Stochastic cost optimization of DNAPL remediation – Method description and sensitivity study

at SciVerse ScienceDirect

Environmental Modelling & Software 38 (2012) 74e88

Contents lists available

Environmental Modelling & Software

journal homepage: www.elsevier .com/locate/envsoft

Stochastic cost optimization of DNAPL remediation e Method description andsensitivity study

Jack Parker a,*, Ungtae Kim a, Peter Kitanidis b, Mike Cardiff c, Xiaoyi Liu b, Greg Beyke d

aDepartment of Civil and Environmental Engineering, University of Tennessee, Knoxville, TN, USAbDepartment of Civil and Environmental Engineering, Stanford University, Stanford, CA, USAcDepartment of Geosciences, Boise State University, Boise, ID, USAd TRS Group, Inc., Nashville, TN, USA

a r t i c l e i n f o

Article history:Received 5 October 2011Received in revised form2 April 2012Accepted 9 May 2012Available online 13 June 2012

Keywords:Stochastic optimizationUncertainty analysisDNAPLModel calibrationThermal source treatmentEnhanced bioremediationRemediation cost

* Corresponding author.E-mail address: [email protected] (J. Parker).

1364-8152/$ e see front matter � 2012 Elsevier Ltd.doi:10.1016/j.envsoft.2012.05.002

a b s t r a c t

A modeling approach is described for optimizing the design and operation of groundwater remediationat DNAPL sites that considers uncertainty in site and remediation system characteristics, performanceand cost model limitations, and measurement uncertainties that affect predictions of remediationperformance and cost. The performance model simulates performance and costs for thermal source zonetreatment and enhanced bioremediation with statistical compliance rules and real-time operationalsystem monitoring. An inverse solution is employed to estimate model parameters, parameter covari-ances, and residual prediction error from site data and a stochastic cost optimization algorithm deter-mines design and operation variables that minimize expected net present value cost over Monte Carlorealizations. The method is implemented in the program SCOToolkit. A series of applications to a hypo-thetical problem yielded expected cost reductions for site remediation as much as 85% compared toconventional non-optimized approaches, while also increasing the probability of achieving “no furtheraction” status in a specified timeframe by more than 60%. Optimizing monitoring frequency forcompliance wells used to make no further action determinations as well as operational monitoring usedto make decisions on individual remediation system components reveals tradeoffs between increaseddirect costs for sampling and analysis versus decreased construction and operating costs that arisebecause more data increases decision reliability. Optimizing protocols for operational monitoring andheating unit shutdown protocols for thermal source treatment (incremental versus all-or-none shut-down, soil versus groundwater sampling, number and frequency of samples) produced cost savings ofmore than 20%. Defining compliance based on confidence limits of a moving time window regressiondecreased expected cost and lowered failure probability compared to using measured extreme valuesover a lookback period. Uncertainty in DNAPL source delineation was found to have a large effect on thecost and probability of achieving remediation objectives for thermal source remediation.

� 2012 Elsevier Ltd. All rights reserved.

1. Introduction

Optimization methods have been used increasingly to improveperformance and reduce costs associated with groundwaterremediation design and monitoring (Teutsch et al., 2001). Consid-erable work has been performed on optimization of long-termmonitoring sampling locations and frequency (Loaiciga et al.,1992; EPA, 2000; Reed et al., 2000; Cameron and Hunter, 2002;Reed and Minsker, 2004; EPA, 2005; Parsons, 2005; EPA, 2007).User-friendly long-term optimization software tools have been

All rights reserved.

developed by Aziz et al. (2003) and Harre et al. (2009) that utilizestatistical methods to eliminate redundant well locations and toreduce sampling frequency.

Many studies have been reported involving optimization ofpump-and-treat system design using deterministic groundwatermodels to minimize total pumping rate as a surrogate for operatingcost (Gorelick et al., 1984) or considering fixed and operating costs(McKinney and Lin, 1996), with regulatory criteria (e.g., plumecontainment, time limits, etc.) treated as an optimization constraint(Wagner and Gorelick, 1987; McKinney and Lin, 1996), as a “penaltycost” for non-compliance in the objective function (Rizzo andDougherty, 1996; Chan-Hilton and Culver, 2005), or as a criteriain multi-objective optimization (Erickson et al., 2002; Singh andChakrabarty, 2011). Cost savings over trial-and-error methods

mailto:[email protected]

www.sciencedirect.com/science/journal/13648152

http://www.elsevier.com/locate/envsoft

http://dx.doi.org/10.1016/j.envsoft.2012.05.002



J. Parker et al. / Environmental Modelling & Software 38 (2012) 74e88 75

ranging from 5 to 50% have been reported Becker et al. (2006)reported that simulation-optimization methods were able toidentify solutions that cost less than, translating to cost savings of$600K to $10M for the sites studied.

Deterministic cost optimization identifies designs that mini-mize predicted costs if model parameters correspond to theirbest estimates. However, such an approach provides no “safetyfactor” for adverse deviations of model predictions from bestestimates. Due to large uncertainties in groundwater modelparameters and their predictions, deterministic optimization isthus likely to yield designs that have an unacceptably highprobability of failure to meet design criteria. A number of authorshave described stochastic optimization methods to take predic-tion uncertainty into consideration in the optimization process(Andricevic and Kitanidis, 1990; Lee and Kitanidis, 1991;Tucciarelli and Pinder, 1991; Wagner et al., 1992; Aly and Peralta,1999; Teutsch and Finkel, 2002; Mugunthan and Shoemaker,2004; Chan-Hilton and Culver, 2005; Feyen and Gorelick, 2005;Ricciardi, 2009).

Remediation of sites with dense nonaqueous phase liquid(DNAPL) source zones is particularly difficult due to their lowsolubility and long persistence (Cohen and Mercer, 1993; NationalResearch Council, 1994). These sites often require source treat-ment to reduce themass of DNAPL by excavation or in situ treatmentvia thermal or chemical oxidation, surfactant flushing or enhancedsource biodecay (Liang and Falta, 2008; Heron et al., 2009; Thomsonet al., 2007). Unfortunately, there is often a great deal of uncertaintyin the location, total mass and spatial distribution of DNAPL withina site, which can introduce large uncertainty in design performancepredictions. ITRC (2004) reviewed methods for identification andcharacterization of DNAPL source zones. Ayvaz (2010) and Dattaet al. (2011) have described methods for source identification andparameter calibration using inverse modeling methods. Parker et al.(2010b) demonstrated that for a given data set available for modelcalibration, uncertainty in predicted source depletion exhibitedincreased above a minimum when model complexity increased ordecreased from an optimum level. The optimum complexityincreased and prediction uncertainty decreased when the infor-mation content of calibration data increased. Dokou and Pinder(2009, 2011) described a stochastic optimization method to designa sampling strategy to minimize uncertainty in DNAPL sourceparameters.

Dissolved plume containment or “polishing” of residual DNAPLsource contamination in many cases will be accomplished morecost-effectively by introducing amendments to enhance in situcontaminant biodecay (Wymore et al., 2006) than by pump-and-treat methods. Mayer and Endres (2007) studied cost tradeoffsbetween source mass removal and dissolved plume remediationusing a deterministic approach. In practice, optimal DNAPL siteremediation may require a combination of technologies withtradeoffs among design variables for different systems. In additionto increasing the number of design variables, models capable ofsimulating multiple remediation technologies will require addi-tional model parameters that will add to performance predictionuncertainty.

Cardiff et al. (2010) presented a semi-analytical model forDNAPL site remediation using thermal source treatment and/orelectron donor injection for enhanced bioremediation with anoptimization module to determine design variables to minimizeexpected cost to meet specified compliance criteria. Hypotheticalcases were considered to optimize the duration of thermal sourcetreatment and electron donor injection. Parker et al. (2010a)extended the approach to employ adaptive remediation termina-tion criteria based on operational monitoring and investigatedeffects of monitoring frequency on expected cost.

In the present study, we extend the work of Cardiff et al. (2010)and Parker et al. (2010a) to consider the following:

� Effects of DNAPL source delineation uncertainty on thermaltreatment performance reliability. In previous modelingefforts, we effectively assumed perfect source delineationknowledge, with no possibility of DNAPL mass outside of thespecified thermal treatment area. Realistically, inaccuratesource delineation is the most significant factor affecting theperformance of thermal source treatment technologies. In thispaper, we explicitly consider uncertainty in source delineationon thermal system performance.

� Methods of dealing with statistical outliers in compliance rules.In our previous efforts, “no further action” decisions weresensitive to outlier data. In the present work, we consider theeffect of a compliance rule that employs regression confidencelimits on a moving time window to attenuate the influence ofoutliers.

� Enhanced bioremediation model extensions. The current workconsiders model refinements to consider enhanced DNAPLdissolution associated with electron donor injection upgra-dient of source zones and nonequilibrium electron donorreactions.

Other improvements include revised cost models that explicitlytreat costs for compliance and operational monitoring, animproved thermal mass removal model, and options to considertransport with nonlinear streamlines and multiaquifer plumesassociated with localized vertical leakage. The methodology isimplemented in the Stochastic Cost Optimization Toolkit (SCO-Toolkit) written in MATLAB.

The objective of this paper is to describe the methodology andpresent selected hypothetical case studies to demonstrate theinteractions of operational and compliance monitoring strategies,compliance rules, and model and parametric uncertainty and theireffects remediation design, cost and reliability.

2. Description of stochastic cost optimization approach

A comprehensive description of the modeling approach isavailable in a report by Parker et al. (2011), which can be retrievedonline or from the authors on request. In the following, we presentan overview that emphasizes previously unpublished features. Asummary of symbols and acronyms used herein is given in Kimet al. (2011).

2.1. DNAPL source depletion and thermal treatment

The simulation model considers multiple DNAPL sources thatmay have different initial masses and dissolution kinetics.Considering the possibility of engineered manipulation in upscaledmass transfer kinetics, we describe the rate of contaminant massdissolution in a given source zone, J [MT�1], versus time, t, by

JðtÞ ¼ FmtðtÞJcal�MðtÞMcal

�b

(1)

where Jcal ¼ J(t ¼ tcal) and Mcal ¼ M(t ¼ tcal) in which tcal denotesa reference date used for model calibration, M is the sourcecontaminant mass remaining, b is a depletion exponent thatreflects the DNAPL source “architecture,” and Fmt is a time-dependent dimensionless mass transfer enhancement factor. Thereference date is arbitrary since the J(t) function is scalable with Jand M values corresponding to any tcal. within the span of timeDNAPL is present. Integration of a source mass balance equation

J. Parker et al. / Environmental Modelling & Software 38 (2012) 74e8876

with (1) yields closed-form expressions for M(t) and J(t) due togradual source dissolution.

During thermal source remediation (TSR), we assume massreduction in the treatment zone to be a function of cumulativeenergy applied. To consider the effects of imperfect source delin-eation and uncertainty in the area requiring thermal treatment, thesource mass at the beginning of TSR,MTSR o, is divided into themasswithin the treatment zone (Mtreatment zone o) and the mass outsidethe treatment zone (Mmiss), such that

MTSR o ¼ Mtreatment zone o þMmiss (2)

And assuming Mmiss does not change substantially duringthermal treatment, the total source mass remaining after thermaltreatment is

MTSR f ¼ Mtreatment zone f þMmiss f (3)

where Mtreatment zone f is the treatment zone mass following sourceheating. The “missing” mass outside the treatment zone isdescribed by

Mmiss ¼ FmissMTSR o (4)

where Fmiss is the fraction of the pre-remediation source mass thatis outside the thermal treatment zone, i.e., Fmiss > 0 indicates thata fraction Fmiss of the estimated source mass is not within thetreatment volume and hence will not be treated by source heating.We treat Fmiss as a stochastic variable controlled by uncertainty inthe actual source volume approximated as

Fmiss ¼ 1�min�1;

VTSR

Vsource

�(5)

where VTSR is the soil volume treated by the thermal system andVsource is the actual volume of contaminated soil for a given sourcezone. The latter is taken as a stochastic variable by virtue ofuncertainty in source zone dimensions based on field investiga-tions and/or model calibration. The “actual” source volume iscomputed inMonte Carlo (MC) simulations as the product of sourcedimensions Lx, Ly and Lz generated from their respective best esti-mates and covariances (or log-transforms if uncertainty is regardedas log-normally distributed).

Observations of thermal treatment systems indicate that sourcemass diminishes with time as the cumulative energy inputincreases and may be approximately described by

Mtreatment zoneðtÞ ¼ Mtreatment zone oREfracðtÞTSRðsoilÞ (6)

where Mtreatment zone(t) is the mass within the treatment zone attime t during thermal treatment when a fraction (or multiple)Efrac(t) of the design energy has been applied, and RTSR(soil) is theratio of target source mass remaining after thermal treatment tothe initial mass, which represents the performance target forthermal treatment (Parker et al., 2010a). Note thatRTSR(soil) ¼ 1 � RTSR m in the notation of Parker et al. (2010a) whereRTSR m is the target mass removal fraction. If energy is applied ata constant rate, then Efrac(t) is simply the fractional operating timerelative to the design estimate. The design energy requirement toachieve a target mass reduction is estimated considering aquiferheat capacity, advective heat loss, latent heat of volatilization ofwater and contaminants, and planned operating temperature.However, in practice, it is advisable to base decisions on when toterminate thermal treatment on real-time data from operationalmonitoring during remediation. The following strategies formonitoring and system operation are considered.

Method 1a e Prior to heating, NTRborei

soil borings withNTRsamp=borei

samples per boring are collected and average initialsoil concentration is computed for each source treatment zone i.After a period of time when a fraction Efrac(init)i of the theoreticalenergy requirement has been applied, the same number of soilsamples as in the pre-heating round are collected and analyzed. Ifthe average measured soil concentration is less than RTSR(soil)itimes the initial average, heating is terminated for all heatingelements within the source. Otherwise, sampling is repeated attime intervals corresponding to a fractional energy use DEfrac untilthe criteria are met.

Method 1b e Same as Method 1a except NTRwelli

groundwatermonitoring wells with NTR

samp=wellisampling depths per well are

employed rather than soil samples with an operational objective toreduce groundwater concentration by a factor RTSR(gw)i. Note thatduring groundwater sampling within the source zone duringtreatment, well heads should remain sealed to avoid degassing(e.g., sampling through tubes through the well head).

Method 1c e Same as Method 1a and 1b but soil and ground-water samples are taken at each sampling event and heating isterminated when both the average measured soil concentration isless than RTSR(soil)i � the initial average soil concentration and theaverage measured groundwater concentration is less than RTSR(gw)i

times the initial average groundwater concentration.Method 2a e This is similar to Method 1a but individual elec-

trodes are turned off when the measured soil concentration fora sample within the zone heated by the electrode is less thanRTSR(soil)i � the average pre-heating concentration. A one-to-onerelation between electrodes and sampling regions is assumed.After an electrode is turned off, no further sampling is performed inthis region.

Method 2b e Same as Method 2a using groundwater rather thansoil samples with a target groundwater concentration reductionfactor RTSR(gw)i.

Method 2c e Same as Method 2a and 2b but both soil andgroundwater samples are taken at each sampling event. Electrodesare shut off incrementally when both the local measured soilconcentration is less than RTSR(soil)i � the initial average soilconcentration and the average measured groundwater concentra-tion is less than RTSR(gw)i times the initial average groundwaterconcentration.

Assuming mass discharge rate J(t) in (1) can be approximated asthe product of dissolved concentration and groundwater velocityindicates that RTSRðgwÞi ¼ Rbcal i

TSRðsoilÞi. We employ this relationship tocompute source zone groundwater concentrations. Measurementsare simulated by applying “noise” to simulated “actual” concen-trations. Note that since measurements are noisy and are collectedat discrete time intervals, the actual mass remaining when treat-ment is terminated may be greater or less than the target value.

2.2. Groundwater and contaminant transport

Dissolved phase transport of contaminants emanating fromDNAPL source zones in an unconfined aquifer is described bya semi-analytical solution to the 2-D vertically-averaged advection-dispersion equation with the source zone function described aboveas a forcing function. The solutionmethod follows that described byCardiff et al. (2010) with a few extensions. To model contaminantmigration in mildly non-planar flow fields, we represent stream-lines passing through each source with a polynomial expressionand map coordinates from the actual nonlinear flow field toa linearized flow field parallel to the plume centerline. MultipleDNAPL sources are modeled by solving for each source separately,mapping back to field coordinates, and superposing in space(Fig. 1).

N

E

x 2

y 2

N

E

x 1 y 1

j=2

j=1

Fig. 1. Mapping a well location to linearized coordinates for two sources (j ¼ 1, 2) withnonlinear streamlines in field coordinates for solution superposition.


Spatially-variable biodecay under ambient (non-engineered)conditions within the primary aquifer can be described in up tothree “zones” at different distances from the source characterizedby defined first-order decay coefficients. Solutions for zonesprogressively further from the actual source are obtained byrescaling the uniform decay solution to enforce a mass balanceconstraint. Leakage from the primary aquifer to a secondary aquifer(e.g., through a “window” in an intervening aquitard) is modeled bycomputing the “decay” coefficient for the leaky zone as l ¼ qz/fLzwhere qz is the vertical darcy velocity in the leaky zone, f is theprimary aquifer porosity, and Lz is the thickness of the primaryaquifer. The leakage flux versus time computed from the primaryaquifer solution is used as the source function for dissolved trans-port in the secondary aquifer in a similar manner to that employedfor the primary aquifer with groundwater flow and transportparameters relevant for the secondary aquifer.

2.3. Electron donor injection

Enhanced biodecay of chlorinated hydrocarbons (CH) is assumedto be limited by the quantity of electron donor (ED) species relativeto electron acceptor (EA) species (Kamath et al., 2006). To estimatethe attenuation of CH due to ED addition, a superpositionmethod isused that is similar to that describedbyBorden andBedient (1986). Ifredox reactions occur serially in order of decreasing reaction freeenergy (e.g., O2>NO3> SO4> Fe(III)>CH), then an electronbalanceyields

c0CHðserialÞ ¼max

"0;cCH�max

0;REDf 0EDc

availED þREDcHnat

ED �cHEARCHf 0CH

!#

(7)

where c0CHðserialÞ is the aqueous CH concentration after serial EDreactions, cCH is the computed CH concentration before ED reactionscomputed from the contaminant transport model described above,cavailED is the aqueous concentration of injected ED available forreactions, cHnat

ED is the background H-equivalent ED concentration inthe aquifer,cHEA is the background H-equivalent concentration all EAspecies in the aquifer, f 0CH is the ratio of H-equivalent to actualcontaminant concentration, f 0ED is the ratio of H-equivalent to actualinjected ED concentration,RCH is theCH retardation factor, andRED isthe ED retardation factor (no retardation is assumed for EA species).

H-equivalent ratios (Hstoch) for common groundwater ED, EA,and solvent species are summarized in Kamath et al. (2006). H-

equivalent ratios for EAs are estimated as f 0EA ¼ fEA/Eeff where fEA isthe stoichiometric ratio for complete EA reduction and Eeff is frac-tional energy yield for the biologically-mediated reaction afterdeducting energy consumed for cell synthesis (Rittman andMcCarty, 2001). The H-equivalent ratio for CH is similarlycomputed as f 0CH ¼ fCH/Eeff, while H-equivalent ratios for ED speciesare computed as f 0ED ¼ fEDEeff, since ED occurs on the opposite sideof the EAeED balance ledger.

If reductive dechlorination of CH is assumed to occur underanaerobic conditions with competition among microbial pop-ulations responsible for reduction of NO3, SO4, etc., an electronbalance yields

c0CHðparallelÞ ¼ min½1; maxð0; aÞ�cCH

a ¼ RCHf 0CHcCH þ cHEA � REDf 0EDcavailED � REDcH nat

ED

RCHf 0CHcCH þ cHEA � cHO2

(8)

where no retardation is assumed for O2. Assuming that actualbiodecay can be approximated as a linear combination of theforegoing pathways, then

c0CHðmixedÞ ¼ Fserialc0CHðserialÞ þ ð1� FserialÞc0CHðparallelÞ (9)

where Fserial is the fraction of reductive dechlorination that followsthe serial pathway.

ED injection may be modeled in one or more injectiongalleries of width LED perpendicular to the groundwater flowdirection. Nonlinear flow fields may be characterized for eachgallery in the manner described for contaminant transport.Nonreactive dissolved phase ED transport is modeled for stepinputs of ED using the Domenico (1987) solution. We note thatsoluble ED injection will generally be pulsed to reduce wellfouling problems and injection of nonaqueous phase ED will beperformed with a frequency that depends on the dissolution rateof ED material. As a result, temporal variations in ED concen-trations will occur near injection galleries. However, since thesevariations will diminish markedly with distance from thegalleries, modeling ED injection with a time-averaged rate willgenerally not affect ED available to drive biodecay through mostof the aquifer.

Kinetics of ED reactions is approximated assuming the fractionof injected ED concentration that is reactive varies exponentiallywith travel time as

cavailED ðx; y; tÞ ¼�1� exp

�axREDv

�cno rxED ðx; y; tÞ (10)

where cavailED is the aqueous ED concentration available for reactionswith EA and CH, cno rx

ED is the ED concentration before reactionsobtained from the Domenico solution, (x, y) are local coordinates,a is a reaction rate coefficient [T�1], v is groundwater pore velocity[LT�1], and RED is the ED retardation factor [�]. The rate coefficientmay be calibrated from pilot test data or from initial observationsduring full-scale ED injection, in which case, operations may bereoptimized using the estimated coefficient.

Mass balance considerations yield the ED concentrationremaining in solution after reactions with EA and CH given by

cnetED ¼ cno rxED �minða; bÞ

RCHf 0CH

a ¼ REDf 0EDcavailED þ REDcH nat

ED

b ¼ cHEA þ RCHf 0CH�cCH � c0CHðmixedÞ

� (11)


which is used to determine effects of ED injection on mass transferenhancement described below. For multiple ED galleries, total EDconcentration at a given location and time is computed by super-position in field coordinates after mapping linearized coordinatesback to field coordinates. An adaptive strategy is employed todecide when to terminate ED injection in a given gallery based onreal-time monitoring.

Studies by Macbeth and Sorenson (2008) indicate an approxi-mately linear mass transfer enhancement with ED concentration asinferred from chemical oxygen demand (COD) in the source zone,which we describe by

Fmt ¼ 1þ fmtcnetED (12)

where fmt is a mass transfer enhancement coefficient. The value ofcnetED in (12) is computed at coordinates corresponding to the center ofthe DNAPL source zone at a date equal to the injection start date plusa duration tlag to allow the ED concentration to reach steady-statevalue estimated as tlag ¼ xR/v þ 3(2ALxR)1/2/v where x is the traveldistance from the ED injection gallery to the center of the DNAPLsource,R is the ED retardation factor, v is themean groundwater porevelocity, and AL is the aquifer longitudinal dispersivity.

2.4. Model calibration and uncertainty analysis

The model calibration and uncertainty analysis methodologyused in SCOToolkit has been described by Cardiff et al. (2010). Thecalibration process seeks to minimize deviations between themodel and various field measurements conditioned by prior esti-mates of parameters and on the uncertainty in measurements andprior estimates. A linearized approximation of the parameterposterior covariancematrix is computed and themagnitude of eachdata type’s uncertainty is estimated using a restricted maximumlikelihood algorithm (Kitanidis, 1987).

After performing model calibration, we utilize linearizeduncertainty propagation methods to generate equiprobablerealizations of calibrated model parameters for the problemunder consideration using standard methods for multivariateGaussian distributions (e.g., Press and Flannery, 2007) based onparameter best estimates and covariances determined from thecalibration. If log-transformations of parameters were usedduring calibration, the same transformations are used forparameter generation. The model also generates covariance-freeparameters, which are not included in calibration but needed toconsider their uncertainty (or randomness). Net present value(NPV) cost is computed for each MC realization and the averageNPV cost for all realizations is computed as an estimate of theexpected NPV cost.

2.5. Cost functions

The total NPV cost for all site remediation activities, includingpenalty costs, for each MC realization is

CallNPV ¼CSWtot

NPV þ CTRtotNPV þ CEDtot

NPV þ IPTCPTcaptotal ð1� dÞtPT�tref

þ IPTXtnfat¼ tPT

CPToptotal ð1� dÞt�trefþIpenC

penNPV ð13Þ

where CallNPV is the total NPV remediation and penalty cost ($K);

CSWtotNPV is the total NPV site-wide cost ($K); CTRtot

NPV is the total NPVthermal remediation cost ($K); CEDtot

NPV is the total NPV ED injectionsystem cost ($K); CPTcap

total is the total pump-and-treat (P & T) fixedcost ($K); CPTop

total is the total P & T operating cost per year ($K/year);CpenNPV is the NPV penalty cost ($K); Ipen is 1 if a penalty cost is

triggered, else 0; IPT is 1 if P & T implementation is triggered, else0; tPT is the year that P & T is triggered (year); tnfa is the yearcompliance is achieved or the max simulation date for non-compliance (year); tstart is the first year capital costs are incurred(year); tref is the basis date for NPV adjustment (year); and d is theannual discount rate (fraction).

Site-wide monitoring, reporting, and maintenance costs arecomputed as

CSWtotNPV ¼ CSWcap

NPV þ CSWopNPV

CSWcapNPV ¼

�CSWcapwell NSW

well þ CSWcapother

�ð1� dÞtstart�tref

CSWopNPV ¼ Ptcomp

t¼ tstart

�CSWopsamp f SWsampN

SWwell þ CSWop

other

�ð1� dÞt�tref

(14)

where CSWcapNPV is the total NPV site-wide fixed cost ($K); CSWcap

well is the

fixed cost for monitoring well construction ($K/well); CSWcapother is any

other site-widefixed costs ($K);CSWoptotal is the totalNPVoperating cost

for site-wide monitoring and reporting ($K); CSWopsamp is the cost per

sample for site-wide monitoring ($K/sample); CSWopother is other annual

site-wide operating costs ($K/year); f SWsamp is the number of samples

per well per year taken for site-wide monitoring; and NSWwell is the

number of site-wide monitoring wells (including compliancewells).Costs for electrical resistance heating (ERH) are described by

CTRtotNPV ¼ CTR

siteð1� dÞtTSR�tref

þ PNsource

i¼1

8>>>>>>>>>><>>>>>>>>>>:

ITRi�1� fE þ fEEfraci

��CTRvoli

ATSRiZTSRi

þCTRareaiATSRi

�RTSRðsoilÞi

gRtsr

þFiCTRmob þ NTR

welliCTRwelli

þFiNTRwelli

NTRsamp=welli

CTRGWsamp

þFiNTRborei

CTRborei

þFiNTRborei

NTRsamp=borei

CTRSOILsamp

9>>>>>>>>>>=>>>>>>>>>>;ð1� dÞtTSR�tref

(15)

where ATSRi is the areal extent of the thermal treatment zone (m2);CTRtotNPV is the total NPV cost for thermal treatment for all sources

($K); CTRsite is a fixed cost for all sources at a site ($K); CTR

voliis a cost

multiplier per unit area of the treatment zone to reach designenergy ($K/m3); CTR

areai is a cost multiplier per unit area of the

treatment zone to reach design energy ($K/m2); CTRmob is the

mobilization cost for each sampling event ($K/event); CTRwelli

is the

installation cost per monitoring well ($K/well); CTRGWsamp is the

sampling and analysis cost per groundwater sample ($K/sample);CTRborei

is the cost per soil boring ($K/boring); CTRSOILsamp is the cost per

soil sample analyzed ($K/sample); Efraci is the ratio of model-computed energy consumed when TSR terminates versus thedesign energy estimate; fE is the fraction of non-monitoring vari-able costs attributable to energy use (w0.22); gRtsr is an exponentestimated empirically as approximately �0.0626 that describes theincrease in cost associated with a given decrease in the design massfraction remaining RTSR(soil)i; Fi is the total number of soil and/orgroundwater samples divided by the number in the pre-treatmentsampling round; ITRi is 1 if thermal treatment is performed forsource i, else 0; Nsource is the number of individual source zones;NTRwelli

is the number of source zone groundwater monitoring wells;

NTRsamp=welli

is the number of sampling depths per well; NTRborei

is the

number of soil boring locations for each sampling time; NTRsamp=borei


is the number of depth intervals sampled per boring; RTSR(soil)i is thetarget ratio of source mass remaining following thermal treatmentto the mass immediately prior to treatment; tTSR is the date thatthermal treatment is performed (year); Xi is a binary switch (¼0 or1) to select/deselect thermal treatment for specific sources; andZTSRi is the vertical extent of the thermal treatment zone (m).Capital and operating costs for enhanced bioremediation aredescribed by

CEDtotNPV ¼ CEDcap

NPV þ CEDopNPV

CEDcapNPV ¼ CEDcap

width

PNEDgali

i¼1IEDi LEDi ð1� dÞtEDoi �tref

þCEDcapmw NED

mwPNEDgali

i¼1IEDi ð1� dÞtEDoi �tref

þmaxi�IEDi�CEDcapother ð1� dÞminiðtEDoi Þ�tref

CEDopNPV ¼ Ptnfa

t¼ tref

0BBBBBBBBBBBBBBBBBB@

CEDopwidth

PNEDgali

i¼1OEDti LEDi

þCEDopmass

PNEDgali

i¼1OEDti MEDi

þCEDopsamp f EDsamp

PNEDgali

i¼1OEDti NED

mw

þCEDopother

PNEDgali

i¼1OEDti

þCEDopall maxi

�OEDti

�

1CCCCCCCCCCCCCCCCCCA

ð1� dÞt�tref

(16)

where the time summation is over integer values of time in years;

CEDcapNPV is the total NPV fixed ED cost ($K); CEDcap

width is the fixed cost per

ED gallery width ($K/m); CEDcapmw is the construction cost per opera-

tional ED monitoring well ($K/well); CEDcapother is any other fixed ED

costs; CEDopNPV is the total NPV operating cost for ED injection ($K);

CEDopwidth is the operating cost per ED gallerywidth formaintenance etc.

($K/m); CEDopmass is the operating cost per unit ED mass injection ($K/

kg); CEDopsamp is the collection and analysis cost per ED monitoring

sample ($K/sample); CEDopother is other EDoperating costs per gallery per

year for reporting etc. ($K/gallery/year); CEDopall is other ED operating

costs regardless of the number of galleries ($K/year); f EDsamp is thenumber of samples per well per year for ED operational monitoring;IEDi is an indicator that is 1 if gallery i is actually implemented else 0;

LEDi is the width of ED gallery i perpendicular to the flow direction

(m);MEDi is themass injection rate of ED forgallery i (kg/year);NEDmw is

the number of operationalmonitoringwells (not injectionwells) perED gallery; NED

gal is the number of potential ED galleries; OEDti is an

indicator that is 1 if gallery i is operating inyear t else 0; and tEDoi is thestart date for ED gallery i (year).

2.6. Remediation criteria and optimization

The overall goal is to reduce contaminant concentrations incompliance wells below risk-based or regulatory-mandated levelswithin a certain timeframe at minimum cost. For the actual systemand hence for each MC realization, we consider that one of thefollowing outcomes will occur:

2.6.1. No further action (NFA)Compliance criteria are met if a specified statistical measure of

contaminant concentrations is less than a maximum allowable

value at all compliance locations after a date tnfa in which case allremedial actions and monitoring cease.

2.6.2. Non-compliance (NC)Non-compliance (“failure”) conditions arise if the statistical

measure of contaminant concentration exceeds the maximumallowable value at one or more compliance locations prior to a datetpenalty or the maximum simulation date tmax is reached withoutattaining NFA status. In either case, a fixed present value penaltycost is incurred and the realization simulation terminates.

2.6.3. Conditional containment (PT)If non-compliance conditions arise at a designatedPT triggerwell,

a pump-and-treat or other containment system is implementedupgradient of the trigger location. Discounted capital and annualoperating costs for the containment system are accrued, while otherremedial actions continue until NFA is met or tmax is reached.

Since concentration measurements at a given compliance wellcan exhibit considerable temporal variability, compliance rulesmust be carefully defined to reduce the possibility of false deter-minations due to measurement “noise”. Two noise-filteringapproaches are considered, which are summarized in Table 1. Thecompliance date tnfa is defined to ensure that low compliance wellconcentrations due to upgradient ED injection are not mis-interpreted as being permanently clean. It is computed as

tnfa ¼ maxijhtTSRfi þ DtTSRij; tSTPi þ DtEDij

iþ Nlookback (17)

where tTSRf is the date thermal treatment terminates, DtTSRij is thetravel time from source i to compliance well j, tSTPi is the date thatED injection stops in gallery i, DtEDij is the travel time from EDinjection gallery i to the compliance well j, maxij is the maximumoverall ij pairs with source/gallery i upgradient of compliancewell j,and Nlookback is the duration of a moving time window used todetermine if compliance conditions are met.

The objective of the design optimizationproblem is tofind a set ofdesign variables that minimizes the expected NPV (ENPV) cost. NFA,NC, and PT rules serve as implicit constraints on the optimizationconditioned through the cost and performance models. We assumethat contaminant concentrations are monitored with a frequency off SWsamp per year at each compliance well location. Log-normalmeasurement “noise” is applied to simulated annual averages inMC realizations with a standard error equal to the lnC standarddeviation from model calibration (based on raw unaveragedmeasurements) divided byf SW 1=2

samp to adjust for variance reductiondue to averaging. Note that increasing sampling frequency thusdecreases measurement noise, which narrows confidence limits,allowsearlierNFA attainment, and lowers non-monitoringoperatingcost. The optimum sampling frequency will occur when this costreduction is just offset by the additional monitoring cost.

The “penalty cost” may be a real cost (e.g., for last ditchcontainment measures) or a fictitious cost applied to constrainthe failure probability. Penalty cost is specified in NPV dollars (i.e.,no discount is applied internally). Care should be taken not tospecify a penalty date (tpenalty) that cannot be realistically ach-ieved with current site conditions and proposed remedial tech-nologies lest compliance will be nearly impossible to meet andthe optimization problem will be ill-defined. Likewise, if tmax istoo early to achieve a high NFA probability, low remediation costsmay be misleading. An exception may be if long-term contain-ment with institutional controls is under consideration, tmax maybe set to reach a pseudo-steady state condition, fixed and penaltycosts set to zero, and design variables optimized to minimizeoperating costs.

1200

1300 Source area Monitoring wells Compliance location ED upgradient monitoring ED injection gallery

1000

ppb

Table 1Compliance rule protocol options.

Extreme value (EXV) rule Regression confidence limit (RCL) rulea

NFA If annually averaged contaminant concentrations for all compliance wellsare less than Cmax for each of the last Nlookback years ending on or after tnfa,then all remediation and monitoring activities are terminated.

If the upper confidence limit of the current value of a regressionof contaminant concentration versus time over the last Nlookback yearsending on or after tnfa is less than Cmax for all compliance wells, thenall remediation and monitoring activities are terminated.

NC If annually averaged contaminant concentrations for any compliance wellsexceed Cmax in any of the last Nlookback years ending on or after tpenalty or if NFAhas not been achieved prior to tmax, then a specified present value penaltycost Dpenalty is added to the cost function and the simulation is terminated.

If the lower confidence limit of the current value of a regression ofcontaminant concentration versus time over the last Nlookback yearsending on or after tpenalty exceeds Cmax for any compliance wells orif NFA has not been achieved prior to tmax, then a present valuepenalty cost Dpenalty is added to the cost function and the simulationis terminated.

PT If annually averaged contaminant concentrations in a designated PT triggerwell exceed CPT for any of the last Nlookback years ending on or after tPT, thendiscounted capital and operating costs for pump-and-treat or other plumecontainment system are accrued. The simulation continues until NFA isachieved or tmax is reached.

If the lower confidence limit of the current value of a regression ofcontaminant concentration versus time over the last Nlookback yearsending on or after tPT exceeds CPT for a designated PT trigger well,then discounted capital and operating costs for pump-and-treat orother plume containment system are accrued. The simulationcontinues until NFA is achieved or tmax is reached.

a Based on Levine (2010).


It is self-evident that the duration of time allowed beforecleanup criteria are required to be met will have a significant effecton remediation design and cost. Specifically, if tpenalty, tPT and/or themagnitude of contingent containment or penalty costs areincreased, then earlier, more aggressive and more costly remedia-tion will be favored. Likewise, if the time discount factor, d, isdecreased, future costs are less sharply discounted, thus favoringearlier and more aggressive action. In the case of no contingentpenalty or containment costs (or tpenalty > tmax and tPT > tmax) witha positive discount rate, the cost optimal solution will be to simplymonitor until tmax or NFA is reached, regardless of the probability ofachieving NFA. A cost consequence of “failure” must be stipulatedto induce active remediation, unless the start date for a remedialaction is specifically stipulated.

This study used the genetic algorithm (GA) toolbox in MATLABversion 2010b, which is applicable to a wide range of complexoptimization problems. GA parameters determined through severaltest runs are 30 for generation size and population size, and 1.75 forthe crossover function ratio. Stopping criteria were 0.1 for theobjective function tolerance limit, 10�6 for the constraints tolerancelimit, and 20 for the stall generation limit (i.e., GA stops when theaverage change of the objective function value is less than thefunction tolerance limit over 20 generations). Half of the initialpopulation was regarded as a set of feasible user guesses ratherthan as pure random values to increase convergence and enhanceperformance. All optimization runs of this study converged within30 generations. Each run took about 40 min on a single 3 GHz CPUwith 3 GHz RAM.

Model output includes optimal ENPV costs (with and withoutpenalty costs), cost breakdowns, cost probability distributions, andconcentration versus time at compliance locations with confidencelimits, in addition to optimized design variables. Cost and perfor-mance for individual MC realizations as well as for expected valuescan be extracted.

900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 2100 700

800

900

1000

1100

MW1

MW2

MW3

MW4

MW5

MW6

MW7 MW8

MW9 MW10

MW11

MW12

MW13

MW14

MW15

MW16

MW17

MW18

MW19

MW20

MW21

MW22

MW23

MW24

MW25

MW26

→ East, m

m

, h t r o N

0

5

100

500

ED1

ED2

ED3

Fig. 2. TCE concentrations in monitoring wells in 2009 and locations of DNAPL source,compliance well, ED injection galleries, and wells for monitoring upgradient of EDgalleries.

3. Hypothetical case study

3.1. Problem description

Ahypothetical problem is considered involving a trichloroethene(TCE) plume in an unconfined aquifer. A DNAPL release wasassumed to commence in 1965 resulting in a DNAPL pool at thebottomof the aquifer and residual DNAPL in the upper portion of theaquifer designated as Source 1 and Source 2, respectively.

Vertically averaged dissolved plume concentrations werecomputed using the “true” parameters at 26 monitoring welllocations between 1985 and 2009. Simulated concentrations weresubjected to ln-normally distributed “noise” to represent devia-tions due to sampling andmeasurement error, spatial and temporalvariability, and model simplifications with a ln-standard deviation(SlnC) of 0.5. The resulting noisy data were assumed to representfield observations available for model calibration. Well locationsand “measured” concentrations in 2009 are illustrated in Fig. 2. Thehypothetical site characterized by different parameter sets aresummarized in Table 2.

Model calibration was performed using synthetic (noisy)monitoring data from 1985 to 2009 described above and priorestimates of model parameters summarized in Table 2 based oninformation assumed to be obtained from site characterizationand/or literature studies. Calibrated parameter estimates andtheir estimation standard errors are also shown in Table 2 (errorcovariances between all parameters were also computed but arenot shown). The final a posteriori estimate of residual error inTCE concentrations not accounted for by the model wasSlnC ¼ 0.56. Observed versus calibrated concentrations arecompared in Fig. 3.

3.2. Remediation options and unit costs

Remediation options to be considered in this hypotheticalproblem are source zone mass reduction using thermal sourceremoval by electrical resistance heating (ERH), and dissolved plume

Table 3Cost variables used in hypothetical problem.

Definition Variable Value Unit

Thermal Treatment CostsFixed costs for design, operation CTR

site 320 $K

Table 2True model parameters, prior information, and final estimates for calibration using1985e2010 monitoring data.

Parameter PDFa Truevalue

Prior estimates Calibrated values

Value St Devc Value St Devc

Source 1 masson ref. dateb (kg)

LN 3646 2715 0.60 2948 0.52

Source 1 rate onref. dateb (kg/d)

LN 0.088 0.120 0.60 0.067 0.21

Source 1 depletionexponent (�)

N 0.60 0.75 0.25 0.73 0.24

Source 2 mass onref. dateb (kg)

LN 56.4 45.0 0.60 44 0.48

Source 2 rate onref. dateb (kg/d)

LN 0.012 0.010 0.60 0.008 0.37

Source 2 depletionexponent (�)

N 1.30 1.26 0.25 1.32 0.21

Source length, Lx (m) LN 20.0 20.0 0.00 20.00 0.00Source width, Ly (m) LN 20.0 23.0 0.50 18.3 0.39Release date (year) N 1965.0 1963.0 3.00 1963.9 2.53Plume darcy

velocity (m/d)LN 0.070 0.065 0.60 0.049 0.15

Aquifer porosity (�) N 0.30 0.35 0.04 0.36 0.04Longitudinal

dispersivity (m)LN 20.0 17.0 0.50 19.8 0.08

Transversedispersivity (m)

LN 2.00 4.00 0.50 2.1 0.03

Coordinate rotation,a (degrees)

N 5.00 5.99 0.00 5.99 0.00

Aquifer thickness (m) LN 30.0 34.0 0.10 34.7 0.10H-equiv EA

concentration (g/m3)LN 2.75 2.39 0.15 e e

H-equiv O2

concentration (g/m3)LN 0.57 0.49 0.15 e e

H-equiv ED ratio (�) LN 0.31 0.26 0.15 e e

H-equiv ratio CH (�) LN 0.061 0.051 0.15 e e

Serial decay fraction (�) LN 0.32 0.50 0.15 e e

a Assumed probability distributions: N ¼ normal, or LN ¼ lognormal.b Source mass and discharge rate on a reference date of 1990.c Standard deviations of LN variables are log-transformed (dimensionless); all

other values are in specified units.


bioremediation with emulsified vegetable oil (EVO) injection as EDin a single injection well gallery about 100 m upgradient of thecompliance location (ED1 in Fig. 2). ERH will be initiated in January2010. The duration of ERH and timing and operation of ED injection

Observation, ppb

b p p , n o i t a l u m

i S

r = 0.9637

10 −1 10 0 10 1 10 2 10 3 10 410 −1

10 0

10 1

10 2

10 3

10 4

Fig. 3. Observed versus calibrated TCE concentrations 1985 e 2009.

will be determined through optimization of relevant design vari-ables. The remediation goal is to achieve compliance wellcontaminant concentrations less than Cmax ¼ 5 mg/L bytpenalty ¼ 2050. If a penalty condition is triggered on or after thepenalty date or NFA is not met by 2110, a penalty cost is incurred.Cost variables summarized in Table 3. Uncertainty in cost variableswas not considered in this problem.

3.3. Optimization for different TSR operational monitoringstrategies (Cases 1 and 2)

A set of optimization simulations was performed to evaluateeffects of the six thermal operational monitoring strategiesdescribed earlier. The simulations are designated as follows:

Case 1a e Optimize design using TSR Method 1 with soilconcentration data,Case 1b e Optimize design using TSR Method 1 with dissolvedconcentration data,Case 1c e Optimize design using TSR Method 1 with soil &dissolved concentration data,Case 2a e Optimize design using TSR Method 2 with soilconcentration data,Case 2b e Optimize design using TSR Method 2 with dissolvedconcentration data, andCase 2c e Optimize design using TSR Method 2 with soil &dissolved concentration data.

A 95% RCL criteria with a 5-year lookback period (Nlookback) wasemployed to define NFA and non-compliance for all simulations.The following design variables were optimized:

� TSR treatment area, ATSR (same for Source 1 and 2),� TSR removal fractions, RTSR(soil)1 for source 1 and RTSR(soil)2 forsource 2,

and reportingTreatment volume cost coefficient CTR

voli0.025 $K/m3

Treatment area cost coefficienta CTRareai

0.188 $K/m2

Cost per source soil boringa CTRborei

3.5 $K

Analysis cost per soil sample CTRSOILsamp

0.1 $K/sample

Source monitoring well installationcost per wella

CTRwelli

7.0 $K

Analysis cost per groundwater sample CTRGWsamp 0.5 $K/sample

ED Injection CostsFixed cost per meter of ED gallery CEDcap

width0.096 $K/m

Fixed cost per ED performancemonitoring well

CEDcapmw

10 $K/well

Other fixed cost for ED injection CEDcapother 65 $K

Operating cost per ED mass injected CEDopmass

0.00632 $K/kg

Other operating cost per year forED injection

CEDopother

240 $K/year

Cost per ED monitoring event CEDopsampNED

mw 5 $K/eventOther CostsPenalty cost incurred fornon-complianceb

CpenNPV 25,000 $K

Cost per site-wide monitoring event CSWopsamp NSW

well 20 $KReference year for present value cost tref 2010 YearDiscount rate used for incurred costs d 0.03 e

a Since sources 1 and 2 are collocated (i.e., pool and residual within the samearea), the treatment thickness and indicated costs are allocated 15% to Source 1 and85% to Source 2.

b Penalty cost is a fictitious value employed to limit non-compliance probability.


� Energy fractions at first sampling during TSR, Efrac(init)1 andEfrac(init)2 for sources 1 and 2,

� ED gallery injection start date, tEDo,� ED injection rate, MED,� TCE concentration in monitoring well(s) upgradient of EDgallery below which injection is stopped, CED, and

� Compliance and EDmonitoring frequency, fsamp¼ f EDsamp ¼ f SWsamp.

The following variables were fixed during optimization:

� TSR start date ¼ 2010,� Energy increment for sampling after Efrac(init) during TSR,DEfrac ¼ 0.2,

� TSR treatment thickness, ZTSR ¼ 3.6 m for Source 1 and 26.4 mfor Source 2,

� Number of source zone soil borings or groundwater wells forTSR, NTR

welli¼ NTR

borei¼ 5,

� Number of source zone soil samples per boring or groundwatersamples per well for TSR, NTR

samp=welli¼ NTR

samp=borei¼ 2 for

Source 1 and 15 for Source 2, and� Width of ED injection gallery, LED ¼ 350 m.

An initial estimate of the ED injection rate was obtained basedon an electron balance to reduce observed levels of electronacceptors and contaminant. Assuming no aqueous-solid partition-ing, the required ED injection rate is estimated as

MEDðestÞ ¼SF qWLz

Pif 0EAiCEAi þ f 0CHC

maxCH

!

f 0ED(18)

where q is darcy velocity,W is the injection well gallery width, Lz issaturated aquifer thickness, Cmax

CH is the maximum contaminantconcentration entering the gallery, SF is a safety factor, and othervariables were defined previously. Employing typical values for EAconcentrations and stoichiometry (e.g., Parker et al., 2010a) withSF ¼ 1 yields MED z 8 kg/d for a 350 m width gallery. Sincebioremediation performance is expected to be ineffective belowthis level and insensitive to changes in injection rate, if MED dropsbelow an MEDmin of 8 kg/d, no ED injection is assumed to be per-formed and all ED costs are set to zero to improve optimizationefficiency.

Measurement “noise” (SlnC) for thermal system monitoring inthe source zone was assumed to be 0.25 for soil concentrations and0.15 for groundwater concentrations for Source 1 and 0.50 and 0.30,respectively, for Source 2.

Results of Case 1ae2c optimization simulations are tabulated inTable 4. Total EPNV costs, excluding penalty costs, ranged from$1852K to $1939K andmaximumNPV costs for 100MC realizationsranged from $1922K to $2409K. For Case 1a, simulated medianconcentration at the compliance location versus time with 95 and99% confidence limits are shown in Fig. 4a and cost probabilityhistograms are given in Fig. 4b. Note that concentrations aretruncated at an assumed detection limit corresponding to 10% ofthe cleanup target. The optimum sampling frequency for compli-ance monitoring was determined to be once per year (fsamp ¼ 1) forall cases except 1b, which was semi-annual (fsamp ¼ 2).

The probability of non-compliance was 3% for all cases except1b, which was 2%. ED injectionwas found not to be cost effective forall optimization cases considered. This may be attributed to the2050 penalty date. The travel time from the source to the compli-ance location is such that thermal source treatment is able toreduce concentrations at the compliance well by 2050, renderingED injection superfluous.Wewill consider the effect of penalty dateon optimization results in a following section of this paper.

All six optimizations yielded design thermal treatment areas(ATSR) about 2.35 times the best estimate of source area (Acal) toreduce the probability of leaving untreated DNAPL beyond thetreatment zone. The large multiplier reflects relatively largeuncertainty in the calibration source area and high sensitivity oftotal cost to untreated mass. Since the cost of thermal treatmentcould be reduced on the order of $500K by decreasing the thermaltreatment area by half, additional source characterization effort isprobably warranted, especially considering that we really do notknow exactly where the unaccounted mass occurs.

Optimized values of the soil mass reduction ratio (RTSR(soil)) forSource 1 (DNAPL pools) ranged from 0.026 to 0.082 for Method 1and from 0.009 to 0.031 Method 2. However, this variable iseffectively merely a minimum mass reduction factor that is over-ridden a high initial energy fraction (Efrac(init)) for the first samplingevent after system startup. The fact that the average number ofsampling events (including the baseline sampling before heating) isexactly 2 for all cases for Source 1 (Table 4) indicates that optimi-zation sets Efrac(init) so large (w1.8e3.5 times the estimated energyrequirement) that the RTSR(soil) criteria is met for all MC realizationsat the first post-startup sampling event. In other words, Efrac(init),which is a surrogate for thermal treatment duration, becomes theprimary design variable rather than the stipulated mass reductionratio for Source 1 (DNAPL pool).

This is not as much the case for Source 2 (residual DNAPL),which has a lower Efrac(init) (0.82e2.99) and an average number ofsource sampling events between 2.01 and 3.5. The optimized soilmass reduction ratio ranges from 0.020 to 0.096. The computedgroundwater reduction ratio (RTSR(gw)) for Source 2 is several timeslower than RTSR(soil) reflecting a source depletion exponent (b)greater than 1, while it is several times higher than RTSR(soil) forSource 1 reflecting a source depletion exponent (b) less than 1.

The further the source depletion exponent deviates from 1, thegreater the difference between soil and groundwater reductionratios. This is important to recognize when setting and monitoringsource cleanup targets. It is notable that a significantly smaller(more aggressive) minimum soil reduction ratio is needed for thelow b source (Source 1, pools) than for the high b source (Source 2,residuals) to obtain a comparable reduction in dissolved concen-trations. This is somewhat offset by the observation that theoptimal minimum groundwater reduction ratio (RTSR(gw)) forSource 1 (0.032e0.103) is less aggressive (higher) than that forSource 2 (0.012e0.046), which likely reflects the fact that the rate ofmass flux reduction with time (dJ/dt) increases with time if b < 1while it decreases with time if b > 1.

Comparison of Cases 1a through 2c indicates that monitoring ofsoil concentration alone during thermal treatment yields thelowest ENPV for Method 1 (turning off all heating units at the sametime when the average soil and/or groundwater concentration inthe source drops below a specified level), while soil and ground-water data yield the lowest cost for Method 2 (turning off theelectrodes incrementally based on local concentration reductions).Method 1 with soil data yields the lowest cost of all six casesstudied. Including the probability-weighted penalty cost in theENPV leads to the same conclusion. Thus, for this particular case,Method 1 with soil data appears most cost effective. Althoughmeasurement error for soil concentration data is assumed to behigher than for groundwater data, the average cost per sample forgroundwater data is higher due to well construction costs if wellsare only sampled 2e3 times.

The average number of sampling events for monitoring Source 2thermal treatment, hence the average thermal monitoring cost, issignificantly higher using Method 2 than Method 1. This reflectsgreater variability in individual measurements used to incremen-tally turn off heating units compared to averaged measurements

Table 4Summary of design simulations, (bold ¼ optimized values; italic ¼ fixed values, normal type ¼ performance results).

Case 1a 1b 1c 2a 2b 2c 3 4 5a 5b 6

ResultsENPVtotal ($K)a 1852 2278 1932 1907 1939 2025 8580 1867 1305 1336 11,525TSRtotal ($K) 1435 1450 1514 1490 1521 1607 2126 1433 887 888 826EDtotal ($K) 0 0 0 0 0 0 6026 0 0 0 8377TSRmonitor ($K) 40 97 135 51 133 208 24 40 34 34 35Site wide ($K) 417 828 418 417 418 418 427 434 418 448 2322Max NPV ($K) 1922 2409 2037 1968 2008 2100 9332 1908 1379 1379 13,036Non compliance (%) 3 2 3 3 3 3 <1 8 3 53 71

Compliance and ED monitoringCompliance RCL RCL RCL RCL RCL RCL RCL EXV RCL RCL RCLfsamp (year�1) 1 2 1 1 1 1 1 1 1 1 4

Thermal treatment parameters (Both sources)TSR method 1 1 1 2 2 2 1 1 1 1 1TSR data S C S þ C S C S þ C S S S S SATSR/Acal 2.37 2.34 2.35 2.35 2.34 2.35 2.72 2.12 1.00 1.00 1.00

Thermal treatment parameters (Source 1 e Pool)RTSR(soil) 0.0444 0.0260 0.0824 0.0090 0.0308 0.0217 0.0001 0.0266 0.0320 0.0320 0.0100RTSR(gw) 0.1027 0.0693 0.1612 0.0320 0.0786 0.0608 0.0011 0.0706 0.0807 0.0807 0.0345Efrac(init) 3.23 1.82 3.52 2.18 2.27 3.23 3.52 3.87 2.31 2.31 0.80Avg sample events 2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.00 3.48

Thermal treatment parameters (Source 2 e Residual)RTSR(soil) 0.0712 0.0414 0.0963 0.0199 0.0351 0.0899 0.0003 0.0327 0.0860 0.0860 0.0100RTSR(gw) 0.0306 0.0150 0.0456 0.0057 0.0120 0.0416 0.0000 0.0110 0.0392 0.0392 0.0023Efrac(init) 1.08 1.03 1.09 2.99 0.84 0.82 0.85 1.34 1.07 1.07 0.80Avg sample events 2.01 2.08 2.01 2.64 3.3 3.54 2.99 2 2.11 2.11 3.55

ED injection for plume bioremediationtEDo (year) e e e e e e 2010/2011b e e e 2010MED (kg/d) e e e e e e 33/38b e e e 16CED (mg/L) e e e e e e 10/10b e e e 5DtED avg (years) e e e e e e 24/6b e e e 71

a NPV costs do not include penalty cost.b Values are shown for ED1/ED3. Optimization did not elect to deploy ED2 gallery.


used to turn off the entire system. For the example problemconsidered here, higher thermal monitoring costs more than offsetcost savings associated with incremental shutdown of heatingunits. Due to the large number of factors and tradeoffs that affectthe total expected cost NPV cost, it is no more likely that givensampling strategy will be universally optimal than that any otherdesign variable will be optimal for all conditions.

The difference between the highest and lowest optimized ENPVcost for the six different operational methodologies for monitoringthermal treatment is $426K without including penalty costs, whichcorresponds to potential cost reduction of 19% relative to the mostexpensive thermal monitoring strategy. Thus, in addition to opti-mizing various treatment design parameters, evaluating variousoptions for monitoring thermal performance can result in signifi-cant additional cost savings.

Year

b p p , n o i t a r t n e c n o C

2010 2020 2030 2040 2050 2060 2070 2080 2090 2100 10 −1

10 0

10 1

10 2

10 3

10 4

Median 95% limit 99% limit MCL

a

Fig. 4. Results for Case 1a: (a) TCE concentrations at compliance

3.4. Effect of penalty date (Case 3)

In the preceding optimization analyses, a relatively late penaltydate (2050) was stipulated, which allows time for source reductionefforts to be felt at the compliance location enabling NFA conditionsto be met without implementing downstream containmentmeasures. Herewe reconsider Case 1a except with a penalty date of2015 and with three potential ED gallery locations (ED1, ED2 andED3) as shown in Fig. 2. The penalty date of 2015 is only five yearsafter the planned start date for remediation. Since the travel timefrom the source area to the compliance well is about 20 years, someremedial action near the toe of the plume will be required to meetcompliance criteria and avoid a penalty cost.

The optimized design employs injection in ED1 (near thecompliance location) at 33 kg/d starting in 2011 and at 38 kg/d in

NPV, $M

%

, y t i l i b a b o r P

1.0 1.1 1.2 1.3 1.4 1.6 1.7 1.8 1.9 2.0 0

10

20

30

40

50

60

70

80

90

100 NPV ENPV Median

b

well and (b) NPV cost distribution (without penalty cost).

NPV, $M

Prob

abilit

y, %

7.90 8.07 8.23 8.40 8.57 8.73 8.90 9.07 9.23 9.400

10

20

30

40

50

60

70

80

90

100NPVENPVMedian

Year

Con

cent

ratio

n, p

pb

2010 2020 2030 2040 2050 2060 2070 2080 2090 210010−1

100

101

102

103

104

Median95% limit99% limitMCL

a b

Fig. 5. Results for Case 3: (a) TCE concentrations at compliance well and (b) NPV cost distribution (without penalty cost).


ED3 (upgradient of the source) starting in 2010. ED2 provided noadditional cost benefit and was not selected for operation. Injectionat ED1 essentially acts as a biological barrier to prevent contami-nation upgradient of ED1 from reaching the compliance well andallows contaminant concentrations at the compliance well to bebrought below 5mg/L before the penalty date andmaintained untilsource treatment eliminates the need for further ED injection.Deployment of ED injection upgradient of the source zone in ED3implies that source mass transfer enhancement reduces theremediation time sufficiently to be cost effective. That is, the cost ofoperating ED3 is offset by cost savings resulting from earliertermination of ED1 injection and site-wide monitoring. Note thatthe injection rate in the shorter ED3 gallery is 6 times higher thanthat for ED1 indicating that ED levels downgradient of ED3 aremuch greater than required for enhanced biodecay alone. Thesehigher levels enable greater mass transfer enhancement as describeby Eq. (12). ED2 provided no additional cost benefit. The averageduration of ED injection was 26 years for ED1, but only 6 years forED3. This difference approximately reflects the travel time fromED3 to ED1.

The earlier penalty date also induced more aggressive operationof the thermal treatment system, with a significantly lower opti-mized target soil cleanup level (RTSR(soil)). The additional cost ofmore aggressive thermal treatment was offset by cost savingsresulting from earlier termination of ED1 and ED3 injection and ofsite-wide monitoring.

The ENPV cost for Case 3 was 4.6 times greater than for Case 1a,primarily due to high costs for long-term ED injection and to

Year


2010 2020 2030 2040 2050 2060 2070 2080 2090 2100 10 −1

10 0

10 1

10 2

10 3

10 4


a

Fig. 6. Results for Case 4: (a) TCE concentrations at compliance

a much lesser degree to higher thermal treatment cost (Table 4,Fig. 5) If there are no immediate exposure risks and the plume is ator near a steady state, relaxing time constraints on cleanup canhave a great effect on cost.

3.5. Effect of compliance rules (Case 4)

To evaluate the effect of compliance rules on remediation design,cost and performance, we performed an optimization identical toCase 1a except that the EXV rulewas used in lieu of the RCL rule. Theremedial designwas similar to that for Case 1awith no ED injection.The optimized thermal treatment area was somewhat less aggres-sive, while mass reduction targets and Efrac(init) were slightly moreaggressive. The net result was a very slightly lower average thermaltreatment cost and a slightly higher average site-wide monitoringduration and cost (Table 4). The 95% upper confidence limit forconcentration versus time shift a few years to the right, while the99% confidence limit becomes nearly flat above the target concen-tration all the way to 2110 (Fig. 6). The more stringent and “noisy”EXV rule results in non-compliance probability 5 percentage pointshigher than for Case 1a.

3.6. Effect of source delineation uncertainty on thermalperformance (Case 5)

To evaluate the effect of uncertainty in source zone delineationon remediation design, cost and performance, we first performedan optimization identical to Case 1a except that the thermal

NPV, $M

%


1.0 1.1 1.2 1.3 1.4 1.6 1.7 1.8 1.9 2.0 0

10

20

30

40

50

60

70

80

90

100 NPV ENPV Median

b


Year


2010 2020 2030 2040 2050 2060 2070 2080 2090 2100 10 −1

10 0

10 1

10 2

10 3

10 4


NPV, $M

%


1.0 1.1 1.2 1.3 1.4 1.6 1.7 1.8 1.9 2.0 0

10

20

30

40

50

60

70

80

90

100 NPV ENPV Median

a b

Fig. 7. Results for Case 5a: (a) TCE concentrations at compliance well and (b) NPV cost distribution (without penalty cost).


treatment area was fixed at the best estimate of the source areafrom calibration and not optimized. However, the treatment areawas assumed to fully encompass the region with DNAPL and no“missing mass” outside the treatment area was simulated. Thisoptimization is designated as Case 5a. The remediation designobtained for Case 5a represents the optimum design that onewould obtain if the possibility of DNAPL mass outside of thethermal treatment area is disregarded. The performance results forCase 5a, however, are overly optimistic because they are based onan unrealistic assumption to perfect delineation.

The optimized design variables determined in Case 5awere thenemployed in an MC simulation without further optimization with“missing mass” outside the assumed treatment zone treated asa stochastic variable. This simulation is designated as Case 5b. Thestatistical performance results for Case 5b represent the true rangeof performance that can be expected from the Case 5a design.

Case 5a yields predicted performance comparable to Case 1a.The probability of non-compliance at 3% is the same as Case 1a andconcentration versus time probabilities are similar (Fig. 7). TheENPV cost for thermal treatment is lower due to the smaller systemfootprint, leading to a lower simulated total ENPV cost.

However, Case 5a is unrealistically optimistic because it disre-gards uncertainty in source zone delineation and hence in thethermal treatment area necessary to reliably reduce the sourcemass. The effects of this Pollyannaish treatment of source delin-eation reliability is seen in Case 5b results, which reveal a highprobability of contaminant concentrations above target levels(Fig. 8) and a 53% probability of non-compliance by 2110 (Table 4).

Year


2010 2020 2030 2040 2050 2060 2070 2080 2090 2100 10 −1

10 0

10 1

10 2

10 3

10 4


a

Fig. 8. Results for case 5b: (a) TCE concentrations at compliance

While thermal source treatment is generally very effective atreducing contaminant mass within the treated soil volume, it issensitive to error in source delineation and disregarding this factcan lead to much poorer performance than expected.

3.7. Improvement attributable to optimization (Case 6)

A non-optimized MC analysis of remediation performance andcost was performed corresponding to Case 1a using design vari-ables that reflect common field engineering practices (Case 6).Thermal source zone remediation was assumed to start in 2010.Thermal treatment area and volume were taken as their best esti-mates from model calibration (i.e., ATSR ¼ Acal). The first round ofsoil sampling after starting thermal treatment is assumed to occurat a fraction Efrac(init)¼ 0.8 of the theoretical energy requirement foreach source with additional sampling rounds at intervalsDEfrac ¼ 0.2 until shutdown according to TSR Method 1. Thermalremediation is terminated when the average measured soilconcentration in the source zone is below RTSR(soil) ¼ 0.01.

ED injection was also assumed to start in 2010 (tEDo) with anannual average injection rate based on (18) with SF ¼ 2 yieldingMED ¼ 16 kg/d. ED injection was terminated when the annually-averaged measured (simulated þ noise) TCE concentration upgra-dient of the ED injection gallery dropped below 5 mg/L.

The Case 6 thermal treatment design is considerably lesseffective than the optimized designs for Cases 1 and 2 even thoughthe source mass reduction target is more aggressive than nearly allof the Case 1 and 2 targets and ED injection is utilized in Case 6. The

NPV, $M

%


1.0 1.1 1.2 1.3 1.4 1.6 1.7 1.8 1.9 2.0 0

10

20

30

40

50

60

70

80

90

100 NPV ENPV Median

b


NPV, $M

%,ytilibaborP

7.0 7.8 8.6 9.3 10.1 10.9 11.7 12.4 13.2 14.00

10

20

30

40

50

60

70

80

90

100NPVENPVMedian

b

Year

bpp,noitartnecnoC

2010 2020 2030 2040 2050 2060 2070 2080 2090 210010−1

100

101

102

103

104

Median95% limit99% limitMCL

a

Fig. 9. Results for Case 6: (a) TCE concentrations at compliance well and (b) NPV cost distribution (without penalty cost).


poor performance is attributable to a high probability of contami-nant mass beyond the limited thermal treatment area, which is 60%smaller than the optimized area. Lower thermal costs result, butthere is a high probability of source mass remaining above targetlevels after thermal treatment that cannot be removed by naturalsource attenuation by 2110. This results in a 71% probability of non-compliance that leads to long durations for ED injection and site-wide monitoring resulted with a total ENPV cost of $11.5M e

more than six times higher than for optimized Case 1a. The costreduction for Case 1a relative to Case 6 is about 84%.

Long duration ED injection can maintain concentrations at thecompliance location below the target level with a high probability(Fig. 9a). However, source mass flux is unlikely to drop low enoughto shutdown the ED injection gallery prior to the maximumsimulation date of 2110, leading to a non-compliance condition. Thecost probability distribution has a positive bias (Fig. 9b) reflectingthe large number of cases with operating costs continuing up to2110.

4. Conclusions

Stochastic cost optimizationwas found to decrease the expectedNPV cost for site remediation as much as 85% compared toconventional non-optimized approaches, while also increasing theprobability of achieving “no further action” status in a specifiedtimeframe by more than 60%.

Optimizing monitoring frequency for compliance wells used tomake no further action determinations as well as operationalmonitoring used to make decisions on individual remediationsystem components involve tradeoffs between increased directcosts for sampling and analysis versus decreased construction andoperating costs that arise because more data increases decisionreliability, which ameliorates the extent to which systems must beoverdesigned to overcome data uncertainty.

Operational monitoring and heating unit shutdown protocolsfor thermal source treatment (incremental versus all-or-noneshutdown, soil versus groundwater sampling, number andfrequency of samples) can significantly affect system effectivenessand cost. Optimizing these protocols alone was found to effect costsavings of more than 20%.

The formulation of compliance rules can also significantly affectremediation design, performance and cost. We found that definingcompliance based on 95% confidence limits of a regression ona moving time window was more reliable than using measuredextreme values on a similar lookback period, resulting in decreasedexpected cost and lower probability of failure.

Disregarding uncertainty in DNAPL source delineation can leadto marked underdesign of thermal treatment systems, which canresult in a low probability of achieving remediation objectives andultimately to higher costs to later rectify the misjudgments.

Application of the SCOToolkit methodology on a given siteshould increase the probability of meeting cleanup objectives withthe least cost. Employed over a large number of sites should yieldsignificant total cost reductions.

Optimization simulations for cases with a penalty date of 2050found ED injection not to be cost effective. When the penalty datewas shortened to 2015, ED injection just upgradient of thecompliance location was necessary to meet the more stringentcompliance date and ED injection upgradient of the source zonewas found to be cost effective by virtue of combined effects ofenhancing dissolved plume bioremediation and source zone masstransfer.

Acknowledgment

This research was conducted with funding from the U.S.Department of Defense Strategic Environmental Research andDevelopment Program (SERDP) Environmental RestorationProgram managed by Dr. Andrea Leeson under project ER-1611.

List of acronyms and symbols

A area of source zone iATSRi areal extent of the thermal treatment zone i [m2]cnetED aqueous ED concentration after reactions [mg/L]CEA Electron acceptor concentration [mg/L]CED TCE-equivalent concentrations to terminate ED injection

[mg/L]CEDopsamp collection and analysis cost per ED monitoring sample

[$K/sample]CTRvoli

cost multiplier per unit area of the treatment zone toreach design energy [$K/m3]

CTRareai cost multiplier per unit area of the treatment zone to

reach design energy [$K/m2]CSWopsamp cost per sample for site-wide monitoring [$K/sample]

CTRborei

cost per soil boring [$K/boring]

CTRSOILsamp cost per soil sample analyzed [$K/sample]

CTRsite fixed cost for all sources at a site [$K]

CTRwelli

installation cost per monitoring well [$K/well]


CpenNPV NPV penalty cost [$K]

CEDopwidth operating cost per ED gallery width for maintenance etc.

[$K/m]

CEDopmass operating cost per unit ED mass injection [$K/kg]

CEDopother other ED operating costs per gallery per year for reporting

etc. [$K/gallery/yr]CEDopall other ED operating costs regardless of the number of

galleries [$K/yr]CEDcapother other fixed ED costs [$K]

CTRGWsamp sampling and analysis cost per groundwater sample [$K/

sample]CEDopNPV total NPV operating cost for ED injection [$K]

CPToptotal total PT operating cost per year [$K/yr]

d annual discount rate [�]DNAPL dense nonaqueous phase liquidEA electron acceptorED electron donorENPV expected net present valueERH electrical resistance heatingEXV extreme value compliance rulefmt mass transfer enhancement coefficient [L/mg]Fmt mass transfer enhancement factor [�]Jcal contaminant mass dissolution rate for source on

calibration date [kg/d]JBLM Joint Base Lewis-McChordMC Monte CarloMCL maximum contaminant levelMcal contaminant mass on calibration date [kg]MEDi mass injection rate of ED for gallery i [kg/d]MEDmin minimum ED injection rateNC non-compliance conditionNFA no further action compliance conditionNSWwell number of site-wide monitoring wells including

compliance wells [�]Nlookback moving time window for compliance evaluation [yr]NPV net present valueP & T pump and treatRCL regression confidence limit compliance ruleRTSR(soil) target soil concentration reduction fraction for thermal

treatment [�]SCOToolkit Stochastic Cost Optimization ToolkitSLA Sea Level AquiferSlnC standard deviation of ln-transformed variable [�]TCE trichloroethenetpenalty date when penalty cost is incurred [yr]tmax maximum simulation date [yr]tref basis date for present value [yr]TSR thermal source reductionb source mass depletion exponent [�]

References

Aly, A.H., Peralta, R.C., 1999. Optimal design of aquifer cleanup systems underuncertainty using a neural network and a genetic algorithm. Water ResourcesResearch 35 (8), 2523e2532.

Andricevic, R., Kitanidis, P.K., 1990. Optimization of the pumping schedule in aquiferremediation under uncertainty. Water Resources Research 26, 875e885.

Ayvaz, M.T., 2010. A linked simulation-optimization model for solving the unknowngroundwater pollution source identification problems. Journal of ContaminantHydrology 117, 46e59.

Aziz, J.J., Ling, M., Rifai, H.S., Newell, C.J., Gonzales, J.R., 2003. MAROS: a decisionsupport system for optimizing monitoring plans. Ground Water 41 (3),355e367.

Becker, D.B., Minser, B., Greeenwald, R., Zhang, Y., Harre, K., Yager, K., Zheng, C.,Peralta, R., 2006. Reducing long-term remedial costs by transport modelingoptimization. Ground Water 44, 864e875.

Borden, R.C., Bedient, P.B., 1986. Transport of dissolved hydrocarbons influenced byoxygen limited biodegradation e theoretical development. Water ResourcesResearch 22, 1973e1982.

Cameron, K., Hunter, P., 2002. Using spatial models and kriging techniques tooptimize long-term groundwater monitoring networks: a case study. Envi-ronmetrics 13, 629e656.

Cardiff, M., Liu, X., Kitanidis, P.K., Parker, J., Kim, U., 2010. Cost optimization ofDNAPL source and plume remediation under uncertainty using a semi-analyticmodel. Journal of Contaminant Hydrology 13, 24e43.

Chan-Hilton, A.B., Culver, T.B., 2005. Groundwater remediation design underuncertainty using genetic algorithms. Journal of Water Resources Planning andManagement 131, 25e34.

Cohen, R.M., Mercer, J.W., 1993. DNAPL Site Evaluation. C. K. Smoley Publication,Boca Raton, FL, 384 p.

Datta, B., Chakrabarty, D., Dhar, A., 2011. Identification of unknown groundwaterpollution sources using classical optimization with linked simulation. Journal ofHydro-environment Research 5, 25e36.

Dokou, Z., Pinder, G.F., 2009. Optimal search strategy for the definition of a DNAPLsource. Journal of Hydrology 376 (3e4), 542e556.

Dokou, Z., Pinder, G.F., 2011. Extension and field application of an integrated DNAPLsource identification algorithm that utilizes stochastic modeling and a Kalmanfilter. Journal of Hydrology 398, 277e291.

Domenico, P.A., 1987. An analytical model for multidimensional transport ofa decaying contaminant species. Journal of Hydrology 91, 49e58.

EPA, 2000. Subsurface remediation: improving long-term monitoring & remedialsystems performance. EPA/542/B-00/002. In: Conference Proceedings. June8e11, 1999. US Environmental Protection Agency, St. Louis, MI, p. 81.

EPA, 2005. Roadmap to Long-term Monitoring Optimization. EPA 542-R-05e003.Report. US Environmental Protection Agency., 48 pp.

EPA, 2007. Long-term Groundwater Monitoring Optimization Newark, Muscoy, andSource Operable Units Newmark Superfund Sites San Bernardino, California.EPA 542-R-07e015. Report. US Environmental Protection Agency, 326 pp.

Erickson, M., Mayer, A., Horn, J., 2002. Multi-objective optimal design of ground-water remediation systems: application of the niched Pareto genetic algorithm(NPGA). Advances in Water Resources 25, 51e65.

Feyen, L., Gorelick, S.M., 2005. Framework to evaluate the worth of hydraulicconductivity data for optimal groundwater resources management in ecologi-cally sensitive areas. Water Resources Research 41 (W03019), 16.

Gorelick, S.M., Voss, C.I., Gill, P.E., Murray, W., Saunders, M.A., 1984. Aquifer recla-mation design: the use of contaminant transport simulation combined withnonlinear programming. Water Resources Research 20, 415e427.

Harre, K., Chaundhry, T., Greenwald, R., Jian, W., Davis, C., Zavislak, M.,Minsker, B., 2009. Adaptive Long-term Monitoring at Environmental Resto-ration Sites. ESTCP Project ER-0629. TR-2317-ENV. Final Report. Environ-mental Security Technology Certification Program (ESTCP). US Department ofDefense, 419 pp.

Heron, G., Parker, K., Galligan, J., Holmes, T.C., 2009. Thermal treatment of eightCVOC source zones to near nondetect concentrations. Ground Water Moni-toring & Remediation 29, 56e65.

ITRC Council Dense Nonaqueous-Phase Liquids Team, 2004. Strategies for Moni-toring the Performance of DNAPL. Interstate Technology & Regulatory Council,205 p.

Kamath, R.K., Newell, C.J., Looney, B.B., Vengelas, K.M., Perex, J., 2006. Biobalance:a Mass Balance ToolKit for Evaluating Source Depletion, Competition Effects,Long-term Sustainability and Plume Dynamics. GSI Environmental, Inc.

Kitanidis, P.K., 1987. A first-order approximation to stochastic optimal control ofreservoirs. Stochastic Hydrology and Hydraulics 1, 169e184.

Lee, S.-I., Kitanidis, P.K., 1991. Optimal estimation and scheduling of aquiferremediation with incomplete information. Water Resources Research 27,2203e2217.

Levine, H., 2010. EPA perspective on site closure: how clean is clean? US Dept ofDefense SERDP/ESTCP Partners in Environmental Technology TechnicalSymposium and Workshop, Washington DC, Nov 30eDec 2.

Liang, H., Falta, R.W., 2008. Modeling field-scale cosolvent flooding for DNAPLsource zone remediation. Journal of Contaminant Hydrology 96, 1e16.

Loaiciga, H.A., Charbeneau, R.J., Everett, L.G., Fogg, G.E., Hobbs, B.F., Rouhani, S.,1992. Review of ground-water quality monitoring network design. Journal ofHydrologic Engineering 118 (1), 11e37.

Macbeth, T.W., Sorenson, Jr. K.S., 2008. Final Report: In Situ Bioremediation ofChlorinated Solvent Source Areas with Enhanced Mass Transfer. ESTCP ProjectER-0218.

Mayer, A., Endres, K.L., 2007. Simultaneous optimization of dense non-aqueousphase liquid (DNAPL) source and contaminant plume remediation. Journal ofContaminant Hydrology 91 (3e4), 288e311.

McKinney, D.C., Lin, M.-D., 1996. Pump-and-treat ground-water remediation systemoptimization. Journal of Water Resources Planning and Management 122,128e136.

Mugunthan, P., Shoemaker, C.A., 2004. Time varying optimization for monitoringmultiple contaminants under uncertain hydrogeology. Bioremediation Journal8, 129e146.

National Research Council, 1994. Alternatives for Ground Water Cleanup. NationalAcademy Press, Washington D.C., 336 p.

Parker, J., Kim, U., Kitanidis, P.K., Cardiff, M., Liu, X., 2010a. Stochastic cost optimi-zation of multi-strategy DNAPL site remediation. Groundwater Monitoring &Remediation 30, 65e78.


Parker, J., Kim, U., Widdowson, M., Kitanidis, P., Gentry, R., 2010b. Effects of modelformulation and calibration data on uncertainty in DNAPL source dissolutionpredictions. Water Resources Research 46 (W12517), 11. doi:10.1029/2010WR009361.

Parker, J., Kitanidis, P., Kim, U., Cardiff, M., Liu, X., Lee, J., 2011. Practical Cost-Optimization of Characterization and Remediation Decisions at DNAPL Siteswith Consideration of Prediction Uncertainty. Project ER-1611 Final Report. U.S.Dept of Defense, SERDP. 92 p.

Parsons, 2005. Keesler Air Force Base U.S. Installation Restoration Final QualityProgram Plan, Environmental Monitoring at Seven Sites. EPA ID No. MS2 570024 164. Prepared for U.S. Air Force, Atlanta, Georgia.

Press, W.H., Flannery, B.P., 2007. Numerical Recipes: the Art of Scientific Computing.Cambridge University Press, New York. 1256 p.

Reed, P., Minsker, B.S., 2004. Striking the balance: long-term groundwater moni-toring design for conflicting objectives. Journal of Water Resources Planningand Management 130 (2), 140e149.

Reed, P.M., Minsker, B.S., Valocchi, A.J., 2000. Cost-effective long-term groundwatermonitoring design using a genetic algorithm and global mass interpolation.Water Resources Research 36 (12), 3731e3741.

Ricciardi, K.L., 2009. Remediation of heterogeneous aquifers subject to uncertainty.Ground Water 47, 675e685.

Rittman, B.E., McCarty, P.L., 2001. Environmental Biotechnology: Principles andApplications. McGraw-Hill. 754 p.

Rizzo, D.M., Dougherty, D.E., 1996. Design optimization for multiple managementperiod groundwater remediation. Water Resources Research 32, 2549e2561.

Singh, T.S., Chakrabarty, D., 2011. Multiobjective optimization of pump-and-treat-based optimal multilayer aquifer remediation design with flexible remedia-tion time. Journal of Hydrologic Engineering 16, 413e421.

Teutsch, G., Finkel, M., 2002. Integrated Physico-chemical-economic Modelling forOptimal Plume Management at Contaminated Sites: a Decision SupportSystem, ModelCARE 2002: Calibration and Reliability in Groundwater Model-ling: a Few Steps Closer to Reality. IAHS Publications, Prague, Czech Republic,69e78 pp.

Teutsch, G., Rugner, H., Zamfirescu, D., Finkel, M., Bittens, M., 2001. Source reme-diation vs. plume management: critical factors affecting cost-efficiency. LandContamination and Reclamation 9, 128e142.

Thomson, N.R., Hood, E.D., Farquhar, G.J., 2007. Permanganate treatment of anemplaced DNAPL Source. Ground Water Monitoring & Remediation 27, 74e85.

Tucciarelli, T., Pinder, G., 1991. Optimal data acquisition strategy for the develop-ment of a transport model for groundwater remediation. Water ResourcesResearch 27, 577e588.

Wagner, B.J., Gorelick, S.M., 1987. Optimal groundwater quality management underparameter uncertainty. Water Resources Research 23, 1162e1174.

Wagner, B.J., Shamir, U., Nemati, H.R., 1992. Groundwater quality managementunder uncertainty: stochastic programming approaches and the value ofinformation. Water Resources Research 28, 1233e1246.

Wymore, R.A., Macbeth, T.W., Rothermel, J.S., Peterson, L.N., Nelson, L.O.,Sorenson Jr., K.S., Akladiss, N., Tasker, I.R., 2006. Enhanced anaerobic bioreme-diation in a DNAPL residual source zone: test Area North case study. Remedi-ation Journal 16, 5e22.

Stochastic cost optimization of DNAPL remediation – Method description and sensitivity study

Documents

Transcript of Stochastic cost optimization of DNAPL remediation – Method description and sensitivity study