to

compare PCE infiltration distributions using four approa-

ches considered permeability and porosity. SIS approach

provided a greater variability in the distributions of

apparent PCE saturation observed in Sets 2 and 3 compared

to the results obtained from Set 1 due to additional inde-

pendent porosity variation incorporated into Sets 2 and 3.

Although simulation sets 1, 2, and 3 shared identical d10

distributions, their porosity values were different. All sets

of generated SIS markedly exhibited variable PCE

spreading and pooling behavior, which was mainly attrib-

uted to the assignment of porosity.

Although all simulations were qualitatively consistent with

the DNAPL source zone conceptual model, the procedure

employed to generate the PCE distribution as well as aquifer

structure in Set 3 perhaps better represented the real aquifer

structure based on the two reasons. Firstly, although both SGS

and SIS approaches were able to replicate the overall d10

histogram (as compared to the real experimental data), SIS

algorithm did capture more information from the original data

set. The spatial variability in grain size distribution profile, in

particular, was accounted for in the distribution of the geo-

statistical indicator class in SIS algorithm. Secondly, the

random porosity assumption generated by SIS could directly

influence the entrapment of PCE.

The results from these numerical simulations addition-

ally demonstrated that independent variation in more than

one aquifer parameter could increase the variance of

numerical model performance. For the heterogeneous

aquifer, the options between parametric and non-paramet-

ric (i.e., SGS vs. SIS) approaches were used to model the

spatial distribution of d10 and porosity; and then later

converted to hydraulic conductivity seemed to have a

major influence on predicted DNAPL distribution in the

saturated aquifer system. The porosity choice (i.e., between

uniform and spatially variable porosity), meanwhile, had a

relatively small effect. This contrast in predicted DNAPL

source zone distribution behavior was expected to lead to

variation in downstream contaminant mass flux as well as

the remediation schemes appropriate for aquifer restora-

tion. Significant findings from this work suggested that

DNAPL recovery was highly realization specific and the

couple influence of textural and chemical heterogeneity

could have observable effects on the dissolution of DNAPL

at the larger scale.

Acknowledgments The authors thank Dr. Lawrence D. Lemke for

gathering all necessary information regarding the site in Oscoda,

Michigan, USA. Also, the authors thank Water Resources System

Research Unit at Chulalongkorn University (CU_WRSRU) for par-

tially providing some computational facility to Suwit Rodphai to

conduct this work.

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