vEPA
United States Office of Research and Office of Solid Waste and EPA/542/R-99/011B
Environmental Protection Development Emergency Response December 1999
Agency Washington, DC 20460 Washington, DC 20460
Hydraulic Optimization
Demonstration for
Groundwater Pump-
and-Treat Systems
Volume II: .Application of
Hydraulic Optimization
-------
-------
EPA/542/R-99/011B
December 1999
Hydraulic Optimization Demonstration For
Groundwater Pump-and-Treat Systems
Volume 2:
Application of Hydraulic Optimization
by
Rob Greenwald
HSI GeoTrans
Freehold, New Jersey 07728
EPA Contract No. 68-C4-0031
Dynamac Corporation
3601 Oakridge Road
Ada, Oklahoma 74820
Project Officer
David S. Burden, Ph.D.
U.S. Environmental Protection Agency
National Risk Management Research Laboratory
Subsurface Protection and Remediation Division
Ada, Oklahoma 74820
Technical Monitors
Kathy Yager, EPA/TIO
David S. Burden, Ph.D., EPA/ORD
OFFICE OF RESEARCH AND DEVELOPMENT
UNITED STATES ENVIRONMENTAL PROTECTION AGENCY
WASHINGTON, DC 20460
-------
-------
NOTICE
The information in this document has been funded by the United States Environmental Protection
Agency under Contract Number 68-C4-0031, to Dynamac Corporation (Subcontract to HSI GeoTrans). It
has been subjected to the Agency's peer review and administrative review, and it has been approved for
publication as an EPA document. Mention of trade names or commercial products does not constitute
endorsement or recommendation for use.
11
-------
-------
PREFACE
This work was performed for the U.S. Environmental Protection Agency (U.S. EPA) under EPA
Contract No. 68-C4-003 Iwith Dynamac Corporation. The technical work was performed by HSI
GeoTrans under Subcontract No. S-OKOO-001. The final report is presented in two volumes:
Volume 1: Pre-Optimization Screening (Method and Demonstration)
• Volume 2: Application of Hydraulic Optimization
Volume 1 provides a spreadsheet screening approach for comparing costs of alternative pump-and-treat
designs. The purpose of the screening analysis is to quickly determine if significant cost savings might
be achieved by modifying an existing or planned pump-and-treat system, and to prioritize subsequent
design efforts. The method is demonstrated for three sites. Volume 1 is intended for a very broad
audience.
Volume 2 describes the application of hydraulic optimization for improving pump-and-treat designs.
Hydraulic optimization combines groundwater flow simulation with linear and/or mixed-integer
programming, to determine the best well locations and well rates subject to site-specific constraints. The
same three sites presented in Volume 1 are used to demonstrate the hydraulic optimization technology in
Volume 2. Volume 2 is intended for a more technical audience than Volume 1.
The author extends thanks to stakeholders associated with the following three sites, for providing
information used in this study:
Chemical Facility, Kentucky
Tooele Army Depot, Tooele, Utah
• Offutt Air Force Base, Bellevue, Nebraska
At the request of the facility, the name of the Kentucky site is not specified in this report.
Information was provided for each site at a specific point in time, with the understanding that new
information, if subsequently gathered, would not be incorporated into this study. Updated information
might include, for instance, revisions to plume definition, remediation cost estimates, or groundwater
models.
The author also extends thanks to Kathy Yager of the U.S. EPA Technology Innovation Office (TIO) and
Dr. David Burden of the U.S. EPA Subsurface Protection and Remediation Division (SPRD), for their
support. Finally, the author extends thanks to the participants of the three Stakeholder Workshops for
providing constructive comments during the course of the project.
ill
-------
-------
FOREWORD
The U.S. Environmental Protection Agency is charged by Congress with protecting the Nation's
land, air, and water resources. Under a mandate of national environmental laws, the Agency strives to
formulate and implement actions leading to a compatible balance between human activities and the
ability of natural systems to support and nurture life. To meet these mandates, EPA's research program
is providing data and technical support for solving environmental problems today and building a science
knowledge base necessary to manage our ecological resources wisely, understanding how pollutants
affect our health, and preventing or reducing environmental risks in the future.
The National Risk Management Research Laboratory is the Agency's center for investigation of
technological and management approaches for reducing risks from threats to human health and the
environment. The focus of the Laboratory's research program is on methods for the prevention and
control of pollution to air, land, water, and subsurface resources; protection of water quality in public
water systems; remediation of contaminated sites and ground water; and prevention and control of indoor
air pollution. The goal of this research effort is to catalyze development and implementation of
innovative, cost-effective environmental technologies; develop scientific and engineering information
needed by EPA to support regulatory and policy decisions; and provide technical support and
information transfer to ensure effective implementation of environmental regulations and strategies.
These case studies demonstrate ways in which hydraulic optimization techniques can be applied
to evaluate pump-and-treat designs. The types of analyses performed for these three sites can be applied
to a wide variety of sites where pump-and-treat systems currently exist or are being considered.
However, the results of any particular hydraulic optimization analysis are highly site-specific, and are
difficult to generalize. For instance, a hydraulic optimization analysis at one site may indicate that the
installation of new wells yields little benefit. That result cannot be generally applied to all sites. Rather,
a site-specific analysis for each site is required. A spreadsheet-based screening analysis (presented in
Volume 1 of this report) can be used to quickly determine if significant cost savings are likely to be
achieved at a site by reducing total pumping rate. Those sites are good candidates for a hydraulic
optimization analysis.
Clinton W. Hall, Director
Subsurface Protection and Remediation Division
National Risk Management Research Laboratory
IV
-------
-------
EXECUTIVE SUMMARY
Hydraulic optimization couples simulations of groundwater flow with optimization techniques such as
linear and mixed-integer programming. Hydraulic optimization allows all potential combinations of well
rates at specific locations to be mathematically evaluated with respect to an objective function (e.g.,
minimize total pumping) and series of constraints (e.g., the plume must be contained). The hydraulic
optimization code quickly determines the best set of well rates, such that the objective function is
minimized and all constraints are satisfied.
For this document, the term "optimization" for pump-and-treat design was refined as follows:
Mathematical Optimal Solution. The best solution, determined with a mathematical
optimization technique, for a specific mathematical formulation (defined by a specific objective
function and set of constraints); and
Preferred Management Solution. A preferred management strategy based on a discrete set of
mathematical optimal solutions, as well as on factors (e.g., costs, risks, uncertainties,
impediments to change) not explicitly considered in those mathematical solutions.
For this demonstration project, hydraulic optimization was applied at three sites with existing pump-and-
treat systems. For each case study, many mathematical formulations were developed, and many
mathematical optimal solutions were determined. For each site, a preferred management solution was
then suggested. The three sites can be summarized as follows:
Site
Kentucky
Tooele
Offutt
Existing
Pumping Rate
Moderate
High
Low
Cost
Per gpm
High
Low
Low
Potential Savings from
System Modification
SMillions
SMillions
Little or None
At two of the sites (Kentucky and Tooele), pumping solutions were obtained that have the potential to
yield millions of dollars of savings, relative to costs associated with the current pumping rates.
In cases where only a few well locations are considered, the benefits of hydraulic optimization are
diminished. In those cases, a good modeler may achieve near-optimal (or optimal) solutions by
performing trial-and-error simulations. This was demonstrated by the Offutt case study. However, as
the number of potential well locations increases, it becomes more likely that hydraulic optimization will
yield improved pumping solutions, relative to a trial-and-error approach. This was demonstrated by
potential pumping rate reductions suggested by the hydraulic optimization results for the Kentucky and
Tooele case studies.
-------
These case studies illustrate a variety of strategies for evaluating pump-and-treat designs with hydraulic
optimization. Components of mathematical formulations demonstrated with these case studies include:
==========;__
Item Demonstrated
====:=======================
objective function minimizes total pumping
objective function minimizes cost
multi-aquifer wells
plume containment with head limits
plume containment with head difference limits
plume containment with relative gradient limits
integer constraints (limiting # of wells selected)
sensitivity of solutions to # of wells selected
scenario for "containment only"
scenarios with core zone extraction
"containment efficiency" of core zone wells evaluated
multiple target containment zones
reinjection of treated water
sensitivity of solutions to conservatism of constraints
sensitivity of solution to non-managed stresses
1
I Kentucky
- -~
X
X
X
X
X
X
X
X
=====
Tooele
======
X
X
X
X
X
X
X
X
X
X
X
I OffUtt
•
X
X
X
X
X
X
X
X
X
For each of the three case studies, an analysis was performed to illustrate the sensitivity of mathematical
optimal solutions to limits placed on the number of wells. For each of the three case studies an analysis
was also performed to evaluate changes in the mathematical optimal solution when new well locations
were considered. For the Kentucky site, an analysis was performed to illustrate the sensitivity of the
mathematical optimal solution to conservatism in the constraints representing plume containment All of
these types of analyses can be efficiently conducted with hydraulic optimization techniques In most
cases, these types of analyses are difficult (if not impossible) to comprehensively perform with a trial-
and-error approach. It is important to note that the case studies presented in this report are for facilities
with existing pump-and-treat systems. Mathematical optimization techniques can also be applied
during initial system design, to generate improved solutions versus a trial-and-error approach.
Hydraulic optimization cannot incorporate simulations of contaminant concentrations or cleanup time
For that reason, hydraulic optimization is generally most applicable to problems where plume
containment is the prominent goal. However, two of the case studies (Kentucky and Offutt) illustrate
that hydraulic optimization can be used to determine the "containment efficiency" of wells placed in the
core zone of a plume. This type of analysis can be performed to compare a "containment only" strategy
to a Strategy With additional nnrp. rnnp \x/f>Ilo f+n o/^,=,l,«-ot,* ^nr,n—~ i\ T,, _«__,. °J
j „—„ VJt/w ^ nuuijroio <^an uc peiiuiiHcu ID Compare a containment only
toa strategy with additional core zone wells (to accelerate mass removal). The "containment
efficiency" of the core zone wells, determined with hydraulic optimization, quantifies potential
pumping
VI
-------
reductions at containment wells when the core zone pumping is added, such that containment is
maintained. These pumping reductions (also difficult or impossible to determine with a trial-and-error
approach) can potentially yield considerable savings, as demonstrated for the Kentucky site.
It is very important to distinguish the benefits of applying hydraulic optimization technology from other
benefits that may be achieved simply by "re-visiting" an existing pump-and-treat design. In some cases,
the underlying benefits associated with a system modification may be primarily due to a modified
conceptual strategy. For instance, the Tooele case study includes analyses for different target
containment zones. The potential pumping reductions and cost savings that result from a change to a
smaller target containment zone primarily result from the change in conceptual strategy. The benefit
provided by hydraulic optimization is that it allows mathematical optimal solutions for each conceptual
strategy to be efficiently calculated and compared (whereas good solutions for each conceptual strategy
may be difficult or impossible to achieve with trial-and-error).
The case studies demonstrate that there are a large variety of objective functions, constraints, and
application strategies potentially available within the context of hydraulic optimization. Therefore, the
development of a "preferred management solution" for a specific site depends not only on the
availability of hydraulic optimization technology, but also on the ability to formulate meaningful
mathematical formulations. That ability is a function of the skill and experience of the individuals
performing the work, as well as the quality of site-specific information available to them.
These case studies demonstrate ways in which hydraulic optimization techniques can be applied to
evaluate pump-and-treat designs. The types of analyses performed for these three sites can be applied to
a wide variety of sites where pump-and-treat systems currently exist or are being considered. However,
the results of any particular hydraulic optimization analysis are highly site-specific, and are difficult to
generalize. For instance, a hydraulic optimization analysis at one site may indicate that the installation
of new wells yields little benefit. That result cannot be generally applied to all sites. Rather, a site-
specific analysis for each site is required. A spreadsheet-based screening analysis (presented in Volume
1 of this report) can be used to quickly determine if significant cost savings are likely to be achieved at a
site by reducing total pumping rate. Those sites are good candidates for a hydraulic optimization
analysis.
VII
-------
-------
TABLE OF CONTENTS (Volume 2 of 2)
PREFACE m
FOREWORD 1V
EXECUTIVE SUMMARY v
TABLE OF CONTENTS (Volume 2 of 2) viii
1.0 INTRODUCTION }"}
1.1 PURPOSE OF PERFORMING HYDRAULIC OPTIMIZATION 1-1
1.2 CASE STUDY EXAMPLES 1-1
1.3 STRUCTURE OF THIS REPORT *"2
2.0 DEFINING "OPTIMIZATION" 24
2.1 TERMINOLOGY (LINEAR AND MIXED-INTEGER PROGRAMMING) 2-1
2.2 SIMULATION-MANAGEMENT MODELING FOR GROUNDWATER SYSTEMS 2-2
2.3 "MATHEMATICAL OPTIMAL SOLUTION" VERSUS "PREFERRED MANAGEMENT SOLUTION" 2-2
2 A DETERMINISTIC HYDRAULIC OPTIMIZATION VERSUS MORE ADVANCED ALTERNATIVES 2-3
2.4.1 Advantages of Deterministic Hydraulic Optimization 2-3
2.4.2 Limitations of Deterministic Hydraulic Optimization 2-4
3.0 APPLICATION STRATEGIES FOR HYDRAULIC OPTIMIZATION 3-1
3.1 CONSTRAINTS 3~j
3.1.1 Constraints Representing Plume Containment 3-1
3.1.2 Constraints Representing Multi-Aquifer Wells 3-3
3.1.3 Constraints Limiting Number of Wells Selected 3-3
3.1.4 Constraints Limiting Head atthe Well 3-4
3.1.5 Other Common Constraints 3'5
3.2 OBJECTIVE FUNCTIONS 3'^
3.2.1 Objective Functions Based Indirectly on Costs (e.g., Minimize Pumping Rate) 3-6
3.2.2 Objective Functions Based Directly on Costs 3-7
3.3 TYPICAL SCENARIOS CONSIDERED WITH HYDRAULIC OPTIMIZATION 3-9
3.3.1 Existing Wells or Additional Wells 3-9
3.3.2 Extraction or Extraction Plus Reinjection • 3-9
3.3.3 "Containment Only" versus Accelerated Mass Removal (Containment Efficiency) .. 3-9
3.3.4 Modifications to the Target Containment Zone 3-10
3.4 ROLE OF THE HYDRAULIC OPTIMIZATION CODE 3-10
4.0 CASE #1: KENTUCKY 4-1
4.1 SITE BACKGROUND 4"j
4'.1.1 Site Location and Hydrogeology 4-1
4.1.2 Plume Definition 4-1
4.1.3 Existing Remediation System 4-1
4.1.4 Groundwater Flow Model 4-2
4.1.5 Goals of a Hydraulic Optimization Analysis 4-2
4.2 COMPONENTS OF MATHEMATICAL FORMULATION 4-3
4.2.1 Representation of Plume Containment 4-3
4.2.2 Representation of Wells 4-3
vm
-------
4.2.3 Objective Function 4.4
4.3 CONTAINMENT SOLUTIONS, ORIGINAL WELLS '',',[ [[' 4.4
4.3.1 Scenario 1: Minimize Pumping at Original 18 BW Wells, Design Rates at SW and OW
Wells 4.4
4.3.2 Scenario 2: Minimize Pumping at Original 18 BW Wells, No Pumping at SW and OW
Wells 4_6
4.4 CONTAINMENT SOLUTIONS, CURRENT WELLS 4.7
4.4.1 Scenario 3: Minimize Pumping at Current 23 BW Wells, No Pumping at SW or OW
Wells 4.7
4.4.2 Scenario 4: Same as Scenario 3, But Varying Limit on Head Adjacent to the River . 4-7
4.5 SCENARIO 5: SOLUTIONS WITH ADDITIONAL CORE ZONE WELLS 4-8
4.6 DISCUSSION & PREFERRED MANAGEMENT SOLUTION 4-9
5.0 CASE #2: TOOELE 5_i
5.1 SITE BACKGROUND 5_l
5.1.1 Site Location and Hydrogeology 5-1
5.1.2 Plume Definition 5_1
5.1.3 Existing Remediation System 5_2
5.1.4 Groundwater Flow Model 5-2
5.1.5 Goals of a Hydraulic Optimization Analysis 5-2
5.2 COMPONENTS OF MATHEMATICAL FORMULATION 5-3
5.2.1 Representation of Plume Containment 5.3
5.2.2 Representation of Wells 5.4
5.2.3 Objective Function Based on Minimizing Total Pumping 5-6
5.2.4 Objective Function Based on Minimizing Total Cost 5-6
5.3 CONTAINING THE 5-PPB TCE PLUME, MINIMIZE TOTAL PUMPING 5-7
5.3.1 Existing Wells (Shallow and Deep Plumes) 5-7
5.3.2 Additional Wells (Shallow and Deep Plumes) 5-7
5.3.3 Quantifying The Benefits of Reinjecting Treated Water 5-8
5.3.4 Additional Wells (Shallow Plume Only) 5-9
5.4 OBJECTIVE FUNCTION BASED DIRECTLY ON COSTS 5-10
5.5 CONTAINING THE 20-PPB AND/OR 50-PPBTCE PLUME 5-10
5.6 DISCUSSION & PREFERRED MANAGEMENT SOLUTION 5-11
6.0 CASE#3: OFFUTT 6-1
6.1 SITE BACKGROUND 6-1
6.1.1 Site Location and Hydrogeology 6-1
6.1.2 Plume Definition 6-1
6.1.3 Existing Remediation System 6-1
6.1.4 Groundwater Flow Model 6-2
6.1.5 Goals of a Hydraulic Optimization Analysis 6-2
6.2 COMPONENTS OF MATHEMATICAL FORMULATION 6-3
6.2.1 Representation of Plume Containment 6-3
6.2.2 Representation of Wells 6-3
6.2.3 Objective Function 6-4
6.3 SOLUTIONS FOR MINIMIZING PUMPING AT THE TOE WELL 6-5
6.3.1 Core Well @ 50 gpm, LF Wells @ 100 gpm (Current Design) '.'.'.'. 6-5
6.3.2 Core Well @ 50 gpm, Vary Rate at LF Wells 6-5
6.3.3 Vary rate at Core Well, LF Wells @ 100 gpm 6-6
6.3.4 Vary rate at Core Well, LF Wells @ 0 gpm 6-7
6.4 CONSIDER NINE ADDITIONAL WELL LOCATIONS AT PLUME TOE 6-7
6.4.1 Solutions for a Single Toe Well 6-7
6.4.2 Solutions for Multiple Toe Wells 6-8
IX
-------
6.5 DISCUSSION & PREFERRED MANAGEMENT SOLUTION 6-9
7.0 DISCUSSION AND CONCLUSIONS : 7-1
8.0 REFERENCES AND DOCUMENTS PROVIDED BY SITES 8-1
List of Figures
Figure 4-1. Site location map, Kentucky.
Figure 4-2. Groundwater elevation contours, Kentucky.
Figure 4-3. EDC concentrations and current remediation wells, Kentucky.
Figure 4-4. Benzene concentrations and current remediation wells, Kentucky.
Figure 4-5. Constraint locations and potential additional wells, Kentucky
Figure 5-1. Site location map, Tooele.
Figure 5-2. Groundwater elevation contours, Tooele.
Figure 5-3. TCE concentrations and current remediation wells, Tooele.
Figure 5-4. Constraint locations and potential additional wells, shallow 5-ppb plume, Tooele.
Figure 5-5. Constraint locations and potential additional wells, deep5-ppb plume, Tooele.
Figure 5-6. Constraint locations and potential additional wells, shallow 20-ppb plume, Tooele.
Figure 5-7. Constraint locations and potential additional wells, 50-ppb plume, Tooele.
Figure 5-8. Shallow particles, layer 1 heads, pumping on April 6,1998 (-7460 gpm, 15 existing wells).
Figure 5-9. Deep particles, layer 2 heads, pumping on April 6,1998 (-7460 gpm, 15 existing wells).
Figure 5-10. Shallow particles, contain shallow and deep 5-ppb plume (4163 gpm, 14 new wells, 3 existing
wells).
Figure 5-11. Deep particles, contain shallow and deep 5-ppb plume (4163 gpm, 14 new wells, 3 existing wells).
Figure 5-12. Shallow particles, contain shallow 5-ppb plume (2622 gpm, 7 new wells, 2 existing wells).
Figure 5-13. Deep particles, contain shallow 5-ppb plume (2622 gpm, 7 new wells, 2 existing wells).
Figure 5-14. Shallow particles, contain shallow 50-ppb plume (1124 gpm, 3 new wells, 0 existing wells).
Figure 5-15. Deep particles, contain shallow 50-ppb plume (1124 gpm, 3 new wells, 0 existing wells).
Figure 5-16. Shallow particles, contain shallow 20-ppb plume (1377 gpm, 2 new wells, 1 existing well).
Figure 5-17. Deep particles, contain shallow 20-ppb plume (1377 gpm, 2 new wells, 1 existing well).
Figure 5-18. Shallow particles, contain shallow 20-ppb plume & 500 gpm for deep 20-ppb plume (1573 gpm, 3
new wells, 1 existing well).
Figure 5-19. Deep particles, contain shallow 20-ppb plume & 500 gpm for deep 20-ppb plume (1573 gpm, 3
new wells, 1 existing well).
Figure 5-20. Shallow particles, contain shallow 20-ppb plume & 50-ppb plume & 500 gpm for deep 20-ppb
plume (2620 gpm, 6 new wells, 0 existing wells).
Figure 5-21. Deep particles, contain shallow 20-ppb plume & 50-ppb plume & 500 gpm for deep 20-ppb
plume (2620 gpm, 6 new wells, 0 existing wells).
Figure 6-1. Site location map, Offutt.
Figure 6-2. Groundwater elevation contours, Offutt.
Figure 6-3. Southern plume and current remediation wells, Offutt.
Figure 6-4. Constraint locations and potential additional wells, Offutt.
Figure 6-5. Solutions for multiple toe wells, Offutt.
List of Tables
Table 4-1. Current system, Kentucky.
Table 4-2. Summary of design well rates and maximum observed well rates (6/97 to 11/97), Kentucky.
Table 5-1. Current system, Tooele.
Table 5-2. Example calculation for "Total Managed Cost", Tooele.
Table 6-1. Current system, Offutt: one new core well, 100 gpm at LF wells.
X
-------
Appendices
Appendix A: Overview of MODMAN
Appendix B: Overview of Simulation-Management Methods incorporating Transport Simulations
Appendix C: Overview of Simulation-Management Methods incorporating Uncertainty and/or Risk
Appendix D: Partial Listing of MODMAN Applications
Appendix E: Sample MODMAN Input: Kentucky
Appendix F: Sample MODMAN Input: Tooele
Appendix G: Sample MODMAN Input: Offutt
Appendix H: Efficiently Making Modifications to MODMAN Formulations
Appendix I: References for Other Optimization Research and Application
XI
-------
1.0 INTRODUCTION
This report (Volume 2 of 2) demonstrates the application of hydraulic optimization for improving the
design of pump-and-treat systems. "Hydraulic Optimization" refers to the use of mathematical
optimization techniques (linear or mixed-integer programming), linked with a groundwater flow model,
to determine the best set of well locations and well rates for a pump-and-treat design. The goal of this
demonstration is to highlight strategies for applying hydraulic optimization techniques. The work
presented herein was commissioned by the U.S. EPA Subsurface Protection and Remediation Division
(SPRD) and the U.S. EPA Technology Innovation Office (TIO).
l.l PURPOSE OF PERFORMING HYDRAULIC OPTIMIZATION
Numerical simulation models for groundwater flow, such as MODFLOW-96 (Harbaugh and McDonald,
1996a,b), are often used to evaluate potential pump-and-treat system designs. The groundwater model is
executed repeatedly to simulate different pumping scenarios. Specific scenarios (i.e., the well locations
and well rates) are usually defined with a. "trial-and-error" approach, guided by professional insight. The
simulation results for each scenario are evaluated with respect to objectives and constraints of the
specific problem (e.g., Does the design contain the plume? Are drawdowns acceptable? What is the total
pumping rate? How many new wells are required?).
One disadvantage of the "trial-and-error" flow modeling approach is that problem-specific objectives and
constraints are often not clearly stated. This makes selection of the "best" strategy somewhat nebulous.
Perhaps more significantly, the "trial-and-error" approach does not ensure that optimal management
alternatives are even considered. This is because the potential combinations of well locations and well
rates is infinite, whereas only a small number of numerical simulations is practical.
Hydraulic optimization is an attractive alternative to the "trial-and-error" flow modeling approach.
Hydraulic optimization yields answers to the following groundwater management questions: (1) where
should pumping and injection wells be located, and (2) at what rate should water be extracted or injected
at each well? The optimal solution maximizes or minimizes a formally-stated objective function, and
satisfies a formally-stated set of constraints. For example, the objective function may be to minimize the
total pumping rate from all wells, and constraints might consist of limits on heads, drawdowns, gradients,
and pumping rates at individual wells.
Unlike the "trial-and-error" approach, the use of hydraulic optimization requires a formal statement of a
site-specific objective function, and a site-specific set of constraints. This clarifies the evaluation of
different scenarios, to determine which is "best". More significantly, hydraulic optimization allows all
potential combinations of well rates and all potential well locations to be rigorously evaluated, rather
than the small number of scenarios that can be considered with "trial-and-error".
1.2 CASE STUDY EXAMPLES
Three sites with existing pump-and-treat systems were evaluated in this study:
•Chemical Facility, Kentucky (hereafter called "Kentucky");
Tooele Army Depot, Tooele, Utah (hereafter called "Tooele"); and
Offutt Air Force Base, Bellevue, Nebraska (hereafter called "Offutt").
1-1
-------
A brief comparison of the three sites is provided below:
Pumping rate, current system (gpm)
Annual Operations & Maintenance (O&M)
Type of treatment
Discharge of treated water
Most significant annual cost
Year system started
Cost of a new well
Flow model exists?
Transport model exists?
Kentucky
600
$1,800,000(1)
Steam Stripping
River
Steam
1992
$20,000
Yes
No
Tooele
7500
$1,800,000
Air Stripping
Reinjection
Electricity
1993
$300,000
Yes
Being Developed
200
$122,000
POTW(2)
N/A
Discharge Fee
1996(3)
$40,000
Yes
Yes
(2) Water is treated at a Publicly Owned Treatment Works.
(3) An interim system has operated since 1996, and a long-term system has been designed.
Three sites were included in this study to demonstrate different strategies for applying hydraulic
optimization that result from site-specific factors.
1.3 STRUCTURE OF Tffls REPORT
This report is structured as follows:
Section 2: Defining "Optimization"
Section 3: Application Strategies For Hydraulic Optimization
Section 4: Case #1: Kentucky
Section 5: Case #2: Tooele
Section 6: Case #3: Offutt
• Section 7: Discussion and Conclusions
Section 8: References
The MODMAN code (Greenwald, 1998a), in conjunction with the LINDO software (Lindo Systems,
1996), was utilized for the hydraulic optimization simulations. MODMAN incorporates MODFLOW-96
(Harbaugh and McDonald, 1996a,b) as the groundwater flow simulator. LINDO solves mathematical
optimization problems that are created by MODMAN, in the form of linear and mixed-integer programs.
The linear and mixed-integer programs are written by MODMAN in Mathematical Programming
System (MPS) format. A description of the MODMAN code is provided in Appendix A.
1-2
-------
2.0 DEFINING "OPTIMIZATION"
2.1 TERMINOLOGY (LINEAR AND MIXED-INTEGER PROGRAMMING)
The word "optimal", according to Webster's New World Dictionary, means "most favorable or
desirable; best". Mathematical techniques have been developed to determine optimal solutions for a
wide variety of mathematical problems. For instance, consider the following mathematical problem,
which is in the form of a linear program:
{Objective Function}
{Constraints}
Maximize 3x + 5y
Subject to:
x ^4
2y < 12
3x + 2y < 18
x ^ 0
y > 0
The decision variables are the variables for which optimal values are desired. A feasible solution is a
combination of values for the decision variables that satisfies all constraints. If there are no feasible
solutions, the problem is called infeasible. A feasible solution that maximizes the objective function is
called an optimal solution. The optimal solution for this problem is "x = 2, y = 6", which yields an
optimal value of 36 for the objective function. It can be mathematically demonstrated that this is the
most favorable (i.e., optimal) solution.
A mixed-integer program is similar to a linear program, but some variables may only take integer
values (integer variables). Integer variables that are restricted to values of 0 or 1 are called binary
variables. Binary variables are often used for logical or yes/no decisions.
A quadratic program is similar to a linear program, except that the objective function may be a
nonlinear combination of the decision variables. Examples of nonlinear combinations of decision
variables are:
2X + Y2
X4 - 6Y3
X + 4XY
A nonlinear program exists when one or more constraints is a nonlinear combination of decision
variables. In a nonlinear program, the objective function may be a linear or nonlinear combination of
decision variables.
In general, linear programs are relatively easy to solve, quadratic programs are harder to solve, and
nonlinear programs are difficult and sometimes impossible to solve. Mixed-integer programs can be
2-1
-------
relatively simple to solve, but can also be extremely difficult to solve. As a rule, mixed-integer programs
become increasingly difficult to solve as the number of integer variables increases.
2.2 SIMULATION-MANAGEMENT MODELING FOR GROUND WATER SYSTEMS
There is a significant body of literature devoted to the coupling of groundwater simulation models with
the mathematical optimization techniques described above, for the purpose of designing groundwater
pump-and-treat systems. These coupled models are referred to as "simulation-management models"
The goal is to determine a set of well locations and well rates that minimizes or maximizes an objective
function (e.g., "minimize total pumping rate"), while satisfying all pertinent constraints (e.g., "the plume
may not grow in size"). To utilize these simulation-management models, the user must formulate a
mathematical problem to solve. The mathematical formulation includes a specific objective function and
a specific set of constraints. The objective function and/or constraints are related to the well rates
through the groundwater simulation model.
Different "optimal solutions" will result if the mathematical formulation is modified (Gorelick et al
1993, page 136). Modifications might include alterations to the objective function, the constraint set or
the underlying simulation model. For example, one formulation may include only existing wells another
formulation may include existing wells plus new wells, and a third formulation may include existing
wells plus a barrier wall. Those authors suggest that "the best use of [simulation-management modeling]
is to develop a family of so-called 'optimal solutions' under a broad and varied menu of design
considerations".
2.3 "MATHEMATICAL OPTIMAL SOLUTION" VERSUS "PREFERRED MANAGEMENT SOLUTION"
The term "optimization" can be vague when applied to pump-and-treat designs. In one sense
"optimization" refers to the use of mathematical solution techniques to determine the best solution for a
specific mathematical formulation. In another sense, "optimization" refers to the process of arriving at a
preferred or improved management strategy, which may be based on multiple "optimal solutions" for
different mathematical formulations, as well as on factors that may not have been explicitly incorporated
in mathematical solutions due to mathematical complexity (e.g., cleanup timeframe, discount rate).
For this document, the term "optimization" for pump-and-treat design was refined as follows:
Mathematical Optimal Solution. The best solution, determined with a mathematical
optimization technique, for a specific mathematical formulation (defined by a specific objective
function and set of constraints).
Preferred Management Solution. A preferred management strategy based on a discrete set of
mathematical optimal solutions, as well as on factors (e.g., costs, risks, uncertainties,
impediments to change) not explicitly considered in those mathematical solutions.
For each case study in this report, many mathematical formulations were developed, and many
mathematical optimal solutions were determined. For each site, a preferred management solution was
then suggested.
2-2
-------
2.4 DETERMINISTIC HYDRAULIC OPTIMIZATION VERSUS MORE ADVANCED ALTERNATIVES
This demonstration project utilizes deterministic hydraulic optimization, which is a relatively simple and
easy-to-apply simulation-management method for the following reasons:
Flow-Based Constraints. Limits on management alternatives are based on groundwater
flow conditions (e.g., heads, drawdowns, gradients), such that a transport simulation
model is not required, and linear or mixed-integer programming algorithms can be
employed (techniques incorporating contaminant concentrations and/or cleanup times as
constraints require nonlinear programming techniques, as discussed in Appendix B); and
Deterministic Simulations. Simulations of groundwater flow are based on one discrete
set of initial conditions, boundary conditions, and parameter values (techniques
incorporating uncertainty and/or risk are discussed in Appendix C).
The use of deterministic hydraulic optimization has advantages and limitations. These are discussed
below.
2.4.1 Advantages of Deterministic Hydraulic Optimization
Advantages of deterministic hydraulic optimization include the following:
for most sites with groundwater contamination, a deterministic flow model exists or can
be easily created at relatively low cost;
many practitioners of groundwater modeling understand the application of groundwater
flow modeling, but have limited understanding or ability to apply transport modeling or
uncertainty (e.g., stochastic) modeling;
the construction of a groundwater transport model requires significantly more input than
a groundwater flow model (e.g., initial concentrations, dispersivity, retardation/sorption,
decay, porosity);
predictions of groundwater flow are subject to less uncertainty than predictions of
contaminant concentrations and/or cleanup time (which form the basis of transport
optimization);
computational effort for transport models and/or stochastic simulations can be
significantly greater than for groundwater flow models;
tools for performing deterministic hydraulic optimization (e.g., MODMAN) are
available as "off-the-shelf technology;
solution of linear and/or mixed-integer programs associated with hydraulic optimization
is straightforward and easily achieved with inexpensive "off-the-shelf technology;
2-3
-------
* computational effort for solutions of nonlinear programs (e.g., transport optimization) is
significantly greater than for linear or mixed-integer programs.
i
For these reasons, real-world applications of hydraulic optimization have been performed for many
years. Appendix D provides a partial listing of MODMAN applications. Appendix I includes discussion
and/or references for real-world applications with other simulation-management codes, some of which
pertain to hydraulic optimization.
2.4.2 Limitations of Deterministic Hydraulic Optimization
The limitations of deterministic hydraulic optimization must be considered when evaluating the potential
application of simulation-management modeling for a specific site. Major limitations include:
contaminant concentrations cannot be included in the mathematical formulation;
• cleanup time cannot be rigorously included in the mathematical formulation;
• for thin unconfined aquifers (and several other circumstances), linear superposition
(which allows the use of linear programming techniques) may be violated; and
• since a deterministic modeling approach is used, uncertainty in model parameters cannot
be directly incorporated into the mathematical formulation (e.g., one cannot specify that
"the constraint must be met with 95% certainty, given anticipated variation in hydraulic
conductivity").
Because contaminant concentrations and cleanup times cannot be included in the mathematical
formulation, hydraulic optimization is generally most applicable to problems where hydraulic
containment of a groundwater plume is the primary goal. However, hydraulic optimization can be
utilized to evaluate some tradeoffs between containment strategies and more aggressive pumping
strategies (discussed later).
For sites where cleanup is the main objective, and predictions of contaminant concentrations or cleanup
time are central to evaluation of the objective function and/or key constraints, the limitations of hydraulic
optimization may be prohibitive. Transport modeling and transport optimization may be applied in such
cases (see Appendix B). However, developing a transport simulation model and performing a transport-
based optimization analysis may require significantly effort and cost, and transport model predictions are
subject to additional uncertainties (relative to flow model predictions).
It is important to note that any simulation-management technique is limited by the predictive ability of
the underlying simulation model, which is not only affected by uncertainty in parameter values, but also
by available data, the conceptual hydrogeological model of the site, the experience of the modeler, input
errors, and many other factors.
2-4
-------
3.0 APPLICATION STRATEGIES FOR HYDRAULIC OPTIMIZATION
The use of hydraulic optimization for plume management requires the specification of a mathematical
formulation, consisting of an objective function and a series of constraints. Various constraint types are
presented in Section 3.1, and various objective functions are presented in Section 3.2.
Alternative pump-and-treat strategies for a specific site can be evaluated with hydraulic optimization by
defining and solving multiple mathematical formulations (e.g., considering only existing wells in one
formulation, and then considering additional well locations in another formulation). Section 3.3 presents
typical variations that are considered by varying the mathematical formulation at a specific site.
3.1 CONSTRAINTS
3.1.1 Constraints Representing Plume Containment
One technique utilized in plume management problems uses a line of head difference, gradient, or
velocity constraints to represent a flow divide. Such a strategy might be used in a case where a plume
flows towards a river. The constraints would mandate that any feasible solution include a hydraulic
divide between the plume and the river. A similar scenario might involve a plume and one or more water
supply wells, where a flow divide between the plume and the water supply wells prevents contamination
of the water supply. An approach of this type, that uses velocity constraints to impose a groundwater
flow divide, is described by Colarullo et al. (1984). Vertical flow can also be restricted with head
difference constraints, to prevent fouling of aquifers above and/or below a contaminated aquifer.
A second useful technique is to apply head difference, gradient, or velocity constraints to create inward
flow perpendicular to a plume boundary. If desired, lower limits other than zero can be imposed, to
increase assurance that the plume will in fact be contained. This type of technique is described by
Gorelick and Wagner (1986). A variation of this technique, utilizing velocity constraints, was described
by Lefkoff and Gorelick (1986). In that project, target boundaries of a shrinking plume were set for four
1-year periods. The velocity constraints insured that these target boundaries were met.
Another technique allows flow directions to be constrained, using relative gradient constraints. This
approach is illustrated by Greenwald (1998a), and is also described by Gorelick (1987). These
constraints limit the direction of flow according to the resultant of two gradients, oriented 90° apart, that
share the same initial location. The concept is illustrated in the schematic presented below. There are
two gradient constraints, A and B. The shared point is the initial point in each gradient constraint.
The user typically desires the actual flow direction, defined by 0, to be greater than some limiting flow
direction (defined by angle B in the schematic). The constraint is derived as follows:
0 ^P
tan@ ^ tan.p
GRAD(A) / GRAD(B) = tan0
GRAD(A) / GRAD(B) ;> tanp
GRAD(A) - tanp* GRAD(B) £ 0
[by trigonometry]
[substitute for tan©]
[rearrange terms as a linear constraint]
3-1
-------
Conceptualization of a relative gradient constraint.
0 =RESULTANT OPTIMAL FLOW DIRECTION
/? =LIMITING FLOW DIRECTION
Conceptualization of a relative gradient constraint.
3-2
-------
3.1.2 Constraints Representing Multi-Aquifer Wells
Multi-aquifer wells in MODFLOW are wells that are screened in more than one model layer.
Specification of these wells in MODFLOW presents a problem, because MODFLOW allows a well to be
specified only in one layer. The technique most widely used is to represent a multi-aquifer well with
multiple wells in MODFLOW, with the rate at each MODFLOW well weighted by transmissivity in each
model layer.
Example:
well pumps 100 gpm, and is screened in model layers 1 and 2
transmissivity of layer 1:
transmissivity of layer 2:
apportionment layer 1:
apportionment layer 2:
well rate layer 1 (Ql):
well rate layer 2 (Q2):
2500 ftVd
7500 ffVd
2500 / (2500 + 7500) = 25%
7500 / (2500 + 7500) = 75%
100 gpm * 25% = 25 gpm
100 gpm * 75% = 75 gpm
When performing hydraulic optimization, the ratio of well rates between layers can be preserved with
properly constructed constraints. For the example above, the following constraint is derived:
Q2/Q1=3.00
Q2-3.00Q1=0.00
This constraint is a linear function of the decision variables. If pumping occurs at one of the wells, it
must also occur at the other well, at the proper ratio. The total rate at the well can be limited by placing a
bound on either of the component wells, or on the sum of the component wells. For instance, assume the
maximum rate to be allowed at the well is 200 gpm. Any of the following constraints will enforce this
limit:
Ql < 50 gpm
- or-
Q2 < 150 gpm
- or-
Ql + Q2 < 200 gpm
This approach is easily extended to multi-aquifer wells screened across more than two layers.
3.1.3 Constraints Limiting Number of Wells Selected
This type of constraint is sometimes desirable when considering a large number of potential well
locations for siting a small number of wells. For instance, assume the objective is to minimize the total
extraction rate, subject to plume containment constraints. Suppose that only 2 wells are desired due to
installation costs and piping construction required, but 9 sites are being considered. If an "x out of y"
constraint is not included, the optimal solution may be to pump at a small rate at all 9 wells, which is not
a desirable solution.
3-3
-------
Constraints limiting the number of wells selected can be implemented with two types of constraints:
• well on/off constraints; and
• integer variable summation constraints.
The on/off constraints are constructed with binary variables, which are integer variables that can only
have a value of 0 or 1. The on/off constraint for a well forces the binary variable to a value of 1 if the
well is on. The form of the on/off constraint is :
where:
EXTRACTION
(Negative Well Rate)
0, + M*!, £0
INJECTION
(Positive Well Rate)
£ 0
Qj = rate at well j (negative for pumping);
M = a large number with an absolute value greater than that of the largest well rate; and
Ij = a binary variable acting as on/off switch for well j .
If Q has a non-zero value, the on/off constraint will only be satisfied if the binary variable is 1.
The integer variable summation constraint, based on the binary variables, enforces the limit on the
number of active wells allowed. For example, if there are nine potential well locations, but only two
may be selected, the integer summation constraint would be:
This technique is describe in more detail in Greenwald (1998a).
3.1.4 Constraints Limiting Head at the Well
Groundwater flow models based on finite differences (e.g., MODFLOW) typically calculate head for a
representative volume (i.e., an entire grid block). In some cases, it is important to constrain head at the
actual location of the well, as opposed to a representative head for larger grid block. For instance, there
may be a legal restriction on allowable drawdown, or there may be a physical constraint associated with
too much drawdown such as drawing water below a pump. Some hydraulic optimization codes (e.g.,
MODMAN) allow head limits to be imposed at a well and/or an entire grid block. The calculations to
approximate head at the well are based on the Thiem equation, and are explained in detail on pages 9 to
10 of the USGS Finite-Difference Model for Aquifer Simulation in Two Dimensions (Trescott et al.,
1976). It is important to recognize that the calculation of head in a well is based on many assumptions,
such as:
• the grid block is square;
• all pumping is at one fully penetrating well, located in the center of the grid block;
• flow can be described by a steady-state equation with no source term except for the well
discharge;
3-4
-------
• the aquifer is homogeneous and isotropic within the grid block containing the well; and
• well losses are negligible.
Many of these assumptions are typically not met. As a result, heads calculated at wells should be viewed
as a more accurate approximation of head at the well, but still an estimate nevertheless.
3.1.5 Other Common Constraints
Many other types of constraints can be represented within a hydraulic optimization formulation. These
include:
• limits on head in specific grid cells;
• limits on drawdown at specific grid cells;
• limits on well rate at specific wells;
• limits on total well rates at combinations of wells; and
• limits on the difference between total pumping and total injection.
A description of constraint types that can be formed as linear functions of the well rates is presented in
the MODMAN documentation (Greenwald, 1998a).
3.2
OBJECTIVE FUNCTIONS
Optimization implies that different solutions are compared to each other, and that a determination can be
made as to which solution is best. This comparison can be made by computing the value of an objective
function based on values of the decision variables for each solution (pumping/injection rates). The
optimal solution is one that minimizes (or maximizes) the objective function.
A general linear objective function for a steady-state plume management problem is:
Min S C;Q. + dl
i=l,n lX:i l l
where:
n = total number of pumping and/or injection wells
Qi = pumping or injection rate at well i ,
I; = 1 if well i is active, 0 if well i is not active
c; = coefficient for well i multiplied by pumping/injection rate at well i
dj = addition to objective function if well i is active (pumping or injection)
The values for coefficients (c; and d;) will depend on site-specifics factors related to the cost of pumping
water, treating water; discharging water, installing new wells, and other factors. The general form of the
objective function is easily extended to transient cases (i.e., multiple stress periods, where pumping rates
are potentially altered each stress period). .......
3-5
-------
In many cases the objective function can be simplified, with many of the coefficients assigned values of
0 or 1. An example of a simplified objective functions is:
Min
(e.g., minimize the total pumping rate)
The applicability of different forms of the objective function for specific types of sites is discussed
below. Examples are provided to illustrate how different types of objective functions can be applied.
3.2.1 Objective Functions Based Indirectly on Costs (e.g., Minimize Pumping Rate)
The true objective of plume management is generally to minimize costs, subject to all constraints
associated with maintaining containment and/or providing satisfactory cleanup. However, developing
cost functions that rigorously account for all costs associated with pumping, treatment, and discharge can
be difficult. Fortunately, many problems can be evaluated with simple objective functions that are only
indirectly based on cost. Examples include:
Min
Min
to Si;
1=1,n 1
(e.g., minimize the total pumping rate)
(e.g., minimize the number of active wells or new wells)
In these cases, the units of the objective function are not units of cost, although it is assumed that the
optimal solution will in fact minimize the total cost.
Minimizing the total pumping rate is appropriate when the cost of pumping, treating, or discharging the
water is rate-sensitive and is the dominant cost factor. Minimizing the number of active wells is
appropriate if the number of pumps (e.g., electrical demand from pumping water) is the dominant cost
factor. Minimizing the number of new wells is appropriate if the capital cost of installing a new well is
the dominant cost factor.
Despite the fact that these objectives do not rigorously consider cost, they can also be used, in
conjunction with appropriate constraints, to evaluate problems where some wells are qualitatively
preferred to others. For example, assume an existing system has four extraction wells, and the treatment
cost is sensitive to total rate (i.e., minimizing total rate is the simplified objective). At the same time, it
may be qualitatively preferable to pump from wells 1 and 2 (located near the source) than from wells 3
and 4 (located near the toe of the plume). This may occur because wells 1 and 2 remove more mass, or
because it costs less to pump at wells 1 and 2 due to depth to water and/or topographic lift back to the
treatment plant.. Assume this problem is initially evaluated with the following objective function:
Min Qj + Q2 + Q3 + Q4 [minimize total pumping]
3-6
-------
and that the following optimal solution is determined (total pumping rate = 700 gpm) :
Q, = 50 gpm
Q2 = 30 gpm
Q3 = 250 gpm
Q4 = 370 gpm
The tradeoff between increased total pumping rate versus additional pumping at the preferred wells can
then be evaluated with the same objective function, by adding a constraint:
Q! + Q2 > 100 gpm
The resulting optimal solution can then be compared to the original optimal solution. This process can
be repeated with different limits assigned in the new constraint:
Constraint
Q, + Q2 = 80 gpm
Q, + Q2 ^ 100 gpm
Q, + Q2 ;> 200 gpm
Q, + Q2 ;> 300 gpm
Q, + Q, ;> 400 gpm
Optimal Solution
(Total Rate)
700 gpm
705 gpm
720 gpm
850 gpm
980 gpm
Comments
Original problem
Shift 20 gpm to preferred wells, total rate increases 5 gpm
Shift 120 gpm to preferred wells, total rate increases 20 gpm
Shift 220 gpm to preferred wells, total rate increases 150 gpm
Shift 320 gpm to preferred wells, total rate increases 280 gpm
Although the objective function for all of these problems ("minimize total pumping rate") does not
directly account for cost, the tradeoff between increased total pumping rate versus the benefits of
increased pumping at the preferred wells can now be analyzed qualitatively. In the example above, 120
gpm can be shifted to the preferred wells with only a small increase (20 gpm) in total pumping rate,
which qualitatively appears favorable. The increased costs of treating an additional 20 gpm can
presumably then be estimated (external to the optimization problem that is actually solved) if a more
detailed cost/benefit analysis is desired.
3.2.2 Objective Functions Based Directly on Costs
Direct consideration of costs in the objective function allows costs to be more quantitatively evaluated in
the determination of the optimal solution. The objective function can be specified directly in units of
cost as follows:
Min E CA + d.
.
where:
j = approximate cost per unit pumping rate at well i
; = additional cost incurred if well i is active (e.g., well installation cost)
3-7-
-------
Because actual cost functions are quite complex, simplifications are typically required to assign the
coefficients (c; and dj). An example is provided below.
Assume a system has 4 existing extraction wells (wells 1 through 4), and that treatment consists of
metals precipitation, Ultraviolet (UV) oxidation, and GAC in series, followed by discharge to POTW
(reinjection is not an option). Current total rate is 400 gpm. The current cost of treating water and
discharging water is $200K/yr. Electrical cost is $10K/yr and monitoring cost is $100K/yr, but neither of
these costs is sensitive to pumping rate. The goal is to contain the plume within the property boundary.
Up to three new wells are to be considered (wells 5 through 7), but installation of a new well and
associated piping will cost approximately $50K per well.
The development of a simple cost function in terms of pumping rates is complicated for this problem,
because the cost of treating and discharging water is an annual cost, while the cost of installing a new
well is a one-time cost. This can be resolved several different ways:
(1) annualize the one-time cost of installing a well over a specific planning horizon (e.g., if a
new well costs $50K to install, approximate it's cost as $10K/yr over a 5 year planning
horizon), so the units of the objective function are "costs per year over a 5 year planning
horizon";
-or-
(2) multiply the annual costs of pumping and treating water by a specified time horizon
(e.g., 5 years) so the units of the objective function are "total cost over 5 year period".
Using the first approach as an example, a simplified objective function (based on cost) for the stated
problem is:
Min 500Q! + 500Q2 + 500Q3 + 500Q4 + 500Q5 + 500Q6 + 500Q7
+ 1OOOOI5 + 1OOOOI6 + 1OOOOI7
where:
500 = approximate cost (in dollars/yr) to treat/discharge 1 gpm of water
10000 = approximate cost (in dollars/yr) to install a new well (annualized for 5 yrs)
Qi = pumping rate at well i (in gpm)
Ij = 1 if new well i is installed (i.e., active)
This objective function minimizes annual cost, over a 5-year period. Up-front and annual costs are
simultaneously considered and rigorously evaluated within the optimization process. Of course, this cost
function includes simplifications, such as the simple annualization of the one-time costs over a five-year
period. However, it still provides a reasonable cost-based framework for comparing alternate strategies
(in this case, the tradeoff between potential pumpage reductions from a new well versus the costs of
installing that well).
Using the second approach, a simplified objective function (based on cost) for the stated problem is:
3-8
-------
2500Q! + 2500Q2 + 2500Q3 + 2500Q4 + 2500Q5 + 2500Q6
+ 2500Q7 + 50000I5 + 50000I6 + 50000I7
where:
2500 = approximate cost (in dollars) to treat/discharge 1 gpm of water for 5 yrs
50000 = approximate cost (in dollars) to install a new well
Qi = pumping rate at well i (in gpm)
I; = 1 if new well i is installed (i.e., active)
This objective function minimizes total cost over a 5-year period. Up-front and annual costs are
simultaneously considered and rigorously evaluated within the optimization process.
3.3
TYPICAL SCENARIOS CONSIDERED WITH HYDRAULIC OPTIMIZATION
3.3.1 Existing Wells or Additional Wells
First, an optimal solution can be obtained with existing wells only. Then optimization can be performed
with one or more new well locations considered. With some optimization packages (e.g., MODMAN), it
is possible to consider many different potential locations for new wells, but to only select a specified
number of those locations in the optimal solution. The costs and benefits of adding the new wells can
then be evaluated.
3.3.2 Extraction or Extraction Plus Reinjection
Pumpage optimization can be performed for cases with and without reinjection of treated water. The
costs and benefits of reinjecting water can then be evaluated.
3.3.3 "Containment Only" versus Accelerated Mass Removal (Containment Efficiency)
For sites where containment is the remediation objective, application of hydraulic optimization is
straightforward. At some sites, however, strategies that incorporate accelerated mass removal are also
considered. As previously discussed, hydraulic optimization is based on groundwater flow, and does not
rigorously account for contaminant concentrations, mass removal, or cleanup time. However, hydraulic
optimization can be used to quantify the "containment efficiency" of wells intended for accelerated mass
removal. This allows the costs and benefits of additional wells intended for accelerated mass removal to
be more rigorously evaluated.
For example, assume hydraulic optimization indicates that three wells located near the toe of a plume,
pumping a total of 500 gpm, will provide containment. However, site managers want to consider several
additional wells near the core of the plume (where concentrations are higher), pumping at 200 gpm, to
accelerate mass removal. Should the resulting strategy consist of 700 gpm? The answer is usually "no",
because pumping in the core of the plume may also contribute to overall plume containment, such that
the addition of core-zone pumping may permit total pumping near the toe of the plume to be reduced
without compromising plume containment.
3-9
-------
Hydraulic optimization can be used to quantify that relationship. This can be expressed as "containment
efficiency" of the core zone pumping, as follows:
containment efficiency = (Potential reduction in toe pumping) / (increase in core pumping)
Assume in the previous example that hydraulic optimization is used to determine that, after 200 gpm is
implemented in the core zone, total pumping at the toe wells can be reduced from 500 gpm to 380 gpm
without compromising containment. Adding 200 gpm in the core zone permits pumping at the toe wells
to potentially be reduced by 120 gpm (500 gpm - 380 gpm). The "containment efficiency" of the core
zone pumping is:
containment efficiency = 120/200 = 60%
Therefore, if this analysis is performed, increased costs associated with the core zone pumping (well
installation and/or treatment costs) can be partially offset by implementing a corresponding pumping rate
reduction at the toe wells.
3.3.4 Modifications to the Target Containment Zone
Hydraulic optimization can be performed for alternate definitions of the target containment zone. This
can provide information regarding the potential reduction in total pumping and/or cost that can result if a
smaller region of water must be contained.
3.4 ROLE OF THE HYDRAULIC OPTIMIZATION CODE
The role of the hydraulic optimization code is to provide mathematical optimal solutions for specific
mathematical formulations. Given the large variety of objective functions, constraints, and application
strategies potentially available, it is clear that the development of a "preferred management solution" for
a specific site depends not only on the availability of hydraulic optimization technology, but also on the
ability of individuals to formulate meaningful mathematical formulations. That ability is a function of
the skill and experience of the individuals performing the work, as well as the quality of site-specific
information available to them.
3-10
-------
4.0 CASE #1: KENTUCKY
4.1
SITE BACKGROUND
4.1.1 Site Location and Hydrogeology
The facility is located in Kentucky, along the southern bank of a river (see Figure 4-1). There are in
excess of 200 monitoring points and/or piezometers at the site. The aquifer of concern is the uppermost
aquifer, called the Alluvial Aquifer. It is comprised of unconsolidated sand, gravel, and clay. The
Alluvial Aquifer has a saturated thickness of nearly 100 feet in the southern portion of the site, and a
saturated thickness of approximately 30 to 50 feet on the floodplain adjacent to the river. The decrease
in saturated thickness is due to a general rise in bedrock elevation (the base of the aquifer) and a decrease
in surface elevation near the floodplain. The hydraulic conductivity of the Alluvial Aquifer ranges from
approximately 4 to 75 ft/d.
Groundwater generally flows towards the river, where it is discharged (see Figure 4-2). However, a
groundwater divide has historically been observed between the site and other nearby wellfields (locations
of wellfields are illustrated on Figure 4-1). The groundwater divide is presumably caused by pumping at
the nearby wellfields.
4.1.2 Plume Definition
Groundwater monitoring indicates site-wide groundwater contamination. Two of the most common
contaminants, 1,2-dichloroethane (EDC) and benzene, are used as indicator parameters because they are
found at high concentrations relative to other parameters, and are associated with identifiable site
operations. Shallow plumes of EDC and benzene are presented in Figures 4-3 and 4-4, respectively.
Concentrations are very high, and the presence of residual NAPL contamination in the soil column is
likely (SVE systems have recently been installed to help remediate suspected source areas in the soil
column).
4.1.3 Existing Remediation System
A pump-and-treat system has been operating since 1992. Pumping well locations are illustrated on
Figures 4-3 and 4-4. There are three groups of wells:
BW wells:
SW wells:
OW wells:
River Barrier Wells
Source Wells
Off-site Wells
The primary goal is containment at the BW wells, to prevent discharge of contaminated groundwater to
the river. The purpose of the SW wells is to accelerate mass removal. The purpose of the OW wells is to
prevent off-site migration of contaminants towards other wellfields. A summary of pumping rates is as
follows:
4-1
-------
BW wells:
Original Design
Current System
SW wells
OW wells
Total System:
Original Design
Current System
Number of Wells
18
23
8
8
34
39
Design Rate (gpm)
549
N/A
171
132
852
N/A
Typical Rate (gpm)
N/A
420-580
80-160
25-100
N/A
500-800
Five BW wells were added after the initial system was implemented, to enhance capture where
monitored water levels indicated the potential for gaps. The operating extraction rates are modified as the
river level rises and falls (when the river level falls, aquifer water levels also fall, and transmissivity at
some wells is significantly reduced). The eight OW wells controlling off-site plume migration have
largely remediated that problem, and will likely be phased out in the near future.
Contaminants are removed by steam stripping. The steam is purchased from operations at the site.
Treated water is discharged to the river. Approximate costs of the current system are presented in Table
4-1 (see Volume 1 for a more detailed discussion of costs).
Site managers have indicated their desire for accelerated mass removal, if it is not too costly. They do
not favor significant reductions in pumping (and associated annual costs) if that will result in longer
cleanup times.
4.1.4 Groundwater Flow Model
An existing 2-dimensional, steady-state MODFLOW (McDonald and Harbaugh, 1988) model is a simple
representation of the system. There are 48 rows and 82 columns. Grid spacing near the river is 100 ft.
The model has historically been used as a design tool, to simulate drawdowns and capture zones (via
particle tracking) resulting from specified pumping rates.
4.1.5 Goals of a Hydraulic Optimization Analysis
A screening analysis performed for this site (see Volume 1) suggests that significant savings (millions of
dollars over 20 years) might be achieved by reducing the pumping rate associated with the present
system, even if five new wells (at $20K/well) were added. In that screening analysis, a pumping rate
reduction of 33 percent was assumed. This could potentially be accomplished by:
!
• a reduction in rates at the BW wells required to maintain containment (via optimization);
• a reduction in pumping at the OW wells; and/or
• a reduction in pumping at the SW wells.
The goals of the optimization analysis are:
4-2
-------
(1) quantify potential pumping rate reductions at the BW wells, without compromising
containment at the river (with the SW and OW wells operating as designed);
(2) quantify the tradeoff between the number of BW wells operating and the total pumping
rate required for containment;
(3) quantify the total pumping required for containment if only the BW wells are operated
(i.e., no pumping at the existing SW or OW wells);
(4) quantify the increase (or decrease) in pumping required for containment if more (or less)
conservative constraints for containment are imposed at the river;
(5) quantify the degree to which pumping at additional core zone wells might be offset by
pumping reductions at barrier wells, while maintaining containment.
Mathematical formulations for achieving these goals are presented below. Then "mathematical optimal
solutions" for these formulations are presented, and discussed within the context of a "preferred
management solution".
4.2 COMPONENTS OF MATHEMATICAL FORMULATION
4.2.1 Representation of Plume Containment
Head constraints were used to represent plume containment at model grid cells adjacent to the river (i.e.,
to prevent discharge of contaminated water to the river). In the groundwater flow model, the river is
simulated with specified head cells, which are assigned a water elevation of 302 ft MSL. In MODMAN,
an upper limit of 301.99 ft MSL is specified at 54 cells adjacent to the river (Figure 4.5). These head
limits prevent discharge of groundwater to the river in each of those cells. Note that head difference
limits and gradient limits are also available in MODMAN, and either could have been used instead of the
head limits to represent plume containment.
The locations of the cells where head limits were assigned correspond to the capture zone of the designed
pump-and-treat system, as determined by the groundwater flow model (with particle tracking). Use of
the containment zone associated with the original system design allows for a fair comparison between
total pumping rates in the original design versus pumping solutions obtained with hydraulic
optimization.
The specific head value of 301.99 was selected because a head difference of 0.01 ft (between the river
and a cell adjacent to the river) is measurable in the field. Sensitivity analyses for. some optimization
scenarios were performed, to assess the change in mathematical optimal solutions resulting from a
smaller head difference limit (e.g., 0.00 ft) and a larger head difference limit (e.g., 0.10 ft).
4.2.2 Representation of Wells
Existing Well Locations:
Locations of existing wells are illustrated on Figures 4-3 and 4-4, and are summarized on Table 4-2. As
previously discussed, five of the BW wells were installed subsequent to the original design (indicated on
Table 4-2).
4-3
-------
New Well Locations Considered:
Four additional well locations, in areas of high contaminant concentrations, were considered in some
scenarios. These locations are illustrated on Figure 4-5. The purpose of considering new wells in these
scenarios was to quantify the "containment efficiency" of wells located in key areas of high
concentration (see Section 3.3.3 for a discussion of "containment efficiency").
Well Rate Limits:
For existing wells, daily well rates were available for June 1997 through November 1997. For managed
wells (i.e., wells in a specific scenario for which an optimal rate was being determined), the maximum
rate observed at each well over this time period (see Table 4-2) was assigned as an upper limit on well
rate. This is conservative, because some wells may be actually be capable of producing more water. For
some wells, the assigned upper limit is less than the original design rate, which was determined on the
basis of groundwater modeling.
Limiting the Number of New Wells Selected:
For some hydraulic optimization scenarios, integer constraints (see section 3.1.3) were specified, to
allow the number of selected wells to be limited.
4.2.3 Objective Function
The objective function is "minimize total pumping in gpm". To achieve this, each pumping rate variable
was multiplied by an objective function coefficient of-0.005194. The value of the coefficient converts
from MODFLOW units (ftVd) into gpm, and the negative value of the coefficient accounts for the fact
that pumping rates in MODFLOW are negative. By multiplying the negative MODFLOW rates by a
negative objective function coefficient, the use of the term "minimize" becomes straightforward for the
objective function.
For this site, the objective function is not based directly on cost. However, impacts on annual O&M
costs resulting from pumping rate modifications are easily evaluated, external to the hydraulic
optimization algorithm. As discussed in Volume 1, the most significant annual cost of this system is
steam (approximately $2000/yr/gpm). Up-front costs associated with new wells are estimated at
$20K/well.
4.3 CONTAINMENT SOLUTIONS, ORIGINAL WELLS
4.3.1 Scenario 1: Minimize Pumping at Original 18 BW Wells, Design Rates at SW and OW
Wells
The first hydraulic optimization formulation considers all of the well locations associated with the
original design. Rates at the SW wells and OW wells are fixed at the original design rates (see Table 4-
2). The goal is to determine if hydraulic optimization suggests improved rates at the BW wells, relative
4-4
-------
to the original design (i.e., had hydraulic optimization been applied during the design, would a better
solution have been determined, using the same well locations?).
As previously discussed, a head difference of 0.01 feet is imposed between the river and adjacent cells in
the aquifer. The target containment zone is identical to the containment zone associated with the original
design (as determined with the model), and the upper limit on well rate at each BW well is based on the
maximum rate observed between June 1997 and November 1997.
The mathematical optimal solution for this scenario is summarized below:
BW wells
SW wells
OW wells
Total System:
Design Rate (gpm)
549
171
132
852
Mathematical Optimal
Solution (gpm)
273
171 (fixed)
132 (fixed)
576
The mathematical optimal solution includes 17 of the 18 original BW well locations, and represents a
reduction of 276 gpm at the BW wells (over 50%). Using the simple relationship between pumping rate
and total annual cost based on steam ($2000/yr/gpm), a reduction of 276 gpm corresponds to a reduction
in annual O&M of $552K/yr.
The same hydraulic optimization scenario was then solved with additional constraints limiting the
number of well locations that may be selected. Results are summarized below:
# of BW Wells
Allowed
17+
16
15
14
13
12
11
10
9
Mathematical Optimal Solution,
Total Pumping at B W Wells (gpm)
273
274
274
275
279
283
288
297
infeasible
4-5
-------
Hydraulic optimization makes this type of analysis easy to perform, and the results suggest that some of
the 18 BW wells in the original design were not necessary. For instance, reducing the number of wells
selected from 17 to 14 only increases the pumping rate required for containment by 1 gpm ($2000/yr in
steam costs).
The results presented above are significant. Had hydraulic optimization been applied when the pump-
and-treat system was originally designed, the design pumping rates at the BW wells might have been cut
in half (potential savings in steam costs of over $500K/yr), and the number of BW wells would likely
have been reduced from 18 wells to 14 wells, and perhaps to as little as 10 or 11 wells. This might have
saved S100K or more in Up-Front costs associated with the installation of those wells.
4.3.2 Scenario 2: Minimize Pumping at Original 18 BW Wells, No Pumping at SW and OW
Wells
This optimization formulation is similar to the previous formulation, except that rates at the SW wells
and OW wells are fixed at zero. This represents a scenario where containment at the river is the only
priority. The goal is to use hydraulic optimization to quantify the "containment efficiency" of the SW
and OW wells in the original design, which allows a more meaningful evaluation of the additional costs
associated with the SW and OW wells.
The mathematical optimal solution for this scenario is summarized below:
BW wells
SW wells
OW wells
Total System:
Mathematical Optimal
Solution, Scenario 2
(gpm)
409
0 (fixed)
0 (fixed)
409
Mathematical Optimal
Solution, Scenario 1
(gpm)
273
171 (fixed)
132 (fixed)
576
When 303 gpm of pumping is added at the SW and OW wells, a corresponding decrease of 136 gpm can
potentially be implemented at the BW wells. As discussed in Section 3.3.3, this can be expressed as
"containment efficiency" of the combined pumping at the SW and OW wells:
containment efficiency = 136/303 = 45%
j
This type of analysis, which is straightforward with hydraulic optimization, is very significant. When
pumping is added upgradient of the containment wells, significant cost savings can be realized by
implementing a corresponding rate reduction at the containment wells. In this case, the addition of 303
gpm at the SW and OW wells, at $2000/yr/gpm, would translate into $606K/yr in added steam costs.
However, by implementing a corresponding reduction of 136 gpm at the BW wells, the net increase in
pumping rate would only be 167 gpm, which would translate into $334K in added steam costs.
Therefore, evaluating the "containment efficiency" could yield savings of $272K/yr for this particular
example.
4-6
-------
4.4 CONTAINMENT SOLUTIONS, CURRENT WELLS
4.4.1 Scenario 3: Minimize Pumping at Current 23 BW Wells, No Pumping at SW or OW Wells
This optimization formulation is similar to Scenario 2 (rates at the SW wells and OW wells are fixed at
zero), but this scenario includes the five BW wells installed after the original system was installed. The
locations of the five additional wells are indicated on Figure 4-5. The goal is to use hydraulic
optimization to quickly determine if the five additional well locations significantly reduce the amount of
pumping required for containment at the river.
The mathematical optimal solution for this scenario is summarized below:
BW wells
SW wells
OW wells
Total System:
Mathematical Optimal Solution,
Scenario 2
(gpm)
409
0 (fixed)
0 (fixed)
409
Mathematical Optimal
Solution, Scenario 3
(gpm)
399
0 (fixed)
0 (fixed)
399
In this case, addition of the five additional wells has only a small impact. Of course, it is quite possible
that the addition of wells in other locations might have a greater impact on the amount of pumping
required for containment, and hydraulic optimization could provide an efficient evaluation of many other
locations (that analysis was not performed as part of this demonstration).
4.4.2 Scenario 4: Same as Scenario 3, But Varying Limit on Head Adjacent to the River
This optimization formulation is similar to Scenario 3, but the head limits imposed adjacent to the river
are varied. In Scenario 3, an inward head difference of 0.01 ft from the river to the aquifer is mandated,
by assigning a head limit of 301.99 ft MSL at cells adjacent to the river (the river is represented with
specified head of 302.00 ft MSL). In this scenario, the following alternative head limits are imposed in
cells adjacent to the river:
302.00 ft MSL
302.95 ft MSL
392.90 ft MSL
(0.00 ft head difference)
(0.05 ft head difference)
(0.10 ft head difference)
The mathematical optimal solutions for this scenario are summarized below:
4-7
-------
Head Difference
Limit Imposed
(ft)
0.00
0.01
0.05
0.10
Mathematical Optimal
Solution
(gpm)
396
399
421
458
Annual Steam Cost
($/yr)
$792K
$798K
S842K
S916K
Note; annual steam cost approximated as $2000/yr/gpm
The results illustrate that, as limits representing containment are made more conservative, the amount of
pumping required for containment increases. In this particular formulation, imposing a head difference
limit of 0.10 ft rather than 0.0 ft leads to a more conservative pumping design, with an additional steam
cost of more than S1 OOK/yr. Hydraulic optimization allows an efficient evaluation of such tradeoffs
(this analysis would be difficult or impossible by trial-and-error).
4.5 SCENARIOS: SOLUTIONS WITH ADDITIONAL CORE ZONE WELLS
This optimization formulation considers the existing 23 BW wells (i.e., as in Scenario 3), plus five
existing SW wells (SW-1920, SW-1921, SW-1926, SW-1942, SW-1943), and four additional wells in
areas of high contaminant concentrations. These locations are indicated on Figure 4-5. All other SW
and OW wells are not pumped. The goal is to determine if the "containment efficiency" of these nine
core zone wells (the five SW wells and the four new wells) is greater than the "containment efficiency"
of the original SW and OW wells (previously determined to be 45% in Section 4.3.2). The reason for
improved containment efficiency would be that some of the OW wells in the original design are not
directly upgradient of the containment wells near the river.
Two variations were evaluated:
(1) add 5 gpm at each of the nine core zone wells, for a total of 45 gpm; and
(2) add 10 gpm at each of nine core zone wells, for a total of 90 gpm.
The hydraulic optimization results are intended to quantify potential reductions in rates that can be
implemented at the BW wells, while maintaining containment.
The mathematical optimal solutions are summarized below:
BW wells
Core Zone Wells
Total System:
Mathematical Optimal
Solution, Scenario 3
(gpm)
399
0 (fixed)
399
Mathematical Optimal
Solution, 45 gpm added
in Core Zone (gpm)
374
45
419
Mathematical Optimal
Solution, 90 gpm added
in Core Zone (gpm)
349
90
439
4-8
-------
When 45 gpm of pumping is added in the core zone, a corresponding decrease of 25 gpm can potentially
be implemented at the BW wells:
containment efficiency = 25/45 = 56%
When 90 gpm of pumping is added in the core zone, a corresponding decrease of 50 gpm can potentially
be implemented at the BW wells:
containment efficiency = 50/90 = 56%
As expected, the containment efficiency of 56 percent is higher than the containment efficiency of 45
percent determined for the SW and OW wells in the original design. This is presumably due to the fact
that combined locations of these wells are more favorable for containment than the combined locations
of the original SW and OW wells.
As previously discussed, this type of analysis is important when additional pumping is considered
upgradient of the containment wells, because implementing a corresponding rate reduction at the
containment wells can result in considerable savings. Without hydraulic optimization, quantifying the
potential rate reduction at the containment wells would be difficult, if not impossible. In this case, the
addition of 90 gpm at the core zone wells, at $2000/yr/gpm, would translate into $180K/yr in added
steam costs. However, by implementing a corresponding reduction of 50 gpm at the BW wells, the net
increase in pumping rate would only be 40 gpm, which would translate into $80K in added steam costs.
Therefore, evaluating the "containment efficiency" could yield savings of $100K/yr for this particular
scenario. :
4.6 DISCUSSION & PREFERRED MANAGEMENT SOLUTION
Interesting results from the hydraulic optimization evaluations for this site include the following:
had hydraulic optimization been applied when the pump-and-treat system was originally
designed, the design pumping rates at the BW wells might have been cut in half
(potential savings in steam costs of over $500K/yr), and the number of BW wells would
likely have been reduced from 18 wells to 14 wells, and perhaps to as few as 10 or 11
wells (potential savings of $100K or more in Up-Front costs associated with the
installation of those wells);
as limits representing containment at the river are made more conservative, the amount
of pumping required for containment increases (in this particular formulation, imposing
a head difference limit of 0.10 ft rather than 0.0 ft leads to a more conservative pumping
design, with an additional steam cost of more than $100K/yr);
core zone wells at this site have a "containment efficiency" of 45% to 55%, such that
each increase of 10 gpm in the core zone can be partially offset with approximately a 5
gpm reduction at containment wells (the containment efficiency improves with better
placement of wells);
for cases where core zone pumping is considered, implementing corresponding rate
reductions at containment wells (based on the "containment efficiency") will potentially
yield significant savings (as much as $100K/yr or more);
4-9
-------
All of these analyses were efficiently conducted with hydraulic optimization techniques. In most cases,
these types of analyses are difficult (if not impossible) to comprehensively perform with a trial-and-error
approach. This is because of the large number of well locations being considered. With a trial-and-error
approach, only a small number of well rate combinations can be evaluated with the simulation model,
whereas hydraulic optimization allows all potential combinations of well rates to be rigorously evaluated
for each scenario.
According to the hydraulic optimization results, a preferred management strategy might include pumping
rate reductions at the BW wells. However, the groundwater flow model at this site is quite simplified,
and additional effort in refining the groundwater flow model (and subsequent re-analysis with hydraulic
optimization) may be worthwhile. If pumping at the SW and OW wells is reduced (or terminated),
corresponding pumping rate increases will be required at the BW wells to maintain containment (for
every 10 gpm reduced, approximately 5 gpm will need to be added at the BW wells.
A significant management issue at this site relates to the net benefits provided by core zone wells (e.g.,
the SW wells). Contaminant levels at this site are high, and residual NAPL in the soil column is likely.
Therefore, cleanup at this site may never be achieved via pump-and-treat (i.e., accelerated mass removal
from groundwater may not provide any tangible benefits). Although hydraulic optimization does not
incorporate predictions of future contaminant concentrations, it does allow the costs of core zone
pumping to be quantified, in conjunction with the "containment efficiency". Assuming steam costs of
$2000/yr/gpm, the increased annual cost for each 50 gpm in the core zone is approximately $50K/yr
(assuming the corresponding pumping rate reduction of 25 gpm at the containment wells indicated by the
"containment efficiency"). These costs can be assessed with respect to the perceived benefits associated
with these core zone wells.
For this site, the hydraulic optimization results potentially lead to large cost savings (Smillions over a 20
to 30 year planning horizon). This is partly due to the fact that the remediation technology at this site
(steam stripping) is expensive. A management strategy at this site might also include an evaluation of
potential alternatives to the steam-stripping technology currently utilized.
4-10
-------
5.0 CASE #2: TOOELE
5.1 SITE BACKGROUND
5.1.1 Site Location and Hydrogeology
The facility is located in Tooele Valley in Utah, several miles south of the Great Salt Lake, (see Figure 5-
1). The aquifer of concern generally consists of alluvial deposits. However, there is an uplifted bedrock
block at the site where groundwater is forced to flow from the alluvial deposits into fractured and
weathered rock (bedrock), and then back into alluvial deposits.
The unconsolidated alluvial deposits are coarse grained, consisting of poorly sorted clayey and silty sand,
gravel, and cobbles eroded from surrounding mountain ranges. There are several fine-grained layers
assumed to be areally extensive but discontinuous, and these fine-grained layers cause vertical head
differences between adjacent water-bearing zones. Bedrock that underlies these alluvial deposits is as
deep as 400 to 700 feet. However, in the vicinity of the uplifted bedrock block, depth to bedrock is
shallower, and in some locations the bedrock is exposed at the surface.
Depth to groundwater ranges from 150 to 300 ft. The hydraulic conductivity of the alluvium varies from
approximately 0.13 to 700 ft/day, with a representative value of approximately 200 ft/day. In the
bedrock, hydraulic conductivity ranges from approximately 0.25 ft/day in quartzite with clay-filled
fractures to approximately 270 ft/day in orthoquartzite with open, interconnected fractures.
Groundwater generally flows to the north or northwest, towards the Great Salt Lake (see Figure 5-2).
Recharge is mostly derived from upgradient areas (south of the facility), with little recharge from
precipitation. Gradients are very shallow where the water table is within in the alluvial deposits. There
are steep gradients where groundwater enters and exits the bedrock block, and modest gradients within
the bedrock block. There is more than 100 ft of head difference across the uplifted bedrock block. This
suggests that the uplifted bedrock area provides significant resistance to groundwater flow. North (i.e.,
downgradient) of the uplifted bedrock block, the vertical gradient is generally upward.
5.1.2 Plume Definition
The specific plume evaluated in this study originates from an industrial area in the southeastern corner of
the facility, where former operations (since 1942) included handling, use, and storage of TCE and other
organic chemicals. Groundwater monitoring indicates that the primary contaminant is TCE, although
other organic contaminants have been detected. TCE concentrations in the shallow (model layer 1) and
deep (model layer 2) portions of the aquifer are presented on Figure 5-2. Concentrations are
significantly lower in the deeper portions of the aquifer than in shallow portions of the aquifer. Also,
the extents of the shallow and deep plumes do not directly align, indicating a complex pattern of
contaminant sources and groundwater flow. Continuing sources of dissolved contamination are believed
to exist.
5-1
-------
5.1.3 Existing Remediation System
A pump-and-treat system has been operating since 1993. The system consists of 16 extraction wells and
13 injection wells (see Figure 5-3 for well locations). An air-stripping plant, located in the center of the
plume, is capable of treating 8000 gpm of water. It consists of two blowers operated in parallel, each
capable of treating 4000 gpm. Sodium hexametaphosphate is added to the water prior to treatment, to
prevent fouling of the air stripping equipment and the injection wells. Treated water is discharged via
gravity to the injection wells. Approximate costs of the current system are presented in Table 5-1 (see
Volume 1 for a more detailed discussion of costs).
Based on the well locations and previous plume delineations, the original design was for cleanup. At the
time the system was installed, the source area was assumed to be north of the industrial area (near a
former industrial waste lagoon). Subsequently, it was determined that the source area extended far to the
south (in the industrial area). As a result, the current system essentially functions as a containment
system (there are no extraction wells in the area of greatest contaminant concentration).
Historically, the target containment zone has been defined by the 5-ppb TCE contour. Given the current
well locations, anticipated cleanup time is "a very long time". However, a revised (i.e., smaller) target
containment zone is now being considered, based on risks to potential receptors. A revised target
containment zone might correspond to the 20-ppb or SOOppb TCE contour.
5.1.4 Groundwater Flow Model
A three-dimensional, steady-state MODFLOW model was originally constructed in 1993 (subsequent to
the design of the original system), and has been recalibrated on several occasions (to both non-pumping
and pumping conditions). The current model has 3 layers, 165 rows, and 99 columns. Cell size is 200 ft
by 200 ft. Model layers were developed to account for different well screen intervals, and are assigned
as follows:
Layer 1: 0 to 150 ft below water table
Layer 2: 150 to 300 ft below water table
Layer 3: 300 to 600 ft below water table
Boundaries include general head conditions up- and down-gradient, no flow at the sides and the bottom.
The model has historically been used as a design tool, to simulate drawdowns and capture zones (via
particle tracking) that result from specified pumping and injection rates.
The current groundwater model is a useful tool for approximating drawdowns and capture zones.
However, the following are noted: (1) near the source area, simulated flow directions are not consistent
with the shape of the observed plume; and (2) the bedrock block is a very complex feature, and accurate
simulation of that feature is very difficult.
5.1.5 Goals of a Hydraulic Optimization Analysis
A screening analysis performed for this site (see Volume 1) suggests that significant savings (millions of
dollars over 20 years) might be achieved by reducing the pumping rate associated with the present
system, even if five new wells (at $300K/well) were added. In that screening analysis, a pumping rate
reduction of 33 percent was assumed. This could potentially be accomplished by:
5-2
-------
• optimizing rates to achieve more efficient containment of the 5-ppb plume; and/or
• reducing the size of the target containment zone (if independently demonstrated to
maintain protection of human health and the environment).
Therefore, the goals of the optimization analysis are:
(1) determine the extent to which pumping rates can actually be reduced at this site, with
and without the addition of new wells, given the current target containment zone (5-ppb
plume);
(2) quantify cost reductions associated with these achievable pumping rates;
(3) quantify the tradeoff between the number of wells operating and the total pumping rate
(and/or cost) required for containment;
(4) quantify potential pumping rate and cost reductions associated with a modified target
containment zone (i.e., the 20-ppb plume or the 50-ppb plume).
Mathematical formulations for achieving these goals are presented below. Then "mathematical optimal
solutions" for these formulations are presented, and discussed within the context of a "preferred
management solution".
5.2
COMPONENTS OF MATHEMATICAL FORMULATION
5.2.1 Representation of Plume Containment
A combination of head difference constraints, gradient constraints, and relative gradient constraints were
used to represent plume containment (see section 3.1.1 for an overview of the approach). For this site,
constraints representing containment were developed for four different plume boundaries:
• shallow 5-ppb plume (Figure 5-4);
• deep 5-ppb plume (Figure 5-5);
• shallow 20-ppb plume (Figure 5-6); and
shallow 50-ppb plume (Figure 5-7).
Along the northeast boundary of the shallow 5-ppb plume, constraints were applied along a "smoothed"
approximation of the plume boundary, rather than the actual plume boundary (which has an irregular
shape). Also, constraints representing plume containment were only applied north of the bedrock block
(for the 5-ppb and 20-ppb plume), near the toe of each plume. This was done because containment at the
toe of each plume was the focus of these efforts. Assigning plume containment constraints in the vicinity
of the bedrock block may have caused infeasible solutions to result, simply because the simulation model
is imperfect in that highly complex region.
Constraints representing plume containment were not applied to the deep 20-ppb plume. Preliminary
simulations indicated that wells containing the shallow 20-ppb plume would also contain the deep 20-
ppb plume. For optimization simulations based on containment of the 20-ppb plume, this simplifying
assumption was verified with particle tracking simulations.
5-3
-------
A summary of the number of constraints used to represent containment for each plume is provided
below:
Plume
5 ppb, shallow
5 ppb, deep
20 ppb, shallow
50 ppb, shallow
Number of Head
Difference Limits
3
9
1
9
Number of
Gradient Limits
38
22
16
14
Number of Relative
Gradient Limits
19
11
8
7
5.2.2 Representation of Wells
Multi-aquifer wells:
]
Presently, 16 extraction wells and 13 injections wells are in operation (see Section 5.1.3). Some of these
wells are multi-aquifer wells. In MODFLOW, the amount of water discharged from a multi-aquifer well
in each model layer is weighted by the relative transmissivity of each layer at the specific grid block.
Balance constraints were specified in MODMAN ( see section 3.1.2) to preserve the ratio of pumping
between model layers for multi-aquifer wells, as follows:
Well
E-6
E-8
E-9
E-10
E-14
E-15
1-2
1-6
1-7
1-9
1-10
1-13
MODMAN Well Numbers
Q8 ( Layer 1), Q9 (Layer 2)
Q10 ( Layer 1), Qll(Layer2)
Q12 ( Layer 1), Q13 (Layer 2),
Q14 (Layer 3)
Q15 ( Layer 1), Q16(Layer2)
Q20 ( Layer 1), Q21 (Layer 2)
Q22 ( Layer 1), Q23 (Layer 2)
Q25 ( Layer 1), Q26(Layer2)
Q30 ( Layer 1), Q31 (Layer 2)
Q32 ( Layer 1), Q33 (Layer 2)
Q35 ( Layer 1), Q36(Layer2)
Q37 ( Layer 1), Q38 (Layer 2)
Q41 ( Layer 1), Q42(Layer2)
Relationship
Q8 -4.88Q9 =0
Q10-1.50Q11=0
Q12-0.20Q13=0
Q12-0.56Q14 = 0
Q15-0.15Q16 = 0
Q20-0.33Q21=0
Q22 - 4.00Q23 = 0
Q25 - 3.54Q26 = 0
Q30-1.22Q31=0
Q32-1.22Q33=0
Q35-1.50Q36 = 0
Q37-3.00Q38 = 0
Q41-4.00Q42 = 0
(i.e., Q8/Q9 =4.88)
(i.e., Q10/Q11 = 1.50)
(i.e., Q12/Q13 = 0.20)
(i.e., Q12/Q14 = 0.56)
(i.e., Q15/Q16 = 0.15)
(i.e., Q20/Q21 = 0.33)
(i.e., Q22/Q23=4.00)
(i.e., Q25/Q26 = 3.54)
(i.e.,Q30/Q31 = 1.22)
(i.e., Q32/Q33 = 1.22)
(i.e., Q35/Q36 = 1.50)
(i.e., Q37/Q38 = 3.00)
(i.e.,Q4 1/Q42 = 4.00)
5-4
-------
New Well Locations Considered:
Depending on the scenario, additional potential well locations were considered as follows:
Plume to Contain Additional Well Locations Considered
5-ppb shallow
5-ppb deep
20-ppb shallow
50-ppb shallow
20 wells in layer 1 (see Figure 5-4)
18 wells in layer 2 (see Figure 5-5)
6 wells in layer 1, and 1 well in layer 2 (see Figure 5-6)
20 wells in layer 1 (see Figure 5-7)
The additional well in layer 2 for scenarios based on containment of the shallow 20-ppb plume is located
near the toe of the deep 20-ppb plume. This allows consideration of solutions with a fixed pumping rate
at that well, to increase efficiency of containing and/or remediating that portion of the plume.
Well Rate Limits:
Maximum pumping rates for all new wells was specified as 500 gpm. For existing wells extraction and
injection wells, operational history was considered in specifying maximum rates. If operation rate on
April 6, 1998 (provided earlier) was less than 500 gpm, then 500 gpm was specified as the maximum
rate. If operation rate on April 6, 1998 (provided earlier) was greater than 500 gpm, then the rate
observed on that date was set as the maximum rate. For multi-aquifer wells, an additional calculation
was made to determine the maximum rate allowed in one specific model layer, based on the maximum
rate allowed for the total well.
Example: Well E-10, max rate = 714 gpm
Well names in MODMAN:
Well rate relationship:
Max rate for total well:
Substitute for Q15:
Determine limit for Q16
Q15 (Layer 1), Q16 (layer 2)
Q15/Q16 = 0.15 (i.e., Q15 = 0.15Q16)
Q15 + Q16< 714 gpm
0.15Q16 + Q16 <, 714 gpm
Q16 < 621 gpm
Limiting the Number of New Wells Selected:
In simulations where additional wells were considered, integer constraints (see section 3.1.3) were
specified, to allow the number of new wells to be limited.
Balance Between Total Pumping and Total Injection
The remediation system at Tooele includes reinfection of treated groundwater. Constraints were
included so that total injection rate cannot exceed total pumping rate (which is not feasible for this
system).
5-5
-------
5.2.3 Objective Function Based on Minimizing Total Pumping
For most of the optimization simulations performed for this site, the objective function is "minimize total
pumping in gpm". To achieve this, each pumping rate variable was multiplied by an objective function
coefficient of -0.005194. The value of the coefficient converts from MODFLOW units (ft3/d) into gpm,
and the negative value of the coefficient accounts for the fact that pumping rates in MODFLOW are
negative. By multiplying the negative MODFLOW rates by a negative objective function coefficient,
the use of the term "minimize" becomes straightforward for the objective function.
For solutions with this objective function, associated "Total Managed Cost" was calculated external to
the optimization algorithm. Managed costs refers to those aspects of total cost that are related to the
variables being optimized (i.e., the well rates). Simple cost functions were established as follows:
managed Up-front Cost ($) = number of new wells * $300K/well
managed Annual Cost ($) = total pumping rate (gal/min) * $150/yr/gpm
The relationship for "managed annual cost" is a simplified and approximate relationship, based on the
costs of electricity and sodium hexametaphosphate in the current system (which are related to total
pumping rate), and an approximate rate of 8000 gpm for the present system:
$l,000,000/yr: electric
$ 200,000/yr: sodium hexametaphosphate
$1.2M/yr for 8000 gpm = $150/yr/gpm
"Total Managed Cost", combines the "Up-Front Costs" with the "Total of Annual Costs" over a specific
time horizon (20 yrs), assuming a specific discount rate (5%). These calculations are performed in a
spreadsheet. An example is provided in Table 5-2.
5.2.4 Objective Function Based on Minimizing Total Cost
For some optimization simulations, the cost functions described above were incorporated directly into
the objective function. The goal was to minimize "Total Managed Cost" (Net Present Value, or NPV)
over a 20-year time horizon, assuming a discount rate of 5%. The objective function takes the following
form:
where:
n=
m =
Min S
+
E dL
j=l,m J J
number of wells
coefficient for annual costs due to pumping rate at well i
pumping rate at well i
number of potential new wells
additional cost incurred if new well j is selected (e.g., well installation cost)
0 if new well j is not selected, 1 if new well j is selected
5-6
-------
The coefficient c; is $1963/gpm, which represents "Managed Annual Cost" of $150/yr/gpm summed over
a 20 year time horizon, assuming a 5% discount rate (in MODMAN, the coefficient c} is further
multiplied by -0.005194, to convert from MODFLOW (ftVd) into gpm, and to account for the fact that
pumping rates are negative in MODFLOW). The coefficient d, is $300K, which is the anticipated up-
front cost of each new well.
Note that the MODMAN input file does not currently permit coefficients d,. to be entered into the
objective function. To solve these problems, appropriate coefficients were manually added to the MPS
file generated by MODMAN, prior to solution with LINDO (see Appendix H for an overview of
modifying linear or mixed-integer programs generated by MODMAN).
5.3 CONTAINING THE 5-PPB TCE PLUME, MINIMIZE TOTAL PUMPING
5.3.1 Existing Wells (Shallow and Deep Plumes)
The first hydraulic optimization simulation considers containment of both the shallow 5-ppb plume and
the deep 5-ppb plume (i.e., neither is allowed to expand beyond the present extent). Only existing well
locations are considered. The objective function is to minimize total pumping.
The hydraulic optimization results indicate that the problem is infeasible. The constraints representing
plume containment for both the shallow and deep 20-ppb plumes cannot all be satisfied, given the
locations of the existing wells and the limits placed on rate at each well. This is consistent with particle
tracking results for a simulation of the existing system, which shows some water within the shallow 5-
ppb plume is not captured (see Figure 5-8). According to site managers, however, adequate remediation
is believed to be occurring in areas near the toe of the plume where capture is not indicated by the model.
Another hydraulic optimization simulation was performed, with the limit on each existing well raised to
2000 gpm. Again, the result indicated that the problem as formulated is mathematically infeasible, given
the groundwater flow model and the constraint set imposed.
5.3.2 Additional Wells (Shallow and Deep Plumes)
This hydraulic optimization formulation considers the same containment zone (i.e., both the shallow 5-
ppb plume and deep 5-ppb plume). However, 20 additional well locations are considered in the shallow
zone (see Figure 5-4), and 18 additional well locations are considered in the deep zone (see Figure 5-5).
Again the objective is to minimize total pumping. Mathematical optimal solutions (i.e., for minimum
total pumping rate) were determined for different limits on the number of new wells. For each of these
mathematical optimal solutions, Total Managed Cost (see section 5.2.3) was calculated, external to the
optimization algorithm. The results are as follows:
5-7
-------
# New Wells
Allowed
14
13
12
11
10
9
8
7
Current System
Minimum
Pumping Rate
4163
4178
4200
4742
4907
5236
5553
5941
7500
# Existing Wells
Selected
3
3
4
4
6
7
9
9
75
Total Managed Cost,
($NPV)
S12.4M
S12.1M
S11.8M
$12.6M
S12.6M
S13.0M
S13.3M
S13.7M
$14.7M
Best
Cost
* BEST *
Adding more than fourteen new wells does not yield a further reduction in total pumping. As the number
of new wells is decreased, total pumping rate required for containment increases.
With the addition of fourteen new wells, containment of both the shallow 5-ppb plume and deep 5-ppb
plume can be achieved with total pumping of 4163 gpm (a reduction of nearly 45% from the current
pumping rate of 7500 gpm). Interestingly, the solution that minimizes total pumping does not minimize
Total Managed Cost. This is because the benefits of reduced pumping rate afforded by two additional
wells (the thirteenth and fourteenth) are not great enough to offset the high up-front costs of those
additional wells ($300K/well). Particle tracking results depicting capture in the shallow and deep zones
for the solution with 4163 gpm are presented in Figures 5-10 and 5-11).
5.3.3 Quantifying The Benefits of Reinjecting Treated Water
This formulation is the same as described in the previous section, but reinjection is not permitted
(conceptually, all water is discharged further downgradient, such that plume capture is not impacted by
the reinjection. The mathematical optimal solution (i.e., minimum pumping rate) for this formulation is:
Without Reinjection: 5237 gpm
With Reinjection: 4163 gpm
With.respect to containment of the 5-ppb plumes, these results indicate that reinjection of treated water at
existing locations, if optimally distributed, reduces pumping required for containment by 20 percent
Presumably, the benefits of reinjection at existing injection wells will decrease if the size of the target
containment zone is reduced (reinjection would be further downgradient from the edge of the target
containment zone).
5-8
-------
5.3.4 Additional Wells (Shallow Plume Only)
This formulation is the same as described in section 5.3.2, but only the shallow 5-ppb plume is
considered. The constraints representing containment of the deep 5-ppb plume are removed, and the 18
additional well locations in the deep zone are not included (particle tracking can be used to assess the
fate of the deep plume for specific solutions determined with this formulation). Mathematical optimal
solutions (i.e., for minimum total pumping rate) were determined for different limits on the number of
new wells. For each of these mathematical optimal solutions, Total Managed Cost (see section 5.2.3)
was calculated, external to the optimization algorithm. The results are as follows:
# New Wells
7
6
5
4
3
2
Current System
Minimum
Pumping Rate
2622
2852
3127
3766
4051
5873
7500
# Existing Wells
Selected
2
3
4
7
6
10
75
Total Managed Cost,
($NPV)
(20 yrs, 5% discount)
S7.2M
$7.4M
$7.6M
$8.6M
$8.9M
S11.5M
$J4.7M
Best
Cost
Solution
* BEST *
Adding more than seven new wells does not yield a further reduction in total pumping. As the number of
new wells is decreased, total pumping rate required for containment increases.
With the addition of seven new wells, containment of the shallow 5-ppb plume can be achieved with
total pumping of 2622 gpm. This is a reduction of approximately 65% from the current pumping rate of
7500 gpm. For this formulation, the solution that minimizes total pumping also minimizes Total
Managed Cost. Particle tracking results depicting capture in the shallow and deep zones for the solution
with 2622 gpm are presented in Figures 5-12 and 5-13. There are two major differences between this
strategy and the strategy where both the shallow and deep 5-ppb plumes are contained:
with this strategy, the western portion of the deep 5-ppb plume is not captured by any
extraction wells; and
with this strategy, many particles starting within the deep 5-ppb plume are captured by
wells located outside the boundary of that plume.
Total Managed Cost is much lower (i.e., as much as $5M over 20 years, NPV) for this scenario than for
the case where both the shallow 5-ppb and deep 5-ppb plumes are contained. This is because the total
pumping rate is reduced, and the number of new wells is also reduced. Whether or not this represents an
acceptable strategy is ultimately a regulatory issue.
5-9
-------
5.4 OBJECTIVE FUNCTION BASED DIRECTLY ON COSTS
This formulation is the same as described in Section 5.2.3 (containment of the shallow 5-ppb plume) but
the objective function is based directly on Total Managed Cost (see Section 5.2.4). The optimal solution
In New Wells
Allowed
7
Minimum
Pumping Rate
(gpm)
2622
# Existing Wells
Selected
2
Total Managed Cost,
($NPV)
This is the same solution that was determined with objective function of "Minimized Total Pumping".
5.5 CONTAINING THE 20-pps AND/OR SO-PPB TCE PLUME
A variety of additional hydraulic optimization formulations were constructed for additional scenarios to
determine solutions that minimize pumping. The formulations included the following:
contain only the shallow 50-ppb plume;
contain only the shallow 20-ppb plume;
contain the shallow 20-ppb plume, plus 500 gpm at a new well near the toe of the deep
20-ppb plume;
contain the shallow 20-ppb plume, plus add a well pumping 500 gpm at a new well near
the toe of the deep 20-ppb plume, plus contain the shallow 50-ppb plume.
For each of these mathematical optimal solutions, Total Managed Cost (see section 5.2.3) was calculated
external to the optimization algorithm. Results for select solutions are as follows:
contain shallow 50-ppb plume
1124
S3.1M
5-14 & 5-15
contain shallow 20-ppb plume
1377
S3.3M
5-16 & 5-17
contain shallow 20-ppb plume,
plus 500-gprn at toe of the deep
20-ppb plume
1573
$4.0M
5-18 & 5-19
contain shallow 20-ppb and 50-
ppb plume, plus 500 gpm at toe
of the deep 20-ppb plume
2620
S6.9M
5-20 & 5-21
5-10
-------
Note that existing wells are not generally selected in these solutions, indicating that existing wells are not
optimally located for containing the 20-ppb and/or 50-ppb plumes. The only existing well selected for
any of these solutions is well E-2-1. Also note that the total number of extraction wells in all of these
solutions (ranging from 3 to 6) is less than half the number of wells (15) currently operating.
Particle tracking results depicting capture in the shallow and deep zones for these solutions are presented
according to the figure numbers listed above.
5.6 DISCUSSION & PREFERRED MANAGEMENT SOLUTION
Some of the interesting results of the hydraulic optimization analysis are:
the current pumping at existing wells (7500 gpm) does not meet all constraints
representing containment of the shallow 5-ppb and deep 5-ppb plume, and no
combination of well rates at existing wells will satisfy those constraints (according to
site managers, however, adequate remediation is believed to be occurring in areas near
the toe of the plume where capture is not indicated by the model);
containing the shallow 5-ppb plume and deep 5-ppb plume can be achieved at a
substantially reduced pumping rate, with the addition of many new wells (pumping can
be reduced to less than 5000 gpm if 10 or more new wells are added);
even with the high cost of new wells ($300K/well), the addition of 10 or more new wells
is cost-effective over 20 years because it permits total pumping rate to be substantially
reduced;
containing only the shallow 5-ppb plume can be achieved at an even lower total pumping
rate, with the addition of new wells (as low as 2622 gpm with the addition of 7 wells),
but portions of the deep 5-ppb plume are not captured by extraction wells;
by basing the target containment zone on the 20-ppb plume rather than the 5-ppb plume
(if independently demonstrated to maintain protection of human health and the
environment), and adding a few new wells, total pumping could be reduced to less than
2000 gpm, with potential savings of $10M or more over 20 years compared to the
present system;
containment of only the 50-ppb plume requires 3 new wells, pumping just over 1100
gpm, and adding these wells to contain the contaminant source, as a stand-alone option,
may'allow portions of the aquifer down-gradient to clean up via natural attenuation; and
adding wells to contain the 50-ppb plume (to contain the contaminant source) should
also be considered in conjunction with any other strategy, since it increases the potential
to clean up the aquifer (and also reduce cost by potentially decreasing the remediation
timeframe).
5-11
-------
The preferred management strategy at this site is not obvious, and to some extent depends on decisions
regarding the size of the target containment zone. However, a preferred management strategy likely
includes the addition of several wells close to the source area, to increase the potential for aquifer
cleanup. Transport simulations and/or transport optimization may be particularly useful to evaluate
cleanup potential for those scenarios.
If containment of the 20-ppb plume (rather than the 5-ppb plume) is independently determined to be
protective of human health and the environment, the following strategy (presented earlier) has
considerable appeal:
Scenario
contain shallow 20-ppb and 50-
ppb plume, plus 500 gpm at toe
of the deep 20-ppb plume
#New
Wells
6
Minimum
Pumping Rate
(gpm)
2620
# Existing
Wells
Selected
0
Total Managed Cost,
($NPV)
(20 yrs, 5% discount)
S6.9M
Six new wells are required (three shallow wells near the source area, two shallow wells near the toe of
the shallow 20-ppb plume, and one deep well near the toe of the deep 20-ppb plume). The area of
highest concentrations (i.e., the 50-ppb plume) is contained. This increases the likelihood of ultimate
(and/or quicker) cleanup in areas downgradient, by containing the source. The shallow 20-ppb plume is
contained, and containment/remediation of the deep 20-ppb plume is enhanced by the addition of the
new deep well. Total number of wells is reduced from 15 to 6 (60%), relative to the current system.
Total pumping rate is reduced from 7500 gpm to 2620 gpm (65%), relative to the current system. Total
Managed Cost over a 20-year period (which incorporates the up-front cost of $1.8M for the six new
wells) is reduced from S14.7M to $6.9M (53%), relative to the current system.
It is very important to distinguish the benefits of applying hydraulic optimization technology from other
benefits that may be achieved simply by "re-visiting" an existing pump-and-treat design. For Tooele,
potential pumping reductions and cost savings that result from a change to a smaller target containment
zone primarily result from a change in conceptual strategy. The benefit provided by hydraulic
optimization is that it allows mathematical optimal solutions for each conceptual strategy to be
efficiently calculated (whereas good solutions for each conceptual strategy may be difficult or impossible
to achieve with trial-and-error).
The hydraulic optimization analysis indicates that additional wells are required to satisfy constraints
representing plume containment for each scenario. However, before new wells are considered,
additional analysis might be performed to determine if containment, in those areas not effectively
captured by the present system (according to the model), is in fact required to maintain protection of
human health and the environment. It is possible that improved solutions with many fewer new wells are
possible, if constraints representing plume containment are relaxed in certain critical areas. Additional
hydraulic optimization simulations could be performed to assess these options.
5-12
-------
6.0 CASE #3: OFFUTT
6.1
SITE BACKGROUND
6.1.1 Site Location and Hydrogeology
The facility is located in Sarpy County, Nebraska, next to the City of Bellevue (see Figure 6-1). The
specific plume evaluated in this study is in the Southern Plume within the Hardfill 2 (HF2) Composite
Site at Offutt. The principal aquifer at the site consists of unconsolidated sediments resting on bedrock.
The aquifer system is heterogeneous and complex. Groundwater flows easterly and southeasterly (see
Figure 6-2). Depth to groundwater is generally 5 to 20 ft. The hydraulic conductivity of the alluvium
varies significantly with location and depth, due the complex stratigraphy.
6.1.2 Plume Definition
Groundwater monitoring indicates that the primary contaminants are chlorinated aliphatic hydrocarbons
(CAH's) including TCE, 1,2-dichloroethene (1,2-DCE), and vinyl chloride. Releases (initially as TCE)
formed localized vadose zone and dissolved groundwater plumes. Subsequent groundwater transport
from these multiple sources has resulted in groundwater contamination in shallow and deeper portions of
the Alluvial Aquifer.
The extent of the Southern Plume is illustrated on Figure 6-3. The core zones are defined as follows:
• shallow zone: upper 20 ft of saturated zone
shallow-intermediate zone: from 930 ft MSL to 20 ft below water table
intermediate zone: 910 ft MSL to 930 ft MSL
deep zone: below 910 ft MSL
The Southern Plume is approximately 2400 ft long, and extends just beyond the southern site boundary.
6.1.3 Existing Remediation System
An interim remediation system is in place, and consists of three wells (see Figure 6-3), pumping a total
of 150 gpm:
one "Toe Well" that is located within the southern plume, at 50 gpm; and
two wells downgradient of the plume (the "LF wells"), at 100 gpm combined.
The extracted water is discharged to a POTW.
The two LF wells are associated with a landfill located downgradient from the Southern Plume
boundary. The LF wells are considered part of the interim system, because they provide a degree of
ultimate containment for the plume. However, allowing the plume to spread towards the LF wells is
considered to be a negative long-term result.
6-1
-------
To prevent further spreading of the Southern Plume, a long term pump-and-treat system has been
designed, with the addition of a "Core Well" within the southern plume (see Figure 6-3). The design of
the long-term system calls for 200 gpm total, as follows:
• one Toe well that is located within the southern plume, at 50 gpm;
• one Core well that is located within the southern plume, at 50 gpm; and
• two wells downgradient of the plume (the "LF wells"), at 100 gpm combined.
The intent is for the Toe well and Core well to prevent the Southern Plume from spreading beyond it's
present extent (rather than allowing the plume to flow towards the LF wells), and also to more effectively
contain the source areas (because the core well is located immediately downgradient from the source
areas). Under this scenario, the LF wells are not actually providing containment or cleanup for the
Southern Plume (in fact, pumping at the LF wells negatively impacts containment of the Southern
Plume). The original purpose of the LF wells is not related to remediation of the Southern Plume, and it
is hoped that pumping at the LF wells may be reduced (or even terminated) in the future.
6.1.4 Groundwater Flow Model
A three-dimensional, steady-state MODFLOW model was originally constructed in 1996. In addition, a
solute transport model was created with the MT3D code (Zheng, 1990). The groundwater models were
used to simulate various groundwater extraction scenarios. The current model has 6 layers, 77 rows, and
140 columns. Cell size varies from 25 by 25 ft to 200 x 200 ft. Layer 4 represents an alluvial sand layer,
and that layer has historically been evaluated with particle tracking to determine if containment is
achieved under a specific pumping scenario.
The solute transport model indicates the following:
• under the interim system, pumping will be required for more than 20 yrs to maintain
containment (due to the continuing source), and concentrations near site boundary will
be reduced to MCL levels within 10 to 20 yrs;
j
• under the long-term design, pumping will be required at the Core well for more than 20
yrs to maintain containment (due to the continuing source), but cleanup of the area
downgradient of the core well will be achieved in less than 10 yrs.
In each case, some component of pumping is anticipated for "a very long time", due to continuing
sources.
6.1.5 Goals of a Hydraulic Optimization Analysis
i
A screening analysis performed for this site (see Volume 1) suggests that little savings are likely to result
from a reduction in total pumping. In that screening analysis, a pumping rate reduction of 33 percent
was assumed. For this project, a hydraulic optimization analysis was nevertheless performed, to provide
additional examples of hydraulic optimization techniques. The goals of the hydraulic optimization
analysis are to:
(1) determine the extent to which pumping rates at the toe of the plume can actually be
reduced at this site, with and without the addition of new toe wells;
6-2
-------
(2) quantify the "containment efficiency" of the Core Well; and
(3) quantify the extent to which pumping required for containment can be reduced in
response to reduced pumping rates at the downgradient LF wells.
Mathematical formulations for achieving these goals are presented below. Then "mathematical optimal
solutions" for these formulations are presented, and discussed within the context of a "preferred
management solution".
6.2 COMPONENTS OF MATHEMATICAL FORMULATION
6.2.1 Representation of Plume Containment
A combination of head difference constraints, gradient constraints, and relative gradient constraints were
used to represent plume containment (see section 3.1.1 for an overview of the approach). For this site,
this was accomplished with 4 head difference constraints, 34 gradient constraints, and 17 relative
gradient constraints (see Figure 6-4). Along the southern boundary of the plume, constraints were applied
along a "smoothed" approximation of the plume boundary, rather than the actual plume boundary
(which has an irregular shape). Constraints were applied in layer 4 of the model, consistent with
previous particle tracking analyses used to assess the interim and final design system (capture in other
model layers was confirmed with particle tracking, external to the optimization algorithm).
6.2.2 Representation of Wells
Multi-aquifer wells:
The baseline scenario includes one Toe Well, one Core Well, and two LF wells. Based on the model
layers and the screened interval of the wells, each is a multi-aquifer well. In MODFLOW, the amount of
water discharged from a multi-aquifer well in each model layer is weighted by the relative transmissivity
of each layer at the specific grid block. Balance constraints were specified in MODMAN ( see section
3.1.2) to preserve the ratio of pumping between model layers for the multi-aquifer wells, as follows:
Well
LF Well (PW3)
LF Well (PW4)
Toe Well
Core Well
MODMAN Well Numbers
Ql (LayerS), Q2 (Layer 4)
Q3 (LayerS), Q4 (Layer 4)
Q5 (Layer 4), Q6 (Layer 6)
Q7 (LayerS), Q8 (Layer 4),
Q9 (LayerJD
Relationship
Ql - 0.44Q2 = 0 (i.e., Q1/Q2 = 0.44)
Q3 - 0.49Q4 = 0 (i.e., Q3/Q4 = 0.49)
Q5 - 1 .28Q6 = 0 (i.e., Q5/Q6 = 1 .28)
Q8-9.03Q7 = 0 (i.e., Q8/Q7 = 9.03)
08-1.3109 = 0 (i.e., Q8/Q9 = 1.31) ,
Some scenarios also considered nine additional well locations near the toe of the plume. These were also
multi-aquifer wells, assigned in model layers 4 and 6. Balance constraints were also specified in
MODMAN for these wells, to preserve the ratio of pumping between model layers. Based on
transmissivities in the model, the ratio of 1.28 calculated for the existing Toe Well was also appropriate
for these additional wells.
6-3
-------
New Well Locations Considered:
For some scenarios, up to nine additional Toe Well locations were considered. These locations are
illustrated on Figure 6-4, and were only placed in locations defined as "acceptable for wells" by the
installation. As previously discussed, these wells were assigned to model layers 4 and 6 (i.e., multi-
aquifer wells).
Well Rate Limits:
Many MODMAN formulations were solved to evaluate the Offutt site. For each formulation, some of
the well rates were "fixed". For instance, each of the LF wells might be fixed at 50 gpm for one
formulation, and at 40 gpm for the next formulation. Although this can be accomplished by altering the
MODMAN input file and re-executing MODMAN for each formulation, it is more efficiently performed
by simply adjusting the well rate bounds in the MPS file that was originally created by MODMAN (see
Appendix H).
For multi-aquifer wells, an additional calculation was made to determine the maximum rate allowed in
one specific model layer, based on the maximum rate allowed for the total well.
Example: LF Well (PW-3), max rate = 50 gpm
Well names in MODMAN: Q1 (Layer 1), Q2 (layer 2)
Well rate relationship: Q1/Q2 = 0.44 (i.e., Q1 = 0.44Q2)
Max rate for total well: Ql + Q2 < 50 gpm
Substitute for Q1: Q2 + 0.44Q2 £ 50 gpm
Determine limit for Ql6 Q2 £34.7 gpm
Limiting the Number of New Wells Selected:
In some hydraulic optimization scenarios where additional wells were considered, integer constraints
(see section 3.1.3) were specified, to allow the number of selected wells to be limited.
6.2.3 Objective Function
The objective function is "minimize total pumping in gpm". To achieve this, each pumping rate variable
was multiplied by an objective function coefficient of-0.005194. The value of the coefficient converts
from MODFLOW units (frVd) into gpm, and the negative value of the coefficient accounts for the fact
that pumping rates in MODFLOW are negative. By multiplying the negative MODFLOW rates by a
negative objective function coefficient, the use of the term "minimize" becomes straightforward for the
objective function.
6-4
-------
6.3 SOLUTIONS FOR MINIMIZING PUMPING AT THE TOE WELL
6.3.1 Core Well @ 50 gpm, LF Wells @ 100 gpm (Current Design)
The current system design assumes total pumping of 100 gpm at the LF wells, and assumes 50 gpm at
the Core Well. In the current design, the Toe Well pumps at 50 gpm. The purpose of this initial analysis
is to determine if pumping at the Toe Well can be reduced while containment is maintained, given the
assumed pumping at the LF wells and the Core Well.
The mathematical optimal solution for this case is very similar to the current design:
LF Wells (Fixed)
Core Well (Fixed)
Toe Well
Total rate
Current Design
(gpm)
100
50
50
200
Mathematical Optimal
Solution (gpm)
100
50
52
202
*Note: Rate at LF wells is combined rate at two wells, divided evenly
The rate at the Toe Well in the mathematical optimal solution is actually higher than in the current
design, which is caused by approximations in the constraints representing plume containment.
These results indicate that current system design is essentially optimal, given these well locations and the
assumed pumping rates for the LF wells and the Core Well.
6.3.2 Core Well @ 50 gpm, Vary Rate at LF Wells
The installation has indicated that, over time, the pumping rate at the LF wells (located downgradient of
the Southern plume) will likely decline. Such decisions may impact management options for containing
the Southern Plume.
These hydraulic optimization simulations are performed to determine the extent that pumping can be
reduced at the existing Toe Well, if pumping at the LF wells is reduced. In each case, the Core Well is
assumed to maintain a pumping rate of 50 gpm. The mathematical optimal solutions are presented
below:
6-5
-------
Fixed Rate at
LF Wells
(gpm)
100
80
60
40
20
0
Fixed Rate at
Core Well
(gpm)
50
50
50
50
50
50
Mathematical Optimal
Solution at Toe Well
(gpm)
52
47
41
36
31
25
Total Rate
(gpm)
202
177
151
126
101
75
*Note: Rate at LF wells is combined rate at two wells, divided evenly
The results indicate that pumping at the Toe Well can be reduced when pumping at the LF wells is
reduced. For each 20 gpm reduction in combined pumping at the LF wells, a 5 gpm reduction in Toe
Well pumping can be realized. This is extremely useful information from a management perspective.
Each 5 gpm reduction in Toe Well pumping reduces discharge costs by approximately $2000/yr.
Therefore, if pumping at the LF wells is reduced from 100 gpm to zero, a corresponding rate reduction of
approximately 25 gpm at the existing Toe Well is possible, with a savings of $10,000/yr.
6.3.3 Vary rate at Core Well, LF Wells @ 100 gpm
The current design includes 50 gpm at the Core Well, to accelerate mass removal. In general,
containment is most efficient when pumping wells remove water near the toe of the plume. However,
pumping in the core of the plume may also contribute to overall plume containment, such that the
addition of core pumping may permit pumping near the toe of the plume to be reduced, without
compromising plume containment. Hydraulic optimization can be used to quantify that relationship.
For these simulations, the LF wells are assumed to pump at total of 100 gpm (as in the baseline system).
The mathematical optimal solutions are as follows:
Fixed Rate at
Core Well (gpm)
50
40
30
20
10
0
Mathematical Optimal
Solution at Toe Well (gpm)
52
56
61
65
69
74
Total Pumping at Toe Well
Plus Core Well (gpm)
102
96
91
85
79
74
6-6
-------
The results indicate that for each increase of 10 gpm at the Core Well, required pumping at the Toe Well
is decreased by approximately 4.5 gpm. As discussed in Section 3.3.3, this can be expressed as
"containment efficiency" of the Core Well:
containment efficiency = 4.5/10.0 = 45%
The results provided by MODMAN allow additional annual costs associated with core well pumping to
be quantified. If the Core Well is not pumped, only 74 gpm at is required to contain the plume (in
addition to the 100 gprn at the LF wells). If the Core Well is pumped at 50 gpm, and the Toe well
pumping is reduced to 52 gpm, a net pumping increase of 28 gpm is incurred. This extra pumping
increases discharge costs by approximately $11,000/yr. This is a relatively small cost, considering that
accelerated mass removal (and potentially a reduced remediation timeframe for a portion of the plume) is
provided by the pumping at the Core Well.
6.3.4 Vary rate at Core Well, LF Wells @ 0 gpm
These simulations are nearly identical to those just presented, except that for these simulations the LF
wells are assumed to pump at total of 0 gpm as (instead of 100 gpm). This allows the impacts of the
Core Well pumping on total pumping rate to be assessed for conditions that might occur in the future.
The mathematical optimal solutions are as follows:
Fixed Rate at
Core Well (gpm)
50
40
30
20
10
0
Mathematical Optimal
Solution at Toe Well (gpm)
25
29
34
38
43
47
Total Pumping at Toe Well
Plus Core Well (gpm)
75
69
64
58
53
47
These results also indicate that for each increase of 10 gpm at the Core Well, required pumping at the
Toe Well is decreased by approximately 4.5 gpm (containment efficiency of 45%). Note these are the
same general results as determined for the case where the LF wells are pumping at 100 gpm. This
indicates that, in this case, that pumping at the LF wells does not impact the containment efficiency of
the Core Well.
6.4 CONSIDER NIKE ADDITIONAL WELL LOCATIONS AT PLUME TOE
6.4.1 Solutions for a Single Toe Well
The purpose of these simulations is to determine if a better location for a single Toe Well might have
been found if mathematical optimization had been performed during the original design process. In
6-7
-------
addition to the existing Toe Well, nine additional locations (referred to as NW-1 through NW-9) were
specified as potential well locations. These locations are illustrated in Figure 6.4, and were only placed
in locations defined as "acceptable for wells" by the installation. Integer constraints were specified to
limit the number of toe wells actively pumping to one (out of 10 potential locations including the
existing Toe Well).
Mathematical optimal solutions were determined for each of the following scenarios:
* Core Well = 50 gpm, LF wells =100 gpm (baseline scenario)
Core Well = 50 gpm, LF wells = 0 gpm
Core Well = 0 gpm, LF wells = 100 gpm
• Core Well = 0 gpm, LF wells = 0 gpm
The results are as follows:
Scenario
Core Well = 50 gpm
LF Wells = 100 gpm
Core Well = 50 gpm
LF Wells = 0gpm
Core Well = 0 gpm
LF Wells = 100 gpm
Core Well = 0 gpm
LW Wells = 0 gpm
Mathematical Optimal
Solution for Existing
Toe Well (gpm)
52
(Existing Toe Well)
25
(Existing Toe Well
74
(Existing Toe well)
47
(Existing Toe Well)
Mathematical Optimal
Solution For Any One of
the 10 Toe Wells (gpm)
38
(NW-4)
21
(NW-4)
74
(Existing Toe Well)
46
(NW-1)
Reduction in
Toe Pumping
Using Alternate Well
14 gpm
(28%)
4 gpm
(18%)
Ogpm
(0%)
1 gpm
(1%)
*note: percentage reductions in last column calculated with non-rounded values
These results indicate that no single Toe Well location is best for all scenarios. For scenarios without
pumping in the core of the plume, the location of the existing Toe Well is essentially optimal. However,
for cases where there is pumping at the Core Well, a different location (NW-4) is optimal, with a
potential reduction in pumping near the toe of the plume of approximately 4 to 14 gpm (18-28%).
6.4.2 Solutions for Multiple Toe Wells
Figure 6-5 illustrates a variety of mathematical optimal solutions for each of the following scenarios:
Core Well = 50 gpm, LF wells =100 gpm
Core Well = 50 gpm, LF wells = 0 gpm
Core Well = 0 gpm, LF wells = 100 gpm
• Core Well = 0 gpm, LF wells = 0 gpm
These figures present the optimal total rate at the selected Toe Wells for solutions with 1 to 5 Toe wells.
Note that there are diminishing returns (in terms of pumping rate reduction) as more Toe Wells are
allowed.
6-8
-------
For scenarios with 50 gpm at the Core Well, there is little benefit to increasing the number of wells. For
instance, the maximum reduction in total Toe Well pumping afforded by adding one well is
approximately 5 gpm, which translates to a savings in discharge costs of approximately $2,000/yr. This
does not compare favorably with the up-front costs of installing a new well (approximately $40,000).
For scenarios without pumping at the Core Well, greater reductions in total Toe Well pumping are
afforded by adding a second well. Potential pumpage reductions of approximately 15 to 20 gpm are
possible by adding a second well, which translates to a savings in discharge costs of $6,000 to $8,000/yr.
However, this yields marginal benefits when one considers the up-front costs of installing a new well
(approximately $40,000).
6.5 DISCUSSION & PREFERRED MANAGEMENT SOLUTION
For the current system design (a Core Well at 50 gpm, a Toe Well at 50 gpm, and two dowgradient LF
wells at a combined rate of 100 gpm), the hydraulic optimization results indicate that the pumping rate at
the Toe Well is essentially optimal for achieving containment (given the fixed rates at the other wells).
This might be expected, because the benefits of hydraulic optimization are diminished in cases where
only a few well locations are evaluated. In those cases, a good modeler may achieve near-optimal (or
optimal) solutions by performing trial-and-error simulations.
The existing Toe Well location plus nine additional Toe Well locations were considered with hydraulic
optimization, in conjunction with various combinations of well rates assigned for the Core Well and the
LF wells. First, only one Toe Well location was allowed. For scenarios without pumping in the core of
the plume, the location of the existing Toe Well was essentially optimal. However, for cases with
pumping at the Core Well, a different location was optimal, with a potential reduction in pumping near
the toe of the plume of approximately 4 to 14 gpm (18-28%). Had hydraulic optimization been
performed during the design process, a different Toe Well location may have been selected on the basis
of these results. However, the annual savings in discharge costs that would have resulted would have
been relatively minor (less than $6K/yr). When selection of two Toe Well locations was allowed, results
indicated that potential pumping rate reductions (and corresponding reductions in discharge costs) would
be marginal, relative to the costs of installing a new well.
Hydraulic optimization allows sensitivity of mathematical optimal solutions to be quantified with respect
to other non-managed stresses. In this case, the pumping rates at the LF wells are managed separately
from the plume management wells, yet increased pumping at the LF wells negatively impacts the ability
of plume management wells to contain the plume. Results of the hydraulic optimization analyses
indicate that, for each 20 gpm reduction at the LF wells, a corresponding reduction of 5 gpm can be
implemented at the Toe Well. This is useful information from a management perspective.
The containment efficiency of the Core Well was quantified (45 percent). For each 10 gpm increase at
the Core Well, containment can be maintained with a corresponding reduction of 4.5 gpm at the Toe
Well. For this site, core zone pumping yields benefits (source area containment, allowing potential
cleanup of downgradient portions of the plume). The additional annual cost of operating a core well
(due to increased total pumping required for containment) is small at this site, and a strategy that
includes a Core Wells seems preferable to a "containment-only" strategy.
The preferred management strategy at this site is to implement the current system design. Little or no
benefit would be achieved by adding an additional Toe Well. However, if pumping rates at the LF wells
6-9
-------
are reduced in the future, corresponding rate reductions can be made at the existing Toe Well (for each
20 gpm reduction at the LF wells, a corresponding reduction of 5 gpm can be implemented at the Toe
Well).
These conclusions are consistent with the screening analysis performed in Volume 1, which indicated
that little potential costs savings would result from reductions in pumping rate of as much as 33 percent.
The reason is that, at this site, annual O&M costs directly related to pumping rates are quite low
(approximately $400/gpm/yr). Therefore, even when improved pumping rate solutions are obtained with
hydraulic optimization, the cost benefits are marginal. Nevertheless, the strategies for applying
hydraulic optimization demonstrated for this site can be applied at other sites, particularly where net cost
benefits are likely to be greater.
6-10
-------
7.0 DISCUSSION AND CONCLUSIONS
Hydraulic optimization couples simulations of groundwater flow with optimization techniques such as
linear and mixed-integer programming. Hydraulic optimization allows all potential combinations of well
rates at specific locations to be mathematically evaluated with respect to an objective function (e.g.,
minimize total pumping) and series of constraints (e.g., the plume must be contained). The hydraulic
optimization code quickly determines the best set of well rates, such that the objective function is
minimized and all constraints are satisfied.
For this document, the term "optimization" for pump-and-treat design was refined as follows:
Mathematical Optimal Solution. The bsst solution, determined with a mathematical
optimization technique, for a specific mathematical formulation (defined by a specific objective
function and set of constraints); and
Preferred Management Solution. A preferred management strategy based on a discrete set of
mathematical optimal solutions, as well as on factors (e.g., costs, risks, uncertainties,
impediments to change) not explicitly considered in those mathematical solutions.
For this demonstration project, hydraulic optimization was applied at three sites with existing pump-and-
treat systems. For each case study, many mathematical formulations were developed, and many
mathematical optimal solutions were determined. For each site, a preferred management solution was
then suggested. The three sites can be summarized as follows:
Site
Kentucky
Tooele
Offutt
Existing
Pumping Rate
Moderate
High
Low
Cost
Per gpm
High
Low
Low
Potential Savings from
System Modification
SMillions
SMillions
Little or None
At two of the sites (Kentucky and Tooele), pumping solutions were obtained that have the potential to
yield millions of dollars of savings, relative to costs associated with the current pumping rates.
In cases where only a few well locations are considered, the benefits of hydraulic optimization are
diminished. In those cases, a good modeler may achieve near-optimal (or optimal) solutions by
performing trial-and-error simulations. This was demonstrated by the Offutt case study. However, as
the number of potential well locations increases, it becomes more likely that hydraulic optimization will
yield improved pumping solutions, relative to a trial-and-error approach. This was demonstrated by
potential pumping rate reductions suggested by the hydraulic optimization results for the Kentucky and
Tooele case studies.
7-1
-------
These case studies illustrate a variety of strategies for evaluating pump-and-treat designs with hydraulic
optimization. Components of mathematical formulations demonstrated with these case studies include:
Item Demonstrated
objective function minimizes total pumping
objective function minimises cost
multi-aquifer wells
plume containment with head limits
plume containment with head difference limits
plume containment with relative gradient limits
integer constraints (limiting # of wells selected)
sensitivity of solutions to # of wells selected
scenario for "containment only"
scenarios with core zone extraction
"containment efficiency" of core zone wells evaluated
multiple target containment zones
reinjection of treated water
sensitivity of solutions to conservatism of constraints
sensitivity of solution to non-managed stresses
Kentucky
X
X
X
X
X
X
X
X
Tooele
X
X
X
X
X
X
X
X
X
X
X
Offutt
X
X
X
X
X
X
X
X
X
X
For each of the three case studies, an analysis was performed to illustrate the sensitivity of mathematical
optimal solutions to limits placed on the number of wells. For each of the three case studies, an analysis
was also performed to evaluate changes in the mathematical optimal solution when new well locations
were considered. For the Kentucky site, an analysis was performed to illustrate the sensitivity of the
mathematical optimal solution to conservatism in the constraints representing plume containment. All of
these types of analyses can be efficiently conducted with hydraulic optimization techniques. In most
cases, these types of analyses are difficult (if not impossible) to comprehensively perform with a trial-
and-error approach. It is important to note that the case studies presented in this report are for facilities
with existing pump-and-treat systems. Mathematical optimization techniques can also be applied
during initial system design, to generate improved solutions versus a trial-and-error approach.
Hydraulic optimization cannot incorporate simulations of contaminant concentrations or cleanup time.
For that reason, hydraulic optimization is generally most applicable to problems where plume
containment is the prominent goal. However, two of the case studies (Kentucky and Offutt) illustrate
that hydraulic optimization can be used to determine the "containment efficiency" of wells placed in the
core zone of a plume. This type of analysis can be performed to compare a "containment only" strategy
to a strategy with additional core zone wells (to accelerate mass removal). The "containment
efficiency" of the core zone wells, determined with hydraulic optimization, quantifies potential pumping
7-2
-------
reductions at containment wells when the core zone pumping is added, such that containment is
maintained. These pumping reductions (also difficult or impossible to determine with a trial-and-error
approach) can potentially yield considerable savings, as demonstrated for the Kentucky site.
It is very important to distinguish the benefits of applying hydraulic optimization technology from other
benefits that may be achieved simply by "re-visiting" an existing pump-and-treat design. In some cases,
the underlying benefits associated with a system modification may be primarily due to a modified
conceptual strategy. For instance, the Tooele case study includes analyses for different target
containment zones. The potential pumping reductions and cost savings that result from a change to a
smaller target containment zone primarily result from the change in conceptual strategy. The benefit
provided by hydraulic optimization is that it allows mathematical optimal solutions for each conceptual
strategy to be efficiently calculated and compared (whereas good solutions for each conceptual strategy
may be difficult or impossible to achieve with trial-and-error).
The case studies demonstrate that there are a large variety of objective functions, constraints, and
application strategies potentially available within the context of hydraulic optimization. Therefore, the
development of a "preferred management solution" for a specific site depends not only on the
availability of hydraulic optimization technology, but also on the ability to formulate meaningful
mathematical formulations. That ability is a function of the skill and experience of the individuals
performing the work, as well as the quality of site-specific information available to them.
These case studies demonstrate ways in which hydraulic optimization techniques can be applied to
evaluate pump-and-treat designs. The types of analyses performed for these three sites can be applied to
a wide variety of sites where pump-and-treat systems currently exist or are being considered. However,
the results of any particular hydraulic optimization analysis are highly site-specific, and are difficult to
generalize. For instance, a hydraulic optimization analysis at one site may indicate that the installation
of new wells yields little benefit. That result cannot be generally applied to all sites. Rather, a site-
specific analysis for each site is required. A spreadsheet-based screening analysis (presented in Volume
1 of this report) can be used to quickly determine if significant cost savings are likely to be achieved at a
site by reducing total pumping rate. Those sites are good candidates for a hydraulic optimization
analysis.
7-3
-------
-------
8.0 REFERENCES AND DOCUMENTS PROVIDED BY SITES
Colarullo, S.J., M. Heidari, and T. Maddock, III, 1984. Identification of an optimal groun dwater
strategy in a contaminated aquifer. Water Resources Bulletin, 20(5): 747-760.
Gorelick, S.M., 1987. Sensitivity analysis of optimal ground-water contaminant capture curves: spatial
variability and robust solutions, in Solving Groundwater Problems With Models, Nat. Water Well
Assoc., Feb. 10-12, 133-146.
Gorelick, S.M., and BJ. Wagner, 1986. Evaluating strategies for groundwater contaminant plume
stabilization and removal, selected papers in the Hydrologic Sciences, U.S. Geological Survey, Water-
Supply Series 2290, 81-89.
Dames & Moore, 1997. Plantwide Corrective Action Program, Evaluation of Effectiveness, Second Half
1997, Kentucky Site (December 30, 1997).
Dames & Moore (date unknown). Isoconcentration Maps, September 1996 (Draft).
Gorelick, S.M., R.A. Freeze, D. Donohue, and J.F. Keely, 1993. Groundwater Contamination: Optimal
Capture and Containment, Lewis Publishers, 385 p.
Greenwald, R.M., 1998a. Documentation and User's Guide: MODMAN, an Optimization Module for
MODFLOW, Version 4.0, HSI GeoTrans, Freehold, New Jersey.
Greenwald, R.M., 1998b. MODMAN4.0 Windows-Based Preprocessor, Preprocessor Version 1.0, HSI
GeoTrans, Freehold, New Jersey.
Harbaugh, A.W. and McDonald, M.G., 1996a. User's documentation for MODFLOW-96, An update to
the U.S. Geological Survey modular finite-difference ground-water flow model, U.S. Geological Survey
Open-File Report 96-485, 56 p.
Harbaugh, A.W. and McDonald, M.G., 1996b. Programmer's documentation for MODFLOW-96, An
update to the U.S. Geological Survey modular finite-difference ground-water flow model, U.S.
Geological Survey Open-File Report 96-486, 220 p.
Kleinfelder, Inc. 1998. Draft, Southeastern Boundary Groundwater Investigation, Report of Findings,
Tooele Army Depot (TEAD, Tooele, Utah, Volume 1 (Draft Report, February 13, 1998).
Lefkoff, L.J., and S.M. Gorelick, 1987. AQMAN: Linear and quadratic programming matrix generator
using two-dimensional groundwater flow simulation for aquifer management modeling, U.S. Geological
Survey, Water Resources Investigations Report, 87-4061, 164 pp.
Lefkoff, L.J., and S.M. Gorelick, 1986. Design and cost of rapid aquifer restoration systems using flow
simulation and quadratic programming, Ground Water, 24(6): 777-790.
Lindo Systems, 1996. LINDO Users Manual, Lindo Systems, Chicago, Illinois.
8-1
-------
McDonald, M.G., and A.W. Harbaugh, 1988. A modular three-dimensional finite-difference
groundwaterflow model, U.S. Geological Survey, Techniques of Water-Resources Investigations Book
6, Chapter Al. •
Trescott, P.C., et al., 1976. Finite-difference model for aquifer simulation in two-dimensions with results
of numerical experiments, U.S. Geological Survey, Techniques for Water Resources Investigations Book
7, Chapter Cl, 116-0118.
Woodward-Clyde, 1997. Draft Feasibility Study, Hardfill 2 Composite Site (SS-40), Offutt Air Force
Base, Nebraska (Draft Report, August 28, 1997)
Woodward Clyde, 1998. Pre-Draft, Pump Cycling Report, Landfill 4, Offutt Air Force Base, Nebraska
(Pre-Draft Report, August 1998).
Zheng, Chunmiao, 1990. A modular Three-Dimensional Transport Model for Simulation ofAdvection,
Dispersion, and Chemical Reactions of Contaminants in Groundwater Systems. S.S. Papadopulos and
Associates, Inc.
8-2
-------
FIGURES
-------
-------
H012009A.DWG
PROPERTY BOUNDARY
SCALE IN FEET
ADAPTED FROM DAMES & MOORE (1997)
HSI
GEOTRANS
Site location map, Kentucky.
Figure 4—1
-------
-------
H012010A.DWG
SCALE IN FEET
NOTE: REMEDIATION WELLS ARE ILLUSTRATED ON THIS FIGURE. ALL WATER LEVEL DATA POINTS NOT SHOWN.
Figure 4-2. Groundwater elevation contours, Kentucky.
WATER LEVEL
ELEVATION (FT MSL)
PROPERTY BOUNDARY
BW (ORIGINAL DESIGN)
BW (SUBSEQUENT TO
ORIGINAL DESIGN)
SW
OW
ADAPTED FROM DAMES & MOORE (1997),
JULY 1997 CONDITIONS
HSI
GEOTRANS
-------
-------
H012011A.DWG
SCALE IN FEET
Figure 4-3. EDC concentrations and current remediation wells, Kentucky.
EDC CONCENTRATION
CONTOUR (ug/L)
PROPERTY BOUNDARY
BW (ORIGINAL DESIGN)
• BW (SUBSEQUENT TO
ORIGINAL DESIGN)
-4- sw
A OW
CONC. CONTOURS PREPARED BY DAMES
& MOORE, SEPTEMBER' 1996 CONDITIONS
HSI
GEOTRANS
-------
-------
H012012A.DWG
100 BENZENE CONCENTRATION
CONTOUR (ug/L)
—--— PROPERTY BOUNDARY
•*• BW (ORIGINAL DESIGN)
• BW (SUBSEQUENT TO
ORIGINAL DESIGN)
4" SW
A OW
SCALE IN FEET
Figure 4-4. Benzene concentrations and current remediation wells, Kentucky.
CONC. CONTOURS PREPARED BY DAMES
& MOORE, SEPTEMBER 1996 CONDITIONS
HSI
GEOTRANS
* TCTIA TECH COUPtHT
-------
-------
H012016A.DWG
BW-1931
BW-19.32
BW-.1933
BV^-1934
BW-1948
BW-1935
1949
BW-1936
BW-1937
BW-1938
BW-1939
BW-1940
BW-1953
BW-1928
BW-1929
BW-1930^- QW-1923
^-*-fr>t
SW-1925/ / V /
LEGEND
PROPERTY BOUNDARY
BW (ORIGINAL DESIGN)
BW-1950
BW-1947
BW-1952
BW (SUBSEQUENT TO ORIGINAL DESIGN)
SW /
HEAD LIMIT CONSTRAINT
POTENTIAL ADDITIONAL WELL
SCALE IN FEET
HSI
GEOTRANS
Figure 4-5. Constraint locations and potential additional wells, Kentucky.
-------
-------
1
O
I
GREAT SALT
'LAKE1'
TOOELEARMY
DEPOT (TEAD)
PROVO
SCALE IN MILES
ADAPTED FROM KLEINFELDER (1998;
Figure 5—1. Site location map, Tooele.
HSI
GEOTRANS
-------
-------
o
o
o
X
INDUSTRIAL
WASTE
LAGOON
INDUSTRIAL
AREA
LEGEND
4480-
Figure 5-2.
DEEP-TCE CONTOUR
SHALLOW TCE CONTOUR
(DASHED WHERE INFERRED)
BEDROCK BLOCK AS IMPLEMENTED
IN MODEL
GROUNDWATER ELEVATION CONTOUR
Groundwater elevation contours,
Tooele.
0
3000
SCALE IN FEET
6000
WATER LEVELS, MARCH 1997, TAKEN
FROM KLE1NFELDER (1998)
HSI
GEOTRANS
-------
-------
o
o
CN
-3-
1-10
I-5
+1-2
1-1
D
INDUSTRIAL
WASTE
LAGOON
LEGEND
I-4 INJECTION WELL
E-4 EXTRACTION WELL
n EX. WELL IN LAYER 1
-t EX. WELL IN LAYER 2
* EX. WELL IN LAYERS 1 & 2
+ EX. WELL IN LAYERS 1, 2 & 3
INDUSTRIAL
AREA
DEEP TCE CONTOUR (ug/L or ppb)
SHALLOW TCE CONTOUR (ug/L or ppb)
(DASHED WHERE INFERRED)
UN LINED DITCH
3000
6000
BEDROCK BLOCK AS
IMPLEMENTED IN MODEL
SCALE IN FEET
ADAPTED FROM KLEINFELDER (1998)
Figure 5—3. TCE concentrations and current
remediation wells, Tooele.
HSI
GEOTRANS
-------
-------
o
o
(N
Hfrl-2
1-1
D
INDUSTRIAL
WASTE
LAGOON
LEGEND
I -4 INJECTION WELL
E-4 EXTRACTION WELL
a EX. WELL IN LAYER 1
-$- EX. WELL IN LAYER 2
-*• EX. WELL IN LAYERS 1
INDUSTRIAL
AREA
DEEP TCE CONTOUR (ug/L or ppb)
SHALLOW TCE CONTOUR (ug/L or ppb)
(DASHED WHERE INFERRED)
UNLINED DITCH
A POTENTIAL SHALLOW WELL
• POTENTIAL DEEP WELL
t HEAD DIFFERENCE
T CONSTRAINT
* RELATIVE GRADIENT
^ CONSTRAINT
0
& 2
EX. WELL IN LAYERS 1, 2 & 3
BEDROCK BLOCK AS
IMPLEMENTED IN MODEL
3000
SCALE IN FEET
6000
Figure 5—4.
Contraint locations and potential
additional wells, shallow 5—ppb plume,
Tooele.
HSI
GEOTRANS
-------
-------
o
S
o
o
01
o
I
INDUSTRIAL
WASTE
LAGOON
LEGEND
1-4 INJECTION WELL
E-4 EXTRACTION WELL
n EX. WELL IN LAYER 1
-t EX. WELL IN LAYER 2
+ EX. WELL IN LAYERS 1
INDUSTRIAL
AREA
— DEEP TCE CONTOUR (ug/L or ppb)
SHALLOW TCE CONTOUR (ug/L or ppb)
(DASHED WHERE INFERRED)
==UNLINED DITCH
A POTENTIAL SHALLOW WELL
• POTENTIAL DEEP WELL
t HEAD DIFFERENCE
• CONSTRAINT
A RELATIVE GRADIENT
^ CONSTRAINT
0
& 2
EX. WELL IN LAYERS 1. 2 & 3
-—BEDROCK BLOCK AS
IMPLEMENTED IN MODEL
3000
SCALE IN FEET
6000
Figure 5—5.
Contraint locations and potential
additional wells, deep 5—ppb plume,
Tooele.
HSI
GEOTRANS
-------
:„; ,:,[:
-------
o
o
1-10
•*•
-,1-12
+1-2
1-1
a
INDUSTRIAL
WASTE
LAGOON
LEGEND
1-4 INJECTION WELL
E—4 EXTRACTION WELL
n EX. WELL IN LAYER 1
-$- EX. WELL IN LAYER 2
•*• EX. WELL IN LAYERS 1
INDUSTRIAL
AREA
— DEEP TCE CONTOUR (ug/L or ppb)
SHALLOW TCE CONTOUR (ug/L or ppb)
(DASHED WHERE INFERRED)
= UNLINED DITCH
POTENTIAL SHALLOW WELL
POTENTIAL DEEP WELL
HEAD DIFFERENCE
CONSTRAINT
RELATIVE GRADIENT
CONSTRAINT
0
& 2
EX. WELL IN LAYERS 1, 2 & 3
BEDROCK BLOCK AS
IMPLEMENTED IN MODEL
3000
SCALE IN FEET
6000
Figure 5—6.
Contraint locations and potential
additional wells, shallow 20—ppb
plume, Tooele.
HSI
GEOTRANS
-------
ii .Jit:.,I ,',
I'1!'*:?
!'"":!•'' 1Ti; I"':'!!!-11
-------
1
s
o
8
o
X
LEGEND
1-4 INJECTION WELL
E-4 EXTRACTION WELL
a EX. WELL IN LAYER 1
•*• EX. WELL IN LAYER 2
* EX. WELL IN LAYERS 1 & 2 ~
•+- EX. WELL IN LAYERS 1, 2 & 3
INDUSTRIAL
AREA
DEEP TCE CONTOUR (ug/L or ppb)
SHALLOW TCE CONTOUR (ug/L or ppb)
(DASHED WHERE INFERRED)
= UNLINED DITCH
-BEDROCK BLOCK AS
IMPLEMENTED IN MODEL
A POTENTIAL SHALLOW WELL
• POTENTIAL DEEP WELL
*. HEAD DIFFERENCE
T CONSTRAINT
-K. RELATIVE GRADIENT
^ CONSTRAINT
1000 2000
•J
SCALE IN FEET
Figure 5—7.
Contraint locations and potential
additional wells, 50—ppb plume,
Tooele.
HSI
GEOTRANS
-------
I
-------
30000
25000—
20000—
15000—
10000—
5000—
Figure 5-8: Shallow Particles, Layer 1 heads, Pumping on April 6, 1J98
(~7460 gpm, 15 existing wells)
I L
A Injection Well
• Well Layer 1
o Well Layer 2
5000
10000
I
15000
A "+" symbol indicates that a particle starting at that location is captured by one of the remediation
wells, based on particle tracking with MODPA TH. Shallow particles originate half-way down in layer 1.
-------
-------
3001
25000—
20000—
1500i
10000—
5000—
Figure 5-9: Deep Particles, Layer 1 heads, Pumping on April 6, 1SJ 8
(-7460 gpm, 15 existing wells)
++•*-+++•
++!±!l±!±±±±±±±±±±±±±±
5000
10000
r
15000
A Injection Well
• Well Layer 1
o Well Layer 2
A "+" symbol indicates that a particle starting at that location is captured by one of the remediation
wells, based on particle tracking with MODPATH. Deep particles originate half-way down in layer 2.
-------
-------
3000&
25000—
20000—
15001
10000—
5000—
Figure 5-10: Shallow Particles, Contain Shallow & Deep 5-ppb Plu.ne
(4163 gpm, 14 new wells, 3 existing wells)
A Injection Well
• Well Layer 1
o Well Layer 2
++++H-+++++++++++++-H"*-
+4H-+t++++++-H-+-M~H-H-H
-i-H-++-'-+'M-'-t-n-+++ll-*-'"M-
•H-++-H-+++++-H-++-H-+-H-+++++++H-+-H'
-------
5000
10000
15000
A "+" symbol indicates that a particle starting at that location is captured by one of the remediation
wells, based on particle tracking with MODPATH. Shallow particles originate half-way down in layer 1.
-------
-------
30000
25000—
20000—
15000—1
10000—
5000—
Figure 5-11: Deep Particles, Contain Shallow & Deep 5-ppb Plur.ie
(4163 gpm, 14 new wells, 3 existing wells)
5000
10000
15000
A Injection Well
• Well Layer 1
o Well Layer 2
A "+" sy/nJbo/ indicates that a particle starting at that location is captured by one of the remediation
wells, based on particle tracking with MODPA TH. Deep particles originate half-way down in layer 2.
-------
-------
3000C
25000—
20000—
15000—
10000—
5000—
Figure 5-12: Shallow Particles, Contain Shallow 5-ppb Plume
(2622 gpm, 7 new wells, 2 existing wells)
I L
A Injection Well
• Well Layer 1
o Well Layer 2
5000
10000
15000
A '*" symbol indicates that a particle starting at that location is captured by one of the remediation
wells, based on particle tracking with MODPATH. Shallow particles originate half-way down in layer 1.
-------
-------
30000— -
25000—
20000—
15000—
10000—
5000—
Figure 5-13: Deep Particles, Contain Shallow 5-ppb Plume
(2622 gpm, 7 new wells, 2 existing wells)
444-H-+4-H-i-+4-4-4-4-H-H-i-
K+++++-H-+H-+-M-H-H-+
+-H-H-H"H"H"H-M-+ttt
++++++ -H-++++++++++
++++++++++++++++t+
~-
-+++++++-H-
-+++++++-»-t t
+++++-M-+++ •*-
••
A Injection Well
• Well Layer 1
O Well Layer 2
5000
10000
15000
A "+" symbol indicates that a particle starting at that location is captured by one of the remediation
wells, based on particle tracking with MODPATH. Deep particles originate half-way down in layer 2.
-------
-------
14000—
12000—
10000—
20I
Figure 5-14: Shallow Particles, Contain Shallow 50-ppb Plume
(1124 gpm, 3 new wells, 0 existing wells)
A Injection Well
• Well Layer 1
o Well Layer 2
2000
4000
6000
8000
10000
A "+" symbol indicates that a particle starting at that location is captured by one of the remediation
wells, based on particle tracking with MODPATH. Shallow particles originate half-way down in layer 1.
-------
-------
Figure 5-15: Deep Particles, Contain Shallow 50-ppb Plume
(1124 gpm, 3 new wells, 0 existing wells)
14000—
12000—
10000—
8000—
6000—
4000—
2000—
A Injection Well
• Well Layer 1
o Well Layer 2
2000
4000
6000
8000
10000
A "+" symbol indicates that a particle starting at that location is captured by one of the remediation
wells, based on particle tracking with MODPATH. Deep particles originate half-way down in layer 2.
-------
-------
Figure 5-16: Shallow Particles, Contain Shallow 20-ppb Plume
(1377 gpm, 2 new wells, 1 existing well)
30000— -
25000—
20000—
15001
10000—
5000—
+++++++4:+
++++-t-++++4-
++++-H-4-+++
•»-•<-+++ 4-++++
A Injection Well
• Well Layer 1
O Well Layer 2
5000
10000
15000
A "+" symbol indicates that a particle starting at that location is captured by one of the remediation
wells, based on particle tracking with MQDPATH. Shallow particles originate half-way down in layer 1.
-------
-------
30000
25000-
20000-
15001
10000—
5000—
Figure 5-17: Deep Particles, Contain Shallow 20-ppb Plum e
(1377 gpm, 2 new wells, 1 existing well)
A Injection Well
• Well Layer 1
o Well Layer 2
5000
10000
15000
A "+" symbol indicates that a particle starting at that location is captured by one of the remediation
wells, based on particle tracking with MODPATH. Deep particles originate half-way down in layer 2.
-------
-------
Figure 5-18-. Shallow Particles, Contain Shallow 20-ppb Plume, & 500 gpm for De jp 20-ppb plume
30000
25000—
20000—
15000—
10000—
5000—
(1573 gpm, 3 new wells, 1 existing well)
I L
A Injection Well
• Well Layer 1
o Well Layer 2
4- -t"t"J-++-M~fH-+^
+ ++++++++++-J-
+ +++++++++++
+++++++++f+
+++++++++£+
++4-+++tt4.++
•H-++++4"i-+++
•i-t"l-++++++++
•!-+++++++++•)-
+ 4.+-i-+4:+++++^
+ -J-H-++++-J-+-H-
+ -t-++++++-i"|-++
+++-{•+++"(•++
+ ++-f + ++-T"*"J-
+-t-4-++++++++
4-++++++4-H-+
5000
10000
15000
A "+* symbol indicates that a particle starting at that location is captured by one of the remediation
wells, based on particle tracking with MODPA TH. Shallow particles originate half-way down in layer 1.
-------
-------
Figure 5-19: Deep Particles, Contain Shallow 20-ppb Plume, & 500 gpm for Deep 20-ppb plume
(1573 gpm, 3 new wells, 1 existing well)
30000
25000—
20000—
15001
10000—
5000—
ffK if:
MTI will!
HH JttHttll
A Injection Well
• Well Layer 1
O Well Layer 2
5000
10000
15000
A "+" symbo/ indicates that a part/c/e starting at that location is captured by one of the remediation
wells, based on particle tracking with MODPATH. Deep particles originate half-way down in layer 2.
-------
-------
Figure 5-20: Shallow Particles, Contain Shallow 20-ppb & 50-ppb Plumes, & 500 gpi.i for Deep 20-ppb plume
(2620 gpm, 6 new wells, 0 existing wells)
I . I L
A Injection Well
• Well Layer 1
O Well Layer 2
30000—
25000—
20000—
15000—
10000—
5000—
++++ ,
+++++•*•+++•!•++-M-+-H-H-+
+++++++-t"H-++++++++++
+++++++++++4- 4-+++++++
5000
10000
15000
A "+" symbol indicates that a particle starting at that location is captured by one of the remediation
wells, based on particle tracking with MODPATH. Shallow particles originate half-way down in layer 1.
-------
-------
Figure 5-21: Deep Particles, Contain Shallow 20-ppb & 50-ppb Plumes, & 500 gpm "or Deep 20-ppb plume
(2620 gpm, 6 new wells, 0 existing wells )
30000
25000—
20000—
15001
10000—
5000—
A Injection Well
• Well Layer 1
o Well Layer 2
5000
10000
15000
A "+" symbol indicates that a particle starting at that location is captured by one of the remediation
wells, based on particle tracking with MODPATH. Deep particles originate half-way down in layer 2.
-------
-------
o
s
o
X
NEBRASKA
Enlarged Map Area
BELLEVUE
IOWA
10
SCALE IN MILES
20
ADAPTED FROM WOODWARD-CLYDE (1998)
Figure 6-1. Site location map, Offutt.
HSI
GEOTRANS
-------
I
-------
H012014A.DWG
957-
LEGEND
WATER LEVEL
ELEVATION (FT MSL)
PROPERTY BOUNDARY
0
500
1000
SCALE IN FEET
ADAPTED FROM WOODWARD-CLYDE (1997)
-N-
Figure 6-2. Groundwater elevation contours, Offutt.
HSI
GEOTRANS
-------
I
-------
H012015A.DWG
LEGEND
SHALLOW CORE ZONE:
TARGET VOCs > 1000 ug/L
SHALLOW-INTERMEDIATE CORE ZONE:
TARGET VOCs > 1000 ug/L
INTERMEDIATE CORE ZONE:
TARGET VOCs > 1000 ug/L
DEEP CORE ZONE:
TARGET VOCs > 1000 ug/L
SOUTHERN PLUME
PROPERTY BOUNDARY
0
500
1000
SCALE IN FEET
ADAPTED FROM WOODWARD-CLYDE (1997)
Figure 6-3. Southern plume and current remediation wells, Offutt.
HSI
GEOTRANS
-------
-------
H012017A.DWG
CORE
WELL
^LEGEND
POTENTIAL ADDITIONAL WELL
HEAD DIFFERENCE
CONSTRAINT
TOE
WELL
RELATIVE GRADIENT
CONSTRAINT
SHALLOW CORE ZONE:
TARGET VOCs > 1000 ug/L
SHALLOW-INTERMEDIATE CORE ZONE:
TARGET VOCs > 1000 ug/L
INTERMEDIATE CORE ZONE:
TARGET VOCs > 1000 ug/L
DEEP CORE ZONE:
TARGET VOCs > 1000 ug/L
SOUTHERN PLUME
PROPERTY BOUNDARY
SCALE IN FEET
Figure 6-4. Constraint locations and potential additional wells, Offutt
HSI
GEOTRANS
-------
-------
Mathematical optimal solution
at toe wells (gpm)
N
O
O -
10 -
o
s
a
(D
Oi
CO
o
32.35
8.77|
8.77 I
8.77 i
^ cn o> •*•! OQ
o o o o o
46
/
f
7
/
i
i
i
r
• 44
.4
/
^51.7
..15
.46
.46
>. 73.73 >
S W
_». v>
0 C
o (i>
<£ o
*.%
2il
H tt
• 0
*z
tt
TI TI
II II
->• O
° §
{
i
i
1
1
/
r
f. 30.07
29.33
i 29.33
7.50
32
tl
r~ r™
•n -n
u u
0 (Q
O T;J
(Q 3
•a
3
Assume i
10 Pol
I«
^1
o *.
< o
•C O
O JJ
2.
"si
s'
C/l
I
3
e
5
•s
JT
I
i
-------
-------
TABLES
-------
-------
Table 4-1. Current system, Kentucky.
Screening Analysis
Site: Kentucky
Scenario: Current System
Discount Rate: 0.05
O&M Costs
-Electric
-Materials (pH adjustment)
-Maintenance
-Discharge Fees
-Annual O&M
-Analytical
-Steam
-Other 2
-Other 3
losts of Analysis
-Flow Modeling
-Transport Modeling
-Optimization
-Other 1
System Modification Costs
-Engineering Desiqn
-Regulatory Process
-New wells/pipes/equipment
-Increased Monitoring
-Other 1
-Other 2
-Other 3
Note: All costs are in present-day d
The PV function in Microsoft B
Up-Front Costs
$0
$0
$0
SO
SO
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
so
so
$0
so
so
$0
Annual Costs # Years Costs
$200,000 20 $2,617,064
$100,000 20 $1,308,532
$50,000 20 $654,266
$0 20 $0
$250,000 20 $3,271,330
$0 20 $0
$1,200,000 20 $15,702,385
$0 20 i
$0 20 '
U
>u
$0 ;
• $0 !
>0
iO
$0 SO
$0 $0
$0 f
>u
$0 !SU
$0 r
$0 '
$0 '
.U
iO
iU
$0 $0
$0 $0
Total Costs
$2,617,064
$1,308,532
$654,266
$0
$3,271,330
$0
$15,702,385
$0
$0
$0
$0
$0
$0
$0
io
$0
$0
$0]
sol
so
ccel was utilized to calculate NPV, with payments applied at the beginning of each year.
Assumptions
Analytical costs not included.
-------
Table 4-2.
Summary of design well rates and maximum observed well rates
(6/97 to 11/97), Kentucky.
Wcll 1 Design Rate (gpm) Max Rate (gpm) Comments
bw-1928
bw-1929
bw-1930
bw-1931
bw-1932
bw-1933
bw-1934
bw-1935
bw-1936
bw-1937
bw-1938
bw-1939
bw-1940
bw-1941
bw-1944
bw-1945
bw-1946
bw-1947
bw-1948
bw-1949
bw-1950
bvv-1952
bw-1953
BWSubtotal
sw-1918
sw-1920
sw-1921
sw-1924
sw-1925
sw-1926
sw-1942
sw-1943
SW^ubtntal
ow-1914
ow-1915
ow-1916
ow-1917
ow-1919
ow-1922
ow-1923
Off Subtotal
7.84
36.67
12.16
2.73
7.69
48.57
43.58
42.59
58.54
62.90
54.44
29.71
35.74
37.97
19.74
19.79
20.05
8.78
N/A
N/A
N/A
N/A
N/A
549.49
21.14
8.26
7.90
81.29
13.77
4.00
21.19
13.04
12.00
11.90
12.41
14.91
21.82
14.70
31.69
7?7/f7
18.16
15.62
25.11
15.56
18.10
36.55
43.11
32.42
62.87
61.84
36.19
34.63
35.42
33.36
34.80
35.21
35.56
35.99
11.64
29.78
36.56
2.04
10.09
7no ai
7.97
20.80
13.03
63.84
6.29
10.61
36.64
30.91
6.96
6.84
7.22
11.13
20.11
43.83
39.96
143 17
Installed after original design
Installed after original design
Installed after original design
Installed after original design
Installed after original design
fioie: M_ax Kate rejers to maximum observed rate between 6/97 and 11/97, based on daily measurements.
-------
Table 5-1. Current system, Tooele.
Screening Analysis
Site: Tooele
Scenario: Current System
Discount Rate: 0.05
|| Up-Front Costs || Annual Costs # Years Costs || Total Costs
O&M Costs
-Electric '
-Materials (Sodium Metaphosphate)
-Maintenance
-Discharge Fees
-Annual O&M
-Analytical
-Other 1
-Other 2
-Other 3
Costs of Analysis
-Flow Modeling
-Transport Modeling
-Optimization
-Other 1
System Modification Costs
-Engineering Design
-Regulatory Process
-New wells/pipes/equipment
-Increased Monitoring
-Other 1
-Other 2
-Other 3
Note: All costs are in present-day dollars
The PV function in Microsoft Excel \
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$c
$1,000,000 20 $13,085,321
$200,000 20 $2,617,064
$30,000 20 $392,560
$0 20 $0
$500.000 20 $6,542,660
$80,ooo 20 $1,046,826
$0 20 $0
$0 20 $0
$0 20 $0
$0 $0
$0 $0
$0 $0
$0 $0
$0 $0
$0 $0
SO $0
$0 $0
$0 $0
$0 $0
$0 $0
$13,085,321
$2,617,064
$392,560
$0
$6,542,660
$1,046,826
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
$0
was utilized to calculate NPV, with payments applied at the beginning of each year.
Assumptions
None
-------
Table 5-2. Example calculation for "Total Managed Cost", Tooele.
Calculate Total Managed Cost (Example)
Site: Tooele
Scenario: 12 new wells, total of 4200 gpm
# New Wells 12
Pumping Rate (gpm) 4200
Discount Rate: 0.05
New WfeHs ($300K/weII)
Managed Annual Costs ($150/vr/gpm)
Up-Front Costs
$3,600,000
$0
Total of Annual
Annual Costs # Years Costs
$00 SO
$630,000 20 $8,243,752
$€30,000 $8,243,752
$3,600,000
$8,243,752
Note: AH costs are in present-day dollars. The discount rate is applied to annual costs to calculate the Net Present Value (NPV).
The PV function in Microsoft Excel was utilized to calculate NPV, with payments applied at the beginning of each year.
-------
Table 6-1. Current system, Offutt: one new core well, 100 gpm at LF wells.
Screening Analysis
Site:
Scenario:
Offutt
Current System (Add 1 new core zone well, pump 200 gpm from 4 wells)
Discount Rate: 0.05
O&M Costs
-Electric
-Materials
-Maintenance (Labor)
-Discharge (Core & LF 150 gpm, 20yrs)
-Annual O&M
-Analytical
-Discharge (Toe Well, 50 gpm. 1 0 yrs)
-Other 2
-Other 3
Costs of Analysis
-Flow Modeling
-Transport Modeling
-Optimization
-Other 1
System Modification Costs
-Fixed Construction/All Scenarios
-Regulatory Process
-New wells/pipes/equipment
-Increased Monitoring
-Other 1 .
-Other 2
-Other 3
Note: All costs are in present-day dollars. T
The PV function in Microsoft Excel was
Up-Front Costs
!t>U
$0
$0
.$0
$0
$0
$o|
$0
$0
$0
$0
-by
$47,000
$0
$40,000
$0
!pU
$0
$0
Annual Costs # Years Costs
$0 20 $0
$12000 20 $157024
$60,ooo 20 $785,119
$3,000 20 $39,256
$25,000 20 $327,133
$20,000 10 $162,156
$0 20 $0
$0 20 $0
$^~~ $6"
$0 $0
$0 $0
$0 $0
$0 $0
ib" ~W
$0 $0
$0 $0
$o $0
io" $o"
$o $0
Total Costs
$26,171
$0
$157,024
$785,119
$39,256
$327,133
$162,156
$0
$0
$0
$0
$0
$0
$47,000
$0
$40,000
$0
$0
$0
$0
utilized to calculate NPV, with payments applied at the beginning of each year.
Assumptions
Toe well can be shut off in 10 yrs
-------
-------
APPENDIX A:
OVERVIEW OF MODMAN
MODMAN Code History
MODMAN (Greenwald, 1998a) is a FORTRAN code developed by HSI GeoTrans that adds optimization capability
to the U.S.G.S. finite-difference model for groundwater flow simulation in three dimensions, called MODFLOW-96
(Harbaugh and McDonald, 1996a,b). MODMAN, in conjunction with optimization software, yields answers to the
following groundwater management questions: (1) where should pumping and injection wells be located, and (2) at
what rate should water be extracted or injected at each well? The optimal solution maximizes or minimizes a user-
defined objective function and satisfies all user-defined constraints. A typical objective may be to maximize the
total pumping rate from all wells, while constraints might include upper and lower limits on heads, gradients, and
pumping rates. A variety of objectives and constraints are available to the user, allowing many types of
groundwater management issues to be considered.
MODMAN Version 1.5 was originally developed for the South Florida Water Management District (SFWMD) in
1989-1990. Emphasis was placed on the solution of water supply problems. The majority of code
conceptualization, code de-bugging, and code documentation to date has been performed under contract to
SFWMD. MODMAN Version 2.0, developed for the USEPA in 1990, included additional features for the solution
of groundwater management problems related to plume containment and plume removal. MODMAN Version 2.1
was developed in 1992 for SFWMD to allow wells to be constrained to pump or inject only at their upper or lower
allowable rates, if they are selected to pump at all in the optimal solution. MODMAN Version 3.0 was linked to a
version of MODFLOW distributed by the International Ground Water Modeling Center (IGWMC). The current
version, MODMAN Version 4.0, has been developed for the USEPA and is linked directly with the MODFLOW-96
code. 'A preprocessor for reading and writing MOMAN input files, and running MODMAN and LINDO from a
user shell, is also now available (Greenwald, 1998b). This preprocessor runs in the Microsoft Windows
environment.
The MODMAN code logic is an extension of AQMAN (Lefkoff and Gorelick, 1987), a code developed by the U.S.
Geological Survey for two-dimensional groundwater management modeling. However, MODMAN is a
significantly more comprehensive package than AQMAN, offering a large variety of management options and
input/output features not available with the AQMAN code.
Flowchart for Executing MODMAN
A flowchart describing the optimization process is presented in Figure A-l. First, a groundwater model is calibrated
with MODFLOW. A management problem is formulated and a MODMAN input file indicating user-defined
choices for the objective function and constraints is created by the user. The decision variables are the pumping
and/or injection rates at potential well locations. MODMAN utilizes the response matrix technique to transform the
groundwater management problem into a linear or mixed-integer program. To perform the response matrix
technique, a slightly modified version of MODFLOW is called repeatedly as a subroutine. The linear or mixed-
integer program is written to an ASCII file in MPS (Mathematical Programming System) format. At this point, the
execution of MODMAN in "mode 1" is complete.
The next step is to solve the linear or mixed-integer program. The MPS file is read into the optimization code
LINDO (Lindo Systems, 1996) to determine the optimal solution. Specific LINDO commands generate an output
file containing the optimal solution. MODMAN is then executed a second time ("mode 2") to read this file and
post-process the optimal results. As part of the post-processing, MODMAN automatically inserts the optimal well
rates into MODFLOW, performs a simulation based on the optimal well rates, indicates which constraints are
"binding" (exactly satisfied by the optimal solution), and indicates if nonlinearities have significantly affected the
optimization process. A methodology is suggested in the User's Guide (Greenwald, 1998a) to solve problems
where nonlinearities significantly affect optimal results.
A-l
-------
Develop Site Specific
Groundwater Flow Model
Formulate
Management Problem
Input Objective Function
and Constraints
Generate
Response Matrix
Transform Management Problem
Into a Linear or Mixed Integer
Program in MPS Format
Solve Linear or Mixed Integer
Optimization Problem
Post-Process Optimal Results
=3-
MODEl
MODE 2
Figure A-1. General flowchart for executing MODMAN.
A-2
-------
Linear Response Theory in Groundwater Systems Upon Which MODMAN is Based
Linear response theory in groundwater systems is based on the principle of linear superposition. The principle of
linear superposition is two-fold in nature:
multiplication of a well rate by a factor increases drawdown induced by that well by the same
factor; and
• drawdown induced by more than one well is equal to the sum of drawdowns induced by each
individual well.
Linear superposition, when applicable, is valid for both steady-state and transient groundwater systems. Linear
superposition is not strictly applicable in unconfined systems, but often may be reasonably applied. Likewise, in
some systems where river leakage, drains, or evapotranspiration are significant components, linear superposition is
not strictly applicable but may often be reasonably applied. A detailed explanation of linear versus nonlinear
responses in groundwater systems is presented in the User's Guide (Greenwald, 1998a).
Concept Of The Response Matrix
A response matrix, generated on the basis of linear superposition, allows drawdown induced by one or more wells to
be calculated with matrix multiplication. For example, drawdown at three control locations, induced by two wells
in a steady-state system, is calculated as follows:
Si
S2
3_
—
R1A R1B
R2A R2B
R3A R3B_
~QA
_QB_
DRAWDOWN RESPONSE WELL-RATE
VECTOR MATRIX VECTOR
where
S; = drawdown at control location i (1, 2, or 3)
QJ = rate at well j (A or B)
RJJ = drawdown response at location i to a unit stress at well j
Once the response matrix is known, any set of well rates may be entered and the resulting drawdowns calculated.
With a response matrix, drawdowns induced by wells are defined as linear combinations of well rates. This allows
implementation of linear programming methodology, with well rates as the decision variables. The objective
function and each constraint are written in terms of well rates, either directly or in terms of drawdowns (which are
linearly determined from well rates). Constraints pertaining to heads, head differences, gradients and velocities may
all be defined in terms of drawdown, and therefore be included in the optimization process.
The first step for generating the response matrix is to define control locations. These are locations where one or
more hydrogeologic constraints, such as limits on head, will be applied. The second step is to define the location of
each managed well (i.e., each decision well). Wells where rates are fixed, and therefore not part of the decision-
A-3
-------
making process, are not managed wells and are called fixed wells. The third step is to compute the unmanaged head
(explained below), in each stress period, at each control location. Then, one groundwater flow simulation is
performed for each managed well location, to determine the coefficients for the response matrix.
4 „ • i' ii ' " • I 1: . <
Unmanaged Heads
lli , „",'p""^
Unmanaged heads refer to simulated heads resulting from unmanaged (i.e., background) flow conditions.
Unmanaged flow conditions are created when all managed wells are tamed off for the entire simulation.
Unmanaged heads are a function of fixed well rates, boundary conditions, initial conditions (in transient cases) and
hydrogeologic properties.
;.'' ' i'l ,? ', ;; • I.
Unmanaged heads must be calculated before the response matrix can be generated. The reason is that drawdowns
jnduced by each managed well must be discernible from drawdowns due to other factors, such as fixed wells. For
Instance, to determine drawdown induced by a well, it is first necessary to simulate heads with no pumping at the
well (unmanaged head). Drawdown induced by rate Q at the well is the difference between heads resulting from
rate Q and the unmanaged heads. All boundary effects, fixed wells, and hydrogeologic conditions are accounted for
in both simulations. Then the drawdown induced by any rate at that particular well can be calculated, using the
principle of linear superposition.
Concent Of A Unit Stress And Scaling
The coefficients in the response matrix are calculated for each managed well by applying a stress at that well, and
determining the drawdown at each control location induced by that stress. The stress applied at a managed well to
'generate these coefficients is called the unit stress, or unit rate. The drawdown at each control location induced by
the unit stress is called the drawdown response:
drawdown
response
unmanaged
head
head resulting from
the unit stress
The unit response is defined as:
unit response = drawdown response / unit rate
and is interpreted as drawdown induced by a rate of one unit. Drawdown due to any other well rate is then
calculated as:
induced drawdown = unit response * well rate.
The magnitude of the unit stress can be quite significant with regard to scaling. In general, a unit rate should be
Chosen that is tjie same magnitude as expected well rates. For example, if actual well rates are constrained to be
between -1000 and -6000 units, a unit rate of-1000 units is much better than a unit rate of-1 unit. One reason is
Jhat a unit rate of-1 unitmay yield such small drawdown responses that FORTRAN precision errors and
MODFLOW convergence criteria become significant. Another reason is that a small unit rate will produce very
Small coefficients in the response matrix, which is not good for the LP/MIP solver (coefficients close to one are
preferred for matrix inversions used to solve the LP or MIP). Both of these situations would be termed "scaling
problems".
Repeated Simulations (Steady-State and Transient Cases^
.,.; .,, • , „ , } '
To determine response coefficients for a managed well in a steady-state case, a unit rate is applied at that well while
all other managed wells are tamed off (rate of zero). This procedure is repeated for each managed well, with one
simulation for each managed well.
A-4
-------
For transient cases the same procedure is followed, but the unit rate is only applied in stress period 1. All stress
periods are required to be of equal length. Drawdown responses in all periods are calculated in terms of a unit rate
applied in stress period 1. The reason is that drawdown in each period is not only induced by pumping in that
period, but also by pumping in previous periods. For instance, drawdown in period 2 is due to pumping in period 2
and pumping in period 1. Because stress periods are of equal length, drawdown in period 3 due to a stress in period
2 is the same as drawdown in period 2 due to the same stress in period 1. This feature allows the entire response
matrix for transient systems to be constructed with one simulation per managed well, by applying unit stresses in
period 1 only.
This concept is best illustrated with an example. Suppose there are two wells (A and B), two control locations (x
and y), and three stress periods. First, unmanaged heads are calculated with MODFLOW, setting rates at wells A
and B to zero for all three stress periods. Then drawdown responses for well A are calculated with MODFLOW, for
the entire three periods, with a unit rate applied at well A during period 1 only, and no pumping at well B. The
process is repeated for well B, with well A not pumping. Suppose the drawdown responses, at the end of each stress
period, are as follows:
DRAWDOWN RESPONSE IN STRESS PERIOD:
LOCATION
X
X
y
y
PUMPING
WELL
A
B
A
B
1
(pumping on)
-0.50
-0.75
-0.15
-1.50
2
(pumping off)
-0.20
-0.40
-0.05
-1.00
3
(pumping off)
-0.10
-0.25
-0.01
-0.60
Note that drawdown responses are negative. The sign convention for drawdown is positive for head lowered below
a datum and negative for head raised above a datum. The sign convention for pumpage is negative for withdrawal
and positive for injection. A negative pumpage (withdrawal) will create a positive drawdown and vice versa.
Accordingly, the drawdown responses (matrix generated from a unit stress) will always be negative. The response
matrix for tin's example, in matrix notation, is:
sx,l
3x,2
x,2
-0.50 -0.75
-0.15 -1.50
-0.20 -0.40
-0.05 -1.00
-0.10 -0.25
-0.01 -0.60
0.00 0.00
0.00 0.00
-0.50 -0.75
-0.15 -1.50
-0.20 -0.40
-0.05 -1.00
0.00 0.00
0.00 0.00
0.00 0.00
0.00 0.00
-0.50 -0.75
-0.15 -1.50
QA,I
QB,I
QA,2
QB,2
QA,3
QB,3
A-5
-------
Managed drawdown, s, at each of the control points (x or y) can be calculated from the response matrix for any time
period. For instance, managed drawdown at point x after period 2 is:
"x.2
-0.20QA>1 + -0.40QB_, +
—due to pumping in—
stress period 1
-0.50QA,2 + -0.75QB|2
—due to pumping in—
stress period 2
Note the predominance of zeroes above the main diagonal of the response matrix. This results because drawdown is
due to current and previous pumpage, but not future pumpage. In the above example, drawdowns in time period 1
only depend on pumping in period 1, while drawdowns in period 2 are based on pumping in periods 1 and 2. Note
the repetition of blocks within the response matrix. This structure is made possible by the fact that stress periods are
of equal length, and allows efficient storage of the response matrix in the MODMAN code. Also note that the
response matrix is fully generated by applying a unit stress, at each decision well, in the first stress period only.
A-6
-------
APPENDIX B:
OVERVIEW OF SIMULATION-MANAGEMENT METHODS
INCORPORATING TRANSPORT SIMULATIONS
Hydraulic optimization is based on simulation of groundwater flow. In many cases, the management objectives or
constraints at a site may involve terms that cannot be rigorously evaluated with a groundwater flow model, such as
contaminant concentrations and/or cleanup time. In those cases, solute transport models can be developed to predict
contaminant concentrations over space and/or time, and simulation-management techniques based on the results of
the contaminant transport simulations can be applied.
Many hydraulic optimization techniques (e.g., those employed by MODMAN) utilize the principle of linear
superposition to transform the groundwater management problem into a linear program (see Appendix A). This is
possible because, when linear superposition applies, drawdown is directly proportional to pumping rate.
Unfortunately, there is no such linear relationship between concentrations and pumping rates. Increasing pumping
rate by a factor of two does not decrease concentrations by a factor of two. Therefore, simulation-management
problems involving contaminant transport require optimization techniques that are significantly more complex than
linear programming.
Since the mid-1980's, a large number of transport-based simulation-management approaches have been described in
the literature. These techniques are typically computer-intensive, but with improved algorithms and constantly
improving computer speeds, these techniques are likely to become more mainstream within the next several years.
A full review of transport-based simulation-management modeling is well beyond the scope of this report. The
interested reader can begin with some of the references indicated in Appendix I of this report. A partial listing of
researchers that are particularly active in code development for transport-based simulation-management modeling is
as follows:
David Dougherty
Richard Peralta
Christine Shoemaker
Brian Wagner
Chunmiao Zheng
Contact information for these individuals is presented in Appendix I.
B-l
-------
-------
APPENDIX C:
OVERVIEW OF SIMULATION-MANAGEMENT METHODS
INCORPORATING UNCERTAINTY AND/OR RISK
The applications of hydraulic optimization presented in this study are based on deterministic ground-water flow
simulations (i.e., model parameters are assumed to be known precisely). Impacts to mathematical optimal solutions
from uncertainties associated with the groundwater flow model are not accounted for. Stochastic groundwater
management tools are required to account for:
(1) parameter uncertainty; and/or
(2) spatially variable aquifer properties that can only be represented statistically.
Coupling of stochastic techniques with simulation-management models can allow uncertainty and risk to be
incorporated into the optimization algorithm. For example, one can specify that constraints be satisfied within a
specified reliability (e.g., constraints satisfied with 95% reliability). Another example is to specify constraints that
satisfy multiple potential realizations for spatial distribution of key aquifer parameters (e.g., hydraulic conductivity),
rather than one realization in a deterministic model. Stochastic approaches to simulation-management modeling
have been applied to both hydraulic optimization and transport optimization problems.
A full review of this topic is well beyond the scope of this report. A brief description is provided in Appendix B of
Gorelick et. al. (1993). An excellent resource for this area of research is Brian Wagner at the U.S.G.S. (see
Appendix I for contact information).
C-l
-------
-------
APPENDIX D:
PARTIAL LISTING OF MODMAN APPLICATIONS
Douthitt, Jeff W. And Bruce E. Phillips, 1994, "Model Assisted Design of a Ground-water Pump and Treat System at
the Paducah Gaseous Diffusion Plant", Toxic Substances and the Hydrologic Sciences, American Institute of
Hydrology, pp. 346 to 365.
Greenwald, Robert M. and Joost C. Herweijer, Ira Star, Mark Gallagher, and Allan L. Dreher, 1992, "Optimization
of Well Locations and Rates for Containment of Contaminants Utilizing an Automated Management Routine
Coupled to MODFLOW: A Case History", Solving Ground Water Problems With Models, Dallas, Texas, February
1992.
Hagemeyer, Todd R., Peter F. Andersen, Robert M. Greenwald, and Jay L. Clausen, 1993, "Evaluation of
Alternative Plume Containment Designs at the Paducah Gaseous Diffusion Plant Using MODMAN, A Well
Pumpage Optimization Module for MODFLOW", IGWMC Modeling Conference, Golden, Colorado, June 1993.
Johnson, Kevin D. and James D. Bowen, 1993, "Trade-Offs Between Pumping and Slurry Walls Under Changing
Hydraulic Parameters", IGWMC Modeling Conference, Golden, Colorado, June 1993.
McCready, Roger W. And Robert M. Greenwald, 1997, "Pump-and-Treat Well Location and Rate Optimization
Using MODFLOW and MODMAN: A Case Study", Midwest Groundwater Conference, Coralville, Iowa, October
1997 (Abstract Only).
Russell, K.T. and A. J. Rabideau, "Decision Analysis for Pump-and-Treat Design", Ground Water Monitoring and
Remediation (in press).
Russell, K.T. and A. J. Rabideau, "Simulating the Reliability of Pump-and-treat Systems", Ground Water Monitoring
and Remediation (in review).
D-l
-------
-------
grmm2a-l.INP: Apples to Apples,
SETO: General Parameters
l(MODE) .01
SET1: Time Parameters
1 1.00
SET2: Well Information
43 0 43
.01
APPENDIX E:
SAMPLE MODMAN INPUT: KENTUCKY
Kentucky
.01 l.E-03 .01 1
1.00
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
1
2
3
4
5
6
7
8
9
10
11
12
13
14
IS
16
17
18
19
20
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
8
9
9
9
9
9
9
11
10
10
10
10
10
11
13
11
9
12
12
13
14
20
25
30
13
14
15
18
22
25
33
35
36
37
8
8
13
11
10
16
15
14
21
28
30
32
34
35
37
39
42
45
48
51
53
55
57
59
64
68
69
40
39
38
36
40
35
66
64
35
33
31
29
26
19
13
6
41
44
58
62
62
62
52
42
40
-3496.04
-3007.06
-4834.01
-2995.51
-3484.49
-7036.36
-8299.25
-6241.28
-1.21E+04
-1.191E+04
-6967.06
-6666.74
-6818.82
-6422.25
-6928.56
-6699.47
-6845.78
-6778.40
-770.00
-2650.00
-1000.
-1000.
-1000.
-1000.
-1000.
-1000.
-1000.
-1000.
-1000.
-1000,
-1000.
-1000.
-1000.
-1000
-1000.
-1000
-1000
-1000
-1000
-1000.
-1000
-1000
-1000
-1000
-1000
-1000
-1000
-1000
-1000
-1000
-1000
-1000
-1000
-1000
-1000
-1000
-1000
-1000
-1000
-1000
-1000
-1000
-1000
O.E+00
O.E+00
O.E+00
O.E+00
O.E+00
O.E+00
O.E+00
O.E+00
O.E+00
O.E+00
O.E+00
O.E+00
O.E+00
O.E+00
O.E+00
O.E+00
O.E+00
O.E+00
-770.00
-2650.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
/bw-1928
/bw-1929
/bw-1930
/bw-1931
/bw-1932
/bw-1933
/bw-1934
/bw-1935
/bw-1936
/bw-1937
/bw-1938
/bw-1939
/bw-1940
/bw-1941
/bw-1947
/bw-1944
/bw-1946
/bw-1945
/SW-1926
/sw-1925
/SW-1924
/SW-1921
/SW-1920
/sw-1918
/sw-1943
/sw-1942
/ow-1923
/ow-1922
/ow-1919
/ow-1917
/ow-1916
/OW-1915
/OW-1914
/ow-1913
/bw-1948
/bw-1949
/bw-1950
/bw-1952
/bw-1953
/new- 1
/new- 2
/new- 3
/new- 4
/bw-1928
/bw-1929
/bw-1930
/bw-1931
/bw-1932
/bw-1933
/bw-1934
/bw-1935
/bw-1936
/bw-1937
/bw-1938
/bw-1939
/bw-1940
/bw-1941
/bw-1947
/bw-1944
/bw-1946
/bw-1945
/SW-1926
/SW-1925
(not used this run)
(not used this run)
(not used this run)
(not used this run)
(not used this run)
(not used this run)
(not used this run)
(not used this run)
(not used this run)
E-l
-------
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
SKT3i
52
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
'41
42
43
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
-l.565E-t.04
-1520.00
-1590.00
-4070.00
-2510.00
-4080.00
-6100.00
-2830.00
-4200.00
-2870.00
-2390.00
-2290.00
-2310.00
-2360.00
O.E+00
O.E+00
O.E+00
O.E+00
O.E+00
O.E+00
O.E+00
O.E+00
O.E+00
-1.565E+04
-1520.00
-1590.00
-4070.00
-2510.00
-4080.00
-6100.00
-2830.00
-4200.00
-2870.00
-2390.00
-2290.00
-2310.00
-2360.00
O.E+00
O.E+00
O.E+00
O.E+00
O.E+00
O.E+00
O.E+00
O.E+00
O.E+00
/sw-1924
/SW-1921
/sw-1920
/sw-1918
/SW-1943
/SW-1942
/ow-1923
/ow-1922
/ow-1919
/ow-1917
/ow-1916
1 /ow-1915
/OW-1914
/OW-1913
/bw-1948
/bw-1949
/bw-1950
/bw-1952
/bw-1953
/new-1
/new- 2
/new- 3
/new- 4
"
i
"
'
]
(not used this
(not used t}iis
(not used this
(not used this
(not used this
(not used this
(not used this
(not used this
(not used this
run)
run)
run)
run)
run)
run)
run)
run)
run)
Control Locations
1
2
3
4
5
S
7
S
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
" I
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
6
6
6
6
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
7
8
8
8
8
8
8
8
8
9
9
10
10
11
11
64
65
66
71
28
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
64
67
68
69
70
29
30
31
32
33
34
61
63
60
63
60
62
59
62
ii
'
'
i
I
"
'
E-2
-------
SET4:
52
SETS:
0
SET6:
0
52
1
12
62
Head Limits
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0,
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
E+00
.E+00
.E+00
, E+00
.E+00
.E+00
.E+00
.E+00
.E+00
,E+00
.E+00
.E+00
.E+00
.E+00
.E+00
.E+00
.E+00
.E+00
.E+00
.E+00
.E+00
.E+00
.E+00
.E+00
.E+00
.E+00
.E+00
.E+00
.E+00
.E+00
.E+00
.E+00
.E+00
.E+00
.E+00
.E+00
.E+00
.E+00
.E+00
.E+00
.E+00
.E+00
.E+00
.E+00
.E+00
.E+00
.E+00
.E+00
.E+00
.E+00
.E+00
.E+00
301.99
301.99
301.99
301.99
301.99
301.99
301.99
301.99
301.99
301.99
301.99
301.99
301.99
301.99
301.99
301.99
301.99
301.99
301.99
301.99
301.99
301.99
301.99
301.99
301.99
301.99
301.99
301.99
301.99
301.99
301.99
301.99
301.99
301.99
301.99
301.99
301.99
301.99
301.99
301.99
301.99
301.99
301.99
301.99
301.99
301.99
301.99
301.99
301.99
301.99
301.99
301.99
Head Difference Limits
Drawdown Limits
SET7A: Gradient
0
SET7B
0
SET7C
0
SETS:
0
SET9:
1
1
2
3
4
5
6
: Velocity
-. Relative
Limits
Limits
Gradient
Limits
Balance Constraints
Integer Constraints
1
B
1
L
18
18
/limit t BW wells to 18 or less
E-3
-------
i' si
9
10
11
12
13
14
15
16
17
18
SETlOl
1
1
1
I
1
1
1
1
"1
1
1
i
:i
i
i
i
i
"i
i
i
l
i
i
i
i
l
i
i
i
i
i
i
i
i
i
i
i
i
l
.'i
"i
1
i
i
2
3
4
s
6
7
8
9
10
11
12
13
14
15
16
17
is
19
20
21
22
23
24
25
26
27
23
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
Objective Function
1 i ,43
-5.194E-03
-S.194B-03
-5.194E-03
-5.194E-03
-5.194E-03
-S.194E.-03
-S.194E-03
-5.194E-03
-S.194Ei-03
-5.194^-03
-S.194^-03
-5.194^-03
-5.194E-03
-5.194E-03
-S.194R-03
-5.194E-03
-5.194E-03
-5.194E-03
-S.194E-03
-S.194E-03
-5.194E-03
-S.194E-03
-S.194E-03
-S.194E'-03
-5.194E-03
-S.194E-03
-S.194E-03
-5.194E-03
-5.194E-03
-S.194E-03
-S.194E-03
-S.194E-03
-S.194E-03
-5.194E-03
-S.194E-03
-5.194E-03
-S.194E-03
-S.194E-03
-S.194E-03
-S.194E-03
-S.194E-03
-5.194E-03
-S.194E-03
/* convert to positive gpm
E-4
l , i, 1 ..ill*
-------
APPENDIX F:
SAMPLE MODMAN INPUT: TOOELE
TOMM1-1: 5 ppb plume, shallow and deep
SETO
1
SET1
SET2
80
: General Parameters
(MODE)
: Time
1
: Well
.01
Parameters
1.00
Information
.01
1
.01
1.00
l.E-03
.01
1
0 80
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
1
1 ,
2
1
2
2
2
1
2
1
2
1
2
3
1
2
1
1
1
1
2
1
2
1
1
2
1
1
1
1
2
1
2
1 ,
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
63
76
77
88
88
102
104
115
115
109
109
94
94
94
95
95
57
45
84
90
90
64
64
72
62
62
58
53
45
40
40
35
35
32
31
31
37
37
42
48
54
54
52
54
54
58
58
63
72
72
48
41
41
49
48
37
45
37
37
45
45
48
48
48
53
53
45
45
28
32
32
34
34
65
61
61
60
58
56
54
54
49
49
43
37
37
33
33
28
20
15
15
41
39
43
37
41
41
34
41
-9.
-9.
-9.
-9
-9
-9
-9
— 9
-9
-9
-9
-9
- 9
-9
-9
-9
-9
-9
-9
-9
-9
-9
-9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
-9
-9
-9
-9
-9
-9
-9
-9
. 626E+04
. 626E+04
.626E+04
. 626E+04
. 626E+04
.626E+04
. 626E+04
. 626E+04
. 626E+04
. 626E+04
. 626E+04
. 626E+04
.626E+04
. 626E+04
. 626E+04
.626E+04
. 626E+04
. 626E+04
.626E+04
. 626E+04
.626E+04
.626E+04
.626E+04
.626E+04
.626E+04
.626E+04
. 626E+04
. 626E+04
. 626E+04
. 626E+04
.626E+04
. 626E+04
.626E+04
.626E+04
.626E+04
.626E+04
.626E+04
.626E+04
.626E+04
.626E+04
.626E+04
.626E+04
.626E+04
.626E+04
.626E+04
.626E+04
.626E+04
.626E+04
.626E+04
.626E+04
el-1
e2-l
e2-2
e3-l
e3-2
e4-2
e5-2
e6-l
e6-2
e8-l
e8-2
e9-l
e9-2
e9-3
elO-1
elO-2
ell-1
612-1
e!3-l
e!4-l
614-2
e!5-l
e!5-2
il-1
12-1
12-2
13-1
i4-l
i5-l
16-1
16-2
17-1
17-2
18-1
i9-l
19-2
ilO-1
110-2
ill-1
112-1
113-1
113-2
/* new
/* new
/* new
/* new
/* new
/* new
/* new
/* new
si
S2
S3
s4
s5
S6
s7
s8
F-l
-------
ill
/I
;. l
:; i
3.
; 1
1
1
1
1
" 1
i
" i
i
i
i
i
L i
i
i
; i
1 i
:'i
i
i
i
' i
i
i
i
i
i
i
i
Tl
'"l
!:1
51
52
53
54
55
56
S7
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
l'
2
i "
4
5
6
7
8
9
10
11
12
13
14
IS
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
1 72
1 79
1 79
1 79
1 85
1 85
1 85
1 47
1 48
1 48
1 50
1 50
2 71
? 71
2 71
2 75
2 75
2 75
2 75
2 80
2 80
2 80
2 80
2 86
2 86
2 86
2 86
2 86
2 87
2 81
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
48
32
41
48
32
41
48
42
41
43
40
43
37
41
45
29
35
41
47
29
35
41
47
23
29
35
41
47
19
23
-9.62SE+04
-9.626E+04
-9.626E+04
-9.62SE+04
-9.626E+04
-1.296E+05
-1.388E+05
-9.626E+04
-1.637E+04
-9.626E+04
-3.85E+04
-9.626E+04
-9.968E+04
-9.626E+04
-9.626E+04
-1.196E+05
-9.S26E+04
-9.626E+04
-1.119E+05
-9.626E+04
-7.523E+04
-8.424E+04
-9.626E+04
O.E+00
O.E+00
O.E+00
O.E+00
O.E+00
O.E+00
O.E+00
O.E+00
O.E+00
O.E+00
O.E+00
O.E+00
O.E+00
-9.62SE+04
-9.62SE+04
-9.626E+04
-9.626E+04
-9.626E+04
-9.62SE+04
-9.62SE+04
-9.626E+04
-9.626E+04
-9.626E+04
-9.62SE+04
-9.S26E+04
-9.626E+04
-9.626E+04
-9.626E+04
-9.626E+Q4
-9.626E+04
-9.626E+04
-9.626E+04
-9.S2SE+04
-9.626E+04
-9.626E+04
-9.626E+04
-9.626E+04
-9.626E+04
-9.S26E+04
-9.626E+04
-9.626E+04
-9.S26E+04
-9.626E+04
O.E+00
O.E+00
O.E+00
O.E+00
O.E+00
O.E+00
O.E+00
O.E+00
O.E+00
O.E+00
O.E+00
O.E+00
O.E+00
O.E+00
O.E+00
O.E+00
O.E+00
O.E+00
O.E+00
O.E+00
O.E+00
O.E+00
O.E+00
9.626E+04
9.626E+04
2.12E+04
9.S26E+04
1.315E+05
1.996E+05
5.548E+04
9.626E+04
1.131E+05
9.626E+04
1.222E+05
8.94E+04
9.626E+04
/* new s9
/* new slO
/* new sll
/* new s!2
/* new s!3
/* new s!4
/* new sis
/* new slS
/* new s!7
/* new s!8
/* new s!9
/* new s20
/* new dl/21
/* new d2/22
/* new d3/23
/* new d4/24
/* new d5/25
/* new dS/26
/* new d7/27
/* new d8/28
/* new d9/29
/* new dlO/30
/* new dll/31
/* new d!2/32
/* new d!3/33
/* new d!4/34
/* new dl5/35
/* new dl6/36
/* new dl7/37
/* new d!8/38
el-1
e2-l
e2-2
e3-l
e3-2
e4-2
e5-2
e6-l
e6-2
e8-l
e8-2
e9-l
e9-2
e9-3
elO-1
elO-2
ell-1
e!2-l
e!3-l
e!4-l
e!4-2
el5-l
el5-2
il-1
i2-l
i2-2
i3-l
i4-l
15-1
16-1
ifi-2
17-1
17-2
18-1
19-1
19-2
F-2
-------
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
SETS :
114
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
7S
77
78
79
80
M
M
M
M
M
M
M
M
M'
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
-9
-9
-9
-9
-9
-9
-9
-9
_ Q
-9
-9
— 9
-9
-9
-9
-9
— 9
_ g
-9
-9
-9
-9
-9
-9
-9
-9
-9
-9
-9
-9
-9
-9
-9
-9
-9
-9
-9
-9
O.E+00 7.
O.E+00 9,
O.E+00 1.
O.E+00 9.
O.E+00 9.
O.E+00 1
. 626E+04
. 626E+04
.626E+04
. 626E+04
. 626E+04
. 626E+04
. 626E+04
. 626E+04
. 626E+04
.626E+04
. 626E+04
.626E+04
.626E+04
. 626E+04
.626E+04
.626E+04
.626E+04
.626E+04
.626E+04
.626E+04
.626E+04
.626E+04
.626E+04
.626E+04
.626E+04
.626E+04
.626E+04
.626E+04
.626E+04
.626E+04
.626E+04
.626E+04
.626E+04
.626E+04
.626E+04
.626E+04
.62SE+04
.626E+04
. 754E+04
. 626E+04
.398E+05
. 626E+04
. 626E+04
. 925E+04
O.E+00
O.E+00
O.E+00
O.E+00
O.E+00
O.E+00
O.E+00
O.E+00
O.E+00
O.E+00
O.E+00
O.E+00
O.E+00
O.E+00
O.E+00
O.E+00
O.E+00
O.E+00
O.E+00
O.E+00
O.E+00
O.E+00
O.E+00
O.E+00
O.E+00
O.E+00
O.E+00
O.E+00
O.E+00
O.E+00
O.E+00
O.E+00
O.E+00
O.E+00
O.E+00
O.E+00
O.E+00
O.E+00
ilO-1
ilO-2
ill-1
112-1
113-1
113-2
/* new
/* new
/* new
/* new
/* new
/* new
/* new
/* new
/* new
/* new
/* new
/* new
/* new
/* new
/* new
/* new
/* new
/* new
/* new
/* new
/* new
/* new
/* new
/* new
/* new
/* new
/* new
/* new
/* new
/* new
/* new
/* new
/* new
/* new
/* new
/* new
/* new
/* new
si
S2
S3
s4
s5
s6
s7
s8
39
SlO
sll
s!2
s!3
s!4
s!5
s!6
s!7
S18
s!9
320
dl/21
d2/22
d3/23
d4/24
d5/25
d6/26
d7/27
d8/28
d9/29
dlO/30
dll/31
d!2/32
dl3/33
d!4/34
dl5/35
dl6/36
d!7/37
dl8/38
Control Locations
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
IS
17
18
19
20
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
85
84
85
80
79
80
76
75
76
73
72
73
68
67
68
63
62
63
58
57
23
23
24
24
24
25
25
25
26
26
26
27
28
28
29
30
30
31
33
33
/*shallow 5-ppb
F-3
-------
qdd-s dssp*/
6£
6£
9E
SE
S£
2£
T£
T£
62
82
82
S2
£2
*2
T2
02
02
8T
LI
LI
91
ST
ST
2S
ES
2S
ES
TS
2S
2S
TS
2S
2S
OS '
TS
TS
6fr
OS
OS
8*
11
L*
8*
8fr
91>
L*
LV
Sfr
9fr
9?
fr^
S^
Sfr
£^
tfc
frfr
2^
OL
69
69
89
69
OL
69
OL
ZL
tL
ZL
SL
TrL
SL
6L
BL
6L
£8
£8
^8
06
68
06
S8
S3
28
28
6L
8L
6L
SL
IrL
SL
1L
OL
tL
89
L9
89
59
59
T9
09
T9
8S
LS
85
VS
£S
TrS
TS
OS
TS
2S
TS
2S
LV
6£
6£
9£
9£
6*
ES
2S
ES
8S
Z
Z
z
z
z
z
z
z
z
z
z
z
z
z
z
z
z
z
z
z
z
z
z
T
T
T
T
t
T
T
T
T
T
T
T
T
T
T
T
T
T
T
"t
T
T
T
T
T
T
T
t
1
T
T
t
T
T
T
T
T
T
T
T
T
T
T
98
S8
£8
28
18
08
6L
BL
LL
9L
SL
IrL
Ei
ZL
tL
OL
69
89
L9
99
59
£9
29
T9
09
65
8S
LS
95
SS
ES
ZS
TS
OS
6*
8V
9V
zv
0*
6£
8E
Lt
9E
SE
E£
2£
IE
0£
62
82
LZ
9Z
SZ
tz
ZZ
12
-------
SET4:
0
SETS:
12
SETS:
0
SET7A:
60
87 2 69
88 2 70
89 2 69
90 2 70
91 2 69
92 2 70
93 2 71
94 2 70
95 2 71
96 2 74
97 2 73
98 2 74
99 2 76
100 2 75
101 2 76
102 2 79
103 2 78
104 2 79
105 2 82
106 2 82
107 2 84
108 2 84
109 2 86
110 2 86
111 2 88
112 2 88
113 2 91
114 2 91
Head Limits
Head Difference Limits
1
2
3
4
5
6
7
8
9
10
11
12
Drawdown
: Gradient
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
1
1
1
1
1
1
1
1
1
1
1
1
Limits
Limits
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
28
60
62
85
87
89
91
105
107
109
111
113
1
1
4
4
7
7
10
10
13
13
16
16
19
19
22
22
25
25
41
41
43
43
45
45
49
49
48
52
52
51
54
54
53
55
55
54
55
54
55
54
55
54
55
54
54
53
29
61
63
86
88
90
92
106
108
110
112
114
2
3
5
6
8
9
11
12
14
15
17
18
20
21
23
24
26
27
.02
.02
.02
.02
.02
.02
.02
.02
.02
.02
.02
.02
-10.00
l.E-04
-10.00
l.E-04
-10.00
l.E-04
-10.00
l.E-04
-10.00
l.E-04
-10.00
l.E-04
-10.00
l.E-04
-10.00
l.E-04
-10.00
l.E-04
l.E+20
l.E+20
l.E+20
l.E+20
l.E+20
l.E+20
l.E+20
l.E+20
l.E+20
l.E+20
l.E+20
l.E+20
l.E+20
l.E+20
l.E+20
l.E+20
l.E+20
l.E+20
l.E+20
l.E+20
l.E+20
l.E+20
l.E+20
l.E+20
l.E+20
l.E+20
l.E+20
l.E+20
l.E+20
l.E+20
/*first 3 are shallow
/*next 9 are deep
/*first 38 are shallow
F-5
-------
|IF
11
•1
SBT7B.'
0
SET7C:
30
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
Velocity
Relative
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
1
1
1
1
1
1
1.
1
1
i
i
i
i
i
i
i
i
i
i
i
1
i
i
I
i
i
i
i
i
i
i
i
i
i
i
i"
i
i
i
i
i
i
Limits
Gradient
2
4
6
8
10
12
14
16
18
20
22
. 24
26
28
30
32
34
36
38
40
30
30
33
33
36
36
39
39
42
42
45
45
48
48
51
51
54
54
57
57
64
64
67
67
70
70
73
73
76
76
79
79
82
82
93
93
96
96
99
99
102
102
Limits
1
3
5
7
9
11
13
15
17
19
21
23
25
27
29
31
33
35
37
39
31
32
34
35
37
38
40
41
43
44
46
47
49
50
52
53
55
56
58
59
65
66
68
69
71
72
74
75
77
78
80
81
83
84
94
95
97
98
100
101
103
104
.36
.36
.36
.36
.47
.70
.70
.70
.84
.70
.27
.27
.27
.27
.27
.27
.27
.27
.18
.27
-10.00
l.E-04
-10.00
l.E-04
-10.00
l.E-04
-10.00
l.E-04
-10.00
l.E-04
-10.00
l.E-04
-10.00
l.E-04
-10.00
l.E-04
-10.00
l.E-04
-10.00
l.E-04
-10.00
l.E-04
-10.00
l.E-04
-10.00
l.E-04
-10.00
l.E-04
-10.00
l.E-04
-10.00
l.E-04
-10.00
l.E-04
-10.00
l.E-04
-10.00
l.E-04
-10.00
l.E-04
-10.00
l.E-04
/*first
/* next
l.E+20
l.E+20
l.E+20
l.E+20
l.E+20
l.E+20
l.E+20
l.E+20
l.E+20
l.E+20
l.E+20
l.E+20
l.E+20
l.E+20
l.E+20
l.E+20
l.E+20
l.E+20
l.E+20
l.E+20 /*
l.E+20
l.E+20
l.E+20
l.E+20
l.E+20
l.E+20
l.E+20
l.E+20
1.E+2Q
l.E+20
l.E+20
l.E+20
l.E+20
l.E+20
l.E+20
l.E+20
l.E+20
l.E+20
l.E+20
l.E+20
l.E+20
l.E+20
19 are shallow
11 are deep
/* next 22 are deep
F-6
-------
21
22
23
24
25
26
27
28
29
30
SET8 : Balance
17
1
2
1 8
1 9
3
1 10
1 11
4
1 12
1 13
5
1 12
1 14
6
1 15
1 16
7
1 20
1 21
8
1 22
1 23
9
1 25
1 26
10
1 30
1 31
11
1 32
1 33
12
1 35
1 36
13
1 37
1 38
14
1 41
1 42
15
115
125
135
145
155
165
175
185
195
1 10 5
1 11 5
1 12 5
42 41
44 43
46 45
48 47
50 49
52 51
54 53
56 55
58 57
60 59
Constraints
A 1
C
1.00
-4.88
C
1.00
-1.50
C
1.00
-.20
C
1.00
-.56
C
1.00
-.15
C
1.00
-.33
C
1.00
-4.00
C
1.00
-3.54
C
1.00
-1.22
C
1.00
-1.22
C
1.00
-1.50
C
1.00
-3.00
C
1.00
-4.00
C
. 194E-03
.194E-03
.194E-03
. 194E-03
.194E-03
.194E-03
.194E-03
.194E-03
.194E-03
.194E-03
.194E-03
.194E-03
.70
.84
1.19
1.73
1.73
5.67
1.73
1.00
1.00
.27
L
E
E
E
E
E
E
E
E
E
I
I
]
]
O.E+00
O.E+00
O.E+00
O.E+00
E O.E+00
E O.E+00
E O.E+00
E O.E+00
O.E+00
E O.E+00
O.E+00
E O.E+00
E O.E+00
E O.E+00
L O.E+00
/*pumping = injection
/*multi-aquifer wells
23 /*sutns existing extraction wells
F-7
-------
' 1 13
1 14
1 15
1 16
1 17
1 18
III 19
!U '20
fl 21
X 22
1 23
16
1 43
1 44
1 45
1 46
1 47
1 48
1 49
1 50
1 51
1 52
1 53
1 54
1 55
1 56
1 57
'.i 58
1 59
1 60
1 61
1 62
17
1 63
1 64
i 65
1 66
1 67
1 68
i 69
1 70
1 71
1 72
i 73
1 74
1 75
1 76
1 77
1 78
1 79
1 80
5.194E-03
S.194E-03
S.194E-03
5.194E-03
S.194E-03
S.194E-03
S.194E-03
S.194E-03
S.194E-03
5.194E-03
5.194E-03
C
S.194E-03
S.194E-03
5.194E-03
5.194E-03
5.194E-03
S.194E-03
5.194E-Q3
S.194E-03
S.194E-03
S.194E-03
S.194E-03
S.194E-03
5.194E-03
5.194E-03
5.19fE-03
5.194E-03
5.194E-P3'
5.194E-03
S.i94E-03
S.194E-03
C
5.194E-03
5.194E-03
5.194E-03
5.194E-03
5.194E-03
5.194E-03
5.194E-03
S.194E-03
5.194E-03
S.194E-03
S.194E-03
5.194E-03
5.194E-03
5.194E-03
5.194E-03
S.194E-03
5.194E-03
S.194E-03
L O.E+00
20 /*sums new shallow extraction
L O.E+00
18 /*sums new deep extraction
Integer Constraints
20
43
44
45
46
47
48
49
SO
51
52
S3
20 /* places limit on # new shallow wells|
F-8
-------
54
55
55
57
58
59
60
61
62
18
18 /*paces limit on # new deep wells
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
38
38 /*places limit on # new total wells
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
F-9
-------
78
79
80
SET10: Objective Function
1 1
1 2
1 3
i 4
1 5
i s
1 7
1 8
1 9
i 10
1 11
1 12
1 13
1 14
1 15
1 16
1 17
1 18
1 19
1 20
\ 21
£' 22
t 23
V 43
1 44
\ 45
i 46
1 47
1 48
1 49
i, so
1 51
1 52
i S3
1 54
1 55
1 56
1 57
1 58
1 59
1 60
1 61
1 62
1 63
1 64
1 65
1 66
1 6?
1 €8
1 69
V70
1 71
1 72
1 73
1 74
1 75
1 76
1 77
1 78
1 79
1 8°
1 61
-S.194E-03
-5.194E-03
-S.194E-03
-S.194E-03"
-5.194E-03 "
-5.194E-03
-S.194E-03
-5. 1941-03
-5.194E-03
-5.194E-03
-5.194E-03
-5.194E-03
-5.194E-03
-5.194E-03
-5.194E-03
-5.194E-03
-S.194E-03
-5.194E-03
-5.194E-03
-5.194E-03
-5.194E-03"1'
-S.194E-03
-S.194E-03,
-5.194E-03
-5.194E-03
-5.194E-03
-5.194E-03
-5.194E-03
-5.194E-03
-5.194E-03
-5.194E-03
-5.194E-03
-5.194E-03
-5.194E-03
-S.194E-03
-S.194E-03
-5.194E-03
-S.194E-03
-5.194E-03
-5.1945-03
-5.194E-03
-S.194E-03
-5.194E-03
-5.194E-03
-5.194E-03
-5.194E-03
-5.194E-03
-5.194E-03
-S.194E-03
-5.194E-03
-5.194E-03
-5.194E-03
-5.194E-03
-5.194E-03
-S.194E-03
-5.194E-03
-5.194E-03
-S.194E-03
-S.194E-03
-S.194E-03
-5.194E-03
/*factor converts to gpm,
/*factor converts to gpm,
/*factor converts to gpm,
/*factor converts to gpm,
/*factor converts to gpm.
/*factor converts to gpm,
/*factor converts to gpm,
/*factor converts to gpm,
/*factor converts to gpm,
/*factor converts to gpm,
/*factor converts to gpm.
/*factor converts to gpm,
/*factor converts to gpm,
/*factor converts to gpm,
/*factor converts to gpm.
/*factor converts to gpm.
/*factor converts to gpm,
/*factor converts to gpm.
/*f actor converts to gpm.
/*f actor converts to gpm.
/* factor converts to gpm.
/*factor converts to gpm,
/*£ actor converts to gpm,
/*factor converts to gpm,
/*factor converts to gpm.
/*factor converts to gpm.
/*factor converts to gpm,
/*factor converts to gpm.
/*f actor converts to gpm.
/*factor converts to gpm,
/*factor converts to gpm.
/*factor converts to gpm.
/*factor converts to gpm.
/*factor converts to gpm.
/*factor converts to gpm.
/*factor converts to gpm.
/*factor converts to gpm,
/*factor converts to gpm,
/*factor converts to gpm,
/*factor converts to gpm,
/*factor converts to gpm,
/*factor converts to gpm,
/*factor converts to gpm.
/*factor converts to gpm,
/* factor converts to gpm,
/*factor converts to gpm.
/*f actor converts to gpm,
/*factor converts to gpm.
/*factor converts to gpm,
/*factor converts to gpm.
/*factor converts to gpm,
/*factor converts to gpm,
/*factor converts to gpm,
/*factor converts to gpm,
/*factor converts to gpm,
/* factor converts to gpm,
/*factor converts to gpm,
/*factor converts to gpm.
/*factor converts to gpm,
/*factor converts to gpm.
/*f actor converts to gpm.
neg allows minimize
neg allows minimize
neg allows minimize
neg allows minimize
neg allows minimize
neg allows minimize
neg allows minimize
neg allows minimize
neg allows minimize
neg allows minimize
neg allows minimize
neg allows minimize
neg allows minimize
neg allows minimize
neg allows minimize
neg allows minimize
neg allows minimize
neg allows minimize
neg allows minimize
neg allows minimize
neg allows minimize
neg allows minimize
neg allows minimize
neg allows minimize
neg allows minimize
neg allows minimize
neg allows minimize
neg allows minimize
neg allows minimize
neg allows minimize
neg allows minimize
neg allows minimize
neg allows minimize
neg allows minimize
neg allows minimize
neg allows minimize
neg allows minimize
neg allows minimize
neg allows minimize
neg allows minimize
neg allows minimize
neg allows minimize
neg allows minimize
neg allows minimize
neg allows minimize
neg allows minimize
neg allows minimize
neg allows minimize
neg allows minimize
neg allows minimize
neg allows minimize
neg allows minimize
neg allows minimize
neg allows minimize
neg allows minimize
neg allows minimize
neg allows minimize
neg allows minimize
neg allows minimize
neg allows minimize
neg allows minimize
F-10
-------
APPENDIX G:
SAMPLE MODMAN INPUT: OFFUTT
OFMM2-1.INP, LF WELLS, CORE WELL,
SETO: General Parameters
KMODE) .01 .01
SETl: Time Parameters
1 1.00 1
TOE WELL, PLUS 9 NEW WELLS
.01 l.E-03 .01
1.00
SET2:
27
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
SET3:
59
Well
Information
0 27
1
2
3
4
S
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
3
4
3
4
4
6
3
4
6
4
6
4
6
4
6
4
6
4
6
4
6
4
g
4
6
4
6
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
59
59
67
67
61
61
44
44
44
57
57
57
57
57
57
60
60
60
60
60
60
63
63
63
63
63
63
127
127
129
129
93
93
73
73
73
100
100
103
103
106
106
101
101
104
104
107
107
100
100
103
103
106
106
-1.
-1.
-1.
-1.
-1.
-1.
-1.
-1.
-1.
-1.
-1.
-1.
-1.
-1.
-1.
-1.
-1.
-1.
-1.
-1.
-1.
-1.
-1.
-1.
-1.
-1.
-1.
E+04
E+04
E+04
E+04
E+04
E+04
E+04
E+04
E+04
E+04
E+04
E+04
E+04
E+04
E+04
E+04
E+04
E+04
E+04
E+04
E+04
E+04
E+04
E+04
E+04
E+04
E+04
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0,
0.
0.
0
0.
0
0
0
0
0
0
0
0
0
0
0
0
-2000.
-2000.
-2000.
-2000.
-2000.
-2000.
-2000.
-2000.
-2000.
-2000.
-2000.
-2000,
-2000.
-2000
-2000
-2000
-2000
-2000
-2000
-2000
-2000
-2000
-2000
-2000
-2000
-2000
-2000
.E+00
.E+00
.E+00
.E+00
.E+00
.E+00
.E+00
.E+00
.E+00
.E+00
.E+00
.E+00
.E+00
.E+00
.E+00
.E+00
.E+00
.E+00
.E+00
.E+00
.E+00
.E+00
.E+00
.E+00
.E+00
.E+00
.E+00
00
00
00
00
00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
If4-pw3
If4-pw3
If4-pw4
If4-pw4
h2c-pwl (toe)
h2c-pwl (toe)
h2c-corel
h2c-corel
h2c-corel
toe-newl
toe-newl
toe-new2
toe-new2
toe-new3
toe-new3
toe-new4
toe-new4
toe-new5
toe-new5
toe-new6
toe-new6
toe-new7
toe -new?
toe -newS
toe-new8
toe-new9
toe-new9
If4-pw3
If4-pw3
If4-pw4
If4-pw4
h2c-pwl (toe)
h2c-pwl (toe)
h2c-corel
h2c-corel
h2c-corel
toe-newl
toe-newl
toe-new2
toe-new2
toe-new3
toe-new3
toe-new4
toe-new4
toe -news
toe -news
toe-new6
toe-new6
toe-new7
toe-new7
toe -newS
toe-new8
toe-new9
toe-new9
Control Locations
1
2
3
4
4
4
4
4
32
32
33
36
79
80
79
83
G-l
-------
5
:''' 6
•• 7
i:1 ' , 1 8
9
10
"" . 11
12
13
14
IS
16
17
18
19
20
21
22
i 23
24
2S
26
27
23
4 36
4 37
4 ,i 40
4 40
4 41
4 43
4 43
4 44
4 46
4 46
4 47
4 49
4 49
4 50
4 52
4 52
4 53
4 54
4, , 54
4 55
4 56
4 56
4 57
4 58
29 4 58
30 4 59
31 4 61
32
33
34
3S
36
37
38
39
40
41
. 42
!! , 43
44
45
46
61
64
65
64
66
67
66
67
68
67
66
67
66
66
65
47 4 66
48 4 67
49 4 65
• SO 4 66
,. 51 4
' 52 4
53 4
54 4
i, SS 4
56 4
57 4
58 4
i .. 59 4
»ET4t Hc«d Limits
0
65
64
65
64
63
64
63
67
66
84
83
86
87
86
90
91
90
94
95
94
99
100
99
103
104
103
106
107
106
109
110
109
110
111
110
111
110
110
110
109
108
108
107
104
104
101
101
98
98
92
92
86
86
79
79
80
70
70
71
65
65
66
103
87
STTSt Head Difference Limits
4
.. 1 1
2 1
3 1
31
41
43
4 1 45
ftfttt Drawdown Limits
'0
32 O.E+00
42 O.E+00
44 O.E+00
46 O.E+00
l.E+20
l.E+20
l.E+20
l.E+20
SET7Ai Gradient Limits
: 34
. : ' .1 i
2 1
3 1
4 1
S 1
6 i
,7 1
8 1
• 9 l
1
1
4
4
7
7
10
10
13
2 -10.00
3 O.E+00
5 -10.00
6 O.E+00
8 -10.00
9 O.E+00
11 -10.00
12 O.E+00
14 -10.00
l.E+20
l.E+20
l.E+20
l.E+20
l.E+20
1.E+
1.E+
20
20
l.E+20
l.E+20
G-2
-------
SET7B :
0
SET7C:
17
SETS:
14
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
2B
29
30
31
32
33
34
Velocity
Relative
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
Limits
13
16
16
19
19
22
22
25
25
28
28
33
33
36
36
49
49
52
52
55
55
39
39
47
47
15
17
18
20
21
23
24
26
27
29
30
35
34
38
37
51
50
54
53
57
56
58
40
59
48
O.E+00
-10.00
O.E+00
-10.00
O.E+00
-10.00
O.E+00
-10.00
O.E+00
-10.00
O.E+00
0.00
-10.00
0.00
-10.00
0.00
-10.00
0.00
-10.00
0.00
-10.00
0.00
-10.00
0.00
-10.00
l.E+20
l.E+20
l.E+20
l.E+20
l.E+20
l.E+20
l.E+20
l.E+20
l.E+20
l.E+20
l.E+20
l.E+20
l.E+20
l.E+20
l.E+20
l.E+20
l.E+20
l.E+20
l.E+20
l.E+20
l.E+20
l.E+20
l.E+20
l.E+20
l.E+20
Gradient Limits
2
4
6
8
10
12
14
16
18
20
21
23
25
27
29
31
33
1
3
5
7
9
11
13
15
17
19
22
24
26
28
30
32
34
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.20
1.43
0.58
1.00
2.14
2.14
2.14
5.67
5.67
Balance Constraints
1
1
2
2
3
4
3
5
6
4
8
7
5
8
s
6
10
11
7
12
13
8
14
15
9
16
17
C
1.00
-.44
C
1.00
-.49
C
1.00
-1.28
C
1.00
-9.03
C
1.00
-1.31
C
1.00
-1.28
C
1.00
-1.28
C
1.00
-1.28
C
1.00
-1.28
E
E
E
E
E
E
E
E
E
O.E+00
O.E+00
O.E+00
O.E+00
O.E+00
O.E+00
O.E+00
O.E+00
O.E+00
2
2
2
2
2
2
2
2
2
*/lf4-pw3
*/lf4-pw4
*/h2c-pwl
*/h2c-corel
*/h2c-corel
*/toe-newl
*/toe-new2
*/toe-new3
*/toe-new4
G-3
-------
li *
i< i
j
!!'!
•1
1
1
1
1
I
I
SETS]
2
10
18
19
11
20
21
12
22
23
13
24
25
14
26
27
Integer
, . C
1.00
-il28
C
*r°0
-1.28
C
1.00
-1.28
C
1.00
-1,28
C
1.00
-1.28
Constraints
O.E+OO
O.E+00
O.EtOO
O.EH-OO
O.E+00
2
2
2
2
2
*/toe-new5
*/toe-newS
*/toe-new7
*/toe-new8
*/toe-new9
1
3
S
7
2 B
ia
12
14
16
19
20 "
22
24,,
26
SETlOi Objective Function
4 */limit on t existing wells
9 /*limit on if new wells
1
1
I
i
i
i
i
i
i
i
l
i
i
i
i
i
i
i
i
i
i
i
i
i
i
i
i
i
2
3
4
S
S
7
a
9
10
11
12
13
14
IS
16
17
18
19
20
21
22
23
24
25
26
27
27
-.005194
-.005194
-.005194
- .005194
-.005194
-.005194
-.005194
-.005194
-.005194
-.005194
-.005194
-.005194
-.005194
-.005194
-.005194
-.005194
-.005194
-.005194
-.005194
-.005194
-.005194
-.005194
-.005194
-.0051^4
-.005194
-.005194
-.005194
/*factor
/•factor
/•factor
/*£actor
/•factor
/•factor
/•factor
/•factor
/•factor
/•factor
/•factor
/•factor
/•factor
/•factor
/•factor
/•factor
/•factor
/•factor
/•factor
/•factor
/•factor
/•factor
/•factor
/•factor
/•factor
/•factor
/•factor
converts
converts
converts
converts
converts
converts
converts
converts
converts
converts
converts
converts
converts
converts
converts
converts
converts
converts
converts
converts
converts
converts
converts
converts
converts
converts
converts
to gpm,
to gpm,
to gpm,
to gpm,
to gpm,
to gpm,
to gpm,
to gpm,
to gpm,
to gpm,
to gpm,
to gpm,
to gpm,
to gpm,
to gpm,
to gpm,
to gpm,
to gpm,
to gpm,
to gpm,
to gpm,
to gpm,
to gpm,
to gpm,
to gpm,
to gpm,
to gpra,
neg allows minimize
neg allows minimize
neg allows minimize
neg allows minimize
neg allows minimize
neg allows minimize
neg allows minimize
neg allows minimize
neg allows minimize
neg allows minimize
neg allows minimize
neg allows minimize
neg allows minimize
neg allows minimize
neg allows minimize
neg allows minimize
neg allows minimize
neg allows minimize
neg allows minimize
neg allows minimize
neg allows minimize
neg allows minimize
neg allows minimize
neg allows minimize
neg allows minimize
neg allows minimize
neg allows minimize
G-4
-------
APPENDIX H:
EFFICIENTLY MAKING MODIFICATIONS
TO MODMAN FORMULATIONS
Numerous hydraulic optimization formulations were solved with the MODMAN cod. > as part of this
project. However, each formulation did not require a separate execution of the MODMAN code. A MODMAN
execution has the following major steps:
(1) execute MODMAN (mode 1) to create an MPS file (a linear or mixed-integer program);
(2) execute LINDO to solve the linear or mixed-integer program; and
(3) execute MODMAN (mode 2) to post-process the LINDO results.
In many cases, it is possible to slightly modify the hydraulic optimization formulation without re-executing
MODMAN in mode 1 . This can be accomplished by:
(1) modifying the MPS file with a text editor, prior to running LINDO; or
(2) modifying the linear or mixed-integer program directly within LINDO.
In many cases, LINDO results can be extracted manually, and there is no need to execute MODMAN in mode 2 (to
post-process LINDO output).
For example Section 4 4.2 discusses a series of mathematical optimal solutions for Kentucky, where the head limit
!t ceSacenno &e , iver is varied. The base formulation has an upper limit of 399.99 ft MSL assigned at 54
fellf To ™ e Z mathematical optimal solutions associated with the other head limits, a text editor was used to
Sodify mfu^per bounds on the appropriate variables in the MPS file. LINDO then solved the modified MPS file.
Another example is the generation of mathematical optimal solutions for related problems where integer constraints
aS uSd to St the number of wells selected. There is a specific constraint that has the following general form (see
Section 3.1.3):
The "right-hand side" of this constraint sets the limit on the number of active wells. This limit can easily be altered
in the MPS file with a text editor, or altered directly within the LINDO software.
A full discussion of the structure of the MPS file, and potential .
(e.g., scaled well rates) is beyond the scope of this report. For more information, refer to the MODMAN User s
Guide (Greenwald, 1998a).
H-l
-------
-------
APPENDIX I:
SOURCES OF INFORMATION AND REFERENCES FOR OTHER OPTIMIZATION
RESEARCH AND APPLICATION
The purpose of this appendix is to guide readers of this report to individuals or organizations that offer additional
information on optimizations of groundwater systems. Although this is by no means a comprehensive reference
section regarding optimization of groundwater systems, it should provide the reader with sufficient data to pursue
additional information on a wide variety of subjects associated with optimization of groundwater systems.
A partial listing of individuals/organizations associated with optimization of groundwater systems is provided
below:
Name
David
Ahlfeld
Paul
Barlow
Wes
Danskin
David
Dougherty
Steve
Gorelick
Rob
Greenwald
George
Karatzas
Ann
Mulligan
Affiliation or
Company
University of
Massachusetts
U.S.G.S
USGS Water
Resources
Subterranean
Research, Inc.
Stanford
University
HSI GeoTrans, Inc.
Technical University
of Crete
University of
Massachusetts
Address
Dept. of Civil and Env. Engineering
139 Marston Hall
University of Massachusetts
Amherst,MA 01003
28 Lord Road
Marlborough, MA 01752
5735 Kearney Villa Road, Suite 0
San Diego, CA 92 123
P.O. Box 1121
Burlington, VT 05402
Dept. of Geological and Env. Sciences
Stanford University
Stanford, CA 94305-2115
2 Paragon Way
Freehold, NJ 07726
Dept. of Environmental Engineering
Polytechneioupolis
73 100 Chania
Greece
Dept. of Civil and Env. Engineering
139 Marston Hall
University of Massachusetts
Amherst,MA 01003
Phone/Fax/Email
Voice: (413) 545-2681
Fax: (413) 545-2202
ahlfeld@ecs.umass.edu
Voice: (508) 490-5070
Fax:
pbarlow@usgs.gov
Voice: 619-637-6832
Fax: 619-637-9201
wdanskin@usgs.gov
Voice: (802)-658-8878
Fax: (802)-658-8878
David.Dougherty@subterra.com
Voice: (415) 725-2950
Fax: (415) 723-1445
gorelick@geo.stanford.edu
Voice: 732-409-0344
Fax: 732-409-3020
rgreenwald@hsigeotrans.com
Phone: (011-30-821) 37473
Fax: (011-30-821)37474
karatzas@emba.uvm.edu
Voice: (413) 545-2681
Fax: (413) 545-2202
mulligan@ecs.umass.edu
1-1
-------
Affiliation or
Company
Phone/Fax/Email
Daenc
McKinney
University of Texas
Department of Civil Engineering
Austin, TX 78712
Voice: 512-471-8772
Fax: 512-471-0072
Daene@AOL.com
Tracy
Nishikawa
5735 Kearney Villa Road, Suite 0
San Diego, CA 92123
Voice: 619-637-6848
Fax: 619-637-9201
tnish@uses.eoi
David
Watkins
US Army Corps of
Eng., Hydrologic
Engineering Center
609 Second Street
Davis, CA 95616-4587
Voice: 530-756-1104
Fax: 530-756-8250
david.w.watkins@usace.armv.mi]
Richard C
Peralta
Utah State University
Building EC-216
Utah State University
Logan, UT 84322-4105
Voice: 801-797-2786
Fax: 801-797-1248
peralta@cc.usu.edu
George
Finder
University of
Vermont
Dept. of Civil and Env. Engineering
371 Votey Building
Burlington, VT 05405-0156
Voice: 802-656-8697
Fax: 802-656-8446
George.Pinder@uvm.edu
5735 Kearney Villa Road, Suite 0
San Diego, CA 92123
Voice: 619-637-6834
Fax: 619-637-9201
egreich@usgs.gov
Subterranean
Research, Inc
P.O. Box 1121
Burlington, VT 05402
Voice: 802-658-8878
Fax: 802-658-8878
Donna.Rizzo@subterra.com
Clmstine
Shoemaker
Cornell University
ivil Engineering
Hollister Hall
Ithaca, NY 14853
Voice: 607-255-9233
Fax: 607-255-9004
cas 12@cornell.edu
Brian
Wagner
Bldg 15, McKelvey Building
345 Middlefield Road, MS 409
vlenlo Park, CA 94025
Voice:650-329-4567
)jwagner@usgs.go)
Chunmiao
Zheng
University of
Alabama
Jepartment of Geology
Jniversity of Alabama
Tuscaloosa, AL 35487
Voice: 205-348-0579
ax: 205-348-0818
czhene(S>.wes.geo.ua.edu
As part of this project, information was solicited from select professionals involved in optimization code development for
groundwater problems. The following pages provide brief summaries of codes and/or applications, provided by those
professionals who responded:
1-2
-------
Code/Method:
Description By:
MODOFC (MODflow Optimal Flow Control)
David Ahlfeld, University of Massachusetts
Brief Description:
Application^):
MODOFC (MODflow Optimal Flow Control) is a FORTRAN computer program which determines
optimal pumping solutions for groundwater flow control problems. MODOFC couples the USGS
MODFLOW simulation program with optimization algorithms. The code can accommodate linear
pumping costs, well installation costs, bounds on head and head difference, bounds on individual and
net well pumping rates and bounds on total number of wells. MODFLOW features that can be
accommodated include three-dimensional heterogeneous aquifers, confined or unconfined units, wells
screened in single or multiple layers and single or multiple stress periods. MODOFC is designed to
utilize existing MODFLOW96 input files along with a user-created file describing the hydraulic
control problem. MODOFC converts the groundwater flow control problem into an optimization
problem by the response matrix method. MODOFC contains a Ml implementation of the simplex
algorithm. The simplex and branch and bound algorithms are used for mixed binary problems.
Sequential linear programming is used for unconfined problems.
An early version of MODOFC was used to design a groundwater pump and treat remediation system
in coastal New Jersey. The aquifer was contaminated with a plume extending over several hundred
acres and nearly 100 feet vertically. The site consisted of approximately 50 extraction wells, several
recharge basins and pumped approximately 3 million gallons per day. The site was modeled with
MODFLOW with five numerical layers and 35,000 grid cells. The results are presented in Ahlfeld et.
al. (1995) and Finder et. al. (1995).
References: Ahlfeld, D. P., R. H. Page, and G. F. Pinder.1995. Optimal Ground-water remediation methods applied
to a superfund site: From formulation to implementation. Groundwater, 33(1):58-70.
G.F. Finder, D.P. Ahlfeld, and R.H. Page, 1995. "Conflict Resolution in Groundwater Remediation
using Management Models: A Case Study", Civil Engineering, Vol. 65, No. 3, March 1995, pgs.
59-61.
Riefler, R.G. and D.P. Ahlfeld, 1996. "The Impact of Numerical Precision on the Solution of Confined
and Unconfined Optimal Hydraulic Control Problems", Hazardous Waste and Hazardous Materials,
Vol 13, No. 2, 1996, pgs 167-176.
Availability: MODOFC is available free of charge on the world wide web at "http://www.ecs.umass.edu/modofc/"
Point(s) of Contact: David Ahlfeld (see table at beginning of this Appendix).
1-3
-------
Code/Method:
Description By:
I • . ' ' , . ;:
Brief Description:
Application(s):
References:
Availability:
MODFLIP
.;, ' I ' ..:•:•:.
David Dougherty, Subterranean Research, Inc.
MODFLIP couples the popular MODFLOW groundwater simulation program with /inear and mixed
integer programming optimization [Fourer et al, 1993]. MODFLIP can be used to compute the
optimal pumping strategies for groundwater management problem for which a reliable MODFLOW
model exists, like other optimization programs described in this Appendix. Linear programming (LP)
is limited in applicability to problems having linear (that is, proportionality) relations among cost,
pumping rates, and all constraints. This approach can be applied, therefore, to groundwater flow in
confined aquifers. If approximations are introduced, it can be applied in other cases that are weakly
nonlinear, such as unconfined aquifers with small drawdowns. Mixed integer programming provides
f°J fixfd or one-time costs. The design of MODFLIPs mathematical optimization relies on a two-part
objective function. The first is proportional to the amounts of pumping out of or into (extraction or
injection) candidate wells. Through a linearization method, the energy costs (lift) can be included. The
second part of the objective function is proportional to a binary (on-off, or one-zero) variable, which
indicates whether a particular candidate well is selected or not, This term allows for costs including
drilling, casing, and screen. Constraints on heads, head differences, and pumping rates are possible. In
addition, the ratio of total injection to extraction can be constrained (e.g., to ensure that all extracted
water is reinjected). Gorelick et al. [1989] provide a large number of two-dimensional examples to
which linear programming is applicable; this software expands on their list by allowing fully 3-D flow
conditions.
MODFLIP is applicable to steady flow optimization, linear programming, and linear mixed-binary
programming problems.
'4 . .. ! ' ' , • : ' . : : ' !|: ". , ;. !.£•
Fourer, R., D. M. Gay, B. W. Kernighan, Ampl: A Mo deling Language for Mathematical
Programming, Duxbury Press, Pacific Grove, CA, 1993.
Gorelick, S., R. A. Freeze, D. Donahue, and J. F. Keely, Groundwater Contamination: Optimal
Capture and Containment, Lewis Publishers, 385 pp., 1989.
Subterranean Research, Inc., MODFLIP, A MODFLOW-basedProgram forFlow Optimization,
http://www.subterra.com/pubhcations/MODFLIP.pdf, 1999.
J ' , , •»"..,•. I • :" ' ' »
"ii • .,';.'... I , ' i' »
Contact points of contact listed below.
*'!'
' i
;!
Hi
T
1-4
-------
Code/Method:
Description By:
REMAX
Richard Peralta, Utah State University
Brief Description: REMAX can compute optimal pumping strategies for any ground-water system for which you have a
reliable simulation model. For simple dynamic stream-aquifer problems REMAX can also compute
optimal conjunctive use strategies. Such a strategy includes optimal surface water diversion and
ground-water pumping rates. REMAX can assure that implementing the optimal water management
strategy will not cause unacceptable physical system responses. To do this the modeler specifies limits
on acceptable responses. REMAX can constrain aquifer hydraulic heads, gradients, and flows. It can
constrain streamflow in simple stream-aquifer management problems. For special situations REMAX
has been adapted to constrain contaminant concentrations in ground water or surface water, or
volumes of nonaqueous phase liquids (free product, residual, extracted). REMAX can address a wide
range of volumetric, economic or environmental problems involving ground-water management. To
do this it solves optimization problems having objective functions and constraints that are linear,
nonlinear, integer or mixed integer. REMAX performs deterministic or stochastic, single- or multi-
objective optimization. REMAX simulates using either standard numerical simulation models such as
MODFLOW or response matrix (superposition) models that use influence coefficients derived via
simulation models. REMAX employs response matrix methods adapted to accurately address
nonlinear systems (unconfined aquifers). For special situations (often involving contaminant
management), linear and nonlinear response surface methods are also used.
Application^): 1. Optimal Pumping Strategy to Capture TCE Plume at Southwest Base Boundary, Norton AFB
(NAFB), California.TCE Plume was about 4 miles long and 1 mile wide. Site modeled using 3-layer
MODFLOW model. Top layer was up to about 300 feet thick.Used REMAX Simulation/Optimization
(S/O) model to optimize steady pumping. Initially assumed over 20 candidate wells, 40 gradient
constraints in optimization problem. It was challenging because base boundary was irregular and all
wells had to be on base. This was steady flow (hydraulic) optimization. Optimal pumping system
design and strategy was built and implemented. It involved a total extraction of 2250 gpm; total of 3
extraction wells and 8 injection wells. It saved about 20% ($5.8M in present value) when compared
with a design provided by a consulting firm that did not use S/O modelling. Sensitivity analysis
demonstrated the strategy should be valid even if hydraulic conductivity differed widely from assumed
mean value (ie 60% underestimation .through 80% overestimation).
2. Multiobjective Optimization: Maximizing Pumping for Water Supply versus Minimizing Pumping
Needed for Plume Containment Subject to Lower Bound on Seepage from Aquifer to River (an
anonymous site in the Northeast US). A contaminant plume existed under an industrial facility that
had 3 wells and used some of the pumped water in industrial processes. Pumping from 3 upgradient
public supply wells causes plume to be captured by those supply wells. MODFLOW was used to
model the three-layer system. An anonymous contractor developed a steady pumping strategy using
simulation model alone. REMAX was used for mulriobiective linear steady flow (hydraulic)
optimization. All scenarios involved Linear Programming. The first scenario was single objective:
minimize total pumping needed to prevent the plume from moving to public wells, subject to
constraints. The optimal pumping strategy required 40 percent less pumping than that developed by
other contractor using only a simulation model. Later the municipality wanted to increase total
pumping for water supply. This would require that the industry increase their total pumping to retain
plume containment. However, the state water resources agency was concerned that the increases in
pumping would dewater the nearby river too much. REMAX was used to develop the pareto optima
solutions for this multiobjective problem.
3. Calibration of a Flow Model and Optimal Pumping Strategies to Capture a TCE Plume at Travis
AFB (TAFB), California. TCE plume had migrated under a runway and emerged on the other side. It
was moving toward a stream that flowed toward and important wetland. Site modeled using 4-layer
MODFLOW model, 5040 cells per layer. Plume exists in top three layers. REMAX was used to
develop the minimum steady pumping needed from many candidate wells. It used many gradient
1-5
-------
References:
constraints. This was steady flow optimization. Optimal pumping system design and strategy involved
5 extraction wells with pumping rates between 5 and 11 gpm. Total extraction is about 40 gpm.
4. Optimal Pumping Strategy to Contain a TCE Plume at March AFB (MAFB), California. TCE plume
had crossed base boundaries and was under an urbanized area and was moving toward water supply
wells. Site was modeled using a 4-layer SWIFT model. Contamination existed in multiple layers.
REMAX was used to develop the minimum steady pumping needed from many candidate wells. It
used many gradient constraints. This was steady flow (hydraulic') optimization.
"ini • • • • ••• '"! v,-;1"'1. •, * | .. •; :>
5. Optimal Pumping Strategies to Maximize Dissolved TCE Extraction at Central Base Area, Norton
AFB, California. TCE plume at a source area was to be remediated. MODFLOW and MT3D were
used for a single layer system. Wells were already installed. Transient (two stress periods) transport
optimization was used to develop maximum mass removal transient pumping strategies a specific
planning horizon. Strategies were developed for a range of scenarios...differing in the maximum total
piimping rate (200-400 gpm) and the wells that could be used. Enhanced REMAX was used. This
$!owed the importance of applying optimization as early in the design process as possible. If one had
'ft) use existing wells and the same upper limit on total pumping, the optimal strategy was not much
better than the existing strategy. If one could use different wells locations and the same total pumping,
the amount of TCE mass removed could increase by about 20%. Increasing total pumping permits
increased mass removal.
,, . I
6. Optimal Pumping Strategies to Maximize Dissolved TCE Extraction at Mather AFB, California.
TCE plume at a source area was to be remediated. MODFLOW and MT3D were used to simulate
flow ^d transport in a two layer system having 2184 cells in each layer. Wells were already installed.
T!ansient ^two stress Periods) transport optimization was used to develop maximum mass removal for
a specific planning horizon. Strategies were developed for a range of scenarios., differing in the
maximum total pumping rate and the wells that could be used. Enhanced REMAX was used. Using
the existing wells and the same total pumping, over twenty percent increase in total mass removal is
possible. Using alternative wells can increase mass removal. Raising upper limit on total pumping
increases TCE mass removal.
i
7. Optimal Pumping Strategies for Cleanup and Containment of TCE and DCE Plumes Near Mission
Drive, Wurtsmith Air Force Base (WAFM), Michigan. TCE and DCE plumes were projected to reach
a stream. The goal is plume containment and cleanup (to specified concentration) within a planning
k°P3?n' MODFLOW and MT3D were the models used to represent this 3-layer system. First,
genetic algorithm was used in nonlinear programming transport optimization to maximize mass
removal subject to constraints. Strategies were developed for a range of total pumping rates being
processed by the treatment plant. Objective was to maximize TCE mass removed subject to: (1) upper
%** on fmal TCE and DCE aquifer concentrations; (2)upper limit on TCE concentration entering the
treatment facility during any time step.; and (3)upper limit on total flow. Then the additional minimal
pumping needed to achieve containment was determined using REMAX. Additional wells were added
as needed. This was linear steady flow (hydraulic") optimization. Objective was to minimize total
pumping subject to: (1) using the cleanup wells to the extent possible; and (2)containing the plume
using hydraulic gradient constraints. Finally, optimal pumping strategies were developed for a range
of treatment facility capacities.
Contact Richard Peralta
Avafjability: For sale (contact Richard Peralta)
Point(s) of Contact: Richard Peralta (see table at beginning of this Appendix).
1-6
-------
Code/Method:
Description By:
Brief Description:
Application(s):
Global Optimization Methods (Genetic Algorithms, Simulated Annealing, and Tabu Search)
Chunmiao Zheng, University of Alabama
As part of our research efforts in the area of groundwater remediation design optimization in the last
several years, we have developed a number of general-purpose flow and transport simulation-
optimization software tools. These software tools combine the MODFLOW (McDonald and
Harbaugh, 1988) and MT3D/MT3DMS (Zheng, 1990; Zheng and Wang, 1998) codes for flow and
transport simulation with a general optimization package for formulating the most cost-effective
groundwater management and remedial strategies under various physical, environmental and
budgetary constraints. The optimization package is implemented with three global optimization
methods, namely, genetic algorithms, simulated annealing and tabu search. The global optimization
methods have the ability to identify the global or near-global optimum, are efficient in handling
discrete decision variables such as well locations, and can be easily linked to any flow and transport
simulation models for solving a wide range of field problems. They are also very easy to understand
and simple to use.
Our global optimization based management tools are capable of determining time-varying
pumping/injection rates and well locations for three-dimensional field-scale problems under very
general conditions. The objective function of the optimization model can be highly nonlinear and
complex.. Most types of constraints that are commonly encountered in the field, such as prescribed
hydraulic gradients, minimum drawdowns, and maximum concentration limits, can be readily
incorporated. To account for the uncertainties in the groundwater flow and contaminant transport
models, our software has a dual formulation to allow the user to perform automated parameter
estimation given observed head and concentration data. Since our software does not require any
changes to the input files prepared for MODFLOW and MT3D/MT3DMS, it can be used with any
graphical user interfaces developed for MODFLOW and MT3D/MT3DMS, including Visual
MODFLOW, DoD GMS, and Groundwater Vista.
The most significant limitation of the global optimization based management tools is their intensive
computational requirements. To mitigate this problem, global optimization methods may be integrated
with linear or nonlinear programming as we have recently demonstrated (Zheng and Wang, 1999).
This integrated approach takes advantage of the fact that global optimization methods are most
effective for dealing with discrete decision variables such as well locations while traditional
programming methods may be more efficient for dealing with continuous decision variables such as
pumping rates. Our preliminary work shows that it is possible to achieve dramatic reductions in
runtime with the integrated approach.
Our simulation-optimization tools have been successfully applied to remediation design optimization
problems at several field sites with complex hydrogeologic conditions. A typical example is presented
by Wang and Zheng (1997) involving optimization of an existing pump-and-treat system at a gasoline
terminal site in Granger, Indiana. Groundwater beneath and down-gradient of the site was found to
contain dissolved compounds associated with petroleum hydrocarbons in extensive field
investigations. Groundwater flow and solute transport models were developed in previous remedial
investigations and feasibility studies to evaluate the various remedial alternatives at the site. A pump-
and-treat system was already designed through the trial-and-error approach and implemented at the
site.
The optimization approach was applied to the same remediation design problem for comparison with
the trial-and-error approach. Because the flow field was considered steady-state, and the fixed capital
costs were negligible relative to the pumping and treatment costs, the objective function was simplified
as minimizing the total pumping at eight existing wells subject to the constraint that the maximum
concentration level in the entire model must not exceed a specified value at a specific time. For
comparison with the trial-and-error solution, the concentration limit for the optimization problem was
set equal to the calculated maximum concentration at the end of the comparison period based on the
1-7
-------
I 'ill!1 i -I* ' it I
References:
pumping rates from the trial-and-error solution. The optimization solution reduces the total extraction
of the trial-and-errqr solution by approximately 64 percent, demonstrating the significant economic
benefits that may be derived from the use of the simulation-optimization models in remediation system
designs.
:! • H
Glover, F. 1986. Future paths for integer programming and links to artificial intelligence. Comp. and
Operations Res., 5, p. 533-549.
:; " '/ ' '. \' . :
IvfcDonald, M.G. and A.W., Harbaugh. 1988. A Modular Three-Dimensional Finite-Difference
Grpundwater Flow Model. Techniques of Water Resources Investigations, Book 6, USGS.
IvfeKinney, D.C. and M.-D. Lin. 1994. Genetic algorithms solution of groundwater management
models, Water Resour. Res., 30(6), p. 1897-1906.
Rizzo, D.M., and D.E. Dougherty. 1996. Design optimization for multiple management period
groundwater remediation, Water Resour. Res., 32(8), p. 2549-2561.
Wang, M. and C. Zheng. 1997. Optimal remediation policy selection under general conditions,
Ground Water, 35(5), p. 757-764.
Wang, M. and C. Zheng. 1998. Application of genetic algorithms and simulated annealing in
groundwater management: formulation and comparison, Journal of American Water Resources
Association, vol. 34, no. 3, p. 519-530.
Zheng, C. 1990. MT3D, A Modular Three-Dimensional Transport Model for Simulation ofAdvection,
Dispersion and Chemical Reactions of Contaminants in Groundwater Systems. Report to the USEPA,
170pp.
Zljeng, C. and P.P. Wang. 1998. MT3DMS, A Modular Three-DimensionalMultispecies Transport
Model, Technical Report, U.S. Army Engineer Waterways Experiment Station.
Zheng, C. and P.P. Wang. 1999. An integrated global and local optimization approach for remediation
system design, Water Resour. Res., 35(1), p. 137-146.
Availability:
Contact "points of contact" listed below.
Poit|t(s) of Contact: Chunmiao Zheng (see table at beginning of this Appendix).
1-8
-------
Code/Method:
Description By:
Simulated Annealing
David Dougherty, Subterranean Research, Inc.
Brief Description:
Simulated annealing (SA) is an optimization method that can be applied to any setting. It has been
applied to confined aquifers, unconfined aquifers, soil vapor extraction, flow-only control,, and solute
transport-driven control with constraints ranging from simple to exceedingly complex. It is structured
to make discrete decisions (e.g., select from discrete pumping rates at remediation wells), although this
can be modified. It can handle multiple management periods (sequences of operating schedules). SA is
very well suited to difficult and large optimization problems, and performs poorly on small linear
problems; it is therefore a perfect companion to LP. Like the outer approximation method, SA does not
require a feasible initial problem to start, unlike many nonlinear (and linear) optimization methods. If
there is no feasible solution to the problem, SA will provide "good" (though infeasible) solutions.
When naively applied, SA can require enormous computing resources and time, while in experienced
hands and when applied to appropriate problems the method is competitive with any other.
Application^): Simulated annealing (SA) and related methods (e.g., elements of tabu search) were introduced into the
groundwater literature by Dougherty and Marryott [1991]. At a central California site, the method was
applied in a post mortem approach to determine if cleanup could have been accomplished with less
expense. Marryott, Dougherty, and Stollar [1991] report that a 40% reduction in pumping rates could
have been achieved. Groundwater simulations used an engineering model developed by LLNL that
was not modified for the optimization process. The method has been applied to a solvent plume at
Lawrence Livermore National Laboratory during the design phase; SA selected clever locations and
operating schedules, and cost reductions in the tens of millions of dollars were identified [Rizzo and
Dougherty, 1996]. SA has also been applied to a soil vapor extraction application [Sacks, Dougherty,
and Guarnaccia, 1994]. To our knowledge, Subterranean Research, Inc. personnel have conducted the
only applications of SA to field-scale problems.
References: Dougherty, D. E., and R. A. Marrott, "Optimal groundwater management, 1. Simulated annealing",
Water Resources Research, 27(10), 2493-2508, 1991.
Marryott, R. A., D. E. Dougherty, and R. L. Stollar, "Optimal groundwater management, 2
Application of simulated annealing to a field-scale contamination site", Water Resources Research,
29(4), 847-860, 1993.
Rizzo, D. M., and D. E. Dougherty, "Design optimization for multiple management period
groundwater remediation", Water Resources Research, 32(8), 2549-2561, 1996.
Sacks, R. L., D. E. Dougherty, and J. F. Guarnaccia, "The design of SVE remediation systems using
simulated annealing", 1994 Groundwater Modeling Conference, Fort Collins, CO, August 10-12,
1994.
Availability:
Contact "points of contact" listed below.
Point(s) of Contact: David Dougherty or Donna Rizzo (see table at beginning of this Appendix).
1-9
-------
Code/Method:
Description By:
Brief Description:
it)1
Augmented Outer Approximation
David Dougherty, Subterranean Research, Inc.
', ': • '„ . \ \, . . : ';." ;
Augmented Outer Approximation can be applied to containment and cleanup groundwater quality
problems, as well as other water resources problems. Like the other methods described in this
Appendix, a suitable and reliable aquifer simulation model is available. Outer approximation has been
combined with the MODFLOW, MT3DMS, and SUTRA simulation models, for example.
The outer approximation method is a cutting plane optimization method designed originally for
concave objectives (minimization) and convex constraints. Karatzas (see listing in this Appendix or
the Karatzas and Finder [1996] paper) describes extensions that accommodate nonconvex constraints,
which occur in transport and other nonlinear optimization problems.
.. , ii • ...... I I . .. i
:.:'iii ' . . • - ' '• , r • in •' p ' r >i||' :• . .. . • i n,i ',
To solve larger problems faster and more effectively, Subterranean Research, Inc. has augmented outer
approximation algorithms for groundwater problems in several ways. Among these are the following:
A completely new data structure has been implemented, resulting in
substantial speedups.
New nonlinear algorithms adapt to nonconvex problems and a new
"cutting depth" strategy.
Completely new pivoting method for generating hyperplanes and
associated data structures.
Innovative method for subspace projection of optimization problem,
resulting in substantially improved efficiency.
Application(s): Karatzas (see listing in this Appendix) cites several applications of the outer approximation method.
|;i ,, Subterranean Research, Inc. has conducted a range of test applications involving both synthetic and
real sites.
References:
I? ' • :il
Availability:
Point(s) of Contact:
Karatzas, G. P., and G. F. Finder, "The solution of groundwater quality management problems have
non-convex feasible region using a cutting plane optimization technique", Water Resources Research,
vol. 32, no.4, 1091-1100, 1996.
Contact "points of contact" listed below.
David Dougherty or Donna Rizzo (see table at beginning of this Appendix).
1-10
-------
Code/Method:
Description By:
The Outer Approximation Method
George Karatzas, Technical University of Crete
Brief Description:
The Outer Approximation method is a cutting plane technique for the minimization of a concave
function over a compact set of constraints that can have a convex or non-convex behavior. The basic
concept of the method is that the minimum of a concave function occurs at one of the most "outer"
points of the feasible region. The concept of the methodology is describe as follows: Initially, the
feasible region is approximated by an enclosing polytope, which is defined by a set of vertices. Then,
the vertex that muiimizes the objective function is determined. If the vertex belongs to the feasible
region this is the optimal solution, if not a cutting plane is introduced to eliminate part of the infeasible
region and create a new enclosing polytope that is a "better" approximation of the feasible region. A
new set of vertices is determined and the process is repeated until the optimal Solution is obtained.
Depending on the behavior of the feasible region, convex or concave, a different approach is applied
to determine the equation of the cutting plane. The method guarantees a global optimal solution. The
Outer Approximation Method has the potential to solve groundwater management problems related to
hydraulic gradient control and/or mass transport optimization problems. Additional features of the
method are:
• It incorporates the well installation cost.
• It can incorporate treatment plant design (under development).
• It can handle combination of hydraulic gradient and concentration constraints.
• For small to average problems it can handle multi-period design problems.
• It can incorporate uncertainty (under development).
Application^): (1) The Woburn aquifer in Massachusetts. A remediation scheme using the developed Outer
Approximation algorithm in combination with the 2-D numerical simulator, GW2SEN.
(2) The Lawrence Livermore National Laboratory Site in California. An optimal design using the
Outer Approximation Algorithm in combination with a 2-D numerical simulation, SUTRA,
and a 3-D numerical simulator, PTC (Princeton Transport Code).
(3) The U.S. Air Force Plant number 44, Tuscon, Arizona. Preliminary studies on the site, testing
the existing pump-and-treat remediation scheme and propose and optimal remediation
scheme using the Outer Approximation algorithm and a 3-D numerical simulator, PTC.
References: Karatzas, G. P., and G. F. Pinder, "Groundwater Management Using Numerical Simulation and the
Outer Approximation Method for Global Optimization", Water Resources Research, vol. 29, no. 10,
3371-3378, 1993.
Karatzas, G. P., and G. F. Pinder, "The Solution of Groundwater Quality Management Problems with
a Non-convex Feasible Region Using a Cutting Plane Optimization Technique", Water Resources
Research, vol. 32, no. 4, 1091-1100, 1996.
Karatzas, G. P., A. A. Spiliotopoulos, and G. F. Pinder, "A Multi-period Approach for the Solution of
Groundwater Management Problems using the Outer Approximation Method", Proceedings of the
North American Water and Environment Congress '96, American Society of Civil Engineers, CD-
ROM, 1996.
Availability:
Code not in public domain, not for sale.
Point(s) of Contact: George Karatzas (see table at beginning of this Appendix).
Ml
-------
4ii '!"
I,!--
!*,
------- |