Optimization of Surfactant-EnhancedAquifer Remediation for a LaboratoryBTEX System under ParameterUncertaintyL I H E , † G U O - H E H U A N G , * , ‡

H O N G - W E I L U , † A N DG U A N G - M I N G Z E N G §

Environmental Systems Engineering Program, Faculty ofEngineering, University of Regina, Regina, SK, Canada S4S0A2, Department of Civil and Environmental Engineering,University of Waterloo, Waterloo, Ontario N2L 3G1, andCollege of Environmental Science and Engineering, HunanUniversity, Changsha, P.R. China, 410082

Received May 11, 2007. Revised manuscript receivedDecember 7, 2007. Accepted December 18, 2007.

This study develops a nonlinear chance-constrained program-ming (NCCP) model for optimizing surfactant-enhanced aquiferremediation (SEAR) processes. The model can not onlyaddress the parameter uncertainty, but provide a reliabilitylevel for the identified optimal remediation strategy. To solvethe NCCP model, stepwise cluster analysis (SCA) is used to createa set of proxy simulators for quantifying the relationshipsbetween operating conditions (i.e., pumping rate) and probabilitiesof benzene levels in violation of standard. Compared toconventionalparametric inferencetechniques,SCAis independentof prior assumptions for model forms (e.g., linear or exponentialones) and capable of reflecting complex nonlinear relationshipsbetween operating conditions and probabilities. To alleviate thecomputational efforts in the optimization process, the generatedproxy simulators are repeatedly called by simulated annealing(SA) to test the feasibility of each potential solution. The implicitof the optimal NCCP solutions is discussed through a laboratory-scale SEAR system where porosity and intrinsic permeabilityare treated as stochastic parameters. It is observed that welllocations, environmental standards, reliability levels andremediation durations would have significant effects on optimalSEAR strategies. By comparing the predicted benzeneconcentration without and with remediation actions, it isindicated that the optimal SEAR process can guarantee thebenzene concentration to meet the environmental standard witha high reliability level.

IntroductionPreviously, a large number of methods based on groundwaterflow and contaminant transport simulation and optimizationmodels were undertaken to identify effective groundwaterremediation strategies (1–19). In detail, Rogers et al. (8)presented a nonlinear optimization approach through ar-tificial neural networks and genetic algorithms to search for

the most cost-effective remediation strategy; this approachwas applied to a practical site, from which the potential ofsaving tens of millions dollars was revealed. Mulligan andAhlfeld (16) advanced an interior-point method for solvingnonlinear optimization problems in groundwater pollutioncontrols. Zheng and Wang (17) applied a genetic algorithmto a pump-and-treat (PAT) system under field conditions;the results showed that the method could provide cost-effective strategies for groundwater remediation processes.Schaerlaekens et al. (19) used a constrained multiobjectiveoptimization method to maximize the removal of densenonaqueous phase liquids (DNAPLs) and minimize the totalcost; the Pareto solutions obtained from the model couldhelp decision makers select an optimal remediation strategyin terms of cost and remediation efficiency. Ahmad et al.(18) applied a response surface approach to a palm oil milleffluent treatment system for mitigating membrane foulingproblems.

Moreover, many uncertain optimization techniques wereused for addressing the complex uncertainties in environ-mental decision making (20–32). For example, Tiedeman andGorelick (23) formulated a stochastic simulation-manage-ment model for the removal of vinyl chloride dissolved in ashallow, unconfined sandy aquifer at a Superfund site. Freezeand Gorelick (26) reviewed the methodologies for dealingwith uncertainties in optimization modeling of the engi-neering design for aquifer remediation systems. Thurstonand Srinivasan (28) presented a chance-constrained opti-mization framework for green engineering decision-makingissues; the framework could deal with unavoidable tradeoffsthat arise from “pollution prevention pays” opportunities.Chen and Frey (29) proposed a Monte-Carlo-based stochasticprogramming method for the optimization of processtechnologies; the method was then applied to an integratedgasification combined cycle system for NOx control. Guanand Aral (30) proposed a fuzzy mathematical programmingapproach to solve groundwater remediation managementproblems; the optimal solutions showed improvements onthe remediation system’s effectiveness. Yan and Minsker (32)advanced an adaptive neural network genetic algorithm forthe design of a groundwater remediation system; the resultspresented that the algorithm was effective for reducingcomputational efforts in optimizing large-scale groundwaterremediation systems.

However, few of the previous studies focused on opti-mizing surfactant-enhanced aquifer remediation (SEAR)processes (33). Compared with conventional processes (e.g.,PAT), SEAR can achieve high remediation efficiency byinjecting surfactant into contaminated zones to increasecontaminant solubility and/or reduce interfacial tensionbetween phases. Therefore, it has been widely used for theremoval of light nonaqueous phase liquids (LNAPLs) andDNAPLs in subsurface (34). Moreover, most of the previousstudies were based on nonproxy optimization approaches,which require complex solution algorithms and huge com-putational burdens (14). This issue is particularly intensifiedwhen the stochasticity of parameters needs to be addressed.To alleviate the computational efforts, researchers attemptedto incorporate a set of proxy simulators into optimizationframeworks (23, 32). Evidence in the previous studies showedthat the frameworks can significantly reduce the optimizationtime required by repetitively calling numerical simulators.Nonetheless, very few proxy simulators were developedparticularly for predicting SEAR processes under uncertaintyassociated with stochastic parameters.

* Corresponding author phone: +1-306-585-4095; fax: +1-306-585-4855; e-mail: huang@iseis.org.

† University of Regina.‡ University of Waterloo.§ Hunan University.

Environ. Sci. Technol. 2008, 42, 2009–2014

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Published on Web 02/13/2008

Therefore, this study aims to develop a nonlinear chance-constrained programming (NCCP) model for optimizingSEAR processes under parameter uncertainties; to solve themodel, a proxy-based optimization method is also proposed.Specifically, the tasks entail (1) generating a number ofstatistical samples (the inputs are operating conditions andthe responses are probabilities of the contaminant concen-tration violating environmental standards) from a stochasticmultiphase multicomponent simulator (SMMS), (2) devel-oping a set of proxy simulators based on a nonparametricstatistical inference method, i.e. stepwise cluster analysis(SCA), (3) searching for the optimal solutions of NCCP viasimulated annealing (SA) technique, and (4) demonstratingthe performance of NCCP through a laboratory-scale SEARsystem where the soil porosity and intrinsic permeability aretreated as stochastic parameters.

Materials and MethodsA laboratory-scale system was used in this study. It was a boxshape with an interior dimension of L (length) × W (width)× H (height)) 3.6 × 1.2 × 1.4 m3. The system was discretizedinto cells 0.15 m (x direction) × 0.15 m (y direction) × 0.35 m(z direction) comprising 180 grid cells (35). A total of 25observation wells were installed to sample contaminants(Figure 1). Porous media in the system were stratified intofour layers (each one being 30 cm (Figure S1 of the SupportingInformation). There were 13 and 12 wells in the third andforth layers, respectively, which were saturated with water.Nonflow boundary conditions were assigned at the top andbottom of the simulation domain, forming a steady ground-water flow from right to left (Figure 1).

The initial contaminant concentrations were assumed tobe zero. To simulate the flow and transport of contaminantsin the system, 12 L of gasoline (used as representative LNAPLcontaminants) was uniformly injected into the bottom ofthe second layer within 1.5 days. The benzene concentrationin the gasoline was 0.97% by volume. Following the injection,a 40-day period of natural attenuation was monitored underthe same flow condition by injecting 20 L tap water per dayinto the system through a peristaltic pump. The water levelsin the upstream and downstream gauges were maintainedto be 55 and 45 cm, respectively. During the processes ofgasoline injection and natural attenuation, benzene con-centration in the groundwater was detected and measuredby a Varian CP-3800 gas chromatograph (GC).

While SEAR is useful in cleaning up dissolved DNAPLs(e.g., trichloroethylene and tetrachloroethylene) in aquifers,recent studies showed its capability in removing BTEX(benzene, toluene, ethyl-benzene, xylenes) (36–39). In thisexperiment, it was applied through continuously injectingsurfactant-mixed clean water into the aquifer to removedissolved BTEX. The nature of the surfactant used in thisexperiment is described in Section S1 of the SupportingInformation. Two remediation durations (i.e., 80 and 120days) were considered. Factors determining the SEAR ef-

ficiency mainly involve injecting and extracting pumpingrates, location of pumping wells, contaminant concentrationsof the extracted groundwater, and surfactant concentrationof the injected clean water. In this study, the pumping ratesof 3 injection wells and 3 extraction wells were consideredas decision variables, and the injection and extractionpumping rates were restricted to be lower than 60 L/day.

Previously, deterministic multiphase multicomponentsimulators (MMSs) were proven to be effective in simulatingthe fate of NAPLs in soil and groundwater (40). Targeted onoptimization of the SEAR process, SMMS was developedbased on MMS and Monte-Carlo technique. Details of thedeveloped SMMS are shown in Section S2 of the SupportingInformation. Table S1 of the Supporting Information showsparts of the determined parameters required for modelingthe SEAR process. The deterministic parameters wereobtained from prior laboratory-scale experiments and mod-eling calibration results. Soil porosity, intrinsic permeability,and hydraulic conductivity may vary spatially and temporally,leading to the uncertainties that can hardly be representedas deterministic values (41–44). Thus, the porosity andpermeability were assumed to be stochastic parametersfollowing normal distributions. Based on the measurementsof a number of soil samples collected from the study system,the mean value and the standard deviation of the porositywere estimated by

µ)∑i)1

n

xi (1)

and

s)� 1n- 1∑

i)1

n

xi (2)

where xi is the porosity of soil sample i, µ and s are mean andsample standard deviation of the soil porosity, and n is thenumber of soil samples. The mean values of intrinsicpermeabilities were determined through calibrating SMMS;in terms of the previous studies (54), the standard deviationswere respectively assumed to be 500, 40, and 5 for sand, till,and clay. Another key parameter, hydraulic conductivity, wasestimated by K ) Fgk/µ where K is hydraulic conductivity,F is water density, g is acceleration due to gravity, k is intrinsicpermeability, and µ is water viscosity (45, 46).

In calibration of SMMS, the average relative error betweenthe predicted and observed benzene concentrations was10.37%. In verification of SMMS, the absolute errors rangedfrom 0.027 to 0.935 mg/L, with an average error of 42.3%.The verification accuracy was not as good as the calibrationone, probably because (1) the practically heterogeneousnature of aquifer was assumed to be homogeneous for thesame soil type, and (2) the background benzene concentra-tion at the beginning of the experiment was assumed to bezero. However, an average relative error of lower than 50%can be regarded as acceptable due to the complexity inpredicting the flow and transport of NAPL contaminants inaquifer (43, 47).

The acceptable verification errors demonstrated that thesimulator can be used for developing NCCP (Section S3 ofthe Supporting Information). Note that components in theLNAPL phase may include benzene, toluene, ethyl-benzene,and xylenes. However, only benzene level was selected forindicating the environmental quality. This is based on theprevious investigations that benzene generally has the highesttoxicity level of the four, and concentrations of the last threecontaminants would become much lower than the respectiveenvironmental standard as long as the benzene concentrationreaches its standard level (48).

FIGURE 1. Well locations of the laboratory-scale system.

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To solve model (S11), a proxy-based optimization methodis proposed (Figure 2). First, a number of statistical samplesneed to be prepared for SCA to create proxy simulators,aiming to quantify the relationships between operatingconditions (i.e., pumping rate) and probabilities of standardviolation. A detailed description of SCA is shown in SectionS4 of the Supporting Information. The generated proxysimulators can be presented as a set of cluster trees. Throughsearching these trees, the probability can be evaluated undera given operating condition. The search procedure only needsto answer “yes” or “no” at each parent node to determinewhich child node will be entered (49). Step by step, thepredicted values (including mean value, standard deviation,and confidence interval of the probability) can be obtainedwhen encountering the leaf node at the bottom of the tree.After creating the proxy simulators, SA (as shown in SectionS5 of the Supporting Information) is then used to search forthe optimal solution to model (S11), through repeatedlybrowsing the cluster trees to test the feasibility of eachpotential solution.

The detailed procedure can be summarized as follows:[step 1] randomly generate the inputs of a sample (Qi

In andQi

Ex) within the range of [0, 60] L/d; [step 2] compute theprobability of the contaminant concentration not greaterthan the environmental standard (i.e., standard violation)under the given stochastic parameters through the Monte-Carlo technique, and use them as the outputs of samples;[step 3] test whether or not the number of samples is enoughfor generating the proxy simulators (i.e., go to step 1 if no,while continue if yes); [step 4] categorize the samples intotraining and testing samples; [step 5] produce the proxysimulators with the given samples; [step 6] use SA to seek theoptimal solution by calling the proxy simulators; [step 7]remember the best solution; [step 8] test whether or not SAcan be stopped after a number of iterations; if yes, then stop;if no, then go to step 5.

Results and DiscussionThe generated proxy simulators were presented as a set ofcluster trees, each of which can be used for predicting thebenzene concentrations at one monitoring well. Figure S2of the Supporting Information gives a simplified cluster treefor well M03 (t ) 80 days and cmax ) 0.5 mg/L). In each layerof the tree, the cluster would be cut into two subclusters ifthe criterion (p-value) is less than 0.05; alternatively, the twosubclusters would be merged if the criterion is greater than0.05. The significant level of variables Q1 to Q6 (representingthe optimal pumping rate at wells M08, M10, M12, M02,M04, and M06, respectively) can be analyzed from the figure.For example, the injection flow rates at wells M04 and M06are the most significant variables in affecting the probabilityvalue, since Q5, Q6, and Q4 are selected as the cutting points

in the first three layers, respectively. The other variables,however, are not as significant as these three, because theyare only regarded as the cutting variables at the bottom.

Figures S3 and S4 of the Supporting Information presentthe training and predicting performances of the proxysimulators at t ) 80 days. The RMSE and R2-value were usedto check the accuracy, and satisfactory predicting perfor-mance was achieved (see Section S6 of the SupportingInformation). However, as they can only provide the globalestimates of the accuracy, the proxy simulators may be locallyaffected by significant estimation errors. Thus, any learningalgorithm that performs exceptionally satisfactorily in onesituation may not be effective under others (50). This impliesthat SCA may hardly be of universal superiority under allsituations. This concern can be mitigated through thefollowing three approaches. The first is to increase thenumber of realizations in Monte-Carlo simulations and ofthe training samples for deriving proxy simulators; neverthe-less, this could substantially enhance the CPU consumptionin producing the training samples. The second is to maintaina skeptical eye on the outputs (i.e., checking whether theyare reasonable or not); those outputs with remarkablecomputation errors can be regarded as outliers and thenremoved. The third is to combine various learning algorithms(e.g., multiple regression and artificial neural network) tocreate proxy simulators on the same problem; by fusing theadvantageous features of these algorithms, the effect ofestimation errors on decision making can be intensivelyreduced.

Provided the gained proxy simulators, SA was employedto seek the optimal solutions of model (S11). The values ofrequired parameters were identified as 10, 0.96, 0.01, 100,and 1 × 10-4 for Markov length, annealing constant, stepfactor, initial temperature, and the maximum tolerance error,respectively. As the proxy simulators cannot always achievesatisfactory accuracy under all situations, the probabilitiesare possible to be underestimated or overestimated, whichleads to the overoptimistic or overconservative solutionsbeing generated. However, the proxy-based optimizationsolutions have been useful for solving groundwater reme-diation problems due to their superior capability in reducingcomputational efforts (32, 35). As the main component ofmost groundwater optimization models, the call to SMMSmay require hundreds of times in those nonproxy-basedmethods, while that to proxy simulators can be substantiallycurtailed. Compared with SMMS that required 5-8 h to assessone pumping sample, SA was able to evaluate approximately3000 samples per second through the proxy simulators. Thus,the computational cost can be substantially saved. A detailedcomparison between the nonproxy- (calling SMMS) andproxy-based (calling proxy simulators) methods in compu-tational efficiency is analyzed in Section S7 of the SupportingInformation.

The optimal remediation strategies were identified byexamining the effects of well locations, environmentalstandards, reliability levels, and pumping durations on thesystem’s performance. Figure 3 shows the optimal pumpingrates of six remediation wells (cmax ) 0.5 mg/L, t ) 80 days)under different reliability levels. It is indicated that wellsM06 and M12 would be the most significant contributors towater injection and groundwater extraction. The pumpingrates at these two wells would be remarkably higher thanthose at other wells under most reliability levels. Wells M10and M04 would have moderate contributions to the reme-diation, with the average pumping rate being about 30 L/dunder all reliability levels. Only a little amount of water (orgroundwater) would be injected (or extracted) at M02 (orM08) unless the reliability level is high (e.g., over 0.9). Thisdiscrepancy might be caused by the varied distribution insoil types. Much permeable and porous soil in the south

FIGURE 2. Flowchart of the solution method.

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stimulates more contaminants to be imported, such that thesouth wells would have more contributions to the benzeneremoval than the north ones.

It is also observed that the rise of reliability level wouldcorrespond to an enhancement of pumping rate (except thesituation at π ) 0.5). For instance, the injection rate at wellM06 would be increased from 26.47 L/day by 122.81% whenthe reliability level rises from 0.5 to 0.95. Particularly underthe highest reliability level (i.e., π ) 0.95), all of the six wellswould have to be fully used (near 60 L/d) to ensure that thegroundwater can be sufficiently cleaned up. Figures 4 and5, respectively, show the TIERs versus reliability levels whenremediation durations are 80 and 120 days. Provided cmax )0.5 mg/L, TIER would rise from 87.01 to 285.95 L/d if thereliability level is increased from 0.50 to 0.95 when t ) 80days; comparatively, it would be increased by 2.44 times from67.62 L/d when t ) 120 days if the reliability level is varied

from 0.50 to 0.99. This reveals that an increased reliabilitylevel would raise the requirement for TIER.

The effect of the environmental standard on TIER canalso be analyzed from the two figures. For example, undera reliability level of 0.95, the increase of the environmentalstandard from 2.0 to 0.5 mg/L would lead to a drop of TIERfrom 112.07 (or 285.95) to 84.73 (or 220.45) L/d for the 80 (or120) days of duration. In general, under a stringent envi-ronmental standard, more volumes of groundwater need tobe extracted for lowering the contaminant concentration.To maintain a stable hydraulic gradient such that thegroundwater can flow directly toward the plume interior,more volumes of clean water would be injected within aspecified pumping period. Therefore, the increased amountsof extracted groundwater and injected clean water wouldraise the total pumping rate for satisfying the reinforcedstringent environmental standard. By comparing Figure 4 toFigure 5, the effect of the remediation duration on TIER wasalso examined. Given a reliability level of 0.95 and a standardof 1.0 mg/L, TIER would be 207.49 L/d under the 80-dayduration, while decreased by 11.24% when t rises to 120 days.Although longer remediation durations were not investigatedin this study, it can be expected that a longer duration wouldensure the groundwater satisfying a more stringent standardand/or the system reliability level being enhanced.

Figures S5 and S6 of the Supporting Information respec-tively exhibit the predicted benzene concentration distribu-tions on the 80th day without and with remediation actions.Without SEAR, the peak mean concentration would be over3.6 mg/L, which is approximately 7.2 times the environmentalstandard. In comparison, it would intensively shrink to 0.32mg/L with a reliability level of 95% when SEAR is undertakenunder the optimal operating condition, where Q1 to Q6 are47.49, 49.90, 45.58, 33.58, 56.65, and 52.74 L/day, respectively.This indicates that the optimal SEAR process can guaranteethe benzene concentration to meet the environmentalstandard with a high reliability level.

The nonlinear chanced-constrained programming(NCCP) model was developed for identifying optimal SEARstrategies under the uncertainty of stochastic parameters.However, the optimal solutions obtained from NCCP maycorrespond to a conservative remediation strategy (e.g.,increased total pumping rate or extended pumping dura-tion). Generally, the higher the uncertainty level, the moreconservative the strategy would be. Thus, the implicationfor the remediation community is that a well-designedSEAR system should be based upon a complete knowledgeof modeling parameters; otherwise, the remediation cost(with the growth of TIER) or the chance of system failurewould be increased. Therefore, in-depth data investigationsare suggested to abate the effect of uncertainties on optimalsolutions, and to further mitigate the degree of systemoverdesign.

The NCCP model does not require that environmentalstandards are completely satisfied; instead, the ground-water could be safe if the chance of the standard violationis higher than the given reliability level. Thus the reliability(or safety) level of the groundwater system providesenvironmental regulators/practitioners a significant cri-terion in addition to those for regulating contaminantconcentrations. The optimal solutions of the model canbe obtained through a proxy-based optimization methodfor saving the tremendous computational cost. This offersan efficient tool for solving a wide class of nonlinearstochastic optimization problems. The proxy simulatorsare obtained through a nonparametric statistical inferencetechnique (SCA) (35, 49, 51). Compared to conventionalparametric inference techniques (52, 53), SCA is inde-pendent of prior assumptions for model forms (e.g., linearor exponential ones), and capable of reflecting complex

FIGURE 3. Optimal pumping rates at the wells (cmax ) 0.5 mg/L, t ) 80 days).

FIGURE 4. Total pumping rate versus reliability (t ) 80 days).

FIGURE 5. Total pumping rate versus reliability (t ) 120 days).

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nonlinear relationships between system inputs and re-sponses (49). The results revealed that the probabilitiespredicted through proxy simulators were consistent withthose through SMMS within acceptable error levels, therebyproviding a bridge between operating conditions andprobabilities.

The study system was particularly designed to mimic apractical petroleum-contaminated site in Western Canada.To simulate the flow and transport of BTEX in groundwater,gasoline was injected into the system as the syntheticcontamination source. A problem that should be stressed isthat the methyl tertiary-butyl ether (MTBE) added in gasolinecould not substantially degrade even if the benzene levelsatisfied the environmental standard. However, MTBE wasnot considered in this study, as BTEX were found to be themajor contaminants according to the previous site investi-gations (47, 48). If MTBE needs to be addressed, the NCCPmodel should be improved by incorporating an additionalcomponent (for simulating the fate of MTBE in the ground-water) into the current optimization framework.

The previous research efforts indicated that porosity andpermeability may be uniformly, normally, or log-normallydistributed (41–44), and statistically correlated. Thereforethe effects of distribution functions and correlations ofstochastic parameters on optimal operating conditions wouldbe the subjects of future studies. Also, since the values ofstandard deviations of soil permeabilities were assumed inthis study, the sensitivity of the optimal results to thedeviations would further be examined. Moreover, dispersivity,similar to intrinsic permeability and soil porosity, also haseffects on the simulation and further optimization results.An investigation by Li (54) revealed that uncertainties in soilporosity and permeability had significant effects on thepredicted contaminant concentrations, while those of dis-persivity had less significant ones. Therefore, this studyassumed that the soil porosity and intrinsic permeability ofthe study system are uncertain, whereas the dispersivity isdeterministic. The effects of dispersivity on optimal operatingconditions will be examined for the study system in futurestudies.

AcknowledgmentsWe thank the Associate Editor and anonymous reviewers fortheir helpful comments and suggestions. This research wassupported by the Major State Basic Research DevelopmentProgram of MOST (2005CB724200 and 2006CB403307), andthe Natural Science and Engineering Research Council ofCanada.

Supporting Information AvailableDetailed descriptions of the surfactant, stochastic multiphasemulticomponent simulator (SMMS), nonlinear chance-constrained programming model (NCCP), stepwise clusteranalysis (SCA), simulated annealing (SA), the fitting andpredicting performances of SCA, and the computationalefficiency of NCCP; also figures for illustrating the laboratory-scale system and the cluster tree, and comparing the predictedbenzene level without and with SEAR actions, as well as thetable listing the estimated parameters in SMMS. This materialis available free of charge via the Internet at http://pubs.acs.org.

Literature Cited(1) Gorelick, S. M.; Evans, B. J.; Remson, I. Identifying sources of

ground-water pollution: An optimization approach. WaterResour. Res. 1983, 19 (3), 779–790.

(2) Gorelick, S. M.; Voss, C. I.; Gill, P. E.; Murray, W.; Saunders,M. A.; Wright, M. H. Aquifer reclamation design: The use ofcontaminant transport simulation combined with nonlinearprogramming. Water Resour. Res. 1984, 20 (4), 415–427.

(3) Ahfeld, D. P.; Mulvey, J. M.; Pinder, G. F.; Wood, E. F.Contaminated groundwater remediation design using simula-tion, optimization, and sensitivity theory- 1. Model development.Water Resour. Res. 1988, 24 (3), 431–442.

(4) Ahfeld, D. P.; Mulvey, J. M.; Pinder, G. F.; Wood, E. F.Contaminated groundwater remediation design using simula-tion, optimization, and sensitivity theory- 2. Analysis of a fieldsite. Water Resour. Res. 1998, 24 (3), 443–452.

(5) Ritzel, B. J.; Eheart, J. W.; Ranjithan, S. Using genetic algorithmto solve a multiple objective groundwater pollution containmentproblem. Water Resour. Res. 1994, 30 (5), 1589–1603.

(6) Wang, W.; Ahlfeld, D. P. Optimal groundwater remediation withwell location as a decision variable, model development. WaterResour. Res. 1994, 30 (5), 1605–1618.

(7) Rogers, L. L.; Dowla, F. U. Optimization of groundwaterremediation using artificial neural networks with parallel solutetransport modeling. Water Resour. Res. 1994, 30 (2), 457–481.

(8) Rogers, L. L.; Dowla, F. U.; Johnson, V. M. Optimal filed-scalegroundwater remediation using neural networks and the geneticalgorithm. Environ. Sci. Technol. 1995, 29, 1145–1155.

(9) McKinney, D. C.; Lin, M. D. Approximate mixed-integernonlinear programming methods for optimal aquifer reme-diation design. Water Resour. Res. 1995, 31 (3), 731–740.

(10) McKinney, D. C.; Lin, M. D. Pump-and-treat groundwaterremediation system optimization. J. Water Resour. PlanningManage. 1996, 122 (2), 128–136.

(11) Huang, C. L.; Mayer, A. S. Pump-and-treat optimization usingwell locations and pumping rates as decision variables. WaterResour. Res. 1997, 33 (5), 1001–1012.

(12) Minsker, B. S.; Shoemaker, C. A. Differentiating a finite elementbiodegradation simulation model for optimal control. WaterResour. Res. 1996, 32 (1), 187–192.

(13) Minsker, B. S.; Shoemaker, C. A. Dynamic optimal control ofin-situ bioremediation of ground water. J. Water Resour.Planning Manage. 1998, 124 (3), 149–161.

(14) Guan, J. B.; Aral, M. M. Optimal remediation with well locationsand pumping rates selected as continuous decision variables.J. Hydrol. 1999, 221, 20–42.

(15) Hsiao, C. T.; Chang, L. C. Dynamic optimal groundwatermanagement with inclusion of fixed costs. J. Water Resour.Planning Manage. 2002, 128 (1), 57–65.

(16) Mulligan, A. E.; Ahlfeld, D. P. A new interior-point boundaryprojection method for solving nonlinear groundwater pollutioncontrol problems. Oper. Res. 2002, 50 (4), 636–644.

(17) Zheng, C.; Wang, P. P. A field demonstration of the simulation-optimization approach for remediation system design. GroundWater 2002, 40 (3), 258–266.

(18) Ahmad, A. L.; Ismail, S.; Bhatia, S. Optimization of coagulation-floculation process for palm oil mill effluent using responsesurface methodology. Environ. Sci. Technol. 2005, 39, 2828–2834.

(19) Schaerlaekens, J.; Carmeliet, J.; Feyen, J. Multi-objective opti-mization of the setup of a surfactant-enhanced DNAPL reme-diation. Environ. Sci. Technol. 2005, 39, 2327–2333.

(20) Wagner, B. J.; Gorelick, S. M. Optimal groundwater qualitymanagement under parameter uncertainty. Water Resour. Res.1987, 23 (7), 1162–1174.

(21) Andricevic, R.; Kitanidis, P. K. Optimization of the pumpingschedule in aquifer remediation under uncertainty. WaterResour. Res. 1990, 26 (5), 875–885.

(22) Morgan, D. R.; Eheart, J. W.; Valocchi, A. J. Aquifer remediationdesign under uncertainty using a new chance constrainedprogramming technique. Water Resour. Res. 1993, 29 (3), 551–561.

(23) Tiedeman, C.; Goreilick, S. M. Analysis of uncertainty in optimalgroundwater contaminant capture design. Water Resour. Res.1993, 29 (7), 2139–2153.

(24) Chan, N. Partial infeasibility method for chance-constrainedaquifer management. J. Water Resour. Planning Manage. 1994,120 (1), 70–89.

(25) Gorelick, S. M. Incorporating uncertainty into aquifer manage-ment models. In Subsurface Flow and Transport, A StochasticApproach; Dagan, G., Neuman, S. P., Eds.; Cambridge UniversityPress: New York, 1997; pp 101–111.

(26) Freeze, R. A.; Gorelick, S. M. Convergence of stochasticoptimization and decision analysis in the engineering designof aquifer remediation. Ground Water 1999, 37 (6), 934–954.

(27) Tien, T. H.; Bettahar, M.; Kumagai, S. Optimization of surfactant/alcohol formulations for the remediation of oily contaminatedporous media. Environ. Sci. Technol. 2000, 34, 3977–3981.

VOL. 42, NO. 6, 2008 / ENVIRONMENTAL SCIENCE & TECHNOLOGY 9 2013

(28) Thurston, D. L.; Srinivasan, S. Constrained optimization for greenengineering decision-making. Environ. Sci. Technol. 2003, 37,5389–5397.

(29) Chen, J. J.; Frey, H. C. Optimization under variability anduncertainty: a case study for NOx emissions control for agasification system. Environ. Sci. Technol. 2004, 38, 6741–6747.

(30) Guan J. B.; Aral M. M. Optimal design of groundwater reme-diation systems using fuzzy set theory. Water Resour. Res. 2004,40(1), doi: 10.1029/2003WR002121.

(31) Hilton, A. B.; Culver, T. B. Groundwater remediation designunder uncertainty using genetic algorithms. J. Water Resour.Planning Manage. 2005, 131 (1), 25–34.

(32) Yan, S.; Minsker, B. Optimal groundwater remediation designusing an adaptive neural network genetic algorithm. WaterResour. Res. 2006, 42(5), doi: 10.1029/2005WR004303.

(33) Schaerlaekens, J.; Mertens, J.; Van, L. J.; Vermeiren, G.; Carmeliet,J.; Feyen, J. A multi-objective optimization framework forsurfactant-enhanced remediation of DNAPL contaminations.J. Contam. Hydrol. 2006, 86, 176–194.

(34) Intera Inc. Surfactant-Enhanced Aquifer Remediation (SEAR)Implementation Manual; NFESC technical report TR-2219-ENV;Naval Facilities Engineering Service Center: Washington, DC,2002.

(35) Huang, Y. F. Development of environmental modeling meth-odologies for supporting system simulation, optimization andprocess control in petroleum waste management. Ph.D. Thesis,University of Regina, Regina, Saskatchewan, 2004.

(36) Bhattacharya, S. K.; Foster, D. H.; Reddy, J. M. Surfactantenhanced electrokinetic remediation of gasoline contaminatedsoils. Non-Aqueous Phase Liquids (NAPLs) in subsurfaceEnvironment: Assessment and Remediation; Proceedings of theSpecialty Conference Held in Conjunction with the ASCENational Convention, Washington, DC, November 1996, pp 311–322.

(37) Huang, Y. F.; Li, J. B.; Huang G, H.; Chakma, A.; Qin, X. S.Integrated simulation-optimization approach for real-timedynamic modeling and process control of surfactant-enhancedremediation at petroleum contaminated sites. Pract. PeriodicalHaz., Toxic, Radioactive Waste Mgmt. 2003, 7 (2), 95–105.

(38) Tworkowski, R. J.; Baer, J. L. Presentation at 11th AnnualInternational Petroleum Environmental Conference, Albuquer-que, NM, October 2004.

(39) Ranck, J. M.; Bowman, R. S.; Weeber, J. L.; Katz, L. E.; Sullivan,E. J. BTEX removal from produced water using surfactant-modified zeolite. J. Environ. Eng. 2005, 131 (3), 434–442.

(40) Katyal, A. Flow and Transport in the Saturated and UnsaturatedZone in 2 or 3 Dimensions; Technical Document; Draper AdenEnvironmental Modeling Inc.: Blacksburg, VA, 1997.

(41) Freeze, R. A.; Massmann, J.; Smith, L.; Sperling, J.; James, B.Hydrogeological decision analysis, 1, a framework. Ground Water1990, 28, 738–766.

(42) Wong, H. S.; Yeh, W. G. Uncertainty analysis in contaminatedaquifer management. J. Water Resour. Planning Manage. 2002,128 (1), 33–45.

(43) Chen, Z.; Huang, G. H. Integrated subsurface modeling and riskassessment of petroleum-contaminated sites in Western Canada.J. Environ. Eng. 2003, 129 (19), 858–871.

(44) McPhee, J.; Yeh, W. G. Experimental design for groundwatermodeling and management. Water Resour. Res. 2006, 42(8), doi:10.1029/2005WR003997.

(45) U.S. Environmental Protection Agency. 1994; Available at http://www.epa.gov/swerust1/pubs/tums.htm.

(46) He, L.; Chan, C. W.; Huang, G. H.; Zeng, G. M. A probabilisticreasoning-based decision support system for selecting reme-diation technologies for petroleum-contaminated sites. ExpertSyst. Appl. 2006, 30 (4), 783–795.

(47) Chen, Z.; Huang, G H.; Chakma, A. Numerical Modeling Soiland Groundwater Contamination–a Study for Petroleum-Contaminated Sites; Technical report prepared for Trans-Ga–SaskEnergy: Regina, Saskatchewan, 1998.

(48) Saskatchewan Environment and Resource Management. RiskBased Corrective Actions for Petroleum Contaminated Sites;Regina, Saskatchewan, 1999.

(49) Huang, G. H. Stepwise cluster analysis method for predictingair quality in an urban environment. Atmos. Environ. 1992, 26B(3), 349–357.

(50) Khalil, A.; McKee, M.; Kaluarachchi, J. J. Applicability of statisticallearning algorithms in groundwater quality modeling. WaterResour. Res. 2005, 41 (5), doi: 10.1029/2004WR003608.

(51) Iorgulescu, I.; Beven, K. J. Nonparametric direct mapping ofrainfall-runoff relationships: an alternative approach to dataanalysis and modeling. Water Resour. Res. 2004, 40 (8), doi:10.1029/2004WR003094.

(52) Karcher, S. C.; Small, M. J.; VanBriesen, J. M. Statistical methodto evaluate the occurrence of PCB transformations in riversediments with application to Hudson River data. Environ. Sci.Technol. 2004, 38, 6760–6766.

(53) MacDonald, J.; Small, M. J. Assessing sites contaminated withunexploded ordnance: Statistical modeling of ordnance spatialdistribution. Environ. Sci. Technol. 2005, 40, 931–938.

(54) Li, J. B. Development of an inexact environmental modelingsystem for the management of petroleum-contaminated sites.PhD Thesis, University of Regina, Regina, Saskatchewan, 2003.

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