Procedure for Calculating Estimated Ultimate Recoveries 

of Bakken and Three Forks Formations Horizontal Wells 

in the Williston Basin

By Troy A. Cook

Open-File Report 2013–1109

U.S. Department of the Interior

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

SALLY JEWELL, Secretary

U.S. Geological Survey

Suzette M. Kimball, Acting Director

U.S. Geological Survey, Reston, Virginia: 2013 

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Suggested citation:

Cook, T.A., 2013, Procedure for calculating estimated ultimate recoveries of Bakken and Three Forks

Formations horizontal wells in the Williston Basin: U.S. Geological Survey Open-File Report 2013–1109, 

14 p., http://pubs.usgs.gov/of/2013/1109/.

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COVER. Photograph was taken a couple miles west of Grassy Butte in McKenzie County, North Dakota. The Paleocene/Eocene contact 

is at the break in slope just above the brightly colored beds. The photo is looking south-southeast. Photo courtesy of Edward C. Murphy, 

State Geologist, North Dakota Geological Survey.
iii

Contents

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

EUR Estimation Procedure......................................................................................................................................... 1

EUR Estimation Procedure by Group ......................................................................................................................... 4

Long-Term Production Group ................................................................................................................................. 4

Short-Term Production Group................................................................................................................................. 4

Starting Production Group....................................................................................................................................... 6

EURs by Assessment Unit........................................................................................................................................ 11

Summary .................................................................................................................................................................. 13

References Cited...................................................................................................................................................... 14

Figures

Figure 1. Flow chart illustrating the procedure for developing estimated ultimate recoveries for producing 

wells in the Bakken and Three Forks Formations, Williston Basin...................................................... 2

Figure 2. Example well showing the positioning of three points that define the initial decline curve in a 

well with 19 or more months of production data.................................................................................. 3

Figure 3. Initial monthly production rates compared to hyperbolic “b” factor for wells with more than 

24 months of production data ............................................................................................................. 5

Figure 4. Plot of binned “b” factors compared to initial monthly production rate using data from figure 3............... 6

Figure 5. Ten-year probabilistic-type curve (PTC) for all horizontal wells in the Bakken Formation ....................... 7

Figure 6. Ten-year probabilistic-type curve (PTC) for all horizontal wells in the Bakken Formation and 

Three Forks Formation ....................................................................................................................... 8

Figure 7. Ten-year probabilistic-type curve (PTC) for all horizontal wells in the Three Forks Formation................ 9

Figure 8. Ten-year probabilistic-type curve (PTC) for all horizontal wells in the upper part of the Bakken 

Formation.......................................................................................................................................... 10

Figure 9. Map of five continuous and one conventional assessment units (AU) in the Bakken Formation........... 11

Figure 10. Map of one continuous and one conventional assessment units (AU) in the Three Forks 

Formation.......................................................................................................................................... 12

Figure 11. Family of curves showing the EURs (estimated ultimate recoveries) for five Bakken Formation 

continuous assessment units (AUs) and one Three Forks Formation continuous AU....................... 13
iv

Initialisms Used in This Report

AU assessment unit

EUR estimated ultimate recovery

MBLS thousand barrels

PTC probabilistic-type curve

TPS total petroleum system

USGS U.S. Geological Survey
Procedure for Calculating Estimated Ultimate Recoveries 

of Bakken and Three Forks Formations Horizontal Wells 

in the Williston Basin

By Troy A. Cook

Introduction

Estimated ultimate recoveries (EURs) are a key component in determining productivity of wells 

in continuous-type oil and gas reservoirs. EURs form the foundation of a well-performance-based 

assessment methodology initially developed by the U.S. Geological Survey (USGS; Schmoker, 1999). 

This methodology was formally reviewed by the American Association of Petroleum Geologists 

Committee on Resource Evaluation (Curtis and others, 2001). 

The EUR estimation methodology described in this paper was used in the 2013 USGS 

assessment of continuous oil resources in the Bakken and Three Forks Formations and incorporates 

uncertainties that would not normally be included in a basic decline-curve calculation. These 

uncertainties relate to (1) the mean time before failure of the entire well-production system (excluding 

economics), (2) the uncertainty of when (and if) a stable hyperbolic-decline profile is revealed in the 

production data, (3) the particular formation involved, (4) relations between initial production rates and 

a stable hyperbolic-decline profile, and (5) the final behavior of the decline extrapolation as production 

becomes more dependent on matrix storage. 

EUR Estimation Procedure

The procedure for estimating well EURs in the Bakken and Three Forks Formations is presented 

as a flow chart in figure 1. All Bakken and Three Forks Formations horizontal wells with production 

data were included in this evaluation. Previous USGS assessments used only wells with 19 or more 

months of production data. The number of months of production data is the basis for determining the 

specific procedure used to estimate EURs. Wells were separated into three groups by the number of 

months of production: (1) wells with 19 months or more of production (long-term production group), 

(2) wells with 5 to 18 months of production (short-term production group), and (3) wells with 1 to 4 

months of production (starting production group).
2

Figure 1. Flow chart illustrating the procedure for developing EURs (estimated ultimate recoveries) for producing 

wells in the Bakken and Three Forks Formations, Williston Basin.
3

These three categories were based in part on the particular behavior of Bakken and Three Forks 

completions, operations, and well-decline curves. The Bakken and Three Forks horizontal wells are 

normally produced through a mechanical lift system that is commonly installed after initial completion 

of the wells. Only after lift equipment is installed can we assume that production is in a stable decline. 

Even after a hyperbolic decline is interpreted to have begun, there is continuing uncertainty as to when 

the hyperbolic decline ends.

The production data for each Bakken and Three Forks well were plotted, and the data for each 

well were “hand-fit” with three points along the temporal-production-data string that allowed us to 

decide which type of decline-curve function to best extrapolate the data (fig. 2). 

Figure 2. Example well showing the positioning of three points that define the initial decline curve in a well with 

19 or more months of production data. The positioning of these three points represents the “hand-fit” to 

production data. Red line signifies the last production-data point in 2012. Year begins with 2008.

The long-term production group consists of wells with 19 or more months of production data 

and is interpreted to be the group of wells with the least amount of uncertainty with respect to the 

“hand-fit” of three points positioned along the temporal data string. Wells having 19 or more months of 

data have production rates and decline curves that are typically well established. The three main sources 

of uncertainty within this group are (1) the timing of the failure of the physical wellbore itself, (2) the 

timing of the depletion of the formation, and (3) the point in time at which the rate of a hyperbolic 

decline transitions to an exponential decline in the latter stage of the well life. 

The short-term production group consists of wells having 5–18 months of data and can exhibit 

similarities to both the long-term and starting production groups. Uncertainty in this category can lead to 
4

a wide range of EUR estimates using the same production data, even among experts using similar 

methods. The probabilistic system developed for this group accounts for the possibility that the existing 

production profile is nearly as limited and uncertain as the starting production group, or as certain as the 

long-term production group. 

The starting production group is defined as 1–4 months of production and is designed to require 

only an approximate well-decline starting point. Using this starting point, a full probabilistic system was 

developed based on production analogs from wells in that formation with longer temporal-productiondata strings, albeit with great uncertainty. 

The EURs estimated for all three production groups are for potential oil resources and should not 

be confused with reserve estimates because no economic criteria were used in the EUR estimation. We 

assumed that all wells capable of production will continue to produce until some uneconomic rate is 

reached. No attempt was made to determine what is, or is not, economic production. 

EUR Estimation Procedure by Group

Long-Term Production Group

The long-term production group (2,954 wells) has the least amount of uncertainty and most 

closely resembles a typical decline-curve analysis. A best-fit hyperbolic or exponential decline is fit to 

existing production data and extrapolated for 60 years (720 months). 

Two probabilistic components are added to the long-term production-group fits. The first is the 

addition of an exponential tail on hyperbolic declines. The well is extrapolated according to the 

hyperbolic best-fit until the extrapolated decline rate becomes less than a given exponential terminal 

decline rate. The extrapolation then uses the exponential decline rate to calculate monthly production 

rates out to 720 months (60 years). The modification of a hyperbolic decline by attaching an exponential 

tail when a certain rate of decline is reached is referred to as a hybrid-decline model. An overview of 

stochastic modeling techniques for well-level production using multiple segments of differently 

declining production data is outlined by Haavardsson and Huseby (2007). The exponential tail method 

is expected to more accurately reflect the reality of long-term production rates in horizontal Bakken and 

Three Forks wells in the Williston Basin.

The second probabilistic component is the uncertainty related to the period of time any single 

well will continue to produce. All production rates in each of the groups were calculated for 720 

months, but these data are truncated probabilistically to reflect that not all wells are capable of 

producing for that length of time. A triangular distribution with a minimum of 240 months (20 years), a 

mode of 540 months (45 years), and a maximum of 720 months (60 years) is used to represent the 

distribution of the well or formation failure during the lifespan of the well. In other words, this model 

represents the chance that any well, on any single iteration, regardless of flow rate, could fail 

somewhere between 20 to 60 years after the start of production. 

A Monte Carlo simulator was used to run 1,000 iterations of this procedure to create an 

empirical distribution of EURs for each well in the production group. The mean of this distribution was 

the primary statistical value carried forward for use in the resource assessment. 

Short-Term Production Group

The short-term production group (1,606 wells) does not contain the most uncertainty of these 

decline-curve projections. Wells in this group, however, can be the most misleading if using common 

deterministic methods to simplify EUR calculations. For example, applying a deterministic decline-type
5

curve or assumed decline parameters and shifting the resulting extrapolation based solely on an initial 

production point is one of the more common procedures. By definition, EUR will then be singularly 

dependent upon the starting point. This type of procedure assumes that the increases in initial production 

are independent of the decline parameters when in fact they are not. 

Figure 3 shows hyperbolic exponents (“b” factor) versus initial production rates using data from 

horizontal wells with enough production to establish a reasonable estimate of hyperbolic behavior. The 

data in figure 3 were binned and used to create figure 4. The decrease in hyperbolic “b” factor as initial 

production rate increased is more apparent than in figure 3 and demonstrates why assumptions of 

independence between initial production and the rest of the parameters used to create deterministic 

decline parameters or a deterministic decline-type curve are not valid. 

Figure 3. Initial monthly production rates compared to hyperbolic “b” factor for wells with more than 24 months of 

production data.
6

Figure 4. Plot of binned “b” factors compared to initial monthly production rate using data from figure 3. Plot 

utilized wells with greater than 24 months of production data.

A key difference in the EUR estimation between the short-term production group and the longterm production group is that there may not be enough data available to make a determination of 

hyperbolic versus exponential decline. Regardless of whether or not a well has been fit as declining 

hyperbolically or exponentially, we assume that the past frequency of decline type in wells of Bakken 

and Three Forks Formations will continue to hold true in the future, including a measure of uncertainty 

around that ratio. 

Wells hand-fit with exponential decline curves are assumed to decline in the same ratio as do 

wells with known exponential declines in Bakken and Three Forks Formations. The remainder of the 

time wells are assigned a hyperbolic decline with a “b” factor chosen from the distribution of “b” factors 

matching initial production rates of those particular wells as provided in figure 4. Wells are extrapolated 

hyperbolically until the year-to-year decline becomes less than the exponential terminal-decline rate. 

The same exponential-decline rate that was used on long-term production-group wells was then used to 

calculate production rates for 720 months. 

Wells hand-fit with a hyperbolic decline are assumed to have an amount of uncertainty related to

the assigned “b” factor. In each iteration, the “b” factor is chosen from the appropriate “b” factor 

distribution in figure 4 that matches that well’s initial production rate. 

This procedure, in combination with the same well-life truncation that was utilized for long-term

production-group wells, is also run through a Monte Carlo simulator 1,000 times to create an empirical 

distribution of EUR for each well in this production group. The mean of this distribution was the 

primary statistic carried forward for use in the resource assessment.

Starting Production Group

The starting production group (678 wells) involves the most uncertainty of the three groups of 

producing wells. Wells within this group are assumed to have established little more than an initial 

production starting point with a large amount of uncertainty in that starting point. Consistent monthly 
7

production from a well could take months to establish because of operational conditions and constraints. 

These conditions and constraints make it possible for some initial, near-term or partial-production point 

to be high or low compared to what it would have been under perfect operational conditions and 

constraints. 

To quantify the range of uncertainty in EURs from an initial monthly production point, a fullproduction performance envelope in the form of a probabilistic-type curve (PTC) was assembled. 

Assembling a PTC requires that all production information for a given formation be normalized to the 

number of months from the start of that production. The Anderson-Darling test (Stephens, 1974) is then 

used to determine the parameters of the distribution for each monthly group. Ordered sequentially from 

the start of production, this sequence of distributions creates a PTC. 

The first 10 years of each PTC used during this procedure are provided in figures 5 through 8. 

Figure 5 is the PTC for all horizontal wells listed as Bakken Formation producers within the dataset. 

Figure 6 is the PTC for all horizontal wells listed as producing from the Bakken and Three Forks 

Formations. Figure 7 is the PTC for all horizontal wells listed as producing from the Three Forks 

Formation. Figure 8 is the PTC for all horizontal wells listed as producing from the upper part of the 

Bakken Formation.

Figure 5. Ten-year probabilistic-type curve (PTC) for all horizontal wells in the Bakken Formation.
8

Figure 6. Ten-year probabilistic-type curve (PTC) for all horizontal wells in the Bakken Formation and Three 

Forks Formation.
9

Figure 7. Ten-year probabilistic-type curve (PTC) for all horizontal wells in the Three Forks Formation.
10

Figure 8. Ten-year probabilistic-type curve (PTC) for all horizontal wells in the upper part of the Bakken 

Formation.

To create an individual well EUR from a given PTC, the initial monthly production rate is 

matched to the corresponding fractile position of the first month distribution of the PTC. The 

uncertainty around this initial point is then estimated to be one-half of the fractile distance between the 

initial point and the maximum fractile and one-half the fractile distance between the initial point and the 

minimum fractile. 

Once a starting point within the first monthly PTC distribution has been established, that fractile 

position is followed consecutively through the formation-specific PTC, assuming perfect positive 

correlation. Each PTC contains 360 sequential distributions, and when completed, the same exponential 

terminal-decline rate that was used on wells in the other two production groups is extrapolated for an 

additional 360 months. The total time frame over which production rates are calculated is 720 months. 

This procedure, in combination with the same well-life truncation that was utilized for the other 

two production groups, was run through a Monte Carlo simulator 1,000 times to create an empirical 

distribution of EUR for each well in this group. The mean of this distribution was the primary statistic 

carried forward for use in the resource assessment.
11

EURs by Assessment Unit

In 2013 the USGS defined geologic assessment units in the Bakken and Three Forks Formations 

in advance of a quantitative resource assessment. We defined six continuous assessment units, five in 

the Bakken Formation and one in the Three Forks Formation (figs. 9 and 10). Following the estimation 

of EURs for all Bakken and Three Forks wells, the EURs and wells were assigned to their designated 

geologically defined assessment unit. Figure 11 represents the full distribution of means of all 

probabilistic well EURs in each of the six assessment units. The means of these empirical distributions

are also shown on figure 11. 

Figure 9. Map of five continuous and one conventional assessment units (AU) in the Bakken Formation. TPS, 

total petroleum system.
12

Figure 10. Map of one continuous and one conventional assessment units (AU) in the Three Forks Formation.

TPS, total petroleum system.
13

Figure 11. Family of curves showing the EURs (estimated ultimate recoveries) for five Bakken Formation

continuous assessment units (AUs) and one Three Forks Formation continuous AU. MBLS, thousand barrels.

Mean EUR as calculated using the procedures outlined in this paper ranges from 363,000 barrels 

for the Eastern Transitional Continuous Oil AU to 148,000 barrels in the Northwest Transitional 

Continuous Oil AU. Mean EUR for the Three Forks Continuous Oil AU (256,000 barrels) is similar to 

the mean EUR for several Bakken AUs. These means are useful to quantify historical well productivity

and do not represent reserves and are not required to be direct inputs to the geologically based 

assessment methodology. 

Summary 

This report outlines the procedure by which EURs were estimated for all producing wells in the 

Bakken and Three Forks Formations in the Williston Basin. This procedure differs from that used in 

previous USGS assessments in which wells with 19 or more months of production data were used in the 

EUR estimation process. The resulting probabilistic EUR distributions were used as guides in the 

process for estimating EURs for assessment units in the Bakken and Three Forks Formations. 
14

References Cited

Curtis, John; Kumar, Naresh; Ray, Pulak; Riese, Rusty; and Ritter, John, 2001, American Association of 

Petroleum Geologists Committee on Resource Evaluation (CORE) Subcommittee to review the 

United States onshore continuous (unconventional) gas assessment methodology used by the USGS: 

Report accessed February 20, 2013, at 

http://certmapper.cr.usgs.gov/data/noga00/natl/text/core_report.pdf. 

Haavardsson, N.F., and Huseby, A.B., 2007, Multisegment production profile models—A tool for 

enhanced total value chain analysis: Journal of Petroleum Science and Engineering, v. 58, issues 1–2, 

p. 325–338. 

Schmoker, J.W., 1999, U.S. Geological Survey assessment model for continuous (unconventional) oil 

and gas accumulations—The “FORSPAN” model: U.S. Geological Survey Bulletin 2168, 9 p., 

accessed January 9, 2013, at http://pubs.usgs.gov/bul/b2168/b2168.pdf. 

Stephens, M.A., 1974, EDF statistics for goodness of fit and some comparisons: Journal of American 

Statistical Association, v. 69, p. 730–737.