U.S. Department of the Interior

U.S. Geological Survey

Scientific Investigations Report 2020–5012

Water Availability and Use Science Program

Estimates of Water Use Associated with Continuous Oil and 

Gas Development in the Williston Basin, North Dakota and 

Montana, 2007–17
Cover. Aerial photograph of oil and gas wells under development in North Dakota. Photograph by 

Vern Whitten Photography, used with permission.
Estimates of Water Use Associated with 

Continuous Oil and Gas Development in 

the Williston Basin, North Dakota and 

Montana, 2007–17

By Ryan R. McShane, Theodore B. Barnhart, Joshua F. Valder, Seth S. Haines, 

Kathleen M. Macek-Rowland, Janet M. Carter, Greg C. Delzer, and 

Joanna N. Thamke

Water Availability and Use Science Program

Scientific Investigations Report 2020–5012

U.S. Department of the Interior

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

DAVID BERNHARDT, Secretary

U.S. Geological Survey

James F. Reilly II, Director

U.S. Geological Survey, Reston, Virginia: 2020

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Although this information product, for the most part, is in the public domain, it also may contain copyrighted materials 

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Suggested citation:

McShane, R.R., Barnhart, T.B., Valder, J.F., Haines, S.S., Macek-Rowland, K.M., Carter, J.M., Delzer, G.C., and 

Thamke, J.N., 2020, Estimates of water use associated with continuous oil and gas development in the Williston 

Basin, North Dakota and Montana, 2007–17: U.S. Geological Survey Scientific Investigations Report 2020–5012, 

26 p., https://doi.org/10.3133/sir20205012.

Associated data for this publication:

Dutton, D.M., Varela, B., Haines, S.S., Barnhart, T.B., McShane, R.R., and Wheeling, S.L., 2019, Water-use data to 

estimate water use associated with continuous oil and gas development, Williston Basin, United States, 1980–2017: 

U.S. Geological Survey data release, accessed October 2019 at https://doi.org/10.5066/P9CPKRLW.

ISSN 2328-0328 (online)
iii

Acknowledgments

The authors thank the North Dakota State Water Commission, the North Dakota Industrial 

Commission, the Montana Department of Natural Resources and Conservation, the Montana 

Bureau of Mines and Geology, and other officials from North Dakota and Montana for their 

support of past and ongoing projects that provided valuable information for this study. Hess 

Corporation and Whiting Petroleum Corporation offered beneficial information on water use 

by oil and gas operators in North Dakota, and the Southwest Water Authority offered useful 

information on water use by water permit holders in North Dakota. The authors also thank IHS 

Markit for approving access to aggregated data on hydraulic fracturing water use in Montana.

This study was supported by the U.S. Geological Survey Water Availability and Use Science 

Program. The authors thank the following colleagues with the U.S. Geological Survey. DeAnn 

Dutton, Robert Lundgren, Roy Sando, and Spencer Wheeling assisted with gathering and 

processing the water-use data. Brian Clark and William Eldridge provided thoughtful edits and 

comments in reviewing this report, and Molly Maupin and Mindi Dalton provided helpful guidance as members of the project management team.

v

Contents

Acknowledgments........................................................................................................................................iii

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

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

Description of Study Area ...................................................................................................................2

History of Oil and Gas Development in the Williston Basin ...........................................................2

Purpose and Scope ..............................................................................................................................5

Methods for Analyzing Water Use ..............................................................................................................6

Procedures for Processing Data for Analysis .................................................................................6

Procedures for Modeling Water Use and Uncertainty ...................................................................9

Results of Water-Use Analysis ..................................................................................................................10

Estimates of Water Use by County and Year ..................................................................................10

Coefficients of Water Use per Oil and Gas Well ............................................................................13

Performance of Regression Models of Water Use .......................................................................15

Comparisons to Water-Use Estimates from Other Studies ...................................................................18

Limitations of Water-Use Analysis for the Williston Basin ...................................................................20

Summary........................................................................................................................................................21

References Cited..........................................................................................................................................22

Appendix 1. R Scripts ...............................................................................................................................25

Appendix 2. Water-Use Estimates and Coefficients ...........................................................................26

Figures

1. Map showing locations of the Williston Basin Province, Bakken and Three 

Forks Assessment Units, and other geologic features in the United States ......................3

2. Cross section showing stratigraphic units of the Williston Basin with 

geologic periods ...........................................................................................................................4

3. Diagram showing various water and energy attributes of conventional and 

continuous (or unconventional) oil and gas development in the Williston Basin ..............5

4. Graph showing number of production wells and volume of oil production in the 

Williston Basin in North Dakota and Montana from 1990 to 2017 ........................................6

5. Graphs showing annual estimates of direct, indirect, and ancillary water use in 

the Williston Basin ......................................................................................................................12

6. Graphs showing mean annual estimates of direct, indirect, and ancillary water 

use by county in the Williston Basin .......................................................................................12

7. Graphs showing linear regression models of population as explained by 

number of oil and gas wells developed per year in the Williston Basin ...........................13

8. Graphs showing linear and quantile regression models of direct, indirect, and 

ancillary water use as explained by number of oil and gas wells developed per 

sampling unit for North Dakota and Montana .......................................................................17

9. Graphs showing relation between observed and estimated direct, indirect, and 

ancillary water use per sampling unit as mean value from linear regression 

models for North Dakota and Montana ..................................................................................18
vi

Tables

1. Information and data sources used to estimate direct, indirect, and ancillary 

water use associated with continuous oil and gas development ........................................7

2. Mean annual estimates from linear and quantile regression models of direct, 

indirect, and ancillary water use associated with continuous oil and gas 

development in the Williston Basin in North Dakota and Montana ...................................11

3. Coefficients from linear and quantile regression models of direct, indirect, and 

ancillary water use per oil and gas well developed in the Williston Basin in 

North Dakota and Montana ......................................................................................................14

4. Goodness-of-fit metrics from leave-one-out cross-validation for linear 

regression models of direct, indirect, and ancillary water use per oil and gas 

well developed in the Williston Basin in North Dakota and Montana ...............................16

5. Estimates of direct, indirect, and ancillary water use associated with 

continuous oil and gas development in the Williston Basin from other studies ..............19

Conversion Factors

U.S. customary units to International System of Units

Multiply By To obtain

Length

foot (ft) 0.3048 meter (m)

mile (mi) 1.609 kilometer (km)

Area

acre 4,047 square meter (m2)

square mile (mi2) 259.0 hectare (ha)

square mile (mi2) 2.590 square kilometer (km2)

Volume

barrel (bbl; petroleum, 1 barrel=42 gal) 0.1590 cubic meter (m3)

gallon (gal) 3.785 liter (L)

gallon (gal) 0.003785 cubic meter (m3)

million gallons (Mgal) 3,785 cubic meter (m3)

cubic foot (ft3) 0.02832 cubic meter (m3)

Mass

pound, avoirdupois (lb) 0.4536 kilogram (kg)

Supplemental Information

Water use is given in million gallons per year (Mgal/yr) or million gallons (Mgal) per well.
vii

Abbreviations

COG continuous oil and gas

NDIC North Dakota Industrial Commission

NDSWC North Dakota State Water Commission

R2 coefficient of determination

RMSE root mean square error

RSR ratio of root mean square error to standard deviation of observations

USGS U.S. Geological Survey

WAUSP Water Availability and Use Science Program

Estimates of Water Use Associated with Continuous Oil 

and Gas Development in the Williston Basin, North Dakota 

and Montana, 2007–17

By Ryan R. McShane, Theodore B. Barnhart, Joshua F. Valder, Seth S. Haines, Kathleen M. Macek-Rowland, 

Janet M. Carter, Greg C. Delzer, and Joanna N. Thamke

Abstract

This study of water use associated with development 

of continuous oil and gas resources in the Williston Basin is 

intended to provide a preliminary model-based analysis of 

water use in major regions of production of continuous oil 

and gas resources in the United States. Direct, indirect, and 

ancillary water use associated with development of continuous 

oil and gas resources in the Williston Basin was estimated in 

North Dakota and Montana from 2007 to 2017. Water-use data 

were aggregated by county and year, which were the sampling 

units used in this analysis. Linear and quantile regression 

models of water use in relation to the number of oil and gas 

wells developed were fit for the direct, indirect, and ancillary 

water-use categories for each State. A 95-percent confidence 

interval for each parameter estimate from the linear regression 

models was computed as a measure of uncertainty. Additional 

information on uncertainty can be gained from modeling 

other distribution parameters, so quantile regression models 

of the 5th, 50th, and 95th percentiles also were fit. To assess 

uncertainty in the estimates from the regression models of 

direct, indirect, and ancillary water use, leave-one-out crossvalidation was used. Model performance was evaluated with 

three goodness-of-fit metrics used to compare the estimates 

and observations of water use.

Mean annual direct and indirect water use for development of continuous oil and gas resources in North Dakota was 

estimated at 4,512 million gallons (Mgal) per year (Mgal/yr), 

with a 95-percent confidence interval of 4,021–5,152 Mgal/

yr, and in Montana was estimated at 196 Mgal/yr, with a 

95-percent confidence interval of 189–203 Mgal/yr. Ancillary 

water use (for domestic and public supply) had an estimated annual mean of 2,753 Mgal/yr in North Dakota and 

396 Mgal/yr in Montana. The coefficient from the linear 

regression model of direct water use was 3.86 Mgal per well 

and hydraulic fracturing water use was 3.70 Mgal per well 

for North Dakota. The mean estimate of direct water use had 

a 95-percent confidence interval of 3.48–4.23 Mgal per well. 

For North Dakota, the coefficient from the linear regression 

model of indirect water use was 0.453 Mgal per well, with a 

95-percent confidence interval of 0.415–0.492 Mgal per well. 

Direct and indirect water use had a mean estimate of about 

4.31 Mgal per well in North Dakota. The mean estimate of 

ancillary water use (for domestic and public supply) in North 

Dakota was 2.03 Mgal per well, with a 95-percent confidence 

interval of 1.76–2.31 Mgal per well. For Montana, the linear 

regression model of hydraulic fracturing water use had a mean 

estimate of 2.04 Mgal per well. The 95-percent confidence 

interval for the mean estimate was 1.80–2.28 Mgal per well. 

Direct and indirect water use in Montana had a mean estimate of 2.49 Mgal per well. The mean estimate of ancillary 

water use (for domestic and public supply) in Montana was 

2.43 Mgal per well, with a 95-percent confidence interval of 

1.76–3.11 Mgal per well.

Introduction

Water is a necessary component for many processes 

required for developing continuous oil and gas (COG) 

resources. Improved COG extraction techniques have greatly 

increased oil and gas production in the United States since the 

mid-2000s (U.S. Energy Information Administration, 2016). 

However, the accompanying rapid increase in demand for 

large volumes of water, often in remote regions, can challenge 

existing infrastructure and require additional resources to meet 

water needs. Addressing this water need requires accurate 

estimates of the volumes of water used to support the various 

processes common to COG development in the United States 

in the 21st century.

In 2015, the U.S. Geological Survey (USGS) started a 

topical study focused on quantifying water use in areas of COG 

development. The topical study was supported through the 

USGS Water Availability and Use Science Program (WAUSP), 

which was authorized by the Science and Engineering to 

Comprehensively Understand and Responsibly Enhance 

Water Act (SECURE Water Act) in the Omnibus Public Land 

Management Act of 2009 (16 U.S.C. 1 note). In the SECURE 

Water Act, the USGS was tasked with conducting a National 

Water Census to better quantify water use in the United States, 
2 Estimates of Water Use Associated with Continuous Oil and Gas Development in the Williston Basin

including water supporting COG development. One of the 

main goals of the WAUSP is to provide accurate estimates of 

water resources in the United States and to offer methods for 

determining the quantity and quality of water available for 

beneficial uses. This topical study to quantify water use related 

to COG development will help achieve that WAUSP goal.

Previous work supporting this study includes two USGS 

reports: (1) Valder and others (2018) developed a conceptual 

model for assessing water use associated with the life cycle of 

COG development based on the quantity and quality of wateruse data available from various sources; and (2) Valder and 

others (2019) constructed an analytical framework for estimating water use related to COG development, including an 

uncertainty analysis of the water-use estimates. The analytical 

framework also included R scripts with the procedures used 

to estimate water use, which can be adapted for application to 

areas of COG production throughout the United States.

This study of water use associated with COG development in the Williston Basin is intended to provide a preliminary model-based analysis of water use in major regions of 

COG production in the United States. The Williston Basin was 

selected as the pilot region for the following reasons: (1) the 

estimated large volume of undiscovered oil and natural gas 

(Gaswirth and others, 2013); (2) the quantity and quality of 

available water-use data; and (3) a population—with its attendant water use—assumed to change largely in response to oil 

and gas development.

Description of Study Area

The Williston Basin is a large intracratonic, roughly 

circular, sedimentary and structural basin that extends from 

South Dakota, North Dakota, and Montana (Gaswirth and 

others, 2013; fig. 1) in the United States to Saskatchewan 

and Manitoba in Canada (not shown), covering more than 

100,000 square miles. The geologic basin is deepest at its 

center, which is located beneath Williston, North Dakota, with 

the strata becoming shallower and thinner towards its margins 

(fig. 2; Long and others, 2014). The stratigraphic sequence of 

the Williston Basin (fig. 2) is described thoroughly in Long 

and others (2014).

The focal area of this study was the Williston Basin 

Province in the United States (not in Canada; fig. 1), a region 

with a boundary that follows the County and State borders 

most closely matching the boundary of the geologicallydefined Williston Basin (Gaswirth and others, 2013). The 

province contains the Bakken and Three Forks Assessment 

Units of conventional and COG accumulations (fig. 1; 

Gaswirth and others, 2013). The primary sources of fresh 

groundwater in the Williston Basin, which are used in part to 

support COG development, are the Fort Union, Fox Hills, and 

Hell Creek Formations (Long and others, 2018) contained in 

the Lower Tertiary-aged and Upper Cretaceous-aged layers 

(figs. 2 and 3). Most water used for supporting COG development is sourced from fresh surface waters of lakes or ponds 

and tributaries of the Missouri River (figs. 1 and 2). The principal COG deposits in the Williston Basin are the Bakken and 

Three Forks Formations in the Mississippian-aged and Upper 

Devonian-aged layers (figs. 2 and 3).

History of Oil and Gas Development in the 

Williston Basin

Since the late 1800s, the type and amount of energy 

development in the Williston Basin has changed based on 

many factors including technological developments, production costs, energy prices, and political decisions. Energy 

resources developed in the Williston Basin have included 

nonrenewable resources such as coal, oil, and gas, and renewable energies such as biofuels and wind. The Williston Basin 

has been an important domestic oil- and gas-producing region 

since the 1950s (Anna and others, 2011; Gleason and Tangen, 

2014; Thamke and others, 2014).

Crude oil and natural gas deposits are categorized as 

conventional or continuous (also referred to as unconventional) based on characteristics of the reservoir (Schmoker, 

2005; Schmoker and Klett, 2005; fig. 3). Conventional oil and 

gas accumulations have discrete deposits with well-defined 

hydrocarbon-water contacts (where the hydrocarbons are 

buoyant on a column of water), generally high matrix permeabilities, apparent seals and traps, and relatively high recovery 

factors (Schmoker and Klett, 2005). COG accumulations are 

an oil or gas resource, or both, dispersed evenly throughout 

a geologic formation rather than existing as discrete and 

localized deposits, such as those in conventional accumulations (Schmoker, 2005). These continuous resources typically 

require specialized extraction techniques involving directional, 

horizontal wells, which have been more costly than extraction 

with vertical wells.

The first recorded energy exploration in the Williston 

Basin was for natural gas, and the first energy wells completed 

were exploratory natural gas wells (Bluemle, 2001). Natural 

gas was first reported in southeastern North Dakota in 1892 in 

an artesian water well producing from the Dakota Sandstone 

(Anderson and Eastwood, 1968; Bluemle, 2001). Several 

years later, shallow deposits of natural gas were discovered in 

north-central North Dakota and were used to supply several 

small towns and farms (Anna and others, 2011). The oldest 

commercial gas production was established in 1913 from shallow Upper Cretaceous units in the northwest part of the Cedar 

Creek anticline in Montana (Anna and others, 2011). The new 

discovery was expanded to 11 fields, and in 1932, more than 

12 billion cubic feet of gas were sold (Bartram and Erdmann, 

1935; Anna and others, 2011).

Before 1910, early oil and gas exploration in the 

Williston Basin was hampered by primitive technology, and 

the existing cable-tool rigs, which used a heavy bit on the end 

of a steel cable to crush the rock by repeatedly dropping the bit 

into the well borehole, could not drill deeply enough (Bluemle, 

2001). Oil was first discovered in the Williston Basin along the 
rol20-0026_fig01

MT

CANADA

WY

SD

ND

50 MILES

0

0 25

25 50 KILOMETERS

108° 107° 106° 105° 104° 103° 102° 101° 100° 99° 98° 97°

49°48°47°46°45°44°

CANADA

MONTANA

NORTH DAKOTA

WYOM SOUTH DAKOTA WYOMINGING

Cedar Creek anticline

Nesson

anticline

EXP

Missouri River

Missouri

River

BakkThree Willi

Study area

Base modified from U.S. Geological Surveydigital data, variously dated, various scalesUniversal Transverse Mercator projection,Zone 14

Geology and thematic boundaries

from Gaswirth and others, 2013

DANIELS SHERIDAN DIVIDE

ROOSEVELT

VALLEY

RICHLAND

DAWSON

MCCONE

GARFIELD

WILLIAMS

MCKENZIE

MOUNTRAIL

WARD

MCLEAN

MERCER

MORTON

DUNN

BURLEIGHSTARK

HETTINGER

EMMONS SLOPE FALLON

CARTER

CUSTER

BOWMAN

BILLINGS

VALLEY

GOLDEN

WIBAUX

RENVILLE BOTTINEAU

MCHENRY

BURKE

Williston

Figure 1. Locations of the Williston Basin Province, Bakken and Three Forks Assessment Units, and other geologic features in the United States others, 2013).
4 Estimates of Water Use Associated with Continuous Oil and Gas Development in the Williston Basin

Cedar Creek anticline in southeastern Montana in the 1920s 

and 1930s (Bluemle, 2001). Several attempts at drilling the 

oil reserves about 40 miles east of Williston, N. Dak., were 

made between 1924 and 1951. In 1938, one of the first modern 

rotary rigs used in North Dakota drilled a deep test hole (more 

than 10,000 feet) near Tioga, N. Dak., but missed an oil reservoir at this location by about 1 mile (Bluemle, 2001).

The Clarence Iverson #1 well, which was drilled on the 

Nesson anticline in northwestern North Dakota, is credited as 

the first oil-producing well in the Williston Basin, and a granite monument marks the site about 10 miles south of Tioga, 

N. Dak. (Bluemle, 2001; Anna and others, 2011; American 

Oil and Gas Historical Society, 2013). On April 4, 1951, the 

Clarence Iverson #1 well was labeled the discovery well of the 

Williston Basin. A month later, multiple oil and gas companies 

and speculators leased more than 30 million acres of mineral 

rights in North Dakota, unofficially beginning the first of several oil booms in the Williston Basin (American Oil and Gas 

Historical Society, 2013).

Vertical drilling techniques were productive and profitable in several reservoirs in the Williston Basin but not 

the Bakken Formation. After 1951, annual oil production 

increased in North Dakota until 1966 to a high of 26 million 

barrels and then declined until 1974 to a low of 20 million 

barrels (Fischer and Bluemle, 1986). Production of 31 million barrels in 1979 surpassed the previous 1966 high, and 

new highs were recorded each year until 1984, when production rose to 53 million barrels (Fischer and Bluemle, 1986; 

Bluemle, 2001). Production then began to decline, falling to 

28 million barrels in 1994 (Bluemle, 2001).

It was not until the late 1990s, when horizontal drilling, 

hydraulic fracturing, and other technologies became sufficiently developed, that production from the low-permeability 

and low-porosity Bakken Formation became economically 

feasible. Moreover, higher prices for domestic and foreign 

oil during this time allowed the more costly COG extraction 

techniques required in the Bakken Formation to become economically viable. Annual oil production in North Dakota alone 

increased from a nominal amount of 35 million barrels in 2005 

to more than 400 million barrels in 2015 (fig. 4).

Increasing oil and gas production resulted in a complementary increase in the number of oil and gas wells and rigs 

used to drill the wells. The annual average oil and gas rig count 

in North Dakota began increasing after 2004 and substantially increased beginning in 2010 (Baker Hughes, 2017). In 

addition, the number of wells producing oil and gas in North 

Dakota began increasing after 2005 and considerably increased 

beginning in 2011 (fig. 4). The annual total oil production 

 Figure 2. Stratigraphic units of the Williston Basin with geologic periods (from Long and others, 2014).

FEET

VERTICAL SCALE EXAGGERATED

6,000

3,000

NAVD 88

−3,000

−6,000

−9,000

−12,000

−13,500

SOUTHWEST

Missouri River

Tertiary

Glacial deposits

Upper Cretaceous

Cretaceous

Lower Cretaceous

Jurassic

Mississippian

Triassic

Pennsylvanian-Permian

Pennsylvanian

Mississippian

Mississippian (upper Bakken Formation)

Precambrian

Cambrian-Ordovician

Devonian*

Silurian

Precambrian

Fault—Arrows show

general direction 

of movement

EXPLANATION

0 50 100 150 MILES

0 50 100 150 KILOMETERS

NORTHEAST

*

Lower part of the Bakken 

Formation exists in the upper 

part of this unit. The Three 

Forks Formation underlies

the Bakken Formation 
Introduction 5

more than doubled between 2010 and 2012 (fig. 4) with the 

introduction of horizontal drilling and hydraulic fracturing of 

deposits in the Bakken Formation in the Williston Basin (U.S. 

Energy Information Administration, 2013). In 2013, the USGS 

estimated 7.4 billion barrels of technically recoverable oil 

for the United States part of the Devonian-aged Three Forks 

Formation and the Devonian- and Mississippian-aged Bakken 

Formation of the Williston Basin (Gaswirth and others, 2013; 

figs. 2 and 3). In 2014, North Dakota surpassed oil production 

of 1 million barrels per day and ranked behind Texas as the 

second largest oil-producing State (U.S. Energy Information 

Administration, 2014). In 2019, about 90 percent of drilling in 

North Dakota targeted the Bakken and Three Forks Formations, 

and the all-time high number of wells producing from these 

formations in North Dakota was 15,943 (Helms, 2019).

Purpose and Scope

Direct, indirect, and ancillary water use associated with 

COG development in the Williston Basin was estimated in 

North Dakota and Montana from 2007 to 2017. Direct water 

use is defined as water used in a wellbore to complete a well, 

which includes water used for drilling, cementing, stimulating, 

and maintaining the well during production. Indirect water use 

is defined as water used at or near the well site, including water 

used for dust abatement, equipment cleaning, materials washing, worker sanitation, and site preparation. Ancillary water 

use is defined as all other water used during the life cycle of 

COG development that is not categorized as direct or indirect, 

such as additional local or regional water use resulting from a 

change (for example, population) related to COG development.

The water-use estimates presented in this report are 

compared with other published values for the Williston Basin, 

and the limitations of the water-use analysis for the Williston 

Basin are described. The water-use data used in the analysis 

includes data from 1980 to 2017 for some sources, which are 

available in a USGS data release (Dutton and others, 2019). 

Appendix 1 includes scripts coded in R (R Core Team, 2019) 

for executing the procedures used in the water-use analysis. 

Appendix 2 includes the estimates of water use by county and 

year and coefficients of water use per developed oil and gas 

well for the Williston Basin in North Dakota for 2007–17 and 

in Montana for 2008–16, which can be reproduced using the 

R scripts in appendix 1. rol20-0026_fig 03

WATER

NOTE: The pump jack shows a conventional well in the production stage and the drill rig derrick shows an unconventional 

well in the drilling stage, although the pump jack and drill rig derrick are used on both well pads

3,000

−3,000

−6,000

−9,000

−12,000

0

Generalized altitude, in feet relative to

North American Vertical Datum of 1988

Potable water wells

Unconventional

oil/gas well

Drill rig derrick

(drilling stage)

Storage

tanks

Lower Tertiary aquifers

(Fort Union Formation)

Lower Cretaceous 

Cretaceous—confining unit

Mississippian/Upper Devonian 

(Bakken and Three Forks Formations)

Undifferentiated—Mississippian 

Precambrian

Undifferentiated—Jurassic 

through Pennsylvanian

Undifferentiated—Devonian through Cambrian

Glacial aquifers

Conventional 

oil/gas well

Pump jack

(production stage)

Disposal

well

Oil/gas reservoir trap

Stream

Ancillary water-use 

processes such as 

recreation

Direct water-use 

processes such as 

hydraulic fracturing 

and borehole maintenance

Indirect water-use processes such 

as crew camps, well pad upkeep, 

and dust abatement on roads

Crew camp

Groundwater and surface water

withdrawn for a variety of uses

Upper Cretaceous aquifers (Fox Hills and Hell Creek Formations)

Continuous oil/gas reservoir

 Figure 3. Various water and energy attributes of conventional and continuous (or unconventional) oil and gas development 

 in the Williston Basin (from Carter and others, 2016).
6 Estimates of Water Use Associated with Continuous Oil and Gas Development in the Williston Basin

Methods for Analyzing Water Use

The analysis of water use associated with COG development presented in this report was based on an analytical 

framework (Valder and others, 2019) derived from a conceptual model (Valder and others, 2018). The conceptual model 

consisted of five components: (1) input data, (2) processes, 

(3) decisions, (4) model output, and (5) assessment outcomes. 

Decisions that could be made in the conceptual model were 

determined by the quality and quantity of data available 

for specific regions of COG extraction, which led to different outcomes of how completely the life cycle of water use 

associated with COG development could be assessed (Valder 

and others, 2018). It was assumed that an almost complete life 

cycle of water use associated with COG development in the 

Williston Basin could be assessed because the Williston Basin 

has a relatively large quantity and high quality of available 

water-use data. The analytical framework established a generic 

approach for estimating the water use—direct, indirect, and 

ancillary—related to COG development, including a generalized description of the input data; data processing, interpretation, and uncertainty analysis; and model output involved in the 

water-use analysis (Valder and others, 2019). The next sections 

describe the procedures for processing the data for analysis and 

the procedures for modeling the water use and uncertainty for 

the Williston Basin. The water-use analysis was executed with 

scripts (appendix 1) coded in R (R Core Team, 2019).

Procedures for Processing Data for Analysis

Several datasets and databases were processed for use 

in the analysis of direct, indirect, and ancillary water use 

associated with COG development in the Williston Basin 

(table 1) and are available in the accompanying data release 

(Dutton and others, 2019). North Dakota data on hydraulic 

fracturing treatment water, wellbore cementing (sacks of 

cement), and wellbore drilling (depth per well) were obtained 

from the North Dakota Industrial Commission (NDIC, 2018). 

Montana data on oil and gas well counts and hydraulic 

fracturing treatment water were provided as 1-square-mile 

aggregated values (table 1). These data for North Dakota and 

Montana were used to estimate direct water use. Reported 

water use by category, such as domestic or industrial, for 

water permits in North Dakota were acquired from the 

North Dakota State Water Commission (NDSWC, 2018). 

By pairing data on direct water use from the NDIC with 

water-use data from the NDSWC, indirect water use was 

estimated for North Dakota. Data from the NDSWC were 

paired with air temperature and precipitation data from the 

PRISM Climate Group (2018) and population data from the 

U.S. Census Bureau (2018) to estimate ancillary water use in 

North Dakota. Ancillary water use in Montana was estimated 

by pairing water-use data from the U.S. Geological Survey 

(2019) with data from the PRISM Climate Group and the 

U.S. Census Bureau (table 1).

rol20-0026_fig 04

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

2002

2003

2004

2005

2006

2007

2008

2009

2010

2011

2012

2013

2014

2015

2016

2017

Year

Number of production wells

Oil production, in millions of barrels

0

5,000

10,000

15,000

0

100

200

300

400

500

EXPLANATION

Production wells

 North Dakota

 Montana

Oil production

 North Dakota

 Montana

 Figure 4. Number of production wells and volume of oil production in the Williston Basin in North Dakota and 

 Montana from 1990 to 2017 (data from North Dakota Oil and Gas Division, 2019; Montana Board of Oil and Gas 

 Conservation, 2019).
Methods for Analyzing Water Use 7

Data on hydraulic fracturing water use were used to 

determine when COG development started the most recent 

(before 2017) boom in oil production in North Dakota and 

Montana (fig. 4). For North Dakota and Montana, data on 

hydraulic fracturing treatment water (table 1) were summed 

by year, resulting in one value of hydraulic fracturing water 

use per year. A regression model of the linear relation 

between hydraulic fracturing water use and year of observation was fit as a segmented, or broken-line, model using the 

“segmented” package for R (Muggeo, 2018). The broken-line 

model attempts to estimate a breakpoint (a change in slope) 

in the linear relation, meaning that data before and after 

the breakpoint could have different slopes fit by the model. 

The breakpoint was used to separate the water-use data into 

observations that preceded the boom in COG development 

and observations that followed. The observations after the 

breakpoint were used to estimate water use associated with 

COG development. The observations before the breakpoint 

were used to model baseline water use before the boom in 

COG development. The breakpoints used in the water-use 

analysis were 2007 for North Dakota and 2008 for Montana. 

For each State, the data from the breakpoint year and those 

that followed (2007–17 for North Dakota and 2008–16 for 

Montana) were used for estimating direct, indirect, and ancillary water use.

Not all data used in the water-use analysis were available 

on the basis of a given oil or gas well or for a given day or 

month (table 1), so water-use data were aggregated by county 

and year, which were the sampling units used in this analysis. 

However, each county did not necessarily have direct, indirect, 

or ancillary water use associated with COG development in 

each year, and each year did not necessarily have water use in 

each county. For example, a given county had direct and indirect water use in only 5 of 11 years, or a given year had water 

use in only 5 of 21 counties. North Dakota had 21 counties 

and 11 years (2007–17) included in the analysis but only 

114 sampling units for analyzing direct and indirect water use. 

Likewise, Montana had 12 counties and 9 years included in 

the analysis (2008–16) but just 55 sampling units for analyzing direct and indirect water use.

Cementing and drilling water use were estimated from 

available data for North Dakota on the number of sacks of 

cement used per well for cementing the casings in the borehole 

and the measured depth reached per well in drilling the borehole (NDIC, 2018; table 1). This study assumed that cementing water use did not vary greatly by well depth and that water 

use per sack of cement averaged a ratio of water weight to 

cement weight of about 0.5. Sacks of cement were multiplied 

by 5 gallons of water, which is the volume of water with a 

weight equal to about one-half the weight of a sack of cement 

(about 47 pounds). This study assumed that drilling water use 

varied mostly by well depth and that water use per well averaged a ratio of water volume to borehole volume of about 2. 

Data were deficient for computing borehole volume per well, 

so it was assumed that wellbores averaged about 0.5 cubic 

foot of volume per 1 foot of depth. Well depth was multiplied 

by 7.5 gallons of water (about 1 cubic foot of water), which is 

the volume of water equal to about twice the average per-foot 

borehole volume.

Indirect water use (water used at oil and gas well sites 

for purposes other than drilling, cementing, or hydraulic 

fracturing wells) was estimated for North Dakota from available water-permit data (NDSWC, 2018; table 1). The water 

permits had water use reported by year for various categories, 

such as industrial or irrigation, in accordance with the wateruse categories used for the USGS National Water Census 

(U.S. Geological Survey, 2019). The industrial water-use 

category included permits for water depots providing water for 

use at oil and gas well sites and permits to oil and gas companies using water for undefined purposes. Additionally, the 

Table 1. Information and data sources used to estimate direct, indirect, and ancillary water use associated with continuous oil and 

gas development.

[IHS, Information Handling Services; PRISM, Parameter-elevation Regressions on Independent Slopes Model]

Information Data source

Hydraulic fracturing treatment water per oil and gas well 

for North Dakota

North Dakota Industrial Commission (2018)

Number of sacks of cement and depth per oil and gas well 

for North Dakota

Oil and gas well count per square mile for Montana IHS Markit (2018) well database

Hydraulic fracturing treatment water per square mile for 

Montana

Reported water use per water permit for North Dakota North Dakota State Water Commission (2018)

Air temperature and precipitation per 4-kilometer grid PRISM Climate Group (2018)

Number of persons per county U.S. Census Bureau (2018)

Estimated water use per county for Montana U.S. Geological Survey (Kenny and others, 2009; Maupin and others, 2014; 

Dieter and others, 2018)
8 Estimates of Water Use Associated with Continuous Oil and Gas Development in the Williston Basin

irrigation water-use category included some permits temporarily repurposed as water depots. This study assumed that water 

use reported by these permits in the industrial and irrigation 

water-use categories was associated with COG development 

(Chris Bader, NDSWC, oral commun., 2018). The reported 

water use from the applicable permits was summed by county 

and year and was assumed to represent the total water use at 

oil and gas well sites in a given county and year. Direct water 

use (water used for hydraulic fracturing, cementing, or drilling 

wells) in a given county and year was subtracted from total 

water use, and the remainder was assumed to represent indirect water use. For this study, direct and indirect water use in 

combination represent the part of the USGS mining water-use 

category related to COG development and is herein referred to 

as COG mining water use.

Water-permit data (NDSWC, 2018; table 1) also were 

used to estimate ancillary water use in North Dakota. Ancillary 

water use is other water used during the life cycle of COG 

development that is not categorized as direct or indirect, 

such as additional local or regional water use resulting from 

a change related to COG development. By default, ancillary 

water use is not combined with direct and indirect water use 

as a part of the USGS mining water-use category; instead, 

ancillary water use is represented separately as parts of other 

nonmining water-use categories. This study assumed that the 

domestic and public-supply water-use categories were most 

directly affected by COG development because of attendant 

population growth, and these categories are herein referred 

to as population-based ancillary water use. Additionally, this 

study assumed that industrial, mining other than COG (herein 

referred to as non-COG mining), and thermoelectric power 

water use might be indirectly affected by COG development 

because of potential accompanying economic growth, and 

these categories are herein referred to as other potential ancillary water use. However, the relation of the other potential 

ancillary water-use categories to COG development was more 

uncertain than for the population-based categories (domestic 

and public supply).

The breakpoint analysis was used to account for preexisting trends in the ancillary water-use categories (domestic, 

public supply, industrial, non-COG mining, and thermoelectric power) before the boom in COG development. A linear 

regression model of water use for these categories in relation 

to a combination of year and county of observation, total 

annual precipitation, mean annual temperature, and population was fit for the years preceding the breakpoint (2007 for 

North Dakota and 2008 for Montana). The antecedent trend 

in water use was extrapolated forward into the years after 

the breakpoint (2007–17 for North Dakota and 2008–16 for 

Montana). The estimates of water use in the years after the 

breakpoint were subtracted from the reported water use from 

the NDSWC water permits for North Dakota and the USGS 

water-use data for Montana, which removed the effect of 

population and climate on the ancillary water-use categories 

before the boom in COG development. The remaining water 

use was attributed to COG development based on the assumption that no factors other than COG development affected the 

ancillary water-use categories. This assumption may be more 

applicable for some categories than others. For example, thermoelectric power, an ancillary water-use category, is affected 

by energy demands in other States connected to the same 

power transmission grid serviced by power plants in Montana 

and North Dakota.

Ancillary water use was more difficult to model than 

direct or indirect water use because data on direct and indirect 

water use represented water use at oil and gas wells developed 

in a given county and year, whereas data on ancillary water 

use represented water withdrawals for any number of wateruse categories (for example, domestic or industrial) in a given 

county and year irrespective of development of oil and gas 

wells. In other words, in a given county and year, ancillary 

water-use data did not necessarily coincide with direct and 

indirect water-use data. Regression models were used to estimate water use in counties with oil and gas wells developed in 

a given year, which required the assignment of ancillary wateruse data from the counties with observed water withdrawals 

to the counties with developed wells. For each State, observed 

water use by category, and the number of oil and gas wells, 

were summed by year. Observed water use then was assigned 

proportionally to the counties with developed oil and gas 

wells by using the ratio of the number of wells in each county 

to the number of developed wells in all counties. Therefore, 

observed water use was restricted to the sampling units 

(county and year) used in the regression models for estimating water use. Estimated water use in a given year then was 

reassigned proportionally to the counties with observed water 

withdrawals by using the ratio of the volume of observed 

water withdrawals in each county to the volume of observed 

water withdrawals in all counties. In other words, ancillary 

water use in a given year was modeled in the counties with 

developed oil and gas wells, and water-use estimates for each 

category then were reallocated to the counties with observed 

water withdrawals for each respective category.

Data on indirect water use and cementing and drilling 

water use were not available for Montana, so coefficients of 

water use per well (in million gallons [Mgal]) derived from 

the analysis for North Dakota for the cementing, drilling, 

and indirect water-use categories were applied to the wateruse analysis for Montana. For example, if the coefficient for 

indirect water use in North Dakota was 0.5 Mgal per well 

and a sampling unit in Montana had 10 oil and gas wells, 

then the indirect water use for the sampling unit was estimated at 5 Mgal (10 wells multiplied by 0.5 Mgal per well). 

Additionally, annual ancillary water-use data were not available for Montana; therefore, water-use data from the USGS 

National Water Census, compiled every 5 years for water-use 

categories such as domestic, public supply, industrial, mining, 

and thermoelectric power (U.S. Geological Survey, 2019), 

were used (table 1). Annual values were estimated by linear 

interpolation between every fifth year.
Methods for Analyzing Water Use 9

Procedures for Modeling Water Use and 

Uncertainty

Linear and quantile regression models of water use in 

relation to the number of oil and gas wells developed were 

fit for the direct, indirect, and ancillary water-use categories 

for each State. A 95-percent confidence interval for each 

parameter estimate (coefficient) from the linear regression 

models was computed as a measure of uncertainty. However, 

a 95-percent confidence interval alone may not adequately 

capture the model uncertainty because linear regression estimates the mean of the sampling distribution, which may not 

sufficiently represent the data variance. Additional information 

on uncertainty can be gained from modeling other distribution parameters, so quantile regression models of the 5th, 

50th (median), and 95th percentiles also were fit using the 

“quantreg” package for R (Koenker, 2018). Quantile regression can provide a more detailed understanding of estimated 

water use at the extremes of the sampling distribution or for 

a skewed sampling distribution (Koenker, 2005). Water-use 

coefficients from the linear and quantile regression models are 

in million gallons per well, whereas water-use estimates from 

the regression models are in million gallons per sampling unit 

(county and year). Therefore, water use was estimated for each 

sampling unit that had observed water use.

The regression models were not fit with other explanatory variables specific to the Williston Basin; instead, they 

were intentionally generalized to apply to other regions of 

COG extraction around the United States, where data availability for explanatory variables likely differs. Water use 

associated with COG development likely depends on many 

factors that vary from region to region and that would be 

prohibitive to quantify nationally with any certainty, such as 

social or economic factors that drive the price of oil and gas 

and the cost of water and labor, or geologic factors that affect 

the development and implementation of new or improved 

extraction techniques. Additionally, for the purpose of developing water-use coefficients applicable to other regions, the 

county and year of the water-use data in the Williston Basin 

were not explicitly factored into the regression models for 

several reasons. A spatial relation of water use to county in 

the Williston Basin would not be analogous to counties with 

COG development in another region, and a temporal relation of water use to year in the Williston Basin might not 

be concurrent with years of COG development in another 

region. Likewise, there is not necessarily a clear trend toward 

more or less water use because various hydraulic fracturing 

methods may be implemented at the same time but in different places.

To assess uncertainty in the estimates from the regression 

models of direct, indirect, and ancillary water use, leaveone-out cross-validation was used (Hastie and others, 2009). 

Leave-one-out cross-validation is an iterative process that 

leaves out a sampling unit and fits a model to all the remaining sampling units. The fitted model then was used to predict 

the observation for the left-out sampling unit. This process 

was repeated for each sampling unit. For example, for direct 

water use in North Dakota, there were 114 sampling units. 

Sampling unit 1 was left out and a model was fit to sampling units 2–114. The fitted model then was used to predict 

the observed water use of sampling unit 1. Then, sampling 

unit 2 was left out and a model was fit to sampling units 1 

and 3–114. The fitted model then was used to predict the 

observed water use of sampling unit 2. This process proceeded 

until all 114 sampling units had been left out once, resulting in 114 estimates of water use. These estimates were then 

validated against the 114 observations of water use for the 

sampling units.

Model performance was evaluated with three 

goodness-of-fit metrics used to compare the estimates and 

observations of water use. The first metric was the coefficient of determination (R2), which is the square of the 

Pearson product-moment correlation coefficient (Legates 

and McCabe, 1999). An R2 value greater than 0.5 may be 

considered good, particularly with the understanding that for 

this study relating water use to the number of developed oil 

and gas wells disregards meaningful spatial and temporal 

variability in the data. The second metric was root mean 

square error (RMSE), which is the square root of the mean 

square error of the regression model (Legates and McCabe, 

1999). This metric also can be defined as the standard deviation of the residuals (unexplained variance) of the regression 

model (Moriasi and others, 2007). A good value for RMSE 

is difficult to determine because the values are specific to 

the modeled data. For example, an RMSE of 1 Mgal per 

well for data with a mean for the observations of 10 Mgal 

per well (10 percent of the mean) would be much better than 

an RMSE of 0.5 Mgal per well for data with a mean for the 

observations of 1 Mgal per well (50 percent of the mean). 

Therefore, this study used RMSE in comparison to the 

parameter estimate from the regression model as a measure 

of goodness-of-fit. The third metric was RMSE relative to 

the standard deviation of the observations (RSR), which 

is the relation of the standard deviation of the unexplained 

variance in the regression model to the standard deviation of 

the observations (Moriasi and others, 2007). For example, if 

the RMSE was 1 Mgal per well, whereas the standard deviation of the observations was 2 Mgal per well, then the RSR 

would be 0.5. A RSR value less than 0.5 is considered good 

(Moriasi and others, 2007).

Population was modeled to provide context for analysis 

of ancillary water use for the domestic and public-supply 

categories, which are based on population, by demonstrating whether population growth could be explained by COG 

development. Population in North Dakota and Montana was 

estimated with a linear regression model of the number of 

persons in relation to the number of oil and gas wells developed in the year of the observed population and in the 1, 2, 

and 3 years before the observed population in case population 

growth had a lagged response to COG development. In other 

words, population in a given year might be better explained by 

prior-year COG development.
10 Estimates of Water Use Associated with Continuous Oil and Gas Development in the Williston Basin

Results of Water-Use Analysis

The water-use analysis for the Williston Basin contains 

three elements: (1) estimates of water use, in million gallons, by 

county and year; (2) coefficients of water use from the regression models, in million gallons per oil and gas well developed; 

and (3) performance (based on goodness-of-fit metrics) of the 

regression models in estimating (predicting) the observed water 

use. Results are presented in the following sections for North 

Dakota and Montana, including a discussion about the differences between the States. Comparisons with estimates of water 

use associated with COG development from other studies and 

limitations of the water-use analysis used for this study are also 

presented in the following sections. Hereafter, unless specified 

otherwise, ancillary water use refers only to the domestic and 

public-supply (population-based) categories.

Estimates of Water Use by County and Year

Estimates (predictions) from the linear and quantile 

regression models of direct, indirect, and ancillary water use 

in the Williston Basin were summed across all counties and 

averaged over all years in the analysis for each State (table 2) 

to facilitate comparison of the water-use categories between 

the States. These mean annual estimates apply to 2007–17 for 

North Dakota and 2008–16 for Montana, and they are specific 

to each State because North Dakota and Montana had different 

data sources for water use associated with COG development.

Water use for COG development (direct and indirect, 

or COG mining; table 2) in the Williston Basin was not 

distributed uniformly between the States—more than 95 percent of direct and indirect water use per year was in North 

Dakota. Mean annual direct and indirect water use for COG 

development in North Dakota was estimated at 4,512 Mgal 

per year (Mgal/yr), with a 95-percent confidence interval 

of 4,021–5,152 Mgal/yr, and in Montana was estimated 

at 196 Mgal/yr, with a 95-percent confidence interval of 

189–203 Mgal/yr. Ancillary water use (for domestic and public supply) had an estimated annual mean of 2,753 Mgal/yr in 

North Dakota and 396 Mgal/yr in Montana (table 2).

Direct and indirect water use in North Dakota and 

Montana varied considerably by year (fig. 5). Direct water use 

(for hydraulic fracturing, cementing, and drilling wells) had 

an upward trend that peaked in 2014 at 9,239 Mgal in North 

Dakota (fig. 5A) and 385 Mgal in Montana (fig. 5B). Mean 

annual direct water use in North Dakota was 3,945 Mgal/yr 

and in Montana was 155 Mgal/yr (table 2), which is about 

25 times more in North Dakota than in Montana. Both States 

declined in direct water use after the peak in 2014; however, 

direct water use in North Dakota expanded to 7,450 Mgal in 

2017 (fig. 5A), whereas Montana’s part of direct water use in 

the Williston Basin continued to contract (fig. 5B). The variability in direct water use reflects differences in the number 

of oil and gas wells developed per year and the volume of 

water used per well among years. Mean annual indirect water 

use was 567 Mgal/yr in North Dakota and 41.2 Mgal/yr in 

Montana (table 2). Indirect water use varied less by year than 

did direct water use. The standard deviation relative to the 

mean (coefficient of variation) for direct and indirect water 

use was about 0.8 and 0.55, respectively, in North Dakota and 

about 0.95 and 0.75, respectively, in Montana, indicating less 

variation by year in indirect water use than in direct water use 

for hydraulic fracturing in both States. Additionally, the ratio 

of indirect to direct water use was larger in Montana (about 

0.25) than in North Dakota (about 0.15). The difference in 

ratios probably results from applying the indirect water-use 

coefficient from the North Dakota analysis to Montana, which 

lacked data to analyze indirect water use.

Ancillary water use (for domestic and public supply) varied by year in North Dakota and Montana (fig. 5) but trended 

upward over the years in both States. For North Dakota, the 

ratio of ancillary water use to direct and indirect water use 

was about 0.6, but it was about 2 for Montana. The difference in ratios most likely results from the difference in data 

sources between the States. The source for Montana was the 

USGS water-use data (U.S. Geological Survey, 2019), which 

compiles water use by county, whereas the source for North 

Dakota was the NDSWC water permits (North Dakota State 

Water Commission, 2018), which reports water use by individual water permit holders. Ancillary water use continued to 

increase after the peak in direct water use in North Dakota and 

Montana in 2014 (fig. 5). This trend in water use demonstrates 

that ancillary water use did not correspond to the years when 

COG mining (direct and indirect) water use was highest; the 

effects of population on ancillary water use associated with 

COG development may occur in later years than when oil and 

gas wells are developed.

Direct and indirect water use in North Dakota and 

Montana also varied substantially by county (fig. 6). Direct 

water use was greatest in McKenzie, Williams, Mountrail, 

and Dunn Counties in North Dakota, ranging from 1,438 to 

611 Mgal/yr (fig. 6A), and greatest in Richland and Roosevelt 

Counties in Montana at 106 and 48.0 Mgal/yr, respectively 

(fig. 6B). A larger proportion of counties in the Williston 

Basin in North Dakota (13 of 21 counties) had at least 1 Mgal/

yr of direct water use than in Montana (4 of 13 counties). 

The county with the most direct water use in North Dakota 

used about 15 times more than the county with the most 

direct water use in Montana. The variation in direct water use 

reflects differences in both the number of oil and gas wells 

developed per county and the volume of water used per well 

among counties (for example, because of differences in the 

geologic formations containing COG reservoirs). In North 

Dakota, McKenzie, Mountrail, Williams, and Dunn Counties 

had the most indirect water use (water used at oil and gas well 

sites for purposes other than drilling, cementing, or hydraulic 

fracturing wells), ranging from 179 to 98.7 Mgal/yr (fig. 6A), 

and in Montana, Richland and Roosevelt Counties had the 

most at 25.5 and 8.33 Mgal/yr, respectively (fig. 6B). Indirect 

water use varied less by county than did direct water use. The 

coefficient of variation for direct and indirect water use was 
Results of Water-Use Analysis 11

about 2 and 1.8, respectively, in North Dakota and about 2.4 

and 1.9, respectively, in Montana, which indicates less variation by county in indirect water use than in direct water use 

for hydraulic fracturing in both States, most likely because 

hydraulic fracturing methods vary greatly among oil and 

gas operators throughout the region. However, comparisons 

between the relative measures of variability by county and 

variability by year suggest that indirect and direct water use 

vary less temporally than spatially.

Ancillary water use (for domestic and public supply) also 

varied by county in North Dakota and Montana (fig. 6) and 

was dispersed unevenly across the counties in each State. A 

much larger proportion of counties in Montana had ancillary 

water use that exceeded direct and indirect water use (9 of 

12 counties) in comparison to North Dakota (10 of 22 counties). The difference between the States suggests that ancillary water use in Montana was more dispersed than in North 

Dakota. However, in North Dakota, more than 50 percent of 

Table 2. Mean annual estimates from linear and quantile regression models of direct, indirect, and ancillary water use associated with 

continuous oil and gas development in the Williston Basin in North Dakota (2007–17) and Montana (2008–16).

[Values in million gallons per year. COG, continuous oil and gas]

Water use Mean 95-percent confidence interval limits Percentiles

Lower Upper 5th 50th 95th

North Dakota

Direct and indirect water use

Direct—All 3,945 3,510 4,515 2,381 3,360 6,473

Direct—Hydraulic fracturing 3,776 3,411 4,236 2,227 3,204 6,294

Direct—Cementing 15.4 13.6 17.7 14.7 15.3 16.1

Direct—Drilling 153 136 177 146 152 164

Indirect 567 512 637 401 596 780

Direct and indirect—COG mining 4,512 4,021 5,152 2,781 3,956 7,253

Ancillary (population-based) water use

All 2,753 2,576 2,961 1,473 2,544 4,530

Domestic 946 721 1,428 742 891 1,287

Public supply 1,808 1,706 1,923 1,350 1,801 2,223

Other potential ancillary water use

Industrial 619 499 825 331 540 1,129

Non-COG mining 1,869 1,182 4,619 1,690 1,905 2,074

Thermoelectric power 443 343 629 247 348 740

Montana

Direct and indirect water use

Direct—All 155 151 158 99.9 156 259

Direct—Hydraulic fracturing 140 110 197 86.9 142 245

Direct—Cementing 1.29 1.20 1.41 1.29 1.29 1.29

Direct—Drilling 12.8 11.9 14.0 12.8 12.8 12.8

Indirect 41.2 38.1 44.8 41.2 41.2 41.2

Direct and indirect—COG mining 196 189 203 141 197 300

Ancillary (population-based) water use

All 396 240 551 247 403 526

Domestic 50.4 12.7 88.1 46.2 54.1 54.7

Public supply 345 211 480 242 331 457

Other potential ancillary water use

Industrial 42.3 6.16 78.7 33.0 38.6 51.0

Non-COG mining 1,851 1,261 2,440 1,309 1,894 2,330

Thermoelectric power 9,195 6,815 11,576 4,687 9,105 11,210
12 Estimates of Water Use Associated with Continuous Oil and Gas Development in the Williston Basin

ancillary water use was in Mercer and Williams Counties; 

in Montana, Roosevelt County alone had about 45 percent 

of ancillary water use. In addition, McKenzie County in 

North Dakota and Richland County in Montana (the counties 

with the most direct water use in their respective State) had 

ancillary water use that was about 10 and 25 percent of their 

respective direct water use. This pattern of water use also 

demonstrates that ancillary water use did not correspond to the 

counties where direct and indirect water use (COG mining) 

was largest; the populations affecting ancillary water use associated with COG development may occur in counties distant 

from where oil and gas wells are developed.

Analysis comparing ancillary water use to direct water 

use indicated that ancillary water use did not change immediately with change in direct water use but instead changed after 

a time lag. In the 21 North Dakota counties in the Williston 

Basin with at least 1 developed oil and gas well, population 

increased from 232,000 in 2007 to 299,000 in 2015 and then 

decreased to 293,000 in 2017 (fig. 7A; U.S. Census Bureau, 

2018). In the 12 Montana counties in the Williston Basin with 

at least 1 developed oil and gas well, population increased 

between 2008 and 2015 from 60,000 to 66,000 and then 

decreased in 2016 to 65,000 (fig. 7B; U.S. Census Bureau, 

2018). This trend in population growth was best explained 

with a linear regression model of the relation between the 

current-year population and the number of oil and gas wells 

developed 2 years previously (a 2-year lag); for example, 

population in 2015 was best explained by the number of 

wells developed in 2013. The mean estimates from the linear 

regression models for North Dakota (R2=0.92) and Montana 

rol20-0026_fig 05

20072008200720102011201220132014201520162017200820092010201120122013201420152016

EXPLANATION

Direct

Indirect

Ancillary

A. North Dakota B. Montana 

Water use, in millions of gallons

Year

0

100

200

300

400

500

600

0

2,000

4,000

6,000

8,000

10,000

 Figure 5. Annual estimates of direct, indirect, and ancillary water use in the Williston Basin. A, North Dakota from 2007 to 2017. 

 B, Montana from 2008 to 2016.

A. North Dakota B. Montana 

County

Water use, in millions of gallons

1,500

1,000

500

0

200

100

150

50

0

McKenzie

Williams Mercer

Mountrail Dunn

Morton

Burleigh

Divide

McHenry Emmons Stark

Burke

Roosevelt Richland Valley

Custer

McCone

Sheridan Wibaux Daniels

Garfield Carter Fallon

Dawson

Ward

Billings

Bowman McLean

Bottineau Slope Golden Valley Renville

Hettinger

EXPLANATION

Direct

Indirect

Ancillary

 Figure 6. Mean annual estimates of direct, indirect, and ancillary water use by county in the Williston Basin. A, North Dakota 

 from 2007 to 2017. B, Montana from 2008 to 2016.
Results of Water-Use Analysis 13

(R2=0.60) were about 27 and 22 additional persons per oil and 

gas well developed, respectively. Even though direct water use 

declined at least temporarily after the peak in 2014, ancillary 

water use continued to increase because population growth 

lagged well development.

Estimates of water use by county and year used in the 

analyses for North Dakota and Montana are available in 

appendix 2. These estimates include direct and indirect water 

use (COG mining) and ancillary water use for the domestic, 

public supply, industrial, non-COG mining, and thermoelectric power categories. Ancillary water use for the domestic 

and public-supply categories (population-based) is directly 

related to COG development, whereas the other potential 

ancillary water-use categories (industrial, non-COG mining, 

or thermoelectric power) are indirectly associated with COG 

development. The values for the ancillary water-use categories 

(appendix 2) represent the part of those categories attributable 

to COG development as determined by the water-use analysis for the Williston Basin. Total water use for the ancillary 

categories, which also includes water use not related to COG 

development, can be found in the USGS water-use data (U.S. 

Geological Survey, 2019).

Coefficients of Water Use per Oil and Gas Well

Coefficients from the linear and quantile regression models of direct, indirect, and ancillary water use in the Williston 

Basin (parameter estimates of water use per oil and gas well 

developed) were produced in the analysis for each State 

(table 3). The coefficients are specific to each State because 

data sources for water use associated with COG development 

were different for North Dakota and Montana. However, the 

coefficients of direct water use for cementing and drilling and 

of indirect water use were the same for each State because the 

coefficients from the North Dakota water-use analysis were 

applied to the analysis for Montana, which lacked data on 

these water-use categories.

The coefficient (mean estimate) from the linear regression 

model of direct water use was 3.86 Mgal per well and hydraulic fracturing water use was 3.70 Mgal per well for North 

Dakota (table 3). The mean estimate of cementing and drilling 

water use was 0.014 and 0.142 Mgal per well, respectively, 

and totaled about 0.156 Mgal per well, which was smaller 

than 5 percent of the mean estimate of hydraulic fracturing 

water use. More than 95 percent of direct water use was for 

hydraulic fracturing. The mean estimate of direct water use 

had a 95-percent confidence interval of 3.48–4.23 Mgal per 

well. From the quantile regression model, the 5th, 50th, and 

95th percentile estimates of direct water use were 1.28, 3.24, 

and 7.66 Mgal per well, respectively. In other words, 95 percent of the oil and gas wells had at least 1.28 Mgal of direct 

water use, 50 percent had at least 3.24 Mgal, and 5 percent had 

at least 7.66 Mgal. Direct water use at the lower and higher 

percentile estimates were outside the confidence interval 

for the mean estimate, which means that spatial, temporal, 

or both variations are characteristic of direct water use in 

North Dakota.

For North Dakota, the coefficient from the linear regression model of indirect water use was 0.453 Mgal per well, 

with a 95-percent confidence interval of 0.415–0.492 Mgal 

per well (table 3). The 5th, 50th, and 95th percentile estimates 

from the quantile regression model were 0.327, 0.555, and 

0.866 Mgal per well, respectively.

Direct and indirect (COG mining) water use had a mean 

estimate of about 4.31 Mgal per well in North Dakota. The 

5th percentile estimate of COG mining water use was about 

1.61 Mgal per well, or less than 50 percent of the mean estimate, whereas the 95th percentile estimate was 8.52 Mgal per 

well, or almost 100 percent higher than the mean estimate. The 

mean estimate of COG mining water use was about 10 percent 

greater than the mean estimate of direct water use, meaning 

that estimates of only direct water use could underestimate 

total water use for COG development, which includes water 

used for completing a well and other water used at the well 

site, by about 10 percent.

rol20-0026_fig 07

A. North Dakota B. Montana 

Year

Number of persons

220,000

240,000

260,000

280,000

300,000

320,000

60,000

62,000

64,000

66,000

68,000

70,000

20072008200720102011201220132014201520162017200820092010201120122013201420152016

EXPLANATION

95-percent confidence interval

Estimated mean

Observation

 Figure 7. Linear regression models of population as explained by number of oil and gas wells developed per year in the Williston 

 Basin. A, North Dakota from 2007 to 2017. B, Montana from 2008 to 2016.
14 Estimates of Water Use Associated with Continuous Oil and Gas Development in the Williston Basin

The mean estimate of ancillary water use (for domestic 

and public supply) in North Dakota was 2.03 Mgal per well, 

with a 95-percent confidence interval of 1.76–2.31 Mgal per 

well (table 3). Public supply water use was almost 75 percent higher than domestic water use. Other potential ancillary water use included 0.354, 1.13, and 0.168 Mgal per well 

(mean estimates) for industrial use, non-COG mining use, 

and thermoelectric power use, respectively. The 5th, 50th, and 

95th percentile estimates for other potential ancillary water use 

ranged from 0.017 Mgal per well for thermoelectric power to 

3.23 Mgal per well for non-COG mining.

For Montana, the linear regression model of hydraulic fracturing water use had a mean estimate of 2.04 Mgal 

per well (table 3), which was almost 50 percent lower than 

the estimate for North Dakota. The 95-percent confidence 

interval for the mean estimate was 1.80–2.28 Mgal per well. 

Table 3. Coefficients from linear and quantile regression models of direct, indirect, and ancillary water use per oil and gas well 

developed in the Williston Basin in North Dakota and Montana.

[Values in million gallons per well. COG, continuous oil and gas]

Water use Mean 95-percent confidence interval limits Percentiles

Lower Upper 5th 50th 95th

North Dakota

Direct and indirect water use

Direct—All 3.86 3.48 4.23 1.28 3.24 7.66

Direct—Hydraulic fracturing 3.70 3.33 4.08 1.12 3.09 7.49

Direct—Cementing 0.014 0.014 0.014 0.014 0.014 0.015

Direct—Drilling 0.142 0.140 0.143 0.134 0.139 0.164

Indirect 0.453 0.415 0.492 0.327 0.555 0.866

Direct and indirect—COG mining 4.31 3.90 4.72 1.61 3.79 8.52

Ancillary (population-based) water use

All 2.03 1.76 2.31 1.32 1.69 5.33

Domestic 0.755 0.679 0.830 0.540 0.639 2.02

Public supply 1.28 1.08 1.48 0.782 1.05 3.64

Other potential ancillary water use

Industrial 0.354 0.255 0.452 0.131 0.416 1.70

Non-COG mining 1.13 0.934 1.33 0.730 0.906 3.23

Thermoelectric power 0.168 0.077 0.259 0.017 0.178 0.486

Montana

Direct and indirect water use

Direct—All 2.04 1.80 2.28 0.703 1.72 3.15

Direct—Hydraulic fracturing 1.88 1.65 2.12 0.547 1.56 2.99

Direct—Cementing 0.014 0.014 0.014 0.014 0.014 0.014

Direct—Drilling 0.142 0.142 0.142 0.142 0.142 0.142

Indirect 0.453 0.453 0.453 0.453 0.453 0.453

Direct and indirect—COG mining 2.49 2.26 2.73 1.16 2.17 3.60

Ancillary (population-based) water use

All 2.43 1.76 3.11 2.02 2.35 2.35

Domestic 0.306 0.205 0.406 0.188 0.309 0.309

Public supply 2.13 1.54 2.71 1.83 2.04 2.04

Other potential ancillary water use

Industrial 0.260 0.193 0.326 0.186 0.242 0.242

Non-COG mining 10.8 7.66 13.9 8.87 10.2 14.8

Thermoelectric power 62.0 48.3 75.7 50.5 64.9 64.9
Results of Water-Use Analysis 15

The ratio of the range of the 95-percent confidence interval to 

the mean estimate was higher for Montana (about 0.25) than 

for North Dakota (about 0.2). The greater uncertainty of the 

mean estimate in Montana compared to North Dakota could 

be explained by the difference in data sources between the 

States; variability in the hydraulic fracturing methods used in 

each State; or differences in the geologic formations containing COG reservoirs in Montana and North Dakota that affect 

the extraction of oil and gas. The 95th percentile estimate 

from the quantile regression model of direct water use for 

hydraulic fracturing was 2.99 Mgal, or less than 50 percent of 

the 95th percentile estimate for North Dakota. However, if the 

data on hydraulic fracturing water use in North Dakota and 

Montana were combined in the analysis, then estimates for 

the Williston Basin in its entirety would more closely match 

the estimates for North Dakota. This closer match likely is 

because of the difference in the number of oil and gas wells 

developed between the States—North Dakota had about 

15 times as many wells developed as Montana.

The mean estimates from the linear regression models of 

cementing and drilling water use in Montana were the same 

as the estimates in North Dakota (table 3) because the coefficients from the North Dakota water-use analysis were applied 

to the analysis for Montana, which lacked data on cementing 

and drilling. Moreover, because the North Dakota coefficients 

were applied uniformly to oil and gas wells in Montana, 

estimates per well did not vary, so the limits of the confidence 

interval did not differ from the mean estimate.

The mean estimate from the linear regression model of 

indirect water use in Montana also was not different from the 

estimate in North Dakota (table 3). The coefficient from the 

North Dakota analysis was applied to the water-use analysis for Montana because Montana had no data from water 

permits. The limits of the confidence interval were the same as 

the mean estimate of indirect water use because there was no 

variation in the per-well estimates.

Direct and indirect water use in Montana had a mean 

estimate of 2.49 Mgal per well, although about 25 percent of 

this value is based on the coefficients of cementing and drilling water use and indirect water use applied from the North 

Dakota analysis. The 95th percentile estimate of direct and 

indirect water use was about 3.60 Mgal per well.

The mean estimate of ancillary water use (for domestic and public supply) in Montana was 2.43 Mgal per well, 

with a 95-percent confidence interval of 1.76–3.11 Mgal per 

well (table 3). Domestic water use was less than 25 percent 

of public supply water use. Other potential ancillary water 

use included mean estimates of 0.260, 10.8, and 62.0 Mgal 

per well for industrial, non-COG mining, and thermoelectric 

power, respectively. The mean and percentile estimates of 

some ancillary water-use categories for Montana ranged from 

double to an order of magnitude larger than for North Dakota 

most likely because of the difference in data sources between 

the States.

Performance of Regression Models of Water 

Use

Model performance was evaluated with goodness-of-fit 

metrics (R2, RMSE, and RSR) computed from leave-one-out 

cross-validation for the linear and quantile regression models 

of direct, indirect, and ancillary water use (table 4); performance metrics of just the linear regression models are presented in table 4. The values of R2 differed less among wateruse categories within a State than between the States (table 4). 

The differences in values of R2 between the States may result 

from differences in sample sizes. For example, North Dakota 

had 114 sampling units for direct water use compared to 55 for 

Montana. In addition, goodness-of-fit metrics were not computed for the model fit of cementing and drilling water use and 

indirect water use in Montana (table 4) because the mean estimates for these water-use categories from the North Dakota 

analysis were applied to the water-use analysis for Montana.

The model performance for direct water use in both 

States was good (table 4), with an R2 of 0.91 for North Dakota 

and 0.87 for Montana. The minor difference in performance 

may reflect a qualitative difference of the data source for 

Montana (data were available as 1-square-mile aggregated 

values for this study) compared to North Dakota (data originated from the individual oil and gas well operators), or it also 

could result from the difference in sample sizes between the 

States. However, the model fits of direct water use to number of oil and gas wells developed were reasonable for both 

North Dakota (fig. 8A) and Montana (fig. 8B), and the differences between estimated and observed values of water use 

were not qualitatively greater for Montana (fig. 9B) than for 

North Dakota (fig. 9A). For North Dakota, values of RMSE 

for the direct water-use categories ranged from 0.008 Mgal 

per well for cementing water use to 1.69 Mgal per well for 

direct water use, ranging from about 45 to 60 percent of their 

respective mean coefficients (also in million gallons per well; 

table 3). Values of RSR for the direct water-use categories 

ranged from 0.10 to 0.40, meaning that the standard deviation 

of the residuals from a linear regression model of a water-use 

category ranged from 10 to 40 percent of the standard deviation of the observations. For Montana, the RSR value for 

hydraulic fracturing water use was 0.10, and the RMSE value 

was 0.373 Mgal per well, or about 20 percent of its respective 

mean coefficient (table 3).

For North Dakota, the model performance for indirect 

water use also was good (table 4), with an R2 of 0.86. The 

model fit of indirect water use in North Dakota also was satisfactory (fig. 8C), as were the differences between water-use 

estimates and observations (fig. 9C). The indirect water-use 

estimates in Montana necessarily equaled their respective 

observed water use as shown in figures 8D and 9D, nullifying 

computations of R2, RMSE, or RSR for the indirect water-use 

category for Montana (table 4) because the coefficients of indirect water use from the North Dakota analysis were applied 
16 Estimates of Water Use Associated with Continuous Oil and Gas Development in the Williston Basin

to the water-use analysis for Montana. The linear regression 

model of indirect water use in Montana could not be compared to the linear regression model for North Dakota. The 

model fit of indirect water use in North Dakota had an RMSE 

of 0.275 Mgal per well (table 4), or about 60 percent of its 

respective mean coefficient (table 3), and the RSR value was 

0.38, which means RMSE less than 40 percent of the standard 

deviation of the observations.

The model performance for ancillary water use was more 

variable for Montana than for North Dakota (table 4). Values 

of R2 for the ancillary water-use categories ranged from 0.82 

to 0.89 for North Dakota and 0.52 to 0.79 for Montana. For 

most categories, values of R2 were about 20 to 25 percent 

higher for North Dakota than for Montana. For example, the 

model performance for domestic water use had an R2 of 0.83 

for North Dakota but 0.57 for Montana. Furthermore, values 

of RMSE for the ancillary water-use categories were larger 

for Montana, except for domestic and industrial water use 

(table 4). However, values of RSR were smaller for Montana 

than for North Dakota for the ancillary water-use categories, 

except for thermoelectric power water use. For Montana, 

the high values of RMSE relative to the low values of RSR 

Table 4. Goodness-of-fit metrics from leave-one-out cross-validation for linear regression models of direct, indirect, and ancillary 

water use per oil and gas well developed in the Williston Basin in North Dakota and Montana.

[R2, coefficient of determination; RMSE, root mean square error; Mgal, million gallons; RSR, ratio of root mean square error to standard deviation of observations; COG, continuous oil and gas; --, none]

Water use R2 RMSE 

(Mgal per well) RSR

North Dakota

Direct and indirect water use

Direct—All 0.91 1.69 0.27

Direct—Hydraulic fracturing 0.91 1.62 0.26

Direct—Cementing 0.78 0.008 0.40

Direct—Drilling 0.78 0.084 0.40

Indirect 0.86 0.275 0.38

Ancillary (population-based) water use

All 0.85 1.23 0.34

Domestic 0.83 0.479 0.38

Public supply 0.86 0.832 0.34

Other potential ancillary water use

Industrial 0.84 0.259 0.28

Non-COG mining 0.82 0.967 0.43

Thermoelectric power 0.89 0.173 0.23

Montana

Direct and indirect water use

Direct—All 0.87 0.485 0.12

Direct—Hydraulic fracturing 0.92 0.373 0.10

Direct—Cementing -- -- --

Direct—Drilling -- -- --

Indirect -- -- --

Ancillary (population-based) water use

All 0.67 1.40 0.23

Domestic 0.57 0.186 0.22

Public supply 0.68 1.23 0.23

Other potential ancillary water use

Industrial 0.79 0.159 0.25

Non-COG mining 0.60 6.31 0.23

Thermoelectric power 0.52 34.4 0.25
Results of Water-Use Analysis 17

suggests greater variability in water-use observations, which 

may reflect the difference in data sources, differences in sample sizes, or a difference in volumes of ancillary water use not 

accounted for by the number of oil and gas wells developed 

for Montana as for North Dakota. Furthermore, the model 

fit of ancillary water use (for domestic and public supply) 

was qualitatively better for North Dakota (fig. 8E) than for 

Montana (fig. 8F). However, the differences between observed 

and estimated water use (figs. 9E and 9F) were nearly equivalent between the States.

rol20-0026_fig 08

0

1,000

2,000

3,000

4,000

5,000

6,000

0

200

400

600

800

1,000

0

8,000

6,000

4,000

2,000

0

100

200

300

400

0

10

20

30

40

50

60

0

400

300

200

10

0 200 400 600 800 1,000 0 20 40 60 80 100 120

C. North Dakota indirect

E. North Dakota ancillary

B. Montana direct

D. Montana indirect

F. Montana ancillary

Number of oil and gas wells developed per sampling unit

Water use, in millions of gallons

EXPLANATION

95-percent confidence interval

Estimated mean

Estimated 95th percentile

Estimated 50th percentile

Estimated 5th percentile

Sampling unit

A. North Dakota direct

 Figure 8. Linear and quantile regression models of direct, indirect, and ancillary water use as explained by number of oil 

 and gas wells developed per sampling unit for North Dakota and Montana. A, North Dakota direct. B, Montana direct. 

 C, North Dakota indirect. D, Montana indirect. E, North Dakota ancillary. F, Montana ancillary.
18 Estimates of Water Use Associated with Continuous Oil and Gas Development in the Williston Basin

Comparisons to Water-Use Estimates 

from Other Studies

Estimates from the water-use analysis in this study 

(table 3) were compared to water-use estimates from other 

studies (table 5) of per-well water use for direct water use 

(for drilling, cementing, and hydraulic fracturing) and ancillary water use (for domestic and public supply). Estimates 

of indirect water use related to COG development were not 

found in other studies. The similarity between water-use 

estimates in this study and from other studies provide some 

validation of the methods used to analyze water use in 

this study.

Drilling and cementing water use was estimated in this 

study at 0.148–0.179 and 0.156 Mgal per well for North 

Dakota and Montana, respectively (table 3), and estimates 

of these water-use categories from other studies ranged 

from 0.150 to 0.236 Mgal per well (Haines and others, 

2017; Scanlon and others 2014; table 5). The similarity 

between estimates of drilling and cementing water use in 

rol20-0026_fig 09

A. North Dakota direct

C. North Dakota indirect

E. North Dakota ancillary

B. Montana direct

D. Montana indirect

F. Montana ancillary

EXPLANATION

Sampling unit

1:1 line

0 0 100 200 300 400

0

500

500

1,000

1,000

1,500

1,500

2,000

2,000

0

100

200

300

400

0

100

50

150

200

250

300

0

100

200

300

400

0

10

20

30

40

50

60

0

500

3,500

3,000

2,500

2,000

1,500

1,000

Observed water use, in millions of gallons

Estimated water use, in millions of gallons

Figure 9. Relation between observed and estimated direct, indirect, and ancillary water use per 

sampling unit as mean value from linear regression models for North Dakota and Montana. A, North 

Dakota direct. B, Montana direct. C, North Dakota indirect. D, Montana indirect. E, North Dakota 

ancillary. F, Montana ancillary.
Comparisons to Water-Use Estimates from Other Studies 19

this study and from other studies may reflect the limited 

data sources available for estimating drilling and cementing 

water use.

Estimates of hydraulic fracturing water use in this study 

were 1.12–7.49 and 0.547–2.99 Mgal per well for North 

Dakota and Montana, respectively (table 3), which are comparable to estimates from other studies that ranged from 1.82 to 

5.58 Mgal per well (Gallegos and others, 2015; Kondash and 

others, 2018; table 5). The published range of values is less 

than the range in this study. The lowest published estimate 

was based on data from 2011 to 2014, the early years of COG 

development in the Williston Basin when hydraulic fracturing 

treatments used less water. Similarly, the highest published estimate was based on data from 2016, and water use for hydraulic 

fracturing treatments have increased with time. In this study, 

the use of linear and quantile regression models provided a 

range of parameter estimates (including the mean, the median, 

and the 5th and 95th percentiles) of per-well hydraulic fracturing water use based on data from 2007 to 2017.

This study estimated ancillary water use (for domestic 

and public supply) in North Dakota and Montana at 1.19–5.24 

and 1.77–3.13 Mgal per well, respectively (table 3), which 

is much greater than the range (1.22–2.44 Mgal per well) 

reported for domestic water use in North Dakota in 2012 

(Horner and others, 2016; table 5). Horner and others (2016)

estimated domestic water use using population estimates near 

Williston, N. Dak., and a range of per-capita water-use coefficients. The estimates from Horner and others (2016) were 

Table 5. Estimates of direct, indirect, and ancillary water use associated with continuous oil and gas development in the Williston 

Basin from other studies.

[--, none]

Water use

Volume per 

well (million 

gallons)

Source Comments

Direct water use

Drilling, cementing0.236 Scanlon and others, 2014, 

table S14a

Drilling use estimated as 6 times borehole volume.

0.150 Haines and others, 2017 Mean value of range estimated for possible future use.

Drilling, maintenance0.461 Lin and others, 2018, 

table S3

Included maintenance water and possibly other uses.

Maintenance 570–850a Horner and others, 2016, 

section 3.2

--

465–685a Lin and others, 2018, 

table S3

--

Hydraulic fracturing1.82 Gallegos and others, 2015, 

table S1

Based on data from 2011 to 2014.

1.97 Kondash and Vengosh, 

2015, table 1

Median value.

3.25 Chen and Carter, 2016, 

table S5

Mean value in 2014 for Montana and North Dakota.

2.14 Horner and others, 2016, 

table 2, section 2.1

Median value of data available from FracFocus at time of study for 

North Dakota.

3.80 Scanlon and others, 2016, 

section 4.4.1

Mean value of potential future range.

4.17 Haines and others, 2017 Mean value of range estimated for possible future use.

5.58 Kondash and others, 2018, 

table S2

Median value in 2016.

3.92 Lin and others, 2018, 

table S2

Mean value in 2014.

Indirect water use

-- -- -- --

Ancillary water use

Domestic 1.22–2.44 Horner and others, 2016 Use by service personnel in 2012 for North Dakota.

a

Units in gallons per day.
20 Estimates of Water Use Associated with Continuous Oil and Gas Development in the Williston Basin

based on a ratio of temporary field personnel to permanent 

workers, which changes with time and could lead to inconsistent estimates. The estimates in this study were based on the 

reported water use from the NDSWC water permits for North 

Dakota and the USGS water-use data for Montana using a 

linear regression model that reduced climate and population 

effects in the modeled data.

Limitations of Water-Use Analysis for 

the Williston Basin

The water-use analysis for the Williston Basin had several limitations that potentially affected how accurately water 

use associated with COG development in the Williston Basin 

could be estimated. These limitations mostly concern the 

availability of water-use data and constraints of the modeling 

approach. The analytical framework from Valder and others 

(2019), derived from a conceptual model (Valder and others 2018), was the basis for this study, and these publications 

provided additional context on some limitations that will be 

discussed in this section.

The coefficients from the regression models of cementing and drilling water use were less certain than those for 

hydraulic fracturing because several assumptions were 

necessary because North Dakota and Montana do not require 

reporting water use for drilling and cementing. Instead, for 

North Dakota, data on the number of sacks of cement used per 

well and the measured depth reached per well were used to 

estimate water use for cementing and drilling. Cementing was 

assumed to use 5 gallons of water per sack of cement, but it 

is likely that this value would vary among wells and within a 

well from the upper to lower depths of cementing the casings 

because of changes in pressure, temperature, and moisture 

and because of variability in the geologic formation, including 

layers containing aquifers. Additionally, drilling was assumed 

to use 7.5 gallons of water per 1 foot of depth, but this value 

also would likely vary among wells, depending on geology of 

the formations, operations of the oil and gas companies, and 

prices of the water and other materials required for drilling. 

Moreover, drilling through the surface geologic layers that 

contain aquifers (fig. 3) uses only water, but the remaining 

depths can be drilled using other fluids in addition to water. 

No data were available on the use of water compared to other 

fluids, so it was assumed that drilling fluids were predominantly water-based. However, the effect of these assumptions 

is probably small because drilling and cementing water use 

contribute less than 5 percent to the direct water-use estimate; 

more than 95 percent of the direct water-use estimate consists 

of hydraulic fracturing water use.

The regression models of the other potential ancillary 

water-use categories had an implied assumption that changes 

in industrial, non-COG mining, and thermoelectric power 

water use were caused by COG development. However, coefficients from the regression models merely suggest water use 

for those categories that might be correlated to the presence of 

COG development; in other words, if COG development were 

absent, water use for those categories might have been reduced 

from what was observed by the estimated value. Therefore, the 

estimates for the other potential ancillary water-use categories 

were treated separately from the estimates for the populationbased categories (domestic and public supply), which had a 

more-certain relation to COG development.

The confidence interval for the coefficient from the linear 

regression model had potential limitations to its capacity to 

adequately capture the data variance. For all water-use categories for each State (except for public supply and thermoelectric 

power water use for Montana), the 5th, 95th, or both percentile 

estimates from the quantile regression model were outside 

the 95-percent confidence interval from the linear regression 

model, suggesting that the mean estimate for these water-use 

categories may be less certain than indicated by the linear 

regression model. Instead, the 95th-percentile estimate provides a more-conservative estimate of water use, which might 

be more appropriate to use in management decisions about 

water available for beneficial uses where regions of COG 

development are in arid climates or when drought is resulting 

in water scarcity. Additionally, a mean estimate does not provide information on the spatial and temporal variation in water 

use, so the 95th-percentile estimate might be more robust to 

changes in water use, particularly with the knowledge that 

hydraulic fracturing water use per well has been trending 

upward nationally (Gallegos and Varela, 2015).

A key assumption affecting the estimates of direct, indirect, and ancillary water use was the estimation of a breakpoint 

in the data on hydraulic fracturing water use. Breakpoints were 

estimated at 2007 and 2008 for North Dakota and Montana, 

respectively; however, other years could have been chosen 

from the breakpoint analysis, and selecting a different year 

would have affected the water-use estimates. Different years of 

data used to model water use after the boom in COG development would affect how much direct water use is estimated 

because the coefficients of the regression models would likely 

differ. Likewise, the trend in direct water use in the years 

preceding the boom in COG development is sensitive to the 

years of data fit by the regression model. Because this trend is 

extrapolated forward into the years after the breakpoint, a different breakpoint would affect how much ancillary water use 

is attributed to COG development and how much of the COG 

mining water use is contributed by indirect water use.

The evaluation of uncertainty in the water-use estimates 

and performance of the linear and quantile regression models was limited by the goodness-of-fit metrics and validation 

procedures used for this study. Although this study used leaveone-out cross-validation, other procedures, including bootstrap, jackknife, or k-fold cross-validation (Hastie and others, 

2009), also may have been appropriate. However, it is unlikely 

the use of other validation procedures would have greatly 

affected model performance. Goodness-of-fit metrics other 

than R2, RMSE, and RSR, which this study used, also can be 

informative. However, these three metrics are commonly used 
Summary 21

to evaluate the performance of hydrologic models (Moriasi 

and others, 2007), and they provided a reasonable assessment 

of model performance in this study.

The simple linear and quantile regression models used 

for this study were potentially limited in their ability to 

explain water use associated with COG development. Linear 

regression models tend to have low variance but high bias, 

underfitting the data, whereas more sophisticated nonlinear 

or multivariate statistical approaches or machine-learning 

algorithms tend to have lower bias but higher variance, overfitting the data. A more complex model than linear or quantile 

regression might have explained more variance in water use 

in the Williston Basin. However, a more complex model 

needs more explanatory variables likely unavailable for all 

regions of COG production, so the best-fitting model for the 

Williston Basin might not be applicable to another region. The 

regression models used for this study do not require data on 

explanatory variables potentially unavailable in other regions, 

so these models are more readily adapted to existing water-use 

data for estimating water use associated with COG development nationally for the USGS National Water Census and 

Water Budget Estimation and Evaluation Project (supported 

by the USGS Water Availability and Use Science Program). 

Additionally, the regionally based coefficients from the regression models (including the mean, the median, and the 5th and 

95th percentiles) deliver a probable range of water use.

Summary

Water is a necessary component for many processes 

required for developing continuous oil and gas (COG) 

resources. Improved COG extraction techniques have greatly 

increased oil and gas production in the United States since 

the mid-2000s. However, the accompanying rapid increase in 

demand for large volumes of water, often in remote regions, 

can challenge existing infrastructure and require additional 

resources to meet water needs. Addressing this water need 

requires accurate estimates of the volumes of water used to 

support the various processes common to COG development 

in the United States in the 21st century.

This study of water use associated with COG development in the Williston Basin is intended to provide a preliminary model-based analysis of water use in major regions of 

COG production in the United States. Direct, indirect, and 

ancillary water use associated with COG development in the 

Williston Basin was estimated in North Dakota and Montana 

from 2007 to 2017. The water-use estimates presented in 

this report are compared with other published values for the 

Williston Basin, and the limitations of the water-use analysis 

for the Williston Basin are described.

The water-use analysis was executed with scripts coded in 

R. Water-use data were aggregated by county and year, which 

were the sampling units used in the analysis. Linear and quantile regression models of water use in relation to the number 

of oil and gas wells developed were fit for the direct, indirect, 

and ancillary water-use categories for each State. A 95-percent 

confidence interval for each parameter estimate from the linear 

regression models was computed as a measure of uncertainty. 

Additional information on uncertainty can be gained from 

modeling other distribution parameters, so quantile regression models of the 5th, 50th, and 95th percentiles also were 

fit. Water-use coefficients from the linear and quantile regression models are in million gallons per well, whereas water-use 

estimates from the regression models are in million gallons per 

sampling unit. To assess uncertainty in the estimates from the 

regression models of direct, indirect, and ancillary water use, 

leave-one-out cross-validation was used. Model performance 

was evaluated with three goodness-of-fit metrics used to compare the estimates and observations of water use.

Mean annual direct and indirect water use for COG 

development in North Dakota was estimated at 4,512 million 

gallons (Mgal) per year (Mgal/yr), with a 95-percent confidence interval of 4,021–5,152 Mgal/yr, and in Montana was 

estimated at 196 Mgal/yr, with a 95-percent confidence interval of 189–203 Mgal/yr. Ancillary water use (for domestic and 

public supply) had an estimated annual mean of 2,753 Mgal/yr 

in North Dakota and 396 Mgal/yr in Montana.

The coefficient from the linear regression model of direct 

water use was 3.86 Mgal per well and hydraulic fracturing 

water use was 3.70 Mgal per well for North Dakota. The mean 

estimate of direct water use had a 95-percent confidence interval of 3.48–4.23 Mgal per well. For North Dakota, the coefficient from the linear regression model of indirect water use 

was 0.453 Mgal per well, with a 95-percent confidence interval of 0.415–0.492 Mgal per well. Direct and indirect water 

use had a mean estimate of about 4.31 Mgal per well in North 

Dakota. The mean estimate of ancillary water use (for domestic and public supply) in North Dakota was 2.03 Mgal per 

well, with a 95-percent confidence interval of 1.76–2.31 Mgal 

per well. For Montana, the linear regression model of hydraulic fracturing water use had a mean estimate of 2.04 Mgal per 

well. The 95-percent confidence interval for the mean estimate 

was 1.80–2.28 Mgal per well. Direct and indirect water use 

in Montana had a mean estimate of 2.49 Mgal per well. The 

mean estimate of ancillary water use (for domestic and public 

supply) in Montana was 2.43 Mgal per well, with a 95-percent 

confidence interval of 1.76–3.11 Mgal per well.

The model performance for direct water use in both 

States was good, with a coefficient of determination (R2) 

of 0.91 for North Dakota and 0.87 for Montana. For North 

Dakota, the model performance for indirect water use also was 

good, with an R2 of 0.86. The model performance for ancillary water use was more variable for Montana than for North 

Dakota. Values of R2 for the ancillary water-use categories 

ranged from 0.82 to 0.89 for North Dakota and 0.52 to 0.79 for 

Montana. For most categories, values of R2 were about 20 to 

25 percent higher for North Dakota than for Montana.

The similarity between water-use estimates in this 

study and from other studies provide some validation of the 

methods used to analyze water use in this study. Drilling 
22 Estimates of Water Use Associated with Continuous Oil and Gas Development in the Williston Basin

and cementing water use was estimated in this study at 

0.148–0.179 and 0.156 Mgal per well for North Dakota 

and Montana, respectively, and estimates of these wateruse categories from other studies ranged from 0.150 to 

0.236 Mgal per well. Estimates of hydraulic fracturing water 

use in this study were 1.12–7.49 and 0.547–2.99 Mgal per 

well for North Dakota and Montana, respectively, which 

are comparable to estimates from other studies that ranged 

from 1.82 to 5.58 Mgal per well. This study estimated ancillary water use (for domestic and public supply) in North 

Dakota and Montana at 1.19–5.24 and 1.77–3.13 Mgal per 

well, respectively, which is much greater than the range 

(1.22–2.44 Mgal per well) reported for domestic water use in 

North Dakota in 2012.

The water-use analysis for the Williston Basin had several limitations that potentially affected how accurately water 

use associated with COG development in the Williston Basin 

could be estimated. These limitations mostly concern the 

availability of water-use data and constraints of the modeling approach. A more complex model than linear or quantile 

regression might have explained more variance in water use in 

the Williston Basin. However, a more complex model needs 

more explanatory variables likely unavailable for all regions 

of COG production, so the best-fitting model for the Williston 

Basin might not be applicable to another region. The regression models used for this study do not require data on explanatory variables potentially unavailable in other regions, so these 

models are more readily adapted to existing water-use data 

for estimating water use associated with COG development 

nationally.

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Appendix 1. R Scripts 25

Appendix 1. R Scripts

The R scripts for the Williston Basin water-use analysis are available at https://doi.org/10.3133/sir20205012 in a 

zipped archive, sir20205012_appendix1.zip, which contains 

the following files and folders:

• README.txt—A “how-to” document for running 

the scripts;

• munge_data_release.R—A script used for preparing 

data from the accompanying data release;

• run_analysis.R—The script used for running the wateruse analysis;

• wrangle.R—A script with functions for preparing input 

data to the water-use analysis;

• model.R—A script with functions for processing the 

water-use analysis;

• visualize.R—A script with functions for preparing 

model output from the water-use analysis as tables 

and figures;

• Raw—A folder for downloading data from the prior 

data release;

• Functions—A folder with the scripts (wrangle.R, 

model.R, and visualize.R) used for processing the 

water-use analysis;

• Data—A folder for saving prepared input data;

• Analyses—A folder for saving model output prepared 

as tables; and

• Plots—A folder for saving model output prepared 

as figures.
26 Estimates of Water Use Associated with Continuous Oil and Gas Development in the Williston Basin

Appendix 2. Water-Use Estimates and Coefficients

The Williston Basin water-use estimates and coefficients 

are available at https://doi.org/10.3133/sir20205012 in a 

zipped folder, sir20205012_appendix2.zip, with the following 

delimited files:

• WaterUseEstimates.csv—A comma-separated values 

file of estimates from the regression models used in the 

water-use analysis; and

• WaterUseCoefficients.csv—A comma-separated values 

file of coefficients from the regression models used in 

the water-use analysis.

The WaterUseEstimates.csv file has 10 columns and 

635 rows. The first column lists the State and contains “North 

Dakota” or “Montana.” The second column lists the County 

and contains one of the following: “Billings,” “Bottineau,” 

“Bowman,” “Burke,” “Burleigh,” “Carter,” “Custer,” 

“Daniels,” “Dawson,” “Divide,” “Dunn,” “Emmons,” 

“Fallon,” “Garfield,” “Golden Valley,” “Hettinger,” 

“McCone,” “McHenry,” “McKenzie,” “McLean,” “Mercer,” 

“Morton,” “Mountrail,” “Oliver,” “Renville,” “Richland,” 

“Roosevelt,” “Sheridan,” “Slope,” “Stark,” “Valley,” “Ward,” 

“Wibaux,” or “Williams.” The third column contains the year 

and ranges from 2007 to 2017. The fourth column lists the 

water-use category and contains one of the following: “COG 

mining,” “Domestic,” “Industrial,” “Non-COG mining,” 

“Public supply,” or “Thermoelectric power.” Descriptions of 

the water-use categories are in the report. The abbreviation 

COG means continuous oil and gas. The fifth column contains the mean coefficients from the linear regression models 

of water use and ranges from 0.028 to 10,701.604. The sixth 

and seventh columns contain the lower and upper confidence 

limits of the 95-percent confidence intervals for the mean 

coefficients and range from 0 to 7,519.259 and from 0.037 to 

15,019.646, respectively. The eighth, ninth, and tenth columns contain the 5th, 50th, and 95th percentile coefficients 

from the quantile regression models of water use and range 

from 0 to 10,614.283, from 0 to 10,614.283, and from 0.033 

to 11,456.377, respectively. Values are in million gallons 

per year.

The WaterUseCoeffients.csv file has 8 columns and 

24 rows. The first column lists the State and contains “North 

Dakota” or “Montana.” The second column lists the wateruse category and contains one of the following: “Hydraulic 

fracturing,” “Cementing,” “Drilling,” “Direct,” “Indirect,” 

“COG mining,” “Domestic,” “Public supply,” “Populationbased ancillary,” “Industrial,” “Non-COG mining,” or 

“Thermoelectric power.” Descriptions of the water-use 

categories are in the report. The third column contains the 

mean coefficients from the linear regression models of water 

use and ranges from 0.014 to 61.991. The fourth and fifth 

columns contain the lower and upper confidence limits of the 

95-percent confidence intervals for the mean coefficients and 

range from 0.014 to 48.309 and from 0.014 to 75.673, respectively. The sixth, seventh, and eighth columns contain the 5th, 

50th, and 95th percentile coefficients from the quantile regression models of water use and range from 0.014 to 50.544, 

from 0.014 to 64.918, and from 0.014 to 64.918, respectively. 

Values are in million gallons per oil and gas well developed.
For more information about this publication, contact:

Director, USGS Wyoming-Montana Water Science Center 

3162 Bozeman Avenue

Helena, MT 59601

406–457–5900

For additional information, visit: https://www.usgs.gov/centers/wy-mtwater/

Publishing support provided by the 

Rolla Publishing Service Center
McShane and others—Estimates of Water Use Associated with Continuous Oil and Gas Development in the Williston Basin—SIR 2020–5012

ISSN 2328-0328 (online)

https://doi.org/10.3133/sir20205012