U.S. Department of the Interior

U.S. Geological Survey

Open-File Report 2013–1055

National Assessment of Geologic Carbon Dioxide Storage 

Resources—Methodology Implementation

Maximum buoyant trapping pore volume

Minimum buoyant trapping pore volume

Residual trapping pore volume

Regional seal

Storage formation

EXPLANATION

Storage Assessment Unit, Cross Section

Land surface

Probable low 

total dissolved 

solids zone Thin regional 

seal zone

Fault

3,000 ft to 13,000 ft

3,000 ft to 13,000 ft
National Assessment of Geologic Carbon 

Dioxide Storage Resources—Methodology 

Implementation

By Madalyn S. Blondes, Sean T. Brennan, Matthew D. Merrill, Marc L. Buursink, 

Peter D. Warwick, Steven M. Cahan, Troy A. Cook, Margo D. Corum, 

William H. Craddock, Christina A. DeVera, Ronald M. Drake II, 

Lawrence J. Drew, Philip A. Freeman, Celeste D. Lohr, Ricardo A. Olea, 

Tina L. Roberts-Ashby, Ernie R. Slucher, and Brian A. Varela

Open-File Report 2013–1055

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:

Blondes, M.S., Brennan, S.T., Merrill, M.D., Buursink, M.L., Warwick, P.D., Cahan, S.M., Cook, T.A., Corum, M.D., 

Craddock, W.H., DeVera, C.A, Drake, R.M., II, Drew, L.J., Freeman, P.A., Lohr, C.D., Olea, R.A., Roberts-Ashby, T.L., 

Slucher, E.R., and Varela, B.A., 2013, National assessment of geologic carbon dioxide storage resources—

Methodology implementation: U.S. Geological Survey Open-File Report 2013–1055, 26 p., http://pubs.usgs.gov/

of/2013/1055/.
iii

Contents

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

1. Criteria for Choosing and Classifying Storage Assessment Units.....................................................2

2. Water Quality..............................................................................................................................................4

3. Distributions................................................................................................................................................5

4. Injectivity Classes......................................................................................................................................6

5. Basin-Scale Geologic Parameters .........................................................................................................6

5.2. Density.............................................................................................................................................6

5.3. Storage Efficiencies ....................................................................................................................10

5.3.1. Residual Trapping Storage Efficiencies .......................................................................10

5.3.2. Buoyant Trapping Storage Efficiencies........................................................................12

6. Parameters Related to Hydrocarbon Production...............................................................................13

6.1. Buoyant Trapping Pore Volume.................................................................................................13

6.1.1. Minimum............................................................................................................................14

6.1.2. Most Likely........................................................................................................................14

6.1.3. Maximum...........................................................................................................................14

6.2. Known Recovery Replacement Storage Resource................................................................15

7. Monte Carlo Simulation ..........................................................................................................................15

8. Aggregation ..............................................................................................................................................20

9. Summary....................................................................................................................................................20

Acknowledgments.......................................................................................................................................20

References Cited..........................................................................................................................................20

Appendix 1. Reservoir Growth Functions ................................................................................................23

A1.1. Data .............................................................................................................................................23

A1.2. Calibration of cumulative growth functions .........................................................................23

Acknowledgments..............................................................................................................................26

References Cited.................................................................................................................................26
iv

Figures

1. U.S. Geological Survey carbon dioxide (CO2) sequestration assessment input data

form.................................................................................................................................................3

2. Schematic cross section through a storage assessment unit (SAU) illustrating the 

relation between buoyant and residual trapping styles in the storage formation.............4

3. Residual trapping injectivity class fractions ............................................................................7

4. Formation volume factors versus depth for the Uinta and Piceance Basins .....................8

5. Carbon dioxide (CO2) density versus depth for the Uinta and Piceance Basins................9

6. Carbon dioxide (CO2) density versus depth for the Appalachian Basin ............................11

7. Residual trapping storage efficiency (class 1 and class 2) versus depth for the 

Uinta and Piceance Basins.......................................................................................................13

8. Example buoyant trapping storage probability density plots used to estimate 

minimum (MIN) and most likely (M. LIKELY) buoyant trapping storage volume

inputs ............................................................................................................................................15

9. Monte Carlo model calculations ..............................................................................................16

10. Flow diagram of the key steps for calculating known recovery replacement 

storage resources (KRRSR), buoyant trapping storage resources (BSR), residual 

trapping storage resources (R1SR, R2SR, R3SR), and technically accessible storage 

resources (TASR)..........................................................................................................................19
v

Conversion Factors

Multiply By To obtain

Length

foot (ft) 0.3048 meter (m)

kilometer (km) 0.6214 mile (mi)

Area

square inch (in2

) 6.452 square centimeter (cm2)

square foot (ft2

) 0.09290 square meter (m2)

acre 43560 square foot (ft2

)

Volume

barrel (bbl) petroleum 42 gallon (gal)

barrel (bbl) petroleum 0.1590 cubic meter (m3

) 

million barrels petroleum (MMbbl) 1000000 barrel (bbl) petroleum

cubic foot (ft3

) 0.02832 cubic meter (m3) 

liter (L) 0.2642 gallon (gal)

cubic meter (m3

) 6.290 barrel (bbl) petroleum

Mass

pound, avoirdupois (lb) 0.4536 kilogram (kg) 

ton, short (2,000 lb) 0.9072 megagram (Mg) 

ton, long (2,240 lb) 1.016 megagram (Mg) 

ton, metric (2,204.62 lb) 1.000 megagram (Mg)

milligram (mg) 0.00003527 ounce, avoirdupois (oz)

kilogram (kg) 2.205 pound, avoirdupois (lb)

megagram (Mg) = 1 metric ton (t) (1,000 kg) 1.102 ton, short (2,000 lb)

megagram (Mg) 0.9842 ton, long (2,240 lb)

million metric tons 1.102 million short tons

Pressure

pound-force per square inch (lbf/in2

 or psi) 6.895 kilopascal (kPa)

Pressure gradient

pound-force per square inch per foot (lbf/in2

/

ft or psi/ft)

22.62 kilopascal per meter (kPa/m)

Density

pound per cubic foot (lb/ft3

) 16.02 kilogram per cubic meter (kg/m3)

pound per cubic foot (lb/ft3

) 0.01602 gram per cubic centimeter (g/cm3)

kilogram per cubic meter (kg/m3

) 0.06242 pound per cubic foot (lb/ft3)
vi

Abbreviations, Acronyms, and Symbols

AU assessment unit, part of the USGS National Oil and Gas Assessment

ASF area of storage formation

Beta-PERT special case of the beta distribution, Program Evaluation and Review Technique

BPV buoyant trapping pore volume

BSE buoyant trapping storage efficiency

BSR buoyant trapping storage resource 

BSV buoyant trapping storage volume

bbl petroleum barrel or barrels

CO2 carbon dioxide 

D darcy

EISA Energy Independence and Security Act 

erfc complementary error function

EPA U.S. Environmental Protection Agency 

FVF formation volume factor 

FVFGAS formation volume factor for gas 

FVFNGL formation volume factor for natural gas liquids

FVFOIL formation volume factor for oil

GOR gas:oil ratio

i index: residual trapping storage injectivity classes

k permeability

krg relative permeability of CO2

KRRES known recovery production volumes converted to reservoir conditions 

KRRSR known recovery replacement storage resource

M mobility factor

MAX maximum estimate for input parameter

mD millidarcy 

mean mean of lognormal distribution transformed to linear space

mg/L milligrams per liter 

MIN minimum estimate for input parameter 

M.LIKELY most likely estimate for input parameter

MMbbl million barrels 

Mt megaton = million metric tons 

NGL natural gas liquids or condensates

NETL National Energy Technology Laboratory, U.S. Department of Energy

Nehring Oil and gas database with production, reservoir, and field characteristics (Nehring 

Associates, Inc., 2010)

NOGA USGS National Oil and Gas Assessment
vii

P5 probability percentile—5-percent probability that the true value is less than the 

given value

P50 probability percentile—50-percent probability that the true value is less than the 

given value; P50 is the median of the probability distribution.

P95 probability percentile—95-percent probability that the true value is less than the 

given value

Pk cumulative probability for permeability distribution

RGV residual trapping gross pore volume

RPV residual trapping pore volume

Ri residual trapping injectivity class fractions

RiSE residual trapping storage efficiency for injectivity class i

RiSR residual trapping storage resource for injectivity class i

RiSV residual trapping storage volume for injectivity class i

RW area fraction of the SAU available for storage after consideration of U.S. 

Environmental Protection Agency (EPA) water-quality guidelines or highly 

fractured seals

SAU storage assessment unit used in this assessment

s.d. standard deviation of lognormal distribution transformed to linear space

SF storage formation

SFPV storage formation pore volume

Sgr residual gas saturation

Swc connate water saturation

TPI thickness of the porous interval

TASR technically accessible storage resource

TASV technically accessible storage volume

TDS total dissolved solids

USDW underground source of drinking water

USGS U.S. Geological Survey 

Z critical value: standard deviations from the mean for a given probability assumption

Γ capillary trapping number

εS storage efficiency

μ mean of continuous distribution

μg viscosity of gas or supercritical fluid (CO2)

μw viscosity of water

ρco2 density of carbon dioxide

σ standard deviation of continuous distribution

φ porosity

φPI porosity of the porous interval
Introduction

In response to the Energy Independence and Security 

Act (Public Law 110-40, 2007), the U.S. Geological Survey 

(USGS) conducted a national assessment of potential geologic storage resources for carbon dioxide (CO2

). Storage of 

CO2 in subsurface saline formations is one important method 

to reduce greenhouse gas emissions and curb global climate 

change (Benson and Cook, 2005). The assessment methodology (Brennan and others, 2010; Burruss and others, 2009) 

describes the probabilistic model developed to calculate 

potential storage resources in subsurface saline formations. 

This report documents both the methodology updates and 

the details of methodology implementation and is meant to 

supplement the Brennan and others (2010) methodology and 

the national assessment final reports. The final reports will 

include (1) an assessment results report with all output results, 

a description of the assessment, and analysis (U.S. Geological 

Survey Geologic Carbon Dioxide Storage Resources Assessment Team, in press, a); (2) an assessment summary report 

(U.S. Geological Survey Geologic Carbon Dioxide Storage 

Resources Assessment Team, in press, b); and (3) an assessment data report, which will include data inputs and outputs, 

assessment forms (fig. 1), resource allocations, and figures.

The assessment has six output categories for each storage assessment unit (SAU). The first is the known recovery 

replacement storage resource (KRRSR), which is the storage 

resource calculated from known production volumes. The second is the buoyant trapping storage resource (BSR), where CO2

may be trapped buoyantly beneath stratigraphic or structural 

geologic traps. Residual trapping storage resources comprise 

the next three categories (R1SR, R2SR, and R3SR) and are in reservoirs where CO2

 is trapped in pore spaces by capillary forces 

after plume migration. The residual trapping reservoirs are 

apportioned into three injectivity classes by rock permeability 

characteristics, each with an associated residual trapping storage efficiency. The final category is the technically accessible 

storage resource (TASR), which is the sum of the buoyant and 

residual trapping storage resources. Over the course of the 

two-year assessment phase of the project, implementation 

adjustments to the methodology were necessary to generate 

the most accurate storage resource estimates. 

All of the outputs, excluding the KRRSR, can be summarized from the Brennan and others (2010) methodology with 

equation 1 

TA B B

A T B R Ri Ri

SR CO PV SE

i

CO SF PI PI PV W SE

= +

 ( ) −  

 =

∑

ρ

ρ φ

2

2

1

3

. (1)

The buoyant trapping storage resource, BSR, is equivalent 

to the first term on the right-hand side of the equation 

(BSR = ρCO2BPV BSE). Each of the three terms in the summation is 

a residual trapping storage-resource output, R1SR, R2SR, or R3SR. 

• ρCO2

 is the density of CO2 and is determined from 

subsurface geothermal and pressure gradient data for 

each basin, by using analog basins, or from published 

gradients (see Section 6 of this report). 

• BPV is the geologically determined pore volume that can 

store CO2 by buoyant trapping. It is estimated based on 

hydrocarbon production, undiscovered resources, and 

volume calculations of geologic traps (see Section 5). 

• BSE and RiSE are the buoyant and residual trapping storage efficiencies, respectively, defined as the fraction 

of accessible pore volume that will be occupied by 

injected CO2. These are determined from estimates of 

subsurface geothermal and pressure gradients, multiphase flow parameters, and fluid chemistry and have 

values between 0 and 1 (see Section 4). 

• ASF is the area of the SAU and is constrained using 

structure maps or data at the relevant depth ranges for 

the storage formation (SF). Methods used to estimate 

area are thoroughly described in Brennan and others 

(2010) and are not further addressed here. 

National Assessment of Geologic Carbon Dioxide Storage 

Resources—Methodology Implementation

By Madalyn S. Blondes, Sean T. Brennan, Matthew D. Merrill, Marc L. Buursink, Peter D. Warwick, 

Steven M. Cahan, Troy A. Cook, Margo D. Corum, William H. Craddock, Christina A. DeVera, 

Ronald M. Drake II, Lawrence J. Drew, Philip A. Freeman, Celeste D. Lohr, Ricardo A. Olea,

Tina L. Roberts-Ashby, Ernie R. Slucher, and Brian A. Varela
2 National Assessment of Geologic Carbon Dioxide Storage Resources—Methodology Implementation

• TPI is the thickness of the net porous interval and is 

generally calculated using net-to-gross thickness 

assumptions applied to the total SAU thickness. 

Methods used to estimate thickness are thoroughly 

described in Brennan and others (2010) and are not 

further addressed here. 

• φPI is the porosity of the net porous interval, which is 

obtained from available or analog rock porosity data. 

Methods used to estimate porosity are thoroughly 

described in Brennan and others (2010) and are not 

further addressed here. 

• RW is the area fraction of the SAU available for storage 

after consideration of U.S. Environmental Protection 

Agency (EPA) water-quality guidelines or highly 

fractured seals and has a value between 0 and 1. This is 

the only new term in the storage resource equation (see 

Section 2) that is not described in Brennan and others 

(2010).

• i = 1, 2, or 3 and are the names of the residual trapping 

injectivity classes. 

• Ri are injectivity class fractions determined from a 

probabilistic distribution of rock-permeability data. All 

three Ri must sum to one (see Section 4).

The sixth category, KRRSR, is calculated separately using 

known recovery production volumes, buoyant trapping storage 

efficiency factors, and ρCO2. To help define the input parameters for TASR and KRRSR, additional parameters were estimated 

by the assessment geologist or the assessment team. Formation volume factors (FVF) for oil, gas, and natural gas liquids 

are used to convert surface production volumes to equivalent 

volumes at depth. These were calculated from basin subsurface geothermal gradients and reservoir characteristics (see 

Section 5). The depth range was determined for each SAU and 

was important for density, storage efficiency, and formation 

volume factor calculations (see Section 5).

The Monte Carlo simulation method is a technique to 

propagate uncertainty from each input parameter through 

to the calculations of storage resources (see Section 7). The 

assessment geologists specify a minimum, most likely, and 

maximum estimate for the mean of each of the input parameters that are then used to define a continuous distribution 

(see Section 3). The one exception is the injectivity class 

fractions, Ri, which are deterministic values in the Monte 

Carlo simulation, yet are themselves determined from a 

probabilistic distribution of rock permeability data (see 

Section 4).

This report addresses details changed from, or not 

covered in, the original methodology of Brennan and others 

(2010), including the following:

1. criteria for choosing and classifying SAUs; 

2. a description of the new multiplicative factor (RW) that 

conforms the assessment to EPA underground sources of 

drinking water (USDW) water-quality restrictions (U.S. 

Environmental Protection Agency, 2009, 2010); 

3. the statistical distributions chosen for all assessment 

inputs in the Monte Carlo simulation; 

4. a new method to determine the injectivity class fractions 

(Ri) for residual trapping storage resources using rock 

permeability estimates;

5. the estimation of basin-scale geologic parameters including formation volume factors (FVF), density (ρCO2

), and 

storage efficiencies (BSE and RiSE); 

6. calculation of input parameters related to hydrocarbon 

production including buoyant trapping pore volume (BPV) 

and known recovery production volumes converted to 

volumes at reservoir conditions (KRRES);

7. a description of the Monte Carlo procedures; and 

8. a description of the probabilistic aggregation procedures.

1. Criteria for Choosing and Classifying 

Storage Assessment Units

In the Brennan and others (2010, p. 26) methodology, a 

SAU is a “mappable volume of rock that includes the storage formation, a reservoir flow unit for CO2

 storage, and a 

regional seal formation.” The methodology, following EPA 

regulations, precludes storage in formations with fresh water, 

defined as having a total dissolved solids (TDS) concentration 

less than 10,000 mg/L (milligrams per liter). Water-quality 

restrictions are addressed twice during the assessment: in the 

criteria for choosing and classifying SAUs (this section) and 

in the residual trapping storage resource calculations (see 

Section 2). 

The EPA has an application process to obtain waivers for storage in existing oil and gas reservoirs containing 

“fresh” water, based on the TDS criterion. Because buoyant trapping storage reservoirs may receive such a waiver, 

water-quality criteria are only applied to residual trapping 

storage resources. This means that even if all known formation water is fresh, a formation may still be assessed if it has 

known or undiscovered (as defined in USGS national oil and 

gas assessments (NOGA)) oil and gas reservoirs. However, 

formations are excluded from assessment if all known formation water is fresh and there are no known or undiscovered 

hydrocarbon reservoirs. This includes regions with nonhydrocarbon-producing structural or stratigraphic traps. If the 

formation meets these initial criteria for high-salinity water 

in residual traps, it may be assessed as a SAU if it meets the 

remaining criteria described in the following paragraph. Section 2 describes how water-quality factors into the residual 

trapping storage resource calculations.
1. Criteria for Choosing and Classifying Storage Assessment Units 3

Assessment geologist: Date:

Assessment region:

Province: Number:

Basin: Number:

Storage Assessment Unit (SAU): Number:

SAU relationship to NOGA AU:

Notes from assessor: 

Lines 1-9 concern data for the SAU at depths of (check one): 3,000-13,000 ft

> 13,000 ft

(1) SAU depth from surface (ft): minimum: most likely:

(2) Area of the SAU (acres): most likely: maximum:

maximum:

(3) Mean total SAU thickness (ft): most likely: maximum:

(4) SAU water quality (check one):

Most of the water in the SAU is saline (greater than 10,000 mg/L TDS).

Water in this SAU is both saline and fresh.

Most of the water in the SAU is fresh (less than 10,000 mg/L TDS).

(5) Area fraction available for storage (generally, the area where SAU pore water has more than 10,000 mg/L TDS):

minimum: most likely: maximum:

(6) Mean thickness net porous interval (ft):

(7) Mean porosity net porous interval (fraction):

(8) Buoyant trapping pore volume (MMbbl):

(9) Permeability of the net porous interval (mD):

STORAGE ASSESSMENT UNIT INPUT DATA FORM

Identification Information

minimum:

minimum:

minimum: most likely: maximum:

minimum: most likely: maximum:

minimum: most likely: maximum:

minimum: most likely: maximum:

Characteristics of the Storage Assessment Unit

Buoyant Trapping Probabilistic Calculation Inputs

Residual Trapping Probabilistic Calculation Inputs

Figure 1. U.S. Geological Survey carbon dioxide sequestration assessment input data form for each storage assessment unit. These 

(SAU) data inputs are used in the calculations described throughout the text and shown in figure 9. Some of the data inputs are solely 

descriptive and are not used in the calculations (for example lines 1, 3, and 4), although they were helpful in determining other data 

input parameters. See Abbreviations, Acronyms, and Symbols table for abbreviation descriptions.
4 National Assessment of Geologic Carbon Dioxide Storage Resources—Methodology Implementation

During the assessment, geologists discussed the merits of 

potential storage formation and regional seal pairs within all 

major sedimentary basins of the United States and designated 

them either as (1) assessed SAUs, (2) nonquantitative SAUs, 

or (3) nonassessed formations. A permanent panel of experienced assessment geologists presided over all assessment 

meetings and worked with the assessment geologist to arrive 

at a consensus for the values entered on the assessment forms. 

Assessed SAUs are those deemed by the assessment panel to 

have good potential storage, a regional seal, and some saline 

formation waters. Assessed SAUs are assigned a SAU number, 

scheduled for inclusion in the geologic framework basin report 

series (Warwick and Corum, 2012), and the SAU number is 

included in the final data tables in both the assessment results 

and assessment data reports. Some formations may have a 

good potential reservoir, a regional seal, and saline formation 

water in residual traps, yet there is a lack of data to build a 

geologic model (fig. 2) that will estimate the storage resource 

accurately. These are classified as nonquantitative SAUs, and 

though each has a SAU number and a full geologic evaluation in the geologic framework basin-report series, no results 

are presented in the assessment results report. Non-assessed 

formations are those that may not have good reservoir quality, 

are lacking a good regional seal, or contain solely fresh formation waters outside of buoyant traps. Some nonassessed formations are described in the geologic framework basin-report 

series, but these are not assigned assessment numbers, and no 

results are presented in the assessment results report.

2. Water Quality

The U.S. Environmental Protection Agency regulations from the Underground Injection Control Program (UIC) 

for Class VI wells prohibits CO2 injection into underground 

sources of drinking water (USDW), defined as groundwater 

with a TDS concentration less than 10,000 mg/L (U.S. Environmental Protection Agency, 2010). In Brennan and others 

(2010), the SAU boundary was limited in extent, regardless of 

depth, by the presence of waters with TDS concentrations less 

than 10,000 mg/L. In practice, defining the specific extent of 

fresh water for excision from the SAU is complicated. At the 

basin scale, available water-quality data (for example, Breit, 

Maximum buoyant trapping pore volume

Minimum buoyant trapping pore volume

Residual trapping pore volume

Regional seal

Storage formation

EXPLANATION

Storage Assessment Unit, Cross Section

Land surface

Probable low 

total dissolved 

solids zone Thin regional 

seal zone

Fault

3,000 ft to 13,000 ft

3,000 ft to 13,000 ft

Figure 2. Schematic cross section through a storage assessment unit (SAU) illustrating the relation between buoyant and residual 

trapping styles in the storage formation. The SAU minimum depth limit criteria of 3,000 ft ensures that carbon dioxide is in a supercritical 

state to minimize the storage volume, and 13,000 ft is the lower limit accessible with average injection pressures. A deep SAU can be 

defined for depths greater than 13,000 ft if favorable reservoir conditions exist. The lateral limit of the SAU is defined by the location 

where the top of the storage formation reaches the defined depth limit. Also shown are zones of probable low total dissolved solids and 

thin regional seal zones, which may be excluded from a SAU. 
3. Distributions 5

2002; U.S. Department of Energy National Energy Technology 

Laboratory, 2010) indicate that some formations contain a mix 

of saline- and fresh-water data. Further, the data are of variable and sometimes unknown quality and do not always exist 

throughout all SAUs. In the Rocky Mountain region basins, 

for example, all potential SAUs have at least some fresh-water 

data among the saline-water data. Under the methodology 

of Brennan and others (2010), all formations, and therefore 

this entire region, would be excluded from assessment. To 

address this problem, a modified concept of SAU creation was 

employed so that the salinity of the formation waters is no 

longer factored into delineating the SAU boundary. Instead, 

the USGS now uses a factor range (0–1) to account for the 

fresh-water fraction and accordingly reduce the total amount of 

the residual trapping storage resource. Note that the following 

procedure is only used if the formation was not excluded from 

assessment for having solely fresh water in residual trapping 

regions (see Section 1). 

To capture water quality and related restrictions, two 

lines were added to the Brennan and others (2010) assessment input form (fig. 1); line 4 is a classification or qualitative 

description of the average water quality in the SAU, and line 5 

is the input for a minimum, most likely, and maximum fraction 

of the SAU that is available for storage. The possible distributions assigned to this input range are described in Section 

3. Generally, the minimum fraction is the area immediately 

surrounding the SAU including known saline data points. 

The maximum fraction is the area remaining after excluding 

regions with fresh-water data points but including regions of 

no data. The most likely value is the assessment geologist’s 

best estimate given the water-quality data, basin structure, and 

groundwater maps. For example, consider a SAU that contains 

a clearly saline-water interval that accounts for 50 percent of 

its volume, a fresh-water interval that accounts for 30 percent 

of its volume, and has poor data availability in 20 percent of 

the volume. The assessment geologist may conclude that the 

inputs for line 5 on the assessment form may be a minimum 

fraction of 0.50, a most likely of 0.60, and a maximum of 0.70 

(fig. 1). Figure 2 shows a schematic cross section through a 

SAU from the methodology of Brennan and others (2010) 

updated to account for this new area fraction.

3. Distributions

In the initial methodology by Brennan and others (2010), 

a lognormal distribution is suggested for the buoyant trapping 

pore volume and triangular distributions are suggested for all 

other parameters. The assessment input form also specified the 

measure of central tendency for each distribution, such as the 

median or the mode. During the course of the USGS assessment, these options were found to be too restrictive, overestimated the high estimates (for the triangular distributions), and 

did not accurately represent geological phenomena. In order 

to facilitate more adaptive interpretation where few data are 

available or where analogs are implemented, and to allow for 

more geologically realistic distributions, the choice of distribution is now flexible. The terms mode and median were 

removed from the form (fig. 1) and replaced with the more 

general “most likely” term, which becomes the appropriate 

measure of central tendency for the chosen distribution. 

The assessment geologist is free to assign the most 

applicable distribution shape to the input parameters, though 

changes from the following suggestions are uncommon. The 

default distribution for inputs other than the buoyant trapping pore volume and permeability, such as area, porosity, 

and thickness, is now a Beta-PERT distribution. Beta-PERT 

distributions are a three-parameter special case of the fourparameter Beta distribution (for example Vose, 1996). Olea 

(2011) showed that the Beta distribution, with finite minima 

and maxima like the triangular distribution, can better represent the shape of distributions found in nature such as the normal or the lognormal. The Beta-PERT distribution was found 

to be a good compromise between the triangular and the Beta 

distributions because, like the triangular distribution, only 

three parameters (minimum, MIN; most likely, M.LIKELY; 

and maximum, MAX) must be specified, but it can still mimic 

distributions typical for geologic data like the Beta, normal, 

and lognormal distributions. The two shape parameters, α1

 and 

α2 for the Beta-PERT distribution used in the @Risk software 

(Palisade Corporation, 2010), are defined as

α μ

1 = 6 −

−





 



 Beta−PERT MIN

MAX MIN (2)

α μ

2 = 6 −

−





 





MAX −

MAX MIN

Beta PERT

(3)

where the mean is

μ Beta PERT

MIN M LIKELY MAX − = + + 4

6

.

. (4)

The updated methodology continues to use a defaulttruncated lognormal distribution for buoyant pore volume 

(BPV) and for permeability in the injectivity class (Ri) calculation (see Section 4). The minimum, most likely, and maximum 

estimates are converted to a truncated lognormal distribution 

for BPV and Ri by the following procedure. The mean, μ, and 

standard deviation, σ, of a normal distribution in log space are 

μ = − ln ( ) M L. IKELY MIN (5)

σ

μ = ln ( ) MAX MIN − −

Z (6)

where MIN, M.LIKELY, and MAX are the input parameters 

defined by the assessment geologist and Z is the critical 

value, or inverse normal probability function, for a particular 
6 National Assessment of Geologic Carbon Dioxide Storage Resources—Methodology Implementation

confidence interval (Attanasi and Charpentier, 2007). For 

example, if the assessment geologist claims that there is 

only a 1/1,000 chance that the maximum estimate may be 

exceeded, then one half of the distribution (the full range, 

ln(MAX – MIN), minus the mean, μ) must fall within Z = 3.09 

standard deviations, σ, from the mean. For less sure 1/100 and 

1/10 chances, Z = 2.33 and 1.28, respectively.

The transformation to a truncated lognormal distribution 

in linear space that conforms to the assessment geologist’s 

minimum, most likely, and maximum inputs (Aitchison, 

1986) is

mean =e

μ σ +1

2

2

(7)

s d. . = − e e ( ) e

2 2 2

1 μ σ σ

. (8) 

These two parameters from equations 7 and 8 are then 

used to generate a truncated lognormal distribution that represents the buoyant trapping pore volume or permeability.

4. Injectivity Classes

In Brennan and others (2010), total residual CO2 storage 

is divided into three injectivity classes based on intrinsic rock 

permeabilities, k, where

class 1: k >1 D (darcy)

class 2: 1 mD (millidarcy) < k <1 D

class 3: k <1 mD

These injectivity classes, which commonly were applied 

inconsistently among the assessment geologists, were the only 

deterministic inputs in a probabilistic assessment and did not 

reflect the reservoir permeability distribution as indicated by 

available data and analogs. Instead of using these deterministic 

percentage inputs, the assessment geologist now specifies a 

minimum, most likely, and maximum estimate of permeability, just as is done for all other parameters (for example area, 

porosity, and thickness). These estimates are used to define a 

truncated lognormal distribution (equations 5 through 8) that 

represents permeability. The percentage of the permeability distribution that falls into each of the three permeability 

classes is calculated from the cumulative probability of the 

distribution, truncated at the minimum and maximum values. 

Figure 3 shows an example in which the minimum permeability estimate is 0.1 mD, the most likely estimate is 100 

mD, and the maximum estimate is 4,000 mD. The cumulative 

probability of the lognormal distribution created following 

equations 5 through 8 and truncated by the minimum and 

maximum estimates is shown as the black curve. Thus the 

cumulative probability (Pk

) at 1mD, Pk (1mD), is equal to the 

percentage of class 1 rocks (equation 9). The remaining equations to determine cumulative probability and injectivity class 

are shown in equation 9.

class 1 1 = −1 Pk ( ) D

class 2 1 = P P k k ( ) D 1 − ( ) mD (9)

class 3 1 = Pk ( ) mD

In the figure 3 example, five percent of the permeability 

distribution is less than 1 mD, the class 3 fraction. Eightytwo percent of the permeability distribution falls between 1 

mD and 1 Darcy, the class 2 fraction. Thirteen percent of the 

permeability distribution lies above 1 Darcy, the class 1 fraction. These fractions are then used as the deterministic inputs 

described in Brennan and others (2010). For each Monte Carlo 

iteration, the total residual area is split into the three classes 

specified by equation 9 (see Section 7).

5. Basin-Scale Geologic Parameters

 Formation volume factors are unitless volume multipliers commonly used in the oil and gas industry to convert 

the volume of produced hydrocarbons at the surface to the 

volume of those hydrocarbons at the depth from which 

they were produced. This parameter is necessary when 

estimating the potential CO2 storage volume of buoyant 

traps in the subsurface; the space available to store CO2

in a buoyant trap is generally at least as large as what has 

already been produced. FVFOIL, FVFGAS, and FVFNGL (natural gas liquids) are estimated from empirical equations that 

simplify a complex dependence on pressure, temperature, 

gas to oil ratio (GOR), and the densities of multiple phases 

(Verma, 2012; Jahediesfanjani, written commun., 2012). 

Using production data for individual basins (Nehring Associates, Inc., 2010), plots of FVFOIL, FVFGAS, and FVFNGL

versus depth were created for each basin where these data 

existed. An example for the Uinta and Piceance Basins 

is shown in figure 4. From each plot, the minimum, most 

likely, and maximum FVFs are estimated for a given basin 

for the depth range of each SAU and fit to a Beta-PERT 

distribution (see Section 3). Formation volume factors are 

applied in the calculations that help estimate the buoyant 

trapping pore volume inputs, BPV (see Section 6.1) and the 

known recovery-replacement storage resource, KRRSR (see 

Section 6.2).

5.2. Density

The USGS methodology requires that a “probabilistic distribution of the density of CO2

 is calculated by 

the assessment team based on the upper and lower depth 

boundaries of the SAU, temperature and pressure gradients 
5. Basin-Scale Geologic Parameters 7

appropriate for the area, and an equation of state for CO2” 

(Brennan and others, 2010, p. 11). The density distribution is needed to compute the known recovery production 

volumes converted to volumes at reservoir conditions 

(KRRES) and to convert all calculated storage volumes 

to mass of CO2 that can be stored within those volumes 

(storage resources). When converted to mass, the assessment results may be easily compared to other published 

estimates of CO2 storage in billion metric tons, such as the 

North American Carbon Sequestration Atlas (U.S. Department of Energy, National Energy Technology Laboratory, 

2012). This section describes the prediction of basin-scale 

density conditions that are appropriate for geologic CO2

sequestration.

In the USGS assessment, CO2 density values are computed from subsurface geothermal gradients. The geothermal gradient expresses the average subsurface temperature 

change, which typically increases in sedimentary basins 

by about 30 degrees Celsius per kilometer (°C/km) below 

the ground surface or sea bed (Holloway, 2001). However, 

there exist considerable variations in geothermal conditions 

both within basins and between basins. In the pore spaces of 

sedimentary rocks, the pressure commonly increases along 

the hydrostatic gradient, which is the pressure generated by a 

column of water of height equal to the depth of the SAU pore 

space. This relation holds because the pore space is mostly 

filled with water and may be connected along a complex path 

to the surface (Holloway, 2001). Nevertheless, when the pore 

space is disconnected, the pressure may be greater than the 

predicted hydrostatic gradient pressure and result in overpressure of the SAU. The opposite condition, underpressure, 

may also exist, either naturally or as a result of fluid withdrawals. However, the required large-scale resolution of the 

current assessment necessitates the determination of basinaveraged gradients that do not account for local variations in 

pressure from the mean trend. Therefore, for the purposes of 

basin-scale density estimates, overpressure and underpressure are ignored.

Cross plots of pressure and temperature data are generated for coincident depths and plotted against warm, critical, 

0.0 

0.2 

0.4 

0.6 

0.8 

1.0 

0.01 0.1 1 10 100 1,000 10,000 

Minimum: 0.1 mD

M. Likely: 100 mD

Maximum: 4000 mD

Permeability, k (millidarcy)

Cumulative Probability 

class 1 = 13%

class 2 = 82%

class 3 = 5%

Figure 3. Injectivity classes. The black curve is the cumulative probability for a truncated lognormal distribution with mean and 

standard deviation calculated from the inset minimum, most likely (M. Likely), and maximum permeabilities. The dotted lines represent 

the cumulative probabilities at 1 millidarcy and 1,000 millidarcy. Five percent of the data are less than 1 millidarcy, so 5 percent of the 

total residual trapping storage for this SAU is in class 3, 82 percent is in class 2, and 13 percent is in class 1.
Figure 4. Formation volume factors versus depth for the Uinta and Piceance Basins. The data represent formation volume factor calculations foBasins derived from Nehring Associates, Inc. (2010). The three panels show (A) Formation volume factor of oil, (B) Formation volume factor of gasfactor of natural gas liquids as a function of depth. The minimum, most likely, and maximum values for a given storage assessment unit (SAU) are values for the appropriate range of SAU depths.

0

2,000

4,000

6,000

8,000

10,000

12,000

14,000

16,000

18,000

Formation volume factor

for oil

0.0 1.0 2.0 3.0

Formation volume factor

for gas

0.000 0.010 0.020 0.030

Formation 

for natu

0 2 4 

Depth (feet)

A B C
Figure 5. Carbon dioxide (CO2) density versus depth for the Uinta and Piceance Basins. All plots use data from Nehring Associates, Inc. (2010). (A) P

The pressure and temperature limits (1,070 pounds per square inch (psi) and 88 °F (degrees Fahrenheit)) above which CO2 is super critical is also show

Geothermal gradients for warm (red), critical (green), and cool (blue) world basins (Bachu, 2003) are shown. (B) Temperature versus depth. A geothershown for a temperature gradient of 1 °F per 70 feet of depth and a surface temperature of 64 °F. (C) Pressure versus depth plot. A hydrostatic gradienpressure gradient of 0.433 psi/ft. (D) Density versus depth using pressure and temperature inputs from figures 5A and 5B. The black curve is a moving 

per cubic meter.

1,000 3,500 6,00

Pressure

(psi)

100 200 300

Temperature

(degrees Fahrenheit)

3,0005,0007,0009,000

11,00013,00015,000

Pressure (psi)

Depth (feet)

2,0004,0006,0008,000

10,000

0

0 100 200 300 400

Temperature 

(degrees Fahrenheit)

A B C 
10 National Assessment of Geologic Carbon Dioxide Storage Resources—Methodology Implementation

and cool trend lines for world basins (Bachu, 2003) (figs. 5A

and 6A). Where possible, reservoir average pressure and 

temperature values from the “Significant Oil and Gas Fields 

of the United States Database” (Nehring Associates, Inc., 

2010) are used as the inputs to the equation of state calculations. In basins lacking Nehring Associates, Inc. (2010) 

data, data from the proprietary IHS Energy Group (2010) 

database are used instead. The IHS dataset contains welltemperature data but lacks significant amounts of pressure 

data, so a standard hydrostatic gradient (0.433 pounds per 

square inch per foot (psi/ft)) is assumed where pressure data 

do not exist. The distribution of the points on the warm or 

cool basin side is checked against maps from the geothermal 

gradient of North America project (Blackwell and others, 

1991; Blackwell and Richards, 2004). The subsurface supercritical CO2

 density is then calculated using the CO2 equation of state (Span and Wagner, 1996; Lemmon and others, 

2010). The results include plots of supercritical CO2

 density 

with depth for the U.S. basins or larger regions investigated 

in our assessment (figs. 5 and 6). Before they are applied to 

the assessment results, the USGS-computed densities are 

compared to published trends of CO2

 density with depth 

(Ennis-King and Paterson, 2001; Bachu, 2003; May and 

others, 2009) and to CO2

 density maps, such as those for the 

Appalachian Basin Oriskany Formation (Dilmore and others, 2008). 

Probabilistic distributions of CO2

 density, with a minimum, most likely, and maximum value are chosen along the 

spread of data based on the minimum, most likely, and maximum depths determined by the assessment geologist for each 

SAU in a basin. Below are two examples of subsurface CO2

density prediction from the Uinta and Piceance Basins and 

the Appalachian Basin assessments. The Uinta and Piceance 

Basins are warm basin examples with Nehring pressure and 

temperature data, whereas the Appalachian is a cool basin 

example with IHS data only (figs 5A and 6A, respectively). 

Temperature versus depth plots are shown in figures 5B and 

6B. Pressure versus depth plots are shown in figures 5C

and 6C. The supercritical CO2

 density calculated for each 

temperature and pressure data pair using the CO2

 equation 

of state (Span and Wagner, 1996) is shown in figures 5D

and 6D. For the warm Uinta and Piceance Basins examples, 

consider a SAU with minimum, most likely, and maximum 

depths of 3,000 ft, 7,000 ft, and 13,000 ft, respectively. The 

corresponding minimum, most likely, and maximum CO2

density estimated from figure 5D would be approximately 

500 kilograms per cubic meter (kg/m3

), 600 kg/m3, and 700 

kg/m3

, respectively. For the cool Appalachian Basin example, 

consider a SAU with a minimum, most likely, and maximum 

depths of 3,000 ft, 7,000 ft, and 9,500 ft, respectively. The 

corresponding minimum, most likely, and maximum CO2

density estimated from figure 6D would be about 760 kg/m3

, 

770 kg/m3

, and 780 kg/m3, respectively. Similar plots are 

generated for each basin, and density inputs are chosen for 

each SAU. For basins where no data or gradients are published, the assessment geologist relies on analogs.

5.3. Storage Efficiencies

5.3.1. Residual Trapping Storage Efficiencies

A component necessary to estimate CO2 storage is typically referred to as storage efficiency, defined as the fraction 

of accessible pore volume that will be occupied by injected 

CO2

. Storage efficiency may be estimated in a number of ways 

but is a function of temperature; pressure; time; lithology and 

rock properties; multiphase flow parameters such as relative 

viscosities, densities, and permeabilities for CO2 and water; 

formation morphology; and assumptions of injection, plume 

migration, and trapping models. For this assessment, the 

USGS must determine the storage resource of the residual and 

buoyant traps separately because they have very different trapping models and thus storage efficiencies. Residual trapping 

storage efficiencies are determined separately for each of the 

injectivity classes (see Section 4).

Attempts to define and estimate the residual trapping 

storage efficiency began with the numerical models of van 

der Meer (1995). Gorecki and others (2009) and the International Energy Agency (IEA) Greenhouse Gas R&D Programme (2009) released a comprehensive report on storage 

efficiency as a function of lithology for the time at which 

CO2

 injection stopped but while the CO2 plume was still 

mobile. Szulczewski and others (2012) estimated efficiency 

numerically for both migration-limited and pressure-limited 

scenarios. Juanes and others (2010), MacMinn and others (2010), and Okwen and others (2010) developed postinjection, post-plume migration, and post-imbibition (when 

water re-enters the pore space after CO2

 plume migration) 

storage efficiency models for capillary trapping. For the 

national assessment, the USGS is evaluating the long-term, 

steady-state storage resource and, therefore, must determine 

appropriate post-migration and post-imbibition residual trapping storage efficiencies. It is also assumed that all injection 

projects will be engineered in such a way to optimize storage 

efficiency and CO2

 sweep efficiency (the percentage of the 

rock or pore space that the nonwetting phase passes through), 

while avoiding CO2

 leakage from the storage formation. 

Thus, the impact of plume and formation morphology can be 

neglected in the storage efficiency calculations, and postimbibition capillary trapping models best estimate residual 

trapping storage efficiencies relevant to the USGS CO2

sequestration assessment.

The MacMinn and others (2010) model can be used to 

estimate the residual trapping storage efficiency of a sloped 

reservoir where the interface between the storage formation and the sealing formation is not horizontal. Using the 

MacMinn and others (2010) model, the residual trapping 

storage efficiency due to capillary trapping of an entire SAU 

can be estimated given temperature and pressure gradients, 

depth ranges, and estimates of the irreducible water saturation at the leading edge of a mobile CO2

 plume, the residual 

gas saturation at the trailing edge of the plume, and the 

relative permeability between the CO2

 and the connate water. 
Figure 6. Carbon dioxide (CO2) density versus depth for the Appalachian Basin. All plots use IHS Energy Group (2010) data. (A) Pressure versus temp

and temperature limits (1,070 pounds per square inch (psi) and 88 °F (degrees Fahrenheit)) above which CO2 is super critical is also shown with dotted 

gradients for warm (red), critical (green), and cool (blue) world basins (Bachu, 2003) are shown. (B) Temperature versus depth. A geothermal gradient a temperature gradient of 1 °F per 70 feet of depth and a surface temperature of 64 °F. (C) Pressure versus depth plot. A hydrostatic gradient line is alsgradient of 0.433 psi/ft. (D) Density versus depth using pressure and temperature inputs from figures 6A and 6B. The black curve is a moving average. 

meter.

4,0006,0008,000

10,00012,000

Depth (feet)

100 200 300

Reservoir Temperature

(degrees Fahrenheit)

1,000 3,500 6,000

Reservoir Pressure

(psi)

A B C 

0

2,0004,0006,0008,000

Pressure (psi)

10,000

0 100 200 300 400

Temperature (degrees Fahrenheit)
12 National Assessment of Geologic Carbon Dioxide Storage Resources—Methodology Implementation

The storage efficiency equation of MacMinn and others 

(2010) also allows for the estimation of storage efficiency 

uncertainty, important for the probabilistic assessment, using 

ranges of input parameters and plotting the output values 

versus depth. The approximation equation of MacMinn and 

others (2010) for capillary trapping post-migration, postimbibition storage efficiency, εs, is

ε S = + Γ M 2 / [09 04 . . 9] (10) 

where Γ is the capillary trapping number and M is the mobility 

factor. The capillary trapping number is defined as

Γ = −

S

S

gr

wc 1

(11)

where Sgr is the residual gas saturation after imbibition and Swc

is the connate water saturation, or irreducible water saturation 

(MacMinn and others, 2010). The mobility factor, derived 

from MacMinn and others (2010) is

M k = rgμ μ w g / (12) 

where krg is the relative permeability of the mobile CO2 phase 

with a value between zero and one, μg is the viscosity of CO2, 

and μw is the viscosity of water. Equation 12 is valid under 

the assumption whereby the mobility in the reservoir region 

containing residually trapped CO2 is equal to the mobility 

in the reservoir region that contains the mobile CO2 plume. 

The mobility factor in the efficiency equation approximates 

fluid flow of a nonwetting fluid phase that is similar to the 

term “sweep efficiency” in enhanced oil recovery parlance. 

The sweep efficiency is an estimate of how much of a porous 

medium will be invaded by the nonwetting phase.

The values of krg, Sgr, and Swc are taken from experimental work (Bennion and Bachu, 2005, 2008; Burton and 

others, 2008; Okabe and Tsuchiya, 2008; Okabe and others, 2010) and modeling efforts (Kopp and others, 2009a,b; 

Juanes and others, 2010; Okwen and others, 2010; Szulczewski and others, 2012). This method is used to calculate 

residual trapping storage efficiencies for class 1 and class 2 

rocks. The procedure for class 3 rocks is described below. 

The values that are chosen for class 1 inputs are = 0.6, Sgr = 

0.25, and Swc = 0.4, and for class 2 inputs are = 0.6, Sgr = 0.3, 

and Swc = 0.4. The class 1 value for Sgr is slightly lower based 

on the assumption that less CO2 would be trapped during 

imbibition in high permeability rocks. Higher permeability 

rocks have fewer instances of “snap off,” where a portion of a nonwetting phase becomes disconnected from the 

mobile phase, typically along the trailing edge of a plume. 

The viscosities of CO2 and water were calculated from 

temperature and pressure data from petroleum reservoirs 

within the United States (Nehring Associates, Inc., 2010) 

using the equation of state by Span and Wagner (1996) for 

CO2

, Wagner and Pruss (2002) for pure water, and Mao and 

Duan (2008) for brines. The Mao and Duan (2008) model 

determines the viscosity of water with varying molalities of 

sodium chloride (NaCl), which is used as a proxy for the viscosity of more complex brines. Because salinity data for each 

petroleum field were not available, and an average salinity 

value was assumed for each basin and used for each storage efficiency calculation within that basin, average salinity 

values were estimated by the assessment geologist using 

available salinity data.

Residual trapping storage efficiencies (equation 10) for 

injectivity class 1 and 2 rocks are then calculated for the temperatures and pressures of each petroleum reservoir within 

each basin (Nehring Associates, Inc., 2010). These values 

are then plotted versus depth for each basin to estimate the 

range of potential storage efficiencies at different depth 

ranges (fig. 7). A sensitivity analysis showed that withinbasin storage efficiency factor variation is much greater than 

variation resulting from considering different lithologies or 

basin geotherms. Therefore, following a similar procedure 

to the formation volume factors and densities, the storage 

efficiency factors are determined from the basin efficiency 

factor versus depth plot for the specific depth ranges for each 

SAU. Separate efficiency factor versus depth profiles were 

created for injectivity class 1 and class 2 storage efficiencies, 

which have different assumptions of residual gas saturation, as described above (fig. 7). Minimum, most likely, and 

maximum estimates of the mean were subjectively chosen 

from these plots at the appropriate depths for the SAU. Class 

3 minimum and most likely storage efficiencies were both 

assumed to be zero, and the maximum was assigned to be the 

same as the class 2 most likely estimate. All storage efficiencies are modeled as Beta-PERT distributions unless otherwise specified.

5.3.2. Buoyant Trapping Storage Efficiencies

Buoyant trapping storage efficiency is controlled 

primarily by the mobility of the CO2, relative to the ambient fluids in the physical trap within the storage formation, 

and the irreducible water fraction (Swc). The residual gas 

value is not important, because the CO2 within the trap will 

be held in place by the high capillary entrance pressure of 

the sealing formation that encloses the trap. The Swc value 

for traps is no different than that of the rest of the storage 

formation and is typically 0.4 (Bennion and Bachu, 2008). 

This gives a high value for CO2 storage as 60 percent of 

the pore space (1 – Swc), but in certain dry natural gas 

fields the methane concentration is up to 80 percent of 

the pore space (Keelan and Pugh, 1975). Therefore the 

maximum amount of CO2 that could be held in a trap is 
6. Parameters Related to Hydrocarbon Production 13

between 60 and 80 percent of the pore space. However, 

as the sweep efficiency of the injected CO2 will not be 

100 percent of the pore space within the trap, the buoyant 

trapping storage efficiency will be less than 60 to 80 percent of the total pore space. To estimate the buoyant trapping storage efficiency, we have assumed that the mobility 

of the CO2 will reduce this 1 – Swc value to approximately 

20, 30, or 40 percent, which are the minimum, most likely, 

and maximum values that are applied to the buoyant pore 

space of each SAU. 

6. Parameters Related to Hydrocarbon 

Production

6.1. Buoyant Trapping Pore Volume

The buoyant trapping pore volume distribution defines 

the amount of CO2 that can be stored through buoyant trapping 

(Brennan and others, 2010). The assessment geologist may 

use any available data to determine the distribution, but the 

class 1

class 2

3,000

4,000

5,000

6,000

7,000

8,000

9,000

10,000

11,000

12,000

13,000

Depth (feet)

0 2 4 6 8 10 12

Storage Efficiency (percent)

Figure 7. Residual trapping storage efficiency (class 1 and class 2) versus depth for the Uinta and 

Piceance Basins. The data represent residual trapping storage efficiency calculations derived from 

Nehring Associates, Inc. (2010) reservoir data from the Uinta and Piceance Basins. Black circles are class 

1 storage efficiencies and gray circles are class 2 storage efficiencies. For class 1 rocks, a residual gas 

saturation of 0.25 was assumed, whereas for class 2 rocks, a residual gas saturation of 0.3 was assumed.
14 National Assessment of Geologic Carbon Dioxide Storage Resources—Methodology Implementation

methodology defines certain default calculations for the minimum and most likely inputs (Brennan and others, 2010). The 

following sections describe the details of these calculations.

6.1.1. Minimum

To determine the buoyant trapping pore volume minimum for a given SAU, one must know the subsurface volume 

necessary to include all oil, gas, and natural gas liquids that 

will be produced from existing conventional reservoirs in the 

formation. Using the national Nehring Associates, Inc. (2010) 

“Significant Oil and Gas Fields of the United States Database,” the known recovery volumes (cumulative production 

plus reserves) for conventional oil and gas reservoirs were 

projected (grown) to year 2050 (appendix 1). These grown 

reservoir volumes were clipped spatially to a given SAU and 

queried for the formation name. All oil, gas, and condensate 

volumes were summed independently. The estimated surface 

volumes were converted to subsurface volumes using formation volume factors (see Section 5.1). 

The USGS NOGA assessments (Klett and others, 2005) 

define oil reservoirs as those with GORs less than 20,000 

cubic feet per barrel (ft3/bbl). Gas reservoirs, conversely, have 

GORs greater than 20,000 ft3/bbl. One cannot simply multiply 

all gas from both the oil and gas reservoirs by the gas formation volume factor; some of that gas will compress greatly 

at depth, yet some will dissolve in the oil, increasing the oil 

volume. This complex behavior is what the formation volume 

factor simplification targets (Verma, 2012). For gas reservoirs, 

gas is multiplied by the FVFGAS, and natural gas liquids are 

multiplied by the FVFNGL. For oil reservoirs, only the oil is 

multiplied by the FVFOIL. Gas and condensates, though they 

are often present in oil reservoirs, are not included in the calculation; the volume increase resulting from the dissolution of 

gas is already covered by the >1 oil formation volume factor. 

The resulting subsurface volumes are converted to the same 

units (MMbbl) and combined to a single volume distribution 

for the SAU.

In Nehring Associates, Inc. (2010), some reservoirs have 

no known recovery data (production plus reserves) specific 

to producing formations and therefore cannot be included 

directly in the calculations. This is particularly a problem for 

certain States (for example Louisiana, Oklahoma, Kansas, 

and Indiana) where the cumulative production and reserves 

for a given field are not allocated to individual reservoirs. To 

resolve this problem to the extent possible, cumulative well 

production data from the IHS database are used (IHS Energy 

Group, 2010). Wells from specific fields in the IHS database 

can be linked to fields from Nehring Associates, Inc. (2010) 

and the associated list of significant producing reservoirs. 

Field-specific well production is summed from producing 

zones corresponding to the producing formations of reservoirs 

from matched fields in Nehring Associates, Inc. (2010). These 

field-level sums of cumulative well production by zones can 

generate ratios used to prorate the Nehring Associates, Inc. 

(2010) cumulative production values at the field level to the 

producing formations. The potential growth of these allocated 

volumes were then calculated for oil, gas, and condensates to 

the year 2050 (appendix 1) and added to the summed oil and 

gas production for each SAU.

6.1.2. Most Likely

The suggested most likely input for the buoyant trapping pore volume is the sum of the minimum estimate (known 

recovery at reservoir conditions grown to 2050) and the undiscovered resources estimated by the USGS NOGA assessments 

(Brennan and others, 2010). The NOGA assessments provide 

P5, P50, P95, and mean values for oil (MMbbl), gas (in billion 

cubic feet of gas (BCFG)), and natural gas liquids (MMbbl) 

for all assessment units (AU). Oil reservoirs include oil, gas, 

and natural gas liquid volumes, and gas reservoirs include gas 

and natural gas liquid volumes. 

A Beta-PERT distribution fit to the P5, P50, and P95 of 

the NOGA volumes was then multiplied by the appropriate 

formation volume factor distribution. Resulting oil, gas, and 

condensate volume distributions were converted to the same 

units (MMbbl) and combined to a single volume distribution 

for each AU. The CO2 assessment geologist then estimated the 

percentage of any NOGA AU production that was within the 

SAU. The volume distributions of all relevant AUs, modified by this percentage, were summed to create a final NOGA 

undiscovered volume distribution for the SAU. Figure 8 shows 

example distributions for the buoyant minimum and most 

likely data inputs. The data inputs for the assessment form 

(fig. 1) are generally the means of these two distributions, 

although the assessment geologist may choose different values 

if geologically appropriate.

6.1.3. Maximum

The maximum buoyant trapping input is essentially a volumetrically defined input that reflects the full extent of known 

and predicted buoyant traps in a SAU. General structural geology and the stratigraphic relations between various lithologies in the reservoir formation are the main determinants of 

the maximum amount of buoyant trapping volume available. 

Traps described in existing fields provide the most certain 

evidence for determining the extent of possible buoyant plume 

storage. These volumes can be derived from structural closure 

maps and thickness information available in the literature. 

In reservoirs where structural traps are not common or 

where structural data are not present, more predictive methods have been employed by the assessment geologists. The 

use of analog reservoirs, when properly selected, can provide 

structural trap sizes from a better known formation in the same 

basin, possibly one with greater exploration data, or from 

the same formation but in a similar basin. Using oil and gas 

field acreages is another method for determining the potential 

buoyant volume in a reservoir. Because oil and gas generation or charge may be limited within a basin, the geologist 

may need to project trap size and density outside of the known 
7. Monte Carlo Simulation 15

productive area in the target formation. Though this does add 

uncertainty to the determination of the input, it may still be 

the best available method for choosing the input. The goal of 

the maximum buoyant trapping input is to put a geologically 

based upper limit on the available volume for storing buoyant 

CO2

 in a SAU. The assessment geologist’s task is to determine 

this value using methods similar to those discussed above, or 

any other method that is geologically defensible and scientifically sound in the eyes of the assessment review panel. 

6.2. Known Recovery Replacement Storage 

Resource

The known recovery replacement storage resource 

KRRSR is one of the six output categories for the national 

assessment. As described in the original methodology 

(Brennan and others, 2010), the KRRSR consists of the 

known recovery production volumes converted to volumes 

at reservoir conditions (KRRES) multiplied by the buoyant 

trapping storage efficiency factor, BSE, and the CO2

 density, 

ρCO2

. KRRES is calculated similarly to the buoyant minimum. 

Whereas the buoyant minimum is a single value estimated 

from the distribution of grown known recovery volumes converted to reservoir conditions using formation volume factors, the KRRES is this entire distribution. This full distribution 

is recreated by assigning P0.1, P50, and P99.9 of the buoyant 

minimum (fig. 8) to the minimum, most likely, and maximum 

for the input form. KRRES is then multiplied by the associated 

CO2 density and BSE distributions to obtain the KRRSR output.

7. Monte Carlo Simulation

For each SAU, the assessment geologist specifies minimum, most likely, and maximum values for the mean of each 

input parameter over the entire SAU (fig. 1), which are used to 

define continuous distributions. The one exception is permeability, whose inputs represent a full distribution rather than a 

Figure 8. Example buoyant trapping storage probability density plots used to estimate minimum (MIN) and most likely (M. 

LIKELY) buoyant trapping storage volume inputs. The tall solid curve represents the volume of produced, grown, oil and gas from 

a given storage assessment unit (see Section 6.1.1). The mean of this distribution is generally the minimum input for the buoyant 

calculation (fig. 9A). The short dashed curve on the left is the volume of undiscovered oil and gas in a given SAU (see Section 

6.1.2). The sum of the produced and undiscovered curves is shown as the long dashed curve on the right of the figure. The mean 

of this distribution is generally the most likely input for the buoyant calculation (fig. 9A). The maximum input calculation does not 

use hydrocarbon volume data and is described in Section 6.1.3.

0.00 

0.04 

0.08 

0.12 

0.16 

0 10 20 30 40 50 60 

Produced + Undiscovered 

(Buoyant M.LIKELY) 

Undiscovered 

Produced 

(Buoyant MIN) 

Volume of hydrocarbons (million metric tons)

Probability density

mean = 16.6mean = 17.6mean = 34.2
16 National Assessment of Geologic Carbon Dioxide Storage Resources—Methodology Implementation

distribution of the mean. The permeability distribution is not 

directly used in the volumetric equation, but rather is used to 

determine injectivity classes (see Section 4), which are the only 

deterministic inputs in the Monte Carlo simulation. These are 

agreed upon or changed through consensus of the assessment 

team. Basin-scale parameters, such as density and storage efficiencies, are calculated separately using the methods described 

above and are presented as tables in the assessment data report. 

Any correlations between input parameters will affect the 

uncertainty of the final resource distributions. Five parameter 

pairs were determined to have positive correlations and were 

given values by expert elicitation (Meyer and Booker, 2001). 

Porosity (φPI) and permeability (used for the calculation of 

Ri) are given a correlation coefficient of 0.3 because the data 

are generally obtained from the same sources. The buoyant 

trapping pore volume (BPV) and area of the storage formation (ASF) are given a correlation coefficient of 0.5 because 

the larger the SAU area, the greater likelihood for structural 

and stratigraphic traps, and therefore, the greater probability of a given maximum buoyant trapping volume estimate. 

The thickness (TPI), porosity of the net porous interval (φPI), 

and known recovery production volumes (KRRES ) are given 

correlation coefficients of 0.7 with the buoyant trapping pore 

volume (BPV) because they are directly used in its calculation. 

The thicker and more porous a buoyant trap, the more potential exists for buoyant trapping storage volume. Though these 

values of 0.3, 0.5 and 0.7 were initially chosen as correlation 

coefficients, it was necessary to adjust these to 0.23, 0.38, and 

0.53, respectively, to create a true positive-definite correlation 

matrix that could be used in the Monte Carlo simulation. See 

Blondes and others (in press) for a more detailed discussion of 

correlation matrices related to the USGS assessment.

Calculation of the KRRSR, BSR, R1SR, R2SR, R3SR, and 

TASR values is performed using the Monte Carlo method with 

Palisade @Risk software (Palisade Corporation, 2010). A 

screen capture of the model spreadsheet is shown in figures 

9A and 9B. The updated methodology flow chart is shown 

in figure 10. Each simulation has 10,000 iterations such that 

each input distribution is sampled 10,000 times using Latin 

Hypercube sampling, without replacement. All intermediate 

calculations follow the methodology of Brennan and others 

(2010) with the exception of the new factor RW applied only to 

the residual volume (see Section 2).

The parameter symbols used throughout this report are 

in the far left hand column of figure 9A. The next columns to 

the right are the parameter name and the measurement units. 

The column labeled “Form” shows the number corresponding 

to the line on the assessment input form (fig. 1). The remaining input data without a Form number can be found in the 

assessment data report. For each input parameter, the geologists define minimum (MIN), most likely (M.LIKELY) and 

maximum (MAX) estimates. These are transformed into 

distributions (see Section 2) and listed under the column 

labeled “Dist Type.” The expected value of this distribution 

is found under the column labeled “Distribution.” For the 

lognormal (Lognorm) distributions, the parameters necessary 

to define the distribution (the mean and standard deviation) 

are calculated following the procedure outlined in Section 3. 

The Z factors, or critical values, necessary for the lognormal 

distributions are shown in figure 9B. To divide the residual 

trapping storage into three injectivity classes, a truncated 

distribution of permeabilities is used (see Section 4; fig. 3). 

The Pk (1mD) and Pk (1D) are calculated and used to determine the class 1, 2, and 3 fractions (see Section 4, fig. 3). The 

fig. 9A “Volume Calculations” section shows the intermediate calculations, all converted to cubic feet. The conversion 

factors, constants, and correlation matrix are found in figure 

9B. Finally, the “OUTPUT CATEGORY RESULTS” section 

(fig. 9A) shows the final calculations, converted to million 

metric tons CO2

. The values in green are the expected values 

of the output distribution. The 10,000 values that make up 

this distribution are used for the aggregation procedure (see 

Section 8). Summary statistics of these distributions, the P5, 

P50, P95, and mean, are also shown in green (fig. 9B) and will 

be presented in the assessment results report. (U.S. Geological Survey Geologic Carbon Dioxide Storage Resources 

Assessment Team, in press, a)

Figure 9 (following pages). Monte Carlo model calculations.

All inputs are shaded in light blue, constants used throughout 

the assessment in dark blue, intermediate calculations in gold, 

and output results in green. Calculation descriptions are in 

gold text. A detailed description of the model can be found 

in Section 7. (A) Calculations, including assessment inputs, 

injectivity class calculations, volume calculations, and output 

results. (B) Correlation matrix, constants, conversion factors, 

and results. Calcs, calculations; Corr, correlation matrix; Dist, 

distribution; Lognorm, lognormal; Z, critical value; lbs, pounds; 

kg/m3

, kilograms per cubic meter; megaton, million metric tons. 

All other abbreviations not defined in figure are in the front part

of the report.
USGS CO2 MONTE CARLO CALCULATIONS SAU Code 

Basin Name 

SAU Name

Inputs Units Form Min M.Likely Max 

ASF Area of Storage Formation Acres 2 2,735,000 3,039,000 3,343,000 

TPI Thickness of Net Porous Interval ft 6 30 5 0 

PI Porosity of Net Porous Interval Fraction 7 0.10 0.15 0.20 

RW Area fraction of SAU that is acceptable (e.g. WQ) Fraction 5 0.00 0.00 0.18 mean s.d. 

BPV Buoyant Trapping Pore Volume MMbbls 8 1,230 1,330 2,000 4.6 0.7 124 92 

KRRES Known Reserves MMbbls 912 1,226 1,623 

CO2 CO2 Density (kg/m3) kg/m3 610 690 790 

R1SE class I Residual Trapping Efficiency Fraction 0.020 0.041 0.052 

R2SE class II Residual Trapping Efficiency Fraction 0.027 0.054 0.075 R3SE class III Residual Trapping Efficiency Fraction 0.000 0.000 0.054 BSE Buoyant Storage Trapping Efficiency Fraction 0.20 0.30 0.40 mean s.d. 

Pk Permeability Distribution mD 9 0.1 60 1,000 4.1 2.2 670 7,462 

Injectivity Class Calculation Units Calculation 1 1000 Class 

Ri Residual Trapping Injectivity Class Fraction Fraction (See Section 4) 0.031 1.000 0.00 

Volume Calculations Units Calculation 

SFPV Storage Formation Pore Volume ft3 ASF * TPI * PI * ft2/acre 

BPV Buoyant Trapping Pore Volume ft3 BPV * Bbls/MMbbls * ft3/Bbls 

RGV Residual Trapping Gross Pore Volume ft3 SFPV - BPV 

BSV Buoyant Trapping Storage Volume ft3 BPV * BSE RPV Residual Trapping Pore Volume ft3 RGV * RW 

OUTPUT CATEGORY RESULTS Units Calculation 

KRRSR Known Recovery Replacement Storage Resource Mt KRRES * BSE * CO2 * bbl/MMbbl * ft3/bbls * (lbs/ft3)/(kg/m3) * tons/lbs * megatons/metric tons 

BSR Buoyant Trapping Storage Resource

Residual Trapping Class 1 Storage ResourceResidual Trapping Class 2 Storage ResourceResidual Trapping Class 3 Storage Resource

Mt BSV * CO2 * (lbs/ft3)/(kg/m3) * metric tons/lbs * megatons/metric tons 

R1SR Mt RPV * R1 * R1SE * CO2 * (lbs/ft3)/(kg/m3) * metric tons/lbs * megatons/metric tons 

R2SR Mt RPV * R2 * R2SE * CO2 * (lbs/ft3)/(kg/m3) * metric tons/lbs *megatons/metric tons 

R3SR Mt RPV * R3 * R3SE * CO2 * (lbs/ft3)/(kg/m3) * metric tons/lbs * megatons/metric tons 

TASR Technically Accessable Storage Resource Mt BSR + R1SR + R2SR + R3SR 

A
Corr Matrix ASF TPI RWQ BPV KRRES R1SE R2SE R3SE BSE Pk Constants & Conversion Fac

ASF 1 area 4356

TPI 0 1 volume 10000

PI 001 volume 5.61 

RW 0001 density 0.0623

BPV 0.38 0.53 0.53 0 1 mass 10000

KRRES 0 0 0 0 0.53 1 mass 2204.6

CO2 0000001 Z (1/10) 1.281 

R1SE 00000001 Z (1/15) 1.5 

R2SE 000000001 Z (1/100) 2.327 

R3SE 0000000001 Z (1/1000) 3.09 BSE 00000000001 Pk 0 0 0 0 (MT) P95 P50 P5 Mean KRRSR 30 40 53 41 BSR 34 44 56 45 R1SR 0.0 0.0 0.0 0.0 R2SR 2 23 91 32 R3SR < 0.1 0.1 0.7 0.2 TASR 43 68 140 77 B PI CO2 0000001 USGS CO2 MONTE CARLO CALCULATIONS SAU Code Basin Name SAU Name USGS CO2 MONTE CARLO RESULTS Basin Name SAU Name SAU Code 0.23
Figure 10. Flow diagram of the key steps for calculating known recovery replacement storage resources, buoyant trapping storage resources, residuastorage resources (R1SR, R2SR, R3SR), and technically accessible storage resources. Residual trapping injectivity categories are represented as class 1 (R

(R2), and class 3 (R3). Also included are steps for water quality, storage efficiency, and carbon dioxide density (ρco2 ) calculation. Abbreviations not defi

are defined in front part of report. 

Buoyant trapping 

resource calculation

Residual trapping 

resource calculation

Storage efficiency

Storage resource

Density (ρ)

Storage volume

Pore volume

Buoyant trapping

pore volume

(BPV)

Residual trapping

pore volume

(RPV)

Buoyant trapping

storage efficiency

(BSE)

Technically acce

storage volum

(TASV)

Buoyant trapping

storage volume

(BSV)

Storage formation 

pore volume 

(SFPV)

Injectivity classes

allotment

(R1, R2, R3)

R1PV R2PV R3PV

R1SE R2SE R3SE

R1SV R2SV R3SV

R1SR R2SR R3SR

Buoyant trapping

storage resource

(BSR)

(ρCO2 (ρ ) CO2)

Technically acce

storage resour

(TASR)

(ρCO2)

Water-quality factor (RW)

Known recovery

production volumes

(KRRES)

Known recovery replacement

storage resource

(KRRSR)

(ρCO2)

Buoyant trapping

storage efficiency

(BSE)

Area fraction

Known recovery replacement

resource calculation
20 National Assessment of Geologic Carbon Dioxide Storage Resources—Methodology Implementation

8. Aggregation

The calculated CO2 mass for each SAU is in the form 

of a probabilistic distribution, reported as the P5, P50, P95, and 

mean, and recorded as 10,000 individual storage resource 

estimates. The CO2 assessment must then combine the SAU 

results to basin, regional, and national scales. The mean values 

may simply be added together, but the same approach is not 

valid for different probability intervals (percentiles), because 

of the effect of input correlations on the shape of the aggregate 

distribution. The aggregation procedure allows calculation of 

new probability percentiles (for example P5 and P95) for the 

combined distributions by using estimated correlation coefficients between each pair of SAUs. This procedure is discussed 

in detail in the forthcoming report on probabilistic aggregation 

of CO2 SAUs (Blondes and others, in press).

9. Summary

In implementing the USGS national geologic carbon 

dioxide storage resources assessment, some minor changes 

to the methodology (Brennan and others, 2010) were deemed 

necessary. In order to allow replication of the output values, it 

is important to document all details of the USGS calculations. 

This report discusses the details of

1. input parameter estimation (density, storage efficiency, injectivity classes, and buoyant trapping 

pore volume),

2. a new input parameter that addresses EPA waterquality regulations,

3. parameter estimation (formation volume factors) that 

factor into the input parameters, and 

4. probabilistic model calculations (choice of distributions, Monte Carlo calculation methods, and 

aggregation methods).

The new water-quality factor and the distribution choices 

are the main changes from the Brennan and others (2010) 

methodology that have the largest effect on storage resource 

estimation. In some cases, the above sections are summaries 

of more detailed reports in preparation or review. All input 

and output data and summaries will be available with the 

assessment data, results, and summary reports scheduled to be 

published in 2013. (U.S. Geological Survey Geologic Carbon 

Dioxide Storage Resources Assessment Team, in press, a,b).

Acknowledgments

We greatly appreciate the reviews of Olga Popova, 

Mitchell Small, Angela Goodman, and Robert Milici. We 

also thank the participants of the USGS/NETL Storage Efficiency Workshop held in Austin Texas, July 17–18, 2012.

References Cited

Aitchison, John, 1986, The statistical analysis of compositional data (15th ed.): London, New York, Chapman and 

Hall, 416 p. 

Attanasi, E.D., and Charpentier, R.R., 2007, A program for 

partitioning shifted truncated lognormal distributions into 

size-class bins: U.S. Geological Survey Open-File Report 

2007–1260, 14 p., accessed October 15, 2012, at http://

pubs.usgs.gov/of/2007/1260/. 

Bachu, Stefan, 2003, Screening and ranking of sedimentary 

basins for sequestration of CO2 in geological media in 

response to climate change: Environmental Geology, v. 44, 

p. 277–289.

Bennion, D.B., and Bachu, Stefan, 2005, Relative permeability characteristics for supercritical CO2

 displacing water 

in a variety of potential sequestration zones in the Western 

Canada Sedimentary Basin, SPE 95547, in Society of Petroleum Engineers Annual Technical Conference and Exhibition, Dallas, Tex., 2005, Proceedings: Richardson, Tex., 

Society of Petroleum Engineers, 15 p. 

Bennion, D.B., and Bachu, Stefan, 2008, Drainage and imbibition relative permeability relationships for supercritical 

CO2/brine and H2S/brine systems in intergranular sandstone, 

carbonate, shale, and anhydrite rocks: Society of Petroleum 

Engineers Reservoir Evaluation and Engineering, v. 11, 

no. 3, p. 487–496.

Benson, S.M., and Cook, Peter, 2005, Underground geological 

storage, chap. 5 of Metz, B., Davidson, O., de Coninck, H., 

Loos, M., and Meyer, L., eds., Intergovernmental Panel on 

Climate Change (IPCC), Working Group III, IPCC special 

report on carbon dioxide capture and storage: New York, 

Cambridge University Press, p. 195–276.

Blackwell, D.D., and Richards, M.C., 2004, Geothermal map 

of North America: American Association of Petroleum 

Geologists, scale 1:6,500,000.

Blackwell, D.D., Steele, J.L., and Carter, L.C., 1991, Heat 

flow patterns of the North American continent: A discussion 

of the DNAG geothermal map of North America, in Slemmons, D.B., Engdahl, E.R., Zoback, M.D., and Blackwell, 

D.D., eds., Neotectonics of North America: Boulder, Colo., 

Geological Society of America, Decade Map, v. 1, 32 p.

Blondes, M.S., Schuenemeyer, J., Olea, R.A. and Drew, L.J., 

in press, Aggregation of carbon dioxide sequestration storage assessment units: Stochastic Environmental Research 

and Risk Assessment (SERRA).

Breit, G.N., 2002, Produced waters database: U.S. Geological Survey online database, accessed October 15, 2012, at 

http://energy.cr.usgs.gov/prov/prodwat/.
References Cited 21

Brennan, S.T., Burruss, R.C., Merrill, M.D., Freeman, P.A., 

and Ruppert, L.F., 2010, A probabilistic assessment methodology for the evaluation of geologic carbon dioxide storage: U.S. Geological Survey Open-File Report 2010–1127, 

31 p., accessed, October 15, 2012, at http://pubs.usgs.gov/

of/2010/1127/. 

Burruss, R.C., Brennan, S.T., Freeman, P.A., Merrill, M.D., 

Ruppert, L.F., Becker, M.F., Herkelrath, W.N., Kharaka, 

Y.K., Neuzil, C.E., Swanson, S.M., Cook, T.A., Klett, T.R., 

Nelson, P.H., and Schenk, C.J., 2009, Development of a 

probabilistic assessment methodology for evaluation of 

carbon dioxide storage: U.S. Geological Survey Open-File 

Report 2009–1035, 81 p., accessed, October 15, 2012, at 

http://pubs.usgs.gov/of/2009/1035/.

Burton, M., Kumar, N., and Bryant, S.L., 2008, Time-dependent injectivity during CO2

 storage in aquifers, SPE 11397, 

in SPE/DOE Symposium on Improved Oil Recovery, Tulsa, 

Okla., 2008, Proceedings: Richardson, Tex., Society of 

Petroleum Engineers, 15 p.

Dilmore, R.M., Allen, D.E., Jones, J.R.M., Hedges, S.W., and 

Soong, Y., 2008, Sequestration of dissolved CO2 in the Oriskany Formation: Environmental Science Technology, v. 42, 

no. 8, p. 2760–2766.

Ennis-King, J., and Paterson, L., 2001, Reservoir engineering issues in the geological disposal of carbon dioxide, in 

Williams, D., Durie, B, McMullan, P., Paulson, C., and 

Smith A., eds.,International Conference on Greenhouse Gas 

Control Technologies, 5th, Cairns, Queensland, Australia, 

2000, Proceedings: Cairns, Queensland, Australia, CSIRO, 

p. 290–295.

Gorecki, C.D., Sorensen, J.A., Bremer, J.M., Knudsen, D.J., 

Smith, S.A., Steadman, E.N., and Harju, J.A., 2009, Development of storage coefficients for determining the effective CO2

 storage resource in deep saline formations, SPE 

126444, in Society of Petroleum Engineers International 

Conference on CO2

 Capture, Storage, and Utilization, San 

Diego, Calif., 2009, Proceedings: Richardson, Tex., Society 

of Petroleum Engineers, 35 p.

Holloway, Sam, 2001, Storage of fossil fuel-derived carbon 

dioxide beneath the surface of the earth: Annual Review of 

Energy and the Environment, v. 26, p. 145–166.

IEA Greenhouse Gas R&D Programme, 2009, Development 

of storage coefficients for CO2 storage in deep saline formations: IEA Greenhouse Gas R&D Programme (IEA GHG), 

no. 2009/13, 118 p.

IHS Energy Group, 2010 [includes data current as of December 23, 2009], PIDM (Petroleum Information Data Model) 

relational U.S. well data: IHS Energy Group, database 

available from IHS Energy Group, 15 Inverness Way East, 

D205, Englewood, CO 80112, U.S.A.

Juanes, Ruben, MacMinn, C.W., and Szulczewski, M.L., 

2010, The footprint of the CO2

 plume during carbon dioxide storage in saline aquifers: Storage efficiency for capillary trapping at the basin scale: Transport in Porous Media, 

v. 82, no. 1, p. 19–30.

Keelan, D.K., and Pugh, V.J., 1975, Trapped-gas saturations in 

carbonate formations: SPE Journal, v. 15, no. 2, p. 149–160.

Klett, T.R., Schmoker, J.W., and Charpentier, R.R., 2005, U.S. 

Geological Survey input-data form and operational procedure for the assessment of conventional petroleum accumulations, chap. 20 of USGS Southwestern Wyoming Province 

Assessment Team, Petroleum systems and geologic assessment of oil and gas in the Southwestern Wyoming Province, 

Wyoming, Colorado, and Utah: U.S. Geological Surve 

Digital Data Series DDS–69–D, 7 p., accessed August 20, 

2012, at http://certmapper.cr.usgs.gov/data/noga00/natl/

text/CH_20.pdf. 

Kopp, A., Class, H., and Helmig, R., 2009a, Investigations 

on CO2

 storage capacity in saline aquifers, Part 1, Dimensional analysis of flow processes and reservoir characteristics: International Journal of Greenhouse Gas Control, v. 3, 

no. 3, p. 263–276.

Kopp, A., Class, H., and Helmig, R., 2009b, Investigations on 

CO2 storage capacity in saline aquifers, Part 2, Estimation 

of storage capacity coefficients: International Journal of 

Greenhouse Gas Control, v. 3, no. 3, p. 277–287.

MacMinn, C.W., Szulczewski, M.L., and Juanes, Ruben, 2010, 

CO2 migration in saline aquifers, Part 1, Capillary trapping under slope and groundwater flow: Journal of Fluid 

Mechanics, v. 662, p. 329–351.

Mao, S., and Duan, Z., 2008, The P,V,T, x properties of 

binary aqueous chloride solutions up to T = 573 K and 100 

MPa: Journal of Chemical Thermodynamics, v. 40, no. 7, 

p. 1046–1063.

May, F., Knopf, S., Müller, C., and Hoth, P., 2009, CO2

 storage options in Germany, in Grobe, M., Pashin, J.C., and 

Dodge, R.L., eds., Carbon dioxide sequestration in geological media—State of the science (1st ed.): AAPG Studies in 

Geology, v. 59, p. 35–45.

Meyer, M.A., and Booker, J.M., 2001, Eliciting and analyzing 

expert judgement, a practical guide: ASA-SIAM Series on 

Statistics and Applied Probability, Alexandria, Va. Society 

for Industrial and Applied Mathematics, 459 p.

Lemmon, E.W., McLinden, M.O., and Friend, D.G., 2009, 

Thermophysical properties of fluid systems, in Linstrom, 

P.J., and Mallard, W.G., eds., NIST chemistry WebBook: 

National Institute of Standards and Technology (NIST) 

Standard Reference Database Number 69, accessed December 10, 2012, at http://webbook.nist.gov/chemistry.
22 National Assessment of Geologic Carbon Dioxide Storage Resources—Methodology Implementation

Nehring Associates, Inc., 2010 [data current as of December 2008], The significant oil and gas fields of the United 

States: Colorado Springs, Colo., Nehring Associates, Inc., 

database available from Nehring Associates, Inc., P.O. Box 

1655, Colorado Springs, CO 80901, U.S.A.

Okabe H., and Tsuchiya Y., 2008, Experimental investigation 

of residual CO2 saturation distribution in carbonate rocks, 

in International Symposium of the Society of the Core Analysts, Abu Dhabi, 2008, Proceedings: Abu Dhabi, Society of 

the Core Analysts, 6 p.

Okabe, H., Tsuchiya, Y., Pentland, C.H., Iglauer, S., and Blunt, 

M.J., 2010, Residual CO2 saturation distributions in rock 

samples measured by X-ray CT, in Alshibli, K.A., and 

Reed, A.H., eds., Advances in computed tomography for 

geomaterials: GeoX 2010, New Orleans, La., 2010, Proceedings: New Orleans, La., p. 381–389.

Okwen, R.T., Stewart, M.T., and Cunningham, J.A., 2010, 

Analytical solution for estimating storage efficiency of geologic sequestration of CO2

: International Journal of Greenhouse Gas Control, v. 4, p. 102–107.

Olea, R.A., 2011, On the use of the beta distribution in probabilistic resource assessments: Natural Resources Research, 

v.20, no. 4, p. 377–388.

Palisade Corporation, 2010, @Risk for Excel, version 5.7: 

Ithaca, N.Y., Palisade Corporation software.

Public Law 110–140, 2007, Energy Independence and Security Act of 2007: Washington, D.C., U.S. Government Printing Office, accessed August 20, 2012, at http://frwebgate.

access.gpo.gov/cgi-bin/getdoc.cgi?dbname=110_cong_

public_laws&docid=f:publ140.110.pdf. 

Span, R., and Wagner, W., 1996, A new equation of state for 

carbon dioxide covering the fluid region from the triplepoint temperature to 1100 K at pressures up to 800 MPa: 

Journal of Physical and Chemical Reference Data, v. 25, 

no. 6, p. 1509–1596.

Szulczewski, M.L., MacMinn, C.W., Herzog, H.J., and Juanes, 

R., 2012, Lifetime of carbon capture and storage as a 

climate-change mitigation technology: Proceedings of the 

National Academy of Sciences of the U.S.A., v. 109, no. 14, 

p. 5185–5189.

U.S. Department of Energy, National Energy Technology 

Laboratory, 2010, Rocky Mountain basins produced water 

database: Department of Energy National Energy Technology Laboratory online database, accessed October 15, 2012, 

at http://www.netl.doe.gov/technologies/oil-gas/software/

database.html. 

U.S. Department of Energy, National Energy Technology 

Laboratory, 2012, The North American Carbon Storage Atlas (1st ed.): U.S. Department of Energy, National 

Energy Technology Laboratory, 52 p., accessed October 15, 

2012, at http://www.netl.doe.gov/technologies/carbon_seq/

refshelf/NACSA2012.pdf.

U.S. Environmental Protection Agency, 2009, Safe Drinking 

Water Act (SDWA): Washington, D.C., U.S. Environmental 

Protection Agency Web site, accessed October 15, 2012, at 

http://www.epa.gov/ogwdw/sdwa/index.html.

U.S. Environmental Protection Agency, 2010, Federal requirements under the Underground Injection Control (UIC) for 

carbon dioxide (CO2

) geologic sequestration (GS) wells: 

Washington, D.C., U.S. Environmental Protection Agency 

Web site, accessed October 15, 2012, at http://water.epa.

gov/type/groundwater/uic/class6/gsregulations.cfm.

U.S. Geological Survey Geologic Carbon Dioxide Storage 

Resources Assessment Team, in press, a, National assessment of geologic carbon dioxide storage resources – results: 

U.S. Geological Survey Circular 1386.

U.S. Geological Survey Geologic Carbon Dioxide Storage Resources Assessment Team, in press, b, National 

assessment of geologic carbon dioxide storage resources 

– summary: U.S. Geological Survey Fact Sheet 2013–3020.

van der Meer, L.G.H., 1995, The CO2 storage efficiency of 

aquifers: Energy Conversion Management, v. 36, no. 6–9, 

p. 513–518.

Verma, M.K., 2012, Calculation of hydrocarbon-in-place in 

gas and gas-condensate reservoirs—Carbon dioxide sequestration: U.S. Geological Survey Open-File Report 2012–

1033, 14 p., accessed October 15, 2012, at http://pubs.usgs.

gov/of/2012/1033/. 

Vose, D., 1996, Quantitative risk analysis, A guide to Monte 

Carlo simulation modeling (1st ed.): New York, Wiley, 

340 p.

Wagner, W., and Pruss, A., 2002, The IAPWS formulation 

1995 for the thermodynamic properties of ordinary water 

substance for general and scientific use: Journal of Physical 

and Chemical Reference Data, v. 31, no. 2, p. 387–535.

Warwick, P.D., and Corum, M.D., eds., 2012, Geologic framework for the national assessment of carbon dioxide storage resources: U.S. Geological Survey Open-File Report 

2012–1024, chaps. A–C, available only at http://pubs.usgs.

gov/of/2012/1024/. 
Appendix 1. 23

Many of the inputs for CO2 storage resource rely on 

estimates of oil and gas resources in the subsurface. In particular, known recovery or reservoir size, defined as the sum 

of cumulative production to date and proved reserves, is used 

to estimate buoyant pore volume (see Section 6.1). However, 

estimates of known recovery tend to increase as reservoir 

development occurs and new recovery techniques are applied 

(Arrington, 1960; Attanasi and Root, 1994). Reservoir growth 

modeling allows the prediction of ultimate reservoir sizes with 

cumulative growth functions. Cumulative growth functions 

predict the reservoir’s size as a multiple of the initial estimate. 

These functions are used to project known recovery volumes 

to the year 2050.

A1.1. Data

The “Significant Oil and Gas Fields of the United States 

Database” by Nehring Associates, Inc. (2010), used in this 

study, included reservoir size estimates for accumulations 

discovered from 1901 through 2008 (Nehring Associates, Inc., 

2010). For each accumulation there is an estimate of known 

recovery from 1982 through 2008. Here, only conventional 

accumulations are used for calibrating the cumulative growth 

functions. Conventional accumulations are discrete deposits 

having a well-defined down-dip oil and gas water contact from 

which oil, gas, or natural gas liquids (NGL) can be extracted 

by standard methods. Reservoirs are classified as either oil or 

gas on the basis of the gas to oil ratio (GOR): gas reservoirs 

have ratios of at least 20,000 cubic ft of gas to barrel of oil 

based on the 2008 estimate of known recovery. Reservoirs 

discovered before 1901 and those without discovery dates are 

excluded. Statisticians also partition the sample data to remove 

parts of the data series where data are known to introduce 

bias. For calibration of oil reservoir cumulative growth functions, California heavy oil reservoirs and Williston Basin oil 

reservoirs (predominantly oils from shale) together representing about 11 percent of the oil discovered, were excluded. 

For calibration of gas reservoir cumulative growth functions, 

to mitigate the effect of gas price regulation on reservoir size 

estimates, growth functions were based on the series of estimates starting from 1993 through 2008. In addition, discrete 

low permeability gas reservoirs (considered conventional by 

the USGS) were removed for the same reason the heavy oil 

was removed from the oil reservoir data. The gas reservoirs of 

southwest Wyoming were removed because gas was actually 

stranded until the Rocky Express Pipeline was built. Reservoirs that were excluded only amounted to 7 percent of the gas 

of the 2008 known recovery estimate.

Table A1-1 shows part of a discovery table from 1982 

through 1985. Each row is a vintage representing the sum of 

the known recoveries of all reservoirs discovered in a specific 

year. Entries from left to right represent the sum of known 

recoveries of that vintage as of a specific estimation date: 

1982, 1983, through 2008. The discovery table is the basic 

data used for calibration of the cumulative growth function.

Table A1–1. Part of a discovery table. Estimated known 

recovery in discovered oil reservoirs by discovery year or 

vintage (vertical) with estimation year (horizontal). The entries 

from left to right are successive estimates of total volume of 

oil in oil reservoirs. Known recovery data are from Nehring 

Associates, Inc. (2010).

Reservoir

discovery 

year

Year of estimate

1982 1983 1984 1985

1979 120 133 157 170

1980 92 109 125 130

1981 97 143 153 156

1982 34 108 142 160

1983 0 40 93 104

1984 0 0 35 88

1985 0 0 0 37

A1.2. Calibration of cumulative growth functions 

Observing table A1-1, for any vintage, the annual growth 

factor for reservoirs of age i is the ratio of the estimated total 

known recoveries at (i+1) years after discovery to the estimated total known recoveries i years after discovery. Similarly for a particular vintage, the cumulative growth factor is 

the ratio of the total estimated reservoir sizes m years after 

discovery to the total of the initial estimated reservoir sizes 

(year 0). Cumulative growth factors can also be computed as 

the successive products of annual growth factors.

For each vintage, the cumulative growth function is represented by the series of cumulative growth factors computed 

for each successive year after discovery. Changes in estimated 

known recovery conform to the relation

ĉ (i,j+m)= c(i,j) [G(j+m-i)/G(j-i)] + d(i,j,m) , (A1)

Appendix 1. Reservoir Growth Functions

By Emil Attanasi
24 National Assessment of Geologic Carbon Dioxide Storage Resources—Methodology Implementation

where c(i,j) is the aggregate known recovery in year j of vintage i reservoirs (that is, reservoirs discovered in year i), m is 

elapsed time (in years where m >0), ĉ(i,j+m) is the estimate of 

aggregate known recovery in year j + m of vintage i reservoirs, 

d(i,j,m) is the deviation or error term and G( ) is the cumulative growth factor. Equation A1 implies that, for a specified 

vintage with discovery year i, the aggregate of the known field 

recoveries in year j+m can be determined by multiplying the 

aggregate of the estimated reservoir recoveries in year j by an 

appropriate factor that is the ratio of cumulative growth factors 

for reservoir ages (j+m-i) and (j-i). G(N) is bounded where 

N is the number of years after which the vintage is no longer 

allowed to grow. In particular, G(0) = 1, and G(n) is a constant 

when n > N, after N years where N may be the same as the 

time span over which the factors were computed (1901–2008).

The cumulative growth factors, G(j+m-i), are computed 

using an optimization algorithm, called an Lp norm minimization (Nyquist, 1983), that minimizes the sum of absolute 

deviations that have been raised to the power p where p > 0,

ssd = ∑|d(i,j,m)|p (A2)

between all combinations of the actual and estimated aggregate field recoveries, ĉ(i, j+m), within the data (that is, the 

discovery table) used in the analysis, where

d(i,j,m)=c(i,j+m,m)- ĉ(i,j+m,m). (A3)

The sources of error which contribute to d(i,j,m) arise 

from incomplete knowledge about geologic properties of the 

reservoir, errors in data, changes in recovery technology, and 

economic and market conditions. The distribution of d(i,j,m) is 

unknown and presumed non-normal. 

The choice of p enables the adaptation of the calibration 

method to the error function. If the errors (residuals) followed 

a normal distribution, p = 2, the minimization of the sum of 

squared errors is optimal (Nyquist, 1983). In the case where 

the data include outliers, it is generally optimal to minimize 

the absolute value of the sum of the deviations, where p = 1 

(Nyquist, 1983). The choice of p allows an extra degree of 

freedom for fitting the cumulative growth function to the data. 

For this study, the choice of p was determined by examining 

model in-sample and out-of-sample prediction performance of 

the calibrated models using alternative values of p. To summarize, the above procedure provides, by the selection of the 

value of p, a means to mitigate outlier influence. The search 

over various values of p for oil reservoirs showed that p = 1.5 

provided the smallest sample forecast error for 2001–2008. 

The search over various values of p for gas reservoirs showed 

optimal sample predictive performance when p = 2. 

The reservoir cumulative growth function coefficients 

for oil and gas reservoirs are shown in table A1-2. The age of 

the reservoir is defined as the number of years elapsed since 

the discovery year (first column in table A1-2). To project 

reservoir size in year 2050, multiply the 2008 estimated reservoir size by the ratio of the cumulative growth coefficient 

corresponding to the reservoir’s age at year 2050 to cumulative growth coefficient corresponding to the reservoir’s age 

at year 2008.1 For example, if an oil reservoir was discovered 

in 2002, then multiply the known recovery in 2008 by the 

ratio of the cumulative growth coefficient for oil reservoirs 

of age 48 to the cumulative growth coefficient for oil reservoirs of age six years. These grown volumes are then used in 

the Section 6 calculations.

1

For cases when age is greater than 107, use the 107-year cumulative 

growth coefficient.

Table A1–2. Growth function coefficients for oil and gas 

reservoirs. The Lp norm calibration exponents for oil and gas 

reservoirs are p = 1.5 and p = 2.0, respectively.—Continued

Years since

discovery

Oil reservoir 

multiplier

Gas reservoir 

multiplier

0 1.00000 1.00000

1 2.70499 2.84112

2 3.69281 3.35768

3 4.22540 3.49949

4 4.47146 3.64729

5 4.59156 3.80133

6 4.71488 3.96188

7 4.84151 4.12921

8 4.97154 4.30361

9 5.10507 4.48537

10 5.24218 4.67481

11 5.38298 4.87224

12 5.52756 5.07802

13 5.65003 5.29249

14 5.77521 5.51602

15 5.83131 5.74899

16 5.88785 5.94284

17 5.94493 6.14324

18 6.00257 6.35039

19 6.06076 6.56452

20 6.11952 6.78588

21 6.17885 7.01470

22 6.23876 7.25124

23 6.29924 7.49575

24 6.36032 7.74851

25 6.42198 8.00979

26 6.48424 8.27988

27 6.54711 8.55908

28 6.61058 8.84769

29 6.67467 9.14603
Appendix 1. 25

Table A1–2. Growth function coefficients for oil and gas 

reservoirs. The Lp norm calibration exponents for oil and gas 

reservoirs are p = 1.5 and p = 2.0, respectively.—Continued

Years since

discovery

Oil reservoir 

multiplier

Gas reservoir 

multiplier

30 6.73939 9.45444

31 6.80472 9.62191

32 6.87070 9.79235

33 6.93731 9.96581

34 7.00457 10.14234

35 7.07248 10.32200

36 7.11626 10.50484

37 7.15668 10.69092

38 7.19734 10.88029

39 7.23822 11.07302

40 7.27933 11.26917

41 7.32068 11.46878

42 7.36226 11.62530

43 7.40408 11.78395

44 7.44614 11.94476

45 7.48843 12.10777

46 7.53097 12.27301

47 7.57374 12.40774

48 7.61676 12.47675

49 7.66003 12.54615

50 7.70354 12.61594

51 7.74729 12.68611

52 7.79130 12.75668

53 7.83556 12.82513

54 7.88006 12.89394

55 7.92482 12.96313

56 7.96984 13.03269

57 8.01511 13.10262

58 8.06063 13.17293

59 8.10642 13.21829

60 8.15167 13.26381

61 8.17814 13.30948

62 8.20470 13.35531

63 8.23134 13.40130

64 8.25807 13.44744

65 8.28441 13.49375

66 8.31082 13.54021

67 8.33097 13.58684

68 8.35118 13.63362

69 8.37143 13.68057

70 8.39172 13.72768

71 8.41207 13.77495

Table A1–2. Growth function coefficients for oil and gas 

reservoirs. The Lp norm calibration exponents for oil and gas 

reservoirs are p = 1.5 and p = 2.0, respectively.—Continued

Years since

discovery

Oil reservoir 

multiplier

Gas reservoir 

multiplier

72 8.43247 13.82238

73 8.45292 13.86998

74 8.47341 13.91774

75 8.49396 13.96566

76 8.51456 14.01375

77 8.53520 14.06201

78 8.55590 14.07959

79 8.57665 14.07959

80 8.59744 14.07959

81 8.61829 14.07959

82 8.63919 14.07959

83 8.66014 14.07959

84 8.68114 14.07959

85 8.70219 14.07959

86 8.72329 14.07959

87 8.74444 14.07959

88 8.76564 14.07959

89 8.78690 14.07959

90 8.80820 14.07959

91 8.82956 14.07959

92 8.85097 14.07959

93 8.87243 14.07959

94 8.89395 14.07959

95 8.91551 14.07959

96 8.93713 14.07959

97 8.95880 14.07959

98 8.98053 14.07959

99 9.00230 14.07959

100 9.02413 14.07959

101 9.03930 14.07959

102 9.05450 14.07959

103 9.06972 14.07959

104 9.08497 14.07959

105 9.10024 14.07959

106 9.11554 14.07959

107 9.13086 14.07959
26 National Assessment of Geologic Carbon Dioxide Storage Resources—Methodology Implementation

Acknowledgments

The authors thank Timothy Klett of the USGS Central 

Energy Resources Science Center and Troy Cook, formerly 

with the USGS Central Energy Resources Science Center, who 

assigned conventional, continuous reservoir designations, and 

province codes to the Nehring reservoir database. 

References Cited

Arrington, J.R., 1960, Predicting the size of crude reserves is 

key to evaluating exploration programs: Oil and Gas Journal, v. 58, no. 9, 130–134.

Attanasi, E.D., and Root, D.H., 1994, The enigma of oil 

and gas field growth: American Association of Petroleum 

Geologists Bulletin, v. 78, no. 3, p. 321–332.

Nehring Associates, Inc., 2010 [data current as of December 2008], The significant oil and gas fields of the United 

States: Colorado Springs, Colo., Nehring Associates, Inc., 

database available from Nehring Associates, Inc., P.O. Box 

1655, Colorado Springs, CO 80901, U.S.A.

Nyquist, H., 1983, The optimal Lp norm estimation in linear 

regression models: Communications in Statistical Theory 

and Methods, v. 12, p. 2511–2524.
Blondes and others—National Assessment of Geologic Carbon Dioxide Storage Resources—Methodology Implementiation—Open-File Report 2013–1055