3 Optimization and Modeling for Remediation and Monitoring prepared by George F. Pinder with contributions by David E. Dougherty, Robert M. Greenwald, George P. Karatzas, Peter K. Kitanidis, Hugo A. Loaiciga, Reed M. Maxwell, Alexander S. Mayer, Dennis B. McLaughlin, Richard C. Peralta, Donna M. Rizzo, Brian J. Wagner, Kathleen M. Yager, William W G. Yeh CONTENTS 3.1Introduction 3.2The User’s Persective 3.2.1The View from the U.S. Environmental Protection Agency (USEPA) 3.2.2The View from the U.S. Department of Energy (DOE) 3.2.2.1Application of Site Characterization and Monitoring Technologies 3.2.2.2Numerical and Optimization Models 3.2.2.3Innovative Technologies and the Regulatory Process 3.2.2.4Technology Needs 3.2.3The View from the U.S. Department of Defense (DoD) 3.2.3.1Optimization Efforts 3.2.3.2Model Development Efforts 3.2.3.3Monitoring Efforts 3.2.4The View from Industry 3.3State of Knowledge and Practice 3.3.1The Simulation Optimization Approach 3.3.1.1Gradient Control Remediation Technology 3.3.1.2Concentration Constraints Remediation Technology L1667_C03.fm Page 107 Tuesday, October 21, 2003 3:49 PM ©2004 CRC Press LLC 3.3.2Stochastic Optimization to Accommodate Potential Design Failure 3.3.2.1Chance-Constrained Ground Water Management Model 3.3.2.2Multiple Realization Ground Water Management Model 3.3.2.3Alternative Stochastic Optimization Methods 3.3.3Uncertainty 3.3.3.1Sources 3.3.3.2Examples 3.3.4Design-Risk Cost Tradeoff 3.3.5Long-Term Ground Water Monitoring 3.3.5.1The Relationship between Remedy and Monitoring 3.3.5.2Performance Monitoring Problems 3.3.5.3Methods 3.4Gaining Acceptance 3.4.1Remediation System Design Optimization Demonstrations 3.4.1.1Dissolved TCE Cleanup at Central Base Area, Norton Air Force Base, California 3.4.1.2Model Calibration and TCE/PCE Plume Containment at March AFB, California 3.4.1.3Containment and Cleanup of TCE and DCE Plumes, Wurtsmith AFB, Michigan 3.4.1.4Dissolved TCE Cleanup at Massachusetts Military Reservation 3.4.2Long-Term Monitoring Field Studies 3.4.3Communication Improvements 3.5Challenges and Emerging Issues 3.5.1Optimization Algorithmic Challenges IdentiÞed through Application Needs 3.5.1.1Natural Variability Over Space and Time 3.5.1.2Multiple Constituents 3.5.1.3Multiple Phases 3.6Summary Acknowledgments References 3.1 INTRODUCTION The focus of this chapter is optimization and modeling for remediation and moni- toring. The goal is to provide the reader with insights into the optimization and modeling tools available for cost-effective resolution of environmental problems, especially as they pertain to ground water contamination and its long-term impacts. To achieve this goal, the technical and practical challenges inherent in this approach are presented as well as documented accomplishments. Utilizing this organizational approach, the reader should comprehend both the Þnancial beneÞts and the antici- L1667_C03.fm Page 108 Tuesday, October 21, 2003 3:49 PM ©2004 CRC Press LLC pated costs associated with using optimal design and modeling when resolving and managing problems addressable via this technology. The chapter is subdivided into the following three main topics: the user’s per- spective, current state of knowledge, and gaining acceptance. Each topic is further subdivided to address many of the speciÞc issues of current importance to the professional ground water community. While the discussion of each speciÞc issue reßects the views of the authors, the issues have been deÞned in such a way as to provide an integrated discussion of the main topics. Nevertheless, the styles, formats, and levels of technical detail found in the various presentations are, by their nature, different. 3.2 THE USER’S PERSECTIVE 3.2.1 T HE V IEW FROM THE U.S. E NVIRONMENTAL P ROTECTION A GENCY (USEPA) Designing and maintaining effective remediation systems that satisfy all technical, regulatory, and social constraints is an extremely challenging task given the variety of hydrogeologic and contaminant settings of hazardous waste sites. The USEPA supports the use of the most efÞcient and effective tools available for all phases of site cleanup — from innovative, Þeld-based site characterization technologies and improved data management and visualization tools to innovative in situ and ex situ remediation technologies. One such promising innovative technology is mathemat- ical optimization for the design and redesign of remediation and monitoring systems. However, as with many innovative technologies, the regulated community has been reluctant to adopt these approaches readily due to the lack of cost and performance data and concern over regulatory acceptance. In 1999, the USEPA completed a demonstration project applying hydraulic optimization techniques for pump-and-treat systems (Greenwald, 1999). The scope of this study included selecting three sites with existing pump-and-treat systems, screening the sites for optimization potential, and applying a hydraulic optimization code at each site. At two of the sites, pumping solutions were obtained that had the potential to yield millions of dollars in savings relative to current pumping rate costs. At the third site, no substantial improvement over the current design was identiÞed with optimization. The general conclusions from this study were that hydraulic optimization has the potential to improve operating pump-and-treat systems and that more complicated sites (i.e., large ground water plumes and many extraction and injections wells) are more likely to beneÞt from hydraulic optimization. It is impor- tant to note that there are many mathematical optimization algorithms available and that this study evaluated only one hydraulic optimization approach. Although this study conclusively determined that mathematical optimization can be beneÞcial at improving pump-and-treat system design, very few applications of this technology have been observed at USEPA or other state-led sites. This lack of application of optimization algorithms can be attributed to several factors, including lack of technology awareness, lack of well-trained optimization modelers in the consulting engineering community, and cost. Certainly the lack of awareness of L1667_C03.fm Page 109 Tuesday, October 21, 2003 3:49 PM ©2004 CRC Press LLC optimization techniques in the remediation community is the primary factor con- tributing to low use. Although optimization algorithms are widespread in many industries, the remediation community has not adopted these techniques as standard practice for remediation. Furthermore, there are few trained users or real-world examples of their applications. For this reason, industry and the consulting engi- neering and government communities are not fully aware of the beneÞts of optimi- zation algorithms and do not have personnel trained in these applications. Without the pull from problem holders requesting these techniques or the push from con- sulting engineers recommending their use, there is minimal demand for applying optimization algorithms in hazardous waste site cleanup. From a regulatory perspec- tive, because few sites have requested the use of mathematical optimization algo- rithms, regulators have not been widely exposed to their applications. Another problem associated with the lack of use of mathematical optimization is cost or perceived cost. Many sites have developed simple ßow models based on limited site-characterization information. These models are generally used as one tool in the decision-making process for the site, but often are not adequate models for use with an optimization algorithm. In order to ensure a worthwhile optimization analysis, the base model(s) might need to be updated or completely redone, which is an additional (and sometimes unforeseen) cost. This additional step prior to an optimi- zation analysis can discourage continuing with the optimization analysis. Although there are several reasons for the lack of use of optimization in the remediation Þeld, there remains a deÞnitive need to improve remediation systems using mathematical optimization or other approaches. The USEPA estimates that over 700 pump-and-treat systems are under construction or operating at Superfund sites across the country per the Records of Decisions (RODs) (USEPA, 1999). Many of these systems are anticipated to operate for years to decades at substantial cost to industry and the government. Furthermore, many of these systems were designed based on limited site information and limited knowledge of the capabilities of pump- and-treat systems. All stakeholders can beneÞt substantially by implementing math- ematical optimization techniques in these cases. Other continuous improvement techniques such as periodically evaluating system performance, labor and monitoring practices, aboveground treatment components, and data management also should be considered. There is a tremendous need to ensure that pump-and-treat systems and other remedial systems are properly designed, maintained, and monitored; the reme- diation community should consider the use of optimization approaches to this end. 3.2.2 T HE V IEW FROM THE U.S. D EPARTMENT OF E NERGY (DOE) The DOE is a major partner in managing the nation’s toxic substances in the subsurface. The DOE has administrative jurisdiction over several sites that contain remnants of radioactive and other toxic wastes generated during the Cold War’s nuclear race. Those sites include, but are not limited to, Hanford Reservation (Washington), Idaho National Environmental Engineering Laboratory (INEEL, Idaho), Oak Ridge National Laboratory (ORNL, Tennessee), Rocky Flats (Colo- rado), and the Savannah River site (SRS, South Carolina and Georgia). Taken in conjunction, these DOE sites represent perhaps the most signiÞcant repository of L1667_C03.fm Page 110 Tuesday, October 21, 2003 3:49 PM ©2004 CRC Press LLC radioactive compounds in the subsurface environment in the U.S. The cost of containment, abatement, and remediation (i.e., environmental restoration) associ- ated with DOE sites outranks that of any other agency, public or private, in the nation. The monitoring, characterization, and modeling of subsurface pollutants at DOE sites present enormous challenges due to the nature of the pollutants and the complexity and heterogeneity of the transport environment. On the other hand, the challenges present opportunities to use innovative optimization methods to help identify environmental restoration technologies at DOE sites. This section summarizes the results of a recent survey of subsurface character- ization, environmental monitoring, and modeling technologies at DOE sites. Numer- ical modeling technologies included optimization models as well. Although the focus of this chapter is on optimization methods, information gathered on all subsurface characterization and environmental monitoring technologies are presented to dem- onstrate that the application of optimization methods at DOE sites cannot be exam- ined in isolation from other technologies. In fact, optimization methods are only beginning to be tested at large-scale DOE sites. In this respect, their usefulness and effectiveness in large-scale and complex subsurface pollution situations at DOE sites is still experimental. It should be noted that the information and opinions presented in this section do not reßect the DOE’s ofÞcial position on subsurface contamination management at its sites. 3.2.2.1 Application of Site Characterization and Monitoring Technologies Table 3.1 shows a summary of technologies currently in use or those that have been used at INEEL, ORNL, and SRS in subsurface characterization, environmental monitoring, and modeling. This table also summarizes the survey responses obtained from the three sites. An “X” in Table 3.1 indicates that the technology is currently used. A blank space indicates neither current nor past use of a speciÞc technology. As seen in the table, a wide range of remote sensing, geophysical technologies, nuclear logging, drilling, ground water and vadose zone sampling, analytical tech- nologies, and numerical/statistical technologies, as well as optimization methods, are currently in use or have been used at all three sites. INEEL and ORNL reported the use of 12 to 13 of the 30 listed analytical technologies. These two sites rely largely on off site analytical laboratories for sample analysis. Thus, many of the listed analytical technologies are not deployed as functional units within INEEL or ORNL. SRS, on the other hand, reported the application of 24 of the 30 listed analytical technologies. This reßects the fact that Westinghouse, the management and operation (M&O) contractor at SRS, maintains fully equipped and staffed analytical laboratories within the SRS boundaries, where many of the Þeld samples undergo analysis. Ecological monitoring, an aspect of site characterization, was overlooked ini- tially and not mentioned in the survey. ORNL and SRS actively monitor vegetation, Þsh, mammals, and other biota, as well as surface water bodies. Living organisms are tested mostly for radionuclides and metals that accumulate in tissues (e.g., cesium and strontium isotopes, mercury). Ecological monitoring is performed by capturing L1667_C03.fm Page 111 Tuesday, October 21, 2003 3:49 PM ©2004 CRC Press LLC TABLE 3.1 Summary of Site Characterization, Environmental Monitoring, and Modeling Technologies Used at Selected DOE Sites Technology INEEL ORNL SRS Remote Sensing Remote sensing/aerial photography X X X Surface Geophysics Electrical resistivity X X X Electromagnetic conductivity X X X Seismic methods Past use X X Ground-penetrating radar X X X Magnetometer surveys X X Borehole Geophysics Resistivity surveys X X X Cross borehole tomography X X Nuclear Logging Density logging X X X Nuclear logging (natural gamma, neutron logging, gamma–gamma radiation) XXX Drilling Geoprobe ® -type penetrometer X X Large SCAPS platform X Standard methods (e.g., hollow-stem auger, rotary) X X X Direct sonic drilling Past use X Rotosonic drilling Past use X X Horizontal drilling Past use X X Ground Water Sampling Sampling (e.g., bladder, dedicated pumps) X X X Sampling bailers (e.g., thief sampler) X X X Soils Characterization Sampling technologies (e.g., discrete, continuous) X X X Vadose Zone Water and Gas Monitoring Lysimeter (e.g., suction, pressure/vacuum) X X X Electrical resistivity blocks Past use Soil–gas monitoring (e.g., probes, chambers) X X Time-domain reßectometry X Electronic leak detection system Thermocouple psychrometers Tensiometers Past use Frequency-domain capacity probes Automatic VOC collection/gas chromatography L1667_C03.fm Page 112 Tuesday, October 21, 2003 3:49 PM ©2004 CRC Press LLC Analytical Technologies Gas chromatography X X High-performance liquid chromatography X Thin-layer chromatography Super-critical ßuid chromatography Gas chromatography/mass spectrometry X X X Mass spectrometry Past use X X Ion mobility spectrometry Atomic absorption spectrometry Past use X X Atomic emission spectrometry X X Laser-induced breakdown spectrometry Infrared spectrometry (e.g., fourier transform) Past use X X Near-IR reßectance/transmission spectrometry Raman spectroscopy UV-visible spectrometry (e.g., ßuorescence, synchronous luminescence) XX Fluorescence spectrometry X X X-ray ßuorescence Past use X Gamma spectrometry X X Radiation detectors (e.g., Geiger counter, solid/liquid scintillator, semiconductor detector) XXX Nuclear magnetic resonance X Photoionization detector X X X Electrical conductivity sensor X X Electrochemical techniques X Explosive sensor X Free-product sensor X Fiber-optics sensor (e.g., solid, porous) X Piezoelectric sensors X In situ chemical probes (e.g., chlorine, pH/ORP, TDS, DO) X X X Membrane-based testing devices (e.g., RDX, TNT, PCBs) X X Environmental test kits (color testing, titrimetric testing, immunoassays) XXX Detector tubes X X Numerical/Spatial/Statistical Models Geostatistical/statistical X X X Flow and transport and optimization models X X X Geographic/expert/decision support systems X X X Notes: X = current use of the technology at a DOE site; SCAPS = site characterization and analysis penetrometer system; VOC = volatile organic compound; IR = infrared spectroscopy; ORP = oxidation reduction potential; TDS = total dissolved solids; DO = dissolved oxygen; RDX = royal demolition explosive; TNT = trinitrotoluene; PCBs = polychlorinated biphenyls. TABLE 3.1 (CONTINUED) Summary of Site Characterization, Environmental Monitoring, and Modeling Technologies Used at Selected DOE Sites Technology INEEL ORNL SRS L1667_C03.fm Page 113 Tuesday, October 21, 2003 3:49 PM ©2004 CRC Press LLC and/or sampling specimens and testing parts or tissue in the laboratory according to standard protocols. The spreading of toxic wastes through living organisms highlights the complex- ity of pathways and exposure hazards associated with contaminants at DOE sites. The situation is worsened by the spatial scale over which contaminants and contam- inant vectors (e.g., Þsh) operate. Therefore, to understand the seriousness of the environmental restoration challenge at DOE sites, one must realize that there are countless point and nonpoint sources of pollution within those sites and many agents of contamination spreading through soil, water, air, and living organisms. 3.2.2.2 Numerical and Optimization Models Environmental restoration has progressed from screening-level and deÞnitive-level characterization to risk analysis, containment, abatement, and remediation. As a result, models have become ßexible and useful tools for creating and analyzing a variety of scenarios in a cost-effective manner. For example, a mass transport numer- ical model can simulate the fate and transport of benzene in ground water that is being pumped, treated, and recharged according to a speciÞc pump-and-treat scheme. Or a vadose zone model such as SESOIL can be implemented to assess the effect of soil capping on long-term metal vertical migration in the vadose zone. Numerical, spatial, and statistical models are accepted and used for a wide range of applications at all three sites (Table 3.1). Modelers at DOE sites typically are part of the risk analysis groups at these sites. The risk analysis groups determine the likelihood of environmental harm caused by pollutants within DOE sites. By and large, they house most of the personnel qualiÞed to work with simulation and optimization models. The state-of-the-art of optimization modeling at DOE sites consists of heu- ristic search techniques based on ground water ßow and transport models. In this approach, the analyst implements ground water and transport models for a selected range of stress or remediation control variables (e.g., pumping rates, soil venting aeration, permeable treatment bed thickness). The measure of effective- ness of a particular control variable is then assessed. For example, the amount of a polar hydrocarbon retained in a permeable treatment bed is determined as a function of the bed’s thickness. Or the concentration of a chlorinated hydrocarbon remaining in solution is assessed as a function of the pumping rate in a pump- and-treat system. The analyst applies his experience and professional judgment in constraining the feasible range of the decision variables, while noting other important factors such as the cost of containment, abatement and remediation, the time required to achieve desired targets, and other regulatory constraints. Expert systems, also called decision support systems (DSS), have been developed to assist risk analysts in the search for the best environmental restoration alter- natives in the heuristic approach (Loaiciga and Leipnik, 2000). The Þnal result of the heuristic search is a series of values of the measure of pollution-control effectiveness and related parameters needed to achieve it. An assessment of the uncertainty associated with each of the entertained pollution-control options can be issued also. The Þnal pollution-control decision, which can be a mixture of L1667_C03.fm Page 114 Tuesday, October 21, 2003 3:49 PM ©2004 CRC Press LLC alternative restoration technologies, is arrived at through a consensus-building approach that involves contractors, DOE personnel, and regulators (state and federal). The implementation of restoration strategies relies heavily on real-time monitoring to make adjustments as needed while the restoration work progresses. In this sense, the restoration work relies on feedback and corrections to achieve pollution-control targets. The implementation of optimization modeling at DOE sites is a distant variation of the classical open-loop optimization prevalent in research literature. Classical open-loop optimization refers to optimizing a system that has no feed- back control and primarily employs linear, nonlinear, and dynamic programming algorithms. Contaminant processes of varying degrees of complexity are imbed- ded in the mathematical formulation of the search algorithm, which yields a set of decision variables that maximizes or minimizes a prespeciÞed restoration beneÞt/cost (objective) function while satisfying a set of constraints imposed by the control, abatement, and remediation technologies; by resource and economic limitations; and by the intervening biological, chemical, and physical processes (Willis and Yeh, 1987). Because restoration strategies derived by the classical optimization approach have no feedback mechanism, they are best interpreted as plausible courses of action that need frequent updating to achieve desired goals. The greatest limitation of classical optimization is its ability to deal with the subtleties and complexities of real-world restoration problems at DOE sites. Another obstacle to its adoption by DOE is the high degree of specialization required by the users. These obstacles render classical optimization out of reach for DOE users and others. 3.2.2.3 Innovative Technologies and the Regulatory Process One of the key issues raised at all surveyed DOE sites is the role that state and federal regulations play in the application of new environmental restoration tech- nologies. According to input received during interviews, state and federal regulators are generally risk-averse when approving new characterization, monitoring, and modeling technologies. Technical procedures for sample collection and analysis approved at each site rely on traditional and presumably well-tested technologies. Thus, for example, a split-spoon sampler is preferred over a Geoprobe ® soil corer at INEEL because the latter has not been proven to regulators to yield samples of at least equal representativeness to those obtained by the former. This preference exists in spite of the fact that the Geoprobe soil corer yields shallow and deep soil cores that preserve the integrity of volatile organic compounds (VOCs) in the soil matrix — a most difÞcult task with split-spoon samplers. On the other hand, some examples justify the risk aversion of regulators toward new technologies. One is the case of a polychlorinated biphenyl (PCB) in situ immunoassay test kit that was used at SRS in an attempt to separate PCB debris at an old, weathered landÞll. About 50% of the in situ results were false positives. Debris separation ultimately relied on standard sample collection and laboratory analysis. DOE sites have so-called technology demonstration programs that seem ideal for testing new environmental restoration technologies. Such a program could be L1667_C03.fm Page 115 Tuesday, October 21, 2003 3:49 PM ©2004 CRC Press LLC a natural framework under which to test a novel apparatus, technique, or model, and, if successful, approve it for Þeld deployment or application. The reality is somewhat different. Contractors work under strict federal facility compliance agree- ments (FFCAs) that stipulate the environmental restoration milestones and dead- lines to be met under agreed-upon budgets. As a result, the contractors have limited funding, time, and resources to develop, test, and permit new equipment and simulation models. Alternatively, the new technology research and development could be undertaken by universities or other research centers and then transferred to DOE if proven successful in test trials. The latter avenue seems a necessity for optimization modeling, which requires signiÞcant mathematical and computational skills rarely found outside university laboratories. Yet, a considerable gap remains between the capabilities currently offered by optimization modeling and the realities and complexities of DOE environmental restoration. It is in this respect that pilot test projects are most needed to determine the potential contribution of optimization techniques to environmental restoration at DOE sites. 3.2.2.4 Technology Needs Finally, site-characterization technology users expressed consensus on the need for a few technologies that, if available, would greatly expedite environmental restoration efforts. First is a Þeld-deployable probe for radionuclide speciation with adequate quantitative accuracy. Such a device would bypass arduous and hazardous sampling, handling, testing, and disposal of radioactive materials. The other technology in the users’ wish lists is an accurate in situ analyzer for VOCs in soils and ground water. VOC loss during sampling is a major problem that biases analytical results, and VOCs represent the second most threatening contaminant after radionuclides at INEEL, ORNL, and SRS. Low priority was given to optimization model application, probably due to limited experience with applications at DOE sites and the lack of familiarity of DOE managers, regulators, and contractors with optimization models in general. 3.2.3 T HE V IEW FROM THE U.S. D EPARTMENT OF D EFENSE (D O D) Congress established the Defense Environmental Restoration Program (DERP) in 1984 to remediate contamination at DoD sites. Since then, the DoD has spent almost $20 billion on the DERP through two accounts. About $5 billion has been spent through the Base Realignment and Closure Act (BRAC) account to remediate bases being closed and transferred to civilian use. The rest of the funds have been spent through the DERP account at bases remaining active. Funding limitations make it necessary to prioritize remedial activities and approaches. After all, some contamination poses less risk than others. Some reme- diation approaches cost less than others, but the cheaper alternative can take longer to achieve about the same result as the more expensive alternative. Selecting a remediation approach for a contaminated site can involve economic analysis and compromise between DoD and environmental regulatory agencies. The DoD has attempted to improve the efÞcacy and reduce the cost of remedi- ation. Included actions have involved innovative technology demonstration projects, L1667_C03.fm Page 116 Tuesday, October 21, 2003 3:49 PM ©2004 CRC Press LLC [...]... with ground water ßow and transport simulators (i.e., MODFLOW and MT3D) The aquifer was discretized into 31 ¥ 20 Þnite-difference nodes per layer, with a total of four layers The size of the aquifer is 4101 ¥ 30 00 ¥ 98 ft (Figure 3. 1) No-ßow boundaries were imposed on ©2004 CRC Press LLC L1667_C 03. fm Page 134 Tuesday, October 21, 20 03 3:49 PM No-Flow Boundary Constant Head Boundary Monitoring Wells Candidate... Annual pump -and- treat system costs reached $40 million by 1996 Many of the pump -and- treat systems were designed before more suitable technologies were available Sometimes the achieved remediation using pump -and- treat was slow Some pump -and- treat systems were not going to achieve required cleanup goals within a reasonable period ©2004 CRC Press LLC L1667_C 03. fm Page 118 Tuesday, October 21, 20 03 3:49 PM... many ground water remediation systems is to contain impacted ground water by preventing ground water ßow beyond a speciÞed boundary (i.e., horizontally or vertically) This containment can be accomplished by controlling hydraulic gradients Most pump -and- treat systems have been designed using ©2004 CRC Press LLC L1667_C 03. fm Page 1 23 Tuesday, October 21, 20 03 3:49 PM numerical simulation models for ground. .. values from the concentration frequency distribution given in Figure 3. 3 ©2004 CRC Press LLC L1667_C 03. fm Page 139 Tuesday, October 21, 20 03 3:49 PM TABLE 3. 3 Risk Assessment Variables Variable I (l/day) ED (year) EF (day/year) AT (year) CSF/BW (day/mg) geometric mean and standard deviation Value 2 30 35 0 70 1.57 ¥ 10 3 7.28 ¥ 100 Figure 3. 5 shows the frequency distribution of risks by using only the mean... Force and DoD sites followed the ERC project 3. 2 .3. 1.2 DoD Pump -and- Treat Operation Evaluation By 1996, DoD was operating 75 pump -and- treat systems as the primary remedy for sites having chlorinated solvent contaminated ground water Because of the large operation and maintenance (O&M) costs, the DoD OfÞce of the Inspector General decided to evaluate the cost and effectiveness of these systems Some of... probability of failure) and cost effectiveness SigniÞcant work has been presented in the past decade by Wagner and Gorelick (1987), Andricevic and Kitanidis (1990), Lee and Kitanidis (1991), Wagner et al (1992), Whiffen and Shoemaker (19 93) , Morgan et al (19 93) , Reichard (1995), Aly and Peralta (1999b), and Freeze and Gorelick (1999) Gorelick (1990, 1997), Wagner (1995), and Freeze and Gorelick (1999)... a chance constraint (e.g., Tung, 1986; Wagner and Gorelick, 1987; and Freeze and Gorelick, 1999): E[Ci] + FN–1(R) S[Ci] < C* (3. 3) where E[Ci] and S[Ci] are the expected value and standard deviation of Ci, respectively, and FN–1(R) is the value of the standard-normal cumulative distribution corresponding to reliability level R An inspection of Equation 3. 3 shows that the chance constraint has the following... optimization to pump -and- treat or pump, treat, and reinject operations (Hereinafter, pump -and- treat is used to refer to both types of systems.) Resulting efforts demonstrated that signiÞcant cost reductions could result from applying simulation optimization modeling to pump -and- treat system design and pumping-strategy development Additional simulation optimization applications at Air Force and DoD sites... models have been presented to pump -and- treat (early 1970s) (Gorelick, 19 83) and bioremediation (late 1990s) Another important area of research and development over the past few years is long-term ground water monitoring design optimization The long-term ground water monitoring issue is signiÞcant because of the duration of monitoring programs, the need to verify remedies, and the potential for remedy modiÞcations... CSF/BW ©2004 CRC Press LLC L1667_C 03. fm Page 140 Tuesday, October 21, 20 03 3:49 PM 40% Frequency 30 % 20% 10% 0% 1.1 x 1 0-7 1 x 1 0-6 1 x 1 0-5 1 x 1 0-4 1 x 1 0 -3 1 x 1 0-2 1 x 1 0-2 Risk FIGURE 3. 6 Frequency distribution of risks incorporating uncertainty in CSF/BW • • • Feedback A strategy should be adaptable to changing conditions and new information This requirement appears easy to meet by using deterministic . Model 3. 3.2.2Multiple Realization Ground Water Management Model 3. 3.2.3Alternative Stochastic Optimization Methods 3. 3.3Uncertainty 3. 3 .3. 1Sources 3. 3 .3. 2Examples 3. 3.4Design-Risk Cost Tradeoff 3. 3.5Long-Term. Cost Tradeoff 3. 3.5Long-Term Ground Water Monitoring 3. 3.5.1The Relationship between Remedy and Monitoring 3. 3.5.2Performance Monitoring Problems 3. 3.5.3Methods 3. 4Gaining Acceptance 3. 4.1Remediation. Technologies and the Regulatory Process 3. 2.2.4Technology Needs 3. 2.3The View from the U.S. Department of Defense (DoD) 3. 2 .3. 1Optimization Efforts 3. 2 .3. 2Model Development Efforts 3. 2 .3. 3Monitoring