U.S. Department of the Interior

U.S. Geological Survey

Scientific Investigations Report 2010–5005

Prepared in cooperation with the Minnesota Department of Health

Evaluation of Methods for Delineating Zones of Transport 

for Production Wells in Karst and Fractured-Rock

Aquifers of Minnesota

Evaluation of Methods for Delineating 

Zones of Transport for Production Wells 

in Karst and Fractured-Rock Aquifers of 

Minnesota

By Perry M. Jones

Prepared in cooperation with the Minnesota Department of Health

Scientific Investigations Report 2010–5005

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: 2010

For more information on the USGS—the Federal source for science about the Earth, its natural and living resources, 

natural hazards, and the environment, visit http://www.usgs.gov or call 1-888-ASK-USGS

For an overview of USGS information products, including maps, imagery, and publications, 

visit http://www.usgs.gov/pubprod

To order this and other USGS information products, visit http://store.usgs.gov

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:

Jones, Perry M., 2010, Evaluation of methods for delineating zones of transport for production wells in karst and 

fractured-rock aquifers of Minnesota: U.S. Geological Survey Scientific Investigations Report 2010–5005, 32 p.
iii

Contents

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

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

Purpose and Scope...............................................................................................................................3

Acknowledgments.................................................................................................................................3

Methods of Investigation...............................................................................................................................4

Minnesota Department of Health Zone-of-Transport Delineation Methods for

Solution-Weathered and Fractured Bedrock Aquifers......................................................4

Empirical Zone-of-Transport Delineation Methods..........................................................................4

Truncated-Parabola Method.......................................................................................................4

Modified-Ellipse Method.............................................................................................................6

Differences Between Delineation Methods......................................................................................8

Physical Description of Aquifers and Study Communities in Minnesota..............................................8

Aquifers...................................................................................................................................................8

Communities.........................................................................................................................................11

Calumet.........................................................................................................................................11

Keewatin......................................................................................................................................11

Marble..........................................................................................................................................14

Taconite........................................................................................................................................14

Askov............................................................................................................................................14

Fridley...........................................................................................................................................18

Hastings........................................................................................................................................18

Le Center......................................................................................................................................18

Fulda..............................................................................................................................................22

Evaluation of Delineation Methods............................................................................................................22

Calumet..................................................................................................................................................24

Keewatin...............................................................................................................................................24

Marble...................................................................................................................................................25

Taconite.................................................................................................................................................25

Askov.....................................................................................................................................................26

Fridley....................................................................................................................................................26

Hastings.................................................................................................................................................26

Le Center...............................................................................................................................................26

Fulda.......................................................................................................................................................27

Implications of Zone-of-Transport Delineations......................................................................................27

Summary........................................................................................................................................................29

References Cited..........................................................................................................................................30
iv

Figures

1. Map of bedrock hydrogeology and communities for which zone-of-transport analyses

were applied to fractured or karst bedrock aquifers, Minnesota.........................................2

2. Schematic diagrams showing A, areas of potential recharge to a well and

examples of B, the truncated-parabola and C, modified-elipse methods............................5

3–11. Maps showing:

3. Zones of transport delineated using the truncated-parabola and

modified-ellipse methods and existing zone of transport delineated

by the Minnesota Department of Health (MDH) for production wells in

Calumet, Minnesota...........................................................................................................12

4. Zones of transport delineated using the truncated-parabola and

modified-ellipse methods and existing zone of transport delineated

by the Minnesota Department of Health (MDH) for production wells in

Keewatin, Minnesota.........................................................................................................13

5. Zones of transport delineated using the truncated-parabola and

modified-ellipse methods and existing zone of transport delineated

by the Minnesota Department of Health (MDH) for production wells in

Marble, Minnesota.............................................................................................................15

6. Zones of transport delineated using the truncated-parabola and

modified-ellipse methods and existing zone of transport delineated

by the Minnesota Department of Health (MDH) for production wells in

Taconite, Minnesota...........................................................................................................16

7. Zones of transport delineated using the truncated-parabola and

modified-ellipse methods and existing zone of transport delineated

by the Minnesota Department of Health (MDH) for production wells in

Askov, Minnesota...............................................................................................................17

8. Zones of transport delineated using the truncated-parabola and

modified-ellipse methods and existing zone of transport delineated

by the Minnesota Department of Health (MDH) for production wells in

Fridley, Minnesota..............................................................................................................19

9. Zones of transport delineated using the truncated-parabola and

modified-ellipse methods and existing zone of transport delineated

by the Minnesota Department of Health (MDH) for production wells in

Hastings, Minnesota..........................................................................................................20

10. Zones of transport delineated using the truncated-parabola and

modified-ellipse methods and existing zone of transport delineated

by the Minnesota Department of Health (MDH) for production wells in

Le Center, Minnesota.........................................................................................................21

11. Zones of transport delineated using the truncated-parabola and

modified-ellipse methods and existing zone of transport delineated

by the Minnesota Department of Health (MDH) for production wells

in Fulda, Minnesota............................................................................................................23
v

Tables

1. Hydraulic properties applied to the truncated-parabola and modified-ellipse

methods to delineate zones of transport for production wells open to karst

and fractured-rock aquifers, Minnesota...................................................................................7

2. Geologic units and general information on production wells in Minnesota

for which zones of transport were determined for karst or fractured-rock

aquifers by using empirical methods.........................................................................................9

3. X-axis coordinates for stagnation points, y-asymptotes, and water particle

travel distances for 10-year and 20-year zones of transport obtained using

the truncated-parabola method for production wells open to karst or

fractured-rock aquifers, Minnesota.........................................................................................22

4. X-axis coordinates, y-axis distances, and areas of ellipses for 10-year

and 20-year zones of transport obtained using the modified-ellipse method

for production wells open to karst or fractured-rock aquifers, Minnesota.......................24

5. Areas of empirical-method 10-year zones of transport within Minnesota

Department of Health (MDH) delineated 10-year zones of transport for

production wells open to karst or fractured-rock aquifers, Minnesota.............................25

Conversion Factors

Multiply By To obtain

Length

foot (ft) 0.3048 meter (m)

mile (mi) 1.609 kilometer (km)

Area

square foot (ft2) 0.09290 square meter (m2)

square mile (mi2) 2.590 square kilometer (km2) 

Volume

cubic foot (ft3) 0.02832 cubic meter (m3) 

Flow rate

foot per day (ft/d) 0.3048 meter per day (m/d)

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

Hydraulic conductivity

foot per day (ft/d) 0.3048 meter per day (m/d)

Hydraulic gradient

foot per mile (ft/mi) 0.1894 meter per kilometer (m/km)

Transmissivity*

foot squared per day (ft2/d) 0.09290 meter squared per day (m2/d) 

Horizontal coordinate information is referenced to North American Datum of 1983 (NAD 83).

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

*Transmissivity: The standard unit for transmissivity is cubic foot per day per square foot times

foot of aquifer thickness. [(ft3/d)/ft2]ft. In this report, the mathematically reduced form, foot

squared per day (ft2/d), is used for convenience.

Abstract

Assessment of groundwater-flow conditions in the 

vicinity of production wells in karst and fractured-rock settings commonly is difficult due in part to the lack of detailed 

hydrogeologic information and the resources needed to collect 

it. To address this concern and to better understand the hydrogeology and aquifer properties of karst and fractured-rock 

aquifers in Minnesota, the U.S. Geological Survey, in cooperation with the Minnesota Department of Health, conducted a 

study to evaluate methods for delineating zones of transport 

for 24 production wells in karst and fractured-rock aquifers 

in Minnesota. Two empirical methods for delineating zones 

of transport around wells were applied to the 24 production 

wells that extract groundwater from karst and fractured-rock 

aquifers in nine Minnesota communities. These methods were 

the truncated-parabola and modified-ellipse methods, and both 

methods assume porous-media flow conditions. The 24 wells 

extracted water from a karst aquifer (Prairie du Chien-Jordan 

aquifer), porous aquifers interspersed with solution-enhanced 

fractures (Jordan and Hinckley aquifers), or fractured-bedrock 

aquifers (Biwabik Iron-Formation and Sioux Quartzite aquifers). Zones of transport delineated using these two empirical 

methods were compared with zones of transport previously 

delineated by Minnesota Department of Health hydrologists 

for the wells using the calculated-fixed-radius method and 

groundwater-flow models. 

Large differences were seen in the size and shapes of 

most zones of transport delineated using the truncated-parabola and modified-ellipse methods compared with the zones of 

transport delineated by the Minnesota Department of Health. 

In general, the zones of transport delineated using the truncated-parabola and modified-ellipse methods were smaller in 

area than those delineated by the Minnesota Department 

of Health and included only small parts of the Minnesota 

Department of Health zones of transport. About two-thirds

(67 percent) of the individual or composite truncated parabolas 

and modified ellipses covered less than 50 percent of the area 

included in zones of transport delineated by the Minnesota 

Department of Health. The shapes of some of the truncated 

parabola and modified ellipses did not closely match the zones 

of transport delineated by the Minnesota Department of Health 

using the calculated-fixed-radius method and groundwaterflow models. Differences between the zones of transport 

delineated by the truncated-parabola and modified-ellipse 

methods and those delineated by the Minnesota Department of 

Health can be explained by variations inherent to the methods 

and by the amount of complexity taken into account by different groundwater-flow models. Additional field hydrogeologic 

studies would be needed at specific sites to support the use of 

these zone-of-transport delineation methods. Application of 

the truncated-parabola and modified-ellipse methods to sites 

for which existing hydrogeologic information is limited can 

produce questionable results in karst and fractured-rock settings, particularly in areas where many high-capacity wells or 

active mining operations are nearby.

Introduction

About 78 percent of Minnesotans use groundwater 

extracted from bedrock and glacial aquifers for their drinking water (Kenny and others, 2009). Approximately one-half 

of the 970 community water supply systems in Minnesota 

are potentially vulnerable to contamination mainly due to 

local hydrogeology and type of well construction (Minnesota 

Department of Health, 2009a).

Communities in northern, southeastern, and southwestern 

Minnesota use production wells to extract water from bedrock 

aquifers in which groundwater flows mainly through karst 

features (solution openings and solution channels or conduits) and fractures (fig. 1). Source waters for these wells are 

particularly vulnerable to contamination due to short residence 

times in the karst features and fracture zones. Groundwater 

flow to wells in these aquifers commonly is complex, occurring as regional flow along bedding planes and large fracture 

networks, as localized flow in discrete fractures near the wells, 

or as a combination of both. Temporal flow conditions in karst 

and fractured-rock aquifers commonly are difficult to characterize or predict. 

Evaluation of Methods for Delineating Zones of Transport 

for Production Wells in Karst and Fractured-Rock 

Aquifers of Minnesota

By Perry M. Jones
2 Evaluation of Methods for Delineating Zones of Transport for Production Wells in Karst snd Fractured-Rock Aquifers

Askov

Marble

Mesabi Iron Range

Calumet

Fridley

Keewatin

Taconite

Le Center

Fulda

Hastings

0 50 100 MILES

0 50 100 KILOMETERS

Base from Minnesota Geological Survey,

Digital data, NAD83,

Universal Transverse Mecator, Zone 15,

central meridian 93 ̊

Modified from Minnesota Geological Survey,

Hydrogeologic Map of Minnesota,

Bedrock Hydrogeology,

R. Kanivetsky, 1978

96°

94°

92°

90°

44°

46°

48°

Cretaceous aquifer

Cedar Valley-Maquoketa-

 Dubuque-Galena aquifer

Red River-Winnipeg aquifer

St. Peter aquifer

Prairie du Chien-Jordan 

 aquifer

Franconia-Ironton-Galesville

 aquifer

Mount Simon-Hinckley-Fond

 du Lac aquifer

Keweenawan volcanic-rock

 aquifer

Sioux Quartzite aquifer

Proterozoic aquifer

Biwabik Iron-Formation aquifer

Precambrian igneous and

 metamorphic rocks

EXPLANATION

Figure 1. Bedrock hydrogeology and communities for which zone-of-transport analyses were applied to fractured 

or karst bedrock aquifers, Minnesota.
Introduction 3

Communities in Minnesota and throughout the United 

States are being required to develop and implement wellhead 

protection plans that safeguard their water sources from 

contamination (Minnesota Department of Health, 2005a). 

The Minnesota Department of Health (MDH) is assisting Minnesota communities in delineating management (or 

protection) areas around production wells to protect groundwater sources for these supplies. Hydrologists from MDH 

are developing tools and techniques for determining zones 

of transport around production wells (Minnesota Department 

of Health, 2005b). A zone of transport is the volume of an 

aquifer supplying water to a discharging well within a specified period of time. Any sources of contamination within the 

zone of transport may eventually be captured by the production well. Thus, it is important for water-resources managers to 

minimize potential sources of contamination within the zone 

of transport.

Several approaches have been applied to delineate 

zones of transport around wells obtaining groundwater from 

karst and fractured-rock aquifers to account for flow through 

solution channels or fractures. Expensive and more detailed 

approaches to zone-of-transport delineation involve use of 

one or both of two approaches: (1) borehole geophysical and 

hydrologic techniques, and hydrogeologic mapping techniques 

to identify the physical and hydraulic properties of solution 

channels and fractures near production wells; and (2) groundwater-flow models to delineate zones of transport for the wells 

(Bair and Roadcap, 1992; Podgorney and Ritzi, 1997; Knochenmus and Robinson, 1996; Barton and others, 1999, 2003). 

The application of borehole geophysics and groundwater-flow 

models is too expensive and impractical for many Minnesota 

communities using groundwater from karst and fractured-rock 

aquifers. 

Communities with limited resources to expend on hydrogeologic studies commonly chose between either (1) making 

broad assumptions in the application of fracture-flow/dual-permeability equations and groundwater-flow models that cannot 

be validated by use of existing data or (2) applying hydrogeologic mapping techniques and porous media equations that use 

data that are more readily available. Typically, small communities use existing hydrogeologic data and empirical methods 

to delineate zones of transport (Delin and Almendinger, 1991; 

Bradbury and others, 1991). However, the accuracy of zones 

of transport delineated by using simple empirical methods may 

be questionable for complex karst and fractured-rock settings. 

The main assumption involved in using these less-expensive 

methods is that non-Darcian flow (that is conduit or fracture 

flow) conditions occur in only a small portion of the zone of 

transport (Long and others, 1982). Demonstration of this type 

of flow commonly requires conducting aquifer, water-quality, 

and other hydrogeologic testing. 

The lack of effective zone-of-transport delineation 

methods for wells completed in karst or fractured-rock aquifers may have a substantial effect on the ability of wellhead 

protection plans to effectively protect the water supplies. 

The MDH cannot approve wellhead protection area (WHPA) 

delineations that do not adequately address the delineation 

criteria specified under current State regulations (Minnesota 

Department of Health, 2005a). The MDH uses empirical 

methods, analytical element methods, numerical modeling 

methods, and dual-porosity methods, incorporating karst and 

fracture-rock flow features, to delineate zones of transport 

needed to determine wellhead protection areas around wells 

in karst and fractured-rock settings. Many of these methods 

assume Darcian flow conditions. Simple empirical methods 

proposed for delineating wellhead protection areas in karst 

and fractured-rock aquifers may not be technically defensible under the criteria if non-Darcian flow conditions govern 

groundwater flow in a large portion of the zone of transport. In 

addition, few cost-effective tools are available to assist communities in delineating WHPAs for wells completed in karst or 

fractured-rock aquifers. To address this concern and to better 

understand the hydrogeology and aquifer properties of karst 

and fractured-rock aquifers in Minnesota, the U.S. Geological Survey, in cooperation with the Minnesota Department of 

Health, conducted a study to apply and evaluate methods for 

delineating zones of transport for 24 production wells in karst 

and fractured-rock aquifers in Minnesota.

Purpose and Scope

This report presents the results from the application of 

two empirical methods for delineating zones of transport 

around 24 production wells in karst and fractured-rock aquifers in the vicinity of nine communities in Minnesota (fig. 1). 

The two empirical methods are the truncated-parabola and 

modified-ellipse methods, and both methods assume porousmedia flow conditions. Existing hydrologic data from MDH 

records and reports and other scientific literature were used 

to delineate the zones of transport. The MDH delineation 

methods and the empirical delineation methods are described 

in some detail in the “Methods of Investigation” section of 

this report. Zones of transport determined from application 

of these methods were compared with zones of transport that 

were from application of the calculated-fixed-radius method 

and groundwater-flow models by MDH hydrologists for the 

same 24 wells.

Acknowledgments

The author thanks the staff of the Minnesota Department 

of Health Drinking Water Protection Program, in particular 

Bruce Olsen, Sheila Grow, James Walsh, Justin Blum, Stephen 

Robertson, and Gail Haglund for providing information on 

the MDH delineated zones of transport and assistance in the 

collection of hydrologic data used in the empirical methods 

zone-of-transport analyses. The author also thanks Alan Epp 

(MDH) for his development of geographic information system 

(GIS) extensions for the truncated-parabola method. The 

author thanks Robert Borgstede and Chris Sanocki (USGS) for 

their work on the figures for this report.
4 Evaluation of Methods for Delineating Zones of Transport for Production Wells in Karst snd Fractured-Rock Aquifers

Methods of Investigation

Two empirical methods, the truncated-parabola and 

modified-ellipse methods, were applied in this study to delineate zones of transport for production wells for which MDH 

hydrologists had previously applied methods outlined in their 

guidance document for delineating wellhead protection zones 

in karst and fractured-rock aquifers in Minnesota (Minnesota 

Department of Health, 2005c). Zones of transport delineated 

by using the two empirical methods were compared with 

zones of transport delineated by MDH to identify and assess 

differences between the zones of transport using the different 

methodologies. 

The study focused on determining zones of transport 

using existing data and methods that are practical for most 

Minnesota communities. Water suppliers and managers commonly do not have the resources to collect the extensive data 

needed to accurately characterize complex groundwater-flow 

conditions present in karst and fractured-rock settings. These 

two empirical methods can be applied to production wells 

by use of existing data obtained from aquifer tests, modeling 

studies, and regional hydrogeologic literature. When possible, 

hydraulic property data used by MDH in their zone-of-transport analyses were incorporated in the empirical methods.

Both empirical methods assume porous-media (Darcian) 

flow conditions in the aquifer being evaluated. The application of zone-of-transport delineation methods in karst and 

fractured-rock settings that are based on the assumptions of 

Darcian flow warrants scrutinization. The assumptions of Darcian flow include laminar flow, in which the Reynolds number 

is less than 1, as well as homogenous and constant hydrologic 

conditions, such as hydraulic conductivity, porosity, and uniform hydraulic gradients in an aquifer (Todd, 1980). In karst 

and fracture-rock settings, these assumptions generally are not 

valid. A single solution channel/fracture or a set of channels/

fractures can be the sole contributor of water to a well. Under 

these conditions, the hydraulic and physical properties of the 

channel or fracture will control the orientation, dimensions, 

and shape of the zone of transport.

Minnesota Department of Health Zone-ofTransport Delineation Methods for SolutionWeathered and Fractured Bedrock Aquifers

Hydrologists from the MDH have developed a guidance document that establishes criteria for determining when 

secondary porosity conditions need to be considered and that 

also identifies techniques for delineating WHPAs in Minnesota 

where bedrock is solution-weathered or fractured (Minnesota 

Department of Health, 2005c). In general, these techniques 

are modifications of techniques applied in porous media. 

The techniques include the calculated-fixed-radius method 

that uses several types of upgradient extensions and extensions along fracture orientation, analytical element methods, 

numerical modeling methods, and dual-porosity methods 

(Minnesota Department of Health, 2005c). These techniques 

can be applied to (1) wells open to a fractured or solutionweathered bedrock aquifer, (2) both a porous media and a 

solution-weathered or fractured bedrock aquifer, (3) a porous 

media aquifer that is hydraulically connected to a solutionweathered or fractured bedrock aquifer, and (4) an aquifer that 

exhibits dual-porosity conditions (Minnesota Department of 

Health, 2005c). The calculated-fixed-radius method applies the 

following equation (U.S. Environmental Protection Agency, 

1987) to determine the radius of a cylinder (R) that represents 

the volume of the aquifer needed to supply the well 

discharge (Q) (Minnesota Department of Health, 2005c): 

R = (Q/nLπ)0.5

where

R is the radius of the cylinder [length (L)],

Q is the well discharge [L3

] = (well pumping rate 

[L3/time (t)])(pumping time period [t]),

n is the effective porosity [dimensionless],

L is the thickness of the saturated portion of the 

aquifer [L], and

π is 3.1416 [dimensionless].

The MDH has determined that either a 10-year or 20-year 

zone of transport be calculated for production wells by using 

either 10 or 20 years for the pumping time period, respectively, depending on the local hydraulic gradient and the ratio 

of well discharge to the absolute groundwater flow through an 

aquifer (Minnesota Department of Health, 2005c). A 10-year 

zone of transport is used for wells that are not part of the supply system but that are within the supply’s zone of transport. 

Methods for overlapping zones of transport also were established in the MDH guidance document (Minnesota Department of Health, 2005c).

Empirical Zone-of-Transport Delineation 

Methods

The truncated-parabola and modified-ellipse methods 

are calculated-variable-shape methods that delineate zones of 

transport on the basis of superposition of the effects of uniform flow gradients on the effects of the pumping well (U.S. 

Environmental Protection Agency, 1987, 1993; Delin and 

Almendinger, 1991). Both methods use hydrogeologic properties for which values often are available to water suppliers and 

managers or that can be estimated from literature values. More 

detailed descriptions of the two methods are provided in Delin 

and Almendinger (1991) and U.S. Environmental Protection 

Agency (1993).

Truncated-Parabola Method

The truncated-parabola method involves a two-step process: (1) calculation of a zone of contribution (fig. 2A) based 

on simple assumptions of steady-state flow conditions in a 
Methods of Investigation 5

Zone of influence

Pumped well

Zone of contribution

Prepumping

water table

10-year zone

of transport

Cone of

depression

Water table

Land surface

Aquifer

Confining unit

X

X X’

X’

Zone of influence

Dividing

streamline

Stagnation

point

Zone of contribution

YL

XL

divide

A VERTICAL PROFILE

B PLAN VIEW −

 TRUNCATED PARABOLA

One-half maximum

width of zone of 

contribution

Distance from well

to stagnation point

X Zone of influence

X’

Not to scale

Groundwater

divide

C PLAN VIEW −

 MODIFIED ELLIPSE

Points where zone-of-transport

boundary crosses x-axis

10-year zone

of transport

X- X+

Explanation

Direction of 

groundwater flow

Groundwater

Stagnation

point

Figure 2. Schematic diagrams showing A, areas of potential recharge (zone of contribution) to a well and examples of B, the 

truncated-parabola and C, modified-elipse methods (modified from the U.S. Environmental Protection Agency, 1987, figure 2-7; 

and Delin and Almendinger, 1991, figure 1).
6 Evaluation of Methods for Delineating Zones of Transport for Production Wells in Karst snd Fractured-Rock Aquifers

confined or unconfined aquifer and (2) application of traveltime of water particles to the calculation of the particle travel 

distance, which is used to define the upgradient boundary of 

the zone of transport (Delin and Almendinger, 1991). The 

zone of contribution is determined by using a set of standard 

groundwater-flow equations (Todd, 1980, p. 121) to establish 

the locations of a stagnation point and asymptotes (±YL) of a 

parabola along a coordinate system (fig. 2). A stagnation point 

is a point in a groundwater-flow field at which groundwater is 

not moving in any direction (Fetter, 2001). The coordinate system for the zone of contribution is oriented so that the x-axis 

is parallel to the uniform groundwater-flow direction, and the 

well is placed at the origin of the coordinate system (Delin 

and Almendinger, 1991). The stagnation point is located XL

distance downgradient from the well, and the asymptotes are 

located ±YL distance along dividing streamlines that form a 

parabola (fig. 2B). These dividing streamlines meet at the 

stagnation point and become parallel to the x-axis upgradient 

from the well as they approach the asymptotes. The stagnation 

point (XL) and the asymptotes (±YL) locations are computed 

using the following equations (U.S. Environmental Protection 

Agency, 1987):

XL = w/(2π), and 

YL = w/2

where

w = Q/(-Kbi) = Q/Qx is the limiting width of aquifer 

from which the well captures flow [L],

Q is the well discharge [L3/t],

K is the horizontal hydraulic conductivity [L/t],

b is the aquifer thickness [L],

i is the hydraulic gradient of uniform field [dimensionless], 

and 

Qx = -Kbi is the “strength” of the uniform flow field [L2/t].

The following equation (U.S. Environmental Protection 

Agency, 1987) is used to produce the dividing streamlines:

X = y/[tan(y/XL)].

Truncation of the parabola assumes that (1) the distance that a 

particle of water travels over a given period of time is primarily a function of the hydraulic gradient, (2) the hydraulic 

effects of pumping on this distance are negligible, and (3) 

the hydraulic gradient is constant near the well (Delin and 

Almendinger, 1991). When these assumptions are applied, the 

following equation (U.S. Environmental Protection Agency, 

1987) can be used to determine the distance traveled for a 

water particle over a specified time period:

X = -t

t

Ki/n

where

X is the distance traveled for a water particle [L],

t

t

 is the time of travel [t],

K is the horizontal hydraulic conductivity [L/t],

i is the hydraulic gradient of uniform field 

[dimensionless], and

n is the porosity [dimensionless].

The distance traveled for a water particle for the specified time 

of travel is measured upgradient from the well along the x-axis 

of the coordinate system. The parabola is truncated at this 

distance. For this study, both 10 and 20 years were used for 

time of travel. 

The well discharge rates and hydraulic properties used 

to compute the zones of transport for the 24 production wells 

are listed in table 1. Well discharge rates were based on the 

maximum volume of water pumped annually during the previous 5 years from water-use records managed by the Minnesota 

Department of Natural Resources (Minnesota Department of 

Natural Resources, 2010). When possible, hydraulic properties 

used by the MDH for their zone-of-transport analyses were 

used in the empirical methods analyses. These values were 

obtained from aquifer and other types of pumping tests conducted on the wells, modeling studies, and existing literature. 

When values for hydraulic properties were not available from 

the MDH analyses, regional values for the aquifer from existing literature were used. 

In this study, when wells were near one another and were 

extracting water from the same aquifer, the pumping rates 

from the wells were summed and used with the empirical 

methods to determine a single zone of transport for multiple 

wells. This was done for the production wells in Askov, Calumet, Fridley (only done for wells 6, 7, and 8), Fulda, Marble, 

and Taconite (table 1). This or a similar approach also was 

used by MDH for delineating zones of transport or the WHPAs 

for these groups of wells.

Modified-Ellipse Method

The modified-ellipse method is used to compute a 

zone-of-transport for water particles under the assumptions 

of steady-state flow conditions in a confined aquifer. In this 

study, this method was applied to confined and unconfined 

settings. Application of the method for unconfined conditions 

produces a computed zone of transport that is a conservative 

estimate for the actual zone of transport, provided that the 

hydraulic head at the well is substituted in the equations for 

the aquifer thickness (Delin and Almendinger, 1991). 

This method uses a coordinate system that is similar to 

the system used in the truncated-parabola method; in both 

methods, the production well is positioned at the origin and the 

assumption of uniform flow is parallel to the x-axis (Delin and 

Almendinger, 1991). The method produces two streamlines 

that are collinear with the x-axis, so that one of the streamlines 

approaches the well directly upgradient, and the other starts at 

the stagnation point and approaches the well directly downgradient. The following equations (U.S. Environmental Protection 

Agency, 1987) are used to find the distances that two water 

particles travel along the two streamlines:

t

t

 = B(Axi – ln(1 + Axi)),

where

B = -n/(AKi2) [t],

A = Kb2π/Q [1/L],
Methods of Investigation 7

x = distance traveled for a water particle [L],

n is the porosity [dimensionless],

t

t

 is the time of travel [t],

K is the horizontal hydraulic conductivity [L/t],

i is the hydraulic gradient of uniform flow 

[dimensionless],

b is the aquifer thickness [L], and 

Q is the well discharge [L3/t].

For each traveltime, the starting positions (X+ and X-) are 

the locations at which the ellipse crosses the x-axis (fig. 2C). 

Assuming that groundwater flow is horizontal and the aquifer 

thickness is constant, the total volume of the aquifer providing water to the well can be represented by its area in the x-y 

plane. When a uniform-flow field is present, the shape of this 

area approximates an ellipse, and its boundary is determined 

from its area and its major axis. The area is determined from 

the following equation (Delin and Almendinger, 1991):

a = (Qtt)/(bn)

where

a = area of the aquifer providing water to well [L2],

Q is the well discharge [L3/t],

t

t

 is the travel time [t],

b is the aquifer thickness [L], and

n is the porosity [dimensionless].

The major axis is simply the distance between X+ and X-

(fig. 2C). As the uniform flow gradient approaches zero, the 

modified ellipse approaches the shape of a circle, and when 

the uniform flow gradient approaches infinity, the ellipse 

approaches a shape similar to the truncated parabola (Delin 

and Almendinger, 1991).

As with the truncated-parabola method, the time of travel 

used in the modified-ellipse analyses was either 10 or 20 years 

for the production well applications. The hydraulic properties used to compute the zones of transport for the production 

wells are listed in table 1.

Table 1. Hydraulic properties applied to the truncated-parabola and modified-ellipse methods to delineate zones of transport for 

production wells open to karst and fractured-rock aquifers, Minnesota.

[ft3/d, cubic foot per day; ft/d, foot per day; ft, feet; MDH, Minnesota Department of Health] 

Community Well number

Well 

discharge rate 

(ft3/d)

Horizontal 

hydraulic 

conductivity (ft/d)

Aquifer 

saturated 

thickness (ft)

Hydraulic 

gradient 

(dimensionless)

Porosity 

(dimensionless)

Askov 3 and 4 5,100 130 282 30.004 40.21

Calumet 2 and 3 5,600 45.0 5200 3.008 5.01

Fridley 6, 7 and 8 170,000 139 1230 3.002 1.15

Fridley 11 97,000 139 1230 3.002 1.15

Fridley 12 100,000 139 1230 3.002 1.15

Fulda 1 and 6 15,000 61.0 5200 7.006 5.01

Hastings 3 68,000 154 1100 1.007 5.2

Hastings 4 58,000 154 1100 1.007 5.2

Hastings 5 84,000 154 1100 1.007 5.2

Hastings 6 100,000 154 1100 1.007 5.2

Hastings 7 110,000 154 1100 1.007 5.2

Keewatin 1 11,000 45.0 5150 3.006 5.1

Keewatin 2 6,000 45.0 5120 3.006 5.1

Le Center 1 and 3 41,000 177 1240 3.002 1.2

Marble 1 and 2 15,000 55.0 5190 5.008 5.1

Taconite 1 and 2 6,300 54.7 594 5.005 5.01

1

Mean value from groundwater-flow model used to delineate MDH zone of transport.

2

Mean value for the two wells.

3

Mean value in the vicinity of wells.

4

 Value from MDH zone-of-transport analysis for wells in Marble.

5

Used in MDH zone-of-transport analysis.

6

Regional mean value for the Sioux Quartzite.

7

Mean value in the vicinity of the wells for glacial aquifers.
8 Evaluation of Methods for Delineating Zones of Transport for Production Wells in Karst snd Fractured-Rock Aquifers

Differences Between Delineation Methods

Differences between the truncated-parabola and modified-ellipse zones of transport and the MDH zones of transport 

(calculated-fixed-radius method and groundwater-flow models) can be explained by variations inherent to the methods and 

by the amount of complexity taken into account for groundwater-flow models. The calculated-fixed-radius method combined with an upgradient extension used by MDH to delineate 

zones of transport for production wells in the communities of 

Askov, Calumet, Fulda, Marble, and Taconite is more conservative (larger zones of transport) than the truncated-parabola 

and modified-ellipse methods because the former method uses 

a total discharge (in cubic feet) over the specified time period 

(for this application 10 years) for the amount of flow through 

the well. In contrast, the truncated-parabola and modifiedellipse methods use only a well discharge rate (in cubic feet 

per day for this study) from which times of travel are determined. Groundwater-flow models used to delineate the MDH 

zones of transport for production wells in the communities of 

Fridley, Hastings, and Le Center accounted for the influence 

of groundwater extraction from nearby multiple large-capacity 

wells. Pumping from nearby wells can reduce the amount of 

groundwater available to the production wells, resulting in 

larger zones of transport.

Physical Description of Aquifers and 

Study Communities in Minnesota

The zones of transport for 24 production wells in nine 

communities located in northeastern, southwestern, or southeastern Minnesota were evaluated in this study (fig. 1). These 

wells extracted water from a karst aquifer (Prairie du Chien 

aquifer), porous aquifers interspersed with solution-enhanced 

fractures (Jordan and Hinckley aquifers), or fractured-bedrock 

aquifers (Biwabik Iron-Formation and Sioux Quartzite aquifers). Depending on location, these aquifers can be confined 

or unconfined. 

Two of the 24 production wells evaluated in this study 

(Hastings wells 4 and 5) extract water from the Cambrian-age 

Jordan Sandstone and Cambrian-age St. Lawrence Formation, and one production well (Fridley well 11) extracts water 

from the Ordovician-age Prairie du Chien Group, the Jordan 

Sandstone, St. Lawrence Formation, and the Cambrian-age 

Franconia Sandstone (table 2). The St. Lawrence Formation 

was not included in zone-of-transport delineations done in this 

study because the MDH did not include the formation in 

groundwater-flow models used in delineating zones of transport around the Hastings wells 4 and 5 (Barr Engineering, 

2003) and Fridley well 11 (Robertson, 2002). The Franconia 

Sandstone also was not included in zone-of-transport delineations done in this study because the top of the Franconia Sandstone was 490 feet below the land surface at Fridley well 11 

and, at that depth, groundwater flow through the sandstone is 

considered mainly intergranular (Runkel and others, 2003).

Aquifers

The Prairie du Chien aquifer consists of the Ordovicianage Prairie du Chien Group. This group consists of two 

formations: the Shakopee Formation and the Oneota Dolomite. The overlying Shakopee Formation consists of thin 

to medium beds of dolostone, shale, and minor amounts of 

siliciclastic sandstone (table 2; Runkel and others, 2003). The 

Oneota Dolomite is primarily thick beds of very fine-grained 

dolostone, and fine and coarse clastic interbeds are common 

in the lower part of the formation (Runkel and others, 2003). 

Solution-enhanced cavities along bedding planes and fractures are pronounced in the Shakopee Formation and along its 

contact with the Oneota Dolomite (Runkel and others, 2003). 

Where karst features are present, the Prairie du Chien-Jordan 

aquifer is sensitive to contamination.

The Jordan aquifer consists of the Cambrian-age Jordan 

Sandstone, which is composed of coarse to fine clastic sediments, with fractures present at various depths below the land 

surface (Runkel and others, 2003). Hydraulic conductivity 

values for the Jordan aquifer generally are higher and more 

variable at shallow depths, indicating that groundwater flow 

through these fractures is more prevalent at shallow depths 

(Runkel and others, 2003).

The Hinkley aquifer contains the Proterozoic-age 

Hinckley Sandstone of the Keweenawan Superpgroup, which 

is fine- to medium-grained and has solution-enhanced fractures (Berg, 2004). The Hinckley Sandstone and overlying 

Cambrian-age Mount Simon Sandstone and Proterozoic-age 

Fond du Lac Formation commonly are difficult to distinguish 

from one another, and therefore they commonly are grouped 

as a single aquifer (Mount Simon-Hinckley-Fond du Lac aquifer). Shade and others (2001, 2002) mapped many sinkholes, 

springs, and caves associated with fractures and bedding 

planes in the Hinckley Sandstone in the Askov area of Pine 

County, Minn., where the sandstone is the upper bedrock unit.

The Proterozoic-age Biwabik Iron Formation of the 

Animikie Group consists of chert and iron minerals (Morey, 

1972). The formation contains the main aquifer (Biwabik 

Iron Formation aquifer) used by water supplies along the 

Mesabi Iron Range (Kanivetsky, 1978). Water in the Biwabik 

Iron Formation aquifer flows mainly along a combination of 

fractures, joints, and solution-weathered channels in the cherty 

layers of the formation (Walsh, 2004). This aquifer is 

particularly susceptible to contamination along the Mesabi 

Iron Range at natural outcrops and mine pits or where it may 

be covered by only a few feet of overlying sediments. 

The Sioux Quartzite aquifer consists of the Proterozoicage Sioux Quartzite, which consists dominantly of red, tightly 

cemented quartzite, but it contains some intercalated beds 

of mudstone and conglomerate (Austin, 1972). The Sioux 

Quartzite is used by water supplies in southwestern Minnesota 

and southeastern South Dakota where there are limited sources 

of water. Water in the aquifer moves through vertical fractures 

and bedding planes along bedrock highlands (Olsen, 2004).
Physical Description of Aquifers and Study Communities in Minnesota 9

Table 2. Geologic units and general information on production wells in Minnesota for which zones of transport were determined for 

karst or fractured-rock aquifers by using empirical methods.—Continued

[Aquifer nomenclature follows the geologic nomenclature of the U.S. Geological Survey. ft BLS, feet below land surface]

Community 

Well 

number System Series Geologic unit/aquifer Lithology

Well 

depth 

(ft BLS)

Depth to 

aquifer 

(ft BLS)

Askov 3 Precambrian Proterozoic Era 

(Middle)

Hinckley Sandstone of the 

Keweenawan Supergroup 

(Hinckley aquifer)

Fine- to medium-grained 

sandstone

193 23

Askov 4 Precambrian Proterozoic Era 

(Middle)

Hinckley Sandstone of the 

Keweenawan Supergroup 

(Hinckley aquifer)

Fine- to medium-grained 

sandstone

200 23

Calumet 2 Precambrian Proterozoic Era 

(Middle)

Biwabik Iron Formation 

of the Animikie Group 

(Biwabik Iron-Formation 

aquifer)

Ferruginous chert, shale, and 

iron minerals, also called 

taconite

495 311

Calumet 3 Precambrian Proterozoic Era 

(Middle)

Biwabik Iron Formation 

of the Animikie Group 

(Biwabik Iron-Formation 

aquifer)

Ferruginous chert, shale, and 

iron minerals, also called 

taconite

500 378

Fridley 6 Paleozoic Cambrian and 

Ordovician

Prairie du Chien Group/

Jordan Sandstone 

(Prairie du Chien-Jordan 

aquifer)

Dolostone and shale with 

fine and coarse clastic interbeds (Prairie du Chien 

Group); coarse and fine 

clastic sandstone (Jordan 

Sandstone)

255 130

Fridley 7 Paleozoic Ordovician Prairie du Chien Group 

(Prairie du Chien aquifer)

Dolostone and shale with 

fine and coarse clastic 

interbeds

262 128

Fridley 8 Paleozoic Ordovician Prairie du Chien Group 

(Prairie du Chien aquifer)

Dolostone and shale with 

fine and coarse clastic 

interbeds

265 186

Fridley 11 Paleozoic Cambrian and 

Ordovician

Prairie du Chien Group, 

Jordan Sandstone 

(Prairie du Chien-Jordan 

aquifer), St. Lawrence 

Formation, and Franconia 

Sandstone (Franconia 

aquifer)

Dolostone and shale with 

fine and coarse clastic interbeds (Prairie du Chien 

Group); coarse and fine 

clastic sandstone (Jordan 

Sandstone); interbeds of 

fine clastic and carbonate 

rock (St. Lawrence and 

Franconia Formations)

669 225

Fridley 12 Paleozoic Cambrian Jordan Sandstone 

(Jordan aquifer)

Coarse and fine clastic 

sandstone

276 225

Fulda 1 Precambrian Proterozoic Era 

(Middle)

Sioux Quartzite 

(Sioux Quartzite aquifer)

Red, tightly cemented 

quartzite, some intercalated beds of mudstone 

and conglomerate

1,400 235

Fulda 6 Precambrian Proterozoic Era 

(Middle)

Sioux Quartzite 

(Sioux Quartzite aquifer)

Red, tightly cemented 

quartzite, some intercalated beds of mudstone 

and conglomerate

550 237

Hastings 3 Paleozoic Cambrian Jordan Sandstone 

(Jordan aquifer)

Coarse and fine clastic 

sandstone 

299 197
10 Evaluation of Methods for Delineating Zones of Transport for Production Wells in Karst snd Fractured-Rock Aquifers

Table 2. Geologic units and general information on production wells in Minnesota for which zones of transport were determined for 

karst or fractured-rock aquifers by using empirical methods.—Continued

[Aquifer nomenclature follows the geologic nomenclature of the U.S. Geological Survey. ft BLS, feet below land surface]

Community 

Well 

number System Series Geologic unit/aquifer Lithology

Well 

depth 

(ft BLS)

Depth to 

aquifer 

(ft BLS)

Hastings 4 Paleozoic Cambrian Jordan Sandstone 

(Jordan aquifer) and 

St. Lawrence Formation

Coarse and fine clastic sandstone (Jordan Sandstone) 

and interbeds of fine clastic and carbonate rock 

(St. Lawrence Formation)

400 290

Hastings 5 Paleozoic Cambrian Jordan Sandstone 

(Jordan aquifer) and 

St. Lawrence Formation

Coarse and fine clastic sandstone (Jordan Sandstone) 

and interbeds of fine clastic and carbonate rock 

(St. Lawrence Formation)

355 264

Hastings 6 Paleozoic Cambrian Jordan Sandstone 

(Jordan aquifer)

Coarse and fine clastic 

sandstone

332 229

Hastings 7 Paleozoic Cambrian Jordan Sandstone 

(Jordan aquifer)

Coarse and fine clastic 

sandstone

285 195

Keewatin 1 Precambrian Proterozoic Era 

(Middle)

Biwabik Iron Formation 

of the Animikie Group 

(Biwabik Iron-Formation 

aquifer)

Ferruginous chert, shale, and 

iron minerals, also called 

taconite

606 211

Keewatin 2 Precambrian Proterozoic Era 

(Middle)

Biwabik Iron Formation 

of the Animikie Group 

(Biwabik Iron-Formation 

aquifer)

Ferruginous chert, shale, and 

iron minerals, also called 

taconite

473 124

Le Center 1 Paleozoic Cambrian and 

Ordovician

Prairie du Chien Group/

Jordan Sandstone 

(Prairie du Chien-Jordan 

aquifer)

Dolostone and shale with 

fine and coarse clastic interbeds (Prairie du Chien 

Group) coarse and fine 

clastic sandstone (Jordan 

Sandstone)

543 280

Le Center 3 Paleozoic Cambrian and 

Ordovician

Prairie du Chien Group/

Jordan Sandstone 

(Prairie du Chien-Jordan 

aquifer)

Dolostone and shale with 

fine and coarse clastic interbeds (Prairie du Chien 

Group), coarse and fine 

clastic sandstone (Jordan 

Sandstone)

520 200

Marble 1 Precambrian Proterozoic Era 

(Middle)

Biwabik Iron Formation 

of the Animikie Group 

(Biwabik Iron-Formation 

aquifer)

Ferruginous chert, shale, and 

iron minerals, also called 

taconite

402 132

Marble 2 Precambrian Proterozoic Era 

(Middle)

Biwabik Iron Formation 

of the Animikie Group 

(Biwabik Iron-Formation 

aquifer)

Ferruginous chert, shale, and 

iron minerals, also called 

taconite

503 135

Taconite 1 Precambrian Proterozoic Era 

(Middle)

Biwabik Iron Formation 

of the Animikie Group 

(Biwabik Iron-Formation 

aquifer)

Ferruginous chert, shale, and 

iron minerals, also called 

taconite

384 unknown

Taconite 2 Precambrian Proterozoic Era 

(Middle)

Biwabik Iron Formation 

of the Animikie Group 

(Biwabik Iron-Formation 

aquifer)

Ferruginous chert, shale, and 

iron minerals, also called 

taconite

394 185
Physical Description of Aquifers and Study Communities in Minnesota 11

Communities

Zones of transport for 24 production wells in nine 

communities (Calumet, Keewatin, Marble, Taconite, Askov, 

Fridley, Hastings, Le Center, and Fulda) were evaluated in 

this study. Physical descriptions of the nine communities are 

presented in this section.

Calumet

The city of Calumet is on the Mesabi Iron Range of 

northeastern Minnesota (fig. 1), and its population is approximately 362 (U.S. Census Bureau, 2005). Zones of transport for 

two production wells in Calumet (wells 2 and 3; table 2) were 

evaluated. The wells are less than 120 feet apart, and both 

wells are completed in the Biwabik Iron-Formation aquifer, 

which is a confined aquifer in the Calumet area. The Biwabik 

Iron Formation is the upper bedrock unit in the northern part 

of the city. At the production wells in Calumet, the Biwabik 

Iron Formation is more than 300 feet below the land surface, 

covered by Pleistocene-age glacial deposits and the Proterozoic-age Virginia Formation of the Animikie Group, which 

is composed of argillites and slates. Glacial deposits in the 

Calumet area consist mainly of a mix of bouldery tills, lake 

and stream sediments, and some ice-contact sand and gravel 

deposits were formed near local natural lakes (Jennings and 

Reynolds, 2005). The Hill Annex iron ore mine pit is located 

approximately 0.5 mile north of the production wells (fig. 3). 

This mine pit is connected to the abandoned Gross Marble, 

Arcturus, and Hill Trumbull mine pits (fig. 3). A series of large 

lakes covering an area of more than 800 acres has formed in 

the pits. High-angle faults generally striking to the northeast/

southwest are prevalent in the Calumet area (Jirsa and others, 

2005). Aquifer tests have not been conducted on the wells. 

Data from the Minnesota Department of Natural Resources 

State Water Use Database (SWUDS) indicates that the 

production wells in Marble are the only other high-capacity 

wells near the Calumet area (Walsh, 2007a). Pumping from 

the production wells in Marble was not included in the zone 

of transport delineations done in this study and by the MDH 

for the production wells in Calumet. A zone of transport was 

delineated by MDH for the two production wells in Marble by 

using the calculated-fixed-radius method combined with an 

upgradient extension (James F. Walsh, Minnesota Department 

of Health, written commun., April 10, 2007).

Keewatin

The city of Keewatin is on the Mesabi Iron Range of 

northeastern Minnesota (fig. 1), and its population is approximately 1,105 (U.S. Census Bureau, 2005). Zones of transport 

for two production wells in Keewatin were evaluated (wells 1 

and 2; table 2). Both wells are completed in the Biwabik Iron 

Formation aquifer, which is a confined aquifer in the Keewatin 

area. In both wells, the Biwabik Iron Formation is more than 

100 feet below the land surface, covered by Pleistocene-age 

glacial deposits and slates of the Proterozoic-age Virginia 

Formation of the Animikie Group. The glacial deposits consist 

mainly of clayey and bouldery till, and some buried drumlins 

are present south of Keewatin (Jennings and Reynolds, 2005).

A series of abandoned and active mine pits (Carlz, Mississippi 

No. 1, St. Paul, Mesabi Chief, Bennett, National Steel, and 

Russell), mine tailings, and mine stockpiles are north, east, 

and west of the production wells (fig. 4). Data from SWUDS 

indicates that the Mississippi No. 1, Mesabi Chief, Russell, 

National Steel, and Bennett Pits are being dewatered (Walsh, 

2003). Lakes are present in the other mine pits (Walsh, 2003). 

Faulting is common in the area (Jirsa and others, 2005). 

Aquifer tests were not conducted at the two wells in Keewatin. 

Walsh (2003) characterized the chemistry and isotopic signatures of mine-pit waters, well waters, and local groundwater 

in the Keewatin area to assess potential sources of water to the 

two production wells. Oxygen-18 and chloride data indicated 

that at least one of the production wells was affected by mine 

dewatering, most likely from the Carlz mine pit. This effect 

may change depending on future dewatering scenarios (Walsh, 

2003). Data from SWUDS indicates that two mine company 

wells are the only other high-capacity wells in the Keewatin 

area (Walsh, 2003). Walsh (2003) used a 10-year calculatedradius equation to determine that the two mine company wells 

would not affect the zones of transport for the two production wells, so the influence of pumping from these wells was 

not included in the truncated-parabola and modified-ellipse 

analyses.

A delineation technique developed by the MDH for confined solution-weathered or fractured-rock aquifers was used 

to calculate 10-year zones of transport for the two production wells (Minnesota Department of Health, 2005c) (fig. 4). 

This technique applied calculated-fixed-radius equations and 

existing water-level and water-quality data to determine zones 

of transport for the wells (Walsh, 2003). The surface-water 

drainage area for the Carlz mine pit was included in the MDH 

zone of transport for the production wells in Keewatin because 

water-quality and isotopic data indicated that the Carlz Pit is 

a source of water to the two production wells. When delineating the orientations of the truncated parabolas and modified 

ellipses, it was assumed that the Carlz pit was the only pit contributing water to the wells. This assumption also was made 

when the MDH zones of transport were delineated (Walsh, 

2003).
12 Evaluation of Methods for Delineating Zones of Transport for Production Wells in Karst snd Fractured-Rock Aquifers

Figure 3. Zones of transport delineated using the truncated-parabola and modified-ellipse methods and existing zone of 

transport delineated by the Minnesota Department of Health (MDH) for production wells in Calumet, Minnesota.

2

3

Marble

Silverwood

Calumet

Cort Jurgenson

¤£169

Twin Lakes

Holman

Lake

Spring

Lake

Bass 

Lake

Upper

Panaca

Lake

Lower

Panaca

Lake

Snowball

Lake

Big

Diamond

Lake

Dunning

Lake

Arcturus Mine Pit Lake

Gross Marble 

Mine Pit Lake

 Hill Annex

 Mine Pit 

Lake

Swan River

Swan

River

Swan River

Swan River

EXPLANATION

Mine stockpiles

Mine tailings/settling basins

Mine pits

MDH 10-year zone of transport—wells 2 and 3

10-year truncated parabola—wells 2 and 3

10-year modified ellipse—wells 2 and 3

2 Production well (number indicates well number)

0 0.5

0 0.5 1 KILOMETER

1 MILE

93°20' 93°17'30" 93°15'

47°20'

47°17'30"

Base from Minnesota Department of Transportation

Base Map 97, 1:24,000, 1997

Universal Transverse Mercator projection, Zone 15

Mine features from Minnesota Department of Natural Resources, 2006
Physical Description of Aquifers and Study Communities in Minnesota 13

Figure 4. Zones of transport delineated using the truncated-parabola and modified-ellipse methods and existing zone of 

transport delineated by the Minnesota Department of Health (MDH) for production wells in Keewatin, Minnesota.

Carlz Mine Pit Lake

St. Paul Mine Pit Lake

Mesabi Chief

Mine Pit

National Steel Mine Pit

Bennett Mine Pit

Mississippi No. 1

Mine Pit

Russell Mine Pit

169

169

571

93°6' 93°5' 93°4' 93°3'

47°25'

47°24'

0 0.5 1 MILE

0 0.5 1 KILOMETER

Keewatin

Base from Minnesota Department of Transportation

Base Map 97, 1:24,000, 1997

Universal Transverse Mercator projection, Zone 15

Mine features from Minnesota Department of Natural Resources, 2006

2

1

EXPLANATION

Mine pits

Mine stockpiles

Mine tailings/settling basins

MDH 10-year zone of transport—wells 1 and 2

MDH drinking-water-supply management area

10-year truncated parabola—well 1

10-year modified ellipse—well 1

10-year truncated parabola—well 2

10-year modified ellipse—well 2

Production well (number indicates well number) 1
14 Evaluation of Methods for Delineating Zones of Transport for Production Wells in Karst snd Fractured-Rock Aquifers

Marble

The city of Marble is just west of the city of Calumet 

on the Mesabi Iron Range of northeastern Minnesota (figs. 1 

and 5), and its population is approximately 678 (U.S. Census 

Bureau, 2005). Zones of transport for two production wells 

in Marble (wells 1 and 2; table 2) were evaluated. Both wells 

are completed in the Biwabik Iron-Formation aquifer, which 

is a confined aquifer in the Marble area. At both wells, the 

Biwabik Iron Formation is approximately 135 feet below the 

land surface, covered by Pleistocene-age glacial deposits. 

Similar to the Calumet area, glacial deposits in the Marble 

area consist mainly of a mix of bouldery tills, lake and stream 

sediments, and some ice-contact sand and gravel deposits 

formed near local natural lakes (Jennings and Reynolds, 

2005). Similar to many production wells on the Mesabi Iron 

Range, abandoned mine pits (Gross Marble, Hill Trumbull, 

Hill Annex, and Arcturus), mine stockpiles, and tailings/settling basins lie in the vicinity of the production wells 

(fig. 5). Lakes have formed in the abandoned mine pits. 

Aquifer tests were not conducted at the production wells. Data 

from SWUDS indicates that the production wells in Calumet 

are the only other high-capacity wells near the Marble area 

(Walsh, 2007a). Pumping from the production wells in Calumet was not included in the zone of transport delineations 

done in this study or for delineations by the MDH for the 

production wells in Marble. A MDH delineation technique for 

unconfined solution-weathered or fractured-rock aquifers that 

applied the calculated-fixed-radius method combined with an 

upgradient extension was used to calculate a 10-year zone of 

transport for the two production wells (Walsh, 2007a) (fig. 5). 

This technique is applied to wells where the local horizontal 

hydraulic gradient is greater than 0.001 and the ratio of well 

discharge to the absolute groundwater flow through an aquifer 

is less than 3,000 (Minnesota Department of Health, 2005c). 

Taconite

The city of Taconite is on the Mesabi Iron Range of 

northeastern Minnesota (fig. 1), and its population is approximately 285 (U.S. Census Bureau, 2005). Zones of transport 

for two production wells in Taconite (wells 1 and 2; table 2) 

were evaluated. Both wells are completed in the Biwabik Iron 

Formation aquifer, which is a confined aquifer in the Taconite 

area. Approximately 178 feet of glacial clay, boulders, and 

sand, and approximately 100 feet of Proterozoic-age Virginia 

Formation and Cretaceous-age bedrock overlie the Biwabik 

Iron Formation in Taconite. Faulting is present near Taconite, 

and the major faults strike northwest/southeast (Jirsa and 

others, 2005). The city and the production wells are southeast 

of the Canisteo Mine Pit (fig. 6), a flooded mine pit in which 

water levels have been rising since the cessation of mine 

dewatering activities in 1984 (Jones, 2002). Future plans for 

the mine may include dewatering for power production. Aquifer tests were not conducted at the two production wells in 

Taconite. Data from SWUDS indicates that a production well 

in Bovey is the only other high-capacity well in the Taconite 

area (Walsh, 2007b). The production well in Bovey is completed in a glacial aquifer, and it is unlikely to affect the zoneof-transport shape and size for the wells in Taconite. Therefore, pumping from the production well in Bovey was not 

included in the MDH zone of transport delineation. Similar to 

the production wells in Marble, a MDH delineation technique 

for unconfined solution-weathered and fractured-rock aquifers 

that applied the calculated-fixed-radius method combined with 

an upgradient extension was used to calculate a 10-year zone 

of transport for the two production wells in Taconite (Walsh, 

2007b) (fig. 6). 

Askov

 The city of Askov is in northeastern Minnesota (fig. 1), 

and its population is approximately 368 (U.S. Census Bureau, 

2005). Zones of transport for two production wells in Askov 

(wells 3 and 4; table 2) were evaluated. Both wells are completed in the Hinckley aquifer, which is an unconfined aquifer 

in the Askov area. The Hinckley aquifer is covered by sandy 

and silty glacial sediments deposited as Superior moraine 

ridges, meltwater stream deposits, and ice margin deposits in 

the Askov area (Patterson and Knaeble, 2001). Glacial deposit 

thicknesses generally are less than 50 feet in the Askov area. 

Both production wells in Askov were determined by MDH 

hydrologists to be vulnerable to contamination due to the lack 

of geologic material between the land surface and the bedrock 

aquifer and the presence of tritium in water sampled from well 

3 (Haglund, 2007). Shade and others (2001, 2002) identified 

a series of sinkholes within 200 feet of the production wells 

in Askov and characterized the formation of sinkholes in the 

Askov area (fig. 7). These sinkholes generally are present 

where fractures and bedding planes intersect. Results from 

aquifer tests conducted on production well 3 and a former production well in Askov indicate that dual-porosity flow within 

enlarged voids occurs in the vicinity of the wells (Haglund, 

2007). Data from SWUDS indicates that no other high-capacity wells are in the Askov area (Haglund, 2007). Hydrologists 

from MDH used two analytical groundwater-flow models and 

calculated-fixed-radius equations to delineate 10-year zones 

of transport for both wells (wells 3 and 4) (Haglund, 2007). 

These zones of transport were used with a combined pumping rate for the two wells, geologic maps, sinkhole maps, and 

fracture-lineament maps to determine a series of upgradient 

extensions that were modified to account for upgradient flow, 

flow direction ambiguity, and the effects of secondary permeability features. The modified zones of transport were used to 

create a composite area of capture zones defining the boundaries of the WHPA for the wells (light green area in fig. 7) 

(Haglund, 2007).
Physical Description of Aquifers and Study Communities in Minnesota 15

169

69

69

12

Twin Lakes

Spring Lake

Bass Lake

EXPLANATION

Mine pits

Mine stockpiles

Mine tailings/settling basins

MDH 10-year zone of transport—wells 1 and 2

10-year truncated parabola—wells 1 and 2 

10-year modified ellipse—wells 1 and 2 

Production well (number indicates well number) 2

93°19'30" 93°18' 93°16'30"

47°19'30"

47°18'

0 0.5 1 MILE

0 0.5 1 KILOMETER

Marble

Calumet

Silverwood

Holman

Lake

Big

Diamond

 Lake

Mud

 Lake

 Upper

Panaca

 Lake

Base from Minnesota Department of Transportation

Base Map 97, 1:24,000, 1997

Universal Transverse Mercator projection, Zone 15

Mine features from Minnesota Department of Natural Resources, 2006 

Gross Marble 

Mine Pit Lake

Hill Trumbull

Mine Pit Lake

Hill Annex

Mine Pit Lake

1 2

Arcturus Mine Pit Lake

Figure 5. Zones of transport delineated using the truncated-parabola and modified-ellipse methods and existing 

zone of transport delineated by the Minnesota Department of Health (MDH) for production wells in Marble, Minnesota.
16 Evaluation of Methods for Delineating Zones of Transport for Production Wells in Karst snd Fractured-Rock Aquifers

169

93°25' 93°22'30" 93°20'

47°20'

47°17'30"

0 0.5 1 MILE

0 0.5 1 KILOMETER

Base from Minnesota Department of Transportation

Base Map 97, 1:24,000, 1997

Universal Transverse Mercator projection, Zone 15 

Coleraine

Bovey

Taconite

Canisteo Mine Pit Lake

Mine features from Minnesota Department of Natural Resources, 2006

Trout

Lake

Holman

Lake

Little Diamond

Lake

Big Diamond

Lake

Twin

Lakes

Swan River

1 2

EXPLANATION

Mine pits

Mine stockpiles

Mine tailings/settling basins

MDH 10-year zone of transport—wells 1 and 2

10-year truncated parabola—wells 1 and 2

10-year modified ellipse—wells 1 and 2

2 Production well (number indicates well number)

Figure 6. Zones of transport delineated using the truncated-parabola and modified-ellipse methods and existing zone of 

transport delineated by the Minnesota Department of Health (MDH) for production wells in Taconite, Minnesota.
Physical Description of Aquifers and Study Communities in Minnesota 17

92°46'30" 92°45'

46°12'

46°10'30"

0

0 0.5 1 KILOMETER

0.5 1 MILE

Askov

Base from Minnesota Department of Transportation

Base Map 97, 1:24,000, 1997

Universal Transverse Mercator projection, Zone 15 

Source for sinkhole data from: Shade, B. L., Alexander, C.A., 

Alexander, S.C., and Martin, S., 2001, Sinkhole Distribution, from

Geologic Atlas of Pine County, Minnesota, Minnesota Geological 

Survey, County Atlas Series C-13, Part A, Plate 6.

4 3

3

4 3

23

32

21

EXPLANATION

MDH 10-year zone of transport—wells 3 and 4

(which is a part of the wellhead protection area)

MDH wellhead protection area - delineated by 

extending a modified zone of transport in the 

directions of karst features from the wells (Haglund, 

2007)

MDH drinking-water-supply management area

Sewage disposal ponds

10-year truncated parabola—Wells 3 and 4

10-year modified ellipse—Wells 3 and 4

Sinkholes

Production well (number indicates well number)

Figure 7. Zones of transport delineated using the truncated-parabola and modified-ellipse methods and existing zone of transport 

delineated by the Minnesota Department of Health (MDH) for production wells in Askov, Minnesota.
18 Evaluation of Methods for Delineating Zones of Transport for Production Wells in Karst snd Fractured-Rock Aquifers

Fridley

The city of Fridley is in east-central Minnesota (fig. 1), 

and its population is approximately 26,515 (U.S. Census 

Bureau, 2005). There are 13 production wells in Fridley: one 

well is completed in Quaternary-age glacial deposits; six wells 

are completed in either the Prairie du Chien Group, Jordan 

Sandstone, or both geologic units; four wells are completed 

in the Mount Simon Sandstone; and two wells are completed 

in multiple formations. For this study, zones of transport for 

five wells were evaluated. The five wells withdraw water from 

the Prairie du Chien aquifer (wells 7 and 8), Jordan aquifer 

(well 12), or both aquifers (wells 6 and 11) (fig. 8 and table 2). 

Well 9, withdrawing water from the Prairie du Chien and 

Jordan aquifers, was not included in the study because it is 

pumped only for emergencies, and the MDH did not include 

this well in their wellhead protection planning (Robertson, 

2002). The five Fridley wells assessed in this study range in 

depth from 255 to 669 feet below land surface (table 2). For 

this study, the Prairie du Chien aquifer and Jordan aquifer 

were grouped together as a single aquifer because groundwater 

levels and flow directions are similar in both aquifers (Robertson, 2002). However, the two aquifers were simulated as separate hydrogeologic units in a multi-layered analytical element 

groundwater-flow model used by MDH to calculate 10-year 

zones of transport (Robertson, 2002) (fig. 8). The WHPAs for 

the wells completed in the Prairie du Chien Group and Jordan 

Sandstone were generated by supplementing the 10-year zones 

of transport with an upgradient extension using hydrogeologic 

mapping techniques. An aquifer test conducted at the production wells in Fridley produced transmissivity values for the 

Shakopee Formation of the Prairie du Chien Group ranging 

from 42,500 to 73,900 feet squared per day (ft2/d) (Robertson, 

2002). A hydraulic conductivity value of 39 ft/d was used in 

the groundwater-flow model to delineate the MDH zones of 

transport (Robertson, 2002). Twenty-two high-capacity wells 

identified in SWUDS were included in the groundwater-flow 

model to assess the effect of water extraction from these wells 

on the shape and size of the zones of transport for the production wells (Robertson, 2002). The influence of these 

22 high-capacity wells on the truncated-parabola and modified-ellipse zones of transport was not assessed for this report.

Hastings

The city of Hastings is in southeastern Minnesota (fig. 1), 

and its population is approximately 20,910 (U.S. Census 

Bureau, 2005). Six production wells are located in Hastings (wells 1, 3, 4, 5, 6, and 7; table 2). All of the wells are 

completed in the Jordan Sandstone except for well 1, which 

is a multi-aquifer well completed in the Jordan Sandstone, 

St. Lawrence Formation, Franconia Formation, Ironton Sandstone, and Galesville Sandstone (Barr Engineering, 2003). 

Well 1 was not included in this study because it is pumped 

only in an emergency, and it was not included in the MDH 

wellhead protection assessment. The other five wells ranged 

in depth from 285 to 400 feet below the land surface (table 2). 

Depth to the Jordan Sandstone in the wells varies from 

approximately 195 to 290 feet below the land surface (table 2). 

The Jordan aquifer is confined in the Hastings area but 

receives water through leakage from upper aquifers and confining layers (Barr Engineering, 2003). Buried bedrock valleys 

cut through the Hastings area in a north-northwest direction 

(Barr Engineering, 2003). All of the production wells in Hastings are susceptible to contamination, and nitrates, herbicides, 

and herbicide metabolites were detected in water samples 

from all five wells. Data analyses of aquifer tests conducted 

at well 5 produced a mean transmissivity of 5,400 ft2/d for 

the Jordan aquifer (Barr Engineering, 2003). A multi-layered, 

finite-difference, groundwater-flow model was used by MDH 

to delineate 1-year and 10-year zones of transport around 

the five wells (Barr Engineering, 2003) (fig. 9). The 10-year 

zones of transport were supplemented by upgradient extensions using hydrogeologic mapping techniques by MDH to 

produce the WHPAs for the wells. Other high-capacity wells 

from a Dakota County database were included in the groundwater-flow model to assess the effect of these wells on the 

zones of transport (Barr Engineering, 2003). The influence of 

these other high-capacity wells on the truncated-parabola and 

modified-ellipse zones of transport for the production wells in 

Hastings was not assessed in this report.

Le Center

The city of Le Center is in southeastern Minnesota 

(fig. 1), and its population is approximately 2,308 (U.S. Census Bureau, 2005). There are three production wells in 

Le Center (wells 1, 2, and 3) (fig. 10); however, well 2 is used 

only in emergencies, and consequently was not included in the 

zone-of-transport analyses. Both wells 1 and 3 extract water 

from the Prairie du Chien and Jordan aquifers (table 2), which 

is confined in the Le Center area. The Prairie du Chien Group 

is approximately 280 feet below land surface and 170 feet 

thick under Le Center, and the Jordan Sandstone is about 

80 feet thick under Le Center (Blum, 2003).

Well 1 is 543 feet deep, and it is uncased through the 

entire aquifer. Analysis of a constant-discharge aquifer test 

conducted at well 1 produced a transmissivity value of 

17,900 ft2/d (Blum, 2003). A nearly instantaneous water-level 

decline in the observation well during this aquifer test indicated the presence of conduit flow in the Prairie du Chien 

and Jordan aquifers between well 1 and the observation well 

(Blum, 2003). Well 3 is 520 feet deep, and it is uncased to the 

Oneota Dolomite of the Prairie du Chien Group and the Jordan 

Sandstone. Approximately 200 to 280 feet of glacial clay-rich 

till cover the Prairie du Chien-Jordan aquifer in Le Center. 

Blum (2003) determined that no other high-capacity wells in 

the Le Center area influence groundwater-flow conditions in 

the vicinity of the production wells. An analytical-element, 

groundwater-flow model and a statistical model were used by 

the MDH to calculate a 10-year composite zone of transport 

for the two production wells (Blum, 2003) (fig. 10).
Physical Description of Aquifers and Study Communities in Minnesota 19

93°16'30" 93°15' 93°13'30" 93°12'

45°6'

45°4'30"

Base from Minnesota Department of Transportation

Base Map 97, 1:24,000, 1997

Universal Transverse Mercator projection, Zone 15 

12

10

11

2 4 5

7 9 8

3

1

0

0 1 2 KILOMETERS

1 2 MILES

6

Locke Lake

Moore 

 Lake

Spring

Lake

Mississippi

River

Long

Lake

Pike

Lake

Rush

Lake

Rice

Creek

Rice

Creek

94

94

35W

694 694

252

10

10

65

EXPLANATION

MDH 10-year zone of transport—well 11

MDH 10-year zone of transport—well 12

MDH 10-year zone of transport—wells 6, 7, and 8

MDH drinking-water-supply management area

10-year truncated parabola—wells 6, 7, and 8

10-year modified ellipse—wells 6, 7, and 8

10-year truncated parabola—well 11

10-year modified ellipse—well 11

10-year truncated parabola—well 12

10-year modified ellipse—well 12

Production well analyzed in this study (number indicates 

well number)

Production well not analyzed in this study (number 

indicates well number)

6

5

Fridley

Figure 8. Zones of transport delineated using the truncated-parabola and modified-ellipse methods and existing zone of transport 

delineated by the Minnesota Department of Health (MDH) for production wells in Fridley, Minnesota.
20 Evaluation of Methods for Delineating Zones of Transport for Production Wells in Karst snd Fractured-Rock Aquifers

3

4

5

6

7

Hastings

1

Vermillion

River

Lake Rebecca

Mississippi

River

Lake

Isabelle

Vermillion

River

0 1 2 MILES

0 1 2 KILOMETERS

Base from Minnesota Department of Transportation

Base Map 97, 1:24,000, 1997

UTM Zone 15 projection

92°55'30" 92°54' 92°52'30" 92°51' 92°49'30"

44°45'

44°43'30"

44°42'

EXPLANATION

MDH 10-year zone of transport—well 6

MDH 10-year zone of transport—well 7

MDH 10-year zone of transport—wells 3, 4, and 5

MDH drinking-water-supply management area

10-year truncated parabola—well 3

10-year modified ellipse—well 3

10-year truncated parabola—well 4

10-year modified ellipse—well 4

10-year truncated parabola—well 5

10-year modified ellipse—well 5

10-year truncated parabola—well 6

10-year modified ellipse—well 6

10-year truncated parabola—well 7

10-year modified ellipse—well 7

3 Production well (number indicates well number)

61

316

61

55

10

Figure 9. Zones of transport delineated using the truncated-parabola and modified-ellipse methods and existing zone of 

transport delineated by the Minnesota Department of Health (MDH) for production wells in Hastings, Minnesota.
Physical Description of Aquifers and Study Communities in Minnesota 21

Figure 10. Zones of transport delineated using the truncated-parabola and modified-ellipse methods and existing 

zone of transport delineated by the Minnesota Department of Health (MDH) for production wells in Le Center, Minnesota.

93°43'

44°24'

44°23'

93°44'

Sautter

Lake

Le Sueur Creek

2

1

3

Le Center

Base from Minnesota Department of Transportation

Base Map 97, 1:24,000, 1997

Universal Transverse Mercator projection, Zone 15

0 0.5 1 MILE

0 0.5 1 KILOMETER

3

EXPLANATION

MDH 10-year zone of transport—wells 1 and 3

MDH drinking-water-supply management area

10-year truncated parabola—well 1

10-year modified ellipse—well 1

10-year truncated parabola—well 3

10-year modified ellipse—well 3

Production well analyzed in this study (number 

indicates well number)

2 Production well not analyzed in this study (number 

indicates well number)

11

11

114

114

110

99
22 Evaluation of Methods for Delineating Zones of Transport for Production Wells in Karst snd Fractured-Rock Aquifers

Fulda

The city of Fulda is in southwestern Minnesota (fig. 1), 

and its population is approximately 1,272 (U.S. Census 

Bureau, 2005). There are five production wells in Fulda. 

Three production wells (wells 4, 5, and 7) extract groundwater 

from a confined aquifer consisting of glacial outwash sands, 

deposited by the Des Moines lobe ice sheet, and thus were not 

included in this study. Zones of transport were evaluated for 

wells 1 and 6, which extract water from the Sioux Quartzite 

aquifer (table 2). The Sioux Quartzite is a confined aquifer in 

the Fulda area, and approximately 60 feet of clay-rich glacial sediments lie between the glacial outwash sands, from 

which wells 4, 5, and 7 obtain groundwater, and the top of the 

quartzite. The Sioux Quartzite forms a highland in the Fulda 

area, and its long axis extends northwest-southeast several 

miles from the city of Fulda (Olsen, 2004). The highland is 

buried by approximately 235 feet of glacial deposits in the city 

of Fulda, but less than 100 feet of deposits overlie it east and 

southeast of the city (Olsen, 2004). An aquifer test conducted 

in well 6 produced a transmissivity of 36.7 ft2/d for the Sioux 

Quartzite aquifer, and this likely represents the connectivity of 

the local fracture system around the well. Data from SWUDS 

indicates that no other high-capacity wells are in the Fulda 

area (Olsen, 2004). The MDH used a calculated-fixed-radius 

equation with an upgradient extension and potentiometric and 

fracture-lineament maps to delineate 10-year zones of transport for the two production wells (Olsen, 2004) (fig. 11).

Evaluation of Delineation Methods

The 10-year zones of transport delineated using the 

truncated-parabola and modified-ellipse methods, along with 

the 10-year zones of transport delineated previously by MDH, 

are shown on figures 3–11 for production wells in each of 

the nine communities included in this study. An evaluation 

of delineation methods for zones of transport indicates that 

the truncated-parabola and modified-ellipse methods can 

produce questionable results in karst and fractured-rock terranes. Substantial differences were seen in the size and shapes 

of most zones of transport delineated using these methods 

compared with the MDH zones of transport (figs. 3–11). Only 

the 10-year zones of transport for the two empirical methods 

were plotted on figures 3–11, because only 10-year zones of 

transport were used by MDH. Calculated parameters for the 

truncated parabolas and modified ellipses for both the 10-year 

and 20-year zones of transport are listed in tables 3 and 4, 

respectively. 

Table 3. X-axis coordinates for stagnation points, y-asymptotes, and water particle travel distances for 10-year and 20-year 

zones of transport obtained using the truncated-parabola method for production wells open to karst or fractured-rock aquifers, 

Minnesota.

[ft3/d, cubic foot per day]

Community Well number

Well discharge 

rate (ft3/d)

X-axis coordinates for stagnation point (ft)

Y-axis asymptotes (±ft) Water particle travel distance (ft)

XL YL 10-year 20-year

Askov 3 and 4 5,100 -84 270 2,050 4,100

Calumet 2 and 3 5,600 -110 350 14,600 29,200

Fridley 6, 7, and 8 170,000 -1,500 4,800 1,900 3,800

Fridley 11 97,000 -860 2,700 1,900 3,800

Fridley 12 100,000 -910 2,900 1,900 3,800

Fulda 1 and 6 15,000 -2,000 6,300 2,200 4,400

Hastings 3 68,000 -290 900 7,000 14,000

Hastings 4 58,000 -240 760 7,000 14,000

Hastings 5 84,000 -350 1,100 7,000 14,000

Hastings 6 100,000 -440 1,400 7,000 14,000

Hastings 7 110,000 -470 1,500 7,000 14,000

Keewatin 1 11,000 -380 1,200 1,100 2,200

Keewatin 2 6,000 -270 840 1,100 2,200

Le Center 1 38,000 -210 670 2,100 4,200

Le Center 3 3,000 -17 53 2,100 4,200

Marble 1 and 2 14,000 -300 950 1,460 2,920

Taconite 1 and 2 6,300 -450 1,400 8,600 17,200
Physical Description of Aquifers and Study Communities in Minnesota 23

Figure 11. Zones of transport delineated using the truncated-parabola and modified-ellipse methods and existing zone of 

transport delineated by the Minnesota Department of Health (MDH) for production wells in Fulda, Minnesota.

Fulda

Second

Lake

Fulda

1

6

Fulda

First Lake

Lime

Creek

95°38' 95°37' 95°36' 95°35’

43°53'

43°52'

Base from Minnesota Department of Transportation

Base Map 97, 1:24,000, 1997

UTM Zone 15 projection

0 0.5 1 MILE

0 0.5 1 KILOMETER

59

62

2

EXPLANATION

MDH 10-year zone of transport—wells 1 and 6

Sewage disposal ponds

10-year truncated parabola—wells 1 and 6

10-year modified ellipse—wells 1 and 6

Production well (number indicates well number) 1
24 Evaluation of Methods for Delineating Zones of Transport for Production Wells in Karst snd Fractured-Rock Aquifers

Table 4. X-axis coordinates, y-axis distances, and areas of ellipses for 10-year and 20-year zones of transport obtained using the 

modified-ellipse method for production wells open to karst or fractured-rock aquifers, Minnesota.

[ft3/d, cubic foot per day; mi2, square mile; ft, foot]

Community

Well 

number

Well 

discharge 

rate (ft3/d)

Area of 

ellipse (mi2)

Hydraulic parameters for

10-year zones of transport

Hydraulic parameters for

20-year zones of transport

X-axis coordinates (ft ) Y-axis 

coordinates 

(±ft)

X-axis coordinates (ft ) Y-axis 

coordinates 

X+ X- X+ X- (±ft)

Askov 3 and 4 5,100 0.04 2,300 -84 290 4,400 -84 150

Calumet 2 and 3 5,600 .36 15,000 -110 420 30,000 -110 220

Fridley 6, 7, and 8 170,000 .63 3,800 -1,300 2,200 6,300 -1,500 1,500

Fridley 11 97,000 .36 3,200 -820 1,600 5,500 -860 2,900

Fridley 12 100,000 .40 3,300 -870 1,700 5,600 -900 4,400

Fulda 1 and 6 15,000 .99 4,600 -1,700 2,800 7,500 -1,900 1,900

Hastings 3 68,000 .43 7,900 -290 970 15,000 -290 1,800

Hastings 4 58,000 .39 7,800 -240 830 15,000 -240 2,300

Hastings 5 84,000 .54 8,100 -350 1,200 15,000 -350 2,100

Hastings 6 100,000 .68 8,300 -440 1,400 15,000 -440 2,200

Hastings 7 110,000 .74 8,300 -470 1,500 16,000 -470 2,700

Keewatin 1 11,000 .09 1,800 -380 790 3,000 -380 490

Keewatin 2 6,000 .06 1,600 -270 620 2,800 -270 380

Le Center 1 38,000 .10 2,700 -210 630 4,900 -210 350

Le Center 3 3,000 .01 2,200 -17 64 4,300 -17 33

Marble 1 and 2 14,000 .10 2,100 -300 740 3,700 -300 440

Taconite 1 and 2 6,300 .86 10,000 -450 1,500 19,000 -450 810

All zones of transport delineated using the truncatedparabola and modified-ellipse methods were smaller in area 

than the MDH zones of transport, and most incorporated only 

a small portion of the MDH zone of transport (table 5). Notable exceptions to this were zones of transport delineated for 

the wells in Fulda, well 12 in Fridley, well 6 in Hastings, and 

well 1 in Keewatin. About two-thirds (67 percent) of the individual or composite truncated parabolas and modified ellipses 

covered less than 50 percent of the area incorporated by the 

MDH zones of transport (table 5). The shapes of some of 

the truncated parabolas and modified ellipses did not closely 

match the zones of transport delineated by the MDH using 

the calculated-fixed-radius methods and groundwater-flow 

models. This was particularly true for the zones of transport 

for the production wells in Calumet (fig. 3), Taconite (fig. 6), 

and Fridley (wells 6, 7, and 8) (fig. 9).

Calumet

The size and the shape of the truncated parabola and 

modified ellipse delineated for wells in Calumet are much 

different from the MDH 10-year zone of transport (fig. 3), 

although key hydraulic properties were the same (table 1). 

The truncated parabola and modified ellipse are more elongated than the MDH zone of transport, stretching to the Swan 

River approximately 3 miles southwest of the production wells 

(fig. 3). The truncated parabola and modified ellipse covered 

9 percent and 8 percent, respectively, of the MDH zone of 

transport (table 5). The low porosity (0.01) used to delineate 

the truncated parabola and modified ellipse resulted in long, 

10-year travel distances for both methods (tables 3 and 4), 

resulting in the elongated zones. In comparison, the higher 

porosity (0.1) used for the truncated parabola and modified 

ellipse for the production wells in Marble resulted in shorter, 

10-year travel distances than in Calumet (table 3 and 4) and 

shorter, wider zones (fig. 5).

Keewatin

The truncated parabolas and modified ellipses for the 

production wells in Keewatin were much smaller than the 

MDH zone of transport (fig. 4). The truncated parabola and 

modified ellipse for well 1 each covered 56 percent of the 

MDH calculated-fixed radii delineated for the well (table 5). 

The truncated parabola and modified ellipse for well 2 each 

covered 43 percent of the MDH calculated-fixed radii delineated for the well (table 5). For well 1, the truncated parabola 

and modified ellipse cover more of the upgradient watershed 

than the MDH zone of transport (fig. 4). Like the zones of 

transport for most production wells in the Mesabi Iron Range, 

the orientation, shape, and size of these zones of transport 

likely will change as dewatering activities change when local 

mine pits are developed or closed.
Evaluation of Delineation Methods 25

Table 5. Areas of empirical-method 10-year zones of transport within Minnesota Department of Health (MDH) delineated 10-year 

zones of transport for production wells open to karst or fractured-rock aquifers, Minnesota.

[Values in parentheses are the percentage of the area of empirical-method zones of transport that is within MDH zones of transport; mi2, square mile]

Community

Well 

number

Area of zone of transport (mi2) 

Area of empirical-method zones of transport within MDH zones of transport (mi2

)

MDH delineation

Truncated 

parabola method

Modified ellipse

method

Truncated 

parabola method

Modified ellipse

method

Askov 3 and 4 10.22 0.04 0.04 0.04 (18) 0.04 (18)

2

.69 3.25 3.28 .23 (33) .26 (38)

Calumet 2 and 3 41.18 .36 .36 .11 (9) .09 (8)

Fridley 6, 7, and 8 51.77 6.56 6.63 .55 (31) .63 (36)

Fridley 11 5.61 .29 .36 .28 (46) .33 (54)

Fridley 12 5.58 .32 .40 .31 (53) .40 (69)

Fulda 1 and 6 4.78 .89 .99 .49 (63) .73 (94)

Hastings 3, 4, and 5 52.45 71.13 71.25 1.13 (46) 1.25 (51)

Hastings 6 5.83 .59 .68 .49 (59) .52 (63)

Hastings 7 52.32 .62 .74 .62 (27) .74 (32)

Keewatin 1 8,9.09 .08 .09 .05 (56) .05 (56)

Keewatin 2 8,9.07 .05 .06 .03 (43) .03 (43)

Le Center 1 and 3 5.55 10.09 10.11 .09 (16) .11 (20)

Marble 1 and 2 4.40 .08 .10 .08 (20) .10 (25)

Taconite 1 and 2 42.28 .11 .86 .11 (5) .70 (31)

1

Zone of transport delineated using calculated-fixed-radius equations, geologic maps, sinkhole maps, and fracture-lineament maps.

2

Area of MDH wellhead protection area.

3

Total area covered by eight zones of transport oriented at different groundwater-flow directions.

4

Zone of transport delineated using calculated-fixed-radius method with an upgradient extension.

5

Zone of transport delineated using a groundwater-flow model.

6

Area is the sum of zones of transport for wells 6, 7, and 8.

7

Area is the sum of zones of transport for wells 3, 4, and 5.

8

Zone of transport delineated using calculated-fixed-radius method with an upgradient extension.

9

Area of calculated-fixed-radius zone around well.

10Area is the sum of zones of transport for wells 1 and 3.

Marble

The truncated parabola and modified ellipse delineated 

for the production wells in Marble are smaller than the MDH 

10-year zone of transport delineated using the calculatedfixed-radius method combined with an upgradient extension 

(fig. 5). The zones of transport delineated using empirical 

methods for wells 1 and 2 covered 20 percent (truncated 

parabola) and 25 percent (modified ellipse) of the MDH zone 

of transport (table 5).

Taconite

The truncated parabola and modified ellipse delineated 

for the production wells in Taconite are shorter and more elongated, respectively, than the MDH 10-year zone of transport 

for the wells (fig. 6). The truncated parabola and modified 

ellipse covered 5 percent and 31 percent, respectively, of the 

MDH zone of transport (table 5). The smaller aquifer saturated thickness (94 feet) for the Taconite wells compared with 

those of other communities on the Mesabi Iron Range (Calumet, Keewatin, and Marble) and low porosity (0.01) (table 

1) resulted in a larger area difference between the truncated 

parabola and the modified ellipse. Similar to the wells in Calumet, the low porosity (0.01) used to delineate the modified 

ellipse resulted in long, 10-year travel distances for both methods (tables 3 and 4), and elongated zones resulted. However, 

the small aquifer thickness (94 feet) compared with the aquifer 

thickness at the Calumet wells (200 feet) resulted in larger XL

and YL values for the truncated parabola for the production 

wells in Taconite (table 3), thus resulting in more groundwater 

obtained downgradient and nearer to the well (fig. 6) than for 

the production wells in Calumet (fig. 3).
26 Evaluation of Methods for Delineating Zones of Transport for Production Wells in Karst snd Fractured-Rock Aquifers

Askov

In general, the MDH zone of transport and WHPA for 

wells 3 and 4 in Askov are more conservative (larger) than the 

truncated parabolas and modified ellipses, even when truncated parabolas and modified ellipses in multiple directions are 

considered. Both the truncated parabola and modified ellipse 

delineated for the production wells in Askov were smaller in 

area and in upgradient extent when compared to the MDH 

zone of transport delineated using calculated-fixed-radius 

methods combined with an upgradient extension (fig. 7). Both 

the truncated parabola and modified ellipse covered only 

18 percent of the MDH zone of transport (fig. 7 and table 5). 

The truncated parabolas and modified ellipses were smaller 

than the MDH zone of transport because a well discharge rate 

(in cubic feet per day) was used for these methods rather than 

a total well discharge (cubic feet) over the 10-year time period 

that was used for the calculated-fixed-radius method (See Differences Between Delineation Methods Section). As a result, 

a larger zone of transport was delineated using the calculatedfixed-radius method when compared to the two empirical 

methods used for this study.

The truncated parabola and modified ellipse were 

extended from the wells in eight different potential groundwater-flow directions identified in the MDH zone-of-transport 

analysis (fig. 7). This was done to create a composite truncated 

parabola and a composite modified ellipse to compare to the 

WHPA (fig. 7), which was delineated by MDH by calculating a fixed radius and extending it in eight directions to the 

location of sinkholes, wetlands, and a buried bedrock valley 

(Haglund, 2007). The composite truncated parabola covered 

33 percent of the WHPA, and the composite modified ellipse 

covered 38 percent of the WHPA (table 5). The larger WHPA 

includes many of the sinkholes near the production wells, 

but the composite truncated parabola and composite modified ellipse do not include sinkholes north, east, west, and 

southwest of the production wells. Extension of the truncated 

parabolas and modified ellipses that extend to the north, west, 

and east to the hydrogeologic features used to delineate the 

WHPA in those directions would incorporate more of the 

sinkholes (fig. 7).

Fridley

All of the truncated parabolas and modified ellipses 

for the five production wells evaluated in Fridley and that 

are open to the Prairie du Chien-Jordan aquifer are smaller 

but similar in shape to the MDH 10-year zones of transport 

(fig. 8). The composite truncated parabola and composite modified ellipse for wells 6, 7, and 8 covered only 31 percent and 

36 percent, respectively, of the MDH zone of transport for the 

wells (table 5). The truncated parabola and modified ellipse 

for well 11 covered 46 percent and 54 percent, respectively, 

of the MDH composite zone of transport delineated for the 

well (fig. 8 and table 5). The truncated parabola and modified 

ellipse for well 12 were the best fit to the MDH zones of 

transport for any of the production wells in Fridley. The 

truncated parabola and modified ellipse covered 53 percent 

and 69 percent, respectively, of the MDH zone of transport 

delineated for the well (table 5). Groundwater extraction from 

22 other high-capacity wells near the Fridley production wells 

was taken into account in the groundwater-flow model used 

to delineate the MDH zones of transport, but it was not taken 

into account in the delineation of the truncated parabolas and 

modified ellipses. This water extraction could explain the 

larger MDH zones of transport compared with those delineated by the truncated-parabola and modified-ellipse methods.

Hastings

All of the truncated parabolas and modified ellipses 

for the five production wells in Hastings that are open to the 

Jordan aquifer are smaller than the MDH 10-year zones of 

transport (fig. 9). The total area for the composite truncated 

parabola and composite modified ellipse for wells 3, 4, and 5 

covered 46 percent and 51 percent, respectively, of the MDH 

composite zone of transport for the wells (table 5). The truncated parabola and modified ellipse for well 4 seem to be good 

fits to the portion of the MDH composite zone of transport (for 

wells 3, 4, and 5) that is upgradient from the well (fig. 9).

The truncated parabola and modified ellipse for well 6 

covered 59 percent and 63 percent, respectively, of the MDH 

zone of transport delineated for the well (table 5). Both the 

truncated parabola and modified ellipse for the well extend 

farther upgradient than the MDH zone of transport, but they 

are smaller in the direction perpendicular to flow (fig. 9). A 

larger hydraulic gradient used in the empirical methods than 

that determined by the groundwater-flow model in the vicinity 

of well 6 may explain these differences. The truncated parabola and modified ellipse for well 7 covered only 27 percent 

and 32 percent, respectively, of the MDH zone of transport 

delineated for the well (table 5).

Groundwater extraction from other high-capacity wells 

near the production wells in Hastings was taken into account 

in the groundwater-flow model used to delineate the MDH 

zones of transport, but it was not taken into account in 

delineation of the truncated parabolas and modified ellipses. 

Similar to the zone-of-transport analyses in Fridley, this 

water extraction could result in larger MDH zones of transport compared with the zones of transport delineated by the 

truncated-parabola and modified-ellipse methods. This is 

particularly true for the composite MDH zone of transport for 

wells 3, 4, and 5 and the MDH zone of transport for well 7 

(fig. 9).

Le Center

The truncated parabolas and modified ellipses for 

the production wells in Le Center were much smaller than the 

MDH composite zone of transport for the wells (fig. 10). 
Implications of Zone-of-Transport Delineations 27

The sum of the truncated parabolas and modified ellipses 

for wells 1 and 3 covered only 16 percent and 20 percent, 

respectively, of the MDH composite zone of transport delineated for the wells (table 5). No high-capacity wells extract 

groundwater from the Prairie du Chien and Jordan aquifers 

near the production wells in Le Center (Blum, 2003); therefore, additional groundwater extraction not taken into account 

in the truncated-parabola and modified-ellipse methods is 

an unlikely cause for the difference between the empirically 

derived zones of transport and the MDH zone of transport. 

In the groundwater-flow model used to delineate the MDH 

zone of transport, the Prairie du Chien aquifer and the Jordan 

aquifer were simulated as separate aquifers with separate 

sets of hydraulic parameters (Blum, 2003). The two aquifers 

were combined in the truncated-parabola and modified-ellipse 

analyses, which used weighted-mean values of the hydraulic 

conductivities and porosities used in the groundwater-flow 

model for the two hydrogeologic units. The combining of the 

hydrogeologic units for the empirical methods rather than 

separate simulations of the units may explain the differences in 

the areas covered by the empirically derived zones of transport 

and MDH zone of transport.

Fulda

Of the nine communities for which zones of transport 

were delineated, the truncated parabola and modified ellipse 

for the two production wells in Fulda best fit the MDH zones 

of transport (fig. 11). The areas of the truncated parabola and 

modified ellipse only covered 63 percent and 94 percent, 

respectively, of the MDH zone of transport delineated for the 

wells (table 5), but are larger than the MDH zone of transport 

(fig. 11). Both the truncated parabola and modified ellipse 

cover more of the aquifer downgradient from the well than the 

MDH zone of transport (fig. 11). 

The better fit between the MDH and empirical-methods 

zones of transport for the Fulda wells compared with results 

for other study communities where the calculated-fixed-radius 

method combined with an upgradient extension was used 

to delineate the MDH zones of transport (Askov, Calumet, 

Marble, and Taconite) may be explained by the method used 

to composite multiple well zones of transport. The MDH zone 

of transport was delineated based on a composite calculatedfixed radius determined from two overlapping, separate zones 

of transport delineated for wells 1 and 6 (Olsen, 2004). The 

composite calculated-fixed radius was extended upgradient 

(west) in the direction of preferential fracturing in the aquifer to a buried bedrock valley (Olsen, 2004). The truncated 

parabola and modified ellipse for the production wells in Fulda 

were delineated on the basis of a single well representation 

of the two wells that combined the total pumping rates for 

the two wells in the calculation of a single truncated parabola 

and modified ellipse for the wells. This approach was used to 

delineate truncated parabolas, modified ellipses, and MDH 

zones of transport for the other communities for which the 

calculated-fixed-radius method combined with an upgradient 

extension was used. This combination of the discharge rates 

of the two wells prior to zone-of-transport delineation, rather 

than a composite of the two separate zones of transport for the 

two wells, may have resulted in the truncated parabola and 

modified ellipse being larger than the MDH zone of transport.

Implications of Zone-of-Transport 

Delineations

The large variability in size and shape of the zones of 

transport using the truncated-parabola and modified-ellipse 

methods delineated for the nine communities raises questions about the validity of using these methods in karst and 

fractured-rock settings. The variations often were largest when 

local hydrogeologic data were not available and regional 

values for hydraulic properties were used in the equations. For 

example, a lack of site-specific values of permeability, aquifer 

thicknesses, and porosity for the Biwabik Iron Formation 

resulted in various shapes and sizes for the wells in Calumet, 

Keewatin, Marble, and Taconite. These large variations had 

less effect on the final drinking-water-supply management area 

(DWSMAs) delineations where hydrologic boundaries were 

close to the production wells; for example, where the mine 

pits are near the production wells in Keewatin. The DWSMAs 

are surface and subsurface management and protection areas 

delineated around production wells using identifiable geographical landmarks that reflect as closely as possible the scientifically calculated zones of transport boundaries (Minnesota 

Department of Health, 2009b).The DWSMAs delineated by 

MDH typically were much larger than the zones of transport 

delineated for the communities.

Results from the empirical methods are particularly 

questionable under complex flow settings where many highcapacity wells or active mining operations are located in the 

vicinity of the production wells. These empirical methods 

did not take this additional water extraction into account. 

The methods tend to underestimate the extent of the zones of 

transport, particularly upgradient from the well, and this was 

true for the communities of Fridley and Hastings, where MDH 

zones of transport account for the additional water extraction 

in their groundwater-flow models. If this additional water 

extraction could be accounted for in the empirical methods, 

then the areas of the zones of transport may be similar to the 

zones of transport delineated by groundwater-flow models 

for some of the wells. Mining operations in the Mesabi Iron 

Range of Minnesota change their dewatering operations 

over time on the basis of mine expansion, closure, and local 

community water-use needs. Changes in dewatering activities can result in substantial changes in hydraulic gradients 

and groundwater-flow directions. As the water level rises in 

an abandoned mine pit following cessation of dewatering, the 

mine pits may become incorporated into a zone of transport 

and provide water to the well. Mine dewatering activities and 

any changes to them, therefore, need to be addressed in any 

zone-of-transport analyses for local production wells. 
28 Evaluation of Methods for Delineating Zones of Transport for Production Wells in Karst snd Fractured-Rock Aquifers

The application of the truncated-parabola method 

for the production wells in Askov demonstrated that if the 

truncated-parabola method is applied in karst and fracturedrock settings, the parabola needs to be extended at least to 

local hydrogeologic boundaries to include possible identified 

or unidentified upgradient karst features and fractures near 

the wells. This is similar to the approach used for the MDH 

calculated-fixed-radius method combined with upgradient 

extensions. The WHPA for the production wells in Askov, 

which was delineated by MDH by using extensions, included 

many sinkholes near the municipal wells; however, the composite truncated parabola, which was not extended, excluded 

many sinkholes near the production wells (fig. 7). Extension 

of the truncated parabolas to known hydrogeologic boundaries incorporated many, but not all, sinkholes. Hydrogeologic 

mapping could confirm that all karst features and fractures are 

included in the final WHPA.

With the exception of Askov, results from the application 

of the empirical methods to wells in the selected communities indicated that more field characterization at specific sites 

would be needed to support the use of these empirical zoneof-transport delineation methods. The assumption that Darcian 

flow governs groundwater flow in the zones of transport would 

have to be validated before the application of any zone-oftransport delineation methods that do not account for groundwater-flow conditions in solution channels and fractures. Data 

collection would contribute to the accomplishment of this validation, to the determination of the hydraulic properties needed 

for the zone-of-transport methods, and to a better understanding of the flow conditions to the well. Data requirements may 

include solution channel or fracture density, orientations, 

apertures dimensions, and other factors controlling water flow 

through the features.

The large scale of zones of transport commonly can 

make data collection for some detailed information impractical. Many equations and models exist for accounting for 

non-Darcian, groundwater flow through solution channels and 

fractures and for assessing dual primary and secondary permeability conditions (Faybishenko and others, 2000; Mackie, 

1983). However, the practical application of these equations is 

lacking due to deficiencies in existing data and lack of detailed 

knowledge of the physical setting of the flow system; more 

complete information would improve the application of the 

equations and enhance understanding of the scale of the zones 

of transport.

A possible data collection approach to characterizing 

groundwater-flow conditions in the vicinity of a well in karst 

and fractured-rock settings could include the following steps: 

(1) creation of hydrogeologic maps, (2) aquifer/pumping tests, 

(3) water-quality/age-dating analyses, (4) borehole geophysical logging, hydrologic, and water-quality analyses, (5) surficial geophysical studies, and (6) dye tracing and water-quality 

tests. This data collection approach can be used to verify the 

assumption of Darcian flow conditions within a zone of transport, to characterize fracture-flow conditions in the vicinity 

of the well, and to determine an appropriate zone-of-transport 

delineation method to be used. For small communities that have 

limited resources to expend on studies, this approach could be 

done incrementally, over many years.

The inclusion of any karst and fractured-rock features that 

are identified through hydrogeologic mapping, near production wells and in any protection area delineated for the wells, 

would contribute to improved protection of the water supply. 

Hydrogeologic mapping techniques could include mapping 

of surficial features, such as sinkholes and springs, outcrop 

fractures, stream patterns, type of karst aquifer, such as epikarst 

and paleokarst, and lineaments. The Tennessee Division of 

Water Supply delineated a protection zone for the water supply 

of the small town of Orme, Tenn., by surveying the locations 

and elevations of various karst features in the drainage area for 

the spring (Schroll and McCormick, 1999). They found this 

approach to produce an effective protection area for the water 

supply without the cost and possible water disruptions of tracer 

tests. 

Existing water-level data from aquifer or pumping tests 

and existing water-quality data from a well can be interpreted 

to provide an initial indication of the influence of fractures 

or solution channels on groundwater flow to a well. Aquifer 

and specific-capacity tests commonly are done on production 

wells installed in Minnesota as part of an aquifer test plan for 

delineating a wellhead protection area (Minnesota Department 

of Health, 2010a). Assessment of the water-level data from 

an aquifer test may indicate if groundwater flow to the well is 

diffuse or if it results from a single fracture or set of fractures 

(Gernand and Heidtman, 1997). Water-quality analyses for 

bacteria, nitrate, arsenic, and other water-quality constituents 

are required for public supply wells in Minnesota (Minnesota 

Department of Health, 2010b). Water-quality analyses and 

age dating of water, such as analyses for chlorofluorocarbons 

(CFCs), sulfur hexafluoride (SF6), or tritium-helium, may 

indicate if the groundwater is from shallow or deeper solution 

channels or fractures. Water-quality analyses and isotopic characterization of well water and nearby surface-water bodies can 

be helpful for identifying groundwater and surface-water interactions and upgradient sources of water to a production well, 

as was done by Walsh (2004) for the MDH zone-of-transport 

analysis for the Keewatin wells.

If downhole access to the well is available, then borehole 

techniques are valuable for determining the location, geologic 

formations, and flow characteristics of major fractures or zones 

of fractures contributing water to the well. These techniques 

may include the application of borehole flow meters, packers, 

caliper logging tools, gamma logging tools, and water-quality 

sampling at discrete solution channels or fractures in the well. 

If the well is only accessible by a small-diameter monitoring pipe within the well, then less pervasive techniques, such 

as continuous downhole water-temperature and water-quality 

probes, may provide some insight into where water is entering 

the well and how it may vary seasonally and over storm events. 

Once a potential link between surficial and borehole features 

is suspected, surficial geophysical techniques, dye tracing, and 

water-quality sampling may be done to verify these linkages.
Summary 29

The cost and long-time period required for conducting 

a detailed analysis of groundwater-flow conditions in or near 

production wells may be excessive for small communities. 

Where this is true, communities may consider taking one of 

the following approaches: (1) assessment of the vulnerability 

of the water supply to potential contamination and of the cost 

of follow-up water treatment or water-supply replacement or 

(2) delineation of large protection areas incorporating multiple 

production wells. For example, the Center of Hydrogeology 

of the University of Neuchâtel, Switzerland, developed and 

applied a multi-attribute approach to mapping intrinsic vulnerability of a karst catchment area for a well or spring to be used 

to define protection zones (Doerfliger and others, 1999). Four 

attributes of a karst aquifer were considered in this approach: 

(1) level of epikarst development, (2) thickness and hydrogeology of protective cover, (3) type of recharge (diffuse or 

concentrated) to the karst aquifer, and (4) solution channel 

network development. These attributes are weighted and subdivided into classes that are mapped over the catchment area 

of the well or spring.

The costs of water treatment or water-supply replacement 

can be high, depending upon the treatment needed, the type of 

replacement water (surface or groundwater), and the water distribution system. Options for replacing a current water supply 

that is contaminated may include locating new wells outside of 

the contaminated area or using potential surface-water sources. 

The cost of additional water treatment for surface waters used 

for drinking water is a substantial consideration in the cost 

assessment.

The delineation of large protection areas to protect 

many water supplies has been applied in karst settings. This 

approach commonly is used in karst and fractured-rock settings where little is known of groundwater-flow paths. The 

Ohio Environmental Protection Agency and the Great Lakes 

Rural Community Assistance Program delineated an entire 

region where water is contributed to wells by a karst aquifer 

in northwestern Ohio as a drinking-water source protection 

area, encompassing 15 water supplies (U.S. Environmental 

Protection Agency, 2010). Delineation of a large protection 

area around multiple water supplies requires an inventory and 

the management of a large number of potential sources of 

contamination.

Summary

Communities in northern, southeastern, and southwestern Minnesota use production wells to extract groundwater 

from bedrock aquifers in which groundwater flows through 

karst features and fractures. Source waters for these wells are 

particularly vulnerable to contamination mainly due to short 

residence times for groundwater in these aquifers. Several 

approaches that account for flow through solution channels or 

fractures have been used to delineate zones of transport around 

wells that obtain groundwater from karst and fractured-rock 

aquifers. However, the more detailed approaches to zone-oftransport delineation commonly are too expensive and impractical for many Minnesota communities using groundwater 

from karst and fractured-rock aquifers. Simple, less empirical methods that apply porous media equations and existing 

hydrogeologic data are available; however, the accuracy of 

zones of transport delineated by using empirical methods may 

be questionable for complex karst and fractured-rock settings.

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

with the Minnesota Department of Health (MDH), applied 

and evaluated two empirical methods—the truncated-parabola 

and modified-ellipse methods—to 24 production wells that 

extract groundwater from karst and fractured-rock aquifers 

in nine Minnesota communities. These wells extracted water 

from a karst aquifer (Prairie du Chien and Jordan aquifers), 

porous aquifers interspersed with solution-enhanced fractures (Jordan and Hinckley aquifers), or fractured-bedrock 

aquifers (Biwabik Iron Formation and Sioux Quartzite 

aquifers), which are confined or unconfined depending on 

location. Two of the production wells evaluated in this study 

(Hastings wells 4 and 5) also extract water from the St. Lawrence Formation, and one production well (Fridley well 11) 

also extracts water from the St. Lawrence Formation and Franconia Sandstone. The St. Lawrence Formation and Franconia 

Sandstone were not included in zone-of-transport delineations 

done in this study. Results from application of these methods 

were compared with zones of transport previously delineated 

by MDH hydrologists for the wells. The study focused on 

producing zones of transport using existing data and empirical 

methods.

The truncated-parabola and modified-ellipse methods 

are calculated-variable-shape methods that delineate zones of 

transport based on the superposition of the effects of uniform 

flow gradients on the effects of the pumping well. These methods use hydrogeologic properties for which values typically 

are available to water suppliers and managers or can be estimated from literature values. Both empirical methods assume 

porous-media (Darcian) flow conditions in the aquifer. The 

application of zone-of-transport delineation methods derived 

under the assumptions of Darcian flow to karst and fracturedrock settings requires scrutinization.

Large differences were seen in the size and shapes 

of most zones of transport delineated using the truncatedparabola and modified-ellipse methods compared with the 

MDH zones of transport. In general, the zones of transport 

delineated using the truncated-parabola and modified-ellipse 

methods were smaller in area than the MDH zones of transport and incorporated only a small portion of the MDH zone 

of transport. About two-thirds (67 percent) of the individual 

or composite truncated parabolas and modified ellipses 

covered less than 50 percent of the area incorporated by the 

MDH zones of transport. The shapes of some of the truncated 

parabola and modified ellipses did not closely match the MDH 

delineated zones of transport, which were delineated by use 

of the calculated-fixed-radius methods and groundwater-flow 

models.
30 Evaluation of Methods for Delineating Zones of Transport for Production Wells in Karst snd Fractured-Rock Aquifers

Differences between the truncated-parabola and modified-ellipse zones of transport and MDH zones of transport 

can be explained by variations inherent to the methods and in 

the amount of complexity taken into account by groundwaterflow models. The calculated-fixed-radius method combined 

with an upgradient extension used by MDH to delineate zones 

of transport for wells in the communities of Askov, Calumet, 

Fulda, Marble, and Taconite is more conservative and produces larger zones of transport than the zones of transport 

delineated by the truncated-parabola and modified-ellipse 

methods. This is because the calculated-fixed-radius method 

uses a total discharge (in cubic feet) over the specified time 

period, for this application 10 years, for the amount of flow 

through the well rather than a well discharge rate (in cubic feet 

per day). Groundwater-flow models used to delineate some of 

the MDH zones of transport for wells in Fridley, Hastings, and 

Le Center accounted for the influence of groundwater extraction from nearby multiple large-capacity wells, which was not 

taken into account in the two empirical methods. Results from 

zone-of-transport analyses for the wells in Askov indicated 

that if the truncated-parabola method is applied in karst and 

fractured-rock settings, then the parabola needs to be extended 

at least to local hydrogeologic boundaries to include possible 

identified or unidentified upgradient karst features or fractures 

near the wells.

In general, additional field hydrogeologic characterization 

would be needed at specific sites to support the use of these 

empirical zone-of-transport delineation methods. Results from 

the evaluation of the empirical methods indicate that the application of the truncated-parabola and modified-ellipse methods 

using limited existing hydrogeologic information can produce questionable results in karst and fractured-rock settings, 

particularly in areas where many high-capacity wells or active 

mining operations are present in the vicinity of the production well. The assumption that Darcian flow conditions govern 

groundwater flow in the zones of transport would need to be 

supported using site-specific hydrogeologic characterization 

before applying any zone-of-transport delineation methods 

that do not account for groundwater-flow conditions in solution channels and fractures. Hydrogeologic data collection to 

support groundwater-flow characterization in the vicinity of a 

production well may include hydrogeologic mapping, aquifer 

or pumping tests, water-quality and age-dating analysis of 

local surface and groundwater, borehole geophysical logging, 

surficial geophysical analyses, and dye tracing. For communities that have a limited amount of resources to expend on 

studies, data-collection efforts could be done incrementally 

over many years.

References Cited

Austin, G.S., 1972, The Sioux Quartzite, southwestern 

Minnesota, in Sims, P.K., and Morey, G.B., eds., Geology 

of Minnesota—a centennial volume: Minnesota Geological 

Survey, p. 450–455.

Bair, E.S., and Roadcap, G.S., 1992, Comparison of flow 

models used to delineate capture zones of wells—1. Leakyconfined fractured-carbonate aquifer: Ground Water, v. 30, 

no. 2, p. 199–211.

Barr Engineering, 2003, Wellhead protection plan for the city 

of Hastings, Minnesota, part 1: Minnesota Department of 

Health, 35 p.

Barton, G.J., Risser, D.W., Galeone, D.G., and Goode, D.J., 

1999, Case study for delineating a contributing area to a 

water-supply well in a fractured crystalline-bedrock aquifer, 

Stewartstown, Pennsylvania: U.S. Geological Survey 

Water-Resources Investigations Report 99–4047, 38 p.

Barton, G.J., Risser, D.W., Galeone, D.G., and Goode, 

D.J., 2003, Case study for delineating a contributing 

area to a well in a fractured siliciclastic-bedrock aquifer 

near Lansdale, Pennsylvania: U.S. Geological Survey 

Water-Resources Investigations Report 02–4217, 46 p.

Berg, J.A., 2004, Hydrogeology of the unconsolidated 

and bedrock aquifers, in Geologic atlas of Pine County, 

Minnesota, part B, hydrogeology: Minnesota Department of 

Natural Resources, County Atlas Series C–13, plate 8.

Blum, J.L., 2003, Wellhead protection plan for the city of 

Le Center, Minnesota, part 1: Minnesota Department of 

Health, 28 p.

Bradbury, K.R., Muldoon, M.A., Zaporozec, A., and Levy, J., 

1991, Delineation of wellhead protection areas in fractured rocks: Wisconsin Geological and Natural History 

Survey/U.S. Environmental Protection Agency Report EPA 

570/9–91–009, 144 p.

Delin, G.N., and Almendinger, J.E., 1991, Delineation of 

recharge areas for selected wells in the St. Peter Prairie du Chien-Jordan aquifer, Rochester, Minnesota: 

U.S. Geological Survey Water-Supply Paper 2397, 39 p.

Doerfliger, N., Jeannin, P.Y., and Zwahlen, F., 1999, Water 

vulnerability assessment in karst environments—a new 

method of defining protection areas using a multi-approach 

and GIS tools (EPIK method): Environmental Geology, 

v. 39, no. 2, p. 165–176.

Faybishenko, B., Witherspoon, P.A., and Benson, S.M., 2000, 

Dynamics of fluids in fractured rock: American Geophysical 

Union, Geophysical Monograph, 122, 400 p.
References Cited 31

Fetter, C.W., 2001, Applied hydrogeology: Upper Saddle 

River, New Jersey, Prentice Hall, Inc., 598 p.

Gernand, J.D., and Heidtman, J.P., 1997, Detailed pumping 

test to characterize a fractured bedrock aquifer: Ground 

Water, v. 35, no. 4, p. 632–637.

Haglund, G., 2007, Wellhead protection plan for the city of 

Askov, Minnesota, part 1: Minnesota Department of Health, 

46 p.

Jennings, C.E., and Reynolds, W.K., 2005, Surficial geology of the Mesabi Iron Range, Minnesota: Minnesota 

Geological Survey, Miscellaneous Map Series, Map M–164.

Jirsa, A., Chandler, V.W., and Lively, R.S., 2005, Bedrock 

geology of the Mesabi Iron Range, Minnesota, Minnesota 

Geological Survey, Miscellaneous Map Series, Map M–163.

Jones, P.M., 2002, Characterization of ground-water flow 

between the Canisteo mine pit and surrounding aquifers, 

Mesabi Iron Range, Minnesota: U.S. Geological Survey 

Water-Resources Investigations Report 02–4198, 30 p.

Kanivetsky, R., 1978, Hydrogeologic map of Minnesota, 

bedrock hydrogeology: Minnesota Geologic Survey, sheet 

1 (map), sheet 2 (cross-sections) and accompanying text, 

scale 1:500,000.

Kenny, J.F., Barber, N.L., Hutson, S.S., Linsey, K.S., 

Lovelace, J.K., and Maupin, M.A., 2009, Estimated use of 

water in the United States in 2005: U.S. Geological Survey 

Circular 1344, 52 p.

Knochenmus, L.A., and Robinson, J.L., 1996, Descriptions 

of anisotropy and heterogeneity and their effect on groundwater flow and areas of contribution to public supply wells 

in a karst carbonate aquifer system: U.S. Geological Survey 

Water-Supply Paper 2475, 47 p.

Long, J.C.S., Remer, J.S., Wilson, C.R., and Witherspoon, 

P.A., 1982, Porous media equivalents for networks of 

discontinuous fractures: Water Resources Research, v. 18, 

no. 3, p. 645–658. 

Mackie, C.D., 1983, Determination of non-linear formation 

losses in pumping wells: Proceedings of the International 

Conference on Groundwater and Man, Sydney, Australia, 

p. 199–210.

Minnesota Department of Health, 2005a, Wellhead protection, 

accessed May 11, 2005, at http://www.health.state.mn.us/

divs/eh/water/swp/whp/index.htm.

Minnesota Department of Health, 2005b, Tools for wellhead 

protection teams, accessed May 11, 2005, at http://www.

health.state.mn.us/divs/eh/water/swp/whp/whptools.html.

Minnesota Department of Health, 2005c, Guidance for delineating wellhead protection areas in fractured and solutionweathered bedrock: Minnesota Department of Health, 87 p.

Minnesota Department of Health, 2009a, Community 

public water supply general information, accessed 

October 29, 2009, at http://www.health.state.mn.us/divs/eh/

water/com/index.htm.

Minnesota Department of Health, 2009b, Wellhead protection 

area delineation, accessed October 30, 2009, at http://www.

health.state.mn.us/divs/eh/water/swp/whp/fs/swpadfs.htm.

Minnesota Department of Health, 2010a, Wellhead protection 

area delineation, accessed January 20, 2010, at http://www.

health.state.mn.us/divs/eh/water/swp/whp/fs/swpadfs.html.

Minnesota Department of Health, 2010b, Monitoring and 

testing of drinking water in Minnesota, accessed January 

20, 2010, at http://www.health.state.mn.us/divs/eh/water/

factsheet/com/sampling.html.

Minnesota Department of Natural Resources, 2006, Mesabi 

iron range mine features, Arc/Info export files and shape 

files of mine features: CD-ROM data.

Minnesota Department of Natural Resources, 2010, Water 

use–water appropriations permit program, accessed 

January 19, 2010, at http://www.dnr.state.mn.us/waters/

watermgmt_section/appropriations/wateruse.html.

Morey, G.B., 1972, Mesabi Range, in Sims, P.K., and Morey, 

G.B., eds., Geology of Minnesota—a centennial volume: 

Minnesota Geological Survey, p. 204–217.

Olsen, B., 2004, Wellhead protection plan for the city of 

Fulda, Minnesota, part 1: Minnesota Department of Health, 

37 p.

Patterson, C.J., and Knaeble, A.R., 2001, Surficial geology, in

Geologic atlas of Pine County, part A, geology Minnesota: 

Minnesota Geological Survey, County Atlas Series C–13, 

part A, plate 4.

Podgorney, R.K., and Ritzi, R.W., Jr., 1997, Capture zone 

geometry in a fractured carbonate aquifer: Ground Water, 

v. 35, no. 6, p. 1040–1049.

Robertson, S.W., 2002, Wellhead protection plan for the city 

of Fridley, Minnesota, part 1: Minnesota Department of 

Health, 59 p.

Runkel, A.C., Tipping, R.G., Alexander, E.C., Jr., Green, 

J.A., Mossler, J.H., and Alexander, S.C., 2003, Hydrogeology of the Paleozoic bedrock in southeastern Minnesota: 

Minnesota Geological Survey Report of Investigations 61, 

105 p., 2 pls.
32 Evaluation of Methods for Delineating Zones of Transport for Production Wells in Karst snd Fractured-Rock Aquifers

Scholl, J.S., and McCormick, J.R., 1999, Delineation of the 

recharge area for a karst spring serving a small community 

on the Cumberland Plateau Escarpment: Proceedings of 

the National Cave and Karst Management Symposium, 

Chattanooga, Tennessee, p. 178–182.

Shade, B.L., Alexander, C.A., Alexander, S.C., and Martin, 

S., 2001, Sinkhole distribution, in Geologic atlas of Pine 

County, Minnesota, part A, geology: Minnesota Geological 

Survey, County Atlas Series C–13, part A, plate 6.

Shade, B.L, Alexander, S.C., and Alexander, E.C., Jr., 2002, 

Karst features in Pine County, Minnesota, in Contributions to the geology of Pine County, Minnesota: Minnesota 

Geological Survey, Report of Investigations 60, p. 53–70.

Todd, D.K., 1980, Groundwater hydrology: New York, N.Y., 

John Wiley and Sons, 535 p.

U.S. Census Bureau, 2005, American FactFinder, population finder: Information available on the Web, accessed 

March 13, 2007, at http://www.census.gov/.

U.S. Environmental Protection Agency, 1987, Guidelines for delineation of wellhead protection areas: U.S. 

Environmental Protection Agency, EPA 440/6–87–010.

U.S. Environmental Protection Agency, 1993, Guidelines for 

delineation of wellhead protection areas: U.S. Environmental 

Protection Agency, EPA 440–5–93–001; update of same 

document produced in 1987 (EPA 440/6–87–010). 

U.S. Environmental Protection Agency, 2010, Our goal: all people in Region 5 served by public water supplies will have water 

that is consistently safe to drink, accessed February 8, 2010, at 

http://www.epa.state.oh.us/ddagw/pdu/swap_karst.html. 

Walsh, J.F., 2003, Wellhead protection plan for the city of 

Keewatin, Minnesota, part 1: Minnesota Department of Health, 

33 p.

Walsh, J.F., 2004, Isotopic and chemical characterization of 

water from mine pits and wells on the Mesabi Iron Range, 

northeastern Minnesota, as a tool for drinking water protection: 

2004 U.S. EPA/NGWA Fractured Rock Conference, Portland, 

Maine, September 13–15.

Walsh, J.F., 2007a, Wellhead protection plan for the city of Marble, Minnesota, part 1: Minnesota Department of Health, 39 p.

Walsh, J.F., 2007b, Wellhead protection plan for the city of 

Taconite, Minnesota, part 1: Minnesota Department of Health, 

40 p.

Jones—Evaluation of Methods for Delineating Zones of Transport for Production Wells in Karst and Fractured-Rock Aquifers of Minnesota—SIR 2010–5005

Printed on recycled paper