Cyclic Injection, Storage, and Withdrawal of Heated Water in a Sandstone Aquifer at 

St. Paul, Minnesota

By R.T. MILLER1 and G.N. DELIN2

Analysis of Thermal Data and Nonisothermal Modeling

of Short-Term Test Cycles

U.S. Geological Survey Professional Paper 1530–B

Prepared in cooperation with the University of Minnesota

and the Minnesota Geological Survey

1 Groundwater Investigations, Inc., Pine Bush, New York

2 U.S. Geological Survey, Mounds View, Minnesota
U.S. DEPARTMENT OF THE INTERIOR

Gale A. Norton, Secretary

U.S. GEOLOGICAL SURVEY

Charles G. Groat, Director

Use of brand names in this report is for identification purposes only and does not 

constitute endorsement by the U.S. Geological Survey.

Mound View, Minnesota, 2002

Library of Congress Cataloging in Publications Data

Miler, R.T., and Delin, G.N., 

Cyclic injection, storage, and withdrawal of heated water in a sandstone aquifer at St. Paul, Minnesota / R. T. Miller and G.N. Delin.

66 p., 28 cm. — (Analysis of thermal data and nonisothermal modeling of short-term test cycles) (U.S. Geological Survey Professional 

Paper; 1530-B)

“Prepared in cooperation wth the University of Minnesota and the Minnesota Geological Survey.”

Includes bibliographic references (p. 65).

ISBN 0-607-99150-X

Supt. of Docs. no.: I 19.16: 1530-B

1. Hot-air heating. 2. Hot water. 3. Water-storage—Minnesota—St. Paul. 4. Aquifers—Minnesota—St. Paul. I. Univesity of Minnesota. 

II. Minnesota Geological Survey. III. Title. IV. Series. V. Series: U.S. Geological Survey professional paper; 1530-B.

TH7602.M55 2002 92–23497

697’.4—dc20 CIP

For sale by U.S. Geological Survey, Information Services,

Box 25286, Federal Center,

Denver, CO 80225
III

CONTENTS

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

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

Purpose and scope ....................................................................................................................................................... 2

Hydrogeologic setting.................................................................................................................................................. 2

Aquifer selection.......................................................................................................................................................... 4

Description of test facility ........................................................................................................................................... 4

Preliminary injection of heated water.......................................................................................................................... 7

Short-term test cycles I–IV.................................................................................................................................................... 13

Analysis of thermal data for short-term test cycles ............................................................................................................... 15

Temperature graphs ..................................................................................................................................................... 15

Potential aquifer clogging............................................................................................................................................ 35

Time-lag effect............................................................................................................................................................. 37

Temperature profiles.................................................................................................................................................... 37

Nonisothermal modeling of short-term test cycles................................................................................................................ 44

Model design ............................................................................................................................................................... 45

Discretization of aquifer system........................................................................................................................ 45

Flux calculation at model boundaries................................................................................................................ 46

Representation of thermal properties................................................................................................................. 47

Model calibration......................................................................................................................................................... 50

Analysis of simulations ............................................................................................................................................... 63

Summary................................................................................................................................................................................ 64

References ............................................................................................................................................................................. 65

Illustrations

Figure 1. Map and block diagram showing location and generalized schematic of hydrogeology at the Aquifer 

Thermal-Energy Storage site .................................................................................................................................... 3

2. Map showing plan view of the Aquifer Thermal-Energy Storage site ....................................................................5

3. Schematic diagram of sites A and B at the Aquifer Thermal-Energy Storage site.................................................. 6

4. Schematic section showing depths of screened intervals of observation wells, stratigraphy, and location of 

measurement points of the Aquifer Thermal-Energy Storage site ..........................................................................8

5. Diagram showing model grid and position of observation wells at various depths ................................................ 10

Figures 6–14. Graphs showing:

6. Pressure changes in production well A and in observation well AM2 for about 2 days of injection of 

ambient water and about 2 days of injection of heated water at 18.6 liters per second .......................................... 11

7. Well efficiency for production well A after initial completion and after redevelopment by acidization ................ 12

8. Pressure changes in production well A during injection at 18.6 liters per second before heat injection

and after redevelopment by acidization................................................................................................................... 13

9. Aquifer temperature, heat conduction, and time-lag effects during injection and maintenance periods 

of test cycle I in observation well AM1 .................................................................................................................. 15

10. Temperatures at the wellhead in production well A for the four short-term test cycles during periods 

of injection, and withdrawal .................................................................................................................................... 16

11a. Temperatures in observation well AM1 during periods of injection and withdrawal for test cycle I, 

and test cycle II........................................................................................................................................................ 18

11b. Temperatures in observation well AM1 during periods of injection and withdrawal for test cycle III, 

and test cycle IV ...................................................................................................................................................... 20

12a. Temperatures in observation well AS1 during periods of injection and withdrawal for test cycle I, 

and test cycle II........................................................................................................................................................ 22

12b. Temperatures in observations well AS1 during periods of injections and withdrawal for test cycle III, 

and test cycle IV ...................................................................................................................................................... 24
IV

Illustrations--Continued

13a. Temperatures in observation well AM2 during periods of injection and withdrawal for test cycle I, 

and test cycle II ........................................................................................................................................................26

13b. Temperatures in observation well AM2 during periods of injection and withdrawal for test cycle III,

and test cycle IV.......................................................................................................................................................28

14a. Temperatures in observation well AM3 during periods of injection and withdrawal for test cycle I, 

and test cycle II ........................................................................................................................................................30

14b. Temperature in observation well AM3 during periods of injection and withdrawal for test cycle III, 

and test cycle IV.......................................................................................................................................................32

Figures 15–16. Diagrams showing:

15. Bridging of fine material at a pore restriction ........................................................................................................36

16. Generalized temperature profiles after periods of injection and storage in a cross-section of sandstone 

and shale with different permeabilities ....................................................................................................................38

Figures 17–20. Graphs showing:

17. Vertical profile of temperature for measurement points in observation well AM1, 7 meters from

production well A ....................................................................................................................................................39

18. Vertical profile of temperature for measurement points in observation well AS1, 7 meters from 

production well A ....................................................................................................................................................40

19. Vertical profile of temperature for measurement points in observation well AM2, 14 meters from 

production well A43 ................................................................................................................................................41

20. Vertical profile of temperature for measurement points in observation well AM3, 14 meters from 

production well A ....................................................................................................................................................42

Figures 21–24. Diagrams showing:

21. Model grid and flow net for the Ironton and Galesville Sandstones near production well A for the 

short-term test cycles ...............................................................................................................................................47

22. Model grid and flow net for the upper part of the Franconia Formation near production well A for the 

short-term test cycles ...............................................................................................................................................48

23. Finite-difference grid, in three dimensions, for the Aquifer Thermal-Energy Storage site model ........................49

24. Model cells near production well A in which heat transport was simulated..........................................................51

Figures 25–29. Graphs showing:

25. Model-computed and measured injection temperatures at production well A for the four short-term 

test cycles during periods of injection and withdrawal............................................................................................52

26. Model-computed and average measured injection temperatures at observation well AM1 for the four 

short-term test cycles during periods of injection and withdrawal ..........................................................................54

27. Model-computed and average measured injection temperatures at observation well AS1 for the four

short-term test cycles during periods of injection and withdrawal ..........................................................................56

28. Model-computed and average measured injection temperatures at observation well AM2 for the four 

short-term test cycles during periods of injection and withdrawal ..........................................................................58

29.Model-computed and average measured injection temperatures at observation well AM3 for the four 

short-term test cycles during periods of injection and withdrawal ..........................................................................60

Tables

Table 1. Summary of duration, average rate of injection and withdrawal, and average temperature of injection for 

four short-term test cycles..........................................................................................................................................14

2. Temperature front arrival time at measurement points in the upper part of the Franconia Formation and 

in the Ironton and Galesville Sandstones for short term test cycle I ....................................................................... 34

3. Layer number, thickness, and corresponding hydrogeologic unit for the three-dimensional model of heat

transport................................................................................................................................................................... 50

4. Thermal properties used for simulation of the short-term test cycles ...................................................................... 51

5. Altitudes of measurement points where temperatures were averaged to correspond with model layers................. 62

6. Hydraulic properties used for simulation of the short-term test cycles.................................................................... 63

7. Comparison of model-computed thermal efficiencies of the aquifer and final withdrawal-water temperatures 

at production well A with corresponding calculated and measured values for the four short-term

test cycles................................................................................................................................................................. 63
V

CONVERSION FACTORS, VERTICAL DATUM, AND ABBREVIATIONS

Temperature in degrees Celsius (°C) may be converted to degrees Fahrenheit (°F) as follows: °F = (1.8 × °C) + 32

Sea level: In this report, "sea level" refers to the National Geodetic Vertical Datum of 1929 (NGVD of 1929)—a geodetic datum

derived from a general adjustment of the first-order level nets of both the United States and Canada, formerly called Sea Level

Datum of 1929.

Altitude, as used in this report, refers to distance above or below sea level.

Transmissivity: The standard unit for transmissivity is cubic foot per day per square foot times foot of aquifer thickness [(ft3d)/

ft2]ft. In this report, the mathematically reduced form, foot squared per day (ft2/d), is used for convenience.

Specific conductance is given in microsiemens per centimeter at 25 degrees Celsius (μS/cm at 

25 °C).

Concentrations of chemical constituents in water are given either in milligrams per liter (mg/L) or micrograms per liter (μg/L).

NOTE TO USGS USERS: Use of hectare (ha) as an alternative name for square hectometer (hm2) is restricted to the measurement of small land or water areas. Use of liter (L) as a special name for cubic decimeter (dm3) is restricted to the measurement of liquids and gases. No prefix other than milli should be used with liter. Metric ton (t) as a name for megagram (Mg)

should be restricted to commercial usage, and no prefixes should be used with it.

Multiply By To obtain

Length

centimeter (cm) 0.3937 inch

meter (m) 3.281 foot 

Area

square meter (m2) 0.0002471 acre

Flow rate

liter per second (L/s) 15.85 gallon per minute 

cubic meter per day (m3

/d) 264.2 gallon per day 

Mass

kilogram (kg) 2.205 pound avoirdupois

Pressure

kilopascal (kPa) 0.1450 pound-force per inch 

Density

kilogram per cubic meter (kg/m3) 0.06242 pound per cubic foot 

gram per cubic centimeter (g/cm3) 62.4220 pound per cubic foot 

Energy

joule 0.0000002 kilowatt-hour

watt per square meter (W/m2

) 8.804 x 10-5 British thermal unit per square foot per second

watt per cubic meter (W/m3

) 2.684 x 10-5 British thermal unit per cubic foot per second

joule per meter per day per degree [((J/m)/d)/°C] 1.605 x 10-4

British thermal unit per foot Celsius per day per 

degree Fahrenheit

joule per cubic meter per degree [(J/m3)/°C] 1.491 x 10-5 British thermal unit per cubic pound avoirdupois per

joule per kilogram per degree [(J/kg)/°C] 2.388 x 10-4

British thermal unit per pound avoirdupois per degree 

Fahrenheit

Hydraulic conductivity

meter per day (m/d) 3.281 foot per day 

Hydraulic gradient

meter per kilometer (m/km) 5.27983 foot per mile 

Transmissivity

meter squared per day (m2/d) 10.76 foot squared per day 
VI
B1

Cyclic Injection, Storage, and Withdrawal of Heated Water in a Sandstone Aquifer at St. 

Paul, Minnesota

Analysis of thermal data and nonisothermal 

modeling of short-term test cycles

By R.T. Miller1 and G.N. Delin2

ABSTRACT

In May 1980, the University of Minnesota began a 

project to evaluate the feasibility of storing heated water 

(150 degrees Celsius) in the Franconia-IrontonGalesville aquifer (183 to 245 meters below land 

surface) and later recovering it for space heating. The 

University’s steam-generation facilities supplied hightemperature water for injection. The Aquifer ThermalEnergy Storage system is a doublet-well design in 

which the injection-withdrawal wells are spaced 

approximately 250 meters apart. Water was pumped 

from one of the wells through a heat exchanger, where 

heat was added or removed. This water was then 

injected back into the aquifer through the other well.

Four short-term test cycles were completed. Each 

cycle consisted of approximately equal durations of 

injection and withdrawal ranging from 5.25 to 8.01 

days. Equal rates of injection and withdrawal, ranging 

from 17.4 to 18.6 liters per second, were maintained for 

each short-term test cycle. Average injection 

temperatures ranged from 88.5 to 117.9 degrees 

Celsius.

Temperature graphs for selected depths at individual 

observation wells indicate that the Ironton and 

Galesville Sandstones received and stored more thermal 

energy than the upper part of the Franconia Formation. 

Clogging of the Ironton Sandstone was possibly due to 

precipitation of calcium carbonate or movement of finegrain material or both. Vertical-profile plots indicate 

that the effects of buoyancy flow were small within the 

aquifer.

A three-dimensional, anisotropic, nonisothermal, 

ground-water-flow, and thermal-energy-transport 

model was constructed to simulate the four short-term 

test cycles. The model was used to simulate the entire 

short-term testing period of approximately 400 days. 

The only model properties varied during model 

calibration were longitudinal and transverse thermal 

dispersivities, which, for final calibration, were 

simulated as 3.3 and 0.33 meters, respectively. The 

model was calibrated by comparing model-computed 

results to (1) measured temperatures at selected 

altitudes in four observation wells, (2) measured 

temperatures at the production well, and (3) calculated 

thermal efficiencies of the aquifer. Model-computed 

withdrawal-water temperatures were within an average 

of about 3 percent of measured values and modelcomputed aquifer-thermal efficiencies were within an 

average of about 5 percent of calculated values for the 

short-term test cycles. These data indicate that the 

model accurately simulated thermal-energy storage 

within the Franconia-Ironton-Galesville aquifer.

INTRODUCTION

The concept of Aquifer Thermal-Energy Storage 

(ATES) has received increasing attention regarding its 

potential to decrease energy consumption and 

environmental contamination. Kazmann (1971), Meyer 

and Todd (1973), Hausz (1974), and Meyer and others 

(1976) were among the first to discuss the ATES 

concept. Most of these discussions, however, were 

restricted to economic and institutional concerns. 

Injection of heated or cooled fluids into aquifers had 

been practiced for many years (Leggette and Brashears, 

1938; Guyton, 1946), but field experiments designed to 

evaluate the feasibility of ATES for long-term, largescale energy storage were not conducted until 1975 

(Werner and Kley, 1977), and the first demonstration 

project in the United States did not begin until 1976 

(Molz and others, 1978). Many other contributions to 

understanding and evaluating ATES are described or 

summarized in Lawrence Berkeley Laboratory (1978), 

Tsang (1979), and Mercer and others (1980).

The University of Minnesota started a project in May 

1980 to evaluate aquifer thermal-energy storage in a 

confined, sedimentary bedrock about 180 m beneath the 

1Groundwater Investigations, Inc., Pine Bush, New York

2U.S. Geological Survey, Minnesota District 
B2

St. Paul campus. The project was funded by the U.S. 

Department of Energy through Battelle Pacific 

Northwest Laboratories. Other participants in the 

project include the Minnesota Geological Survey, the 

Minnesota Energy Agency, Orr-Schelen-Mayeron and 

Associates, National Biocentrics, Inc., and the U.S. 

Geological Survey. The project was designed to 

evaluate the feasibility and effects of storing hightemperature (150°C) water in the Franconia-IrontonGalesville aquifer beneath the St. Paul campus and later 

recovering the heat for water and space heating.

The specific objectives of the U.S. Geological Survey 

in this investigation were to (1) develop an 

understanding of the ground-water-flow system near 

the site, (2) identify the hydraulic properties of the 

ground-water-flow system that are most important with 

respect to thermal-energy storage and identify datacollection needs for monitoring and evaluating the 

aquifer-system performance, (3) develop a method to 

evaluate flow and thermal-energy transport for various 

cyclic injection and withdrawal schemes to aid in 

selection of an efficient well-system design, and (4) 

assist in the collection of hydraulic and thermal data 

during injection-withdrawal tests and design a dataprocessing system to facilitate entry of the data into 

computer storage. Miller (1984 and 1985) describes the 

anisotropy of the Franconia-Ironton-Galesville aquifer 

and preliminary modeling at the ATES site. Miller and 

Voss (1986) describe design of the finite-difference grid 

at the ATES site. Miller and Delin (1993) describe (1) 

analysis of field observations for aquifer 

characterization and observation-network design, (2) 

preliminary model analyses to determine model 

sensitivity to hydraulic and thermal characteristics and 

to facilitate final model design, and (3) model 

simulations of the aquifer’s thermal efficiency.

Purpose and Scope

This report describes the analysis of thermal data and 

nonisothermal modeling for four short-term test cycles 

of heated-water injection, storage, and withdrawal. This 

report is one in a series that describes the potential for 

thermal-energy storage within the Franconia-IrontonGalesville aquifer beneath the St. Paul campus of the 

University of Minnesota.

Hydrogeologic Setting

The St. Paul metropolitan area is underlain by a 

stratified sequence of Proterozoic and early Paleozoic 

sedimentary formations consisting of porous sandstone 

and fractured dolomite, which can by grouped into four 

major regional aquifers. The aquifers generally are 

separated by semipermeable sandstone, siltstone, and 

shale formations. The major aquifers are the St. Peter, 

Prairie du Chien-Jordan, Franconia-Ironton-Galesville, 

and Mount Simon-Hinckley-Fond du Lac (fig. 1).

The St. Peter aquifer consists of the St. Peter 

Sandstone, which is composed of a light-yellow or 

white, massive, quartzose, fine- to medium-grained, 

well-sorted, and friable sandstone. Thin beds of 

siltstone and shale near the base of the St. Peter 

Sandstone form a lower confining layer. The upper 

confining layer, consisting of the Platteville and 

Glenwood Formations, overlies the St. Peter Sandstone 

and is in contact with glacial drift. At the test site the St. 

Peter aquifer is approximately 57 m below land surface 

and is 50 m thick. Transmissivity ranges from 220 to 

280 m2/d and the storage coefficient ranges from 9.0 x 

10-5 to 9.75 x 10-3

. Porosity ranges from 0.28 to 0.30. 

The hydraulic gradient was estimated to be 0.006 and 

the pore velocity was estimated to be 0.18 m/d Norvitch 

and others (1973).

The Prairie du Chien-Jordan aquifer consists of the 

Prairie du Chien Group and the Jordan Sandstone (fig. 

1). The Prairie du Chien Group is predominantly a light 

brownish-gray or buff, sandy, thin- to thick-bedded 

dolomite that is vuggy and fractured and contains some 

thin layers of interbedded grayish-green shale. The 

underlying Jordan Sandstone is a white to yellow, 

quartzose, fine- to coarse-grained sandstone that is 

massive or thick to thin bedded and varies from friable 

to well cemented. Despite the differing lithologies, the 

Prairie du Chien Group and Jordan Sandstone function 

as one aquifer because there is no regional confining bed 

between them. At the test site the aquifer is 

approximately 107 m below land surface and is 69 m 

thick. The average transmissivity is approximately 

1,235 m2/d, with a porosity of 0.3. The hydraulic 

gradient was estimated to be approximately 0.005 and 

the pore velocity was estimated to be 0.30 m/d by 

Norvitch and Walton (1979).

The St. Lawrence Formation is 176 m below land 

surface and is approximately 7 m thick at the test site. It 

is a gray and greenish-gray, laminated, thin-bedded, 

dolomitic siltstone, silty dolomite, and shale. The 

porosity ranges from 0.15 to 0.20 and transmissivities 

range from 1 to 10 m2/d.

The Franconia-Ironton-Galesville aquifer consists of 

the Franconia Formation, and the Ironton and Galesville 

Sandstones. The Franconia Formation is divided into 

four members: Reno, Mazomanie, Tomah, and 
B3

Buildings

Building

SITE B

SITE A

SITE C

North

Glacial drift aquifer

Platteville-Glenwood confining unit

St. Peter aquifer

Prairie du Chien-Jordan aquifer

St. Lawrence confining unit

Franconia-Ironton-Galesville aquifer

Eau Claire confining unit

Mount Simon-Hinckley-Fond du Lac aquifer

HYDROGEOLOGIC UNIT

Quaternary

Ordovician

Cambrian

Proterozoic

SYSTEM

Glacial drift

Platteville and Glenwood Formations

St. Peter Sandstone

Prairie du Chein Group

Jordan Sandstone

St. Lawrence Formation

Franconia Formation

Ironton and Galesville Sandstones

Eau Claire Formation

Mount Simon Sandstone

Hinckley Sandstone, Fond du Lac

Formation, and other rocks

STRATIGRAPHIC UNIT

Project Site

LOCATION MAP

Figure 1. Location and generalized schematic diagram of hydrogeology

of the Aquifer Thermal-Energy Storage (ATES) site.
B4

Birkmose (Walton and others, 1991). The Reno 

Member in the upper part of the Franconia is a fine- to 

very-fine-grained, quartz, and glauconitic sandstone. 

The Reno is divided into two sections and is located 

approximately between 180 and 183 m and between 193 

and 206 m below land surface. The Mazomanie 

Member in the upper part of the Franconia is located 

between the depths of 174 and 184 m below land 

surface. The Mazomanie also is a fine- to very-finegrained, quartz sandstone, but has minor glauconite 

content. The Tomah Member in the lower part of the 

Franconia is an interbedded sequence of fine- to veryfine-grained, silty sandstone with interbedded siltstone 

or shale. The Tomah is located between 206 and 219 m 

below land surface. The Birkmose Member in the lower 

part of the Franconia is a dolomitic siltstone with some 

shale and fine- to very-fine-grained glauconitic 

sandstone interbedded. Based on laboratory 

permeability tests (Walton and others, 1991), the 

horizontal hydraulic conductivity of the upper part of 

the Franconia is about 158 times the hydraulic 

conductivity of the lower part of the Franconia. Natural 

gamma logs indicate a thick shale layer in the lower part 

of the Franconia Formation corresponding to the lower 

Reno, Tomah, and Birkmose Members (Walton and 

others, 1991). Analysis of results of packer tests 

indicate two hydraulic zones within the Franconia 

Formation (Miller and Delin, 1993). Based on the 

distinct differences in grain size, geophysical logs, and 

hydraulic properties between the upper and lower parts 

of the Franconia Formation, the upper 14 m of the 

Franconia was considered an aquifer and the lower 25 m 

of the Franconia was considered a confining unit. The 

Ironton Sandstone is white, medium-grained, 

moderately well-sorted quartz arenite that contains 

some silt-sized material. The Galesville Sandstone 

consists of a white to light-gray slightly glauconitic, 

well- to moderately well-sorted, mostly mediumgrained quartzose sandstone. The approximate depth 

and thickness of the Franconia-Ironton-Galesville 

aquifer beneath the site are 183 m and 62 m, 

respectively. The total transmissivity is 97.5 m2/d and 

the storage coefficient is 2.75 x 10-5. Transmissivity of 

the Franconia-Ironton-Galesville aquifer is anisotropic, 

with the principal axis of transmissivity oriented about 

30 degrees east of north. Average porosity ranges from 

0.25 to 0.31 with a hydraulic gradient of 0.002 and an 

estimated pore velocity of 0.05 m/d.

The Eau Claire Formation consists of interbedded 

siltstone, shale, and fine silty sandstone with a few thin 

layers of dolomite. The approximate depth and 

thickness of the formation beneath the site are 245 m 

and 29 m, respectively. Transmissivity ranges from 0.5 

to 5 m2

/d and porosity ranges from 0.28 to 0.35 

(Norvitch and others, 1973)

The Mount Simon-Hinckley-Fond du Lac aquifer 

consists of the Mount Simon and Hinckley Sandstones 

and the Fond du Lac Formation. The Mount Simon 

Sandstone is fine to coarse grained, contains very thin 

beds of shale, and commonly is gray, white, or pink. The 

Hinckley Sandstone is fine to coarse grained and pale 

red to light pink. The Fond du Lac Formation contains 

lenticular beds of fine to medium grained arkosic 

sandstone interbedded with mudstone and is dark red to 

pink. The top of the aquifer is approximately 274 m 

below land surface and the aquifer is approximately 60 

m thick. The transmissivity is approximately 250 m2/d 

and the storage coefficient is about 6 x 10-5 (Norvitch 

and others, 1973). The porosity averages 0.25, the 

hydraulic gradient is 0.0025, and the pore velocity is 

approximately 0.03 m/d (Norvitch and others, 1973).

Aquifer Selection

The selection of an aquifer for heat-storage testing 

was based on the following criteria: (1) minimal use of 

water from the aquifer in the Twin Cities area, (2) ability 

of the confining units above and below the aquifer to 

contain the injected heated water, and (3) the 

hydrogeologic properties and natural gradients within 

the aquifer and their effect on the transfer of heat.

Description of Test Facility

The University of Minnesota test facility was a 

doublet-well system in which the wells were spaced 

approximately 250 m apart (fig. 2). Production wells A 

and B were screened from about 180 to 195 m (upper 

part of the Franconia Formation) and from 225 to 240 m 

(Ironton and Galesville Sandstones) below land surface, 

respectively (Miller and Delin, 1993). The land surface 

is 287 m above sea level. Initial testing of the ATES 

system was with a series of short-term cycles of heatedwater injection, storage, and withdrawal. Each cycle 

was planned to be approximately 24 days long; the 

injection, storage, and withdrawal steps for each cycle 

were to be approximately 8 days in duration. 

Conversely, the duration of the long-term test cycles 

was planned to be 180 days long; with injection, 

storage, and withdrawal steps of 60 days each. During 

injection, water was pumped from the FranconiaIronton-Galesville aquifer from production well B at 

site B (fig. 1), transported through a heat exchanger 
B5

Figure 2. Plan view of the Aquifer Thermal-Energy Storage (ATES) sites.

477.7 METERS

280.5 METERS

254.7 METERS

Production

well A

AM1

AM2

AM3

AC1 AS1

Site A

Production well B

BS1 BC1

Site B

CM1

Site C

EXPLANATION

AM2 Observation well and identifier

(See Insert)

N

Production well A

AM1

AM2

AM3

AC1

AS1

7 METERS

7 METERS

7 METERS

14 METERS

INSET

0

0

20 40

100

60

200

80 100 METERS

300 FEET
B6

(fig. 3) where it was heated, and then injected back into 

the aquifer through production well A at site A. During 

withdrawal, water was pumped from the FranconiaIronton-Galesville aquifer from production well A, 

transported through the radiator, where it was cooled, 

and then injected back into the aquifer through 

production well B. The doublet-well system and sites A 

and B at the ATES site are shown diagrammatically in 

figure 3. 

Temperature measurements within the observation 

wells (fig. 4) were made by use of type-T (copperconstantan) thermocouples. As described in detail by 

FILTERS

Data recording,

field laboratory,

and field office

TRAILER

AM1

AM2

AC1

AM3

HEAT

EXCHANGERS

HEAT LOAD

(RADIATIOR)

Tunnel

Condensate

Steam

Aquifer Water

To Site B via

steam tunnel

To Site A via

steam tunnel

SITE A

SITE B

Figure 3. Schematic diagram of sites A and B at the Aquifer Thermal-Energy

Storage (ATES) site. (Modified from Walton and others, 1991).

Production

Well A

Production

well B

BS1 BC1

0

0

10

10 20 30 40 50 FEET

20 METERS

14 METERS

7 METERS 7 METERS

7 METERS 7 METERS

AM2

EXPLANATION

Observation well and identifier

Value

Aquifer water movement direction

 Withdrawal step, from production

 well A to B

 Injection step, from production

 well B to A

Tunnel

AS1
B7

Miller and Delin (1993), as many as 12 thermocouples 

were installed in 1 or 2 manufactured strings (one 

containing 8 thermocouples and one containing 4) in a 

protective 3.2- or 5.1-cm-diameter steel casing within 

the observation wells at the altitudes shown in figure 4. 

Individual thermocouples were coated with Teflon for 

resistance to heat, and each 4- or 8-thermocouple string 

was covered with a stainless-steel overbraid to add 

rigidity and to protect each string as it was lowered into 

the steel casing. The overbraid tended to twist and kink, 

however, and created excessive wear to the 

thermocouple wire where the kinks rubbed on the side of 

the well casing. Several thermocouples failed because 

of electrical shorts in thermocouple wires at these points 

of excessive wear. Temperatures measured at the 

thermocouples probably were slightly less than the 

actual temperatures in the aquifer because of conductive 

heat losses to the well casing; however, these 

temperature losses are minimal and measured 

temperatures are considered representative of 

temperatures in the aquifer.

Submersible pressure transducers were used to 

measure pressures in the observation wells. Pressures 

from 0 to 1,724 kPa could be measured in a temperature 

range of 10 to 121°C. Measurement accuracy was +2 

percent of the full-scale output over the compensated 

temperature range, or a maximum of +34 kPa at 121°C.

All temperature and pressure-transducer data were 

transmitted through buried cables to a central data 

logger with which data were recorded on electrostatic 

paper and nine-track computer tape. The operation of 

the data logger and the computer programs written to 

reduce the stored data are described in detail by 

Czarnecki (1983).

Individual data-collection points will be referred to in 

this report by their observation-well location with 

respect to production well A and by their vertical 

position within each observation well as referenced to 

sea level. Reference to sea level is justified because the 

formations are flat lying and of uniform thickness across 

the area. The locations of observation wells AM1, AM2, 

AM3, and AS1 with respect to production well A are 

shown in figure 3. The altitudes of individual 

measurement points for the observation wells are shown 

in figure 4. 

Downhole gyroscopic surveys were conducted in 

several observation wells (Hoyer and others, 1991; 

Miller and Delin, 1993) to determine deviations of each 

well bore with respect to land surface. The bottoms of 

some wells deviate from their land-surface locations by 

as much as 8 m horizontally (fig. 5). These horizontal 

deviations were considered during interpretation of 

temperature data. 

Preliminary Injection of Heated Water

Prior to conducting the short-term test cycles, a 

preliminary heat-injection phase was completed to test 

equipment at the ATES site and finalize plans for the 

actual tests. For this pilot phase of the study, water at 

ambient temperature was pumped from production well 

B and injected in production well A at 18.6 L/s for 

approximately 2 days in May 1982. The temperature of 

the injection water then was increased to 82°C, and 

injection continued for approximately 2 more days. As 

a result of the temperature increase, calcium carbonate 

precipitated within the above-ground piping and within 

the well bore of production well A and caused pressures 

in the above-ground piping and well bore to increase 

(fig. 6). Injection of heated water was stopped after 

pressures in production well A increased beyond the 

maximum pressures measured during an 8-day injection 

test with ambient-temperature water done earlier in the 

month. The initial pressure drop observed during 

injection of the heated water was related to decreases in 

the viscosity and density of the heated water as it mixed 

with ambient-temperature water. 

Indications of clogging of the well bore at production 

well A also were apparent from pressure changes in the 

upper part of the Franconia Formation and the Ironton 

and Galesville Sandstones at observation well AM2 

(fig. 6). During ambient-temperature injection, 

pressures in these formations measured at observation 

well AM2 were similar to pressures measured during the 

previous 8-day ambient-temperature injection test; 

pressures in the Ironton and Galesville Sandstones 

ranged from 100 to 110 kPa, greater than pressures in the 

upper part of the Franconia Formation. This trend 

continued until after about 1,250 minutes of heatedwater injection. At that time, pressures in the Ironton 

and Galesville Sandstones started to decrease while 

pressures in the upper part of the Franconia Formation 

started to increase. Until the test was stopped, pressures 

in the upper part of the Franconia Formation increased 

while pressures in the Ironton and Galesville Sandstones 

decreased. These variations in recorded pressure 

probably are due to clogging of production well A in the 

interval screened opposite the Ironton and Galesville 

Sandstones. The Ironton and Galesville Sandstones are 

known to have a hydraulic conductivity at least twice 

that of the upper part of the Franconia Formation 
B8

275

250

225

200

175

150

125

100

75

50

25

0

-25

PRODUCTION

WELL A

AC1 AS1 AM1 AM2 AM3

33.2-32.3

9.4-8.6

93

88

81

73

58

45

66

110

104

38

99

52

93.8-93.0

73.1-72.2

50.3-49.4

94.9-93.0

73.1-72.2

50.3-49.4

108.2-107.3

115.2-114.3

49.7-48.8

3.2 centimeters3.2 centimeters3.2 centimeters3.2 centimeters3.2 centimeters3.2 centimeters2.5 centimeters2.5 centimeters3.2 centimeters5.1 centimeters3.2 centimeters2.5 centimeters2.5 centimeters5.1 centimeters

ALTITUDE, IN METERS ABOVE AND BELOW SEA LEVEL

LAND SURFACE

EXPLANATION

110

49.7-48.8

Well diameter

SITE A

Figure 4. Depths of screened intervals of observation wells,

 Thermal-Energy Storage (ATES) site. (Horizontal

Screened interval in production well

Altitude range of screened interval, in meters

Temperature measurement point and altitude, in meters

 (refer to well AM3 for measurement altitudes)

Glacial

Drift

Platteville Formation

Glenwood Formation

St. Peter

Sandstone

Prairie du

Chien

Group

Jordan

Sandstone

St. Lawrence Formation

Franconia

Formation

Ironton and

Galesville

Sandstones

Eau Claire

Formation

Mount Simon

Sandstone

287 287

239

230

180

140

111

104

63

42

13
B9

275

250

225

200

175

150

125

100

75

50

25

0

-25

LAND SURFACE

BC1 BS1 PRODUCTION CM1

WELL B

SITE B SITE C

278

241

232

182

145

112

106

65

41

15

287

242

238

183

146

113

106

67

42

48.5-47.6

36.3-35.4

11.3-10.4

59.8-58.4

83.8-82.9

106-105.1

108.2-107.3

117.4-111.3

49.4-48.8

97.1-96.2

Glacial

Drift

Platteville Formation

Glenwood Formation

St. Peter

Sandstone

Prairie du

Chien

Group

Jordan

Sandstone

St. Lawrence Formation

Franconia

Formation

Ironton and

Galesville

Sandstones

Eau Claire

Formation

Mount Simon

Sandstone

stratigraphy, and location of measurement points of the Aquifer

arrangement of wells is arbitrary and not to scale.) 2.5 centimeters 2.5 centimeters 3.2 centimeters

3.2 centimeters2.5 centimeters2.5 centimeters2.5 centimeters2.5 centimeters1.5 centimeters1.5 centimeters

ALTITUDE, IN METERS ABOVE AND BELOW SEA LEVEL
B10

(Miller, 1984); therefore, it is likely that twice as much 

water per unit time can be injected into this part of the 

aquifer. Because more water can be injected into the 

Ironton and Galesville Sandstones, the potential for 

precipitation of calcium carbonate is greater in this part 

of the aquifer than in the upper part of the Franconia 

Formation. If the permeability near the well bore in the 

Ironton and Galesville Sandstones were lowered 

because of the clogging, more water would be forced 

into the upper part of the Franconia Formation, and the 

pressure in the upper part of the Franconia would rise. 

Because less water would be injected into the Ironton 

and Galesville Sandstones than before, and because 

most of the head loss through the Ironton and Galesville 

0 10 20 30 40 METERS

Figure 5. Model grid and position of observation wells at various depths.

AM2

AM3 AS1

AM1

Production well A

AM4

North

0 10 20 30 40 50 60 70 80 90 100 FEET

EXPLANATION

Position of observation well

 Land surface and well number

 Model-layer 1 (St. Lawrence Formation)

 Model-layer 6 (Eau Claire Formation)
B11

Sandstones would take place near the well bore, the 

pressure measured in this formation at observation well 

AM2 would decrease.

Because additional water would be injected into the 

upper part of the Franconia Formation, and because the 

upper part of the Franconia would not clog at the same 

rate as the Ironton and Galesville Sandstones, pressures 

measured in upper part of the Franconia at observation 

well AM2 would increase. If aquifer clogging had 

increased, pressures in the upper part of the Franconia 

Formation and in the Ironton and Galesville Sandstones 

would likely have stabilized. Pressure stabilization was 

not observed in the field data; therefore, the well bore 

and aquifer probably were not completely clogged.

Production well A was treated with acid and then 

pumped at rates ranging from 18.9 to 27.0 L/s for 

several hours during September 1982. After 

redevelopment ended, the well was allowed to recover 

for approximately 16 hours. Water levels in production 

well A recovered to within 0.03 m of prepumping water 

levels. This recovery was considered sufficient to 

conduct a step-drawdown test on production well A. 

The step-drawdown test done in September 1982 was 

similar to tests done on production wells A and B in 

October 1981 (Miller, 1984). The test included three 

pumping steps at rates of 20.8 L/s for 120 minutes, 

23.0 L/s for 120 minutes, and 25.7 L/s for 160 minutes.

 The water temperature measured at the wellhead in 

production well A increased during the test from 20.0°C 

to 28.3°C as residual stored heat from the aborted heat 

injection test was pumped out. Because pressures 

measured in the well will vary with water viscosity, a 

temperature-correction factor was applied to the 

recorded pressure data, as described by Wenzel (1942) 

and Sniegocki (1963). The correction factor adjusted 

the resulting drawdowns to a temperature of 10°C, the 

ambient temperature of the ground water, which 

enabled the analysis of the data to be directly 

comparable with the step-drawdown tests done in 1981.

The minimization technique described by Labadie 

and Helweg (1975) for calculation of the aquifer- and 

well-loss coefficients in the step-drawdown equation 

was used to analyze the test data. This method was used 

to analyze step-drawdown data from tests done on 

0.01 0.10 0.25 0.50 1 2 3 4 5

TIME, IN DAYS

5 10 50 100 500 1,000 5,000 10,000

TIME, IN MINUTES

PRESSURE, IN KILOPASCALS250

350

300

200

150

100

50

0

Production well A

AM2, Ironton and Galesville Sandstones

AM2, Upper part of Franconia Formation

Heated-water

injection

Ambient-water injection

Figure 6. Pressure changes in production well A and in observation well AM2 for about 2 days of injection of

ambient water and about 2 days of injection of heated water (82 degrees Celsius) at 18.6 liters per second.
B12

production wells A and B in 1981 and is described in 

Miller and Delin (1993).

Well-efficiency curves were constructed for 

production well A using the method of Rorabaugh 

(1953) just after initial well completion and after well 

redevelopment by acidization (fig. 7). The well 

efficiency of 83 percent, calculated for an 18.9-L/s 

pumping rate, indicates adequate redevelopment of 

production well A by acidization. The comparison of 

these two curves can be somewhat misleading, 

however, if variations in equipment efficiency are not 

considered. During removal of the pump in production 

well A on April 30, 1982, the pump-shaft spider-bearing 

holders were found to have been initially installed 

backwards. Because the bearing holders are designed to 

minimize the turbulence of pumped water flowing past 

them, reverse installation would probably increase 

turbulence. The increased turbulence could effectively 

increase the well-loss part of the step-drawdown 

equation and decrease the overall efficiency of the well. 

The increased well loss probably resulted in a low 

efficiency at high pumping rates computed for the stepdrawdown test done in 1981. Thus, it is likely that the 

efficiencies calculated for the step-drawdown tests done 

in 1981 would have been higher if the pump-shaft 

spider-bearing holders had been installed correctly. In 

addition to reinstallation of the bearing holders, one 

pump bowl was removed from the pump shaft, and the 

lifting capability of the pump was decreased. Removal 

of the pump bowl resulted in a lower efficiency because 

the pump shaft was spinning at a greater rate than 

previously to maintain the injection rate.

Ambient-temperature water at 10°C was injected into 

production well A at 18.6 L/s for approximately 2.5 

days in late September 1982 to obtain information on 

the feasibility of injecting water into production well A 

and to further assess the extent of well redevelopment 

with acid. Pressure changes in the well during the 8-day 

injection test in May 1982 (before heat injection) and 

during the 2.5-day injection test after well 

redevelopment are illustrated in figure 8. The effects of 

residual calcium-precipitate are reflected in the 

approximately 35-kPa increase in pressure in the well 

compared with pressures measured during the 8-day 

After acidization

(September 1982)

Initial completion

(October 1981)

100

90

80

70

60

50

40

30

20

10

0

0 10 20 30 40 50 60 70 80

PUMPING RATE, IN LITERS PER SECOND

WELL EFFICIENCY, IN PERCENT

Figure 7. Well efficiency for production well A after initial completion and after redevelopment by acidization.
B13

injection test. This increase in pressure was not 

considered significant and, after approximately 2 days, 

the rate of change of pressure with time was similar to 

the rates for the test before heat injection.

In October 1982, a precipitation filter was installed in 

the above-ground piping between the heat exchanger 

and production well A (fig. 3) to reduce precipitation of 

calcium carbonate on the well screen during future 

testing. The precipitation filter consisted of two sets of 

three tanks approximately 1.8 m long and 0.36 m in 

diameter connected in series and filled with a graded, 

high-purity limestone aggregate. Heated water was 

pumped through the tanks where calcium was allowed 

to precipitate out of solution onto the limestone.

The limestone filter effectively reduced the degree of 

calcium carbonate supersaturation and reduced the 

potential for calcium carbonate precipitation within the 

well bore; however, because water was pumped through 

the heat exchanger before it was filtered, calcium 

carbonate precipitation was not reduced within the heat 

exchanger. Precipitation of calcium carbonate within 

the heat exchanger resulted in increased pressures in the 

above-ground pipeline (fig. 3). Consequently, it was 

necessary to clean the heat exchanger with acid during 

subsequent tests after approximately every 40 hours of 

operation to remove all carbonate precipitate. The 

limestone filter material was replaced with new 

aggregate while the heat exchanger was cleaned. 

Maintenance of the filters and heat exchanger required 

8 to 15 hours.

SHORT-TERM TEST CYCLES I–IV

Four short-term test cycles of heat injection were 

conducted from November 1982 through December 

1983. The duration, average rate of injection and 

withdrawal, and average temperature during injection 

for the four short-term test cycles are summarized in 

table 1. The time required for removing the carbonate 

precipitate from the heat exchanger and for changing 

the graded limestone material in the precipitation filters 

interrupted the injection period of each cycle; therefore, 

the total calendar time of the injection period for a 

particular cycle was longer than the total storage or total 

withdrawal periods, although the actual time of heated 

water injection was approximately equal to that of 

storage and withdrawal. Four maintenance periods were 

needed during each of the four test cycles; the result was 

five individual injection superegos (termed heat 1 

through heat 5 in this report) within each respective 

cycle (fig. 9). For example, the total duration of 

350

300

250

200

150

100

50

0

400

10 50 100 500 1,000 5,000 10,000

TIME, IN MINUTES

PRESSURE, IN KILOPASCALS

Figure 8. Pressure changes in production well A during injection at 18.6 liters

per second before heat injection and after redevelopment by acidization.

After acidization

(September 1982)

Before heat injection

(May 1982)
B14

injection during test cycle I is equivalent to the sum of 

the five heats, or 5.25 days. This terminology will be 

used in the report to describe specific events during 

injection periods of individual test cycles.

The average injection rates in each test cycle were 

maintained below the scheduled 18.6 L/s to reduce the 

back pressure within the above-ground piping because 

pressure increased during injection as the limestone 

filters plugged. The injection rate generally started 

0.2 L/s higher and ended 0.2 L/s lower than the average 

value reported in table 1 for each heat step in each 

injection cycle. The average injection temperature for 

water in each test cycle ranged from approximately 

91°C in test cycle I to approximately 115°C in test cycle 

 Table 1. Summary of duration, average rate of injection and withdrawal, and average temperature of injection for four short-term test 

cycles

[--, not applicable]

Period

Subperiod 

(heat) number

Duration 

(days)

Average rate of injection and 

withdrawal

 (liters per second)

Average injection 

temperature 

(degrees Celsius)

TEST CYCLE I

Injection 1 1.26 17.9 88.5

2 1.13 18.3 92.6

3 0.94 18.3 90.0

4 .96 18.3 91.9

5 .96 19.3 91.7

Total duration of injection 1–5 5.25 18.4 90.9

Storage -- 13.03 -- --

Withdrawal -- 5.28 18.4 --

TEST CYCLE II 

Injection 1 1.71 18.2 95.5

2 1.63 17.7 96.3

3 1.83 17.6 97.9

4 1.64 17.5 98.0

5 1.20 17.4 99.7

Total duration of injection 1–5 8.01 17.7 97.5

Storage -- 89.71 -- --

Withdrawal -- 8.00 17.7 --

TEST CYCLE III

Injection 1 1.70 18.6 104.4

2 1.75 18.5 107.2

3 1.49 18.2 105.6

4 1.67 18.2 106.1

5 1.09 18.0 105.0

Total duration of injection 1–5 7.70 18.3 105.7

Storage -- 9.62 -- --

Withdrawal -- 7.91 17.8 --

TEST CYCLE IV 

Injection 1 1.83 18.4 111.9

2 1.70 17.9 115.6

3 1.71 17.5 117.9

4 1.66 17.9 114.9

5 .79 17.7 112.6

Total duration of injection 1–5 7.69 17.9 114.6

Storage -- 10.13 -- --

Withdrawal -- 7.71 17.8 --
B15

IV. The average rate of injection and withdrawal for all 

cycles was approximately 18.1 L/s. 

Injection of heated water during test cycle I was 

shortened to approximately 5 days to evaluate the newly 

installed limestone precipitation filters and to repair a 

major pipe rupture in the heat exchanger. Repair of the 

above-ground piping necessitated the longer-thanscheduled (13 days instead of 5 days) storage period 

during test cycle I. Injection during test cycle II totaled 

8 days. Problems with bearings in the turbine shaft pump 

in production well A and subsequent repair caused the 

storage period to extend to approximately 90 days. 

Withdrawal during test cycle II was 8 days. Test cycles 

III and IV were done as scheduled with approximately 8 

days of injection and withdrawal and approximately 10 

days of storage. 

The time lag shown in figure 9 is the time needed for 

the water temperature in the aquifers and confining units 

to equilibrate. This is discussed in the Time-Lag Effect 

section.

ANALYSIS OF THERMAL DATA FOR SHORT-TERM 

TEST CYCLES

The following sections of the report summarize 

thermal data from the test cycles and describe the 

movement of heat and the changes in temperature in 

relation to the hydraulic and thermal properties of the 

aquifer and confining units. Several possible 

explanations are given for observed trends at individual 

observation wells and measurement points. Temperature 

data for the individual observation wells at site A for the 

four test cycles are presented graphically as plots of 

temperature as a function of time (figs. 10–14b) and as 

vertical-profile plots of temperature (figs. 17–20).

Temperature Graphs

Temperature graphs were used to determine the 

transient effects of temperature change at specific points 

within the aquifer, especially points at which aquifer 

properties changed. Included are plots of temperatures at 

production well A and observation wells AM1, AS1, 

AM2, and AM3. The temperatures shown for production 

140

130

120

100

110

90

80

70

TEMPERATURE, IN DEGREES CELSIUS

TIME SINCE BEGINNING OF INJECTION, IN DAYS

Figure 9. Aquifer temperature, heat-conduction, and time-lag effects during injection

and maintenance periods of test cycle 1 in observation well AM1.

60

50

40

30

20

10

0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 Heat 1 Heat 2 Heat 3 Heat 4 Heat 5

Injection

period

Time-lag

Drop in temperature due

to heat conduction

Temperature at 52 meter altitude

Maintenance period

(heat exchanger and filtration unit serviced)
B16

Heat 1 Heat 1Heat 2 Heat 2Heat 3

Heat 3

Heat 4

Heat 4

Heat 5

Heat 5

140

140

130

130

120

120

110

110

100

100

90

90

80

80

70

70

60

60

50

50

40

40

30

30

20

20

10

10

0

0

2 12 14 16 18 4 6 8 10

TIME SINCE BEGINNING OF

INJECTION, IN DAYS

TIME SINCE BEGINNING OF

WITHDRAWAL, IN DAYS

TEMPERATURE, IN DEGREES CELSIUS

2 4 6 8 10

Figure 10. Temperatures at the wellhead in production well A for the

TEST CYCLE l

TEST CYCLE ll
B17

Heat 1 Heat 1Heat 2 Heat 2Heat 3

Heat 3

Heat 4

Heat 4 Heat 5

Heat 5

140

140

130

130

120

120

110

110

100

100

90

90

80

80

70

70

60

60

50

50

40

40

30

30

20

20

10

10

0

0

2 12 14 16 18 4 6 8 10

TIME SINCE BEGINNING OF

INJECTION, IN DAYS

TIME SINCE BEGINNING OF

WITHDRAWAL, IN DAYS

TEMPERATURE, IN DEGREES CELSIUS

2 4 6 8 10

four short-term test cycles during periods of injection and withdrawal.

TEST CYCLE lll

TEST CYCLE lV
B18TEMPERATURE, IN DEGREES CELSIUS

100

100

120

140

80

80

60

60

40

40

20

20

0

0

100

80

60

40

20

0

100

100

80

80

60

60

40

40

20

20

0

0

Eau Claire Formation

Ironton and Galesville Sandstones

Lower part of Franconia Formation

Upper part of Franconia Formation

St. Lawrence Formation

2 12 14 16 18 4 6 8 10

TIME SINCE BEGINNING OF

INJECTION, IN DAYS

TIME SINCE BEGINNING OF

WITHDRAWAL, IN DAYS

2 4 6 8 10

A. Test Cycle l

Figure 11a. Temperatures in observation well AM1 during periods of

Temperature at 109.7 meter altitude

Temperature at 104.2 meter altitude

Temperature at 93.0 meter altitude

Temperature at 88.4 meter altitude

Temperature at 80.8 meter altitude

Temperature at 73.1 meter altitude

Temperature at 38.1 meter altitude

Galesville

Ironton Temperature at 58.2 meter altitude

Temperature at 51.5 meter altitude

Temperature at 44.8 meter altitude
B19

injection and withdrawal for (A) test cycle l and (B) test cycle ll. TEMPERATURE, IN DEGREES CELSIUS

100

100

120

140

80

80

60

60

40

40

20

20

0

0

100

80

60

40

20

0

100

100

80

80

60

60

40

40

20

20

0

0

2 12 14 16 18 4 6 8 10

TIME SINCE BEGINNING OF

INJECTION, IN DAYS

TIME SINCE BEGINNING OF

WITHDRAWAL, IN DAYS

2 4 6 8 10

B. Test Cycle ll

Eau Claire Formation

Ironton and Galesville Sandstones

Lower part of Franconia Formation

Upper part of Franconia Formation

St. Lawrence Formation Temperature at 109.7 meter altitude

Temperature at 104.2 meter altitude

Temperature at 93.0 meter altitude

Temperature at 88.4 meter altitude

Temperature at 80.8 meter altitude

Temperature at 73.1 meter altitude

Temperature at 38.1 meter altitude

Galesville

Ironton Temperature at 58.2 meter altitude

Temperature at 51.5 meter altitude

Temperature at 44.8 meter altitude
B20TEMPERATURE, IN DEGREES CELSIUS

100

100

120

140

80

80

60

60

40

40

20

20

0

0

100

80

60

40

20

0

100

100

80

80

60

60

40

40

20

20

0

0

Eau Claire Formation

Ironton and Galesville Sandstones

Lower part of Franconia Formation

Upper part of Franconia Formation

St. Lawrence Formation

2 12 14 16 18 4 6 8 10

TIME SINCE BEGINNING OF

INJECTION, IN DAYS

TIME SINCE BEGINNING OF

WITHDRAWAL, IN DAYS

2 4 6 8 10

C. Test Cycle lll

Figure 11b. Temperatures in observation well AM1 during periods of

Temperature at 109.7 meter altitude

Temperature at 104.2 meter altitude

Temperature at 93.0 meter altitude

Temperature at 88.4 meter altitude

Temperature at 80.8 meter altitude

Temperature at 73.1 meter altitude

Temperature at 38.1 meter altitude

Galesville

Ironton Temperature at 58.2 meter altitude

Temperature at 51.5 meter altitude

Temperature at 44.8 meter altitude
B21

injection and withdrawal for (C) test cycle lll and (D) test cycle lV. TEMPERATURE, IN DEGREES CELSIUS

100

100

120

140

80

80

60

60

40

40

20

20

0

0

100

80

60

40

20

0

100

100

80

80

60

60

40

40

20

20

0

0

2 12 14 16 18 4 6 8 10

TIME SINCE BEGINNING OF

INJECTION, IN DAYS

TIME SINCE BEGINNING OF

WITHDRAWAL, IN DAYS

2 4 6 8 10

D. Test Cycle lV

Eau Claire Formation

Ironton and Galesville Sandstones

Lower part of Franconia Formation

Upper part of Franconia Formation

St. Lawrence Formation Temperature at 109.7 meter altitude

Temperature at 104.2 meter altitude

Temperature at 93.0 meter altitude

Temperature at 88.4 meter altitude

Temperature at 80.8 meter altitude

Temperature at 73.1 meter altitude

Temperature at 38.1 meter altitude

Galesville

Ironton Temperature at 58.2 meter altitude

Temperature at 51.5 meter altitude

Temperature at 44.8 meter altitude
B22TEMPERATURE, IN DEGREES CELSIUS

100

100

120

140

80

80

60

60

40

40

20

20

0

0

100

80

60

40

20

0

100

100

80

80

60

60

40

40

20

20

0

0

Eau Claire Formation

Ironton and Galesville Sandstones

Lower part of Franconia Formation

Upper part of Franconia Formation

St. Lawrence Formation

2 12 14 16 18 4 6 8 10

TIME SINCE BEGINNING OF

INJECTION, IN DAYS

TIME SINCE BEGINNING OF

WITHDRAWAL, IN DAYS

2 4 6 8 10

A. Test Cycle l

Figure 12a. Temperatures in observation well AS1 during periods of

Temperature at 109.7 meter altitude

Temperature at 104.2 meter altitude

Temperature at 99.1 meter altitude

Temperature at 93.0 meter altitude

Temperature at 88.4 meter altitude

Temperature at 80.8 meter altitude

Temperature at 73.1 meter altitude

Temperature at 65.5 meter altitude

Temperature at 38.1 meter altitude

Galesville

Ironton Temperature at 58.2 meter altitude

Temperature at 51.5 meter altitude

Temperature at 44.8 meter altitude
B23

TEMPERATURE, IN DEGREES CELSIUS

100

100

120

140

80

80

60

60

40

40

20

20

0

0

100

80

60

40

20

0

100

100

80

80

60

60

40

40

20

20

0

0

Eau Claire Formation

Ironton and Galesville Sandstones

Lower part of Franconia Formation

Upper part of Franconia Formation

St. Lawrence Formation

2 12 14 16 18 4 6 8 10

TIME SINCE BEGINNING OF

INJECTION, IN DAYS

TIME SINCE BEGINNING OF

WITHDRAWAL, IN DAYS

2 4 6 8 10

injection and withdrawal for (A) test cycle l and (B) test cycle ll.

B. Test Cycle ll

Temperature at 109.7 meter altitude

Temperature at 104.2 meter altitude

Temperature at 99.1 meter altitude

Temperature at 93.0 meter altitude

Temperature at 88.4 meter altitude

Temperature at 80.8 meter altitude

Temperature at 73.1 meter altitude

Temperature at 65.5 meter altitude

Temperature at 38.1 meter altitude

Galesville

Ironton Temperature at 58.2 meter altitude

Temperature at 51.5 meter altitude

Temperature at 44.8 meter altitude
B24TEMPERATURE, IN DEGREES CELSIUS

100

100

120

140

80

80

60

60

40

40

20

20

0

0

100

80

60

40

20

0

100

100

80

80

60

60

40

40

20

20

0

0

Eau Claire Formation

Ironton and Galesville Sandstones

Lower part of Franconia Formation

Upper part of Franconia Formation

St. Lawrence Formation

2 12 14 16 18 4 6 8 10

TIME SINCE BEGINNING OF

INJECTION, IN DAYS

TIME SINCE BEGINNING OF

WITHDRAWAL, IN DAYS

2 4 6 8 10

C. Test Cycle lll

Figure 12b. Temperatures in observation well AS1 during periods of

Temperature at 109.7 meter altitude

Temperature at 104.2 meter altitude

Temperature at 99.1 meter altitude

Temperature at 93.0 meter altitude

Temperature at 88.4 meter altitude

Temperature at 80.8 meter altitude

Temperature at 73.1 meter altitude

Temperature at 65.5 meter altitude

Temperature at 38.1 meter altitude

Galesville

Ironton Temperature at 58.2 meter altitude

Temperature at 51.5 meter altitude

Temperature at 44.8 meter altitude
B25

TEMPERATURE, IN DEGREES CELSIUS

100

100

120

140

80

80

60

60

40

40

20

20

0

0

100

80

60

40

20

0

100

100

80

80

60

60

40

40

20

20

0

0

Eau Claire Formation

Ironton and Galesville Sandstones

Lower part of Franconia Formation

Upper part of Franconia Formation

St. Lawrence Formation

2 12 14 16 18 4 6 8 10

TIME SINCE BEGINNING OF

INJECTION, IN DAYS

TIME SINCE BEGINNING OF

WITHDRAWAL, IN DAYS

2 4 6 8 10

injection and withdrawal for (C) test cycle lll and (D) test cycle lV.

D. Test Cycle lV

Temperature at 109.7 meter altitude

Temperature at 104.2 meter altitude

Temperature at 99.1 meter altitude

Temperature at 93.0 meter altitude

Temperature at 88.4 meter altitude

Temperature at 80.8 meter altitude

Temperature at 73.1 meter altitude

Temperature at 65.5 meter altitude

Temperature at 38.1 meter altitude

Galesville

Ironton Temperature at 58.2 meter altitude

Temperature at 51.5 meter altitude

Temperature at 44.8 meter altitude
B26TEMPERATURE, IN DEGREES CELSIUS

100

100

120

140

80

80

60

60

40

40

20

20

0

0

100

80

60

40

20

0

100

100

80

80

60

60

40

40

20

20

0

0

Eau Claire Formation

Ironton and Galesville Sandstones

Lower part of Franconia Formation

Upper part of Franconia Formation

St. Lawrence Formation

2 12 14 16 18 4 6 8 10

TIME SINCE BEGINNING OF

INJECTION, IN DAYS

TIME SINCE BEGINNING OF

WITHDRAWAL, IN DAYS

2 4 6 8 10

A. Test Cycle l

Figure 13a. Temperatures in observation well AM2 during periods of

Temperature at 109.7 meter altitude

Temperature at 104.2 meter altitude

Temperature at 99.1 meter altitude

Temperature at 93.0 meter altitude

Temperature at 88.4 meter altitude

Temperature at 80.8 meter altitude

Temperature at 73.1 meter altitude

Temperature at 65.5 meter altitude

Temperature at 38.1 meter altitude

Galesville

Ironton Temperature at 58.2 meter altitude

Temperature at 51.5 meter altitude

Temperature at 44.8 meter altitude
B27

TEMPERATURE, IN DEGREES CELSIUS

100

100

120

140

80

80

60

60

40

40

20

20

0

0

100

80

60

40

20

0

100

100

80

80

60

60

40

40

20

20

0

0

Eau Claire Formation

Ironton and Galesville Sandstones

Lower part of Franconia Formation

Upper part of Franconia Formation

St. Lawrence Formation

2 12 14 16 18 4 6 8 10

TIME SINCE BEGINNING OF

INJECTION, IN DAYS

TIME SINCE BEGINNING OF

WITHDRAWAL, IN DAYS

2 4 6 8 10

injection and withdrawal for (A) test cycle l and (B) test cycle ll.

B. Test Cycle ll

Temperature at 109.7 meter altitude

Temperature at 104.2 meter altitude

Temperature at 99.1 meter altitude

Temperature at 93.0 meter altitude

Temperature at 88.4 meter altitude

Temperature at 80.8 meter altitude

Temperature at 73.1 meter altitude

Temperature at 65.5 meter altitude

Temperature at 38.1 meter altitude

Galesville

Ironton Temperature at 58.2 meter altitude

Temperature at 51.5 meter altitude

Temperature at 44.8 meter altitude
B28TEMPERATURE, IN DEGREES CELSIUS

100

100

120

140

80

80

60

60

40

40

20

20

0

0

100

80

60

40

20

0

100

100

80

80

60

60

40

40

20

20

0

0

Eau Claire Formation

Ironton and Galesville Sandstones

Lower part of Franconia Formation

Upper part of Franconia Formation

St. Lawrence Formation

2 12 14 16 18 4 6 8 10

TIME SINCE BEGINNING OF

INJECTION, IN DAYS

TIME SINCE BEGINNING OF

WITHDRAWAL, IN DAYS

2 4 6 8 10

C. Test Cycle lll

Figure 13b. Temperatures in observation well AM2 during periods of

Temperature at 109.7 meter altitude

Temperature at 104.2 meter altitude

Temperature at 99.1 meter altitude

Temperature at 93.0 meter altitude

Temperature at 88.4 meter altitude

Temperature at 80.8 meter altitude

Temperature at 73.1 meter altitude

Temperature at 65.5 meter altitude

Temperature at 38.1 meter altitude

Galesville

Ironton Temperature at 58.2 meter altitude

Temperature at 51.5 meter altitude

Temperature at 44.8 meter altitude
B29

TEMPERATURE, IN DEGREES CELSIUS

100

100

120

140

80

80

60

60

40

40

20

20

0

0

100

80

60

40

20

0

100

100

80

80

60

60

40

40

20

20

0

0

Eau Claire Formation

Ironton and Galesville Sandstones

Lower part of Franconia Formation

Upper part of Franconia Formation

St. Lawrence Formation

2 12 14 16 18 4 6 8 10

TIME SINCE BEGINNING OF

INJECTION, IN DAYS

TIME SINCE BEGINNING OF

WITHDRAWAL, IN DAYS

2 4 6 8 10

injection and withdrawal for (C) test cycle lll and (D) test cycle lV.

D. Test Cycle lV

Temperature at 109.7 meter altitude

Temperature at 104.2 meter altitude

Temperature at 99.1 meter altitude

Temperature at 93.0 meter altitude

Temperature at 88.4 meter altitude

Temperature at 80.8 meter altitude

Temperature at 73.1 meter altitude

Temperature at 65.5 meter altitude

Temperature at 38.1 meter altitude

Galesville

Ironton

Temperature at

58.2 meter altitude

Temperature at

51.5 meter altitude

Temperature at

44.8 meter altitude
B30TEMPERATURE, IN DEGREES CELSIUS

100

100

120

140

80

80

60

60

40

40

20

20

0

0

100

80

60

40

20

0

100

100

80

80

60

60

40

40

20

20

0

0

Eau Claire Formation

Ironton and Galesville Sandstones

Lower part of Franconia Formation

Upper part of Franconia Formation

St. Lawrence Formation

TIME SINCE BEGINNING OF

INJECTION, IN DAYS

TIME SINCE BEGINNING OF

WITHDRAWAL, IN DAYS

A. Test Cycle l

Figure 14a. Temperatures in observation well AM3 during periods of

Temperature at 109.7 meter altitude

Temperature at 104.2 meter altitude

Temperature at 99.1 meter altitude

Temperature at 93.0 meter altitude

Temperature at 88.4 meter altitude

Temperature at 80.8 meter altitude

Temperature at 73.1 meter altitude

Temperature at 65.5 meter altitude

Temperature at 38.1 meter altitude

Galesville

Ironton Temperature at 58.2 meter altitude

Temperature at 51.5 meter altitude

Temperature at 44.8 meter altitude
B31

TEMPERATURE, IN DEGREES CELSIUS

100

100

120

140

80

80

60

60

40

40

20

20

0

0

100

80

60

40

20

0

100

100

80

80

60

60

40

40

20

20

0

0

Eau Claire Formation

Ironton and Galesville Sandstones

Lower part of Franconia Formation

Upper part of Franconia Formation

St. Lawrence Formation

2 12 14 16 18 4 6 8 10

TIME SINCE BEGINNING OF

INJECTION, IN DAYS

TIME SINCE BEGINNING OF

WITHDRAWAL, IN DAYS

2 4 6 8 10

injection and withdrawal for (A) test cycle l and (B) test cycle ll.

B. Test Cycle ll

Temperature at 109.7 meter altitude

Temperature at 104.2 meter altitude

Temperature at 99.1 meter altitude

Temperature at 93.0 meter altitude

Temperature at 88.4 meter altitude

Temperature at 80.8 meter altitude

Temperature at 73.1 meter altitude

Temperature at 65.5 meter altitude

Temperature at 38.1 meter altitude

Galesville

Ironton Temperature at 58.2 meter altitude

Temperature at 51.5 meter altitude

Temperature at 44.8 meter altitude
B32TEMPERATURE, IN DEGREES CELSIUS

100

100

120

140

80

80

60

60

40

40

20

20

0

0

100

80

60

40

20

0

100

100

80

80

60

60

40

40

20

20

0

0

Eau Claire Formation

Ironton and Galesville Sandstones

Lower part of Franconia Formation

Upper part of Franconia Formation

St. Lawrence Formation

2 12 14 16 18 4 6 8 10

TIME SINCE BEGINNING OF

INJECTION, IN DAYS

TIME SINCE BEGINNING OF

WITHDRAWAL, IN DAYS

2 4 6 8 10

C. Test Cycle lll

Figure 14b. Temperatures in observation well AM3 during periods of

Temperature at 109.7 meter altitude

Temperature at 104.2 meter altitude

Temperature at 99.1 meter altitude

Temperature at 93.0 meter altitude

Temperature at 88.4 meter altitude

Temperature at 80.8 meter altitude

Temperature at 73.1 meter altitude

Temperature at 65.5 meter altitude

Temperature at 38.1 meter altitude

Galesville

Ironton Temperature at 58.2 meter altitude

Temperature at 51.5 meter altitude

Temperature at 44.8 meter altitude
B33

TEMPERATURE, IN DEGREES CELSIUS

100

100

120

140

80

80

60

60

40

40

20

20

0

0

100

80

60

40

20

0

100

100

80

80

60

60

40

40

20

20

0

0

Eau Claire Formation

Ironton and Galesville Sandstones

Lower part of Franconia Formation

Upper part of Franconia Formation

St. Lawrence Formation

2 12 14 16 18 4 6 8 10

TIME SINCE BEGINNING OF

INJECTION, IN DAYS

TIME SINCE BEGINNING OF

WITHDRAWAL, IN DAYS

2 4 6 8 10

D. Test Cycle lV

injection and withdrawal for (C) test cycle lll and (D) test cycle lV.

Temperature at 109.7 meter altitude

Temperature at 104.2 meter altitude

Temperature at 99.1 meter altitude

Temperature at 93.0 meter altitude

Temperature at 88.4 meter altitude

Temperature at 80.8 meter altitude

Temperature at 73.1 meter altitude

Temperature at 65.5 meter altitude

Temperature at 38.1 meter altitude

Galesville

Ironton Temperature at 58.2 meter altitude

Temperature at 51.5 meter altitude

Temperature at 44.8 meter altitude
B34

well A were for the injected water measured at the 

wellhead. Relatively small temperature fluctuations of 

between 1 and 5°C, which represent intermittent failure 

of some thermocouples due to insulation wear at kinks 

in the wires, are evident in some of the graphs for the 

observation wells and should be ignored.

The highest temperatures measured in all cycles in 

every observation well were at altitudes of 45, 52, and 

58 m. These altitudes represent the Ironton and 

Galesville Sandstones, which are the most permeable 

parts of the Franconia-Ironton-Galesville aquifer 

(Miller and Delin, 1993). The Ironton part of the aquifer 

(from 52 to 63 m in altitude) is approximately four times 

as permeable as the Galesville part of the aquifer (from 

42 to 52 m in altitude). Examples of relative arrival 

times for temperature fronts at the observation wells can 

be seen in data from observation well AS1 (figs. 12a, 12 

b, and table 2). For this study, arrival time was defined 

as the time at which the temperature first began to rise 

at a given monitoring point.

For the Ironton and Galesville Sandstones, the 

earliest arrival times for temperature fronts at every 

observation well for all cycles were at the 58 m altitude, 

the upper part of the Ironton Sandstone. The next arrival 

times for temperature fronts were at the 45 m altitude, 

and the latest arrival times were at the 52 m altitude. 

Although temperature fronts arrived last at the altitude 

of 52 m, the highest temperatures were recorded at this 

altitude for all observation wells except AM3. Although 

observation wells AM1 and AS1 are both 7 m from 

production well A at land surface, arrival times for well 

AM1 were earlier. This probably is because the bottom 

of well AM1 was about 6 m from production well A, 

whereas the bottom of well AS1 was about 13 m from 

production well A (fig. 5).

The movement of heat in the upper part of the 

Franconia Formation was considerably slower than in 

the Ironton and Galesville Sandstones. Temperature 

fronts reached observation well AS1 about 2.85 days 

into the first test cycle, or about at the start of heat 3, in 

 Table 2. Temperature front arrival time at measurement points in the upper part of the Franconia Formation and in the Ironton and 

Galesville Sandstones for short term test cycle I

[m, meters; nd, temperature front not detected; --, no data; do., ditto]

Well number and 

distance from 

injection well Geologic unit

Altitude of 

measurement point, 

in meters above sea level

Time of temperature 

front arrival, in days 

since start of injection

AM1 Upper part of the Franconia Formation 99 2.80

7 m do. 93 2.80

do. 88 2.85

Ironton and Galesville Sandstones 58 .52

do. 52 .87

do. 45 --

AS1 Upper part of the Franconia Formation 99 2.85

7 m do. 93 2.85

do. 88 2.85

Ironton and Galesville Sandstones 58 .82

do. 52 1.35

do. 45 1.19

AM2 Upper part of the Franconia Formation 99 2.86

14 m do. 93 1.61

do. 88 1.66

Ironton and Galesville Sandstones 58 1.62

do. 52 1.66

do. 45 1.66

AM3 Upper part of the Franconia Formation 99 nd

14 m do. 93 nd

do. 88 nd

Ironton and Galesville Sandstones 58 3.00

do. 52 nd

do. 45 8.88
B35

the upper part of the Franconia Formation (figs. 12a and 

12b). The first temperature fronts to reach observation 

well AS1 in the upper part of the Franconia Formation 

were at altitudes of 93 m, then 88 m, and finally 99 m, 

as illustrated by the maximum temperatures in figures 

12a and 12b. Temperature fronts were not observed in 

the upper part of the Franconia Formation at 

observation well AM3 (fig. 14a), the farthest 

observation well from production well A, for test cycles 

I and II. This is because the relative permeability of the 

upper part of the Franconia Formation is about one-half 

that of the most permeable part of the Ironton and 

Galesville Sandstones.

Interpretation of the temperature graphs indicates 

little heat-conduction loss to the overlying St. Lawrence 

confining unit, altitude 110 m, the underlying Eau 

Claire confining unit, altitude 38 m, and the unscreened 

lower part of the Franconia Formation, altitudes 66 to 

81 m. Between these three formations, however, heatconduction losses were greatest in the Eau Claire 

confining unit. Some of the temperature increase in well 

AM1 may be due to horizontal heat convection, because 

the screened interval of production well A extended into 

the top 1.5 m of the Eau Claire Formation (Miller and 

Delin, 1993). Although observation wells AM1 and 

AS1 were both 7 m from production well A at land 

surface, heat-conduction losses were greater for well 

AM1. This probably results because temperatures were 

greater at well AM1 than at AS1; the bottom of well 

AM1 was closer to the bottom of production well A than 

was the bottom of well AS1 (fig. 5). Because the water 

temperatures were greater near well AM1 than near well 

AS1, greater heat-conduction losses to the Eau Claire 

confining unit occurred.

Temperatures measured during the withdrawal 

periods indicate that the transport of heat within the 

aquifers is probably a function of permeability. The 

aquifer temperature cooled more rapidly in the Ironton 

and Galesville Sandstones than in the upper part of the 

Franconia Formation.

Temperatures at the beginning of the withdrawal 

period indicate there was convective heat loss down the 

well bore of production well A from the upper part of the 

Franconia Formation to the Ironton and Galesville 

Sandstones. Temperatures measured in the Ironton and 

Galesville Sandstones at the beginning of withdrawal 

were very similar to those at the end of injection for 

most of the observation wells (figs. 11a–14b) indicating 

that heat-conduction losses were minimal in the 

sandstones during storage, but the temperatures 

measured in the upper part of the Franconia Formation 

(altitudes 88 and 93 m) in wells AM1 and AS1 at the 

beginning of withdrawal were significantly less than the 

temperatures measured at the end of the storage period. 

This heat loss likely was due to convective losses of heat 

from the upper part of the Franconia Formation down 

the well bore of production well A to the Ironton and 

Galesville Sandstones. Because the well was open to 

both formations and because hydraulic heads decrease 

with depth in the well, ground-water flow was down the 

well bore during periods of storage. Thus, a net loss of 

heat occurred because of the convective flow of heated 

water between the formations. In addition, the 

withdrawal plots illustrate that not all of the injected 

heat was recovered.

Although observation wells AM2 and AM3 were 

approximately the same radial distance away from 

production well A at land surface (fig. 5), the 

temperatures at well AM2 were nboticeably higher than 

those at well AM3 (figs. 13a –14b). The graphs should 

be similar if the hydraulic and thermal properties are 

similar in both directions. The most likely explanation 

for the measured differences is the fact that the bottom 

of well AM2 was about 16 m from production well A, 

whereas the bottom of AM3 was about 19 m from 

production well A (fig. 5).

Potential Aquifer Clogging

Upon initial examination, the temperatures registered 

by the thermocouples at the 58 m altitude in observation 

wells AM1 and AS1 (figs. 11a–12b) appear 

unrepresentative of aquifer temperatures. The 

temperatures increased rapidly during the start of each 

heat phase and then either remained steady or decreased 

slowly through the remainder of that heat phase. These 

data differ considerably from temperatures measured in 

observation wells AM2 and AM3 (figs. 13a –14b) and 

seem to be contrary to expectations.

One possible explanation for the different trends at 

the 58 m altitude for AM1 and AS1 is that the aquifer 

rather than the well bore was gradually becoming 

clogged during injection; the permeability and porosity 

of the aquifer, and thus its ability to transmit heat, were 

reduced. Examination of aquifer materials indicates that 

mechanical and chemical processes of clogging 

probably were responsible. M.C. Hoyer (Minnesota 

Geological Survey, 1985, written commun.) described 

the sandstone core taken from observation well AC1 

(fig. 3) at the 58 m altitude as being a coarse- to finegrained, friable sandstone with little carbonate cement. 
B36

Hoyer also noted that the Franconia-Ironton-Galesville 

aquifer is most friable at this location. Because of the 

lack of carbonate cement, it is possible that fine sand 

may have physically moved near production well A 

where ground-water velocities were highest during 

periods of injection and withdrawal. This sand could 

have moved away from production well A during 

injection, have repacked within pore spaces at some 

radial distance from the well bore, and effectively 

reduced the local permeability and porosity.

Muecke (1978) studied the movement of fine 

sandstone particles, termed formation fines, in relation 

to oil- and gas-well development. Muecke determined 

that mechanical bridging at pore restrictions occurs if 

certain conditions are met with respect to particle size 

and the rate of fluid moving through the pores. Although 

Muecke was unable to make quantitative 

measurements, he indicates that the percentage of fines 

that bridge pore spaces depends greatly on the 

concentration of the fines. When bridges form at pore 

exits, they act as effective traps for the particles that 

follow (fig. 15). Bridges can be broken by pressure 

surges or by reversing fluid-flow direction. Bridge 

stability, however, depends on the flow velocity where 

the bridges form. Bridges that form at high flow 

velocities are tightly packed and are stable during flow 

reversals. Bridges that form at low flow velocities are 

unstable, and even slight reversals in flow can unseat 

them; these fines are then free to move in the reverse 

direction until bridging occurs in that direction. 

An additional observation made by Muecke during 

his single-phase flow experiments is that continued 

injection of a solids-free liquid into a matrix containing 

liquid and mobile fines results in rapid establishment of 

an equilibrium bridged condition. When this condition 

is established, continued injection of a solids-free liquid 

at a constant rate results in virtually no further 

movement of fine particles.

Mechanical clogging may have been compounded by 

precipitation of calcium carbonate that was not totally 

removed by the above-ground filter system. During the 

withdrawal of water, some carbonate could have reentered solution, and some pores in the fine-grained 

sandstone could have unclogged. Some pores, however, 

could have remained bridged and generally decreased 

the permeability. Because the aquifer never returned to 

Fine material

bridged at

pore restriction

Fluid flow

direction

Mobile fine

material

Figure 15. Bridging of fine material at a pore restriction. (Modified from Muecke, 1978).
B37

its initial ambient temperature, some carbonatecemented grains would have also remained. As a result 

of this process, the permeability and porosity near the 

well bore would have decreased. Consequently, the 

temperature would actually have decreased as injection 

continued because of a lessening of advective heat 

transport and an increase in conductive heat transport. A 

lowering of permeability, and corresponding 

temperature, was not detected at the 58 m temperaturemeasurement altitude in observation wells AM2 and 

AM3 because fluid velocities probably were not high 

enough to induce migration of fine particles at these 

radial distances from production well A. 

Time-Lag Effect

The concept of time-lag, as defined by Jaeger (1950) 

and described by Carslaw and Jaeger (1959), states that 

temperatures in a transport medium increase by 

advection during periods of heated water injection until 

they reach maximum values. Rates of heat transport are 

a function of the heat capacity and thermal conductivity 

of the aquifers and confining units. The transport of heat 

within an aquifer is primarily by advection (that is, by 

flow of the injected water) and is secondarily by 

conduction through the aquifer materials. During 

periods of injection, temperatures at the same radial 

distance from the injection well are lower in confining 

units than in aquifers because heat transport in 

confining units is primarily by the slower process of 

conduction (fig. 16). When heat injection stops and 

conduction becomes the main heat-transport 

mechanism, temperatures in aquifers and confining 

units approach equilibrium. During periods of storage, 

temperatures increase in the confining units and 

decrease in the aquifers; the line of equal temperature 

approaches the vertical (fig. 16). The period from 

immediately after injection stops until an equilibrium 

temperature is achieved is defined as the time lag 

(fig. 9).

The duration of the time lag depends on the number 

of low-permeability zones within an aquifer and on the 

thickness, heat capacity, and thermal conductivity of the 

aquifers and confining units. Also of importance is the 

location of the temperature-measurement point, both 

vertically relative to confining units and horizontally 

relative to the injection well.

Time-lag heat conduction was detected at most 

temperature-measurement altitudes in the Ironton and 

Galesville Sandstone and in the upper part of the 

Franconia Formation in observation wells AM1 and 

AS1 (figs. 11a– 12b), the wells closest to production 

well A. A time lag was also detected, but generally less 

pronounced, at some of the temperature-measurement 

altitudes in these formations in observation wells AM2 

and AM3 (figs. 13a– 14b), the most distant wells from 

production well A. A time lag was detected in 

observation well AM3 only at the 58 m altitude, which 

corresponds to the most permeable part of the injection 

zone.

Temperature Profiles

Temperature profiles at individual observation wells 

(figs. 17–20) are useful in (1) determining the effects of 

buoyancy flow (Miller and Delin, 1993), (2) examining 

temperature variations in relation to hydraulic and 

thermal properties of the aquifer, and (3) determining 

possible long-term trends of vertical heat loss from the 

aquifer. Temperature profiles are presented for the end 

of each heat phase during the injection period (heats 1 

through 5), each storage period, and each withdrawal 

period. The temperature-measurement altitudes for 

each of the observation wells are shown in figure 4.

The temperature profiles were constructed by 

connecting the successive temperature-measurement 

altitudes with straight lines. This linear interpolation 

may not be totally representative of the temperature 

between the temperature-measurement points, 

especially where the temperature was interpolated 

across a major hydraulic or thermal boundary such as 

near confining layers and the unscreened lower part of 

the Franconia Formation. Contrasts in temperature 

across these boundaries were large (20 to 40°C), 

especially at observation wells AM1 and AS1, which 

were closest to production well A. The contrast in the 

advective heat-transport rate in the most permeable part 

of the aquifer and the conductive heat-transport rate in 

the least permeable parts of the aquifer and in the 

confining layers was most noticeable near production 

well A. Although detail is lacking for temperature 

variation at the hydraulic and thermal boundaries, the 

linear-interpolation method did not seriously hinder use 

of the temperature profiles in describing the energytransfer processes within the aquifer and confining 

units.

The shape of the temperature profiles shown in 

figures 17 through 20 generally reflects the distribution 

of permeability described by Miller and Delin (1993) 

for the Franconia-Ironton-Galesville aquifer. Highest 

temperatures were in the Ironton and Galesville 

Sandstones, and lowest temperatures were in the lower 

part of the Franconia Formation. Temperatures in the 

Ironton and Galesville Sandstones and in the upper part 
B38

of the Franconia Formation at each observation well 

generally reached a maximum during heat 5, as 

expected (figs. 17–20). The maximum temperature did 

not occur, or was not detected, during heat 5 in some of 

the test cycles because of one or more of the following 

factors: (1) an insufficient number of vertical 

monitoring points at each well; (2) the variation in 

injection temperature during each heat phase (table 1), 

which resulted in maximum temperatures that were not 

comparable; and (3) the relatively small changes in 

temperature (less than 5°C) that occurred over relatively 

short time periods of several hours that cannot be 

accounted for because of the complexity of the test 

cycles.

The convection of ground water created by the 

difference in density between the ambient-temperature 

aquifer water and the warmer injected water is termed 

buoyancy flow, (Hellstrom and others, 1979). 

Buoyancy flow causes thermal stratification and tilting 

of the thermal front (Miller and Delin, 1993). The 

effects of buoyancy flow are most readily observed near 

the top of an aquifer at the end of storage periods.

The effects of buoyancy flow were not readily 

noticeable in the temperature profiles at the test facility 

(figs. 17–20). The effects of buoyancy flow were most 

Siltstone or

shale layer

Sandstone

aquifer

Lower

confining

layer

Fluid flow direction

Figure 16. Generalized temperature profiles after periods of injection and storage in a cross-section

of sandstone and shale with different permeabilities. (Modified from Carslaw and Jaeger, 1959).

EXPLANATION

Line of equal temperature after periods of injection

Line of equal temperature after periods of storage

Direction of energy transport by condition

Direction of energy transport by advection
B39

35

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45

50

50

55

55

60

60

65

65

70

70

75

75

80

80

85

85

90

90

95

95

100

100

105

105

110

110

115

115

0 20 40 60 60 80 80 100 100 120 120 140 140 0 20 40

TEMPERATURE, IN DEGREES CELSIUS

ALTITUDE, IN METERS ABOVE SEA LEVEL

TEST CYCLE lV

TEST CYCLE ll

TEST CYCLE lll

TEST CYCLE l

Eau Claire Formation

Ironton and Galesville Sandstones

Lower part of Franconia Formation

Upper part of Franconia Formation

St. Lawrence Formation

Eau Claire Formation

Ironton and Galesville Sandstones

Lower part of Franconia Formation

Upper part of Franconia Formation

St. Lawrence Formation

Eau Claire

Formation

Ironton and Galesville Sandstones

Lower part of Franconia Formation

Upper part of Franconia Formation

St. Lawrence Formation

Eau Claire Formation

Ironton and Galesville

 Sandstones

Lower part of Franconia Formation

Upper part of Franconia Formation

St. Lawrence Formation

EXPLANATION

Start of Heat 1

End of Heat 1

End of Heat 2

End of Heat 3

End of Heat 4

End of Heat 5

End of Storage

End of Withdrawal

Figure 17. Vertical profile of temperature for measurement points

in observation well AM1, 7 meters from production well A.
B40

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50

50

55

55

60

60

65

65

70

70

75

75

80

80

85

85

90

90

95

95

100

100

105

105

110

110

115

115

0 20 40 60 60 80 80 100 100 120 120 140 140 0 20 40

TEMPERATURE, IN DEGREES CELSIUS

ALTITUDE, IN METERS ABOVE SEA LEVEL

TEST CYCLE lV

TEST CYCLE ll

TEST CYCLE lll

TEST CYCLE l

Eau Claire Formation

Ironton and Galesville

 Sandstones

Lower part of Franconia Formation

Upper part of Franconia Formation

St. Lawrence Formation

Eau Claire Formation

Ironton and Galesville

 Sandstones

Lower part of Franconia Formation

Upper part of Franconia Formation

St. Lawrence Formation

Ironton and Galesville

 Sandstones

Lower part of Franconia Formation

Upper part of Franconia Formation

St. Lawrence Formation

Eau Claire Formation Eau Claire Formation

Ironton and Galesville

 Sandstones

Lower part of Franconia Formation

Upper part of Franconia Formation

St. Lawrence Formation

EXPLANATION

Start of Heat 1

End of Heat 1

End of Heat 2

End of Heat 3

End of Heat 4

End of Heat 5

End of Storage

End of Withdrawal

Figure 18. Vertical profile of temperature for measurement points

in observation well AS1, 7 meters from production well A.
B41

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45

50

50

55

55

60

60

65

65

70

70

75

75

80

80

85

85

90

90

95

95

100

100

105

105

110

110

115

115

0 20 40 60 60 80 80 100 100 120 120 140 140 0 20 40

TEMPERATURE, IN DEGREES CELSIUS

ALTITUDE, IN METERS ABOVE SEA LEVEL

TEST CYCLE lV

TEST CYCLE ll

TEST CYCLE lll

TEST CYCLE l

Eau Claire Formation

Ironton and Galesville

 Sandstones

Ironton and Galesville

 Sandstones

Lower part of Franconia Formation

Upper part of Franconia Formation

St. Lawrence Formation

Eau Claire Formation

Ironton and Galesville Sandstones

Lower part of Franconia Formation

Upper part of Franconia Formation

St. Lawrence Formation

Lower part of Franconia Formation

Upper part of Franconia Formation

St. Lawrence Formation

Eau Claire Formation Eau Claire Formation

Ironton and Galesville

 Sandstones

Lower part of Franconia Formation

Upper part of Franconia Formation

St. Lawrence Formation

EXPLANATION

Start of Heat 1

End of Heat 1

End of Heat 2

End of Heat 3

End of Heat 4

End of Heat 5

End of Storage

End of Withdrawal

Figure 19. Vertical profile of temperature for measurement points

in observation well AM2, 14 meters from production well A.
B42

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75

80

80

85

85

90

90

95

95

100

100

105

105

110

110

115

115

0 20 40 60 60 80 80 100 100 120 120 140 140 0 20 40

TEMPERATURE, IN DEGREES CELSIUS

ALTITUDE, IN METERS ABOVE SEA LEVEL

TEST CYCLE lV

TEST CYCLE ll

TEST CYCLE lll

TEST CYCLE l

Eau Claire Formation

Ironton and Galesville Sandstones

Lower part of Franconia Formation

Upper part of Franconia Formation

St. Lawrence Formation

Eau Claire Formation

Ironton and Galesville Sandstones

Lower part of Franconia Formation

Upper part of Franconia Formation

St. Lawrence Formation

Lower part of Franconia Formation

Upper part of Franconia Formation

St. Lawrence Formation

Eau Claire Formation

Ironton and Galesville

 Sandstones

Eau Claire Formation

Ironton and Galesville

 Sandstones

Lower part of Franconia Formation

Upper part of Franconia Formation

St. Lawrence Formation

EXPLANATION

Start of Heat 1

End of Heat 1

End of Heat 2

End of Heat 3

End of Heat 4

End of Heat 5

End of Storage

End of Withdrawal

Figure 20. Vertical profile of temperature for measurement points

in observation well AM3, 14 meters from production well A.
B43

noticeable in the Ironton and Galesville Sandstones at 

observation well AM2 at the end of storage for test cycle 

II (fig. 19) and in the Ironton and Galesville Sandstones 

at observation well AM3 at the end of storage for test 

cycles II, III, and IV (fig. 20). The effects of buoyancy 

flow were most noticeable at the end of the storage 

period for test cycle II because the storage period lasted 

approximately 90 days instead of the planned 8 days, 

because of above-ground mechanical problems. This 

90-day length of storage probably is more realistic than 

8 days for an operational thermal-energy storage system 

and, perhaps, more accurately represents the potential 

long-term effects of buoyancy flow for the FranconiaIronton-Galesville aquifer. Regardless of the length of 

storage, the actual buoyancy flow was small in 

comparison to the buoyancy flow as described by the 

sensitivity analysis for the Franconia-IrontonGalesville aquifer (Miller and Delin, 1993).

The lack of consistent buoyancy flow in the test 

results probably was due to: (1) the relatively short 

duration of the storage periods; (2) an insufficient 

density of temperature-measurement locations; and (3) 

the presence of generally continuous, thin, horizontally 

bedded silt, shale, and clay stringers within the 

Franconia-Ironton-Galesville aquifer (Miller and Delin, 

1993). These stringers could have reduced the effects of 

buoyancy flow by acting as barriers to convective flow 

induced by density differences in the water.

Another effect of the 90-day storage period for test 

cycle II was that temperatures in the upper part of the 

Franconia Formation decreased more at observation 

wells AM1 and AS1 than at observation well AM2, 

which was farther from production well A (figs. 17–20). 

Temperatures actually increased slightly at observation 

well AM3 in the upper part of the Franconia Formation, 

the observation well that was farthest from production 

well A. 

Earlier model-sensitivity analyses (Miller and Delin, 

1993) indicated that the decreases in temperature within 

the upper part of the Franconia Formation near 

production well A could be due to interformation flow 

within the well bore of production well A. The 

interformation flow, which was confirmed by use of a 

flow meter, resulted from a natural downward vertical 

gradient between the upper part of the Franconia 

Formation and the Ironton and Galesville Sandstones 

during periods of storage. This interformation flow 

caused advective flow of water in the upper part of the 

Franconia Formation past the observation wells toward 

production well A. Water from the upper part of the 

Franconia Formation was cooled as it traveled down 

production well A past the cooler, unscreened lower 

part of the Franconia Formation. This cooled water 

mixed with warmer water in the Ironton and Galesville 

Sandstones and maintained a positive advective flow 

outward into the sandstones. This flow of water into the 

Ironton and Galesville Sandstones tended to increase, or 

maintain, the temperatures measured at the observation 

wells.

During periods of storage, temperatures in the upper 

part of the Franconia Formation decreased at wells 

AM1 and AS1 (figs. 17 and 18), remained relatively 

constant at well AM3 (fig. 20), and increased slightly at 

well AM2 (fig. 19). Temperatures in the Ironton and 

Galesville Sandstones during periods of storage 

remained relatively constant at wells AM1 and AS1, 

increased at well AM3, and decreased at well AM2. The 

decrease in temperature in the upper part of the 

Franconia Formation at wells AM1 and AS1 likely 

resulted from interformation flow through production 

well A. The increase in temperature measured at well 

AM2 could be related to the areal anisotropy of the 

aquifer (Miller, 1984). Because well AM2 is on the 

minor axis of permeability relative to production well 

A, it could be less affected by advective heat flows than 

were wells AM1 and AS1; therefore, the temperature 

increase measured in the upper part of the Franconia 

Formation at well AM2 likely was due to vertical heat 

conduction rather than to horizontal advective flow. 

Similarly, the temperature decrease measured in the 

Ironton and Galesville Sandstones at well AM2 likely 

resulted from vertical heat-conduction losses.

The temperature increases measured in production 

well A at the beginning of each withdrawal period (fig. 

10) likely were caused primarily by the effects of the 

well being completed in two different units. 

Interformation flow during periods of storage, 

described earlier, resulted in a slight cooling of water 

that flowed into the Ironton and Galesville Sandstones 

near the well bore. At the beginning of withdrawal 

periods, the water withdrawn from the Ironton and 

Galesville Sandstones was cooled as it traveled up the 

well bore past the unscreened lower part of the 

Franconia Formation. The water also lost heat through 

conduction to the well bore and casing at the beginning 

of each withdrawal period. Consequently, thermal 

equilibrium at the wellhead was not reached until from 

12 to 24 hours into each withdrawal period (fig. 10).
B44

NONISOTHERMAL MODELING OF SHORT-TERM 

TEST CYCLES

A three-dimensional, anisotropic, nonisothermal, 

ground-water-flow and thermal-energy-transport 

model was used to simulate the four short-term test 

cycles. The model has the same discretization as the 

preliminary three-dimensional, isothermal groundwater-flow model described by Miller and Delin (1993). 

Miller and Voss (1986) describe discretization of the 

model and the sensitivity of the lateral boundary 

conditions for various rates of heated-water injection.

The finite-difference, ground-water-flow, and 

thermal-energy-transport model used in this study was 

developed for waste-injection problems (Intercomp 

Resources Development and Engineering, 1976) and 

will be referred to in this report as the Survey Waste 

Injection Program (SWIP) code. The SWIP code can be 

used to simulate ground-water flow and heat and solute 

transport in a liquid-saturated porous medium; it 

contains both reservoir and well-bore modeling 

capabilities.

The major model assumptions are as follows:

1. Ground-water flow is laminar (Darcy), three

dimensional, and transient.

2. Fluid density is a function of pressure, temperature,

and concentration.

3. Fluid viscosity is a function of temperature and

concentration.

4. The injected fluid is miscible with the in-place fluids.

5. Aquifer properties vary with location.

6. Hydrodynamic dispersion is a function of fluid

velocity.

7. The energy equation can be described as: enthalpy in

minus enthalpy out equals the change in internal

energy of the system.

8. Boundary conditions allow natural water movement

in the aquifer and heat losses to adjacent

formations.

9. Thermal equilibrium exists within the simulated 

area.

The basic equation describing single-phase flow in a 

porous medium is derived by combining the continuity 

equation and Darcy equation for three-dimensional 

flow (Intercomp Resources Development and 

Engineering, 1976, p. 3.4):

(1)

where

ρ = fluid density [M/L3] (kg/m3),

μ = fluid viscosity [M/L-T] (kPa-s),

k = intrinsic permeability [L2

] (m2),

g = gravitational acceleration [L/T2] (m/s2

),

z = spatial dimension in direction of gravity [L](m),

p = pressure [M/L-T2] (kPa),

q’ = mass rate of flow per unit volume from sources or

sinks [M/T-L3

] (kg/s-m3),

t = time [T] (s),

φ = porosity [dimensionless], and

∇ = gradient (for an axially symmetric cylindrical

coordinate system ∇ is

where r is the radial dimension).

The energy-balance equation describing the transport 

of thermal energy in a ground-water system (Intercomp 

Resources Development and Engineering, 1976, p. 3.4) 

is:

(2)

where

H = enthalpy per unit mass of fluid [E/M] (J/kg),

K = hydrodynamic thermal dispersion plus

convection [E/T-L-t] (W/m-°C),

T = temperature [t] (°C),

qL = heat loss across boundaries [E/T] (W)

U = internal energy per unit mass of fluid [E/M]

(J/kg),

(ρCp)R = heat of aquifer matrix [E/L3-t] (J/m3-°C), and

Cp= specific heat of aquifer matrix [E/M-t] (J/kg-°C)

(All other terms are previously defined.)

Equations 1 and 2 are a nonlinear system of coupled 

partial-differential equations that is solved numerically 

by discretizing the aquifer into three dimensions (or two 

dimensions for radial flow) and developing finitedifference approximations.

Finite-difference equations (Intercomp Resources 

Development and Engineering, 1976, p. 3.5) whose 

solutions closely approximate the solutions of equations 

1 and 2 are, for the basic flow equation:

(3)

and for the energy equation:

∇ ρk

μ • -----( ) ∇ ρ p – g∇z – q′ ∂t

∂ = ( ) φρ

∂

∂r

----- 1

r

-- ∂

∂θ------ ∂

∂z

+ + -----

∇ ρk

μ

-----H( )∇ ∇p – ρg∇z K ∇T qL • + • • – – q′H =

∂

∂t

---- φρU ( )ρ 1 – φ Cp ( ) TR [ ] +

∆ T[ ] w( ) ∆p – ρg∆z – q

V

∆t = -----δ φρ ( )

∆ T[ ]∆ wH( ) ∆p – ρg∆z T( ) c∆T qL + = – – qH
B45

(4)

where

q = mass rate of production or injection of liquid for a 

grid block [M/t] (kg/s)

V= volume of the grid block [L3] (m3

)

Tw = (5)

Tc = (6)

A = the area perpendicular to flow (that is, ∆x∆y,

∆x∆z, or ∆y∆z), and 

l = the distance between grid block centers.[L] (m)

(All other terms are previously defined.)

The finite-difference operators are defined as:

(7)

with the terms:

(8)

and

(9)

where

x, y, z = cartesian-space coordinates,

i, j, k = grid-block indices,

n = time level, t n,

(All other terms are previously defined.)

Finally, the thermal-conductance term, K, in equation 

6 may be further defined as (Intercomp Resources 

Development and Engineering, 1976, p. 3.7):

(10)

where

α = thermal dispersivity [L] (m),

φ = porosity [dimensionless],

u = volumetric flux (Darcy velocity) [L/T] (m/s),

(ρCp)w = heat capacity of water [E/L3-t] (J/m3-°C), and

Km = molecular heat conductivity of porous media

[E/T-L-t] (W/m-°C).

Model Design

Analysis of aquifer-test data (Miller and Delin, 1993; 

Miller, 1984) indicates that the Ironton and Galesville 

Sandstones and the upper part of the Franconia 

Formation are areally anisotropic and that the angle 

between the major axis of transmissivity and the axis 

between production wells A and B is approximately 30 

degrees. Although the anisotropy may be considered 

small (less than 3:1), its effect on the movement and 

direction of heat flow for the hydrologic conditions at 

the ATES site is not known. Use of a radial-flow 

equation would neglect the effect of anisotropy. The 

potential errors introduced in the radial-flow 

assumptions are discussed by Miller and Delin (1993) in 

the section of that report describing the radial-flow 

model. On the basis of Miller and Delin’s discussion, a 

three-dimensional model was constructed to represent 

anisotropic conditions and to simulate the ATES shortterm test cycles.

Discretization of aquifer system

The area that can be modeled around the ATES 

doublet-well system is limited by (1) the constraint on 

the finite-difference grid spacings required by the 

model-solution techniques, (2) the lack of alignment of 

the axis of aquifer anisotropy and the axis on which the 

doublet wells are located, and (3) running the model for 

large three-dimensional problems exceeded allocated 

resources available at that time. Miller and Voss (1986) 

describe the construction of the finite-difference grid 

for the doublet-well system at the ATES site. The grid 

was simplified and the simulated region was reduced in 

size by use of an analytical solution for flow in an 

isotropic, isothermal, doublet-well system. The solution 

was modified to account for the effects of aquifer 

anisotropy and nonalignment of the principal direction 

of hydraulic conductivity with the doublet-well axis. 

The procedure is summarized below and described in 

more detail by Miller and Voss (1986).

The analytical solution for flow in the Ironton and 

Galesville Sandstones and in the upper part of the 

Franconia Formation are shown by Miller and Delin 

(1993, p. 48 and 49). The equipotentials and streamlines 

illustrated by Miller and Delin are the steady-state 

solutions to two-dimensional, isothermal flow in a 

homogeneous, confined, infinite, anisotropic aquifer 

that has no regional hydraulic gradient. For practical 

purposes, the Franconia-Ironton-Galesville aquifer may 

be treated as infinite, because lateral boundaries are not 

present within several kilometers of the test facility 

(Kanivetsky, 1979). The regional head gradient was 

estimated as less than 1 x 10-3, which is negligible.

The cells in a finite-difference grid for a groundwater-flow model are generally sized to minimize 

computer storage and computation time while 

maintaining adequate discretization in space. The 

maximum cell size is determined by the nature of the 

finite-difference approximation of the ground-waterV

∆t -----δ φρU ( )ρ 1 – φ Cp ( ) TR [ ] +

kAρ

μl ---------

KA

l

-------

∆ T( )∆ w∆p x Tw∆x ( )∆ p y Tw∆y = + + ( ) p

∆z + Tw∆z ( ) p

∆x Tw∆x ( ) p Tw i , + 0.5, ,j k pi + 1, ,j k

n + 1

pijk , ,

n + 1 = [ ] –

Tw i , – 0.5, ,j k – pijk , ,

n + 1

pi – 1, ,j k

n + 1 [ ] –

δχ χn + 1χn = –

K φ αu

φ

------     ρCp ( )w = + Km
B46

flow or transport equations. For the solution of transport 

equations, cell dimensions more than 1.5 times larger 

than an adjacent cell may cause oscillations in the 

distribution of the transported quantity in space. In order 

to prevent such oscillations, Intercomp Resources 

Development and Engineering (1976) suggests that cell 

size should be restricted to less than twice the value of 

hydrodynamic dispersivity. For example, the 

hydrodynamic dispersivity of about 3 m used in this 

study restricts the maximum cell size to 6 m. 

Although it is possible to construct a finite-difference 

grid that would encompass the entire area illustrated by 

Miller and Delin (1993, p. 48 and 49), the number of 

resulting cells and corresponding calculations would be 

impractical to model with the SWIP code. If cells were 

6 m on a side, for example, 10,000 cells would be 

required to simulate the two-dimensional area shown by 

Miller and Delin. The flow-net analysis (Miller and 

Voss, 1986), makes it possible to reduce the modeled 

area and to simulate flow only in the area around 

production well A, the flow region where energy 

transport is of greatest concern (figs. 21–22). Flow 

outside this modeled region is represented by a 

specified flux at model boundaries, as determined by 

flow-net analysis.

The finite-difference grid for the ATES-site model 

was oriented such that the axis of maximum 

transmissivity was aligned with the horizontalcoordinate direction (Miller and Delin, 1993, p. 48 and 

49). The origin of the field-coordinate system shown in 

figures 21 and 22 was arbitrarily chosen to be halfway 

between production wells A and B. A variably-spaced 

grid was designed because of restrictions on grid size for 

solution accuracy and stability inherent to the difference 

approximation used in the SWIP code (Intercomp 

Resources Development and Engineering, 1976). Cell 

sizes range from 0.3 m on a side at production well A to 

a maximum of 4.6 m on a side at the periphery of the 

model; cell sizes increase in all directions equally by a 

factor of 1.5 or less. The grid has 6 layers with 594 cells 

per layer (fig. 23). Vertical grid spacings were selected 

to correspond with aquifers and confining units (table 

3). The lateral boundaries of the model correspond to 

the 10 m equipotential for the Ironton and Galesville 

Sandstones (fig. 21) and to the 2.9 m equipotential for 

the upper part of the Franconia Formation (fig. 22).

Flux calculation at model boundaries

Appropriate flux rates must be specified at the model 

boundaries such that the boundaries accurately 

represent ground-water flow and heat transport between 

the modeled area and the area outside the simulated 

region. The correct boundary fluxes can be determined 

by analysis of the flow net for steady-state conditions. 

The total flow crossing an equipotential (figs. 21 and 

22) is equal to the injection rate and is thus known. In 

addition, an equal amount of flow is represented by 

each streamtube. Therefore, if quasi-steady-state flow 

is assumed, the distribution of fluxes along an equipotential is known for any injection rate.

One form of boundary-flux specification simulated 

by use of the SWIP code (Intercomp Resources 

Development and Engineering, 1976, p. B.11) is:

(11)

where

 = the fluid-influx rate at boundary cell i,j [L/T]

(m3/s),

αij = a constant factor that gives the fraction of the

entire grid boundary that cell i,j represents

[dimensionless],

V = an aquifer-flux coefficient [L3/(M/L-T2)] (m3/

kPa),

PI = a fixed pressure at some distance outside the

model boundary [M/L-T2] (kPa), and

 = the pressure in boundary cell i,j at time of the

(n+1)th time step [M/L-T2] (kPa), and

∆t = time [T] (s).

For an infinite aquifer, the pressure outside the model 

boundary (PI) is maintained at the initial system 

pressure (Pij

0) before pumping. For simulation of the 

doublet-well system, the initial pressure (Pij

0

) is held 

constant along a locus somewhere between the wells. In 

a homogeneous, isotropic aquifer, this locus would be 

the perpendicular bisector of the well axis; however, in 

the anisotropic Franconia-Ironton-Galesville aquifer, 

the locus is along a line at an oblique angle to the well 

axis (Miller and Delin, 1993, p. 48 and 49).

The aquifer-flux coefficient (V), is calculated by use 

of equation 11 for an equipotential by letting PI equal the 

initial pressure (P0

ij), αij equal 1 (representing the entire 

boundary), ew equal the steady-state injection rate for 

each formation, and equal the steady-state 

pressure at the equipotential. Values of V were 

calculated for the 10-m equipotential (fig. 21) for the 

Ironton and Galesville Sandstones and the 2.9 m 

equipotential (fig. 22) for the upper part of the 

Franconia Formation, as 12.6 and 3.8 m3/kPa (cubic 

meters per day-kilopascal), respectively. Because the 32 

streamtubes illustrated in figures 21 and 22 represent 

ewij

∆t αijV PI Pij

n + 1 = ( ) –

ewij

Pij

n + 1

Pij

n + 1
B47

equal rates of flow, values for the constant αij were 

determined for the model boundary in each layer from 

the percentages of streamtubes that intersect each 

boundary cell. The location of lateral-flux boundaries in 

the model that represent these equipotentials are 

illustrated in figure 24.

Miller and Delin (1993) describe calibration of the 

model to isothermal conditions to define the hydraulic 

properties and boundary conditions that best 

characterize the doublet-well system. From results of 

these model analyses, the boundary fluxes computed by 

flow-net analysis accurately represented the doubletwell flow field in the anisotropic aquifer. Therefore, the 

hydraulic representation of the ground-water-flow 

system by the model was considered to be satisfactory.

Representation of Thermal Properties

This section of the report provides a brief description 

of the thermal properties of the aquifer used as variables 

in the nonisothermal model. The relation of these 

variables to hydraulic properties of the aquifer is 

described, and possible effects of these variables on the 

50

60

70

80

90

40

30

20

Streamline Model grid 10-meter equipotential Steamtube

70 80 90 100 150 160 170 110 120 130 140

DISTANCE FROM MIDPOINT OF WELLS, IN METERS

DISTANCE FROM MIDPOINT OF WELLS, IN METERS

EXPLANATION

Figure 21. Model grid and flow net for the Ironton and Galesville Sandstones

near production well A for the short-term test cycles.

Streamtube

Model flux boundary
B48

transport of energy in the modeled aquifer system is 

discussed.

Heat capacity is the amount of heat required to raise 

the temperature of a material a specified amount. It is 

the product of density and specific heat and is a measure 

of the ability of a material to store heat. Values of 1.81 

x 106

 and 3.89 x 106 J/m3−°C were used for heat capacity 

of rock and water, respectively (table 4). These values 

were based on data from Sommerton and others (1965), 

Clark (1966), Helgeson and others (1978), and Robie 

and others (1978). The values were calculated by use of 

methods described by Martin and Dew (1965). The 

value of rock heat capacity represents sandstones 

similar to those in the Franconia-Ironton-Galesville 

aquifer. 

The constant of proportionality between the heat flux 

and the temperature gradient is termed thermal 

conductivity. It is the quantity of heat transmitted in unit 

time through a unit cross-sectional area under a unit 

temperature gradient. For purposes of data analysis, 

thermal conductivity was assumed to be isotropic in the 

aquifer system. For a parallel-conduction model (Bear, 

1972), where heat conduction occurs simultaneously 

through the fluid and the aquifer matrix (rock), thermal 

conductivity is defined as

50

60

70

80

90

40

30

20

Streamline Model grid 2.9-meter equipotential Steamtube

70 80 90 100 150 160 170 110 120 130 140

DISTANCE FROM MIDPOINT OF WELLS, IN METERS

DISTANCE FROM MIDPOINT OF WELLS, IN METERS

EXPLANATION

Figure 22. Model grid and flow net for the upper part of the Franconia Formation

near production well A for the short-term test cycles.

Streamtube

Model flux boundary
B49

X

Y

Z

Eau Claire Formation

Galesville Sandstone

Ironton Sandstone

Lower part of

Franconia Formation

Upper part of

Franconia Formation

St. Lawrence Formation

Layer 1

Layer 2

Layer 3

Layer 4

Layer 5

Layer 6

Figure 23. Finite-difference grid, in three dimensions, for the

Aquifer Thermal-Energy Storage (ATES) site model.

(12)

where

 Υ = thermal conductivity of the aquifer [E/L-T-t] (W/m-

-°C),

Υf = thermal conductivity of the fluid [E/L-T-t] (W/m-

-°C),

Υr = thermal conductivity of the rock [E/L-T-t] (W/m-

-°C), and

θ = aquifer porosity [dimensionless].

Thermal conductivity tends to decrease with 

increasing temperature (Blair and others, 1985). This 

should not be a problem in data analysis or in application 

of model results at the ATES site because the 

temperatures required to seriously affect the value of 

thermal conductivity were well above those measured 

during short-term testing. Values of thermal conductivity 

(table 4) were obtained from Clark (1966).

Thermal diffusivity is defined as the transport of 

energy by conduction due to the exchange of kinetic 

energy between molecules. Thermal diffusion is 

Υ θΥf ( )Υ 1 – θ = + r
B50

independent of fluid velocities and is usually constant 

in saturated porous media. Thermal diffusivity for an 

isotropic system may be defined as:

(13)

where

K = thermal diffusivity [L2/T] (m2/s),

Υ = thermal conductivity of the aquifer [E/L-T-t]

(W/m--°C),

ρf = the density of fluid [M/L3

](kg/m3),

ρr = the density of rock [M/L3] (kg/m3),

Cf = specific heat of fluid [E/M-t] (J/kg-°C),

Cr = specific heat of rock [E/M-t] (J/kg-°C), and

θ = aquifer porosity [dimensionless].

The value of 1.56 x 106

 m2/s (table 4) used for thermal 

diffusivity is representative of sandstones in the Franconia-Ironton-Galesville aquifer (Kappelmeyer and 

Haenel, 1974).

K Υ

ρf

Cf ( )ρ 1 – θ + rCr [ ] = --------------------------------------------------

 Table 3. Layer number, thickness, and corresponding 

hydrogeologic unit for the three-dimensional model of heat 

transport

Layer

Thick-ness 

(meters) Hydrogeologic unit

1 8 St. Lawrence Formation 

(confining unit)

2 14 Upper part of the Franconia 

Formation (aquifer)

3 24 Lower part of the Franconia 

Formation

(confining unit)

4 15 Ironton Sandstone

(aquifer)

5 6 Galesville Sandstone

(aquifer)

6 30 Eau Claire Formation

(confining unit)

For an isotropic medium, the dispersion tensor may be written 

in matrix notation as:

(14)

where

Dij = the coefficient of thermal dispersion [L] (m),

λ11,λ22 = the longitudinal and transverse dispersivities

respectively for an isotropic medium [L](m),

K = thermal diffusivity [L2/T] (m2/s).

Bear (1972) points out that diffusion is negligible and dispersion is dominant in flow systems with relatively large fluid 

velocity. Diffusion dominates dispersion for small fluid 

velocities.

 The terms λ11, λ22 in equation 14 are values of dispersivity 

for an isotropic medium where λ11 is considered longitudinal, 

or parallel to the direction of fluid flow, and λ22 is considered 

transversal, or perpendicular to fluid flow. Green (1963) and 

Bear (1972) suggest that dispersivity is of small importance in 

dispersion compared to thermal conduction. Sauty and others 

(1979) suggest that Bear may have considered only laboratory 

values of dispersivity, however, and not field or 

macrodispersivities in his determination of the importance of 

the dispersivity term.

Model Calibration

Model-computed temperatures were compared to measured 

data at each of the observation wells for each period of 

injection and withdrawal for the four short-term test cycles. 

Plots of measured and simulated temperatures (figs. 25–29) 

are arranged so that injection and withdrawal periods can be 

compared for the four test cycles at each observation well. The 

colored solid lines (figs. 25–29) represent averages of 

measured temperatures and the corresponding colored dashed 

lines represent the model-computed values. Actual 

temperature measurements were averaged for all measurement 

points within each hydrogeologic unit in an attempt to make 

measured and model-computed data comparable. Table 5 lists 

the measurement-point altitudes for which data were averaged 

to correspond with the model's vertical layering.

A detailed description of the differences between modelcomputed and average temperatures is beyond the scope of this 

report. Trends in the average temperatures will be discussed 

and related to model results to describe thermal processes that 

may explain the results. As described earlier, some 

thermocouples failed intermittently because of insulation wear 

at kinks in the wires. These failures appear as small 

temperature fluctuations in figures 25 through 29 and are not 

discussed further in the report.

Dij

λ( ) 11 + K 0 0

0 λ( ) 22 + K 0

0 0 λ( ) 22 + K

=

Thermal dispersion (Dij), resulting from fluctuations 

of velocity and temperature in the pore space, is similar 

to the more common term of mechanical hydrodynamic 

dispersion used in solute mass-transport problems. The 

coefficient of thermal dispersion term consists of two 

parts: (1) energy transport due to changes in the local 

velocity vector; and (2) energy transport due to the 

exchange of kinetic energy between molecules, or to 

thermal diffusivity. Bear (1972) notes that the coefficient 

of thermal dispersion is a second-order tensor that 

depends on a fourth-order tensor (dispersivity).

For the case of a local-coordinate system where one of 

the axes coincides with the velocity vector, the X and Y 

axes also coincide with the principal axes of dispersion. 
B51

 Table 4. Thermal properties used for simulation of the short-term test cycles

Thermal property Amount and unit of measure

Thermal conductivity, rock = 2.20 watts per meter-degree Celsius1

1

From Clark, 1966

Thermal conductivity, aquifer water at 20 degrees Celsius = 0.60 watts per meter-degree Celsius1

Thermal diffusivity = 1.56 x 106 square meter per second

Heat capacity, rock = 1.81 x 106 joules per cubic meter-degree Celsius

Heat capacity, aquifer water = 3.89 x 106 joules per cubic meter-degree Celsius

Longitudinal dispersivity = 3.33 meters

Transverse dispersivity = 0.33 meters

Y

X

Model flux boundaries

EXPLANATION

Figure 24. Model cells near production well A in which heat transport was simulated.

Cell in which heat transport was simulated:

 Layers 1-3, St. Lawrence and Franconia Formations

 Layers 4-6, Ironton and Galesville Sandstones and

 the Eau Claire Formation
B52

140

140

130

130

120

120

110

110

100

100

90

90

80

80

70

70

60

60

50

50

40

40

30

30

20

20

10

10

0

0

2 12 14 16 18 4 6 8 10

TIME SINCE BEGINNING OF

INJECTION, IN DAYS

TIME SINCE BEGINNING OF

WITHDRAWAL, IN DAYS

TEMPERATURE, IN DEGREES CELSIUS

2 4 6 8 10

Figure 25. Model-computed and measured injection temperatures

 during periods of

TEST CYCLE l

TEST CYCLE ll

Model-computed wellhead

temperature

Measured wellhead

temperature

Model-computed wellhead

temperature

Measured wellhead

temperature
B53

140

140

130

130

120

120

110

110

100

100

90

90

80

80

70

70

60

60

50

50

40

40

30

30

20

20

10

10

0

0

2 12 14 16 18 4 6 8 10

TIME SINCE BEGINNING OF

INJECTION, IN DAYS

TIME SINCE BEGINNING OF

WITHDRAWAL, IN DAYS

TEMPERATURE, IN DEGREES CELSIUS

2 4 6 8 10

at production well A for the four short-term test cycles

injection and withdrawal.

TEST CYCLE lll

TEST CYCLE lV

Model-computed wellhead

temperature

Measured wellhead

temperature

Model-computed wellhead

temperature

Measured wellhead

temperature
B54

140

130

120

110

100

90

80

70

60

50

40

30

20

10

0

140

130

120

110

100

90

80

70

60

50

40

30

20

10

0

2 12 14 16 18 4 6 8 10

TIME SINCE BEGINNING OF

INJECTION, IN DAYS

TIME SINCE BEGINNING OF

WITHDRAWAL, IN DAYS

TEMPERATURE, IN DEGREES CELSIUS

2 4 6 8 10

TEST CYCLE l

TEST CYCLE ll

EXPLANATION

Averaged temperatures of thermocouples at:

 88 and 93 meters, upper part of Franconia Formation

 73 and 81 meters, lower part of Franconia Formation

 52 and 58 meters, Ironton Sandstone

 45 meters, Galesville Sandstone

Model-computed temperatures

 Model layer 2

 Model layer 3

 Model layer 4

 Model layer 5

Figure 26. Model-computed and average measured injection

 cycles during periods of
B55

140

130

120

110

100

90

80

70

60

50

40

30

20

10

0

140

130

120

110

100

90

80

70

60

50

40

30

20

10

0

2 12 14 16 18 4 6 8 10

TIME SINCE BEGINNING OF

INJECTION, IN DAYS

TIME SINCE BEGINNING OF

WITHDRAWAL, IN DAYS

TEMPERATURE, IN DEGREES CELSIUS

2 4 6 8 10

TEST CYCLE lll

TEST CYCLE lV

temperatures at observation well AM1 for the four short-term test

injection and withdrawal.
B56

140

130

120

110

100

90

80

70

60

50

40

30

20

10

0

140

130

120

110

100

90

80

70

60

50

40

30

20

10

0

2 12 14 16 18 4 6 8 10

TIME SINCE BEGINNING OF

INJECTION, IN DAYS

TIME SINCE BEGINNING OF

WITHDRAWAL, IN DAYS

TEMPERATURE, IN DEGREES CELSIUS

2 4 6 8 10

TEST CYCLE l

TEST CYCLE ll

EXPLANATION

Averaged temperatures of thermocouples at:

 88, 93 and 99 meters, upper part of Franconia Formation

 66, 73 and 81 meters, lower part of Franconia Formation

 52 and 58 meters, Ironton Sandstone

 45 meters, Galesville Sandstone

Model-computed temperatures

 Model layer 2

 Model layer 3

 Model layer 4

 Model layer 5

Figure 27. Model-computed and average measured injection

 cycles during periods of
B57

140

130

120

110

100

90

80

70

60

50

40

30

20

10

0

140

130

120

110

100

90

80

70

60

50

40

30

20

10

0

2 12 14 16 18 4 6 8 10

TIME SINCE BEGINNING OF

INJECTION, IN DAYS

TIME SINCE BEGINNING OF

WITHDRAWAL, IN DAYS

TEMPERATURE, IN DEGREES CELSIUS

2 4 6 8 10

TEST CYCLE lll

TEST CYCLE lV

temperatures at observation well AS1 for the four short-term test

injection and withdrawal.
B58

140

130

120

110

100

90

80

70

60

50

40

30

20

10

0

140

130

120

110

100

90

80

70

60

50

40

30

20

10

0

2 12 14 16 18 4 6 8 10

TIME SINCE BEGINNING OF

INJECTION, IN DAYS

TIME SINCE BEGINNING OF

WITHDRAWAL, IN DAYS

TEMPERATURE, IN DEGREES CELSIUS

2 4 6 8 10

TEST CYCLE l

TEST CYCLE ll

Figure 28. Model-computed and average measured injection

 cycles during periods of

EXPLANATION

Averaged temperatures of thermocouples at:

 88, 93 and 99 meters, upper part of Franconia Formation

 66, 73 and 81 meters, lower part of Franconia Formation

 52 and 58 meters, Ironton Sandstone

 45 meters, Galesville Sandstone

Model-computed temperatures

 Model layer 2

 Model layer 3

 Model layer 4

 Model layer 5
B59

140

130

120

110

100

90

80

70

60

50

40

30

20

10

0

140

130

120

110

100

90

80

70

60

50

40

30

20

10

0

2 12 14 16 18 4 6 8 10

TIME SINCE BEGINNING OF

INJECTION, IN DAYS

TIME SINCE BEGINNING OF

WITHDRAWAL, IN DAYS

TEMPERATURE, IN DEGREES CELSIUS

2 4 6 8 10

TEST CYCLE lll

TEST CYCLE lV

temperatures at observation well AM2 for the four short-term test

injection and withdrawal.
B60

140

130

120

110

100

90

80

70

60

50

40

30

20

10

0

140

130

120

110

100

90

80

70

60

50

40

30

20

10

0

2 12 14 16 18 4 6 8 10

TIME SINCE BEGINNING OF

INJECTION, IN DAYS

TIME SINCE BEGINNING OF

WITHDRAWAL, IN DAYS

TEMPERATURE, IN DEGREES CELSIUS

2 4 6 8 10

TEST CYCLE l

TEST CYCLE ll

Figure 29. Model-computed and average measured injection

 cycles during periods of

EXPLANATION

Averaged temperatures of thermocouples at:

 88, 93 and 99 meters, upper part of Franconia Formation

 66, 73 and 81 meters, lower part of Franconia Formation

 52 and 58 meters, Ironton Sandstone

 45 meters, Galesville Sandstone

Model-computed temperatures

 Model layer 2

 Model layer 3

 Model layer 4

 Model layer 5
B61

140

130

120

110

100

90

80

70

60

50

40

30

20

10

0

140

130

120

110

100

90

80

70

60

50

40

30

20

10

0

2 12 14 16 18 4 6 8 10

TIME SINCE BEGINNING OF

INJECTION, IN DAYS

TIME SINCE BEGINNING OF

WITHDRAWAL, IN DAYS

TEMPERATURE, IN DEGREES CELSIUS

2 4 6 8 10

TEST CYCLE lll

TEST CYCLE lV

temperatures at observation well AM3 for the four short-term test

injection and withdrawal.
B62

A factor that should be considered when comparing 

model-computed temperatures with measured data is the 

radial distance of measurement points from production 

well A. Because of the limitations of finite-difference 

modeling, the actual location of measurement points 

may not be exactly simulated in the model at the correct 

radial distance (fig. 5). The smallest deviations within 

the model area are for production well A and observation 

well AM1, and the greatest deviation is for observation 

well AM3. Model-computed temperatures for each 

monitoring point at the site were correlated with 

measured values on the basis of results of the deviation 

survey.

Representation of variable pumping rates and 

injection temperatures must be considered when 

comparing model-computed and average temperatures. 

This is illustrated in figure 25, which shows injection 

temperatures recorded at the wellhead and injection 

temperatures simulated with the model. The filtration 

system for calcium carbonate removal caused an overall 

decrease in efficiency of the above-ground heat 

exchanger and resulted in a decrease of injection 

temperatures with time. Therefore, an average 

temperature was used for the period of heat injection and 

for the period when the filtration unit was serviced. 

Thus, the initial high and low temperature peaks 

measured at the wellhead were not simulated by the 

model. 

The four short-term test cycles, including the inactive 

or rest periods between individual test cycles, were 

simulated. Therefore, the total length of the simulation, 

approximately 400 days, represented a period from the 

start of injection in test cycle I to the end of withdrawal 

for test cycle IV. A continuous model simulation of the 

four test cycles was necessary because of conductive 

flow of thermal energy away from the injection zones, 

 Table 5. Altitudes of measurement points where temperatures 

were averaged to correspond with model layers

Model 

layer Hydrogeologic unit

Altitude(s) of 

measurement 

points

1 St. Lawrence Formation 110, 104

2 Upper part of the 

Franconia Formation

99, 93, 88

3 Lower part of the 

Franconia Formation

81, 73, 66

4 Ironton Sandstone 58, 52

5 Galesville Sandstone 45

6 Eau Claire Formation 38

particularly near production well A, during periods of 

storage between test cycles. 

Temperature was redistributed within the aquifer and 

confining units because of thermal conduction between 

each test cycle. The rate of heat conduction depended on 

the length of time between periods of injection and on 

the amount of thermal energy in the aquifers and 

confining units. Knowledge of the initial distribution of 

energy within the aquifer at the start of a test cycle, 

therefore, was critical in determining the overall 

thermal efficiency of the aquifer for the cycle. Thermal 

efficiency of the aquifer was computed by dividing the 

total energy injected into the aquifer system by the total 

energy withdrawn from the system. 

The initial thermal conditions for the simulation of 

test cycle I were approximated because of the aborted 

heated-water injection test in May 1982, before the 

installation of the calcium carbonate filtration units. 

Although an attempt was made to recover the heat 

injected during the aborted test and to return the aquifer 

to its ambient temperature of approximately 10°C, 

temperature measurements in observation wells AM1 

and AS1 indicated that some residual heat remained 

within 7 m of production well A. Because there were not 

enough temperature-measurement points near 

production well A to determine the distribution of 

temperature, the residual heat from the aborted test was 

not precisely known. Therefore, a vertically-uniform 

temperature of 10°C was assumed as the initial 

condition for the simulation of test cycle I. 

The model was calibrated to nonisothermal 

conditions to ensure that the hydraulic and thermal 

properties selected were reasonable for simulation of 

heat transport in the flow system. The relative 

importance of each property was evaluated during 

preliminary model analyses (Miller and Delin, 1993). 

Model sensitivity to changes in the hydraulic properties 

of hydraulic conductivity, porosity, and vertical 

anisotropy, plus model sensitivity to changes in the 

thermal properties of thermal conductivity of rock, heat 

capacity of rock, and thermal dispersivity were tested. 

The individual model properties were varied from 

assumed base values. The hydraulic and thermal 

properties simulated in the model are shown in tables 6 

and 4, respectively. On the basis of results of this 

sensitivity analysis, the model was most sensitive to 

changes in thermal dispersivity. Therefore, only the 

longitudinal and transverse thermal dispersivities were 

varied during nonisothermal model calibration. The 

remaining hydraulic and thermal properties were 
B63

estimated within the range of published values (Miller 

and Delin, 1993).

Calibration of the model to nonisothermal conditions 

consisted of comparing model-computed thermal 

efficiencies and withdrawal-water temperatures to 

calculated and measured values (table 7). Calibration of 

the model also was achieved by comparing modelcomputed and average temperatures at the observation 

wells during the test cycles (figs. 25–29). The 

longitudinal and transverse dispersivities were varied 

during nonisothermal model calibration on the basis of 

relative hydraulic conductivities of the aquifer in the 

longitudinal and transverse directions (Miller, 1984; 

Miller and Delin, 1993). The longitudinal dispersivity 

was varied from 1.0 to 30 m and the transverse 

dispersivity was varied from 0.1 to 3.0 m. Values of 3.3 

and 0.33 m for longitudinal and transverse dispersivity, 

respectively, simulated aquifer thermal efficiencies, 

wellhead temperatures, and average temperatures close 

to measured values.

Analysis of Simulations

The model accurately calculated thermal efficiencies 

of the aquifer to within an average of about 5 percent of 

calculated values for the four short-term test cycles 

(table 7). The poor correspondence between modelcomputed and calculated efficiencies for test cycle II is 

likely related to the long storage period of 90 days 

compared to storage periods of 10 to 13 days for the 

other cycles (table 1). The model also accurately 

calculated withdrawal-water temperatures to within an 

average of about 3 percent of measured values for the 

four test cycles (table 7). The lack of correspondence 

between model-computed and averaged temperatures 

for test cycle II is once again likely due to the 

abnormally long storage period for this cycle. 

Model-computed and averaged temperatures for 

production well A compare closely (fig. 25). The closest 

overall agreement between model-computed and 

average temperatures was for observation well AM2 

(fig. 28). The trends of the model-computed 

temperature profiles and the model-computed 

temperatures at the end of each injection and 

withdrawal cycle acceptably match average 

temperatures for most model layers. The acceptable 

match between model-computed and average 

temperatures for observation well AM2 is likely related 

to lack of aquifer clogging in this direction. Observation 

well AM2 is on the axis of minimum transmissivity 

(Miller, 1984). The trends of the model-computed 

injection- and withdrawal-temperature profiles for 

observation wells AS1 (fig. 27) and AM3 (fig. 29) do 

not agree as well with average temperatures. The 

model-computed temperatures at the end of injection 

are generally about 5 to 10°C lower than average 

temperatures for these wells. In contrast, the modelcomputed temperatures at the end of injection for 

observation well AM1 (fig. 26) were generally 5 to 

20°C higher than average temperatures. These 

 Table 6. Hydraulic properties used for simulation of the short-term test cycles

Hydraulic conductivity, in meters per day

Model layer Kx Ky Kz Anisotropy, Kx/Ky Porosity (percent)

1 0.003 0.003 0.00003 1.00 26.8

2 2.89 1.71 .222 1.69 28.2

3 .03 .03 .0003 1.00 27.3

4 5.78 2.51 .380 2.30 25.2

5 1.45 .628 .095 2.30 25.6

6 .003 .003 .00003 1.00 31.6

 Table 7. Comparison of model-computed thermal efficiencies of the aquifer and final withdrawal-water temperatures at production well A 

with corresponding calculated and measured values for the four short-term test cycles

Short-term test-cycle 

number

Thermal efficiency of aquifer 

(in percent)

Final withdrawal-water temperature 

(in degrees Celsius)

Calculated Model computed Measured Model computed

I 59.0 60.0 39.4 39.9

II 46.0 49.4 39.4 43.8

III 62.0 58.0 56.7 58.3

IV 59.0 62.0 63.9 64.4
B64

differences might result from the fact that the model 

does not simulate the effects of aquifer clogging by 

mechanical or chemical processes. Consequently, 

duplication of the trends in measured temperatures at 

observation wells AM1 and AS1 related to aquifer 

clogging was not expected in the model-computed 

graphs. This lack of correspondence between modelcomputed and average temperatures at observation 

wells AM1 and AS1 lends some support to the 

hypothesis of aquifer clogging.

As described earlier, aquifer clogging within the 

Galesville Sandstone at observation well AM1 resulted 

in a general decrease in temperature measured at the 

well at the 58 m altitude. Results of the model indicate 

that an increase in temperature would be expected at this 

location if the aquifer were not clogged. 

Correspondence between model-computed and average 

temperatures at other levels in observation well AM1 is 

acceptable during periods of injection and withdrawal 

for all four test cycles. On the basis of model-computed 

results at observation well AM1, therefore, the model 

accurately represents field conditions.

Although observation wells AM2 and AM3 are at 

approximately the same radial distance from production 

well A (fig. 5), the model-computed temperatures more 

closely match the average temperatures for well AM2 

than for well AM3 (figs. 28 and 29). The lack of 

correspondence for observation well AM3 may be 

related to hydrofracturing of the Ironton and Galesville 

Sandstones during installation of observation well AS1 

(M.C. Hoyer, Minnesota Geological Survey, 1985, 

written commun.). Hydrofracturing may have caused an 

increase in permeability near well AS1. Because well 

AS1 is much closer to well AM3 than to AM2 (fig. 5), 

aquifer permeability near well AM3 may be higher than 

was indicated by hydraulic tests at the site (Miller, 

1984). The resultant increase in flow towards well AM3 

would have caused higher average temperatures for this 

well than for well AM2. Because the model did not 

simulate the effects of hydrofracturing, any increase in 

average temperatures at well AM3 caused by this 

mechanism could not be duplicated. Long-term testcycle data would be helpful to describe the potential 

effects of hydrofracturing and to evaluate use of the 

model as a tool in predicting temperatures at the 

observation wells.

The calibrated nonisothermal model is a tool for 

evaluating aquifer thermal-energy storage. The model 

can be used to calculate the recovery temperature and 

thermal efficiency of the aquifer for selected rates of 

withdrawal and injection, injection temperature, and 

duration of injection, storage, and withdrawal periods. 

Results of model analyses indicate that the model is 

accurate in computing thermal efficiency of the aquifer 

and temperatures at production well A during periods of 

withdrawal. The model is less accurate in simulating 

temperatures at the observation wells because of the 

effects of aquifer anisotropy, aquifer clogging, and, 

possibly, hydrofracturing. The model necessarily is a 

simplification of the flow system, and accuracy of the 

model results is limited by the accuracy of the hydraulic 

and thermal input data on which the computations are 

based. In addition, different combinations of input data 

could conceivably yield the same results.

SUMMARY

The University of Minnesota started a project in May 

1980 to evaluate use of the Franconia-IrontonGalesville aquifer for thermal-energy storage. Hightemperature water (88.5 to 117.9°C) was injected 

through a well during four periods ranging in duration 

from 5.25 to 8.01 days. Periods of storage ranged in 

duration from 9.62 to 89.71 days, and periods of 

withdrawal ranged from 5.28 to 8.00 days. 

Approximately equal rates of injection and withdrawal, 

from 17.4 to 18.6 L/s, were maintained for each test 

cycle. Each period of injection was interrupted four 

times to service the heat exchanger and above-ground 

chemical-precipitation filters.

Temperature graphs indicate that the shortest arrival 

times for temperature fronts, and the hottest 

temperatures measured at all observation wells, were in 

the Ironton and Galesville Sandstones. The next 

shortest arrival times, and somewhat cooler 

temperatures, were in the less permeable upper part of 

the Franconia Formation. The latest arrival times for 

temperature fronts were measured in the lower part of 

the Franconia. Because the lower part of the Franconia 

was not screened, heat within this part of the aquifer was 

transported by conduction. Very little heat conduction 

was measured in the St. Lawrence Formation and in the 

Eau Claire Formation, which are confining layers to the 

aquifer. 

Clogging within the aquifer by calcium carbonate 

precipitation and by movement of fine-grained material 

near the well bore could explain some anomalies of 

temperatures and pressures measured in the Ironton 

Sandstone. A decrease in temperature was measured at 

several of the temperature-measurement locations in the 

upper part of the Franconia Formation and in the Ironton 
B65

and Galesville Sandstones immediately after heatedwater injection was stopped. The exact mechanism for 

this temperature change is not fully understood, but it is 

probably related to the difference between conductive 

and advective rates of thermal-energy transport and to 

variations in permeability within the aquifer. Buoyancy 

flow within the aquifer was minimal, as evidenced by 

temperature profiles at individual observation wells 

during periods of injection, storage, and withdrawal.

A three-dimensional, anisotropic, nonisothermal, 

ground-water-flow, and thermal-energy-transport 

model was used to simulate the four short-term test 

cycles. The model simulated a 400-day period from the 

start of injection of test cycle I to the end of withdrawal 

for test cycle IV and included the storage periods 

between test cycles. Calibration of the model to 

nonisothermal conditions consisted of comparing 

model-computed thermal efficiencies and withdrawalwater temperatures to calculated and measured values. 

Calibration of the model also was achieved by 

comparing model-computed and average temperatures 

at the observation wells during the test cycles. 

Sensitivity of the model to adjustments of hydraulic 

conductivity, porosity of the aquifer, thermal 

conductivity and heat capacity of rock, vertical 

anisotropy, and thermal dispersivity was tested during 

preliminary model analyses. On the basis of these 

analyses, the only input properties varied during model 

calibration were the longitudinal and transverse thermal 

dispersivity, which were simulated at 3.3 and 0.33 m, 

respectively. The model accurately simulated aquifer 

thermal efficiencies to within an average of about 5 

percent of calculated values for the four short-term test 

cycles. The model accurately simulated withdrawalwater temperatures to within an average of about 3 

percent of measured values for the four short-term test 

cycles. Graphs of model-computed temperatures 

acceptably matched graphs of average temperatures. 

The calibrated nonisothermal model is a tool for 

evaluating aquifer thermal-energy storage. The model 

can be used to calculate the recovery temperature and 

thermal efficiency of the aquifer for selected rates of 

injection and withdrawal, injection temperature and 

duration of injection, storage, and withdrawal periods. 

Results of model analyses indicate that the model is 

most accurate in simulating thermal efficiency of the 

aquifer and temperatures of production well A during 

periods of withdrawal. The model is less accurate in 

simulating temperatures at the observation wells 

because of the effects of aquifer anisotropy, aquifer 

clogging, and possibly hydrofracturing. 

REFERENCES

Bear, Jacob, 1972, Dynamics of fluids in porous media: New 

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energy storage (ATES) field test facility-system 
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