Roger McCready, C.P.G.
Project Manager / Hydrogeologist
Terran Corporation, Beavercreek, Ohio
HSI GeoTrans, Inc., Freehold, New Jersey
Project Completed in May 1996
Computer modeling was used to simulate and optimize the placement of wells to contain and remove a plume of contaminated groundwater.
At the facility in this study, Operable Units One and Nine have completed specific ground water investigations. Operable Unit One (OU-1) addressed the possible chemical contamination of the buried valley aquifer which underlies the original southwest corner of the facility. OU-1 is currently in the final phase of a three phase process. Phase III is the remedial design/remedial action (RD/RA) which will implement the chosen remedial method, a pump-and-treat system.
The purpose of this study was to provide OU-1 Remedial Design with pump-and-treat well placement and pumping rates. The scope was to utilize the existing OU-1 ground water flow model to simulate and optimize the placement and flow rates of the pump-and-treat wells for remediation of OU-1. The OU-1 groundwater flow model was a subarea of the previously developed Operable Unit Nine (OU-9) Ground Water Flow Model.
A method was chosen that simulates the aquifer system and optimizes the locations and pumping rates of wells used to contain and remove the OU-1 contaminant plume. The benefit of the simulation-optimization method is the quantified results. A computer code, MODMAN, was selected that uses the current groundwater flow model to conduct aquifer system simulations. The responses from the simulations were combined with user selected objectives and constraints via linear programming to calculate the optimal solution.
Pump-and-treat systems are designed to hydraulically contain and remove the contaminants. Due to the relatively long duration of pump-and-treat remediations, the objective of the management problem is to minimize total pumping rate. The OU-1 groundwater contamination plume must be contained within a western and southern compliance boundary. Containment refers to an inward hydraulic gradient at the boundary to prevent the movement of groundwater across that boundary. Therefore, the primary constraints are head-differences at the compliance boundary. A secondary constraint is the number of wells to be used.
Design strategies that were considered included field measurable head-difference limits of 0.025, 0.05 and 0.1 feet, between one and five wells, and a maximum total pumping rate of 200 gpm. Results of all design strategies had feasible solutions except one. The design strategy of a 0.05 foot head-difference limit was chosen as the optimal solution because this strategy allows containment to be measured and provides some conservatism to the containment.
A parametric analysis of total pumping rates versus number of pumping wells was completed. This analysis showed that if less than three wells were used, the total pumping rate of groundwater needed to meet the required head-difference limit increased 120 to 190 percent. Conversely, if the number of wells was four or five, the reduction in the total pumping rate was not significant enough to justify an increase in the number of wells. Based on the analysis, it was decided that the pump-and-treat system should consist of three optimally placed wells. The design rates for these wells were determined to be 15, 30 and 25 gpm.
Several simulations were conducted to assess the impacts of removing one or two wells from the system. Particle tracking was used to assess the impacts. If any two wells (or one particular well) remain pumping at corresponding well design rates, the OU-1 plume would be contained. These simulations did not produce the desired 0.05 foot head-difference at the compliance boundary but did produce a sufficient head-difference to cause inward flow and containment.
The federal facility in this study started operation in 1949 and is an integrated research, development, and production facility. The facility was placed on the Comprehensive Environmental Response, Compensation, and Liability Act (CERCLA, also known as Superfund) National Priorities List (NPL) in 1989. The facility was added to the NPL as a consequence of historic disposal practices and releases of contaminants to the environment. The terms of the Federal Facility Agreement (FFA) require the facility to develop and implement remedial investigations (RIs) and feasibility studies (FSs) and conduct interim remedial actions to ensure that environmental impacts associated with past and present activities at the site are thoroughly investigated and appropriate actions are taken to protect the public health, welfare, and the environment.
Due to the number of potential release sites (more than 400) and the overall complexity of the RI/FS, the site is divided into nine operable units (OUs) to facilitate program management. Currently, six OUs remain; the others have been closed. Operable Unit Nine (OU-9) is designated for site-wide studies that provide the framework for the RI/FS. Investigations that are best conducted for the entire facility and its regional setting are included in OU-9. Operable Unit One (OU-1) RI/FS has been completed and work is progressing to implement the remedial actions.
Purpose and Scope of this Study
The purpose of this study was to provide OU-1 Remedial Design with pump-and-treat well placement and pumping rates. The goal was to utilize the existing OU-1 ground water flow model to simulate and optimize, via groundwater modeling, the placement of pump-and-treat wells for remediation of OU-1.
This presentation summarizes important portions of the pump-and-treat optimization procedure and includes a brief review of the OU-1 groundwater flow model, the simulation-optimization methodology, the optimization problem development and the optimization results.
Background and Previous Investigations
The FFA requires the thorough investigation of past and present activities at the facility to determine their environmental impacts. These investigations have shown that the buried valley aquifer has the highest potential for impact by the facilities activities.
Assessment of the groundwater system at and near the facility is an on-going process. OU-1 and OU-9 have included specific ground water investigations. OU-1 addresses possible contamination of the buried valley aquifer which underlies the original southwest corner of the facility. The primary sources of aquifer contamination are a historic landfill, a sanitary landfill and an overflow pond. Investigations conducted in OU-1 have included extensive geologic, soil gas, groundwater quality, and aquifer characterization measurements as well as review of historical documentation related to the contents of the landfill. OU-1 is currently in the final phase of a three-phase process. Phase III is the remedial design/remedial action (RD/RA) and will implement the remedial alternatives chosen in the feasibility studies of Phase II. The remedial alternative chosen for OU-1 will be a pump-and-treat system.
Hydrogeological investigations for OU-1 collected data for remedial investigations that were used to develop and test a groundwater flow model of the buried valley aquifer under the facility. This groundwater flow model was developed and calibrated for OU-9 and thus included OU-1. This is referred to as the "OU-9 model". Information from the OU-9 model was used to define a smaller area and allow more detail within OU-1.
A groundwater flow model for OU-1 was developed, calibrated and verified. The OU-1 flow model is referred to as the "OU-1 model". The OU-1 model development included reviewing existing information to provide a comprehensive conceptual model, model design, model calibration, sensitivity analysis, and model verification.
OU-1 Model Review
A groundwater flow model was developed for the OU-1 area for the optimization of pump-and-treat extraction well locations and pumping rates. The OU-1 model is a subarea of the OU-9 Ground Water Flow Model. The U.S.G.S. Modular Three-Dimensional Finite-Difference Ground Water Flow Model, MODFLOW, (McDonald and Harbaugh, 1988) was used for both the OU-9 and OU-1 models. The OU-1 model covers 367 acres in the center of the OU-9 model which covered 2,669 acres.
The OU-1 conceptual model is identical to the OU-9 model. This conceptual model consists of a sand and gravel unconfined aquifer, the Buried Valley Aquifer (BVA), bounded by shale and limestone bedrock sequences. The unconfined aquifer is heterogeneous and isotropic with no flow from the shale and limestone bedrock. Regional groundwater flow is essentially north to south through the area with recharge from precipitation and at times the Great Miami River. A map of the facility is shown in Figure 1.
Figure 1. OU-1 Conceptual Model and Areal Discretization of Model Area
(DWF version of figure)
Model discretization (division of area) in the vertical and horizontal dimensions is based on model objectives. The principle objective for this model was to optimize the location and rates of pump-and-treat wells. Vertically the OU-1 model was divided into five layers which allow more accurate simulation of the aquifer, well discharge, and partially penetrating well effects. Layer 1 of the OU-9 model was divided into four layers for the OU-1 model. Layer 1 was specified as an unconfined layer with a bottom elevation of 670 feet above Mean Sea Level (MSL) and the top layer as the water level elevation. Layers 2 and 3 have top to bottom elevations that are; 670 to 660 feet above MSL and 660 to 650 feet above MSL respectively. Layer 4 was 30 feet thick (elevation 650 to 620 feet above MSL). Layer 5 is identical to the OU-9 model Layer 2 which has a uniform top elevation of 620 feet above MSL and varying bottom elevation based on the bedrock topography. Detailed analysis of pump-and-treat capture zones required small model cells within a portion of the model. Therefore, model cells 25 feet by 25 feet square were used to provide the necessary detail in the OU-1 area. Outside of OU-1 the model increased to a maximum cell size of 300 feet by 300 feet square.
The model was calibrated to assumed steady-state conditions for the September, 1993 water level configuration. Approximately 45 monitoring well locations were used as calibration target locations. Quantified calibration was conducted during simulations using the root mean square error (RMSE) and Mean Absolute Error (MAE) between measured water levels and simulated water levels at each of the target locations.
Sensitivity analysis and model verification was completed on the calibrated OU-1 model. Based on the parameter changes made, the model was most sensitive to a decrease in hydraulic conductivity, drainage ditch recharge, and the specified head boundaries. Parameter values used to establish model calibration are not unique and there may be many combinations of parameters that will produce a reasonable match to a set of measured water levels. Model verification was conducted to test whether the combination of parameters chosen for the system during calibration could be used under a different set of system stresses and match another set of observed measurements. A set of system stresses for June 23, 1993 were used for the verification. Table 1 provides a summary of several key parameters used for the OU-1 model.
Table 1. OU-1 Calibrated Model Parameter Summary
|Areal Discretization - 69 Rows and 60 Columns.
Total Cells 20700. Total Active Cells 14443.
Cell Dimensions 25 ft. x 25 ft. up to 300 ft. x 250 ft.
|Vertical Discretization - Layer Configuration - Five Layers|
|Layer #||Top Elevation||Bottom Elevation|
|Layer 1||Water Level||670|
|Layer 5||620||Variable 540 to 620|
|Hydraulic Conductivity Zones Kx and Ky values were from 345 to 648 feet/day|
|Vertical Hydraulic Conductivity - Kv = 40 feet/day Between Layer 1-2,2-3,3-4,4-5|
|Areal Recharge Due To Precipitation 0.0029 feet/day|
|Discharge From Facility Production Well 0076 71,712 ft3/day|
|Recharge Due to Miami-Erie Canal Drainage Ditch 0.1285 ft/day|
|Specified Head Boundaries - Extracted from OU-9 Model Heads Along Corresponding Rows
North Elevation 681.10 to 681.0 South 679.6 to 680.3
|Great Miami River - Total recharge to Aquifer 0.12393 E +12 ft3|
|Most Significant Model Sensitivities - Hydraulic Conductivity Decrease, Drainage Ditch Recharge, and Specified Heads|
Optimization Methodology and Management Problem Development
The objective of this study was to provide the locations and pumping rates of a pump-and-treat system that would contain the OU-1 groundwater contaminant plume. A method was chosen that simulates the aquifer system and optimizes the locations and pumping rates of wells used to remove the contaminant plume. An aquifer management method that is both a simulation and optimization technique was used. This technique was best described by Gorelick et al. (1993). "Combined simulation-optimization techniques can be thought of as organized and methodical trial-and-error methods. However, in contrast to most trial-and-error approaches to problem solving, the objective, constraints, and solution search strategies are clearly specified." The prime reason for the simulation-optimization method is that it provides quantified results.
The computer code chosen was a FORTRAN optimization code, MODMAN, written by R. Greenwald (1993) of GeoTrans, Inc. and distributed by the International Groundwater Modeling Center, Colorado School of Mines. MODMAN, in conjunction with MODFLOW and optimization software LINDO is a simulation-optimization technique.
MODMAN converts the objective function and constraints into linear and/or mixed integer programs which are then solved by a proprietary software package called LINDO (Schrage, 1989). MODMAN is essentially a preprocessor and post-processor to MODFLOW and LINDO for groundwater management problems. A key element of MODMAN as a post-processor is that the optimal solution identified by LINDO is input to MODFLOW, which simulates the optimal solution. This sequence is shown in Figure 2.
Figure 2. Flowchart of the MODMAN Process
MODMAN is an acronym for MODflow MANagement. MODMAN was developed to work with the groundwater flow model, MODFLOW to determine the optimal locations and rates for withdrawal well(s) and/or injections well(s). The objective function is to either minimize or maximize pumping subject to constraints on heads, drawdown, gradient or head-differences, flow directions, potential well locations and individual well yields. The optimal well rates and locations minimize or maximize the objective while satisfying all constraints. In addition to the objective and constraints that MODMAN optimizes, there are design strategies. Design strategies are various combinations of the constraints which produce distinct system alternatives.
A groundwater management problem must first be formulated before MODMAN can be applied. The problem must have a primary objective and constraints. In the present study, a record of decision (ROD) has been signed by the facility for OU-1. The remedial alternative chosen is a groundwater pump-and-treat system. Pump-and-treat systems are designed to hydraulically contain and remove the contaminants. The captured water is treated before reinjecting or discharging to a surface water body. Most often, due to the relatively long duration of pump-and-treat remediations the objective of the management problem is to minimize total pumping. Significant cost savings can be achieved by reducing the amount of water pumped and treated. A constraint usually applicable to pump-and-treat systems is head-difference at a boundary such as a compliance boundary. The OU-1 groundwater contamination plume must be contained within a western and southern compliance boundary. Therefore, the primary constraints are head-differences at the compliance boundary. A secondary constraint is the number of wells to be used. Design strategies that were tested include variation on the head-difference limits and variation on the number of wells.
The OU-1 Record of Decision has stated the remedial action will clean up and not allow contamination to migrate beyond the OU-1 compliance boundary. The Remedial Investigation report states that contaminants are concentrated in the area of the sanitary landfill and the assumed location of the historic landfill. The highest concentrations of contaminants in the plume from this source or sources are east and north of the paved roads. The compliance boundary is the paved roads west and south of the landfill area. Several MODMAN constraints and design strategies were developed for the optimization.
The objective of the optimization is to minimize the amount of groundwater pumped and still produce plume containment. For each well, the range of pumping rates was specified to constrain the amount of groundwater pumped. For these simulation-optimizations any individual well could pump from 0 to 200 gpm. However, total pumping from all wells could not exceed 200 gpm.
The primary constraint was to prevent the OU-1 plume from spreading beyond the compliance boundary. Containment refers to an inward hydraulic gradient at the boundary to prevent the movement of groundwater across that boundary. Therefore, the true constraints are head-difference limits used to maintain the inward gradient at the compliance boundary. These head-difference limits are set at each of the model cell nodes along the boundary. The hydraulic head is greater on the non-compliance side of the boundary than the inner compliance boundary.
A requirement in the design of the pump-and-treat system was that, during operation, containment could be field monitored. Optimization of the pump-and-treat well locations and rates was designed to provide field measurable containment. To accomplish this, the head-difference limit has to be greater than an average water level measurement error. A general error associated with hand measurement of groundwater levels is 0.02 to 0.1 feet (Nielsen, 1991). Water levels measured at the facility should be at the low end of this scale. This is due to the instrument required by the Quality Assurance Project Plan for measurements and the measurement point's survey accuracy. Therefore, three measurable head-difference constraints of 0.025, 0.05 and 0.10 feet were chosen to be tested during optimization. The distance between model nodes at the compliance boundary is 25 feet. The resulting hydraulic gradient due to the head-difference limits tested were 0.001, 0.002 and 0.004 feet/feet. The gradients that will be established inward are greater in magnitude than the hydraulic gradient that is currently outward (0.00078 feet/feet). Individually, the head-difference limits are constraints of the optimization problem but alternative head-difference limits are considered design strategies.
A secondary constraint is the number of pumping wells to be used. Based on installation costs and logistics a maximum of five wells was chosen to be tested for containment. Based on the geometry of the compliance boundary and the assumed source area, two lines of potential well locations were chosen to be optimized. There are 17 potential well locations along the west and south compliance boundary. The locations are shown in Figure 3. Spacing between each location is 25 feet, which is the groundwater flow model grid size. MODMAN determines the best locations and rates from all potential locations, subject to the specified limit on the number of wells.
Figure 3. Locations of Compliance Boundary, MODMAN Head Difference Constraint Nodes, and Potential Pump-and-Treat Wells.
(DWF version of figure)
Simulation Results and System Selection
The results of the simulation-optimization are shown in Table 2. The results are organized by head-difference value and maximum number of wells allowed. All optimizations produce feasible results except when only one well is required to maintain a head-difference limit of 0.1 foot along both compliance boundaries. Total system pumping rates range from 28 to 148 gpm. Individual well pumping rates are from 3 to 129 gpm depending on the well configuration. There is greater than a two fold increase in pumping rates needed to satisfy a 0.1 foot head-difference limit compared to a 0.025 foot head-difference at the compliance boundary.
Table 2. Optimization Simulation Results
|HEAD-DIFFERENCE LIMIT OF 0.025 FEET|
|Max # of Wells||Optimal Well Location Control Nodes and Extraction Rates (GPM)||Total
|5||4 (4.16)||24 (4.61)||26 (3.09)||28 (3.81)||32 (12.71)||28.38|
|4||2 (3.51)||24 (4.33)||28 (16.28)||34 (8.89)||NA||33.01|
|3||2 (3.15)||26 (22.44)||32 (11.56)||37.15|
|2||14 (48.11)||34 (15.08)||63.19|
|HEAD-DIFFERENCE LIMIT OF 0.05 FEET|
|Max # of Wells||Optimal Well Location Control Nodes and Extraction Rates (GPM)||Total
|5||4 (9.96)||12 (4.75)||24 (5.48)||28 (20.56)||34 (10.90)||51.65|
|4||4 (10.05)||12 (2.74)||26 (28.93)||32 (14.49)||56.21|
|3||4 (13.14)||26 (27.74)||32 (21.21)||62.09|
|2||2 (4.63)||28 (89.60)||94.23|
|HEAD-DIFFERENCE LIMIT OF 0.1 FEET|
|Max # of Wells||Optimal Well Location Control Nodes and Extraction Rates (GPM)||Total
|5||4 (22.15)||10 (6.08)||16 (11.23)||26 (38.33)||32 (19.29)||97.08|
|4||4 (23.94)||14 (26.0)||26 (35.18)||32 (17.56)||102.68|
|3||4 (28.11)||18 (74.88)||32 (19.98)||122.97|
The local groundwater flow direction in and around the containment area is to the south-southeast. Groundwater flow in this area is affected by the facility Production Well 0076 and the bedrock boundary on the east. This southeast flow across the containment area and the number of wells has a tremendous affect on the total pumping rates and location. The results indicate that the most effective location for plume containment is at the intersection of the eastern model boundary and southern compliance boundary. For all simulations which have three wells, 80 percent or more of the total water pumped is from the southern boundary.
MODMAN simulations can be used to provide various parametric analyses. One such analysis is comparing the relationship between total discharge from all wells versus number of pump-and-treat wells. This analysis, shown in Figure 4, illustrates the trade-off whereby reducing the number of well requires more total pumping. These graphs indicate that total pumping must increase by 120 to 190 percent to reduce the number of wells to less than three. The increase of pumping wells above three but less than five does not significantly reduce the total pumping.
Figure 4. Number of Wells and Pumping Rates
Several design criteria were considered during the optimal system selection process. The most important criteria was that the containment provided by the system be measurable. This means that the inward head-difference at the control locations must be significant enough to be measured in the field. A second criteria was related to system operation and total pumping. There is a significant increase in pumping required to reduce the number of wells to less than three. For system operation it was decided that three wells would provide the balance required if pump failure occurred or pump maintenance was required.
The remediation strategy selected includes three pumping wells and a 0.05 foot head-difference limit at the compliance boundary. The locations of the extraction wells are shown in Figure 5. Extraction Well 1 model cell center is 18 feet southwest of ER Monitoring Well 0307. The model cell center for Extraction Well 2 is 23 feet northwest of ER Monitoring Well 0063. And the third extraction well model cell center is 60 feet northeast of ER Monitoring Well 0063. The rates are 13.14, 27.74, and 21.21 gpm as determined by MODMAN. These rates have been rounded to 15, 30, and 25 gpm for ease of design, and during further analysis they will be referred to as the design rates.
Figure 5. Selected Pump-and-Treat Optimal Well Configuration.
(DWF version of figure)
Containment Verification Via Particle Tracking
The graphical method of particle tracking was used to provide additional support that the selected optimal design and alternatives contains the OU-1 plume. Particle tracking was completed using the USGS particle tracking program MODPATH (Pollock, 1989). MODPATH is a post-processing package developed to compute three-dimensional pathlines from steady-state simulations produced from MODFLOW. MODPATH can only simulate advective contaminant transport.
During operation of a pump-and-treat system there are times when the pumps will be down due to maintenance or failure. The length of time that a portion of the system is down may be minor relative to the groundwater velocity in the area. However, a good contingency plan would be that containment could be achieved with more than one well configuration. This was tested with simulations that had one or two of the three extraction wells not pumping. The simulations were conducted with the OU-1 model and the results were input to MODPATH. The gradients determined from the model and a porosity of 0.30 were used for the particle tracking analysis. Particles were placed near the potential source area and along the western and southern compliance boundary. The particles were allowed to move forward in time until reaching a hydraulic sink.
The first simulation tested was the selected design configuration, with all three wells pumping at the design rates. The particle tracking results indicate that 100 percent of the particles are captured by the three wells. Figure 6 shows the particle tracking results for this simulation. Well 3 captured 70% of the particles while Well 1 and Well 2 captured 26% and 4% of the particles respectively.
Figure 6. Particle Tracking Results for the Pump-and-Treat System Operating at Design Rates.
(DWF version of figure)
Three other particle tracking simulations were conducted. In each simulation, one of the three extraction wells was turned off and the design rates were maintained at the other two wells. When Well 1 was turned off, all of the particles were captured by Wells 2 (41%) and 3 (59%). The second simulation turned Well 2 off and the particles were all captured by Wells 1 (28%) and 3 (72%). The third simulation turned off Well 3, and again all of the particles were captured by Wells 1 (28%) and 2 (72%). A final simulation was conducted in which Wells 1 and 2 were turned off. During this simulation, all of the particles were captured by Well 3.
Particle tracking results indicate that any configuration of the three designed pumping wells will capture particles from the source area within the compliance boundary. These simulations did not maintain a 0.05 foot head-difference but did maintained sufficient head-difference to cause an inward hydraulic gradient. This outcome is due to the slight southeast groundwater flow caused by the facility Production Well 0076. This causes an inward gradient on the western boundary without extraction wells pumping. Therefore, the need for the northern most well (Well 1) and the western well (Well 2) is only slight and there may be containment without them. This is related to the conservative head-difference limit of 0.05 feet. If the head-difference limit of 0.025 feet had been chosen, the resulting pumping rates and capture zones may not have been significant enough to capture particles when fewer than three wells were pumping.
Pump-and-treat well location and rate optimization was completed by a simulation-optimization method. Simulation pertains to the use of a groundwater flow model to simulate the buried valley aquifer in OU-1. The groundwater flow model was used to identify responses from potential pump-and-treat well locations and rates. The accuracy of the simulations is dependent on the ability of the OU-1 groundwater flow model to simulate the hydrogeologic conditions that exist. Optimization refers to combining simulated model responses, an objective function and constraints into a linear programming problem and generating an optimal solution. The objective of the task was to minimize the amount of total pumping required. Primary and secondary constraints were the head-difference along the compliance boundary and the number and location of pumping wells.
Design strategies that were considered included field measurable head-difference limits of 0.025, 0.05 and 0.1 feet, the number of wells between one and five, and a maximum total pumping rate of 200 gpm. Results of all design strategies had feasible solutions except one. A simulation that required a head-difference limit of 0.1 feet at the compliance boundary with only one well was infeasible. All other design strategy simulations had feasible results and therefore provide containment. The design strategy of a 0.05 foot head-difference limit was chosen as the optimal solution. This strategy was chosen to allow containment to be measurable and provide some conservatism to the containment.
MODMAN simulation results provided quantitative analysis of the design strategies. A parametric analysis of total pumping rates versus number of pumping wells was completed. This analysis showed that if less than three wells were used, the total pumping rate of groundwater needed to meet the required head-difference limit increased 120 to 190 percent. Conversely, if the number of wells was four or five, the reduction in the total pumping rate was not significant enough to justify an increase in the number of wells. Based on the analysis, it was decided that the pump-and-treat system should consist of three optimally placed wells.
The three locations determined by MODMAN bound the OU-1 plume. The optimal solution placed Well 1 on the north end of the western compliance boundary near the potential source area and Wells 2 and 3 on the southern compliance boundary at the eastern and western ends respectively. The design rates for these wells were 15, 30, and 25 gpm for Well 1, Well 2 and Well 3 respectively.
Based on the parametric analysis, a three well system was chosen to provide system contingency. Several simulations employing particle tracking were conducted to assess the impact of removing one or two wells from the system. These simulations showed that the OU-1 plume would be contained if any two wells pumped at the designed rates. The plume could also be contained using Well 3 if the northern Well 1 and the southwest compliance boundary Well 2 were removed. These simulations did not produce the desired 0.05 foot head-difference at the compliance boundary but did produce a sufficient head-difference to cause inward flow and containment. This in part is due to the slight southeast local groundwater flow caused by the facility Production Well 0076.
Greenwald, R. M., 1993, "Documentation and User's Guide: MODMAN, An Optimization Module for MODFLOW", International Ground Water Modeling Center, Colorado School of Mines, Version 3.02.
Gorelick, S. M., R. A. Freeze, D. Donohue, and J. F. Keely, 1993, "Groundwater Contamination Optimal Capture and Containment", Lewis Publishers, Boca Raton, Florida, 385 pp.
McDonald, M. G. and A. W. Harbaugh, 1988, "A modular three-dimensional finite-difference ground water flow model", U. S. Geological Survey Techniques of Water-Resources Investigations, Book 6, Chap. A1, (variously paginated).
Nielsen, D. M., editor, 1991, "Practical Handbook of Ground Water Monitoring", Lewis Publishers, Inc., Chelsea, Michigan.
Pollock, D. W., 1989, "Documentation of Computer Programs to Compute and Display Pathlines Using Results from the U. S. Geological Survey Modular Three-Dimensional Finite-Difference Ground Water Flow Model", U. S. Geological Survey, Open File Report 89-381, 199 pp.
Scharge, L., 1991, "User's Manual for Linear, Integer and Quadratic Programming with LINDO Release 5.0", Graduate School of Business, University of Chicago, The Scientific Press, San Francisco.
This paper was presented at:
42nd Annual Midwest Groundwater Conference
October 22-24, 1997