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Optimization of Remediation Operations at Petroleum-Contaminated Sites through a Simulation-basedStochastic-MCDA ApproachX. S. Qin a , G. H. Huang b c , W. Sun a & A. Chakma da Faculty of Engineering , University of Regina , Regina, Saskatchewan, Canadab Sino-Canada Center of Energy and Environmental Research , North China Electric PowerUniversity , Beijing, Chinac Department of Civil and Environmental Engineering , University of Waterloo , Waterloo,Ontario, Canadad Department of Chemical Engineering , University of Waterloo , Waterloo, Ontario, CanadaPublished online: 18 Jun 2008.

To cite this article: X. S. Qin , G. H. Huang , W. Sun & A. Chakma (2008) Optimization of Remediation Operations atPetroleum-Contaminated Sites through a Simulation-based Stochastic-MCDA Approach, Energy Sources, Part A: Recovery,Utilization, and Environmental Effects, 30:14-15, 1300-1326, DOI: 10.1080/15567030801928623

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Energy Sources, Part A, 30:1300–1326, 2008

Copyright © Taylor & Francis Group, LLC

ISSN: 1556-7036 print/1556-7230 online

DOI: 10.1080/15567030801928623

Optimization of Remediation Operations at

Petroleum-Contaminated Sites through a

Simulation-based Stochastic-MCDA Approach

X. S. QIN,1 G. H. HUANG,2;3 W. SUN,1 and A. CHAKMA4

1Faculty of Engineering, University of Regina, Regina, Saskatchewan, Canada2Sino-Canada Center of Energy and Environmental Research, North China

Electric Power University, Beijing, China3Department of Civil and Environmental Engineering, University of Waterloo,

Waterloo, Ontario, Canada4Department of Chemical Engineering, University of Waterloo, Waterloo,

Ontario, Canada

Abstract A simulation-based stochastic-multi-criteria decision analysis (MCDA)approach was developed for optimizing groundwater remediation operations through

integrating the contaminant transport modeling, dual-phase vacuum extraction (DPVE)process modeling, deterministic MCDA, and Monte Carlo simulation into a general

framework. A petroleum-contaminated site in western Canada was selected as thestudy case for demonstrating the applicability of the proposed method. Totally, 12

scenarios were designed for site remediation. Nine criteria were used for evaluatingeach alternative through the developed MCDA methods. The economical factors

consisted of operational cost associated with DPVE and groundwater remediation. En-vironmental performances were determined based on the magnitude of risky and highly

risky areas of benzene, toluene, ethyl-benzene, and xylene (BTEX) contamination thatwere predicted through developed models. The study results demonstrated that the

proposed stochastic MCDA method provides more complete information of possiblerankings of alternatives than conventional methods. The decision makers cannot only

obtain the ranking information under uncertainty directly, but also gain an in-depthunderstanding on the relative derivation and closeness among different alternatives.

Keywords groundwater, MCDA, remediation, simulation, stochastic, subsurface con-tamination

1. Introduction

Leakage and spill of petroleum hydrocarbons from underground storage tanks and pipe-

lines have posed significant threats to groundwater resources across many petroleum-

related sites in North America (Liu et al., 2001). It is thus critical that petroleum waste

management systems (PWMS) and relevant methodologies be developed for supervising

cleanup behaviors for contaminated sites. Although numerous remediation methods wereproposed to mitigate the contamination, complexities of subsurface systems could lead to

challenges in identifying a reasonable remediation technique or technique-combination.

At the same time, customization of these techniques into specific on-site conditions may

Address correspondence to X. S. Qin, Faculty of Engineering, University of Regina, Regina,Saskatchewan S4S 0A2, Canada. E-mail: [email protected]

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Optimizing Groundwater through MCDA Approach 1301

remain to be another challenging issue, due to the diversity of pollution sources and

medium conditions in subsurface systems. Therefore, more effective decision supporttools need to be developed to well conceptualize and represent such complexities (Huang

et al., 1999; Huang and Xia, 2001; Qin et al., 2007a).

Previously, many methods were applied in remediation technologies selection and

risk analysis of subsurface pollution. For instance, a robust decision-support system (DSS)

was developed to provide environmental managers with all integrated measure for tacklingsubsurface contamination problems (Qin et al., 2006). A fuzzy risk assessment approach

(FRA) was developed through incorporation of a multiphase multi-component model-

ing system within a general risk assessment framework and applied to a hydrocarbon-

contaminated site in western Canada (Li et al., 2006). An integrated approach for en-

vironmental and health risk assessment of subsurface contamination was proposed to

identify risky zones with different risk levels under various remediation actions, planningperiods, and land-use patterns (Maqsood et al., 2005). However, remediation systems are

complicated for the multiple involved processes: free-product recovery, residual-phase

removal, and groundwater-pollution control. Studies for individual system components

cannot effectively reflect interactions among various processes of contaminant transport.

Thus, an integrated system that incorporates simulation of subsurface contaminant, pro-cesses modeling of DPVE, uncertainty information and novel decision-making support

tools within a general framework is desirable (Zeng and Trauth, 2005; Olsen et al., 2006).

MCDA is a fruitful decision-making support approach with two distinct features.

One is that it can collect, store, and process both quantitative and qualitative (expert

opinions or experiential knowledge) data (Lahdelma et al., 2000); the other is thatit is conveniently structured to enable a collaborative planning and decision-making

environment for multiple experts and stakeholders (Mendoza and Prabhu, 2003). MCDA

has been applied to a broad range of resource management problems (Mendoza and

Martins, 2006). For example, MCDA was employed to address the efficiency of watershed

instrumentation programs and the efficacy of watershed modeling and applied to a

case study of reconstructed watersheds in northern Alberta, Canada (Elshorbagy, 2006).MCDA was utilized for supporting decisions of solid waste management (Cheng et al.,

2002). However, there are rarely applications of MCDA in groundwater field (Eliasson

et al., 2003).

Furthermore, MCDA has also been combined with other relevant methods to facilitate

the decision-making. For instance, spent oil regeneration (SPORE), a MCDA-baseddecision support tool, was developed to help decision-makers to assess the available

technologies and select the preferred used oil regeneration options (Khelifi et al., 2006).

Inexact mixed integer linear programming (IMILP) methods combined with MCDA was

to support selection of an optimal landfill site and a waste-flow-allocation pattern to

minimize the total system cost (Cheng et al., 2003). Unfortunately, few simulation-basedMCDA studies have been reported.

In addition, the modeling and decision-making processes through MCDA techniques

are complicated with a variety of uncertainties. For example, these uncertainties may

be derived from aquifer heterogeneity and physical, chemical, and biological properties

of the contaminants being released and transported, which finally results in variations

of the criteria performance values in MCDA matrix. The uncertainties may also beassociated with subjective elicitation of criteria weights. There have been some MCDA

application studies addressing the involved uncertainty information, such as extension of

rough sets theory (Greco et al., 2001) and fuzzy sets (Boender et al., 1989; Chiou et al.,

2005; Wang and Elhag, 2006) to MCDA. Recently, a number of researchers have begun

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1302 X. S. Qin et al.

to couple probability information with MCDA-based decision-making support process

(Kangas et al., 2003; Lahdelma et al., 2003; Marinoni, 2006).Therefore, the objective of this study is to develop a simulation-based stochastic-

MCDA system for remediation technologies selection and risk analysis of subsurface

pollution. It will entail: (1) development of a three-dimension multiphase and multi-

component groundwater model; (2) development of a DPVE process simulation model;

(3) development of stochastic-MCDA methodology for remediation technologies selec-tion; (4) integration of the contaminant transport modeling, DPVE simulation with the

stochastic-MCDA to generate a simulation-based stochastic-MCDA method; and (5)

application of the developed method system for management and risk analysis to a

petroleum-contaminated site in western Canada.

2. Methodology

2.1. Contaminant Transport Modeling in Subsurface

A three-dimensional multiphase and multicomponent model is developed to simulate

contaminant transport in subsurface to facilitate real-time system forecasting under dif-

ferent remediation alternatives (Liu, 2005; Qin et al., 2008). The model can accountfor complex-phase behaviors, chemical and physical transformations, and heterogeneous

porous-media properties. It incorporates a variety of physical-, chemical-, and biological-

process models within a general setting to describe various processes of contaminant

transport in aquifers, such as non-equilibrium interphase mass transfer, sorption, decay,

microbiological and geochemical reactions, capillary pressure, and relative permeability.The basic mass conservation equation for components in subsurface can be written

as follows (Brown, 1993; Delshad et al., 1996):

@

@t.� QCk�k/ D Er �

" npX

lD1

�k.Ckl Eul � �SlEEDkl � ErCkl /

#

D Rk (1)

where

k D component index

l D phase index

� D soil porosityQCk D overall concentration of component k (volume fraction)

�k D density of component k [ML�3]

np D number of phases

Ckl D concentration of component k in phase l (volume fraction)Eul D Darcy velocity of phase l [LT�1]

Sl D saturation of phase l

Rk D total source/sink term for component k (volume of component k per unit

volume of porous media per unit time)EEDkl D dispersion tensor

The overall concentration . QCk/ denotes the volume of component k summed over all

phases. The phase flux can be calculated from the multiphase form of the Darcy’s law

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(Brown, 1993):

Eul D �kr l

EEK

�l

� . ErPl � �lg Erz/ (2)

where

kr l D relative permeability of porous medium to phase lEEK D intrinsic permeability tensor [L2]; �l is viscosity of phase l [ML�2 T�1]

�l D density of phase l [ML�3]

g D acceleration of gravity [LT�2]z D vertical distance which is defined as positive downward [L]

Pl D pressure of phase l [ML�1 T�2]

Through (a) substituting the Darcy’s law for the phase velocity terms in mass balance

(Eq. 1) and (b) summing over all components (ncv), a pressure equation can then be

developed. Such an equation can be written explicitly in terms of water phase pressureas follows (Brown, 1993; Delshad et al., 1996):

�Ct

@Pw

@tC Er �

EEK ��rTcErPw D � Er �

npX

lD1

EEK ��r lcErz C Er �

npX

lD1

EEK ��r lcErPclw C

ncvX

kD1

Qk (3)

where

Ct D total compressibility

Pw D water phase pressure

�r lc D relative mobility

�rT c D total relative mobility

Pclw D capillary pressure difference between phase l and the water phase

Qk D injection/production rate for component k per bulk volume

Compositional multiphase models require multiple constitutive relations to close the

system of equations. For a subsurface system, the typical constitutive relations are those

of pressure-saturation-permeability (p-S-k) interactions. The p-S relation in a saturated

zone can refer to Lenhard and Parker (1987) and Delshad et al. (1996). Injection and

production wells are considered as source and sink terms in the flow equations (Eqs. (1)and (3)). Wells can be established vertically in several layers of the aquifer or horizontally

with any length, and can be controlled according to pressure and/or rate constraints. The

well model is based on the formulations of Peaceman (1983) and Babu and Odeh (1989).

The aquifer boundaries are treated as either constant-potential or closed surfaces. The

model can be solved numerically through the block-centered finite difference method.The solution process includes the following procedures: (i) solving the pressure equation

implicitly to yield water phase pressure in all grid blocks; (ii) using capillary pressures

from the previous time step to determine the pressure of other phases in each grid

block; (iii) using the Darcy’s law to determine the phase velocities; (iv) solving mass

conservation equations explicitly to yield concentration of each component in each gridblock; (v) determining phase concentrations and saturations through flash calculations;

(vi) determining new capillary pressures from the new saturations; and (vii) repeating

the procedures for each time step till the simulation ends.

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2.2. DPVE-Process Simulation

In the DPVE process, a vacuum system is used to remove various combinations of

contaminated groundwater, free product, and hydrocarbon vapor from the subsurface.

The extracted liquids and vapors are then collected and treated for disposal or re-

injection into the subsurface. In the remediation system, the subsurface liquids and

soil vapors can be extracted together as a high-velocity dual-phase (liquids and vapors)

stream using a vacuum pump. The vacuum applied to the subsurface creates vapor-phasepressure gradients toward the vacuum well. These vapor-phase pressure gradients are

also transmitted directly to the subsurface liquids, such that liquids existing in continuous

phase (e.g., water and free phase petroleum products) will flow toward the vacuum well

in response to the imposed gradients. As a result, hydraulic control of the contaminant

plume can be provided and thus the contaminants can be prevented from further migration.The vacuum extraction well includes a screened section, which is placed in the zone

of contaminated soil and groundwater; thus the DPVE system can remove contaminants

from both above and below the groundwater table (O’melia and Parson, 1996). Typically,

the DPVE technology is suitable for sites with shallow groundwater tables and low

permeability soils.

Multiphase flow usually occurs around extraction wells in the DPVE system. Itis thus necessary to numerically model the DPVE process through a multiphase-flow

model. The governing equations for a multiphase-flow system may be written within a

three-dimensional Cartesian domain as follows (Parker, et al., 1994; Kaluarachchi, 1996;

Katyal and Parker, 1992):

�@Sw

@tD

@ŒKwij .@hw=@xj C �rwuj /

@xi

CRw

�w

(4a)

�@So

@tD

@ŒKoij .@ho=@xj C �rouj /

@xi

CRo

�o

(4b)

�@�aSa

@tD

@ŒKaij .@ha=@xj C �rauj /

@xi

C Ra (4c)

Sw C So C Sa D 1 (4d)

where

� D porosity

Sp D p-phase saturation

p D air (a), water (w), and oil or nonaqueous phase liquids (NAPLs)

(o) phases

xi (and xj ) D Cartesian coordinates (i; j D 1; 2; 3)

Kpij D p-phase conductivity tensor [LT�1]�p D density of phase p [ML�3]

hp D water height-equivalent pressure head [L]

�rp D p-phase specific gravity (�rp D �p=�0w, where �0

w is density of pure

water, [ML�3])

uj D unit gravitational vector measured positive upwards (uj D @z=@xj ,where z is elevation)

Rp D net mass transfer per unit porous medium volume into (C) or out

of (�) phase p [ML�3 T�1]

t D time [T]

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In order to simulate the recovery of water and hydrocarbons during the DPVE

process, the above equations are integrated in vertical direction. Thus, the volume balanceequation for various phases can be obtained as follows (Kaluarachchi, 1996; Katyal,

1997):

@Vw

@tD

@

@xt

�

Twij

@Zaw

@xj

�

C Rw (5a)

@Vo

@tD

@

@xi

�

Toij

@Zoo

@xj

�

C Ro (5b)

@Va

@tD

@

@xi

�

Taij

@Zaa

@xj

�

C Ra (5c)

where

Vp D specific volume of p-phase (volume of p-phase per horizontal area) [L]

Tpij D p-phase transmissivity [L2 T�1]

Zaw D air-water table elevation [L] where water pressure is zeroZao D air-oil table elevation [L] where oil pressure is zero

Zaa D gas pressure [L]

The above vertically integrated approach can effectively reduce the system dimensionality

from 3 to 2, making it computationally attractive. The specific volume of water, NAPL,and gas can be expressed as follows:

Vw D

Z Zu

ZL

�Swdz (6a)

Vo D

Z Zu

ZL

�Sodz (6b)

Va

Z Zs

Pao

�Sadz (6c)

where

Vw D specific volume of water [L]

Vo D specific volume of NAPL [L]

Va D specific volume of gas [L]

Zu and ZL D upper and lower limits of integration for water and oil (NAPL) phases

[L], respectively

Zs D ground surface elevation [L]Pao D elevation of air-oil interface [L]

In order to solve the above flow equations, relationships among phase permeability,

saturation, and pressure should be specified. These constitutive relationships can be

described by a three-phase extension of the van Genuchten model (Parker et al., 1994)that considers NAPLs entrapment (Katyal, 1997; Morshed and Kaluarachchi, 1998).

Equations for mass balance in water and oil phases are solved simultaneously using

the Galerkin finite element method. The Galerkin approximation procedure has been

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reported by Katyal and Parker (1992). The solution of gas-phase mass balance equation

is uncoupled with water- and oil-phase solutions. The 2-D rectangular or isoparametricelements are used to model the physical boundaries and material boundaries. During each

time step, a steady state gas phase solution is obtained for current boundary conditions.

This can help weaken the coupling between the water-oil phase solution and the gas

phase solution and formulation results in a numerically efficient and stable solution. This

assumption is reasonable because gas phase pressures reach steady state fairly quicklycompared to the entire DPVE period.

2.3. Deterministic Multi-Criteria Decision Analysis

Decision-making in groundwater remediation projects can be complex, principally due

to the inherent existence of tradeoffs between environmental and economic factors (Qin

et al., 2007b,c). MCDA not only provides better-supported techniques for the comparisonof project alternatives based on decision matrices, but also provides structured methods for

incorporating the project stakeholders’ opinions into the ranking of alternatives. Extensive

studies of MCDA techniques have been undertaken over the past decades (Mann and

Evangelos, 1989). Different methods require diverse types of value information and

follow various optimization algorithms. Some techniques rank options, some identify

a single optimal alternative, some provide an incomplete ranking, and others differentiatebetween acceptable and unacceptable alternatives. This paper will focus on methods

of simple additive weighting (SAW), technique ordered preference by similarity to the

ideal solution (TOPSIS), and Preference Ranking Organization Method for Enrichment

Evaluations (PROMETHEE) (Thomas et al., 1990). This is due to the fact that they can

provide complete ranking results and are more suitable to be combined with stochasticanalysis (Korhonen and Wallenius, 1990; Karsak, 2002). In addition, as different MCDA

approaches could result in varied rankings of given options, the use of more than one

method will help enhance the robustness of the decision support (Kok and Lootsma,

1985).

2.3.1. SAW. The SAW method is a classic version of the multi-attribute value method.

A value function is established based on a simple addition of scores that representthe goal achievement under each criterion, multiplied by the particular weights. The

decision makers can declare a one-dimensional value function vk.f .an/, .fk.an/ is the

performance value of alternative an under the kth criteria) that is normalized to interval

[0, 1], where the best score under each criterion gets a utility value of vk D 1, and the

worst one gets vk D 0:

v.an/ D1

N

KX

kD1

wk :vk.fk.an// with wk � 0 and

KX

kD1

wk D 1 (7)

where wk denotes the weight assigned to criterion k and K means the total number of

considered criteria. Thus, we have:

fk.an/ ! max; vk.fk.an// Dfk.an/ � min.fk.an//

max.fk.an// � min.fk.an//(8)

The higher the weighted sum of the utility values, the better the alternative. In this

method, a complete compensation among the criteria is possible and intuitive to the

decision makers.

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2.3.2. TOPSIS. The TOPSIS method is an approach to identify an alternative which

is closest to the ideal solution and farthest to the negative ideal solution in a multi-dimensional computing space (Deng et al., 2000). The first step is to build a decision

matrix (A) with values of attributes (criteria). A normalized decision matrix (R) can be

obtained through the following equation:

rij Dxij

MX

iD1

x2ij

!1=2(9)

where xij is the value of the j th criterion for the i th alternative. A weighted normalized

decision matrix V is then obtained through applying R and weights assigned to the

criteria. In the next step, the ideal solution (IA) and the worst one (WA) can be determinedas follows (Deng et al., 2000):

IA D f.maxi vij jj 2 J1/I .mini vij jj 2 J2/ji D 1; 2; : : : ; N g D fvI1 ; vI

2 ; : : : ; vIM g (10a)

WA D f.mini vij jj 2 J1/I .maxi vij jj 2 J2/ji D 1; 2; : : : ; N g D fvW1 ; vW

2 ; : : : ; vWM g

(10b)

where J1 is associated with the benefit criteria and J2 with the cost ones. Consequently,

the Euclidean distance of each alternative from the overall ideal and worst solutions can

be determined as follows (Deng et al., 2000):

ISi D

v

u

u

t

MX

j D1

.vij � vIj /; .i D 1; 2; : : : ; N / (11a)

WSi D

v

u

u

t

MX

j D1

.vij � vWj /; .i D 1; 2; : : : ; N / (11b)

The relative closeness of each alternative to the ideal solution is computed as ratioISi =.ISi CWSi /, i D 1; 2; : : : ; N . The alternative with the highest ratio is the best option.

2.3.3. PROMETHEE. The PROMETHEE method is based on a pair-wise comparison

of alternatives along each recognized criterion and an aggregation of these compar-

isons to establish outranking of available alternatives (Brans et al., 1984). Two types of

PROMETHEE were widely used, i.e., PROMETHEE I and PROMETHEE II (Bouyssouand Perny, 1992). In both methods, the outranking degree ….ak ; al/, describing the

credibility of the outranking relation that ‘alternative ak is better than alternative al ,’ for

each pair of alternatives .ak ; al / is calculated as

….ak ; al/ DPX

j D1

wj Fj .ak ; al / (12)

where Fj .ak ; al/ is the preference function and wj are the relative importance of the

different criteria (scaled to add up to one in the formula). In PROMETHEE outranking

method, the threshold values are assumed to be constant (Salminen et al., 1998). The

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value of preference function Fj .ak ; al/ for a pair of alternatives ak and al with respect

to criteria j are calculated using thresholds pj and qj as

Fj .ak ; al/ D

8

ˆ

<

ˆ

:

1; if gj .ak/ � gj .al / � pj

0; if gj .ak/ � gj .al / � qj

.gj .ak/ � gj .al / � qj /=.pj � qj /; otherwise

(13)

In this formula, the linear threshold function is utilized. However, six different forms

of threshold function can be applied, which can be either linear, nonlinear, or a step

function (Brans et al., 1984). The criteria and threshold values together constitute thepseudo-criteria. The outranking degrees, …, are used to calculate for each alternative the

leaving flow, entering flow and net flow,

ˆC.ak/ DX

l¤k

….ak ; al/=.n � 1/ (the leaving flow) (14a)

ˆ�.ak/ DX

l¤k

….ql ; ak/=.n � 1/ (the entering flow) (14b)

ˆ.ak/ D ˆC.ak/ � ˆ�.ak/ (the net flow) (14c)

In PROMETHEE I, the alternatives are ranked based on both the leaving and

entering flows, which leads to a partial preorder where certain alternatives may remain

incomparable. In PROMETHEE II the net flow is used, which leads to complete ranking(Hokkanen and Salminen, 1997). Thus, only PROMETHEE II will be used in this study.

2.4. Monte Carlo Simulation

In the past decades, the increasing awareness for uncertainties of porous media led to an

improved understanding of contaminant transport in subsurface. A number of techniques

were developed, where the stochastic modeling through Monte Carlo simulation was

the most well known one (Huang, 1998). Such a method consists of iterative individual

sampling to produce multiple simulation realizations, and then analysis of all of the

realizations to present the final output results. The output realization is usually presentedin the form of a probability distribution or a cumulative frequency distribution.

Monte Carlo simulation will be used to tackle uncertainties that can be described

by probability distribution functions (PDFs). Monte Carlo techniques utilize repeated

executions of numerical models to simulate stochastic processes of groundwater flow

and contaminant transport. Each execution of the model produces a sample output. Theoutput samples can then be examined statistically and distributions can be determined.

The primary components of a Monte Carlo simulation include (1) probability distribu-

tion functions, (2) random number generator, (3) sampling rule, (4) scoring, (5) error

estimation, (6) variance reduction techniques, and (7) parallelization and vectorization.

Monte Carlo techniques have a number of advantages, such as (1) it has the capability tohandle uncertainty and variability associated with model coefficient, (2) it can potentially

be applied in deterministic modeling structure, and (3) it is flexible to choose the types

of probability distributions that can be used to characterize model inputs.

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2.5. Simulation-Based Stochastic-MCDA Method

The simulation-based stochastic-MCDA method will be developed through integrating

the contaminant transport modeling, DPVE process modeling, deterministic MCDA,

and Monte Carlo simulation into a general framework. Figure 1 shows the block di-

agram. The attributes in MCDA performance matrix consist of two main categories, i.e.,

environmental and economic performances. The environmental performance provides

information of future contaminant distributions as well as relevant impacts under variousremediation scenarios. Such information is obtained through developed DPVE process

and contaminant-transport simulations. DPVE simulation is capable in predicting free-

product recovery and provides initial conditions of oil distributions for further con-

taminant transport modeling. The uncertainties associated with subsurface conditions

will be addressed as stochastic parameters with probabilistic distributions. Monte Carlosimulation will be coupled with the developed simulators for generating system outputs

described by probabilistic density functions.

The modeling outputs described in PDFs will be put directly into the MCDA

performance matrix. The economical information of various alternatives can be obtained

through public survey and literature review. As the remediation cost is site specific

and has large variations, it will be assumed as random variables with either uniformor normal distributions. Criteria weights indicate a criterion’s relative importance and

pose significant impact on the ranking of alternatives. However, the determination of

criteria weights is often subjective, ambiguous and imprecise and leads to uncertainties

in results of decision analysis. Therefore, the criteria weights will also be tackled as

random variables with probabilistic distributions. The PDFs can be obtained throughstatistical analysis coupled with extensive public survey.

After the performance matrix and weighting information are determined, the stochas-

tic MCDA process can be undertaken. The operation process can be summarized as

follows:

Figure 1. Block diagram of simulation-based stochastic-MCDA method.

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(a) Generate a random value for each stochastic item in MCDA performance matrix

and criteria weightings according to relevant PDF.(b) Use the generated performance matrix and weightings to conduct decision anal-

ysis through deterministic MCDA.

(c) Store the resulting output of the rankings of alternatives for further statistical

analysis.

(d) Repeat steps (a)–(c) a pre-determined number of times.(e) Analyze the final ranking outputs and perform uncertainty analysis.

3. Case Study

3.1. Background

A petroleum contaminated site in western Canada was selected as the study case todemonstrate the proposed methodology for providing decision support of screening de-

sired remediation options. This site had been operated as processing plant to remove

naphtha condensate from the natural gas stream prior to transporting to a regional

transmission line. Throughout the site history, naphtha condensate, which was a waste

liquid removed from the gas by a series of scrubbers, was disposed of in an underground

storage tank (UST). Due to leakage of this UST in the past years, the site was seriouslycontaminated. During the past years, a number of field investigations were conducted to

examine the hydrogeologic and environmental conditions at the site.

Generally, the stratigraphy at the study site consists of native silt and silty clay

extending from the surface to between approximately 7.6 m and 12.5 m depth. Underlying

silty clay was clay matrix till extending to between 9.4 m and 15.2 m depth. Sand isencountered with or underlying the clay matrix till between approximately 9.4 m and

15.2 m depth. Silty clay and sand underlying the topsoil are over the majority of the site.

Clay/till underlies the sand over the majority of the site, and extends to the maximum

exploration depth of 14.0 m. Groundwater table was measured between approximately 4.8

and 13.2 m below ground surface, predominantly located in the clay tills. The groundwaterflow direction is westerly with a gradient of approximately 0.01 m/m from southeast

towards northwest. The field rising head tests indicated a hydraulic conductivity of 10�7

to 10�5 m/s in clay tills and sand. The pH was found in the range of 7.7 to 9. The free

phase hydrocarbons have infiltrated through fractures near the point source (i.e., UST)

into the subsurface. The naphtha migrated along saturated fissures in the clay vertically

toward the groundwater table, and finally piled up at the groundwater surface.During monitoring in the fall of 1999 at the site, liquid petroleum hydrocarbon

(LPH) with thickness of trace to >1,800 mm was encountered at a depth of 10 to 13 m

below surface. Residual phase hydrocarbons were encountered in many monitoring wells.

Groundwater samples indicate that BTEX concentrations exceed SERM (Saskatchewan

Environment and Resource Management) portable groundwater guidelines. An initialDPVE program was operated from April 27, 2000 through to September 14, 2000; in

that period, a total of 7,800 L of hydrocarbons in the naphtha range were recovered.

Previous remedial efforts at the site include a manual bailing program conducted between

December 1998 and the end of 1999; during that period, approximately 2,300 L of

hydrocarbons in the naphtha range were recovered.Although the DPVE remediation was implemented at the site, the hydrocarbons have

still been continuously dissolving into the groundwater. The highest level of free-product

thickness was around 800 mm. The groundwater in the study area serves as supply for res-

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idential drinking, agricultural irrigation, and stockbreeding. Further remediation actions

were desired for removing free-product and cleaning groundwater systems. However, anumber of questions needed to be answered before any actions were to be taken, such

as how long should the DPVE program continue? What efficiency should be taken for

groundwater remediation? The proposed methodology will help answer these questions

and provide decision support for identifying desired remediation options for the study

site.

3.2. MCDA Settings

A number of scenarios (DPVE plus further bioremediation) were designed for site

remediation. There are three options for DPVE program: (1) zero-day operation, (2)

6-month operation, and (3) 1-year operation. Further groundwater bio-remediation will

include four options: (1) no further remediation action, (2) remediation action withan efficiency rate of 30%, (3) remediation action with an efficiency rate of 60%, and

(4) remediation action with an efficiency rate of 90%. Combination of the above options

leads to 12 potential alternatives for site remediation, as shown in Table 1. Totally,

9 criteria will be used for evaluating each alternative; they include economical and

environmental factors. The economical factors are consisted of operational cost associated

with DPVE and groundwater remediation. Environmental performance will be determinedbased on the magnitude of risky and highly risky areas of BTEX. According to the

SERM guidelines, the regulated BTEX concentrations in potable groundwater are 5, 24,

2.4, and 300 ppb respectively. Based on these criteria, the contaminated groundwater

can be characterized into two zones: (1) Risky Zone—SERM-guideline violated zone

Table 1

MCDA scenarios

Scenarios

DPVE

program,

days

Remediation

program,

�% Criteria Descriptions

Weights

(normal

distribution)

A1 0 0 P1 Free product treatment

cost ($)

(0.2012, 0.05)

A2 0 30 P2 Groundwater remediation

cost ($)

(0.2012, 0.05)

A3 0 60 P3 Benzene risky area (m2) (0.0610, 0.025)

A4 0 90 P4 Toluene risky area (m2) (0.0153, 0.006)

A5 180 0 P5 Ethyl-benzene risky area

(m2)

(0.1220, 0.055)

A6 180 30 P6 Xylene risky area (m2) (0.0031, 0.001)

A7 180 60 P7 Benzene high-risk area

(m2)

(0.1219, 0.030)

A8 180 90 P8 Toluene high-risk area

(m2)

(0.0305, 0.012)

A9 365 0 P9 Ethyl-benzene high-risk

area (m2)

(0.2439, 0.060)

A10 365 30

A11 365 60

A12 365 90

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and (2) Highly Risky Zone—10-times-SERM-guideline exceeded zone. Generally, the

smaller the area of risky or highly risky zones, the better the environmental performanceof the remediating alternative. It is found that the highly risky areas of xylenes (P10) is

zero even at the initial condition, thus it is not listed in the table. The criteria weights

were obtained through extensive public survey and consultation with local stakeholders.

As the weights from multiple actors may have large variations, statistical methods were

used to investigate their uncertain features. It was found that the weights were in normaldistributions, with detailed mean and variances being provided in Table 1.

3.3. Cost Analysis

The cost of DPVE operations included the following items: (1) fixed cost items (extraction

well and vacuum system installation, off-gas treatment system installation, and monitoring

well installation); (2) variable cost items (operating and maintenance labor, utilities,site supervision, site quality assurance and health and safety support, and sampling and

analysis for process control); and (3) residuals management activities (disposal of treated

water to publicly owned treatment works via site sewer and off-gas treatment). On the

contrary, pre-treatment activities and indirect costs are not included such as project

management, design and engineering, vendor selection, home office support, permitpreparation and fees, regulatory interaction, site characterization, treatability testing,

performance bond, and contingencies. Through extensive literature review and expert

consultation, the estimated daily operational cost for the studied site is around $157.7 to

$273.3 Canadian dollars (CAD). Further in-situ bioremediations for cleaning up ground-

water systems are to be undertaken following the DPVE operations. The approximate costof this technology is mainly associated with design, installation and operations, and is

highly site specific. Based on literature review and site characteristics, it is estimated that

the total cost for the studied site is around $120,000 to $270,000. Assume an exponent

relationship between treatment efficiency � and system cost Cb , i.e., Cb D �a, where a

is the scale-economy coefficient. Figure 2 presented the curves of treatment efficiency

vs. system cost under both average and extreme conditions. The cost values for variousalternatives of groundwater remediation can be estimated based on the developed curves.

3.4. Model Calibration and Verification

Since the modeling study will examine the long-term pollutant transport fate in the

subsurface under various remediation strategies, a relatively large simulation domainthat exceeds the site property boundary is considered. The site is considered as a three-

dimensional domain, and the area is 180 � 150 m2 with only one vertical layer (saturated

zone). The vertical grid block size is 10 m. The whole simulation domain is discretized

into 30 � 25 grid blocks. Each grid has dimensions of 6, 6, and 10 m in x, y, and

z directions, respectively. The total number of grids in the 3-D computational gridsystem is 750 (30 � 25 � 1). Figure 3 shows the simulation domain and grid system

as well as distribution of the initial free-product thickness. Wells 101, 103, 105, 108, 9,

and 401 were used for DPVE extractions. Other wells were used for monitoring both

free-product thickness and BTEX concentrations in groundwater. It is indicated that the

contaminant mainly distributed around wells 105, 108, and 101, with a maximum free-product thickness at 831 mm and a total impact area of 4,950 m2.

The monitoring data from the 2000 DPVE program were used for calibrating the

developed multiphase DPVE simulator. The site information and contamination condi-

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Figure 2. An empirical curve between bioremediation cost and efficiency.

Figure 3. The simulation domain and distribution of initial free-product thickness (mm).

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Table 2

Part of modeling input parameters

Parameter Value Unit Parameter Value Unit

Residual water saturation 0.10 Transverse dispersivity of

sandy soil

0.5 m

Residual oil saturation 0.20 Transverse dispersivity of clay

till

0.5 m

Residual gas saturation 0.10 Transverse dispersivity of silty

clay

0.5 m

Permeability of sandy soil in

x, y, and z direction

29000 MD Hydraulic gradient 0.006 m/m

Permeability of clay till in x,

y, and z direction

195 MD NAPL/water partition

coefficient of benzene

0.00203

Permeability of silty clay in

x, y, and z direction

380 MD NAPL/water partition

coefficient of ethyl-benzene

0.000173

Porosity of sandy soil 0.35 NAPL/water partition

coefficient of toluene

0.000594

Porosity of till 0.30 NAPL/water partition

coefficient of xylenes

0.000175

Porosity of silty clay 0.53 Benzene solubility 1,750 mg/l

NAPL/water interfacial

tension

45 Dynes/cm Ethyl-benzene solubility 152 mg/l

NAPL density 0.713 g/cm3 Toluene solubility 535 mg/l

Longitudinal dispersivity of

sandy soil

5 m Xylenes solubility 175 mg/l


clay till

5 m Time step at t D 0 0.101 Day


silty clay

5 m Maximum time step size 10 Day

Transverse dispersivity of

sandy soil

0.5 m Tolerance for concentration

change

0.001

tions in 1998 and 1999 were also used for estimating model parameters of the developed

multiphase compositional simulator. Table 2 lists all estimated parameters. The developed

multiphase DPVE simulator was applied to predict the free product thickness after theinitiation of DPVE program. Figure 4 presents the monitored and predicted free product

thickness of October 12, 2001 by using the calibrated model. It was found that the

mean absolute error is 39.4 mm, and the root mean square error (RMSE) is 90.5 mm.

The differences between the predicted and observed free product thickness are generally

acceptable. The RMSE was calculated using the formula as follows:

RMSE D

v

u

u

t

1

n

nX

iD1

.yi � Oyi /2 (15)

where yi is the observed value, Oyi is the predicted value, and n is the number of samples.

The monitoring data of BTEX in 2000 were used to verify the multiphase multicom-

ponent contaminant transport model. Figure 5 presented comparisons of the predicted vs.monitored data. The result indicates that the errors between the simulated and observed

benzene concentrations range from �0.068 to 0.085 mg/L, with a RMSE of 0.029 mg/L,

and a mean relative error of 4.88%. For toluene, the errors between the simulated and

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Figure 4. Predicted vs. monitored free-product thickness for 2001 DPVE program.

observed concentrations range from �0.114 to 0.183 mg/L, with a RMSE of 0.0843 mg/L,and a mean relative error of 4.98%. For Ethyl-benzene, the errors between the simu-

lated and observed concentrations range from �0.131 to 0.235 mg/L, with a RMSE of

0.0906 mg/L, and a mean relative error of 1.56%. For xylenes, the errors between the

simulated and observed concentrations range from �0.378 to 0.190 mg/L, with a RMSE

of 0.139 mg/L, and a mean relative error of �15.58%.The above verification results indicate that the developed 2-D multiphase DPVE

simulator can successfully simulate the DPVE system performance. The 3-D multiphase

compositional model can successfully predict the transport fate of BTEX in the ground-

water. The models developed in this project hold reasonably low errors. Therefore,

the models can be further used for predicting BTEX concentrations at a number of

temporal/spatial units under different remediation scenarios.

3.5. Result Analysis

3.5.1. Multiphase and Multi-Component Simulation. For many real-world sites, hydro-geological parameters could vary significantly from one site to another and exhibit high

spatial variability even within the same site. In this study, soil structures are complicated

with a variety of uncertainties due to system complexities, leading to imprecise/vague

modeling parameters. Three key parameters will be assumed to be random variables

with normal PDFs; they include the intrinsic permeability (Kxx) (mean of InKxx D 7:5,variance of InKxx D 2:5), the longitudinal dispersivity (aL) (mean D 2.5 m, variance

D 0.5 m), and the porosity (n) (mean D 0.35, variance D 0.1). Through Monte Carlo

simulation, the contaminant distribution in the study domain under various scenarios

can be obtained. It was found that the results were in normal distributions, where the

means and variances could be obtained through standard statistical analysis. Figure 6presented the distributions of the initial free-product thickness, the predicted mean level

of free-product thickness after a 6-month DPVE program and the predicted mean level

of free-product thickness after a one-year DPVE program respectively.

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Figure 5. Predicted vs. monitored BTEX concentrations in 2000.

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Figure 6. Predicted mean free-product thickness (mm) after (a) 6-month and (b) 1-year DPVE

operations.

Results in Figure 6 indicate that the DPVE program can considerably reduce the free-

product thickness. Compared with the free-product distribution in Figure 3, the maximum

thicknesses drop approximately 260 and 440 mm under the 6-month and 1-year DPVE

operations, respectively. For both scenarios, the high concentration free-product zones

mainly accumulate around extraction well 105, followed by wells 101 and BH108. Underthe 6-month DPVE scenario, the contaminant area (about 4,350 m2) decreases slightly

compared with the initial level. Under the 1-year DPVE scenario, the contaminant area

(about 2,600 m2) will shrink significantly and is only half the level of the initial one.

The variances of the predicted free-product thickness are different in various grid cells,

ranging from 0 to 87 mm. The results from DPVE process simulation imply that theremoval efficiency is not linearly proportional to the period of operations. The previous

6-month DPVE program will lead to a relatively higher removal rate (32.5%) compared

with the latter one (22.5%). This demonstrates the complexities associated with DPVE

operations.

The predicted results of free-product thickness (in probabilistic distributions) will beused directly as the source items to the contaminant transport model for predicting BTEX

fate in groundwater under a variety of scenarios (see Table 1). The results indicated that

the predicted BTEX concentrations could also be described as stochastic variables with

normal distributions. For example, Figure 7 and Figure 8 present the obtained mean

concentrations of BTEX 10 years later under two scenarios: (A1) no further remediation

after zero-day DPVE operation and (A7) 60% remediation efficiency after 6-month DPVEoperation. The results demonstrate a significant difference between scenarios A1 and A7.

The maximum benzene concentration in scenario A1 is about 4.3 times higher than that

in scenario A7; the contaminant impact area of A1 is about 3 times larger than that of A7.

The simulation results indicated that the variances of benzene concentrations are about

900 and 288 m2 for scenarios A1 and A7, respectively. Generally, it is indicate thatthe developed multiphase multicomponent simulator can well predict the contaminant

fate and transport in subsurface and provide valuable information of environmental

performance under a variety of remediating scenarios; the system uncertainties can be

tackled effectively through coupling the simulator and Monte Carlo technique.

For further environmental impact analysis, the risky and highly risky zones wereidentified based on counting the number of grids containing BTEX levels exceeding the

environmental criteria, and timing the number with the area of a single grid. For example,

in Figure 7, the risky (violating SERM criteria) and highly risky areas (10-times higher

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Figure 7. Mean concentration of BTEX (ppb) 10 years later under no remediation scenario after

zero-day DPVE process.

Figure 8. Mean concentration of BTEX (ppb) 10 years later under 60% remediation efficiency

after 6-month DPVE operation.

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than SERM criteria) cover 98 and 57 grid cells; as each grid cell covers an area of 36 m2,

the total areas of risky and highly risky zones are 3528 and 2052 m2, respectively. Table 3gives a summary of all predicted means and variances of BTEX risky and highly risky

areas for all remediating alternatives.

3.5.2. The Performance Matrix. A MCDA performance matrix, as shown in Table 3,

can be generated through cost analysis, DPVE-process modeling, contaminant-transport

modeling and Monte Carlo simulation. P1 and P2 list the cost associated with DPVEoperations and groundwater remediation under various scenarios. They could be described

as intervals or uniformly distributed random variables. P3 to P9 are used to address

the environmental performance under various scenarios. Their values are described as

random variables with normal PDFs obtained from modeling efforts. It is indicated that

the risky and highly risky areas of ethyl-benzene are relatively larger than those of

other contaminants; the risky area of xylenes is significantly smaller than others. Thisis due to the fact the SERM criteria is only 2.4 ppb for ethyl-benzene and the criteria

level for xylenes is about 125 times higher. It is found that an increase of treatment

efficiency generally leads to an increase of environmental performance. For example,

comparing scenarios A1 and A2, the mean risky area of toluene decreases from 3,384

to 2,736 m2 and the mean highly risky area drops from 1,836 to 972 m2. However, itis not always the case. For example, comparing scenarios A7 and A8, the risky areas

of toluene and ethyl-benzene increases from 1,080 to 1,332 m2 and 1,476 to 1,944 m2,

respectively; the mean highly-risky areas of these two substances drops from 504 to 0 m2

and 180 to 0 m2, respectively. This is due to a possible dissolution of free-product into

the groundwater systems, leading to expanded area of groundwater contamination. Theabove results imply the necessity of applying two different levels of risks in evaluating

environmental performances, as is the case for this study.

3.5.3. Ranking through Deterministic MCDA Techniques. After the performance matrix

is established, the decision analysis can be preceded. For comparison purposes, an

investigation on deterministic MCDA will be undertaken first. The mean levels of allrandom variables in the performance matrix and criteria weights will be used. Table 4

shows the ranking results through three MCDA techniques (i.e., SAW, TOPSIS, and

PROMETHEE-II) where the results are mostly consistent. For example, all methods

suggest A6 is the best remediating alternative followed by A10, A7, and A11; A1 is the

worst option. This is obvious since A1 has no environmental consideration that is mostly

undesirable; A6 adopts an average period of DPVE operation and applies a mediumlevel of groundwater treatment, leading to a sound balance between environmental and

economical factors. There are slight variations on a number of rankings under different

MCDA methods. For example, A10 is ranked the second by SAW and PROMETHEE-II

and the third by TOPSIS; A7 is ranked the third by SAW and PROMETHEE-II and the

second by TOPSIS. Based on a combined consideration of different methods, a balancedranking result can be determined as follows: A6 > A7, A10 > A11 > A3, A4 > A5

> A8, A9 > A2, A12 > A1. This ranking result can be verified through investigating

the weighted sum by SAW, the relative closeness by TOPSIS, and the net-flow levels by

PROMETHEE-II for various alternatives. For example, the weighted sums for A7 and

A10 through SAW are 0.7127 and 0.7135 respectively; for TOPSIS, the closeness forA7 and A10 are 0.7198 and 0.6778 respectively; for PROMETHEE-II, the net-flows for

A7 and A10 are 0.0305 and 0.033 respectively; the results indicate that A7 and A10 are

very close to each other and can be grouped into one category.

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Table 3

MCDA performance matrix

Property

Alternatives P1 P2 P3 P4 P5 P6 P7 P8 P9

A1 [0, 0] [0, 0] (3,528, 900) (3,384, 864) (4,104, 1,044) (1,728, 432) (2,052, 504) (1,836, 468) (3,960, 1,008)

A2 [0, 0] [5,640, 10,266] (3,204, 792) (2,736, 684) (3,492, 864) (756, 180) (1,296, 324) (972, 252) (2,520, 648)

A3 [0, 0] [32,793, 67,436] (2,556, 648) (2,088, 540) (2,808, 720) (432, 108) (1,008, 252) (792, 216) (1,872, 468)

A4 [0, 0] [91,828, 202,815] (1,728, 432) (1,584, 396) (1,944, 504) (0, 0) (0, 0) (0, 0) (1,008, 252)

A5 [28,386, 49,203] [0,0] (1,836, 468) (1,764, 432) (2,376, 612) (792, 216) (1,008, 252) (828, 216) (2,088, 540)

A6 [28,386, 49,203] [5,640, 10,266] (1,656, 432) (1,080, 288) (1,296, 324) (720, 180) (432, 108) (396, 108) (1,152, 288)

A7 [28,386, 49,203] [32,793, 67,436] (1,188, 288) (1,080, 288) (1,476, 360) (288, 72) (504, 144) (180, 36) (792, 216)

A8 [28,386, 49,203] [91,828, 202,815] (1,008, 252) (1,332, 324) (1,944, 504) (0, 0) (0, 0) (0, 0) (864, 216)

A9 [56,772, 98,406] [0,0] (1,152, 288) (1,224, 324) (2,052, 504) (468, 108) (288, 72) (468, 108) (1,944, 504)

A10 [56,772, 98,406] [5,640, 10,266] (1,044, 252) (1,224, 324) (1,116, 288) (0, 0) (288, 72) (252, 72) (540, 144)

A11 [56,772, 98,406] [32,793, 67,436] (432, 108) (612, 144) (1,008, 252) (0, 0) (0, 0) (180, 36) (504, 144)

A12 [56,772, 98,406] [91,828, 202,815] (108, 36) (0, 0) (720, 180) (0, 0) (0, 0) (0, 0) (288, 72)

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Table 4

Ranking results based on deterministic MCDA methods

MCDA A1 A2 A3 A4 A5 A6 A7 A8 A9 A10 A11 A12

SAW 12 11 6 5 7 1 3 9 10 2 4 8

TOPSIS 12 10 5 6 7 1 2 9 8 3 4 11

PROMETHEE-II 12 9 6 8 7 1 3 10 5 2 4 11

3.5.4. Inexact Rankings by Stochastic MCDA Methods. The developed stochastic MCDA

method will then be used for investigating the impact of uncertainties on rankings.

Figure 9 shows the ranking distributions through Monte Carlo simulation. Instead of

a deterministic result, the rankings are presented as curves with various distributions.For example, in Figure 9a, A6 has a 64.5% probability of ranking in the first position,

21.4% in the second position, and 10% in the third position; A7 may be ranked in

the second, third, and fourth positions, with probabilities of 28.7, 30.1, and 28.8%,

respectively; A1 has the least uncertainty (with a probability around 95.7%) to be ranked

in the last position. Generally, a rough ranking can be determined by identifying the

maximum possibilities for various alternatives. For SAW method, the rankings are: A6(64.5%) > A10 (34.8%) > A7 (30.1%) > A11 (32.5%) > A4 (33.0%) > A3 (28.1%)

and A12 (21.7%) > A8 (22.6%) > A5 (26.1%) and A9 (21.5%) > A2 (40.9%) > A1

(95.7%). The result is consistent with the one obtained through the deterministic SAW

method. However, the ranking results may vary significantly under system uncertainties.

For example, A4 may become the best choice with a probability of 12.4%, althoughit is more likely to be positioned in the fifth position with a probability of 30.0%;

the ranking of A8 has a high uncertainty as it could be located in the 7th to 11th

positions with probabilities of 22.6, 15.5, 15.2, 19.9, and 17.6%, respectively. The above

results demonstrated that the proposed stochastic MCDA method provides more complete

information of possible rankings than conventional methods. The decision makers cannotonly obtain the ranking information directly, but also gain an in-depth understanding on

the relative derivation and closeness among different alternatives.

It is possible that the ranking curves may overlap for different alternatives. This

corresponds to situations when multiple alternatives are really close and can hardly be

differentiated. For example, in Figure 9c, A3 and A5 are both likely to be ranked in the

6th position with exactly the same probability of 26.4%; A7 and A10 are both likely tobe ranked in the second position with probabilities of 36.9 and 35.4%, respectively, and

in the third position with probabilities of 24.8 and 24.9%. In such cases, the shapes and

relative positions of different curves can be used for a rough judgment. For example,

A10 is slightly offsetting toward R1 compared with A7, and then it may be considered

as somewhat advantageous.Similar conclusions can be drawn from the results of TOPSIS and PROMETHEE-

II methods. As the ranking distributions may vary with different MCDA methods, a

combinative investigation can be undertaken. Figure 10 lists all potential alternatives that

could be ranked in the first, seconds, and third positions with different methods. The

results indicate that A6 is suggested to be the best option, followed by A10; alternativesA6, A7 and A10 are likely to be ranked in the second position, with average possibilities

around 20.0%, 40.2%, and 28.3%, respectively; alternatives A7, A10, and A11 are

potential candidates to be ranked in the third position, with average possibilities around

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Figure 9. Rank distributions with different MCDA methods.

23.8%, 28.9%, and 18.4%, respectively. Similar results can be obtained for other rankings.

The main advantage of such ranking representations is that more quantitative information

is provided regarding behaviors of various remediating alternatives. For example, it is

concluded that A7 and A10 are very close and hard to compare by conventional method;

it is now clear that A7 is more pervasive in the second position than A10, and A10 ismore widespread than A7 as it could be positioned in both the first and second positions.

Generally, scenario A6 (6-month DPVE operation C 30% further remediating effi-

ciency) was identified as the best option for the studied site remediation, followed by

scenarios A7 (6-month DPVE operation C 60% further remediating efficiency) and A10

(1-year DPVE operation C 30% further remediating efficiency). It was indicated thatthe suggested methodology is effective in ranking the remediating alternatives under a

variety of system uncertainties. The obtained ranking information is more thorough than

conventional deterministic MCDA methods and can make more reasonable comparisons

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Figure 10. Ranks 1 to 3 with different MCDA methods.

between various alternatives. This can help site managers gain deeper insight into theadvantages/disadvantages of all potential remediating candidates and make final decisions

based on availability of instruments and labors, complexities of site conditions and

strictness of local environmental authorities.

4. Conclusions

(1) A simulation-based stochastic MCDA method was proposed in this study. The

contaminant transport modeling, DPVE process modeling, deterministic MCDA,

and Monte Carlo simulation were integrated into a general framework. A petro-leum-contaminated site in western Canada was selected as the study case for

demonstrating the applicability of the proposed method.

(2) Totally, 12 scenarios were designed for site remediation. Nine criteria were

used for evaluating each alternative through the developed MCDA methods.

The economical factors consisted of operational cost associated with DPVE andgroundwater remediation. Environmental performances were determined based

on the magnitude of risky and highly risky areas of BTEX contamination that

were predicted through developed models.

(3) The study results demonstrated that the proposed stochastic MCDA method

provided more complete information of possible rankings of alternatives thanconventional methods. The decision makers can not only obtain the ranking

information under uncertainty directly, but also gain an in-depth understanding

on the relative derivation and closeness among different alternatives.

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(4) In mostly MCDA cases, it is difficult to say that one alternative is superior to

another under a deterministic condition; the result may have large variations un-der uncertainties. The proposed methodology can effectively tackle this problem.

However, if these uncertainties cannot be addressed by stochastic distributions,

the applicability of this method will be restricted. It is desired in further studies

that the fuzzy-set and interval theory be applied into this emerging area.

Acknowledgments

This research was supported by the Major State Basic Research Development Program of

MOST (2005CB724200 and 2006CB403307) and the Natural Science and Engineering

Research Council of Canada.

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