Contaminated Ground Water and Sediment - Chapter 3 pdf

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

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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-

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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

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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

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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

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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

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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

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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

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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

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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,

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technology transfer, system operation evaluations, research, and development. In
DoD parlance, optimization refers to any effort to improve a process. Optimization
can involve reducing costs of construction, labor, energy, treatment, monitoring,
analysis, reporting, documentation, data retrieval, or data archiving without endan-
gering human health and safety or the environment. This section mentions some
DoD optimization efforts in monitoring, analysis, and remediation. Most do not
include formal mathematical optimization. All the major defense services and agen-
cies support some efforts in optimization.

3.2.3.1 Optimization Efforts

DoD agencies share information and methods with each other and other organiza-
tions. The Technology Transfer Division of the Air Force Center for Environmental
Excellence (AFCEE/ERT) organizes an Annual Technology Transfer Conference
highlighting new developments and lessons learned by DoD services and agencies,
the U.S. Geological Survey (USGS), and the USEPA.
Each military service has at least one center developing improvements in reme-
diation technology, often in collaboration with other organizations. For example, the
Naval Facilities Engineering Service Center (NAVFAC), in cooperation with the
other services and the USEPA, currently leads a project demonstrating pump-and-
treat optimization. The Army has several centers of expertise that apply and publish
remediation guidance. This section does not mention all DoD centers or initiatives;
however, it does discuss example demonstration and technology transfer initiatives
promoting optimized methods

.

3.2.3.1.1 AFCEE Pump-and-Treat Optimization

AFCEE/ERC conceived and awarded a project in 1993 to demonstrate applying
formal optimization to pump-and-treat or pump, treat, and reinject operations. (Here-
inafter, 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 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 the Þndings
are as follows:
• 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.

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• Many of the pump-and-treat systems had indeÞnite shutoff dates.
• Continuing the operations and monitoring of pump-and-treat systems
would consume an increasing portion of the DERA (DoD, 1998).
The DoD recommended that military services and agencies evaluate the existing

systems to determine whether replacing pump-and-treat with other technologies
might improve performance or reduce cost. The Inspector General



recommended
that the military cooperate with the public, scientists, and environmental regulators
to determine more effective alternate remediation methods.
Respondents to the DoD evaluation in 1998 indicated that monitored natural
attenuation was the preferred remediation approach and that this approach was being
selected for new sites, if possible. Partially as a result of the DoD report, the military
increased efforts to improve pump-and-treat management and use better and less
costly approaches when appropriate.

3.2.3.1.3 Air Force/Defense Logistics Agency Remediation
Process Optimization (RPO)

RPO is a program-management tool developed by the AFCEE/ERT to provide a
systematic iterative approach to evaluate all phases of remedial actions and update
and optimize the effectiveness and efÞciency of efforts to achieve cleanup goals.
RPO provides a mechanism to feed information back into the decision process so
that goals can be updated (if necessary) and met. The objective of RPO is to utilize
best practice technical and management approaches to protect human health and the
environment (AFCEE, 1999). The Air Force Base Conversion Agency (AFBCA) is
applying the RPO process through AFCEE/ERT and is responsible for remediation
programs of bases being closed and converted to civilian use. Contaminated property
cannot be transferred to civilian ownership until a remediation method approved by
regulators is in place. Because Congress wants property ownership to proceed as
quickly as possible, AFBCA remediation projects have a strong temporal component.
The AFBCA is eager to get approved remedies in place as quickly as possible, within

funding limits, so it can transfer property ownership. With this in mind, the AFBCA
has initiated a program to periodically (usually every 5 years) reevaluate pump-and-
treat operations and the need for existing remediation systems.
One of the Þrst RPO reports concerned Operable Unit 1 (OU1) of AFBCA’s
George Air Force Base. OU1 contains a pump-and-treat system to treat a trichloro-
ethene (TCE) plume that originates in an upper unconÞned stratum and reaches a
lower stratum. Per the ROD, the pump-and-treat system must contain the plume of
dissolved TCE and reduce concentrations to below 5 ppb. The pump-and-treat system
began operation in 1991 and was augmented in 1996. Treated water is injected into
the upper stratum upgradient of the plume. Regulators fear that the injection increases
contamination migration to the lower stratum. The Air Force and environmental
regulators have not yet reached agreement on the site conceptual model and on how
the contamination reaches the lower stratum.
The RPO report states that the pump-and-treat system has been inefÞcient in
reducing mass, and it is questionable whether this method will achieve cleanup goals
within a reasonable period. RPO recommendations included the following:

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•Ceasing pumping at 11 of the 18 extraction wells, reducing ßow by up
to 50%
•Evaluating water treatment and disposal alternatives
•Reducing sampling frequency to annual from semiannual
•Reducing the number of sampled monitoring wells from 47 to 34
•Pursuing alternative cleanup goals
•Fully evaluating other potential remediation measures (e.g., monitored
natural attenuation, phytoremediation)
The RPO team considers that implementing short-term recommendations could
reduce annual costs by more than $170,000, and long-term recommendations could

save $5 million during the remaining 33-year project life.

3.2.3.2 Model Development Efforts

In response to the need for improved integrated software to aid ground water cleanup,
the DoD, in partnership with the DOE, USEPA, Cray Research, and 20 academic
partners, has developed the DoD Ground Water Modeling System (GMS)
( The GMS is comprehensive, integrated
software for simulating subsurface ßow and contaminant fate and transport. It
includes many popular or public domain simulation models. GMS simpliÞes ground
water ßow and transport modeling by making it easy to use an assemblage of
computational tools. GMS provides tools for simulation, site characterization, model
conceptualization, mesh and grid generation, geostatistical evaluation, visualization,
and simulation.

3.2.3.3 Monitoring Efforts

3.2.3.3.1 Passive Diffusion Bag (PDB) Samplers

Using PDB samplers (developed by Don Vroblesky of the USGS) can signiÞcantly
reduce the cost of ground water sampling. PDB samplers can obtain representative
VOC ground water concentrations from monitoring wells. A typical PDB sampler
consists of a low-density polyethylene tube that is closed at both ends and lies ßat
when empty. The tube is Þlled with deionized water and is positioned at the target
location in the aquifer by attachment to a weighted line. The PDB samplers equil-
ibrate within approximately 48 h for TCE and tetrachloroethene (PCE). Vinyl chlo-
ride and some chloroethanes can require between 96 and 168 h to equilibrate. The
samplers remain in a well at least 2 weeks to allow the well water to restabilize after
the disruption and absorption caused by the sampler. Recovery consists of removing
the samplers from the well and immediately transferring the enclosed water to 40-

ml sampling vials for analysis. The samplers can help delineate contaminant strat-
iÞcation in wells having insigniÞcant vertical ßow, and multiple PDB samplers can
be used to help identify chemically stratiÞed wells or wells with ßow pattern changes
through the screen as a result of ground water pumping or seasonal ßuctuations.
However, PDB samplers are ineffective for inorganic ions or for highly soluble
organics such as methyl tert butyl ether (MTBE).

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Three years of intensive testing at Air Force and Navy sites indicate that sampling
with PDBs produces data as accurate as those obtained through other presently
approved sampling techniques. Using PDB samplers can result in cost savings of
50 to 70%. The AFCEE/ERT and USGS are evaluating a new passive sampler
exclusively for inorganic and natural attenuation parameters and analytes.
An interagency workgroup, including the Air Force, Army, Navy, Defense Logis-
tics Agency (DLA), USEPA, Interstate Technology and Regulatory Cooperation
(ITRC), and USGS, published a user’s guide for PDB samplers (USGS, 2001). The
AFCEE/ERT sponsored development of the guidance and is implementing its use
at 20 DoD installations.

3.2.3.3.2 Pneumatic Well Logging (PneuLog

®

) of Soil Vapor
Extraction (SVE) Wells

PneuLog (a product of Praxis Environmental Technologies) is an in-well instru-
ment used to quickly deÞne the vertical distribution of contamination and soil

permeability in SVE wells. PneuLog provides much greater vertical proÞling data
than any other available technique optimizing or supporting closure of SVE sys-
tems. Under active vapor extraction, the PneuLog device is lowered and raised
along a well screen using an automated cable reel while simultaneously recording
the ßow rate and total vapor concentration. Flow can be attributed to speciÞc soil
intervals from the measured changes in cumulative ßow. Additionally, this change
in ßow over a depth interval effectively deÞnes its permeability. The contaminant
vapor concentration is measured continuously through a Teßon

®

sampling tube
located just above the ßow sensor and conveyed to the surface where it is analyzed
using a photoionization detector (PID). A mass balance is used to determine a
proÞle of the soil-gas contamination from the changes in cumulative ßow and total
concentration measured in the well. In addition, vapor samples can be collected
at discrete depths for compound-speciÞc analyses. Site conceptual models are
improved by deÞning preferential ßow paths that bypass contaminated intervals
and by identifying mass transfer limited soils that extend cleanup times. The data
allow SVE to focus on the most contaminated intervals and avoid stagnation zones.
A more detailed soil-gas concentration proÞle allows more accurate contaminant
transport modeling to assess the risk from residual contamination. More accurate
risk evaluation allows remedial managers to know when the vadose zone is sufÞ-
ciently clean to terminate SVE. This technology is applicable only to the screen
intervals of active SVE wells.
PneuLog has been utilized at numerous BRAC and active Air Force bases to
improve conceptual site models, enhance SVE operations, and support closure of
SVE systems. The AFCEE funded use of the technology in the initial characterization
of the vadose zone at three sites and supported efforts to optimize SVE operations
at seven sites using PneuLog. The optimization effort at the seven sites has saved

the Air Force an estimated $300,000 to $500,000 to date. Additional cost savings
will be achieved over time as these sites achieve closure based on the detailed data
set provided by PneuLog. Further details of these site-speciÞc efforts are provided
in the Þnal report submitted by Praxis to the AFCEE (Praxis Environmental Tech-
nologies, 2000).

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3.2.4 T

HE

V

IEW



FROM

I

NDUSTRY

Industry is primarily interested in reducing long-term cost liability. Therefore, indus-
try generally is willing to spend money up front for an optimization analysis (plus
any subsequent costs associated with system modiÞcations) if it is considered likely
that the total life-cycle cost will be reduced as a result. Making this assessment
requires a site-speciÞc cost-beneÞt analysis prior to a full optimization evaluation

that accounts for the expected cost of the optimization analysis, expected costs of
system modiÞcations, and expected savings.
Industry generally performs cost evaluations in terms of net present value
(NPV), using a discount rate that adjusts future expenditures to their present value.
(Money not spent today can generally be invested by industry at a rate that exceeds
inßation; therefore, current dollars are worth more than future dollars.) Conse-
quently, optimization analyses performed for industry should be performed with
respect to NPV.
Industry must gain the approval of regulatory agencies to implement or modify
remedial strategies. Strategies that are derived by using mathematical optimization
techniques linked to ground water simulation models are no different in this regard
than strategies derived solely on the basis of ground water modeling, because the
mathematical optimization algorithms simply perform a series of simulations with
the ground water model in an efÞcient order. Therefore, regulatory issues should
focus on the validity of the ground water model predictions. Once that is established
(i.e., the simulation model is accepted as a valid design tool by the regulators), the
linkage of mathematical optimization algorithms with the simulation model should
not create additional regulatory concerns.
Industry is keenly aware that new approaches to ground water remediation
continue to evolve. In some cases, the evolution is because of new technology (e.g.,

in situ

bioremediation, chemical oxidation, permeable reactive barriers), and in other
cases, regulatory reform (e.g., monitored natural attenuation). The determination of
whether to apply simulation optimization techniques must consider not only the
potential beneÞts with respect to the current remediation strategy (e.g., pump and
treat), but also whether resources are better spent pursuing alternative remedial
approaches that might replace and/or augment the current remediation strategy. At
many sites, long-term ground water monitoring costs can in fact be the greatest life-

cycle cost component. At these sites, the optimization of ground water monitoring
can represent the greatest opportunity for future cost savings.

3.3 STATE OF KNOWLEDGE AND PRACTICE

The contamination of ground water supplies poses widespread and signiÞcant envi-
ronmental problems. In the past few decades, different remediation strategies have
been applied and a great deal of research is in progress. The most common ground
water remediation techniques are as follows:
• Pump and treat
• Bioremediation

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• Air stripping
•Vapor extraction
• Permeable walls (e.g., iron walls, biological barriers, chemical barriers)
•Phytoremediation
In recent years, optimization management models have been developed to design
ground water remediation strategies. These models combine mathematical optimi-
zation techniques with ground water ßow and mass transport simulators to determine
an optimal remedial design. Regarding the aforementioned remediation techniques,
optimization management models have been presented to pump-and-treat (early
1970s) (Gorelick, 1983) 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 if either the
remedy or monitoring plan does not perform adequately. In addition, long-term

ground water monitoring has received substantially less attention than remediation
process design optimization, so a greater potential exists for signiÞcant impacts.
Time-robust monitoring networks (i.e., monitoring networks that perform well for
extended periods of time) have not been investigated extensively to date and are
recommended as a research focus area.

3.3.1 T

HE

S

IMULATION

O

PTIMIZATION

A

PPROACH

The development of ground water simulation models in the early 1970s provided
planners with quantitative techniques for analyzing alternative management strategies.
In recent years, simulation models have been combined with optimization models to
identify the best management alternatives while considering management objectives
and constraints. Typical ground water remediation problems involve the design of the
well Þeld, that is, the determination of the number, location, and pumping/recharge
schedule of all pumping/recharge wells. Gorelick (1983), Yeh (1992), Ahlfeld and
Heidari (1994), Wagner (1995), and Ahlfeld and Mulligan (2000) have provided

extensive reviews on coupling simulation models with optimization models.
The mathematical formulation of a ground water management problem consists
of an objective function that is related either to total remediation cost or to the total
amount of pumped water, subject to a set of constraints that are based on hydraulic
heads, ßows, or concentrations at selected locations. Depending on the kind of
constraints, whether hydraulic heads or concentrations, the following two basic
approaches appear to be employed: ground water management models involving
hydraulic constraints and those involving concentration constraints.

3.3.1.1 Gradient Control Remediation Technology

The primary goal of 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

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numerical simulation models for ground water ßow, such as MODFLOW (Har-
baugh and McDonald, 1996a, 1996b). Traditionally, the hydraulic simulation
model is run repeatedly to simulate different pumping scenarios. Each scenario is
typically evaluated with respect to the number of wells required and the total
pumping rate necessary to achieve the required hydraulic containment while main-
taining compliance with other design constraints (e.g., limits on water levels,
drawdowns). These manually iterative simulations rely heavily on the experience
and insight of the modeler, who must personally determine each successive trial.
A limitation of this manually iterative approach is that there are an inÞnite number
of well location and well rate combinations to consider, and only a small number
of numerical simulations are practical.

The linkage of mathematical optimization techniques with the ground water
ßow simulator is an attractive alternative for gradient control problems. The most
popular technique is the response matrix technique, which is described in detail in
Gorelick et al. (1993) and Ahlfeld and Mulligan (2000). This approach capitalizes
on the linear relationship between pumping rate and drawdown that applies to many
ground water systems (i.e., the law of linear superposition) and easily extends to
a linear relationship between pumping rates and hydraulic gradients. This linear
relationship allows an optimization problem to be formulated as a linear (or mixed-
integer linear) program, where the decision variables are the pumping locations
and pumping rates. The optimization seeks to minimize an objective function (e.g.,
minimize total pumping rate) subject to a set of constraints that all must be satisÞed
according the simulation model results, including limits on gradients that establish
hydraulic control.
Hydraulic optimization for gradient control problems is implemented easily
because of the following: (1) most sites with ground water contamination have a
site-speciÞc ground water ßow model, (2) the optimization approach is straightfor-
ward and easily understood, and (3) tools for performing the optimization are
available as off-the-shelf technology. Applications of hydraulic optimization have
appeared in the literature since the 1970s, and several codes for performing these
evaluations are freely available such as MODMAN (Greenwald, 1998) and MOD-
OFC (Ahlfeld and Rießer, 1999). A detailed discussion of formulation options
associated with gradient control applications and demonstrations of these techniques
for three sites is provided in Greenwald (1999).
Gradient control techniques are limited by the predictive ability of the under-
lying simulation model, which is affected by uncertainty in parameter values, the
conceptual hydrogeological model of the site, the experience of the modeler, input
errors, and many other factors. Additional limitations of gradient control problems
include the following: (1) contaminant concentrations cannot be included in the
mathematical formulation; (2) cleanup time cannot be rigorously included in the
mathematical formulation; and (3) for thin unconÞned aquifers (and several other

circumstances), linear superposition (which allows the use of linear programming
techniques) can be violated. For sites where cleanup is the main objective and
predictions of contaminant concentrations or cleanup time are central to evaluating
the objective function and key constraints, the limitations of hydraulic optimization
can be prohibitive. Transport modeling and transport optimization can be applied

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in such cases. However, developing a transport simulation model and performing
a transport-based optimization analysis can require signiÞcant effort and cost, and
transport model predictions are subject to additional uncertainties (relative to ßow
model predictions).

3.3.1.2 Concentration Constraints Remediation Technology

As mentioned previously, ground water management problems combine a ground
water numerical simulator and an optimization model. In the past few decades,
several ground water numerical simulators have been presented and employed (e.g.,
MODFLOW, MT3DMS, SUTRA, FEMWATER [3-D], PTC) to represent ground
water ßow and contaminant transport. The following optimization models can be
categorized based on the theory that is used:
• Nonlinear models (using nonlinear programming)
• Dynamic models (using dynamic programming)
• Genetic algorithm models
• Simulated annealing models
• ArtiÞcial neural network (ANN) models
• Cutting plane techniques models
The main characteristic of the ground water contaminant management problem
is that the problem is nonconvex due to nonconvex behavior of the mass transport

equation (constraints) and/or the objective function. Therefore, the majority of the
above models have difÞculty determining a globally optimal solution. The main
characteristics of and a historical review of each category of the above models are
as follows:
• Nonlinear Models
The majority of these models rely on gradient-based techniques. They
require calculation of the derivative matrix for concentrations with re-
spect to the decision variables, and a globally optimal solution is not
guaranteed. In the past, a combination of ground water simulation with
nonlinear programming techniques to solve ground water management
problems has been presented by Gorelick et al. (1984), Willis and Yeh
(1987), Ahlfeld et al. (1988), Charbi and Peralta (1994), McKinney and
Lin (1995), Peralta et al. (1995), and Emech and Yeh (1998).
• Dynamic Models
These models are based on dynamic programming theory where non-
linear and stochastic features of the ground water system can be trans-
lated into the formulation. SigniÞcant cost savings have been reported
using these models (between 20 and 70%). In some cases, dynamic well
strategies (i.e., the well locations are not Þxed between different man-
agement periods) have been incorporated. These models are mathemat-
ically complicated, numerical difÞculties have been reported, and a
globally optimal solution is not guaranteed. Work on dynamic models

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has been presented by Jones et al. (1987), Chang et al. (1992), Culver
and Shoemaker (1992, 1993, 1997), and Huang and Mayer (1997). In
addition, some individuals have opted not to use the dynamic program-
ming theory directly but rather the multiperiod approach. This work has

been presented by Ahlfeld (1990), Rizzo and Dougherty (1996), and
Karatzas et al. (1998).
• Genetic Algorithm Models
One of the main characteristics of these models is that derivatives are
not required. They are computationally intensive, but parallel comput-
ing can be applied. A globally optimal solution is not guaranteed. Their
application to ground water problems began appearing in the early
1990s, and representative works have been presented by McKinney and
Lin (1994), Rogers et al. (1995), Wang and Zheng (1997, 1998), and
Aly and Peralta (1999a).
• Simulated Annealing Models
These models are devised to solve large combinatorial optimization
problems and do not require derivative computation. They have shown
ßexibility in the selection of cost functions (convex or not convex) and,
theoretically, they can Þnd global optima (but not in practice). They are
computationally intensive, but parallel computing can be applied. Some
studies suggest that they are competitive with other optimization tech-
niques. Dougherty and Marryott (1991)

,

Kuo et al. (1992), Marryott et
al. (1993), Rizzo and Dougherty (1996), and Wang and Zheng (1998)
have presented work on simulated annealing models.
• ANN Models
These models are computationally intensive due to the neural network
training. Following the training, they are consistent with most of the
nonlinear models, with fewer calls to the simulator. Parallel computing
can be also applied. Work on ANN models for ground water manage-
ment has been presented by Rogers and Dowla (1994), Rogers et al.

(1995), Rizzo and Dougherty (1996), and Aly and Peralta (1999b).
• Cutting Plane Technique Models
In this category, the models are characterized as global optimization
techniques due to the formulation of the objective function, which is
required to be concave. When the objective function is concave, these
optimization methods can be characterized as global optimization
techniques. Only one function derivative (of the most violated con-
straint) is required at each iteration until the optimal solution is ob-
tained. These models are based on cutting plane theory where the
feasible region is enclosed into a polytope and where the most ex-
treme point of the feasible region is determined by eliminating parts
of the infeasible region (using cutting hyperplanes) (Karatzas and
Pinder, 1993, 1996).
In the past few years, work has been presented where bioremediation simulators
have been combined with optimization techniques such as Minsker and Shoemaker

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(1998), Yoon and Shoemaker (1999), and Smalley et al. (2000). In addition, models
of multiple contaminants have been presented that are related to pulsed or continuous
pumping for removing contaminants subject to rate-limited mass (Haggerty and
Gorelick, 1994).

3.3.2 S

TOCHASTIC

O

PTIMIZATION



TO

A

CCOMMODATE

P

OTENTIAL


D

ESIGN

F

AILURE
The uncertainties underlying ground water ßow and transport models (e.g., asso-
ciated with characterizing subsurface heterogeneities, contaminant sources and
plumes, reaction pathways and rates) have a profound effect on the reliability with
which cleanup system performance can be predicted. Consequently, simulation
model uncertainty is viewed as the most important source of errors in the simulation
optimization design model. Research to date has focused on incorporating simula-
tion model uncertainty into the optimization framework to assess the tradeoffs
between reliability (or probability of failure) and cost effectiveness. SigniÞ cant

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 (1993), Morgan et al. (1993), Reichard (1995), Aly and
Peralta (1999b), and Freeze and Gorelick (1999). Gorelick (1990, 1997), Wagner
(1995), and Freeze and Gorelick (1999) provide a detailed review of stochastic
ground water optimization models.
The goal of ground water remedial design is to develop a remediation strategy
that will lead ultimately to compliance with the ground water quality performance
standards set forth by the controlling regulatory agencies. Therefore, failure of a
remediation strategy is deÞned as any incident that violates the established perfor-
mance criteria. As discussed previously, performance standards typically serve as
constraints in the simulation optimization model. Therefore, the deÞnition of failure
can be further extended to be the violation of performance constraints in the opti-
mization model.
Under ideal conditions, the design optimization model is a perfect represen-
tation of the remediation problem, and there is no possibility of failure. The
objectives and constraints would reßect perfectly the goals and performance
standards set forth by the regulatory agencies: the ground water simulation
model(s) would reßect perfectly the geologic, hydrologic, and chemical condi-
tions of the contamination site and would perfectly predict ßow and transport
under alternative remediation strategies. Further, the optimization model would
identify, with complete certainty, the design that best meets the problem’s objec-
tives and constraints. Obviously, this does not occur in real-world applications.
As a result, simulation optimization models will always be speciÞed incorrectly
to some degree. The goal then is to develop remediation design optimization
models that provide assurance, albeit risk qualiÞed, that remediation performance
criteria will be met.
Traditionally, engineering design has relied on the use of standardized design
codes that deÞne deterministic safety factors to account for uncertainty in the design
process. For ground water remediation, however, each problem is distinctly unique

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with little or no precedent on which standardized safety factors can be established.
Consequently, the trend in ground water remediation design has moved away from
the traditional “one size Þts all” safety factor approach and toward the use of more
sophisticated stochastic analyses that account for site-speciÞc uncertainties. As
discussed in later sections, many of these approaches do not completely abandon
the safety factor approach; instead, they reÞne that approach to develop safety
factors on a site-by-site basis. It is important to note that with uncertainty included
in the optimization model, there is no longer a single best solution as in the
deterministic case. Rather, there is a spectrum of stochastic optima, with each
optimal solution associated with a speciÞed level of reliability (the complement of
the probability of failure).
The majority of research to date has focused on the following two stochastic
optimization methods: chance-constrained optimization and multiple realization
(sometimes referred to as stacking) approaches. Both methods assume that some
simulation model parameters are unknown, and both approaches begin by estimating
the unknown parameters and quantifying their uncertainties. They then introduce
the effects of the model parameter and prediction uncertainties into the optimization
model. It is at this point that the chance-constrained and multiple realization
approaches diverge based largely on the manner in which the two approaches
categorize simulation model uncertainty. The chance-constrained approach is linked
with a conceptualization in which the simulation model parameters are viewed as
uniform over large zones. In this case, model parameter and prediction uncertainties
are included in the optimization model via Þrst-order uncertainty analysis. The
multiple realization approach, on the other hand, is not limited to the small variance
assumption with respect to the aquifer properties, and parameter uncertainty is
included in the optimization model using Monte Carlo methods that are not con-
strained by the limitations of Þrst-order uncertainty analysis.
3.3.2.1 Chance-Constrained Ground Water

Management Model
The typical deterministic remediation design optimization model has a constraint
set limiting the maximum permissible concentrations at selected compliance points:
C
i
< C
i
*
(3.1)
where C
i
is the simulated concentration at a space–time location i and C
i
*
is the
maximum permissible concentration.
When predicting system performance under simulation model uncertainty, there
is a probability that a constraint will not be met (i.e., a probability of system failure),
and it is necessary to replace the deterministic constraint with a stochastic one:
Prob [C
i
< C*] > R (3.2)
where R is the accepted reliability level (or one minus the accepted probability of
failure).
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As deÞned above, the probabilistic constraint cannot be solved in the optimization
model; however, if it is assumed that the simulated concentrations as a function of
model parameter uncertainty are (or are well approximated as) normally distributed,
it can be reformulated as a deterministic equivalent known as a chance constraint (e.g.,

Tung, 1986; Wagner and Gorelick, 1987; and Freeze and Gorelick, 1999):
E[C
i
] + F
N
–1
(R) S[C
i
] < C
*
(3.3)
where E[C
i
] and S[C
i
] are the expected value and standard deviation of C
i
, respec-
tively, and F
N
–1
(R) is the value of the standard-normal cumulative distribution cor-
responding to reliability level R.
An inspection of Equation 3.3 shows that the chance constraint has the
following two components: an expected value component (Þrst term on left side)
and a stochastic component (second term on left side). When the reliability is
0.5, F
N
–1
(R) is zero, the stochastic component drops out, and the chance con-

straint reduces to the deterministic constraint (Equation 3.1). Thus, the deter-
ministic optimization model that ignores uncertainty corresponds to the case
where there is a 50% chance of failure. The stochastic component in Equation
3.3 is essentially a safety factor that controls the amount of overdesign needed
to achieve the desired level of performance reliability. For a given level of model
uncertainty, the stochastic component of Equation 3.3 increases with increasing
reliability requirement. The effect of this can be best understood by moving the
stochastic component to the right-hand side of Equation 3.3, which is equivalent
to imposing a safety factor that redeÞnes (i.e., reduces) the maximum permissible
concentration. However, unlike standardized safety factors used in many engi-
neering disciplines, the magnitude of the stochastic component is a unique
function of the simulation model uncertainty and the reliability level, and it is
unknown prior to solving the chance-constrained optimization model (Tiedeman
and Gorelick, 1993).
One advantage of the chance-constrained approach is that the reliability level is
explicitly considered in the optimization model, allowing the development of a
remediation strategy designed to meet the decision maker’s reliability preference. It
also allows the development of reliability–cost tradeoff curves (Wagner and Gorelick,
1987; Tiedeman and Gorelick, 1993; Freeze and Gorelick, 1999). Although it is
natural to think that a decision maker will take a risk-averse stance and choose a
design with a high degree of reliability, it is not realistic to assume that a reliable
design will be implemented regardless of cost. The reliability–cost tradeoff curve
allows the decision maker to evaluate the marginal cost associated with an increase
or decrease in reliability and select a design that provides an acceptable balance
between reliability and cost.
Based on Þeld data to date, there have been two applications of the chance-
constrained ground water management model. One involves the application of
a nonlinear chance-constrained optimization model to identify optimal pumping
schemes for plume capture at a landÞll site near Ottawa, Canada (Gailey and
Gorelick, 1993). The other applies nonlinear chance-constrained optimization

to identify minimum pumping strategies for plume containment at a site in
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southwest Michigan (Tiedeman and Gorelick, 1993). Both examples demonstrate
the need for overdesign (pumping above that required in the deterministic case)
to account for the performance uncertainties that arise from model parameter
uncertainties. For the plume capture problem presented by Gailey and Gorelick,
an overdesign of 27% was needed to achieve a reliability level of 0.90. For the
plume containment problem presented by Tiedeman and Gorelick, a 40% over-
design was needed for a reliability level of 0.90. Tiedeman and Gorelick also
provide an interesting analysis of the stochastic component of the chance con-
straints. Their analysis showed that not only could the safety factors not be
deÞned a priori, they could vary signiÞcantly from one constraint to another
within a given problem.
3.3.2.2 Multiple Realization Ground Water
Management Model
The chance-constrained optimization method is based on Þrst-order uncertainty
analysis, which is known to have accuracy limitations that are frequently violated
in real-world applications. The question then is: How is uncertainty originating
from highly uncertain and heterogeneous subsurface properties incorporated into
the ground water management model? The answer is to use a stacking approach
in which multiple realizations of the uncertain parameters are included in the
optimization model.
Consider again the deterministic concentration constraint given in Equation 3.1.
In the multiple realization model, this single constraint is replaced with the following
series of constraints:
C
i1
< C
i

* for parameter realization 1 (3.4a)
C
i2
< C
i
* for parameter realization 2 (3.4b)
C
in
< C
i
* for parameter realization n (3.4c)
where C
i1
,

C
i2
, and C
in
are the simulated concentrations at space-time location (i)
for parameter realizations 1, 2, and n. It is important to understand the structure of
the multiple realization management model in order to understand how it identiÞes
failure-averse designs. The multiple realization model solves the optimization prob-
lem simultaneously for all n parameter realizations. From the standpoint of failure,
this means that the model provides a robust solution that is feasible (i.e., successful)
for all parameter realizations included in the model. This simultaneous solution
approach recognizes that, in general, no single realization can be used to identify
a reliable remediation strategy. Rather, the unique design demands of each realiza-
tion must be pooled in order to deÞne the optimal reliable solution. For example,
consider the problem of minimizing pumping for plume containment. Each param-

eter realization can dictate pumping in a different part of the aquifer in order to
meet the design constraints. By considering the inßuence of pumping across all
realizations, the multiple realization method identiÞes the scenario requiring the
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least pumping that meets the demands of each realization. This pooled solution
requires pumping in excess of that which would be required for any single realiza-
tion. As in the chance-constrained model, this overdesign can be thought of as a
safety factor, and, as in the chance-constrained model, this safety factor cannot be
deÞned prior to solving the multiple realization model. It is important to note that
the multiple realization management model is different from Monte Carlo optimi-
zation which solves a series of individual optimization problems, each with a
different parameter realization. Monte Carlo optimization can provide information
about the variability of the optimal solution from realization to realization, but,
except for very limiting cases, it cannot identify reliability-based optimal designs.
Wagner and Gorelick (1989) and Freeze and Gorelick (1999) provide a more
detailed discussion of Monte Carlo optimization.
Unlike the chance-constrained model, the multiple realization model does not
explicitly contain reliability in its formulation. However, Chan (1993) presents the-
oretical analyses that deÞne the design reliability as a nonparametric function of the
number of realizations included in the management model, R = n/(n+1). For example,
if the model is formulated with 99 realizations, the estimated design reliability would
be 0.99. For the case of optimal plume containment in the presence of a spatially
varying and uncertain transmissivity, Chan (1993) evaluates the accuracy of the
reliability estimator. Monte Carlo analyses show agreement between the reliability
predicted by the nonparametric formula and the average reliability provided by the
Monte Carlo results. (Analyses by Wagner and Gorelick [1989] similarly show agree-
ment between the nonparametric reliability estimate and the design reliability
obtained through Monte Carlo analysis.) Chan (1993) also presents a series of tests
to gauge reliability prediction sensitivity to model parameter and structure changes.

The results indicate that the nonparametric reliability estimate is robust with respect
to a variety of changes (e.g., changes in the covariance and correlation structure of
the transmissivity Þeld, changes in the location and magnitude of velocity constraints).
The multiple realization approach described above has been modiÞed in a number
of ways. Wagner et al. (1992), Morgan et al. (1993), and Chan (1994) present multiple
realization methods that allow for constraint violations within the stack of constraint
sets. All these works deal with designing reliable hydraulic containment strategies.
Wagner et al. (1992) modify the objective function to include a penalty cost for
constraint violations. Morgan et al. (1993) and Chan (1994) develop heuristic algo-
rithms that generate solutions in which R
n
of the constraint sets are satisÞed, where R
is the design reliability level and n is the number of realizations. The assumption here
is that if R
n
of the constraint sets are satisÞed, the management strategy will satisfy
R% of the constraint sets across the entire ensemble of realizations. Monte Carlo testing
by Chan (1994) shows that the accuracy of this approach improves as the number of
realizations increases. Ranjithan et al. (1993) used an ANN to reduce the number of
realizations considered by the multiple realization model. The pattern recognition
capabilities of the ANN were used to identify realizations that are likely to dictate the
Þnal design. The multiple realization model was then applied to a small subset of these
critical realizations. This approach was compared with that presented by Morgan et
al. (1993) and was found to closely reproduce the cost–reliability trade-offs using
fewer realizations and less computational time. Ritzel and Eheart (1994) use the
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multiple realization approach in a multiobjective model to evaluate the cost–reliability
tradeoffs for optimal plume containment. Finally, Smalley et al. (2000) present a
promising stacking model that is solved using a noisy genetic algorithm. They study

the problem of risk-based design of in situ bioremediation where uncertainty stems
from a heterogeneous hydraulic conductivity and unknown parameters of the exposure
and risk model. For the test example, the noisy genetic algorithm was able to identify
a reliable design from a relatively small number of parameter realizations.
3.3.2.3 Alternative Stochastic Optimization Methods
The focus on chance-constrained and multiple realization methods in the above
discussion mirrors the focus of stochastic ground water optimization methods
research to date. A number of papers present alternatives or enhancements to these
methods, such as those in the areas of coupled ground water management and
monitoring. The above discussion highlights that the effect of failure-averse design
is to introduce a cost of overdesign that increases with increasing model uncertainty
or reliability. Additional data can potentially reduce model uncertainty and thereby
reduce overdesign. The important issue in coupled ground water management and
monitoring design is whether the reduction in management costs offsets data col-
lection costs. Among those that address this problem are Andricevic and Kitanidis
(1990), Tucciarelli and Pinder (1991), and Wagner (1999).
This section would not be complete without a discussion of decision analysis,
which has emerged as an alternative to stochastic optimization for reliable ground
water management design. Like the stochastic optimization approach, the decision
analysis approach seeks the least-cost, reliable design solution that accounts for
ground water simulation model uncertainty. However, there are two important dif-
ferences between the two decision-making frameworks. First, whereas stochastic
optimization typically deals with minimizing costs, decision analysis involves a risk-
cost minimization. Second, stochastic optimization normally seeks to identify the
least-cost solution for only one technological strategy, whereas decision analysis
considers a suite of technological strategies from which one (not necessarily optimal)
strategy is selected. A detailed comparison of the stochastic optimization and deci-
sion analysis frameworks can be found in Freeze and Gorelick (1999).
3.3.3 UNCERTAINTY
Typically, the limitations of subsurface remediation technologies are thought of

in a process engineering sense. In engineered systems, the efÞciency of a process
can be improved through theoretical or experimental investigations. In the reme-
diation of natural subsurface systems, however, there is far less control over the
behavior of the process and much greater degrees of variability and uncertainty.
Thus, the most signiÞcant technological limit in subsurface remediation is a soft
limit: uncertainty.
Engineers and others involved in designing and making decisions on subsurface
remediation systems need to be familiar with the sources of uncertainty and their
signiÞcance with regard to system performance. An informed decision maker is one
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