Prepared in cooperation with the Colorado Water Conservation Board

Demonstration Optimization Analyses of Pumping from 

Selected Arapahoe Aquifer Municipal Wells in the 

West-Central Denver Basin, Colorado, 2010–2109

Scientific Investigations Report 2012–5140

U.S. Department of the Interior

U.S. Geological Survey

Demonstration Optimization Analyses of 

Pumping from Selected Arapahoe Aquifer 

Municipal Wells in the West-Central 

Denver Basin, Colorado, 2010–2109

By Edward R. Banta and Suzanne S. Paschke

Prepared in cooperation with the Colorado Water Conservation Board

Scientific Investigations Report 2012–5140

U.S. Department of the Interior

U.S. Geological Survey
U.S. Department of the Interior

KEN SALAZAR, Secretary

U.S. Geological Survey

Marcia K. McNutt, Director

U.S. Geological Survey, Reston, Virginia: 2012

This and other USGS information products are available at http://store.usgs.gov/

U.S. Geological Survey

Box 25286, Denver Federal Center

Denver, CO 80225

To learn about the USGS and its information products visit http://www.usgs.gov/

1-888-ASK-USGS

Any use of trade, product, or firm names is for descriptive purposes only and does not imply endorsement by the 

U.S. Government.

Although this report is in the public domain, permission must be secured from the individual copyright owners to 

reproduce any copyrighted materials contained within this report.

Suggested citation:

Banta, E.R., and Paschke, S.S., 2012, Demonstration optimization analyses of pumping from selected Arapahoe 

aquifer municipal wells in the west-central Denver Basin, Colorado, 2010–2109: U.S. Geological Survey Scientific 

Investigations Report 2012–5140, 37 p. 
iii

Contents

Abstract ..........................................................................................................................................................1

Introduction ....................................................................................................................................................1

Purpose and Scope .............................................................................................................................2

Study Area .............................................................................................................................................2

Denver Basin Bedrock Aquifer System ....................................................................................................2

Numerical Model ..........................................................................................................................................2

Demonstration of Optimization Analyses of Pumping from Municipal Wells ...................................10

Software and Analytical Framework ..............................................................................................10

Selection of Wells ..............................................................................................................................10

Application of Optimization Analysis to Arapahoe Aquifer Pumping ........................................13

Non-Optimized Simulation ................................................................................................................16

Analysis 1: Optimization of Pumping for Managed Withdrawals Over 50-Year Period ..........21

Analysis 2: Optimization of Pumping for Managed Withdrawals Over 100-Year Period ........21

Comparison with Non-Optimized Simulation ................................................................................26

Effects of Managed-Flows Pumping ..............................................................................................26

Limitations ...........................................................................................................................................34

Possible Additional Analyses ....................................................................................................................34

Address Issue of Effects of Pumping in Arapahoe Aquifer on Denver Aquifer ......................34

Refine Spatial and (or) Temporal Discretization ...........................................................................35

Simulate and Place Constraints on Water Levels in Production Wells ....................................35

Include Infrastructure Costs in Optimization Analysis ................................................................35

Summary and Conclusions ........................................................................................................................35

Acknowledgments ......................................................................................................................................36

References Cited .........................................................................................................................................36

Figures

1. Map showing location of Denver Basin in Colorado .............................................................3

2. Map showing Denver Basin aquifer outcrops and selected municipal wells ..................4

3. Map showing extent of upper and lower Arapahoe aquifers ..............................................6

4. Map showing Denver Basin model grid ...................................................................................7

5. Map showing simulated 2009 potentiometric (hydraulic-head) surfaces for upper 

and lower Arapahoe aquifers ....................................................................................................8

6. Map showing height of layer 8 simulated 2009 potentiometric (hydraulic-head) 

surface relative to top of Arapahoe aquifer ............................................................................9

7. Map showing combined 2009 simulated saturated thickness of upper and lower 

Arapahoe aquifers .....................................................................................................................11

8. Map showing selected municipal wells ................................................................................12

9. Map showing simulated 2059 potentiometric (hydraulic head) surfaces for upper 

and lower Arapahoe aquifers ..................................................................................................22

10. Map showing height of layer 8 simulated 2059 potentiometric (hydraulic head) 

surface relative to top of Arapahoe aquifer ..........................................................................23

11. Map showing combined 2059 saturated thickness of upper and lower Arapahoe 

aquifers ........................................................................................................................................24
iv

12. Graph showing simulated hydrographs and head constraint for cell (8, 63, 18; 

layer, row, column) for optimization analyses and for model results using 

non-optimized pumping rates ..................................................................................................25

13. Graph showing simulated hydrographs and head constraint for cell (8, 73, 20; 

layer, row, column) for optimization analyses and for model results using nonoptimized pumping rates ..........................................................................................................26

14. Graph showing simulated hydrographs and head constraint for cell (8, 64, 24; 

layer, row, column) for optimization analyses and for model results using nonoptimized pumping rates ..........................................................................................................27

15. Map showing simulated 2109 potentiometric (hydraulic head) surfaces for upper 

and lower Arapahoe aquifers ..................................................................................................28

16. Map showing height of layer 8 simulated 2109 potentiometric (hydraulic head) 

surface relative to top of Arapahoe aquifer ..........................................................................29

17. Map showing combined 2109 saturated thickness of upper and lower Arapahoe 

aquifers ........................................................................................................................................30

18. Simulated flow rates for selected Arapahoe aquifer (model layers 8–10) waterbudget components, showing (2004–2009) antecedent rates (indicated by 

simulation times less than zero) and (2010–2059) responses to managed flows of 

Analysis 1 ....................................................................................................................................31

19. Simulated hydrographs for cell in layer 6, row 63, column 18 ............................................32

20. Pie charts showing sources of water for managed flows, relative to simulation 

without managed flows, at A, 64 days; B, 4.9 years; and C, end of 50-year 

optimization-analysis simulation .............................................................................................33

Tables

1. Hydrogeologic units of the Denver Basin ................................................................................5

2. Flow-rate decision variables and results of optimization analyses ..................................14

3. Head constraints and simulated heads .................................................................................17

4. Pumping rates for managed and unmanaged wells, by model package used to 

simulate the wells ......................................................................................................................21
v

Conversion Factors

Inch/Pound to SI

Multiply By To obtain

Length

foot (ft) 0.3048 meter (m)

mile (mi) 1.609 kilometer (km)

Area

square mile (mi2) 2.590 square kilometer (km2) 

Volume

cubic foot (ft3) 0.02832 cubic meter (m3) 

Flow rate

cubic foot per second (ft3/s) 0.02832 cubic meter per second (m3/s)

cubic foot per day (ft3/d) 0.02832 cubic meter per day (m3/d)

acre-foot per year (acre-ft/yr) 1,233 cubic meter per year (m3/yr)

Vertical coordinate information is referenced to the North American Vertical Datum of 1988 

(NAVD 88).

Altitude, as used in this report, refers to distance above the vertical datum.

Demonstration Optimization Analyses of Pumping from 

Selected Arapahoe Aquifer Municipal Wells in the 

West-Central Denver Basin, Colorado, 2010–2109

By Edward R. Banta and Suzanne S. Paschke

Abstract

Declining water levels caused by withdrawals of water 

from wells in the west-central part of the Denver Basin 

bedrock-aquifer system have raised concerns with respect to 

the ability of the aquifer system to sustain production. The 

Arapahoe aquifer in particular is heavily used in this area. 

Two optimization analyses were conducted to demonstrate 

approaches that could be used to evaluate possible future 

pumping scenarios intended to prolong the productivity of 

the aquifer and to delay excessive loss of saturated thickness. 

These analyses were designed as demonstrations only, and 

were not intended as a comprehensive optimization study.

Optimization analyses were based on a groundwater-flow 

model of the Denver Basin developed as part of a recently 

published U.S. Geological Survey groundwater-availability 

study. For each analysis an optimization problem was set up 

to maximize total withdrawal rate, subject to withdrawal-rate 

and hydraulic-head constraints, for 119 selected municipal 

water-supply wells located in 96 model cells. The optimization analyses were based on 50- and 100-year simulations of 

groundwater withdrawals. 

The optimized total withdrawal rate for all selected wells 

for a 50-year simulation time was about 58.8 cubic feet per 

second. For an analysis in which the simulation time and headconstraint time were extended to 100 years, the optimized total 

withdrawal rate for all selected wells was about 53.0 cubic feet 

per second, demonstrating that a reduction in withdrawal rate 

of about 10 percent may extend the time before the hydraulichead constraints are violated by 50 years, provided that pumping rates are optimally distributed. 

Analysis of simulation results showed that initially, the 

pumping produces water primarily by release of water from 

storage in the Arapahoe aquifer. However, because confining 

layers between the Denver and Arapahoe aquifers are thin, 

in less than 5 years, most of the water removed by managedflows pumping likely would be supplied by depleting overlying hydrogeologic units, substantially increasing the rate of 

decline of hydraulic heads in parts of the overlying Denver 

aquifer.

Introduction

The Denver Basin bedrock aquifers are a primary source 

of water for much of the population of the southern part of the 

Denver metropolitan area and adjacent rural areas. Because of 

the slow rate of natural recharge, groundwater in the Denver 

Basin commonly is regarded for practical purposes as nonrenewable. Municipal-well pumping in the west-central part of 

the basin has contributed to water-level declines and, in some 

areas, declining well yields. Concerns related to the rates of 

water-level decline and the longevity of the usefulness of the 

aquifers (Topper and Raynolds, 2007) have prompted investigations (Hydrosphere Resource Consultants, Inc., and others, 

1999; Black and Veatch and others, 2003) with the goal of prolonging productivity of the aquifers for beneficial use. A recent 

report on groundwater availability (Paschke, 2011) presents 

a three-dimensional groundwater flow model of the Denver 

Basin and describes the decline of water levels in wells in 

these areas as the rate of withdrawal of water from wells in the 

area has increased. 

The U.S. Geological Survey (USGS), in cooperation with 

the Colorado Water Conservation Board (CWCB), developed 

a series of groundwater-flow simulations to demonstrate how 

optimization techniques could be used to design pumping 

schemes that may prolong the productivity of the Arapahoe 

aquifer. These analyses were designed as demonstrations only 

and were not intended as a comprehensive optimization study. 

The optimization analyses were based on the groundwaterflow model of the Denver Basin bedrock aquifers and overlying alluvial aquifer described by Banta and others (2011). The 

analyses demonstrate the applicability of optimization technology to the problem of maximizing production of water while 

maintaining saturated thickness of the Arapahoe aquifer of at 

least 90 percent of the aquifer thickness for 50 or 100 years.
2 Demonstration Optimization Analyses of Pumping from Selected Arapahoe Aquifer Municipal Wells

Purpose and Scope

This report describes results of a groundwater-flow modeling investigation designed to demonstrate the application of 

optimization techniques to understand the effects of various 

possible future pumping schemes and to delay excessive loss 

of saturated thickness in the Arapahoe aquifer. The optimization goals were developed in cooperation with CWCB and the 

Colorado Division of Water Resources (CDWR). The investigation focused on pumping from the Arapahoe aquifer in the 

metropolitan area south of Denver in the west-central part of 

the Denver Basin. The other bedrock aquifers of the Denver 

Basin and the overlying alluvial aquifer were included in the 

modeling simulations because of the hydrologic connections 

among the aquifers. These analyses were designed as demonstrations only and were not intended as a comprehensive 

optimization study.

Study Area

The project study area is the area underlain by the Denver 

Basin bedrock aquifer system, which occupies about 6,700 mi2

in eastern Colorado (fig. 1). The metropolitan area south of 

Denver (hereinafter, the south Denver metropolitan area) is 

the main area of interest for this study because it contains a 

large number (119) of municipal wells completed in the upper 

and lower Arapahoe aquifers (fig. 2). For the purposes of this 

study, the south Denver metropolitan area is considered to 

include northern Douglas County and southwestern Arapahoe 

County. The groundwater model encompasses the entire study 

area; however, the optimization analyses only involve wells 

operated by municipal water providers in the south Denver 

metropolitan area. Two wells included in the optimization 

analyses are east of Denver and somewhat isolated from the 

other selected wells, but they belong to a water provider that 

operates wells within the area of greatest interest.

Denver Basin Bedrock Aquifer System

As residential development has expanded beyond Denver, 

particularly to the south of Denver, newly developed areas 

have become increasingly dependent on water from Denver 

Basin bedrock aquifers. Estimated production from all wells 

completed in the Denver Basin bedrock aquifers increased 

from about 15 ft3/s in 1958 to about 41 ft3/s in 1978 (Robson, 

1987) and about 118 ft3/s in 2003 (Paschke and others, 2011a). 

In 2003, municipal water providers in the study area withdrew 

an estimated 48 ft3/s (35,000 acre-ft/yr) from wells completed 

in the upper and lower Arapahoe aquifers, the aquifers of 

interest in this investigation (Paschke and others, 2011a). A 

detailed description of the hydrogeologic framework is provided by Paschke and others (2011b) and is summarized in the 

following paragraph. 

The bedrock aquifers of the Denver Basin are in wateryielding sandstones of Cretaceous and Tertiary age in a 6,700-

mi2 area in eastern Colorado located between Greeley on the 

north, Colorado Springs on the south, Limon on the east, and 

the Rocky Mountain Front Range on the west (fig. 1). Rules 

relating to withdrawal of groundwater of the Denver Basin 

(Colorado Division of Water Resources, 1985) are based on 

a hydrogeologic framework in which four primary bedrock 

aquifers (the Dawson, Denver, Arapahoe, and Laramie–Fox 

Hills aquifers) are defined; the Dawson and Arapahoe aquifers 

locally are further differentiated into upper and lower aquifers (fig. 2, table 1). The aquifers generally are separated by 

confining units. The lower Dawson, Denver, and Arapahoe 

aquifers represent the synorogenic deposition of sediments in 

the Denver Basin during Laramide uplift of the Rocky Mountain Front Range (Raynolds, 2002). The prominent Wildcat 

Mountain alluvial fan mapped in the lower Arapahoe aquifer 

is also present in the Denver and lower Dawson portions of 

the sequence, and the Denver confining units are thin (mean 

thicknesses of 50 ft) compared to the thickness of the Denver 

aquifer (mean thickness of 740 ft). A confining unit separates 

the upper Arapahoe aquifer from the lower Arapahoe aquifer 

in approximately the northern one-third of the basin (fig. 3). 

In the southern two-thirds, the confining unit is absent and, for 

the purposes of this study, the Arapahoe aquifer is considered 

undifferentiated. Alluvial sediments of the South Platte River 

and numerous tributaries of the South Platte and Arkansas 

Rivers, some of which are ephemeral or intermittent, overlie 

substantial areas of the bedrock basin and, where saturated, 

form an unconfined alluvial-aquifer system. This investigation 

uses the same hydrogeologic framework as the groundwaterflow model described by Paschke and others (2011b). 

Numerical Model

For the optimization analyses, the MODFLOW-2000 

(Harbaugh and others, 2000) model of the Denver Basin 

aquifer system (Banta and others, 2011) was converted to 

a MODFLOW-2005 (Harbaugh, 2005) format. The finitedifference model grid (fig. 4) encompasses the Denver Basin 

bedrock-aquifer system and immediately adjacent areas of the 

alluvial aquifer of the South Platte River (fig. 2). The grid has 

84 columns and 124 rows of square cells; each cell represents 

a 1-mile by 1-mile area. In the vertical dimension, the aquifers and confining units are represented by 12 model layers, 

as indicated in table 1. Details of model conceptualization 

and parameterization are fully described in Banta and others 

(2011). This section only describes aspects of the model that 

are particularly relevant to the optimization analyses or that 

differ from the model described in that report.

The calibration period for the Denver Basin groundwater 

model extended from 1880 through 2003 (Banta and others, 

2011). In that model, one MODFLOW-2000 (Harbaugh and 

others, 2000) steady-state stress period was used to simulate 
Numerical Model 3

groundwater conditions before 1880, and 15 transient-state 

stress periods simulated conditions from January 1, 1880, 

through December 31, 2003. The lengths of the stress periods 

ranged from 2 to 27 years. The final 4-year stress period of 

that model represented January 1, 2000, through December 

31, 2003. Transient stress periods are subdivided into multiple time steps for accuracy. In each stress period, simulated 

stresses, for example pumping rates, are held constant. However, individual model cells can be deactivated at any time 

step if, during solution of the groundwater-flow equation, 

the approximated head is below the bottom of a model cell. 

If a cell where a pumping well is simulated is deactivated, 

the discharge associated with that well is no longer simulated.

The simulation periods for the optimization analyses 

described in this report begin January 1, 2010. To bridge 

the gap between the end of the calibration period and the 

beginning of the optimization-analysis period, a 6-year 

period (2004–2009) was simulated in which all simulated 

hydraulic stresses on the system were identical to those used 

for 2000–2003, the final stress period of the calibration period. 

These stresses included simulated recharge from precipitation 

and irrigation, evapotranspiration, withdrawals from wells, 

exchange with streams and reservoirs, discharge to springs, 

and alluvial-aquifer outflow (Banta and others, 2011). Hydraulic heads calculated for the end of 2009 were used as starting heads for the optimization model runs. Simulated 2009 

potentiometric (hydraulic head) surfaces for the upper (model 

layer 8) and lower (model layer 10) Arapahoe aquifers are 

shown in figure 5. For the optimization analyses, the model 

was run with constant stresses for either 50 or 100 years. 

Maps showing the height of the layer-8 simulated potentiometric surface relative to the top of the Arapahoe aquifer are 

provided at various simulation times to facilitate interpretation 

of the optimization analyses. Figure 6 shows the height of the 

layer 8 simulated 2009 potentiometric surface above the top of 

the Arapahoe aquifer in the area of interest.

Figure 1. Location of Denver Basin in Colorado. 

"

"

"

"

" "

"

"

"

"

"

"

"

"

"

"

"

"

"

"

"

"

"

Lamar

Pueblo

Cortez

Durango

La Junta

Base from U.S. Geological Survey digital data, 2009, 1:100,000

Colorado State Plane Central

Lambert Conformal Conic projection

Standard parallels 38o

27' N and 37o45' N, central meridian -105o

75

75

50 100 MILES

0 50

25

25 100 KILOMETERS

0

Yampa River

White River

Colorado River

Glenwood Springs

Grand

Junction

Gu nnison River

San Juan

River

Rio Grand

Alamosa

Arkansas River

Gunnison Salida

COLORADO

Leadville Kiowa Limon

Castle Rock

Colorado Springs

Greeley

Fort Collins

Boulder

Sterling

Julesburg

Fort Morgan

Craig

ROCKY

MOUNTAIN FRO

NT

RANGE

South Platte River

Denver Denver

Basin

37°

38°

39°

40°

41°

109° 108° 107° 106° 105° 104° 103°
4 Demonstration Optimization Analyses of Pumping from Selected Arapahoe Aquifer Municipal Wells

Figure 2. Denver Basin aquifer outcrops and selected municipal wells.

Base from U.S. Geological Survey digital data, 2009, 1:100,000

Colorado State Plane Central

Lambert Conformal Conic projection

Standard parallels 38°27' N and 37°45' N, central meridian -105°

t

EXPLANATION

Alluvial aquifer

Area of interest

Little Thompson

15

15

10 20 MILES

0 10

5

5 20 KILOMETERS

0

Upper Dawson aquifer

Lower Dawson aquifer

Denver aquifer

Upper Arapahoe aquifer

LowerArapahoe aquifer

Laramie-Fox Hills aquifer

Confining unit

Denver Basin study area

 boundary

Perennial stream

Ephemeral stream

Selected municipal well

Muddy Creek

Badger Creek

Coal Creek

Greeley

LARIMER

WELD

MORGAN

WASHINGTON

BOULDER

ADAMS

BROOMFIELD

DENVER

JEFFERSON

River

Denver

Boulder Creek

Golden

Clear Creek

Little Dry

Creek

Wolf Creek

Bear Creek

Saint Vrain Creek

Boulder

Big Thompson River

Cache la Poudre River

Big Dry Creek

Box Elder Creek

South Platte River

Lost Creek

Fort Morgan

Bijou

Creek

Rock

Creek Antelope Creek

Comanche Creek

West Sand Creek

Sand Creek

First Creek

ARAPAHOE

Plum Creek

West Plum

Creek

Castle

Rock

Cook

Creek

Running

Creek

Dry

Creek

DOUGLAS

Monument

Dry

Creek

Fountain Creek

Colorado Springs

TELLER EL PASO

LINCOLN

Kettle Creek Black Squirrel Creek

Brackett Creek

PALMER DIVIDE

Cherry Creek

West Kiowa Creek

ELBERT

Limon

Steels Fork

Horse Creek Adobe Creek

Mustang Creek

Middle Rush Creek

Big Sandy Creek

West Bijou

Creek

East Bijou Creek

Middle Bijou Creek

Kiowa Creek

40°00'

39°30'

39°00'

40°30' 105°00' 104°30' 104°00'
Numerical Model 5

Table 1. Hydrogeologic units of the Denver Basin.

Hydrogeologic 

unit Age Stratigraphic unit

Model 

layer

Lithologic 

description

Thickness 

(feet)

Hydrogeologic 

description

Alluvial aquifer 

where saturatedQuaternary

Alluvial, floodplain, terrace, 

colluvial, and 

eolian sand, 

gravel, and 

clay deposits

1 Unconsolidated sand and 

gravel with clay lenses 0 to 175 Productive unconfined alluvial aquifer where saturated

upper Dawson 

aquifer Eocene Dawson Formation 2

Arkosic fluvial sandstone 

and conglomerate with 

interbedded claystone

200 to 840 Productive unconfined to confined aquifer

Dawson confining unit Paleocene Dawson Formation 3 Claystone 1 to 350

Claystone confining unit in 

northern part of Dawson 

extent

lower Dawson 

aquifer

Paleocene

Dawson Formation 4

Mixed arkosic and andesitic fluvial sandstone with 

interbedded claystone, 

lignite, and volcanics

100 to 

570 where 

undifferentiated

Productive confined aquifer

upper Denver 

confining unit

Denver Formation

5

Predominantly claystone with 

interbedded sandstone, 

lignite, and volcanics

1 to 150 Fine-grained confining unit in 

upper Denver Formation

Late 

Cretaceous

Denver aquifer 6 Mixed arkosic and andesitic 

fluvial sandstone

280 to 

1,100

Confined to unconfined aquifer. 

Lower hydraulic conductivity and less productive than 

Arapahoe aquifers

lower Denver 

confining unit 7 Predominantly claystone with andesitic fluvial sandstone 5 to 150 Fine-grained confining unit at base of Denver Formation

upper Arapahoe 

aquifer1

Arapahoe Formation

8 Arkosic fluvial sandstone 

with interbedded claystone 50 to 300

Productive confined aquifer 

above Arapahoe confining 

unit in northern one-third of 

basin

Arapahoe confining unit1 9 Predominantly claystone 50 to 180 Claystone confining unit in 

northern one-third of basin

lower Arapahoe 

aquifer1 10

Alluvial fan conglomerate 

and sandstone with interbedded claystone

200 to 

600 where 

undifferentiated

Productive confined aquifer. 

Greatest thickness and 

hydraulic conductivity in 

west-central part of basin

Laramie confining unit Laramie Formation

11 Gray to black shale, coal, 

siltstone, and sandstone 100 to 500 Confining unit in upper part of Laramie Formation

Laramie-Fox 

Hills aquifer 12

Poorly consolidated deltafront fluvial sandstone

100 to 500

Productive confined to unconfined aquifer composed of 

sandstones of lower Laramie 

Formation and Fox Hills 

Sandstone

Fox Hills SandstoneYellow-brown marine deltafront and beach sandstone

Pierre Shale confining unit Pierre Shale

not 

simulated

Dark to light gray marine 

shale 5,200 Low-permeability base of Denver Basin aquifer system

1

Where Arapahoe confining unit is absent, upper Arapahoe and lower Arapahoe aquifers are considered undifferentiated.
6 Demonstration Optimization Analyses of Pumping from Selected Arapahoe Aquifer Municipal Wells

Figure 3. Extent of upper and lower Arapahoe aquifers.

Base from U.S. Geological Survey digital data, 2009, 1:100,000

Colorado State Plane Central

Lambert Conformal Conic projection

Standard parallels 38°27' N and 37°45' N, central meridian -105°

EXPLANATION

Area of interest

15

15

10 20 MILES

0 10

5

5 20 KILOMETERS

0

Upper Arapahoe aquifer

LowerArapahoe aquifer

Arapahoe confining unit

Denver Basin study area

 boundary

Perennial stream

Ephemeral stream

Selected municipal well

Muddy Creek

Badger Creek

Coal Creek

Greeley

LARIMER

WELD

MORGAN

WASHINGTON

BOULDER

ADAMS

BROOMFIELD

DENVER

JEFFERSON

River

Denver

Boulder Creek

Golden

Clear Creek

Little Dry

Creek

Wolf Creek

Bear Creek

Saint Vrain Creek

Boulder

Big Thompson River

Cache la Poudre River

Big Dry Creek

Box Elder Creek

South Platte River

Lost Creek

Fort Morgan

Bijou

Creek

Rock

Creek Antelope Creek

Comanche Creek

West Sand Creek

Sand Creek

First Creek

ARAPAHOE

Plum Creek

West Plum

Creek

Castle

Rock

Cook

Creek

Running

Creek

Dry

Creek

DOUGLAS

Monument

Dry

Creek

Fountain Creek

Colorado Springs

TELLER EL PASO

LINCOLN

Kettle Creek Black Squirrel Creek

Brackett Creek

PALMER DIVIDE

Cherry Creek

West Kiowa Creek

ELBERT

Limon

Steels Fork

Horse Creek Adobe Creek

Mustang Creek

Middle Rush Creek

Big Sandy Creek

West Bijou

Creek

East Bijou Creek

Middle Bijou Creek

Kiowa Creek

Little Thompson

40°00'

39°30'

39°00'

40°30' 105°00' 104°30' 104°00'
Numerical Model 7

Figure 4. Denver Basin model grid.

Base from U.S. Geological Survey digital data, 2009, 1:100,000

Colorado State Plane Central

Lambert Conformal Conic projection

Standard parallels 38°27' N and 37°45' N, central meridian -105°

EXPLANATION

Area of interest

15

15

10 20 MILES

0 10

5

5 20 KILOMETERS

0

Upper Arapahoe aquifer

LowerArapahoe aquifer

Arapahoe confining unit

Denver Basin study area

 boundary

Perennial stream

Ephemeral stream

Model grid cell

LARIMER

WELD

MORGAN

WASHINGTON

BOULDER

ADAMS

BROOMFIELD

DENVER

JEFFERSON

ARAPAHOE

DOUGLAS

TELLER EL PASO

LINCOLN

ELBERT

Column 1

Row 1

Column 84

Row 124

Row 47

Row 79

Column 10

Column 39

40°00'

39°30'

39°00'

40°30'

105°00' 104°30' 104°00'
8 Demonstration Optimization Analyses of Pumping from Selected Arapahoe Aquifer Municipal Wells

Figure 5. Simulated 2009 potentiometric (hydraulic-head) surfaces for upper and lower Arapahoe aquifers.

Base from U.S. Geological Survey digital data, 2009, 1:100,000

Colorado State Plane Central

Lambert Conformal Conic projection

Standard parallels 38°27' N and 37°45' N, central meridian -105°

CONTOUR INTERVAL 100 FEET

NORTH AMERICAN VERTICAL DATUM OF 1988 

EXPLANATION

Layer 8 line of equal

 hydraulic head

15

15

10 20 MILES

0 10

5

5 20 KILOMETERS

0

Upper Arapahoe aquifer

LowerArapahoe aquifer

Arapahoe confining unit

Layer 10 line of equal

 hydraulic head

Denver Basin study area

 boundary

Perennial stream

Ephemeral stream

Note: In southern part of study area, closely

spaced contours merge and cannot be

resolved in areas where the potentiometric

surface is depressed in the vicinity of

pumping wells. 

4,900

LARIMER

WELD

MORGAN

WASHINGTON

BOULDER

ADAMS

BROOMFIELD

DENVER

JEFFERSON

ARAPAHOE

DOUGLAS

EL PASO

TELLER

LINCOLN

ELBERT

4,800

4,900

4,900

5,000

5,000

5,000

5,100

5,200

5,300

5,000

5,000

5,000

5,000

4,800

5,000

5,200 5,100

5,400

5,600

5,500

5,500

5,400

5,300

5,100

5,100

5,200

5,700

5,200

5,300

5,500

5,400

5,700

6,100

6,100

6,100

6,400

6,400

6,600

6,500

6,700

6,700

6,800

6,700

7,000

7,000

7,200 7,300

7,400

7,100

6,700

5,700

5,900

5,900

6,800

6,500

6,600

6,900

6,900

6,800

6,600

6,600

6,600

6,500

6,600

6,500

6,300

6,300

6,200

6,200

6,200

6,000

6,000

6,000

5,900

5,900

5,800

5,600

5,900

6,000

7,400

6,600

6,200

6,100 6,000

6,000

6,200

6,400

7,000

7,000

7,000

7,200

6,400

6,300

6,200

6,100

40°00'

39°30'

39°00'

40°30' 105°00' 104°30' 104°00'
Numerical Model 9

Figure 6. Height of layer 8 simulated 2009 potentiometric (hydraulic-head) surface relative to top of Arapahoe aquifer.

EXPLANATION

Height of simulated poten-

 tiometric surface above

 top of Arapahoe aquifer

Upper Arapahoe aquifer

LowerArapahoe aquifer

Arapahoe confining unit

Denver Basin study area

 boundary

Area of interest

500

105°00' 104°45' 104°30'

39°45'

39°30'

39°15'

ADAMS

ARAPAHOE

Base from U.S. Geological Survey digital data, 2009, 1:100,000

Colorado State Plane Central

Lambert Conformal Conic projection

Standard parallels 38°27' N and 37°45' N, central meridian -105°

CONTOUR INTERVAL 100 FEET

NORTH AMERICAN VERTICAL DATUM OF 1988 

6

6

4 8 MILES

0 4

2

2 8 KILOMETERS

0

ADAMS

DENVER

DOUGLAS

ELBERT

0

100

100

100

100

100

0

100

100

200

500

300

400

600

600

800

800

800

700

700

900

900

1,000

1,000

1,700

1,400

1,600

1,500

1,100

1,100

1,300

1,200

1,200

400

300

300

400

500

500

600

400

400

400

200

200

200

300
10 Demonstration Optimization Analyses of Pumping from Selected Arapahoe Aquifer Municipal Wells

Maps showing simulated saturated thickness of the 

Arapahoe aquifer provide additional information related to the 

effects of sustained pumping on the aquifer at various simulation times. Figure 7 shows the simulated 2009 combined 

saturated thickness of the upper and lower Arapahoe aquifers. 

Combined saturated thickness was calculated as the sum of 

the saturated thickness of the upper Arapahoe aquifer and the 

saturated thickness of the lower Arapahoe aquifer; where the 

Arapahoe confining unit is present, the thickness of the confining unit is not included in the combined saturated thickness. 

Because 2009 simulated heads are above the top of the upper 

Arapahoe aquifer nearly everywhere in the area of interest, 

figure 7 also illustrates (nearly everywhere) the combined 

thickness of the upper and lower Arapahoe aquifers.

Demonstration of Optimization 

Analyses of Pumping from Municipal 

Wells

Optimization analyses were conducted to demonstrate the 

potential benefits of using available optimization-modeling 

capabilities to address questions related to prolongation of 

the productivity of the Arapahoe aquifer and to limitation of 

the loss of saturated thickness of the Arapahoe aquifer. These 

analyses were designed as demonstrations only and were not 

intended as a comprehensive optimization study. Potential 

benefits that could be expected to result from an appropriately designed and executed comprehensive study include: 

(1) extended usefulness of the aquifers as a municipal water 

source; (2) a cost/benefit evaluation of alternative water-supply strategies, including infrastructure costs; (3) evaluation of 

trade-offs between the use of potential surface-water sources 

and the continued use of groundwater; or (4) an analysis 

of the benefits of aquifer storage and recovery or artificial 

recharge. The primary benefit of this demonstration project is 

to illustrate the general usefulness of some of the capabilities 

of optimization analysis as they could be applied to distribution of possible future pumping from municipal wells in the 

Denver Basin. A discussion of possible additional analyses and 

technical issues that may be applicable or of concern in a more 

comprehensive study also is provided. 

Software and Analytical Framework

Optimization analyses described in this report utilized 

the MODFLOW-based Groundwater Management Process 

(GWM) (Ahlfeld and others, 2005, 2009). Ahlfeld and Mulligan (2000) describe key concepts and examples of optimization methods as applied to groundwater modeling. In 

optimization modeling, a problem is formulated by defining a 

set of decision variables, a set of constraints, and an objective 

function. Decision variables are used to control model input. 

Constraints are defined to assign acceptable limits on decision 

variables and model results. Values extracted or derived from 

model output commonly are referred to as state variables. The 

objective function is a mathematical expression that quantifies the effects of management decisions on outcomes of the 

managed system. A goal of optimization is to maximize or 

minimize the objective function. An optimization algorithm 

manipulates decision variables and executes model runs so as 

to maximize or minimize the objective function without violating any constraints. 

Decision variables supported by GWM include flow-rate 

decision variables, which are used to control a withdrawal 

(discharge) or injection (recharge) flow rate at a managed-well 

(or well-field) location. As noted by Ahlfeld and others (2005), 

the decision variables of a management problem are the quantifiable controls that are to be determined by the mathematical model of the management decision-making process. Each 

decision variable in the analyses described in this report was 

defined to control the simulated withdrawal rate from one or 

more wells in a model cell.

GWM supports several options for defining constraints. 

Two types of constraints were specified in the optimization 

models developed for this study: upper- and lower-bound constraints on withdrawal rates controlled by the flow-rate decision variables, and lower limits on simulated heads at selected 

model cells. The lower limit for managed withdrawal rates 

was zero. In each analysis the objective was to maximize the 

sum of withdrawal rates controlled by all decision variables 

involved in the analysis, subject to the specified constraints. 

With this approach the maximized total withdrawal might be 

obtained when one or more flow rates at individual cells is set 

to zero. This situation can happen when calculated head at a 

constraint location declines to the head-constraint value even 

though the decision variable controlling pumping at that location is zero. 

Selection of Wells

Optimization of pumping distribution can be expected to 

have the most substantial benefits in areas where well-interference effects are most pronounced. In contrast, in areas where 

spacing between wells is so large that well-interference effects 

are small or negligible, optimization of pumping distribution is 

unlikely to be worthwhile. The west-central part of the Denver 

Basin was selected for analysis because the large concentration 

of municipal wells in the area produces conditions in which 

well-interference effects are most likely to have an effect on 

productivity of adjacent wells. In all, 119 wells (fig. 8) were 

used to define locations at which simulated withdrawal rates 

were to be controlled with the flow-rate decision variables. All 

municipal wells completed in the Arapahoe aquifer and currently being used in the south Denver metropolitan area were 

considered for inclusion in the analyses; wells were eliminated 

from consideration only if available data were insufficient to 

define the well location or aquifer of completion. Two wells in 

southwestern Adams County also were included because they 

are operated by one of the major water providers of western 
Demonstration of Optimization Analyses of Pumping from Municipal Wells 11

Figure 7. Combined 2009 simulated saturated thickness of upper and lower Arapahoe aquifers.

Base from U.S. Geological Survey digital data, 2009, 1:100,000

Colorado State Plane Central

Lambert Conformal Conic projection

Standard parallels 38°27' N and 37°45' N, central meridian -105°

CONTOUR INTERVAL 50 FEET

NORTH AMERICAN VERTICAL DATUM OF 1988 

EXPLANATION

6

6

4 8 MILES

0 4

2

2 8 KILOMETERS

0

Line of equal saturated

 thickness of Arapahoe

 aquifer

Upper Arapahoe aquifer

LowerArapahoe aquifer

Arapahoe confining unit

Denver Basin study area

 boundary

Area of interest

400

300

105°00' 104°45' 104°30'

39°45'

39°30'

39°15'

250

500

550

550

ADAMS

ADAMS

DENVER

ARAPAHOE

DOUGLAS

ELBERT

250

250

350

450

450

500

350

350

350

300

350

350

350

350

400

400

400

350

350

400

400

400

450

400

400

400

400

400

350

350

350

300

500

450

450

450

450

550

500

500

500

500

500

450

350

300

400

350

300

250

550

550

550

600

500

450

450

450

400

350

550

400

500

500

450

400

350

250

300

550

600

550

450

550

400

450

500

400

400

350400

400

400

400

350

300

300

300

200

200

350

350

400

400

350

400

400

500

500

400

500

350
12 Demonstration Optimization Analyses of Pumping from Selected Arapahoe Aquifer Municipal Wells

Figure 8. Selected municipal wells.

Base from U.S. Geological Survey digital data, 2009, 1:100,000

Colorado State Plane Central

Lambert Conformal Conic projection

Standard parallels 38°27' N and 37°45' N, central meridian -105°

6

6

4 8 MILES

0 4

2

2 8 KILOMETERS

0

105°00' 104°45' 104°30'

39°45'

39°30'

39°15'

ADAMS

DENVER

ARAPAHOE

DOUGLAS

ELBERT

Column 10

Column 20Column 39

Row 47

Row 50

Row 60

Column 30

Row 70

Row 79

ADAMS

EXPLANATION

Upper Arapahoe aquifer

LowerArapahoe aquifer

Arapahoe confining unit

Denver Basin study area

 boundary

Model grid cell

Area of interest

Selected municipal well
Demonstration of Optimization Analyses of Pumping from Municipal Wells 13

Arapahoe County. Of the 119 wells, 78 were simulated in the 

2004–2009 model and were converted to be represented as 

managed wells for the optimization analyses. The remaining 

41 managed wells were newly constructed or otherwise not 

included in the 2004–2009 simulation.

Application of Optimization Analysis to 

Arapahoe Aquifer Pumping

The concept behind the project documented in this report 

was to use the groundwater model of Banta and others (2011) 

in conjunction with GWM (Ahlfeld and others, 2005, 2009) to 

demonstrate methods to investigate pumping options that may 

prolong the productivity of the Arapahoe aquifer. As waterlevel declines cause increasing desaturation of an aquifer in 

the vicinity of pumping wells, well yields, and thus productivity of the aquifer, necessarily decline. Any measures taken to 

delay excessive drawdowns will tend to prolong productivity. 

Optimization analysis can be helpful in the development of 

such measures. 

Two optimization analyses were designed to address 

issues related to the excessive loss of saturated thickness in 

the Arapahoe aquifer caused by pumping for municipal water 

supplies. In addition a baseline, non-optimized simulation was 

performed. The common goal in both optimization analyses 

was to maximize withdrawals from the Arapahoe aquifer while 

constraining drawdowns of water levels in the Arapahoe aquifer such that dewatering of the aquifer was limited to less than 

a specified percentage of the overall aquifer thickness at specified locations. In consultation with CWCB and CDWR, the 

constraint was defined as 10 percent, so that at least 90 percent 

of the overall aquifer thickness would remain saturated. This 

percentage allows unconfined yield to be considered in the 

analyses, and it produces optimization results in which pumping rates are substantially constrained to avoid violating the 

head constraints. The two analyses differed in the simulation 

time at which the head constraints applied.

In these analyses the term “managed-flow cell” refers 

to a model cell where simulated withdrawal rate is controlled 

by a flow-rate decision variable and determined as part of the 

solution to the optimization formulation. In many instances, a 

managed-flow cell contains a single municipal well. In other 

instances, a single managed-flow cell contains multiple municipal wells because multiple wells are located within the area 

represented by the model cell. Ninety-six managed-flow cells 

were required to include all 119 wells and, thus, 96 flow-rate 

decision variables were defined. Depending on the completion 

interval of a well, the corresponding managed-flow cell was 

either in model layer 8 or layer 10 (table 1). 

For each managed well included in the analysis, a maximum withdrawal rate was assigned. The bases for the maximum withdrawal rates for the various wells depended on data 

availability, according to the following order of preference: 

1. The maximum pumping rate supplied by the municipal 

water provider that operates the well;

2. The “pump_rate” entry obtained from the WellView Web 

online data base maintained by the CDWR (Colorado 

Division of Water Resources, 2009);

3. The “yield” entry obtained from a well-permit data base 

provided by the CDWR (Brian Ahrens, written commun., 

2004); or

4. Calculation from reported production volumes or meter 

readings.

Any maximum withdrawal rate based on the data sources 

above that exceeded the decreed annual rate provided by 

CDWR was reassigned as the decreed rate. Decreed rates conform to the one-percent annual withdrawal limitation (James 

Heath, Colorado Division of Water Resources, oral commun., 

2011) established by the Colorado statewide nontributary 

groundwater rules (Colorado Division of Water Resources, 

1986).

A decision variable was defined for each model cell 

corresponding to one or more managed municipal wells, and 

a maximum withdrawal rate was defined for each decision 

variable (table 2) from the maximum withdrawal rate(s) for 

any managed-flow well(s) in that cell. Each flow-variable 

name is composed of “FV” (where “FV” stands for “flow 

variable”), followed by a string of characters identifying the 

location of the corresponding managed-flow cell, in the format 

LL_RR_CC, where LL is the layer number in the model grid, 

RR is the row number, and CC is the column number. If a 

cell contained multiple municipal wells, the decision-variable 

maximum withdrawal rate was determined as the sum of the 

maximum withdrawal rates of all managed-flow wells within 

the cell. Wells included in the simulations but not included in 

any decision variable are referred to as “unmanaged” wells. 

Withdrawal rates for unmanaged wells were specified at the 

rates that applied for the 2004–2009 period. 

In the Denver Basin, most wells are completed in a single 

aquifer; however, some wells are completed in multiple aquifers. In the model simulations, pumping from wells completed 

in a single aquifer is simulated using the Well Package of 

MODFLOW-2005 (Harbaugh, 2005). Pumping from wells 

completed in multiple aquifers is simulated using the MultiNode Well (MNW) Package (Halford and Hanson, 2002). For 

the 2004–2009 simulation, the simulated pumping rate for all 

wells completed in the upper, lower, or undifferentiated Arapahoe aquifer and simulated by the Well Package was 43.4 ft3

/s; 

this rate is for wells of all water uses (not just municipal) in 

the entire Arapahoe aquifer (not just the area of interest). 

Some wells represented by the MNW Package are completed in the upper and lower Arapahoe aquifers; some are 

completed in the Denver aquifer in addition to the upper and 

lower Arapahoe aquifers, and some are completed in aquifers other than the Arapahoe. Even though MNW withdrawal 

rates are held constant for 2004 and later, interaquifer flow 

simulated by the MNW Package changes slightly during the 

course of a simulation in response to changing hydraulic heads 

near the MNW-simulated wells. However, the variability in 
14 Demonstration Optimization Analyses of Pumping from Selected Arapahoe Aquifer Municipal Wells

Table 2. Flow-rate decision variables and results of optimization analyses.—Continued

[ft3/s, cubic feet per second; yrs, years]

Decisionvariable

name

Number

of wells Layer Row Column

Maximum

withdrawal rate

(ft3/s)

Analysis 1 (50 yrs) 

optimized withdrawal rate

(ft3/s)

Analysis 2 (100 yrs) 

optimized withdrawal rate

(ft3/s)

FV08_58_13 1 8 58 13 0.111 0.111 0.111

FV08_61_18 1 8 61 18 0.044 0.000 0.000

FV08_66_17 1 8 66 17 0.423 0.423 0.423

FV08_72_19 1 8 72 19 0.279 0.279 0.279

FV08_75_20 1 8 75 20 0.579 0.579 0.579

FV08_76_21 1 8 76 21 0.134 0.134 0.134

FV08_77_22 2 8 77 22 0.690 0.690 0.690

FV10_48_37 1 10 48 37 0.099 0.099 0.099

FV10_51_31 1 10 51 31 0.076 0.076 0.076

FV10_57_28 2 10 57 28 0.500 0.500 0.500

FV10_58_27 1 10 58 27 0.102 0.102 0.102

FV10_59_26 1 10 59 26 0.322 0.322 0.322

FV10_59_27 2 10 59 27 0.617 0.617 0.617

FV10_59_28 1 10 59 28 0.668 0.668 0.668

FV10_60_12 1 10 60 12 0.067 0.067 0.067

FV10_60_24 1 10 60 24 0.516 0.516 0.516

FV10_60_25 1 10 60 25 0.414 0.414 0.414

FV10_60_26 1 10 60 26 0.607 0.607 0.607

FV10_60_27 2 10 60 27 0.985 0.985 0.985

FV10_60_28 2 10 60 28 1.131 1.131 1.131

FV10_61_18 2 10 61 18 0.651 0.630 0.122

FV10_61_19 1 10 61 19 0.331 0.331 0.331

FV10_61_21 1 10 61 21 0.889 0.721 0.619

FV10_61_22 2 10 61 22 1.492 1.090 0.894

FV10_61_24 2 10 61 24 0.825 0.825 0.825

FV10_61_28 1 10 61 28 0.791 0.791 0.791

FV10_62_18 1 10 62 18 0.442 0.000 0.000

FV10_62_19 1 10 62 19 0.442 0.347 0.257

FV10_62_21 2 10 62 21 0.552 0.397 0.229

FV10_62_24 1 10 62 24 0.261 0.261 0.261

FV10_62_31 1 10 62 31 0.557 0.557 0.557

FV10_63_14 1 10 63 14 0.066 0.066 0.066

FV10_63_18 2 10 63 18 1.255 0.463 0.348

FV10_63_19 1 10 63 19 0.442 0.442 0.442

FV10_63_21 2 10 63 21 1.104 1.104 0.971

FV10_63_23 1 10 63 23 0.469 0.469 0.469

FV10_63_25 1 10 63 25 0.276 0.276 0.276

FV10_63_31 1 10 63 31 0.557 0.557 0.557

FV10_64_13 1 10 64 13 0.145 0.145 0.145

FV10_64_14 1 10 64 14 0.663 0.275 0.180

FV10_64_16 1 10 64 16 0.663 0.663 0.583

FV10_64_18 1 10 64 18 0.663 0.663 0.663

FV10_64_21 1 10 64 21 0.345 0.345 0.345

FV10_64_22 1 10 64 22 0.345 0.345 0.345

FV10_64_24 4 10 64 24 1.519 1.519 0.927

FV10_64_26 1 10 64 26 0.276 0.276 0.276

FV10_65_17 1 10 65 17 0.663 0.663 0.663

FV10_65_18 1 10 65 18 0.663 0.663 0.663

FV10_65_22 1 10 65 22 0.414 0.414 0.414

Table 2. Flow-rate decision variables and results of optimization analyses.

[ft3/s, cubic feet per second; yrs, years]
Demonstration of Optimization Analyses of Pumping from Municipal Wells 15

Table 2. Flow-rate decision variables and results of optimization analyses.—Continued

[ft3/s, cubic feet per second; yrs, years]

Decisionvariable

name

Number

of wells Layer Row Column

Maximum

withdrawal rate

(ft3/s)

Analysis 1 (50 yrs) 

optimized withdrawal rate

(ft3/s)

Analysis 2 (100 yrs) 

optimized withdrawal rate

(ft3/s)

FV10_65_24 2 10 65 24 0.525 0.525 0.525

FV10_65_25 1 10 65 25 0.207 0.207 0.207

FV10_65_26 1 10 65 26 1.560 1.560 1.560

FV10_66_15 1 10 66 15 0.668 0.668 0.501

FV10_66_16 1 10 66 16 0.377 0.377 0.377

FV10_66_17 1 10 66 17 0.663 0.663 0.429

FV10_66_25 1 10 66 25 0.780 0.780 0.780

FV10_66_26 1 10 66 26 0.128 0.128 0.128

FV10_67_16 1 10 67 16 0.291 0.291 0.291

FV10_67_18 1 10 67 18 0.663 0.663 0.663

FV10_67_23 1 10 67 23 0.197 0.197 0.197

FV10_67_24 1 10 67 24 0.051 0.051 0.051

FV10_67_25 2 10 67 25 0.058 0.058 0.058

FV10_68_15 1 10 68 15 0.600 0.600 0.455

FV10_68_16 1 10 68 16 0.851 0.828 0.609

FV10_68_18 1 10 68 18 1.154 1.154 1.039

FV10_68_19 1 10 68 19 0.446 0.446 0.446

FV10_68_24 2 10 68 24 3.509 2.041 1.382

FV10_68_26 1 10 68 26 0.891 0.891 0.891

FV10_68_27 1 10 68 27 0.118 0.118 0.118

FV10_68_28 1 10 68 28 0.367 0.367 0.367

FV10_69_15 1 10 69 15 0.847 0.847 0.847

FV10_69_17 1 10 69 17 0.769 0.769 0.769

FV10_69_19 1 10 69 19 2.225 1.972 1.276

FV10_69_24 1 10 69 24 1.950 1.662 1.148

FV10_69_25 1 10 69 25 1.894 1.585 1.063

FV10_70_16 1 10 70 16 0.831 0.831 0.831

FV10_70_18 1 10 70 18 1.038 1.038 1.038

FV10_70_23 1 10 70 23 1.000 1.000 1.000

FV10_70_28 1 10 70 28 0.362 0.362 0.362

FV10_71_20 1 10 71 20 0.552 0.552 0.552

FV10_71_24 1 10 71 24 0.456 0.456 0.456

FV10_71_28 1 10 71 28 0.668 0.668 0.668

FV10_72_19 1 10 72 19 0.552 0.552 0.552

FV10_72_20 1 10 72 20 0.552 0.552 0.552

FV10_72_25 1 10 72 25 0.380 0.380 0.380

FV10_73_20 2 10 73 20 1.215 1.215 1.215

FV10_74_18 1 10 74 18 0.388 0.388 0.388

FV10_74_19 2 10 74 19 1.008 1.008 1.008

FV10_74_20 1 10 74 20 1.025 1.025 1.025

FV10_75_19 1 10 75 19 0.695 0.695 0.695

FV10_75_20 2 10 75 20 2.400 1.191 0.857

FV10_75_23 2 10 75 23 1.318 1.318 1.318

FV10_75_24 1 10 75 24 0.276 0.276 0.276

FV10_76_23 2 10 76 23 0.906 0.906 0.906

FV10_77_22 2 10 77 22 0.652 0.652 0.489

FV10_78_21 1 10 78 21 0.690 0.690 0.690

Totals 64.874 58.820 52.971
16 Demonstration Optimization Analyses of Pumping from Selected Arapahoe Aquifer Municipal Wells

discharge from the Arapahoe aquifer caused by changes in 

interaquifer flow was small. The rate of withdrawals from the 

upper and lower Arapahoe aquifers simulated by the MNW 

Package, rounded to the nearest 0.1 ft3/s, remained at 4.9 ft3/s; 

again, this rate is for wells of all water uses in the entire 

Arapahoe aquifer. The total well withdrawal rate for wells 

of all water uses in the entire Arapahoe aquifer, including 

single-aquifer and multi-aquifer wells, was, therefore, about 

48.3 ft3/s. The optimization analyses did not involve management of multi-aquifer wells. For this reason, discussion of the 

optimization focuses primarily on the single-aquifer wells.

For the non-optimized simulation and for the optimization analyses, a subset of wells simulated by the Well Package 

was removed and simulated instead with rates controlled by 

GWM. During these simulations, the total pumping rate for 

all Arapahoe aquifer wells simulated by the Well Package was 

37.7 ft3/s, rather than the 43.4 ft3/s of the 2004–2009 simulation. The difference in withdrawals simulated by the Well 

Package, 5.7 ft3/s, is the rate simulated during 2004–2009 

for 78 wells that were removed from the Well Package 

and included in decision variables for the non-optimized 

simulation and optimization analyses. The other 41 of the 119 

wells included in decision variables are wells that either were 

newly constructed or otherwise were absent from the set of 

wells identified and simulated as Arapahoe aquifer municipal 

wells in the Denver Basin model (Banta and others, 2011).

A single set of altitudes was defined and incorporated 

into hydraulic-head constraints for the optimization analyses. 

Two head-constraint altitudes were defined for each managedflow cell location: one in layer 8 and one in layer 10. In much 

of the area affected by pumping from wells in the westcentral Denver Basin, the confining bed between the upper 

and lower Arapahoe aquifers is absent, and, for the purposes 

of this investigation, the Arapahoe aquifer is considered 

undifferentiated. 

Head-constraint altitudes were chosen for each flow-rate 

decision-variable location such that, depending on the layer 

and the presence or absence of the Arapahoe confining bed, 

if the head for the cell was at the constraint head, the saturated thickness of either the upper, lower, or undifferentiated 

Arapahoe aquifer would be 90 percent of the aquifer thickness. 

Where the Arapahoe confining bed is present, a constraint was 

defined for the layer-8 cell at an altitude that would represent 

90 percent of the thickness of the layer-8 cell, and a constraint 

was defined for the layer-10 cell at an altitude that would 

represent 90 percent of the thickness of the layer-10 cell. In 

areas where the Arapahoe confining bed is absent, the bottom 

of layer 8 was set equal to the midpoint altitude of the Arapahoe aquifer, and the bottom of layer 9 was assigned to be 0.1 ft 

below the bottom of layer 8 (Banta and others, 2011). The 

head constraint for both the layer 8 and the layer 10 cells were 

defined at an altitude that would represent 90 percent of the 

overall thickness of layers 8 through 10. 

Locations and head values for all head constraints are 

listed in table 3. The constraint names were generated as “HC” 

followed by a string of characters in the format LL_RR_CC, 

where LL is the layer number, RR is the row number, and CC 

is the column number of the model cell where the constraint 

applied. For the two optimization analyses, the total simulation 

time was either 50 or 100 years. All pumping rates remained 

constant throughout the 50- or 100-year simulation period. In 

each analysis the constraints applied at the end of the simulation time. The height of the 2009 simulated head above 

each constraint altitude (table 3), which ranges from 65.1 to 

966.9 ft, indicates the amount of drawdown available at each 

constraint location for the 50- or 100-year simulation period.

Because of nonlinear computational behavior during 

solution of the Denver Basin model (Banta and others, 2011), 

the sequential linear programming (SLP) approach of GWM 

(Ahlfeld and others, 2005, 2009) was selected to solve the 

optimization problems. MODFLOW and SLP solver settings 

and convergence criteria were defined to calculate model 

results with sufficient precision to enable the SLP algorithm to 

generate reliable results. Details of the SLP method and solver 

settings are provided in Ahlfeld and others (2005).

Table 2 lists the flow-rate decision variables used in the 

optimization analyses. The purpose of each analysis was to 

determine the optimum spatial distribution of pumping among 

all wells for either 50 or 100 years, subject to the maximum 

withdrawal-rate constraints and head constraints. The formulation of each optimization analysis can be expressed in terms of 

the following objective function and constraints:

Maximize objective function: 1

NV

i

i

Q

=

∑

subject to maximum withdrawal constraints: 

, 1, u Qi Qi ≤ i = NV

and head constraints: , 1, l H j H j ≥ j = NC at the end of the 

simulation,

where 

NV is the number of flow-rate decision 

variables; 

Qi is the withdrawal rate for decision variable i; u Qi is the maximum withdrawal rate for decision 

variable i;

Hj is the simulated head corresponding to head 

constraint j at the end of the simulation; 

l H j is a lower head constraint listed in table 3; 

and 

NC is the number of head constraints. 

Non-Optimized Simulation

To provide a basis for evaluating the optimization 

analyses, a 100-year simulation using non-optimized pumping 

rates was performed, representing Jan. 1, 2010, through Dec. 

31, 2109. For this simulation, pumping rates for all decision 

variables were assigned as the maximum withdrawal rates 

(table 2). Other stresses were assigned at the 2004–2009 simulated values. 
Demonstration of Optimization Analyses of Pumping from Municipal Wells 17

Table 3. Head constraints and simulated heads.—Continued 

[deactiv., cell was deactivated; --, constraint was not violated]

Constraint 

name Layer Row Column

Cell 

top 

elevation

2009 

simulated 

hydraulic 

head

Lower 

head 

constraint 

(feet)

Height 

of 2009 

simulated 

head above 

constraint 

(feet)

Nonoptimized 

(2109) 

simulated 

hydraulic 

head

Headconstraint 

violation year 

(non-optimized 

simulation)

Analysis 

1 (2059) 

simulated 

hydraulic 

head

Analysis 

2 (2109) 

simulated 

hydraulic 

head

HC08_48_37 8 48 37 4,809.5 5,235.4 4,790.6 444.9 5,166.6 -- 5,182.9 5,167.0

HC10_48_37 10 48 37 4,516.9 5,215.1 4,494.2 720.9 5,141.7 -- 5,158.2 5,142.1

HC08_51_31 8 51 31 4,772.7 5,218.8 4,753.4 465.5 5,100.3 -- 5,123.1 5,100.9

HC10_51_31 10 51 31 4,434.9 5,213.8 4,417.8 796.0 5,081.9 -- 5,104.9 5,082.5

HC08_57_28 8 57 28 4,693.7 5,260.5 4,674.7 585.8 4,955.8 -- 4,993.9 4,956.5

HC10_57_28 10 57 28 4,413.9 5,257.7 4,394.5 863.2 4,908.6 -- 4,946.9 4,909.3

HC08_58_13 8 58 13 4,987.0 5,106.1 4,974.8 131.3 4,992.5 -- 5,008.1 4,997.5

HC10_58_13 10 58 13 4,785.8 5,107.1 4,757.0 350.1 4,993.7 -- 5,009.5 4,998.7

HC08_58_27 8 58 27 4,682.4 5,245.9 4,664.7 581.3 4,875.5 -- 4,915.7 4,876.0

HC10_58_27 10 58 27 4,420.4 5,244.2 4,397.3 846.8 4,848.3 -- 4,888.7 4,848.8

HC08_59_26 8 59 26 4,662.2 5,233.2 4,643.3 589.9 4,797.1 -- 4,837.6 4,796.8

HC10_59_26 10 59 26 4,385.3 5,224.3 4,362.5 861.8 4,743.8 -- 4,784.6 4,743.5

HC08_59_27 8 59 27 4,687.1 5,246.4 4,669.2 577.3 4,799.4 -- 4,844.0 4,800.0

HC10_59_27 10 59 27 4,439.2 5,244.6 4,415.3 829.4 4,737.3 -- 4,781.8 4,738.0

HC08_59_28 8 59 28 4,671.6 5,269.5 4,656.6 612.9 4,852.7 -- 4,898.3 4,853.7

HC10_59_28 10 59 28 4,437.9 5,268.3 4,415.6 852.7 4,788.6 -- 4,834.0 4,789.7

HC08_60_12 8 60 12 5,108.5 5,128.4 5,062.5 65.9 5,094.6 -- 5,104.8 5,095.2

HC10_60_12 10 60 12 4,878.4 5,127.6 5,062.5 65.1 5,093.7 -- 5,103.9 5,094.3

HC08_60_24 8 60 24 4,627.8 5,199.2 4,606.8 592.4 4,731.1 -- 4,759.6 4,724.7

HC10_60_24 10 60 24 4,360.0 5,195.0 4,335.4 859.6 4,689.3 -- 4,718.6 4,683.2

HC08_60_25 8 60 25 4,605.0 5,219.3 4,584.7 634.6 4,732.6 -- 4,771.8 4,730.8

HC10_60_25 10 60 25 4,342.2 5,218.3 4,318.3 900.0 4,689.6 -- 4,729.4 4,688.1

HC08_60_26 8 60 26 4,619.2 5,235.6 4,600.3 635.2 4,735.9 -- 4,780.9 4,736.1

HC10_60_26 10 60 26 4,338.2 5,234.6 4,318.3 916.3 4,669.1 -- 4,714.9 4,669.6

HC08_60_27 8 60 27 4,635.6 5,254.9 4,621.4 633.6 4,745.1 -- 4,794.6 4,746.4

HC10_60_27 10 60 27 4,420.2 5,254.1 4,394.5 859.6 4,665.6 -- 4,715.0 4,666.9

HC08_60_28 8 60 28 4,653.8 5,276.4 4,638.9 637.5 4,796.2 -- 4,846.4 4,797.8

HC10_60_28 10 60 28 4,446.2 5,276.0 4,421.0 854.9 4,729.1 -- 4,779.1 4,730.8

HC08_61_18 8 61 18 4,790.2 5,103.3 4,766.5 336.8 4,696.8 2039 4,766.9 4,788.2

HC10_61_18 10 61 18 4,460.1 5,091.3 4,439.3 652.1 4,595.6 -- 4,674.3 4,761.9

HC08_61_19 8 61 19 4,788.6 5,113.7 4,759.6 354.1 4,697.2 2044 4,760.5 4,764.6

HC10_61_19 10 61 19 4,407.1 5,105.6 4,384.6 721.0 4,636.4 -- 4,704.9 4,713.4

HC08_61_21 8 61 21 4,684.8 5,157.4 4,635.4 522.0 4,515.2 2033 4,636.3 4,636.1

HC10_61_21 10 61 21 4,437.7 5,157.3 4,635.4 522.0 4,514.6 2031 4,635.4 4,635.3

HC08_61_22 8 61 22 4,612.8 5,160.5 4,571.4 589.1 deactiv. 2025 4,572.4 4,572.5

HC10_61_22 10 61 22 4,405.7 5,160.4 4,571.4 589.0 deactiv. 2025 4,571.4 4,571.6

HC08_61_24 8 61 24 4,572.8 5,193.1 4,526.9 666.2 4,612.6 -- 4,649.0 4,610.2

HC10_61_24 10 61 24 4,343.2 5,192.9 4,526.9 666.0 4,611.9 -- 4,648.2 4,609.4

HC08_61_28 8 61 28 4,636.4 5,298.6 4,588.3 710.2 4,785.3 -- 4,841.3 4,788.0

HC10_61_28 10 61 28 4,396.2 5,298.5 4,588.3 710.2 4,784.8 -- 4,840.8 4,787.5

HC08_62_18 8 62 18 4,844.4 5,141.7 4,781.6 360.1 4,624.8 2027 4,782.3 4,781.8

HC10_62_18 10 62 18 4,530.2 5,141.4 4,781.6 359.8 4,623.6 2027 4,781.6 4,781.3

HC08_62_19 8 62 19 4,794.8 5,151.8 4,733.9 417.8 4,632.0 2039 4,734.9 4,734.3

HC10_62_19 10 62 19 4,490.4 5,151.6 4,733.9 417.6 4,631.1 2039 4,733.9 4,733.5

HC08_62_21 8 62 21 4,687.3 5,168.5 4,633.7 534.8 4,529.9 2039 4,634.4 4,633.8

HC10_62_21 10 62 21 4,419.5 5,168.3 4,633.7 534.6 4,529.3 2039 4,633.7 4,633.3

Table 3. Head constraints and simulated heads. 

[deactiv., cell was deactivated; --, constraint was not violated]
18 Demonstration Optimization Analyses of Pumping from Selected Arapahoe Aquifer Municipal Wells

Table 3. Head constraints and simulated heads.—Continued 

[deactiv., cell was deactivated; --, constraint was not violated]

Constraint 

name Layer Row Column

Cell 

top 

elevation

2009 

simulated 

hydraulic 

head

Lower 

head 

constraint 

(feet)

Height 

of 2009 

simulated 

head above 

constraint 

(feet)

Nonoptimized 

(2109) 

simulated 

hydraulic 

head

Headconstraint 

violation year 

(non-optimized 

simulation)

Analysis 

1 (2059) 

simulated 

hydraulic 

head

Analysis 

2 (2109) 

simulated 

hydraulic 

head

HC08_62_24 8 62 24 4,559.6 5,228.3 4,512.4 715.9 4,605.2 -- 4,659.3 4,617.7

HC10_62_24 10 62 24 4,323.4 5,228.2 4,512.4 715.9 4,605.0 -- 4,659.0 4,617.4

HC08_62_31 8 62 31 4,726.6 5,380.7 4,678.7 702.0 5,009.0 -- 5,062.6 5,011.2

HC10_62_31 10 62 31 4,486.9 5,380.7 4,678.7 702.0 5,008.7 -- 5,062.3 5,010.9

HC08_63_14 8 63 14 5,171.3 5,356.1 5,119.8 236.3 5,112.9 2099 5,152.3 5,140.7

HC10_63_14 10 63 14 4,913.4 5,356.0 5,119.8 236.2 5,112.3 2096 5,151.7 5,140.2

HC08_63_18 8 63 18 4,759.6 5,187.4 4,703.3 484.1 deactiv. 2022 4,704.3 4,703.9

HC10_63_18 10 63 18 4,478.0 5,187.1 4,703.3 483.8 4,415.4 2021 4,703.3 4,703.0

HC08_63_19 8 63 19 4,706.0 5,199.9 4,656.8 543.0 4,598.7 2070 4,696.5 4,678.1

HC10_63_19 10 63 19 4,460.0 5,199.6 4,656.8 542.8 4,597.8 2070 4,695.6 4,677.3

HC08_63_21 8 63 21 4,594.5 5,200.9 4,548.2 652.7 4,481.3 2066 4,567.6 4,548.9

HC10_63_21 10 63 21 4,363.0 5,200.7 4,548.2 652.4 4,480.4 2066 4,566.4 4,547.9

HC08_63_23 8 63 23 4,581.3 5,215.5 4,533.0 682.5 4,548.3 -- 4,594.3 4,569.3

HC10_63_23 10 63 23 4,339.4 5,215.2 4,533.0 682.3 4,547.6 -- 4,593.6 4,568.6

HC08_63_25 8 63 25 4,627.5 5,276.2 4,574.1 702.0 4,627.7 -- 4,702.9 4,645.2

HC10_63_25 10 63 25 4,360.4 5,276.1 4,574.1 702.0 4,627.3 -- 4,702.6 4,644.9

HC08_63_31 8 63 31 4,712.0 5,417.8 4,664.9 752.9 5,036.5 -- 5,095.0 5,039.2

HC10_63_31 10 63 31 4,476.8 5,417.8 4,664.9 752.9 5,036.2 -- 5,094.6 5,038.9

HC08_64_13 8 64 13 5,225.8 5,384.0 5,190.5 193.5 5,193.9 -- 5,222.2 5,215.6

HC10_64_13 10 64 13 5,049.3 5,383.8 5,190.5 193.3 5,193.4 -- 5,221.7 5,215.1

HC08_64_14 8 64 14 5,187.1 5,394.7 5,137.9 256.8 4,998.3 2025 5,138.8 5,138.5

HC10_64_14 10 64 14 4,941.0 5,394.4 5,137.9 256.5 4,997.2 2024 5,137.9 5,137.9

HC08_64_16 8 64 16 4,897.5 5,350.5 4,849.4 501.1 4,815.7 2063 4,855.1 4,850.3

HC10_64_16 10 64 16 4,656.8 5,350.3 4,849.4 500.9 4,814.7 2059 4,854.0 4,849.3

HC08_64_18 8 64 18 4,723.5 5,288.0 4,674.1 613.9 4,614.7 2063 4,701.6 4,678.9

HC10_64_18 10 64 18 4,476.1 5,287.8 4,674.1 613.8 4,613.7 2063 4,700.6 4,678.0

HC08_64_21 8 64 21 4,591.1 5,251.6 4,542.9 708.6 4,583.7 -- 4,646.4 4,601.1

HC10_64_21 10 64 21 4,350.2 5,251.4 4,542.9 708.4 4,583.1 -- 4,645.9 4,600.6

HC08_64_22 8 64 22 4,580.7 5,247.0 4,533.1 713.9 4,564.8 -- 4,621.0 4,577.6

HC10_64_22 10 64 22 4,342.2 5,246.9 4,533.1 713.8 4,564.3 -- 4,620.6 4,577.1

HC08_64_24 8 64 24 4,581.6 5,253.1 4,532.4 720.8 4,428.8 2066 4,545.4 4,533.0

HC10_64_24 10 64 24 4,335.4 5,252.9 4,532.4 720.5 4,427.9 2066 4,543.8 4,532.1

HC08_64_26 8 64 26 4,621.2 5,319.0 4,571.8 747.1 4,649.3 -- 4,735.7 4,662.0

HC10_64_26 10 64 26 4,374.2 5,318.9 4,571.8 747.1 4,649.0 -- 4,735.3 4,661.7

HC08_65_17 8 65 17 4,784.2 5,386.7 4,733.0 653.7 4,704.8 2079 4,753.1 4,734.7

HC10_65_17 10 65 17 4,528.3 5,386.5 4,733.0 653.5 4,703.9 2079 4,752.1 4,733.8

HC08_65_18 8 65 18 4,728.1 5,366.2 4,675.7 690.5 4,665.6 2103 4,724.8 4,697.3

HC10_65_18 10 65 18 4,466.0 5,366.0 4,675.7 690.3 4,664.6 2103 4,723.7 4,696.4

HC08_65_22 8 65 22 4,629.1 5,295.1 4,578.3 716.8 4,614.6 -- 4,686.0 4,621.9

HC10_65_22 10 65 22 4,374.9 5,295.0 4,578.3 716.7 4,613.9 -- 4,685.4 4,621.2

HC08_65_24 8 65 24 4,560.1 5,274.2 4,516.1 758.1 4,517.4 -- 4,592.7 4,540.1

HC10_65_24 10 65 24 4,340.2 5,274.0 4,516.1 757.8 4,516.7 -- 4,592.1 4,539.4

HC08_65_25 8 65 25 4,536.8 5,295.7 4,496.1 799.6 4,536.9 -- 4,612.4 4,551.0

HC10_65_25 10 65 25 4,332.9 5,295.6 4,496.1 799.5 4,536.6 -- 4,612.1 4,550.7

HC08_65_26 8 65 26 4,571.6 5,325.6 4,528.4 797.2 4,529.5 -- 4,601.2 4,540.4

HC10_65_26 10 65 26 4,355.4 5,325.5 4,528.4 797.1 4,528.3 2109 4,599.9 4,539.1
Demonstration of Optimization Analyses of Pumping from Municipal Wells 19

Table 3. Head constraints and simulated heads.—Continued 

[deactiv., cell was deactivated; --, constraint was not violated]

Constraint 

name Layer Row Column

Cell 

top 

elevation

2009 

simulated 

hydraulic 

head

Lower 

head 

constraint 

(feet)

Height 

of 2009 

simulated 

head above 

constraint 

(feet)

Nonoptimized 

(2109) 

simulated 

hydraulic 

head

Headconstraint 

violation year 

(non-optimized 

simulation)

Analysis 

1 (2059) 

simulated 

hydraulic 

head

Analysis 

2 (2109) 

simulated 

hydraulic 

head

HC08_66_15 8 66 15 5,033.9 5,449.4 4,984.3 465.0 4,939.4 2066 4,991.0 4,985.1

HC10_66_15 10 66 15 4,785.9 5,449.0 4,984.3 464.7 4,938.6 2066 4,990.0 4,984.3

HC08_66_16 8 66 16 4,903.0 5,462.0 4,852.0 609.9 4,843.2 2103 4,886.9 4,874.1

HC10_66_16 10 66 16 4,648.3 5,461.9 4,852.0 609.9 4,842.6 2099 4,886.2 4,873.5

HC08_66_17 8 66 17 4,799.4 5,444.0 4,748.6 695.3 4,691.7 2059 4,749.2 4,748.8

HC10_66_17 10 66 17 4,545.5 5,443.9 4,748.6 695.2 4,691.4 2059 4,748.8 4,748.6

HC08_66_25 8 66 25 4,555.1 5,340.0 4,513.4 826.6 4,538.1 -- 4,610.8 4,541.0

HC10_66_25 10 66 25 4,346.5 5,340.0 4,513.4 826.6 4,537.3 -- 4,610.0 4,540.2

HC08_66_26 8 66 26 4,565.3 5,335.5 4,525.4 810.1 4,624.8 -- 4,713.4 4,630.5

HC10_66_26 10 66 26 4,365.5 5,338.3 4,525.4 813.0 4,624.6 -- 4,713.1 4,630.3

HC08_67_16 8 67 16 4,968.5 5,501.5 4,917.8 583.7 4,900.3 2090 4,942.7 4,927.9

HC10_67_16 10 67 16 4,714.8 5,499.9 4,917.8 582.1 4,899.8 2090 4,942.1 4,927.4

HC08_67_18 8 67 18 4,799.5 5,480.4 4,747.3 733.1 4,744.9 2109 4,798.2 4,773.9

HC10_67_18 10 67 18 4,538.6 5,480.3 4,747.3 732.9 4,744.1 2109 4,797.4 4,773.1

HC08_67_23 8 67 23 4,581.8 5,407.4 4,538.6 868.8 4,731.5 -- 4,788.4 4,693.5

HC10_67_23 10 67 23 4,365.9 5,407.3 4,538.6 868.7 4,731.3 -- 4,788.1 4,693.2

HC08_67_24 8 67 24 4,570.8 5,405.2 4,525.9 879.2 4,671.3 -- 4,708.5 4,631.1

HC10_67_24 10 67 24 4,346.4 5,405.1 4,525.9 879.2 4,671.2 -- 4,708.2 4,630.9

HC08_67_25 8 67 25 4,587.5 5,399.9 4,544.6 855.3 4,648.1 -- 4,714.0 4,637.7

HC10_67_25 10 67 25 4,373.1 5,399.9 4,544.6 855.3 4,648.0 -- 4,713.8 4,637.5

HC08_68_15 8 68 15 5,103.3 5,546.1 5,054.2 491.9 5,019.9 2070 5,061.2 5,054.8

HC10_68_15 10 68 15 4,857.7 5,546.0 5,054.2 491.7 5,019.3 2066 5,060.5 5,054.2

HC08_68_16 8 68 16 5,000.8 5,552.8 4,949.7 603.1 4,902.6 2059 4,950.6 4,950.3

HC10_68_16 10 68 16 4,745.3 5,552.7 4,949.7 603.0 4,901.9 2056 4,949.7 4,949.7

HC08_68_18 8 68 18 4,834.5 5,534.9 4,781.9 753.0 4,741.4 2079 4,809.3 4,782.9

HC10_68_18 10 68 18 4,571.5 5,534.9 4,781.9 752.9 4,740.4 2079 4,808.1 4,781.9

HC08_68_19 8 68 19 4,797.1 5,504.5 4,741.9 762.5 4,746.5 -- 4,816.2 4,791.0

HC10_68_19 10 68 19 4,521.0 5,504.3 4,741.9 762.4 4,745.7 -- 4,815.6 4,790.3

HC08_68_24 8 68 24 4,587.1 5,446.4 4,543.1 903.3 deactiv. 2020 4,544.9 4,544.2

HC10_68_24 10 68 24 4,366.8 5,446.3 4,543.1 903.2 deactiv. 2019 4,543.0 4,542.9

HC08_68_26 8 68 26 4,630.5 5,423.5 4,584.9 838.5 4,637.4 -- 4,720.4 4,637.4

HC10_68_26 10 68 26 4,402.5 5,423.4 4,584.9 838.4 4,636.5 -- 4,719.3 4,636.4

HC08_68_27 8 68 27 4,614.3 5,419.3 4,567.6 851.7 4,791.2 -- 4,890.3 4,796.8

HC10_68_27 10 68 27 4,380.4 5,419.1 4,567.6 851.6 4,791.0 -- 4,890.1 4,796.5

HC08_68_28 8 68 28 4,595.9 5,479.0 4,556.5 922.5 4,919.7 -- 5,012.2 4,926.1

HC10_68_28 10 68 28 4,399.1 5,479.0 4,556.5 922.5 4,919.3 -- 5,011.8 4,925.7

HC08_69_15 8 69 15 5,105.6 5,581.2 5,060.3 520.9 5,052.5 2103 5,091.6 5,067.0

HC10_69_15 10 69 15 4,879.0 5,581.1 5,060.3 520.8 5,051.8 2099 5,090.8 5,066.3

HC08_69_17 8 69 17 4,937.2 5,573.8 4,883.6 690.1 4,903.0 -- 4,940.6 4,921.7

HC10_69_17 10 69 17 4,669.2 5,573.6 4,883.6 690.0 4,902.2 -- 4,939.8 4,920.9

HC08_69_19 8 69 19 4,834.8 5,536.8 4,778.8 758.0 4,633.2 2050 4,780.8 4,780.0

HC10_69_19 10 69 19 4,554.4 5,536.7 4,778.8 757.9 4,632.0 2047 4,778.8 4,778.7

HC08_69_24 8 69 24 4,621.2 5,498.1 4,576.1 922.0 deactiv. 2039 4,577.8 4,577.2

HC10_69_24 10 69 24 4,395.8 5,498.1 4,576.1 922.0 deactiv. 2039 4,576.1 4,576.0

HC08_69_25 8 69 25 4,649.6 5,480.4 4,603.0 877.4 deactiv. 2042 4,604.9 4,604.2

HC10_69_25 10 69 25 4,416.9 5,480.4 4,603.0 877.3 4,250.2 2039 4,603.0 4,602.9
20 Demonstration Optimization Analyses of Pumping from Selected Arapahoe Aquifer Municipal Wells

Table 3. Head constraints and simulated heads.—Continued 

[deactiv., cell was deactivated; --, constraint was not violated]

Constraint 

name Layer Row Column

Cell 

top 

elevation

2009 

simulated 

hydraulic 

head

Lower 

head 

constraint 

(feet)

Height 

of 2009 

simulated 

head above 

constraint 

(feet)

Nonoptimized 

(2109) 

simulated 

hydraulic 

head

Headconstraint 

violation year 

(non-optimized 

simulation)

Analysis 

1 (2059) 

simulated 

hydraulic 

head

Analysis 

2 (2109) 

simulated 

hydraulic 

head

HC08_70_16 8 70 16 5,089.6 5,612.1 5,034.6 577.5 5,055.5 -- 5,091.9 5,064.4

HC10_70_16 10 70 16 4,814.6 5,612.0 5,034.6 577.4 5,054.7 -- 5,091.2 5,063.6

HC08_70_18 8 70 18 4,883.8 5,576.3 4,827.9 748.4 4,870.8 -- 4,930.7 4,883.0

HC10_70_18 10 70 18 4,604.4 5,576.1 4,827.9 748.2 4,869.7 -- 4,929.6 4,881.9

HC08_70_23 8 70 23 4,626.3 5,550.9 4,584.0 966.9 4,763.8 -- 4,800.4 4,715.3

HC10_70_23 10 70 23 4,414.8 5,550.8 4,584.0 966.8 4,762.9 -- 4,799.4 4,714.4

HC08_70_28 8 70 28 4,645.9 5,536.7 4,630.0 906.7 4,967.5 -- 5,055.8 4,973.3

HC10_70_28 10 70 28 4,425.1 5,536.6 4,630.0 906.6 4,966.6 -- 5,054.9 4,972.4

HC08_71_20 8 71 20 4,675.2 5,584.3 4,624.2 960.1 4,847.9 -- 4,930.1 4,859.3

HC10_71_20 10 71 20 4,420.4 5,584.2 4,624.2 960.0 4,847.2 -- 4,929.4 4,858.7

HC08_71_24 8 71 24 4,652.9 5,560.4 4,609.7 950.7 4,859.4 -- 4,913.2 4,827.6

HC10_71_24 10 71 24 4,437.0 5,560.4 4,609.7 950.6 4,858.8 -- 4,912.5 4,827.0

HC08_71_28 8 71 28 4,666.0 5,578.9 4,619.9 959.0 4,932.9 -- 5,013.6 4,937.6

HC10_71_28 10 71 28 4,435.4 5,578.8 4,619.9 958.9 4,931.3 -- 5,012.0 4,936.0

HC08_72_19 8 72 19 4,785.6 5,609.4 4,736.2 873.2 4,881.3 -- 4,949.5 4,884.6

HC10_72_19 10 72 19 4,538.5 5,609.4 4,736.2 873.1 4,880.9 -- 4,949.1 4,884.2

HC08_72_20 8 72 20 4,719.3 5,597.2 4,669.9 927.4 4,815.2 -- 4,882.4 4,818.3

HC10_72_20 10 72 20 4,471.9 5,597.1 4,669.9 927.3 4,814.5 -- 4,881.7 4,817.6

HC08_72_25 8 72 25 4,654.9 5,576.7 4,613.0 963.6 4,971.4 -- 5,046.1 4,963.5

HC10_72_25 10 72 25 4,445.7 5,576.5 4,613.0 963.5 4,970.7 -- 5,045.4 4,962.8

HC08_73_20 8 73 20 4,803.9 5,608.0 4,753.7 854.3 4,774.9 -- 4,815.0 4,772.6

HC10_73_20 10 73 20 4,552.9 5,607.9 4,753.7 854.2 4,773.5 -- 4,813.6 4,771.2

HC08_74_18 8 74 18 4,900.9 5,671.6 4,860.1 811.4 5,101.8 -- 5,137.9 5,080.4

HC10_74_18 10 74 18 4,697.0 5,671.5 4,860.1 811.4 5,101.5 -- 5,137.6 5,080.1

HC08_74_19 8 74 19 4,832.3 5,637.8 4,790.3 847.5 4,876.7 -- 4,897.7 4,846.7

HC10_74_19 10 74 19 4,622.2 5,637.7 4,790.3 847.4 4,875.9 -- 4,896.8 4,845.9

HC08_74_20 8 74 20 4,783.2 5,641.6 4,739.7 901.9 4,766.0 -- 4,782.7 4,756.4

HC10_74_20 10 74 20 4,565.6 5,641.6 4,739.7 901.9 4,764.9 -- 4,781.6 4,755.2

HC08_75_19 8 75 19 4,911.6 5,684.9 4,867.9 817.1 5,044.8 -- 4,991.1 4,949.8

HC10_75_19 10 75 19 4,692.7 5,684.8 4,867.9 817.0 5,044.1 -- 4,990.3 4,949.0

HC08_75_20 8 75 20 4,814.7 5,667.2 4,772.9 894.3 deactiv. 2017 4,773.9 4,773.4

HC10_75_20 10 75 20 4,605.7 5,667.1 4,772.9 894.2 deactiv. 2017 4,772.9 4,772.9

HC08_75_23 8 75 23 4,771.9 5,667.2 4,719.6 947.6 4,741.6 -- 4,769.3 4,732.4

HC10_75_23 10 75 23 4,510.5 5,667.1 4,719.6 947.5 4,738.1 -- 4,765.7 4,728.9

HC08_75_24 8 75 24 4,780.4 5,687.0 4,724.6 962.4 4,999.3 -- 5,050.7 4,996.4

HC10_75_24 10 75 24 4,501.1 5,687.0 4,724.6 962.4 4,998.1 -- 5,049.5 4,995.1

HC08_76_21 8 76 21 4,866.0 5,671.3 4,814.9 856.4 5,078.3 -- 5,036.2 4,993.9

HC10_76_21 10 76 21 4,610.6 5,671.0 4,814.9 856.1 5,078.1 -- 5,035.9 4,993.6

HC08_76_23 8 76 23 4,856.2 5,652.9 4,796.0 856.9 4,828.3 -- 4,852.4 4,823.5

HC10_76_23 10 76 23 4,555.0 5,652.4 4,796.0 856.4 4,824.5 -- 4,848.5 4,819.7

HC08_77_22 8 77 22 4,885.3 5,658.5 4,828.5 830.0 4,796.0 2079 4,838.9 4,829.0

HC10_77_22 10 77 22 4,601.1 5,657.7 4,828.5 829.2 4,795.2 2079 4,837.8 4,828.5

HC08_78_21 8 78 21 4,984.4 5,724.9 4,930.4 794.5 5,098.0 -- 5,121.1 5,073.6

HC10_78_21 10 78 21 4,714.3 5,724.1 4,930.4 793.6 5,095.2 -- 5,118.2 5,070.8
Demonstration of Optimization Analyses of Pumping from Municipal Wells 21

For the non-optimized simulation, 63 of the 182 head 

constraints were not met, and 10 of the head-constraint cells 

were deactivated (converted to no-flow cells) because the 

estimated head in the cell dropped below the cell bottom 

during solution of the groundwater-flow equation. These 10 

deactivated head-constraint cells (table 3) are associated with 

6 managed-flow cells (table 2). The head constraints that were 

violated during the non-optimized simulation are identified in 

table 3 by the presence of a year in the column labeled “Headconstraint violation year (non-optimized simulation).” Head 

constraints were violated in years ranging from 2017 to 2109.

If no managed-flow cells had been deactivated, the 

total pumping rate for managed-flow cells would have been 

64.9 ft3/s throughout the non-optimized simulation (table 4). 

However, four of the managed-flow cells were deactivated; as 

a result, the total pumping rate for managed-flow cells at the 

end of the simulation was 54.9 ft3/s. The total rate of withdrawals from the Arapahoe aquifer was 107.5 ft3

/s (table 4) 

at the beginning of the simulation, when no cells had been 

deactivated.

Analysis 1: Optimization of Pumping for 

Managed Withdrawals Over 50-Year Period

Analysis 1 was designed to establish an optimal set 

of constant withdrawal rates for 96 decision variables 

representing 119 municipal wells. In this 50-year analysis, the 

optimal solution was obtained when 81 of the 96 decision variables were assigned (by GWM) at their maximum withdrawal 

rates, and 2 of the decision variables were assigned (by GWM) 

a withdrawal rate of zero. The other 13 decision variables had 

nonzero values less than their maximum rates. No constraints 

were violated. Table 2 lists the optimized withdrawal rates 

for individual decision variables for this analysis. The total 

optimized withdrawal rate for managed wells for the 50-year 

analysis was about 58.8 ft3/s (table 4). This rate is about 9 

percent smaller than the sum of the maximum withdrawal 

rates for managed wells, which is about 64.9 ft3/s. Of the 

58.8 ft3/s total managed withdrawals, 39.4 ft3/s was associated with wells that were included in the 2004–2009 simulation and were converted to be represented as managed wells. 

The remaining 19.4 ft3/s was associated with wells that were 

newly constructed or otherwise not included in the 2004–2009 

simulation. The rate of pumping from the Arapahoe aquifer as 

a whole for this analysis was 101.4 ft3/s (table 4).

The 2059 potentiometric surfaces for the upper and lower 

Arapahoe aquifers, as simulated using the withdrawal rates 

from the 50-year optimization analysis, are shown in figure 9. 

The difference in altitude between the simulated 2059 layer-8 

potentiometric surface and the top of the Arapahoe aquifer 

is shown in figure 10. Areas where the 2059 potentiometric 

surface is below the top of the Arapahoe aquifer (unconfined 

conditions) are shaded in figure 10. The combined 2059 

saturated thickness of the upper and lower Arapahoe aquifers 

is shown in figure 11. Figures 12–14 (orange curves) show 

simulated hydrographs for layer-8 cells at three managed-flow 

cell locations selected as being representative of a range of 

simulated conditions. The hydrographs illustrate that the optimization results in heads being limited by the head constraints 

at cell (8, 63, 18) (fig. 12). At cells (8, 73, 20) (fig. 13) and 

(8, 64, 24) (fig. 14), the head constraints are not limiting and 

do not affect the optimization outcome. However, the simulated head at cell (8, 64, 24) at the end of the 50-year analysis 

is only 13 ft above the head constraint (table 3).

Analysis 2: Optimization of Pumping for 

Managed Withdrawals Over 100-Year Period

Analysis 2 was designed to provide insight into the 

question “How much would the total withdrawal rate need 

to be reduced to extend the time before the hydraulic-head 

constraints are violated from 50 to 100 years, given the same 

constraints as in Analysis 1?” Analysis 2 used the same set 

of 96 decision variables as in Analysis 1, and the maximum 

withdrawal rate for each decision variable was the same as 

in Analysis 1. The only differences between Analysis 1 and 

Analysis 2 were the simulation duration and the simulation 

time at which the head constraints applied. In Analysis 2 the 

head constraints applied at the end of the 100-year (2010 

through 2109) simulation rather than at the end of the 50-year 

simulation.

Table 4. Pumping rates for managed and unmanaged wells, by 

model package used to simulate the wells. 

[ft3/s, cubic feet per second; GWM, Groundwater Management Process; 

MNW, Multi-Node Well Package]

Managed or

unmanaged

Package 

or process

Pumping rate for indicated simulation

(ft3/s)

2004–2009

Nonoptimized

2010–2109

Analysis 1

2010–2059

Analysis 2

2010–2109

Managed GWM1 0.0 264.9 58.8 53.0

Unmanaged Well3 43.4 37.7 37.7 37.7

Unmanaged MNW4 4.9 4.9 4.9 4.9

Total 48.3 5107.5 101.4 95.6

1

Ahlfeld and others (2009).

2

Initial pumping rate. Because four managed-flow cells were deactivated 

during the simulation, the total pumping rate for managed wells was 54.9 ft3/s 

at the end of the simulation.

3

Harbaugh (2005) for wells completed in a single aquifer.

4

Halford and Hanson (2002) for wells completed in multiple aquifers.

5

Initial total pumping rate. Because four managed-flow cells were 

deactivated during the simulation, the total pumping rate was 97.5 ft3/s at the 

end of the simulation.
22 Demonstration Optimization Analyses of Pumping from Selected Arapahoe Aquifer Municipal Wells

Figure 9. Simulated 2059 potentiometric (hydraulic head) surfaces for upper and lower Arapahoe aquifers.

Base from U.S. Geological Survey digital data, 2009, 1:100,000

Colorado State Plane Central

Lambert Conformal Conic projection

Standard parallels 38°27' N and 37°45' N, central meridian -105°

CONTOUR INTERVAL 100 FEET

NORTH AMERICAN VERTICAL DATUM OF 1988 

EXPLANATION

6

6

4 8 MILES

0 4

2

2 8 KILOMETERS

0

Layer 8 line of equal

 hydraulic head

Upper Arapahoe aquifer

LowerArapahoe aquifer

Arapahoe confining unit

Layer 10 line of equal

 hydraulic head

Denver Basin study area

 boundary

Selected model cell showing

 (row, column) indices

Area of interest

Note: In southern part of study area, closely

spaced contours merge and cannot be

resolved in areas where the potentiometric

surface is depressed in the vicinity of

pumping wells. 

5,200

5,200

105°00' 104°45' 104°30'

39°45'

39°30'

39°15'

6,300

(73, 20)

(64, 24)

(64, 24)

(63, 18)

5,200

5,100

5,100

5,200

5,300

5,400

5,500

5,000

4,900

4,800

5,300

5,200

4,900

4,800

5,100

5,100

5,400

5,500

5,300

5,400

5,600

5,700

5,800

5,900

5,900

5,800

5,700

5,500

5,500

5,300

4,8004,900

4,900

5,200

5,100

5,100

5,000

4,900

4,800

4,700

4,700

4,700

4,600

5,000

5,400

5,600

6,000

6,000

6,200

6,200

6,500

6,600

6,800

6,900

6,800

6,700

6,700

6,300

6,400

6,0005,900

5,500

4,800

4,600

4,600

ADAMS

ADAMS

DENVER

ARAPAHOE

DOUGLAS

ELBERT

6,100

5,300

5,200
Demonstration of Optimization Analyses of Pumping from Municipal Wells 23

Figure 10. Height of layer 8 simulated 2059 potentiometric (hydraulic head) surface relative to top of Arapahoe aquifer.

Base from U.S. Geological Survey digital data, 2009, 1:100,000

Colorado State Plane Central

Lambert Conformal Conic projection

Standard parallels 38°27' N and 37°45' N, central meridian -105°

CONTOUR INTERVAL 100 FEET

NORTH AMERICAN VERTICAL DATUM OF 1988 

EXPLANATION

6

6

4 8 MILES

0 4

2

2 8 KILOMETERS

0

Area where Arapahoe

 aquifer is simulated as

 unconfined in 2059

Upper Arapahoe aquifer

LowerArapahoe aquifer

Arapahoe confining unit

Line of equal height relative

 to top of Arapahoe aquifer

Denver Basin study area

 boundary

Area of interest

300

Selected model cell showing

 (row, column) indices (64, 24)

105°00' 104°45' 104°30'

39°45'

39°30'

39°15'

200 100

100

100

100

100

100

100

100

100

200

300

300

300

300

400

400

400

200

200

200

200

200

200

300

400

500

400

600

800

700

900

900

900

700

800

600

500

300

300

200

0

0

0

0

0

0

0

,

700

300

800

400

400

1,000

0

0

0

1,200

ADAMS

ADAMS

DENVER

ARAPAHOE

DOUGLAS

(73, 20) ELBERT

(64, 24)

(63, 18)

100

100

1,000

1,100

1,100

1,000 1,200

1,300

1,300

1,300

1,400

1,400

1,500

1,600

1,700

1,200 1,100
24 Demonstration Optimization Analyses of Pumping from Selected Arapahoe Aquifer Municipal Wells

Figure 11. Combined 2059 saturated thickness of upper and lower Arapahoe aquifers.

Base from U.S. Geological Survey digital data, 2009, 1:100,000

Colorado State Plane Central

Lambert Conformal Conic projection

Standard parallels 38°27' N and 37°45' N, central meridian -105°

CONTOUR INTERVAL 50 FEET

NORTH AMERICAN VERTICAL DATUM OF 1988 

EXPLANATION

6

6

4 8 MILES

0 4

2

2 8 KILOMETERS

0

Upper Arapahoe aquifer

LowerArapahoe aquifer

Arapahoe confining unit

Line of equal saturated

 thickness

Denver Basin study area

 boundary

Area of interest

300

Selected model cell showing

 (row, column) indices (64, 24)

105°00' 104°45' 104°30'

39°45'

39°30'

39°15'

400

200

400

200

200

350

350

350

350

350

350

350

350

350

350

350

350

300

300

450

450

450

350

350

300

450

450

500

500

500

500

500

550

550

500

500 500

500

500

550

500

550

600

500

450

450

450

450

400

400

450

450

450

450

450

400

400

400

350

350

350

350

350

300

250

250

300

450

400

500

550

550

550

400

400

400400

500

350

300

300

250

250

250

250

200

200

300

300

400

400

400

400

400

450

500

400

500

400

450

450

450

350

350

350

350

250

300

300

250

200

400

400

300

300

300

250

250

250

200

150

150 200

300

350

400

450

100

50

550

400

500

400

500

350

500

550

ADAMS

ADAMS

DENVER

ARAPAHOE

DOUGLAS

(73, 20) ELBERT

(64, 24) (63, 18)

450

500

500

350

300 500

250

400

400 450

500

400

50

400

300

400
Demonstration of Optimization Analyses of Pumping from Municipal Wells 25

Figure 12. Simulated hydrographs and head constraint for cell (8, 63, 18; layer, row, column) for optimization analyses and for model 

results using non-optimized pumping rates.

4,400

4,500

4,600

4,700

4,800

4,900

5,000

5,100

5,200

Altitude, in feet, North American Vertical Datum of 1988

2010 2020

EXPLANATION

cell bottom (4,478.1 feet)

cell top (4,759.6 feet)

head constraint (4,703.3 feet)

2030 2040 2050 2060 2070 2080 2090 2100 2110

Simulated hydraulic head

Non-optimized simulation

50-year analysis

100-year analysis

Year

In this analysis the optimal solution was obtained when 

73 of the 96 decision variables were assigned (by GWM) at 

their maximum withdrawal rates and 2 of the decision variables were assigned (by GWM) a withdrawal rate of zero. 

The other 21 decision variables had nonzero values less than 

their maximum rates. No constraints were violated. The 

optimized withdrawal rates for managed wells are listed in 

table 2. The total optimized withdrawal rate for managed 

wells for the 100-year analysis was about 53.0 ft3/s. This 

withdrawal rate represents a reduction in the optimized withdrawal rate from managed wells of about 10 percent, relative 

to the Analysis 1 result. The total optimized withdrawal rate 

from managed wells is about 18 percent smaller than the 

sum of the maximum withdrawal rates for managed wells. 

Of the 53.0 ft3/s total managed withdrawals, about 35.3 ft3/s 

was associated with wells that were included in the 2004–2009 

simulation and were converted to be represented as managed 

wells. The remaining 17.7 ft3/s was associated with wells 

that were newly constructed or otherwise not included in 

the 2004–2009 simulation. The rate of pumping from the 

Arapahoe aquifer as a whole for this analysis was 95.6 ft3/s 

(table 4).

The 2109 potentiometric surfaces for the upper and lower 

Arapahoe aquifers, as simulated using the withdrawal rates 

from the 100-year optimization analysis, are shown in figure 15. The difference in altitude between the simulated 2109 

potentiometric surface and the top of the Arapahoe aquifer is 

shown in figure 16. The area where the 2109 potentiometric 

surface is below the top of the Arapahoe aquifer (unconfined 

conditions, shaded in fig. 16) is somewhat larger than for 

Analysis 1 (fig. 10). Even so, this area is mainly limited to the 

vicinity of the municipal wells. The combined 2109 saturated 

thickness of the upper and lower Arapahoe aquifers is shown 

in figure 17. In general, the maps showing the results of the 

100-year analysis (figs. 15–17) are substantially similar to 

those showing the results of the 50-year analysis (figs. 9–11). 

The similarity results from the similarity in design of the two 

analyses, which used identical decision-variable and head 

constraints. Figures 12–14 show simulated hydrographs for 

layer-8 cells at selected managed-flow cell locations. The 

hydrographs illustrate that the optimization solution results in 

heads being limited by the head constraints at cells (8, 63, 18) 

(fig. 12) and (8, 64, 24) (fig. 14) but not at cell (8, 73, 20) 

(fig. 13).
26 Demonstration Optimization Analyses of Pumping from Selected Arapahoe Aquifer Municipal Wells

4,500

4,600

4,800

5,000

5,100

5,200

5,400

5,500

5,700

Altitude, in feet, North American Vertical Datum of 1988

2010 2020

EXPLANATION

cell bottom (4,553.0 feet)

cell top (4,803.9 feet)

head constraint (4,753.7 feet)

2030 2040 2050 2060 2070 2080 2090 2100 2110

4,700

4,900

5,300

5,600 Simulated hydraulic head

Non-optimized simulation

50-year analysis

100-year analysis

Year

Comparison with Non-Optimized Simulation

Hydrographs for the non-optimized simulation are plotted 

in gray along with hydrographs generated by the optimization 

analyses in figures 12–14. The differences among the hydrographs vary depending on location of the cell of interest. 

The differences between the hydrograph for the nonoptimized simulation and the hydrographs for the optimized 

simulations are dramatic at cell (8, 63, 18) (fig. 12). For the 

non-optimized simulation, the head in this cell violates the 

head constraint in 2022, and the cell is deactivated at the first 

time step in 2100. Optimizing the pumping prevents simulated heads at this cell (and other cells at managed-flow and 

head-constraint locations) from violating head constraints and, 

therefore, prevents cell deactivation.

At first glance the benefit of optimization is not obvious 

at cell (8, 73, 20) (fig. 13). The hydrograph for the nonoptimized simulation is just below the hydrograph generated 

by the 50-year optimization analysis until 2056, at which point 

the hydrograph for the non-optimized simulation rises a few 

feet before declining again and closely following the hydrograph generated by the 100-year optimization analysis. This 

apparent anomaly is an artifact, however, resulting from the 

deactivation of managed-flow cells and the resulting elimination of pumping associated with those cells.

At cell (8, 64, 24) the hydrograph generated by the nonoptimized simulation again is slightly below the hydrograph 

for the 50-year optimization analysis. The benefit of optimization becomes apparent when the non-optimized hydrograph is 

compared with the hydrograph for the 100-year optimization 

analysis. In the non-optimized simulation, the head in cell (8, 

64, 24) violates the head constraint (4,532.4 ft) in 2066 and 

declines to 4,428.8 ft at the end of the simulation, more than 

100 ft below the head constraint. In the 100-year optimization 

analysis, in contrast, the head constraint is not violated.

Effects of Managed-Flows Pumping

As described in the section titled “Application of Optimization Analysis to Arapahoe Aquifer Pumping,” the total 

2004–2009 simulated withdrawal rate for Arapahoe aquifer 

wells was 48.3 ft3/s, and for both optimization analyses, 

pumping from unmanaged wells was 42.6 ft3/s (table 4). For 

Figure 13. Simulated hydrographs and head constraint for cell (8, 73, 20; layer, row, column) for optimization analyses and for model 

results using non-optimized pumping rates.
Demonstration of Optimization Analyses of Pumping from Municipal Wells 27

4,300

4,400

4,500

4,700

4,800

4,900

5,100

5,200

5,300

Altitude, in feet, North American Vertical Datum of 1988

2010 2020

EXPLANATION

cell bottom (4,335.5 feet)

cell top (4,581.6 feet)

head constraint (4,532.4 feet)

2030 2040 2050 2060 2070 2080 2090 2100 2110

4,600

5,000

Simulated hydraulic head

Non-optimized simulation

50-year analysis

100-year analysis

Year

Figure 14. Simulated hydrographs and head constraint for cell (8, 64, 24; layer, row, column) for optimization analyses and for model 

results using non-optimized pumping rates.

Analysis 1, optimized pumping from managed wells was 58.8 

ft3/s, and the total of pumping from unmanaged and managed wells was 101.4 ft3

/s (table 4). For Analysis 2, optimized 

pumping from managed wells was 53.0 ft3/s (table 2), and the 

total was 95.6 ft3/s (table 4). In comparison to the 2004–2009 

rate of 48.3 ft3/s, these total well-pumping rates for the optimization analyses represent a substantial increase in pumping. 

This section describes the simulated effects of the increased 

pumping.

Water-budget analyses using the program Zonebudget 

(Harbaugh, 1990) illustrate the effects of the managed-flows 

pumping rate simulated in Analysis 1. For the Zonebudget 

analyses, the model domain was divided into three zones: 

model layers (1–7) representing units that overlie the Arapahoe aquifer, model layers (8–10) representing the Arapahoe 

aquifer and the Arapahoe confining unit, and model layers 

(11–12) representing units that underlie the Arapahoe aquifer (table 1). Figure 18 illustrates selected components of 

the volumetric budget for all time steps of the 2004–2009 

simulation and the 2010–2059 Analysis 1 simulation, using 

optimized flow values for the managed wells. Components 

not shown account for less than 1 percent of the volumetric 

budget. The horizontal axis represents time, in years, relative 

to January 1, 2010, the beginning of the Analysis 1 simulation 

time. In figure 18 flow rates for the 2004–2009 simulation plot 

to the left of zero, and flow rates for the 2010–2059 simulation 

plot to the right of zero.

The “managed withdrawals” line of figure 18 represents 

the total flow rate for all managed flows, as optimized in 

the 50-year analysis. The “unmanaged withdrawals” curve 

represents well pumping simulated using the Well Package. 

The other curves shown in figure 18 illustrate the response 

of selected other water-budget components to the optimized 

managed-flows pumping. The “storage in” curve represents 

water released from confined and unconfined storage in the 

Arapahoe aquifer and Arapahoe confining unit. The “from 

overlying units” curve of figure 18 represents flow into the 

Arapahoe aquifer across its upper boundary; the values are a 

combination of all sources of water in those units, including 

removal of water from storage, induced recharge, and capture 

of discharge. Similarly, the “from underlying units” curve 

represents flow into the Arapahoe aquifer across its lower 

boundary. The “to overlying units” curve represents flow out 

of the Arapahoe aquifer across its upper boundary.
28 Demonstration Optimization Analyses of Pumping from Selected Arapahoe Aquifer Municipal Wells

Figure 15. Simulated 2109 potentiometric (hydraulic head) surfaces for upper and lower Arapahoe aquifers.

Base from U.S. Geological Survey digital data, 2009, 1:100,000

Colorado State Plane Central

Lambert Conformal Conic projection

Standard parallels 38°27' N and 37°45' N, central meridian -105°

CONTOUR INTERVAL 100 FEET

NORTH AMERICAN VERTICAL DATUM OF 1988 

EXPLANATION

6

6

4 8 MILES

0 4

2

2 8 KILOMETERS

0

Line of equal hydraulic head

 in upper Arapahoe aquifer

Upper Arapahoe aquifer

LowerArapahoe aquifer

Arapahoe confining unit

Line of equal hydraulic head

 in lower Arapahoe aquifer

Denver Basin study area

 boundary

Area of interest

5,200

5,200

Selected model cell showing

 (row, column) indices (64, 24)

105°00' 104°45' 104°30'

39°45'

39°30'

39°15'

,

5,200

4,900

5,000

5,100

5,200

5,300

5,400

4,800

5,300

5,100

5,200

5,000

5,300

5,400

5,500

5,600

5,700

5,900

5,900

5,800

5,800

ADAMS

ADAMS

DENVER

ARAPAHOE

DOUGLAS

ELBERT (73, 20)

(63, 18)

5,100

4,800

4,700

4,900

5,000

5,100

4,900

4,600

4,600

4,700

4,800

4,900

4,800

4,900

5,100

5,200

5,000

5,500

5,400

5,400

5,300

5,200

5,100

5,300

5,300

5,400

5,500

5,600

5,700

5,700

5,800

6,000 6,100

6,200

6,400

6,600

6,300

6,500

5,900

(64, 24)

4,600

5,200

4,900

6,0006,100

6,200

6,300

6,400

6,600

6,700

6,700

6,700

6,700

6,800 6,800

6,900

6,500
Demonstration of Optimization Analyses of Pumping from Municipal Wells 29

Figure 16. Height of layer 8 simulated 2109 potentiometric (hydraulic head) surface relative to top of Arapahoe aquifer.

Base from U.S. Geological Survey digital data, 2009, 1:100,000

Colorado State Plane Central

Lambert Conformal Conic projection

Standard parallels 38°27' N and 37°45' N, central meridian -105°

CONTOUR INTERVAL 100 FEET

NORTH AMERICAN VERTICAL DATUM OF 1988 

EXPLANATION

6

6

4 8 MILES

0 4

2

2 8 KILOMETERS

0

Area where Arapahoe

 aquifer is simulated as

 unconfined in 2059

Upper Arapahoe aquifer

LowerArapahoe aquifer

Arapahoe confining unit

Line of equal height relative

 to top of Arapahoe aquifer

Denver Basin study area

 boundary

Area of interest

300

Selected model cell showing

 (row, column) indices (64, 24)

105°00' 104°45' 104°30'

39°45'

39°30'

39°15'

300

300

400

400

200

100

100

100

100

100

100

100

200

300

400

500

700

700

700

600

600

700

800

900

800

900

800

900

900 800

600

400

500

500

300

200

200

200

0

0

0

0

0

0

0

0

0

300

1,000

0

0

400 ADAMS

ADAMS

DENVER

ARAPAHOE

DOUGLAS

ELBERT (73, 20)

(64, 24)

(63, 18)

200

200

300

300

200

100

200

200

400

300

100

1,000

1,000

1,100

1,200

1,300

1,400

1,200

1,300

1,400

1,500

1,600

1,500

1,100
30 Demonstration Optimization Analyses of Pumping from Selected Arapahoe Aquifer Municipal Wells

Figure 17. Combined 2109 saturated thickness of upper and lower Arapahoe aquifers.

Base from U.S. Geological Survey digital data, 2009, 1:100,000

Colorado State Plane Central

Lambert Conformal Conic projection

Standard parallels 38°27' N and 37°45' N, central meridian -105°

CONTOUR INTERVAL 50 FEET

NORTH AMERICAN VERTICAL DATUM OF 1988 

EXPLANATION

6

6

4 8 MILES

0 4

2

2 8 KILOMETERS

0

Upper Arapahoe aquifer

LowerArapahoe aquifer

Arapahoe confining unit

Line of equal saturated

 thickness

Denver Basin study area

 boundary

Area of interest

300

Selected model cell showing

 (row, column) indices (64, 24)

105°00' 104°45' 104°30'

39°45'

39°30'

39°15'

250

300

300

350

350

400

400

400

450

450

450

500

400

350

350

350

350

400

400

400

400

400

500

400

350

300

450

350

350

350

350

400

450

400

400

450

500

500 450

350

350

350

350

350

400

350

330

450

550

450

500

500

550

550

450

250

400

350

300

450

500

550

550

500 500

500

450

450

400

450

450

450

550

500

500

500

600

400

450

450

250

200

400

500

400

500

400

500

550

400

400

350 400

ADAMS

ADAMS

DENVER

ARAPAHOE

DOUGLAS

(73, 20) ELBERT

(64, 24) (63, 18)

400

300

300

300

400

400

400

250

300

350

350

400

350

200
Demonstration of Optimization Analyses of Pumping from Municipal Wells 31

The “managed withdrawals” line of figure 18 has a value 

of zero during 2004–2009 and increases to 58.8 ft3/s in 2010. 

The “unmanaged withdrawals” curve, as described above, 

decreases from 43.4 ft3/s during 2004–2009 to 37.7 ft3/s in 

2010. The difference, 5.7 ft3/s, supplies a small part of the 

managed-flows rate. In the first time step after time zero, the 

“storage in” curve increases from 3.3 ft3/s to 41.2 ft3/s; this 

change in flow from storage is associated with a rapid initial 

decline in hydraulic heads in the Arapahoe aquifer in response 

to the onset of managed-flow withdrawals. The rate of release 

from storage in layers 8–10 decreases rapidly after the first 

time step, however, and by 4.9 years into the Analysis 1 

simulation period, the rate of release from storage is 6.5 ft3/s. 

This decline in the rate of release from storage is indicative 

of a change in the source of water for managed flows from 

storage to other sources of water, primarily flow from adjacent units. Flow from overlying units increases from 66.3 ft3

/s 

at the beginning of the Analysis 1 simulation to 111.8 ft3/s 

at 4.9 years. Other budget components are affected by the 

managed-flows pumping, but much less substantially. 

The large increase of flow from units overlying the 

Arapahoe aquifer resulting from managed-flows pumping is 

indicative of substantial changes in hydrologic conditions in 

overlying units resulting from the increase in withdrawals 

from the Arapahoe aquifer. The most significant change is the 

effect on hydraulic heads in the Denver aquifer (model layer 

6), which is attributed, in part, to the thinness of the confining 

bed separating the Denver and Arapahoe aquifers, especially 

on the west side of the basin (Paschke and others, 2011a). 

Results for the calibration period of the groundwater-flow 

Figure 18. Simulated flow rates for selected Arapahoe aquifer (model layers 8–10) water-budget components, showing (2004–2009) 

antecedent rates (indicated by simulation times less than zero) and (2010–2059) responses to managed flows of Analysis 1.

0

20

40

60

80

100

120

Flow rate, in cubic feet per second

-5 0

EXPLANATION

5 10 15 20 25 30 35 40 45 50

Managed withdrawals

Storage in

Unmanaged withdrawals

From overlying units

From underlying units

To overlying units

Simulation time, in years
32 Demonstration Optimization Analyses of Pumping from Selected Arapahoe Aquifer Municipal Wells

model (1880–2003) and predictive simulations indicate 

substantial simulated vertical connection between these layers and downward flow induced by the increase in pumping 

in the Arapahoe aquifers (Paschke and others, 2011b). For 

comparison purposes, a model run was set up to simulate 

aquifer response to stresses that were used in the 2004–2009 

simulation but extended through 2109 with the stress-period 

and time-step lengths matching those of the Analysis 1 and 

Analysis 2 runs; this simulation had no managed-flows pumping. Figure 19 is a hydrograph for the cell in model layer 6 

(Denver aquifer), row 63, column 18. Cell (6, 63, 18) is in an 

area of substantial drawdown in the Arapahoe aquifer resulting from the managed-flows pumping (figs. 8–11 and 15–17). 

The top curve in figure 19, for the simulation without managed-flows pumping (using 2004–2009 stresses), shows the 

calculated head in the Denver aquifer at this location declining 

during the 106-year simulation from an initial value of 5,368 

ft to 4,998 ft in 2109, which is 215 ft above the cell bottom 

at 4,783 ft. The other two curves are for the Analysis 1 and 

Analysis 2 simulations. In the Analysis 2 simulation, this cell 

in model layer 6 is converted to inactive as the calculated head 

approaches the cell bottom.

Figure 18 also indicates that the response of volumetricbudget components to managed-flows pumping changes over 

time. Another Zonebudget (Harbaugh, 1990) analysis was performed using the results of the simulation without managedflows pumping for comparison with the Analysis 1 results. 

Differences between the two simulations in the flow rates for 

selected budget components for all time steps are shown in 

figure 20. Components not shown account for less than 1 percent of the managed flows. The differences show the extent 

to which each selected budget component contributes to the 

managed-flows pumping. Three pie charts (fig. 20) illustrate 

how these differences change over time. Figure 20A is for 

64 days, figure 20B for 4.9 years, and figure 20C for 50 years 

after managed-flows pumping begins. As the sequence of 

charts in figure 20 shows, most of the managed-flows pumping initially comes from release of water from storage in the 

Arapahoe aquifer. However, the primary source of water 

rapidly shifts, so that by 4.9 years after the start of managedflows pumping and through the rest of the simulation, most 

of the water comes from increased flow from overlying 

hydrogeologic units, primarily layer 6, which represents the 

Denver aquifer. 

Figure 19. Simulated hydrographs for cell in layer 6, row 63, column 18.

4,700

4,800

4,900

5,000

5,100

5,200

5,400

5,500

5,200

Altitude, in feet, North American Vertical Datum of 1988

2004

EXPLANATION

Top of Denver aquifer

Bottom of Denver aquifer

 2024 2044 2064 2084 2104

5,300

Simulated hydraulic head

Head, constant stresses of 2004–2009,

 without managed flows

Head, 50-year optimization analysis

Head, 100-year optimization analysis

Year
Demonstration of Optimization Analyses of Pumping from Municipal Wells 33

Figure 20. Sources of water for managed flows, relative to simulation without managed flows, at A, 64 days; B, 4.9 years; and C, end of 

50-year optimization-analysis simulation. Data are flow rates, in cubic feet per second, based on Zonebudget (Harbaugh, 1990) analyses 

of Arapahoe aquifer (model layers 8–10). Sources not shown supply less than 1 percent of combined managed flows.

EXPLANATION

Conversion of pumping from unmanaged

 to managed

Released from storage in Arapahoe aquifer

Increased flow from overlying units

Increased flow from underlying units

Decreased flow from overlying units

Decreased flow from underlying units

5.72

percent

37.84 percent

14.39 percent 

0.17 percent 0.09 percent 0.50 percent

1.32 percent

2.63 percent

1.62 percent

0.60 percent

A. 64 days after start of 50-year optimization-analysis simulation

B. 4.9 years after start of 50-year optimization-analysis simulation

C. End of 50-year optimization-analysis simulation

44.86 percent

42.91 percent

5.72

percent

5.72

percent

3.69

percent

3.69

percent

0.34 percent

0.56 percent
34 Demonstration Optimization Analyses of Pumping from Selected Arapahoe Aquifer Municipal Wells

Limitations

As with any modeling analysis, appropriate interpretation 

and use of analysis results necessarily are limited by practical 

considerations. It is important for readers to recognize these 

limitations and resist the temptation to over-interpret simulation and optimization results. This section describes some of 

those considerations.

The groundwater-flow simulations on which the optimization analyses rely are based on assumptions regarding future 

stresses on the aquifer system. The accuracy of the simulations 

also are limited by the degree to which the groundwater-flow 

model approximates the physical aquifer system. Banta and 

others (2011) present a pertinent discussion of model uncertainty and limitations. Simulation results and optimizationanalysis results are not intended to be interpreted as absolute 

predictions of future conditions. These results are intended to 

be most informative in the context of comparison of starting 

and final aquifer conditions and of comparison between results 

of the two optimization analyses. 

The head constraints as implemented in the optimization 

analyses are surrogates for field conditions of concern in the 

operation of municipal water wells. In particular, the optimization analyses use model-calculated hydraulic head in 1-mile 

by 1-mile model grid cells instead of the water level in a 

pumping well, which would be more appropriate from an 

operational standpoint. The head to which the simulated head 

is compared, either the altitude of 90-percent saturated thickness of the Arapahoe aquifer or the altitude of 90-percent 

saturated thickness of the upper or lower Arapahoe aquifer, 

was selected in recognition that the head in a pumping well 

would be substantially lower than the average head in a onesquare-mile area of aquifer. A more rigorous approach would 

be to use an analytical tool, possibly the Multi-Node Well 

(MNW2) Package (Konikow and others, 2009), to simulate 

heads in pumping wells and to use pump-intake altitudes as 

head constraints, but such a high-resolution approach was 

beyond the scope of the current project. Given the approach 

that was used, it is recognized that the maps and hydrographs 

based on simulated head and presented in this report represent 

only a coarse resolution of possible future conditions that 

could be expected to result from the long-term average pumping rates that are described. For example, apparent uniformity 

of the large shaded area in figure 16 where head is below the 

top of the Arapahoe aquifer but where saturated thickness is 

at least 90 percent of the aquifer thickness (indicated by nonviolation of the head constraints) is an artifact generated by the 

coarseness of the grid cells relative to the scale of drawdown 

effects in the vicinity of a pumping well. Although it may be 

possible to obtain such a saturated-thickness distribution by 

distributing the simulated pumping much more evenly, for 

example by installing a large number of wells in each squaremile cell and pumping each at a small fraction of the total 

pumping rate indicated for the cell, for practical purposes this 

distribution needs to be interpreted as a spatial and temporal 

generalization. Actual field conditions would be much less 

uniform. 

The discretization of the model domain into rows and 

columns is insufficiently refined to allow withdrawals from 

municipal wells to be resolved to a degree that would allow 

for reasonably accurate well-interference effects. In many 

instances, the area represented by a single model cell contains 

multiple municipal wells with interwell spacing that is far 

smaller than the 1-mile cell dimensions. Finer discretization 

could reduce this problem, but practical limitations related to 

model discretization (for example, computer memory requirement and execution time) likely would prevent elimination of 

the problem.

Model stress periods were of multiyear duration rather 

than some duration appropriate for day-by-day, month-bymonth, or season-by-season well operations. This temporal 

discretization of stresses prevents the model from predicting 

seasonal fluctuations of aquifer hydraulic heads and substantially limits the accuracy with which simulation results can be 

expected to represent actual field conditions.

The performance of wells completed in the bedrock 

aquifers of the Denver Basin under unconfined conditions 

has been a subject of debate among water providers, hydrologists, and engineers in Colorado. Of particular concern is the 

potential effect of numerous shale and mudstone intervals 

having relatively small permeability interlayered with more 

productive, higher permeability layers in the various aquifers, 

including the Arapahoe aquifer. Preliminary analyses (Mark 

Palumbo, HRS Water Consultants, Inc., written commun., 

2002) indicate that effects of such layering on water levels 

(increased drawdown) in, and in the immediate vicinity of, 

pumping wells may be substantial. The analyses described 

in this report do not consider layering in the aquifers and its 

effects on hydraulic heads in the vicinity of pumping wells. As 

aquifer conditions convert from confined to unconfined in the 

vicinity of pumping wells, water providers may find it necessary to install and produce from multiple wells to achieve 

production rates comparable to production rates attained under 

confined conditions.

Possible Additional Analyses

The analyses documented in this report demonstrate 

examples of possible formulations of optimization problems 

designed to address excessive loss of saturated thickness 

due to municipal pumping in the Arapahoe aquifer. These 

examples are only a small subset of the possible optimization 

approaches that could be used to analyze the costs, effects, and 

benefits of municipal pumping. This section presents a number 

of possibilities for additional optimization analyses.

Address Issue of Effects of Pumping in 

Arapahoe Aquifer on Denver Aquifer 

Results of the optimization analyses described in the 

section titled “Effects of managed-flows pumping” indicate 

that pumping from Arapahoe wells can produce substantial 
Summary and Conclusions 35

drawdowns in the Denver aquifer. The analyses described in 

this report did not include any mechanism for constraining 

the effects of Arapahoe withdrawals on the Denver aquifer. In 

a future analysis, it may be desirable to include a mechanism 

by which constraints on the effects on the Denver aquifer 

would be incorporated into the optimization scheme. One 

possible mechanism, currently supported by GWM (Ahfeld 

and others, 2009), would be to define drawdown constraints 

for selected cells representing locations in the Denver aquifer. 

Alternatively, a mechanism involving the use of Zonebudget 

(Harbaugh, 1990) and separate optimization software could be 

developed to implement a constraint on changes to flow from 

the Denver aquifer to the Arapahoe aquifer, compared to a 

base simulation. 

Refine Spatial and (or) Temporal Discretization

Accuracy of modeled effects of pumping could be 

improved by refining the spatial and (or) temporal discretization of the Denver Basin model. The Local Grid Refinement 

Package (Mehl and Hill, 2005, 2010) could be used to refine 

the model grid in the area of greatest interest to improve resolution of well-interference effects. 

More accurate simulation of pumping effects could be 

achieved by defining stress periods and corresponding well 

withdrawals on a seasonal or monthly basis. This would 

require a substantial effort to estimate seasonal or monthly 

pumping rates. It also would require similar revisions to at 

least part of the calibration period (1880–2003) of the Banta 

and others (2011) model and recalibration of that model. The 

benefit of refined spatial and temporal discretization would 

be that calculated hydraulic heads would enable the model to 

more closely approximate the conditions that limit the operation of wells.

Simulate and Place Constraints on Water Levels 

in Production Wells

The MNW2 Package (Konikow and others, 2009) can be 

used with MODFLOW-2005 to simulate water levels in pumping wells. Note that, despite the “multi-node” descriptor in the 

package name, the MNW2 Package also can be used to simulate a well connected to a single model cell with the benefit 

that water level in the well can be calculated. The version of 

GWM (Ahlfeld and others, 2005, 2009) used for the analyses 

described in this report does not support constraints on water 

levels in wells calculated by MNW2. To include this type of 

constraint in an optimization analysis would require the use 

of alternative optimization software or addition of support 

for MNW2-based head constraints in GWM. Appropriate use 

of the MNW2 Package also would require analyses and (or) 

calibration to establish settings and realistic coefficients that 

determine the head loss between a well and the model cell in 

which the well is located. As for the suggested refinement of 

spatial and temporal discretization, simulation of water levels 

in wells and basing constraints on those simulated water levels 

would enable the model and the optimization algorithm to 

more closely approximate the conditions that limit the operation of wells.

Include Infrastructure Costs in Optimization 

Analysis

Implementation of optimized pumping distributions, 

such as those described in this report, could involve construction of additional infrastructure, in which case municipalwater providers would incur substantial costs. Optimization 

software, including GWM, generally is designed to support 

analyses involving objective functions of various kinds. An 

objective function could be written in terms of financial costs, 

for example, rather than withdrawal rates. An analysis that 

considers construction, operation, and maintenance costs 

as well as hydrologic benefits and effects would be useful 

in a cost/benefit analysis related to potential infrastructure 

construction.

Summary and Conclusions 

Optimization analyses were performed to demonstrate 

approaches that might be used to address issues related to 

operation of municipal wells in an area of interest of the 

Arapahoe aquifer in the west-central part of the Denver Basin. 

The analyses used a previous conceptual model and groundwater-flow model of the Denver Basin. These analyses were 

designed as demonstrations only and were not intended as a 

comprehensive optimization study. For each analysis an optimization problem was set up to maximize a total withdrawal 

rate, subject to withdrawal-rate and hydraulic-head constraints. 

The head constraints were at the 90-percent saturated thickness altitude of the Arapahoe aquifer where it is undifferentiated. Where the Arapahoe aquifer is divided into upper and 

lower parts by a confining unit, head constraints were defined 

at the 90-percent saturated thickness altitudes of the upper and 

lower Arapahoe aquifers.

In Analysis 1 an optimal withdrawal distribution for 96 

flow-rate decision variables representing 119 wells was determined using a 50-year simulation period. The distribution was 

determined by setting up an optimization problem to maximize the sum of withdrawals for all decision variables, subject 

to a set of minimum head constraints at the end of the 50-year 

period. The optimized total withdrawal rate for all managed 

wells was 58.8 ft3/s.

Analysis 2 was similar to Analysis 1, except that the 

simulation time was 100 years instead of 50 years, and the 

head constraints applied at 100 years after the beginning of 

the analysis period, rather than at 50 years after the beginning 

of the analysis period. For this analysis, the optimized total 

withdrawal rate for all managed wells was 53.0 ft3/s. These 

results indicate that with optimal pumping distributions, the 
36 Demonstration Optimization Analyses of Pumping from Selected Arapahoe Aquifer Municipal Wells

time until violation of the 90-percent saturated-thickness constraints might be extended from 50 years to 100 years 

by a 10-percent decrease in total pumping rates of the managed wells. 

Analyses of the simulated groundwater volumetric budget 

show time-dependent effects on various budget components 

in response to managed-flows pumping. Initially, the pumping 

produces water primarily by release of water from storage in 

the Arapahoe aquifer. In less than 5 years, however, most of 

the water removed by managed-flows pumping likely would 

be supplied from overlying hydrogeologic units.

Comparison of Denver aquifer simulated heads generated from model runs with optimized pumping with heads 

generated from a run using pumping rates unchanged from 

the 2004–2009 simulation showed that the optimized pumping rates could result in an increase in the rate of decline of 

hydraulic heads in parts of the Denver aquifer because of 

the simulated hydraulic connection between the Denver and 

Arapahoe aquifers. Additional analyses would be needed to 

determine the extent to which Arapahoe aquifer pumping rates 

would need to be modified to limit drawdown effects in the 

Denver aquifer to acceptable amounts.

Acknowledgments

The authors extend thanks to Andy Moore (CWCB) and 

Brian Ahrens, Mary Halstead, and James Heath (CDWR) 

for suggestions related to the development of optimization 

scenarios and for assistance in database development. Thanks 

also are extended to the municipal water providers for providing data related to wells and historical water withdrawal rates, 

including: Arapahoe County Water and Wastewater Authority, 

Castle Pines Metropolitan District, Centennial Water and Sanitation District, City of Englewood, City of Littleton, Parker 

Water and Sanitation District, and Pinery Water and Wastewater District.

References Cited

Ahlfeld, D.P., Baker, K.M., and Barlow, P.M., 2009, 

GWM-2005—A groundwater-management process for 

MODFLOW-2005 with Local Grid Refinement (LGR) 

capability: U.S. Geological Survey Techniques and Methods, book 6, chap. A33, 65 p., available at http://water.usgs.

gov/nrp/gwsoftware/mf2005_gwm/MF2005-GWM.html.

Ahlfeld, D.P., Barlow, P.M., and Mulligan, A.E., 2005, 

GWM—A ground-water management process for the 

U.S. Geological Survey modular ground-water model 

(MODFLOW-2000): U.S. Geological Survey Open-File 

Report 2005–1072, 124 p., available at http://water.usgs.

gov/nrp/gwsoftware/mf2k-gwm/MF2K-GWM.html.

Ahlfeld, D.P., and Mulligan, A.E., 2000, Optimal management of flow in groundwater systems: San Diego, Academic 

Press, 185 p.

Banta, E.R., Paschke, S.S., and Litke, D.W., 2011, Groundwater flow simulations of the Denver Basin aquifer system, 

chap. C of Paschke, S.S., ed., Groundwater availability of 

the Denver Basin aquifer system, Colorado: U.S. Geological Survey Professional Paper 1770, p. 181–274.

Black & Veatch, Rick Giardina & Associates, Inc., HRS Water 

Consultants, Inc., Hydrosphere Resource Consultants, and 

Mulhern MRE, Inc., 2003, South metro water supply study 

executive summary: [Littleton, Colorado], South Metro 

Water Supply Study Board, 19 p., accessed March 18, 

2011 at http://www.colorado.edu/geography/geomorph/

envs_5810/South_Metro_Exec_Summary.pdf.

Colorado Division of Water Resources, 1985, Rules and 

regulations applying exclusively to the withdrawal of 

ground water from the Dawson, Denver, Arapahoe and 

Laramie–Fox Hills aquifers in the Denver Basin: Code of 

Colorado Regulations, 2 CCR 402–6, accessed Aug. 4, 

2011, at http://water.state.co.us/DWRDocs/Rules/Pages/

DenverBasinRules.aspx.

Colorado Division of Water Resources, 1986, Rules and 

regulations applying to well permits to withdraw ground 

water pursuant to section 37-90-137(4), C.R.S.: Code of 

Colorado Regulations, 2 CCR 402–7, accessed Aug. 4, 

2011, at http://water.state.co.us/DWRDOCS/RULES/Pages/

WellPermittingRules.aspx.

Colorado Division of Water Resources, 2009, Colorado’s 

WellView Web: http://www.dwr.state.co.us/WellViewWeb/, 

accessed September 14, 2009.

Halford, K.J., and Hanson, R.T., 2002, User guide for the 

drawdown-limited, Multi-Node Well (MNW) Package for 

the U.S. Geological Survey's modular three-dimensional 

finite-difference ground-water flow model, versions 

MODFLOW-96 and MODFLOW-2000: U.S. Geological 

Survey Open-File Report 02–293, 33 p., available at 

http://water.usgs.gov/nrp/gwsoftware/modflow2000/

MNW_text.pdf.

Harbaugh, A.W., 1990, A computer program for calculating 

subregional water budgets using results from the U.S. Geological Survey modular three-dimensional finite-difference 

ground-water model: U.S. Geological Survey Open-File 

Report 90–392, 46 p., available at http://water.usgs.gov/nrp/

gwsoftware/zonebud3/zonebudget3.html.

Harbaugh, A.W., 2005, MODFLOW-2005, the U.S. Geological Survey modular ground-water model—The groundwater flow process: U.S. Geological Survey Techniques

and Methods, book 6, chap. A16, variously paginated, 

available at http://pubs.usgs.gov/tm/2005/tm6A16/PDF/

TM6A16.pdf.
References Cited 37

Publishing support provided by

Denver and Lafayette Publishing Service Centers

Harbaugh, A.W., Banta, E.R., Hill, M.C., and McDonald, 

M.G., 2000, MODFLOW-2000, the U.S. Geological Survey 

modular ground-water model—User guide to modularization concepts and the ground-water flow process: U.S. 

Geological Survey Open-File Report 00–92, 121 p., available at http://water.usgs.gov/nrp/gwsoftware/modflow2000/

ofr00-92.pdf.

Hydrosphere Resource Consultants, Inc., HRS Water Consultants, Inc., Mulhern MRE, Inc., and Spronk Water 

Engineers, Inc., 1999, Metropolitan water supply investigation final report, report to the Colorado Water Conservation Board: Boulder, Colorado, Hydrosphere Resource 

Consultants, 207 p., accessed March 18, 2011, at 

http://www.hydrosphere.com/publications/metro_water/

MWSI_report.pdf.

Konikow, L.F., Hornberger, G.Z., Halford, K.J., and Hanson, 

R.T., 2009, Revised Multi-Node Well (MNW2) Package 

for MODFLOW ground-water flow model: U.S. Geological 

Survey Techniques and Methods, book 6, chap. A30, 67 p., 

available at http://pubs.usgs.gov/tm/tm6a30/.

Mehl, S.W., and Hill, M.C., 2005, MODFLOW-2005, the U.S. 

Geological Survey modular ground-water model—Documentation of shared node Local Grid Refinement (LGR) and 

the Boundary Flow and Head (BFH) Package: U.S. Geological Survey Techniques and Methods, book 6, chap. A12, 

68 p., available at http://pubs.usgs.gov/tm/2006/tm6a12/.

Mehl, S.W., and Hill, M.C., 2010, MODFLOW-LGR—Modifications to the Streamflow-Routing Package (SFR2) to 

route streamflow through locally refined grids: U.S. Geological Survey Techniques and Methods, book 6, chap. A34, 

15 p., available at http://water.usgs.gov/nrp/gwsoftware/

modflow2005_lgr/tm6a34.pdf.

Paschke, S.S., ed., 2011, Groundwater availability of the Denver Basin aquifer system, Colorado: U.S. Geological Survey 

Professional Paper 1770, 274 p.

Paschke, S.S., Banta, E.R., and Litke, D.W., 2011a, Effects 

of development on groundwater availability in the Denver 

Basin aquifer system, chap. B of Paschke, S.S., ed., Groundwater availability of the Denver Basin aquifer system, 

Colorado: U.S. Geological Survey Professional Paper 1770, 

p. 95–180.

Paschke, S.S., Banta, E.R., Webbers, Ank, and Capesius, J.P., 

2011b, Introduction, conceptual model, hydrogeologic 

framework, and predevelopment groundwater availability of 

the Denver Basin aquifer system, chap. A of Paschke, S.S., 

ed., Groundwater availability of the Denver Basin aquifer 

system, Colorado: U.S. Geological Survey Professional 

Paper 1770, p. 1–93.

Raynolds, R.G., 2002, Upper Cretaceous and Tertiary stratigraphy of the Denver Basin, Colorado: Rocky Mountain 

Geology, v. 37, no. 2, p. 111–134.

Robson, S.G., 1987, Bedrock aquifers in the Denver Basin, 

Colorado—A quantitative water-resources appraisal: U.S. 

Geological Survey Professional Paper 1257, 73 p., 5 plates 

in pocket.

Topper, Ralf, and Raynolds, Bob, 2007, Citizen’s guide to 

Denver Basin groundwater: Denver, Colorado Foundation 

for Water Education, 33 p., accessed March 18, 2011, at 

https://www.cfwe.org/index.php?option=com_content&view

=article&id=49:citizens-guide-to-denver-basin-groundwate

r&catid=61:groundwater&Itemid=107.
Banta and Paschke—Demonstration Optimization Analyses of Pumping from Selected Arapahoe Aquifer Municipal Wells—SIR 2012–5140