Uncertainty Analysis of Groundwater Remediation Outcomes...

ANSCSE16 Chiang Mai University, Thailand

May 23-25, 2012

Uncertainty Analysis of Groundwater Remediation Outcomes

Using Stochastic Modeling Method

S. Taweelap and S. SaentonC

Department of Geological Sciences, Faculty of Science, Chiang Mai University,

239 Huaykaew Rd., Tambon Suthep, Mueang District, Chiang Mai 50200 Thailand CE-mail: [email protected]; Fax: +66 (0) 5394 3444; Tel. +66 (0) 5394 3418 ext. 1073

ABSTRACT Movement of groundwater contaminants from source to receptors has normally been

predicted using groundwater flow and solute transport models. These models are based on

a conventional deterministic approach. In such approach, a particular model produces an

output from a set of input parameters which considers neither the uncertainty of the model

parameters nor the uncertainty of the hydraulic conductivity field. The uncertainty of the

hydraulic conductivity field in the model normally arises from the interpolation of

hydrogeologic units based on a very limited set of well-log data. If site’s heterogeneity is

high, the model prediction of flow and transport will likely be less accurate. Therefore, in

order to assess the uncertainty of remediation outcomes due to aquifer’s heterogeneity, a

stochastic modeling approach should be used in developing flow and transport models [3].

In this approach, a number of 3-D hydrogeologic models based on randomly and spatially

variable hydraulic conductivities (K) will be generated from well-log data; each model is

called realization. Then, each realization is used to setup groundwater flow, transport, and

remediation models. The outcome of all stochastically generated models will then be

statistically analyzed and assessed for remediation outcome uncertainties [1,5]. In this

research, 3-D groundwater flow and solute transport of chemicals in aquifers were

simulated using MODFLOW [4] and RT3D [2]. Then stochastic modeling method was

applied to evaluate the uncertainty of in-situ bioremediation outcome for treating aquifers

that has been contaminated with chlorinated solvents. The results showed that envelop of

remediation efficiency, represented in terms of reduced concentrations emanating from the

source zone, can be satisfactorily quantified.

Keywords: Hydrogeology, Stochastic, Groundwater Modeling, Remediation.

1. INTRODUCTION

Accidental release and improper handle of volatile chlorinated solvents are recognized as one

of the most widespread causes of groundwater contamination by organic compounds. In

subsurface soil-water environments, these contaminants often persist as a separate phase due to

their generally low aqueous solubility (called, non-aqueous phase liquids or NAPLs). NAPLs that

are denser than water (called DNAPL), when spilled, can migrate through the unsaturated zone

and continue on a downward migration through the water table under the influence of gravity into

the saturated zone below. Chlorinated solvents such as trichloroethene (TCE) and

tetrachloroethene (PCE) used in industrial and manufacturing operations are a common form of

this contaminant. As groundwater flows through the DNAPL entrapment zone, its constituents

slowly dissolves into the aqueous phase resulting in a dissolved contaminant plume downstream

of the source zone. This can cause pollution of local water supplies and have detrimental effects

on both human health and the ecological environment. Consequently, attention has been focused

on the identification and characterization of the source zone and the plume as well as the

assessment of risk associated with remedial measures.


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In order to maximize the chance of success in remediating DNAPL site, accurate site

characterization and comprehensive mathematical modeling of groundwater flow and

contaminant transport must be conducted. However the accuracy remediation modeling have been

the subject of an intense research effort in recent years. At any DNAPL sites there is considerable

uncertainty regarding the contaminant source and the dissolved plume behavior. When source and

plume remediation efforts are implemented, there is uncertainty in the effectiveness of these

actions, and in the relationship between source mass removal, and source discharge. Conventional

deterministic modeling approach does not reflect the uncertainties that occur in the groundwater

contaminant fate-and-transport and remediation process. A deterministic modeling approach takes

a single value for each parameter and yields a single prediction of the system response resulting

in overestimates or underestimates of results. One way to incorporate uncertainty is probabilistic

modeling using either the Monte Carlo or stochastic technique where uncertain parameters are

represented by probability density functions (PDFs) or random field, respectively. All of the

possible outcomes are then statistically analyzed and presented as envelop of outputs.

This paper, on the other hand, presents the probabilistic simulation predictions of plume

remediation for a trichloroethylene (TCE)-contaminated site using stochastic approach. In such

approach, several hydraulic conductivity fields (random fields or realizations) of the study area

were generated based on field-surveyed geostatistical data and used in all simulations to

determine the envelop of uncertainty in remediation outcome. The site is an actual (but,

anonymous) DNAPL contaminated site in Rayong province, Thailand. Finite-difference based

flow and transport models, MODFLOW [4] and RT3D [2] were used in this study.

2. THEORY

2.1 Groundwater Flow Simulation Using MODFLOW

MODFLOW [4] is the most commonly used computer code for simulating groundwater flow

thorough porous medium (called aquifer). It is a modular, three-dimensional finite-difference

flow code developed by U.S. Geological Survey. It solves the following partial differential

equation (Eq. 1) for hydraulic head (h) in heterogeneous and anisotropic aquifer, and capable of

simulating all kinds of boundary conditions such as constant head (Dirichlet), pumping well

(Neuman), and river (Cauchy).

s ii s

i i

h hS K q

t x x (1)

where Ss and Kii are specific storage and diagonal components of hydraulic conductivity tensor

(K). The quantity qs represents source/sink of volumetric water flux per unit volume of aquifer.

The hydraulic head (h) can be used to solve for velocity fields (vi) based on Darcy’s law as shown

in Eq. 2.

iii

i

K hv

x, (2)

where is aquifer’s porosity. This (average pore) velocity field will be used as input for the

subsequent solute/contaminant transport simulation. 2.2 Contaminant Transport Simulation Using RT3D

The fate and transport of dissolved contaminants in groundwater can be described by the

advection-dispersion-reaction equation:


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ij i n

i j i

c hD v c R

t x x x (3)

where Dij is dispersion coefficient tensor, Rn is a reaction term, and vi is the pore velocity.

Advection represents the movement of a contaminant with the flowing groundwater.

Hydrodynamic dispersion on the other hand, involves both molecular diffusion and mechanical

mixing. The latter is a result of local variations in velocity around some mean velocity of the flow

as a result of soil heterogeneity. Laboratory investigations indicate that at the macroscopic scale,

dispersion is a function of pore velocity and a factor called dispersivity. The dispersion of solutes

in groundwater can occur not only in the direction of groundwater flow, but also lateral to the

direction of flow. The last term in Eq. (3) represents the total mass loss or generation due to other

physical, chemical and biological processes such as adsorption, biodegradation, and self-decay

(e.g. radionuclides).

2.3 Stochastic Methods

The flow and transport parameters that appeared in the equations governing equations (1)-

(3), are generally measured or determined at only a few locations despite the fact that they are

highly variable in space at all length scales (macroscopic to regional). A combination of sparsity

of observations and measurement errors lead to uncertainty in the values of the formation

properties and thus uncertainty of predictions using simulation models that solve the governing

equations. The stochastic theory provides a method for evaluating these uncertainties using

probability or related quantities such as statistical moments [6]. Material properties that define

field heterogeneity are not completely random, but assumed to exhibit some correlation structure

resulting from natural depositional processes that created the formation. This spatial correlation

structure is defined using random space functions that are quantified using joint probability

distributions or joint statistical moments.

A commonly used geostatistical approach used in stochastic formulations is to characterize

the heterogeneity (in terms of permeability) of the aquifer by the first and second moments of a

probability distribution function (pdf) which are referred to as mean, and variance/covariance,

respectively. In modeling flow and transport, the hydraulic conductivity (K) introduces the

greatest uncertainty as its value varies over a very wide range in aquifer materials. The

uncertainty is not only associated with the measurement at a point but also with the uncertainty of

the value at locations where it is not measured. The general approach used in developing the

technique assumes that the log of K is normally distributed:

y lnK . If n points in the aquifer are

sampled, the estimate of the population mean is obtained from

1

1n

i

i

y yn

(4)

and the estimate of the variance is given by,

2 2

1

1( ) .

n

y i

i

S y yn

(5)

The pdf of the ln K distribution is defined by the mean and the variance. The variance

measures the degree of heterogeneity of the aquifer. If the yi is measured at a fixed set of points,

and if it is necessary to estimate the value of y at other locations where measurements are not


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made, the mean and the standard deviation (square root of variance) can be used to provide the

most likely estimate of the un-measured value. That is, the estimated value is the mean with an

uncertainty that is normally distributed with a standard deviation equal to the standard deviation

of the measurements.

A stochastic random process is a collection of random variables that vary continuously in

space (or time). The stochastic process K(x) can be thought of as a collection (or ensemble) of

realizations with the same statistical properties. A realization is single observation of the spatial

variation of the process. If the pdf of a spatially random process is invariant under shifts of the

spatial origin, then it is considered to be second-order stationary and commonly referred to as

“stationary.” The importance of stationarity is the suggestion of underlying repetitive structure of

the parameter. A physical description of the stationarity is captured in the covariance function

that is given as,

1 2 1 1 2 2cov[ ] [{ }{ }]y y E y y (7)

whose estimator is,

1

1( ) ( )( )

n

y i r i

i

R r y y y yN r

(8)

where N-r term is the number of pairs separated by a distance r. The covariance is independent of

the origin but depends on the distance between observations. The heterogeneous aquifers can be

represented as a spatially correlated random field. The descriptive statistics of the random field

include the mean and variance of Kln and correlation length. Spatial correlation increases the

probability that a given point will have permeability similar to that of a neighboring point. K

values at points that are separated by a short distance are more likely to be similar and as the

separation becomes larger they are less likely to be similar. The correlation scale is a

characteristic length of the average spatial persistence of Kln . A geoststistical tool for the

quantification of spatial structure is the experimental semivariogram (referred to as variogram).

Variograms are useful in identifying the underlying spatial structure and identifying trends. The

classical experimental semivaraigram estimator (h), for Gaussian data is calculated as,

( )

2

1

1( ) [ ( ) ( )]

2 ( )

n h

i i

i

h y x h y xn h

(9)

where h is the separation distance between observations and n(h) is the number of data pairs

separated by distance h. If the Kln data are statistically homogeneous (stationary), then the

variogram is dependent only on h. A theoretical exponential model can be fitted to the variogram

as,

2( ) (1 )hh e (10)

The model parameter is the correlation length that is a measure of the distance over which

the y values are correlated. Fig. 1 shows a plot of the theoretical and a measured semivariagram

from a laboratory sand packing experiment conducted by Compos [7]. For a small separation

distance h, the correlation between sample pairs is high and (h) is small. When distance between

points increases, the correlation decreases (i.e. (h) increases) and variogram will eventually

reach a plateau.


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In general, two approaches of stochastic formulations are used. In the first approach,

uncertainty analysis is incorporated directly into the model to define the predictions in terms of

their mean and covariance. The second approach uses a Monte Carlo-type analysis involving a

series of realizations of the uncertain parameters [8]. In our laboratory experiments and numerical

studies, the second approach was used. Several realizations of hydraulic conductivity field (more

correctly, log K) were generated and used for further analyses.

Figure 1. Typical semivariogram for stationary process [7].

3. SITE INFORMATION AND MODEL SETUP

DNAPL contaminated site in Rayong province, Thailand were selected for this numerical

modeling study (Fig. 2). The site, operated for 30 years, was an abandoned secure landfill where

organic liquid wastes, used metal (catalyst) powder, acids, toxic chemicals, etc., were disposed

from factories in the industrial estate. Prior to the completion of the lining construction of this

landfill, there was a report indicating that several drums of organic liquid wastes, sitting on a bare

ground near well no. 7 (see Fig. 2), were damaged an leaked resulting in a downward migration

of DNAPL to the upper (unconfined) aquifer. Hence groundwater in unconfined aquifer has been

contaminated with TCE and PCE (and also their biodegraded daughter products such as cis-DCE

and vinyl chloride) in the monitoring wells (wells no. 2, 3, and 7) located downstream of the

source. The concentrations of these contaminants were found to be as high as hundreds of ppb.

The only positive aspect is that there is a natural attenuation of these contaminants in the affected

aquifers. According to the recent geochemical and geomicrobial site characterization, it was

found that there were sulfate- and iron-reducing microbes degrading these chemicals and keeping

the contamination level low from a possible ppm-level down to ppb-level.

Since it is not possible to access and manage the DNAPL source zone because it was located

underneath the landfill, the site remediation’s objective has been set to rather manage the

downstream plume concentration of these contaminants by reducing them down below the

regulatory standards (< 5 ppb). The comprehensive site characterization was conducted to obtain

a clear picture of the 3-D soil structure of the site as well as other aspects such as geologic and

hydrogeologic conditions (e.g., number and types of aquifers, regional groundwater flow

directions and velocities), geochemical characteristics (types and level of naturally available

electron acceptors, redox potential, and ion contents), and microbial population types and sizes.

Fig. 3 shows the result of borehole investigation. These borehole information will be interpolated

to obtain site’s solid model in order to calculate and construct the variogram similar to Fig. 1. The

variogram was then fitted with exponential model and the parameter (correlation length) was

obtained from regression analysis. Subsequently, ten realizations of the hydraulic conductivity

field were generated and used to predict uncertainty of contaminant’s concentration. Fig. 4 shows

examples of hydraulic conductivity fields (or random fields or realizations).


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Figure 2. Site’s topview picture and general groundwater flow direction (green and red dots

represent soil-investigation boreholes).

Figure 3. Borehole locations and soil structure showing sparse data available for constructing a

3-D solid model for subsequent numerical modeling.

The study area was discretized into a non-uniform finite-difference grid of 126 columns, 130

rows, 15 layers covering the area of approximately 300350 m2 and the maximum depth of 20 m

(see Fig. 4). This grid system will be used to generate random fields and used in all subsequent

flow (MODFLOW) and transport (RT3D) simulations. Ten realizations of hydraulic conductivity

fields were generated based on the geostatistical parameters obtained from analysis of field

survey data (Fig. 5).


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Figure 4. Non-uniform finite-difference discretization of the unconfined aquifer

(Grids: 126 COL, 130 ROW, 15 LAY).

4. RESULTS AND DISCUSSION

The flow simulation for all realizations was conducted using MODFLOW program. Simulated

boundary conditions include river (RIV) and time-variant specified head (CHD) packages. The

simulated hydraulic heads for all realizations are shown in Fig. 6. As can be seen from the

hydraulic head contours Fig. 6, it is clear that the configuration of hydraulic conductivity field or

aquifer materials significantly affect the flow field.

The contaminant transport simulation was conducted using RT3D program. The contaminant

of concern consists of tetrachloroethene (PCE) and trichloroehtene (TCE) which can be naturally

degraded generating daughter products of cis-DCE (1,2-dichloroethene) and VC (vinyl chloride).

The source zone containing free-phase and dissolved PCE/TCE was located within the landfill

(close to Well no. 7; see Fig. 2) which has continuously been generating a high downstream

plume concentration of PCE and TCE (regulated standards for both PCE and TCE are 5 ppb). The

resulting downstream TCE plumes in some cases at t = 7300 days are shown in Fig. 7

(concentrations are in ppm!). Obviously, the plume size and shapes are different according to the

difference in hydraulic conductivity field and, hence, the flow field.

The remediation simulation was also conducted using RT3D but slightly differed from regular

transport model by adding the bio-permeable reactive barrier (PRB) downstream of the landfill.

The bio-PRB was achieved by adding carbon source (glucose), nutrients (phosphate, urea) and

electron acceptors (sulfate) into the wells (Wells No. X01-X10). By enhancing the growth of

microbial communities in these wells, the degradation of TCE/PCE in the plume can increase

several orders of magnitude. As a result the downstream concentration of the source zone can be

significantly reduced. Fig. 7 shows the contaminant plume when bio-PRB is implemented.

Total mass of TCE crossing the compliance plane (column #69, for example) was monitored

(calculated) and plotted as a function of time. Fig. 8 compares TCE mass for the cases with and

without implemented bio-PRB. It is clear that the model prediction of TCE mass released from


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the source zone for both cases is highly uncertain. In some cases, mass outflux is very small

whereas the others show very high TCE mass in the plume. With implemented bio-PRB, the

amount of TCE mass removed by bioremediation ranges from 20-40% (see Fig. 9). This mass

removal range indicates there is always uncertainty associated with site characterization, and,

hence, subsequent remediation.

Figure 5. Hydraulic conductivity fields for all 10 realizations.


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Figure 6. Hydraulic heads distribution (top view) of all realizations.


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No Remediation With Bio-PRB Remediation

Figure 7. Contaminant plume with and without remediation (top view) of realizations #2, 4, 6, 8,

and 10.


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Figure 8. Mass of TCE crossing the compliance plane (column 69) as a function of time (with

and without remediation).

Figure 9. Mass removal efficiency for all cases (removal efficiency is in the range of 20-40%).

5. CONCLUSION

Based on the numerical simulation of this study, it was found that if the site characterization

(in this case, the hydraulic conductivity field) was not accurately or completely determined, there

is always uncertainty in model prediction of the flow and transport of contaminant in the

subsurface environment.

REFERENCES

1. Benekos, I.D., Shoemaker, C.A., and Stedinger, J.A., Stoch. Environ. Res. Risk Assess.,

2007, 21: 375–390

2. Clement, T.P. RT3D Manual. PNNL-11720. Pacific-Northwest National Laboratory,

Richmond, WA, 2000.

3. Dagan, G. Stoch. Environ. Res. Risk Assess., 2010, 18: 266-267.

4. Harbaugh, A.W., Banta, E.R., Hill, M.C., and McDonald, M.G., MODFLOW-2000 Manual.

U.S. Geological Survey Open-File Report 00-92, 2000.

5. Ye, M., Meyer, P.D., Lin, Y.-F., and Neuman, S.P., Stoch. Environ. Res. Risk Assess., 2010,

24: 807-808.

6. Zhang, D., 2002. Stochastic Methods for Flow in Porous Media, Academic Press, pp. 350.


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7. Compos, R. 1998. Hydraulic conductivity distribution in a DNAPL entrapped zone in a

spatially correlated random field. M.S. Thesis, University of Colorado.

8. Gelhar, L.W., Axness, C.L. 1983. Three-dimensional stochastic analysis of macrodispersion

in aquifers. Water Resource Research. 19(1): 161-180.

ACKNOWLEDGMENTS

This work was supported partly by a grant from Environmental Research and Training Center,

Department of Environmental Quality Promotion, and the Faculty of Science, Chiang Mai

University. In addition the Office of the Higher Education Commission is gratefully

acknowledged for a financial support of the first author.

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