i

DEVELOPMENT OF A SEMI-ANALYTICAL MODEL TO

CALCULATE PRESSURE BUILDUP AND FRONT

MOVEMENT FOR CO2 SEQUESTRATION SITES AND ITS

APPLICABILITY TO THE TWO ELK ENERGY PARK IN

THE POWDER RIVER BASIN OF WYOMING

A REPORT SUBMITTED TO THE DEPARTMENT OF ENERGY

RESOURCES ENGINEERING

OF STANFORD UNIVERSITY

IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE

DEGREE OF MASTER OF SCIENCE

By

Whitney Sargent

June 2012

iii

I certify that I have read this report and that in my opinion it is fully adequate, in scope and in

quality, as partial fulfillment of the degree of Master of Science in Petroleum Engineering.

__________________________________

Prof. Sally Benson

(Principal Advisor)

v

Abstract

A goal for carbon capture and sequestration (CCS) is to reduce CO2 emissions into the

atmosphere and store the CO2 permanently in underground reservoirs. This work develops an

extended semi-analytical model and performs a reservoir simulation study. The purpose is to assess

the injectivity and capacity of CO2 storage in a portion of the Powder River Basin (PRB) called the

Two Elk Energy Park (TEEP). The motivation for a new semi-analytical model is motivated by the

need to estimate CO2 injectivity, pressure buildup, and CO2 plume migration in stacked layers, such

as those present in the PRB. In addition to this, the reservoir simulation study can assess the effects

of formation structure and heterogeneity. The lithology of the PRB targeted for CO2 storage consists

of highly heterogeneous layers of sandstone, shale, and carbonates. No single formation is suitable

for large scale injection, but a very thick sequence of moderate to low permeability units may

provide sufficient injectivity and capacity for a large scale carbon sequestration project.

First, this study applies a semi-analytical model to estimate the injectivity and capacity of the

PRB. The two issues to be addressed are the heterogeneous layering and the different pressure

gradient between the well, filled with CO2, and the formation, a saline aquifer, at different depths.

The work by Kumar and Bryant (2009) provides the basis for the extended semi-analytical model.

The model calculates the well pressure along a perforated interval and accounts for the density

difference of CO2 in the well and includes a method to estimate the dry-out zone and a two-phase

zone radius in a single homogeneous layer. The new model is the SAHCO2 injection model, a semi-

analytical solution for predicting pressure buildup and plume migration in a heterogeneous system

comprised of permeable layers separated by low permeability rocks.

The SAHCO2 injection model takes advantage of the Kumar and Bryant (2009) model but

has added functionality to include a heterogeneously layered system, an expanding constant pressure

boundary to mimic an infinite-acting reservoir, and updated phase front definition. Comparison with

a representative numerical model yields good agreement with the extended semi-analytical model.

The SAHCO2 injection model can be used for several applications; namely, for complex sandstone

layering formations, large storage reservoirs, and for quick and easy screening of potential CO2

storage sites.

Four reservoir/sealing units identified in the PRB are characterized from literature and well

data from locations far from the injection site. SAHCO2 injection model results conclude the

estimated pressure buildup is 14.3% of initial reservoir pressure after 50 years of constant injection

of 3 Mt/yr of CO2. The maximum plume migration is 2.6 km in the Hulett formation.

The second approach for assessing the PRB for CO2 injectivity is to carry out regional-scale

three-dimensional numerical simulations. The newly developed geological model assesses the

influence of the formation dip, discontinuous layering, and boundary conditions on the long-term

fate of injected CO2.

The largest reservoir/sealing unit is the Minnelusa-Madison/Goose Egg formations. A static

geologic model representing these units is used for numerical simulation of this region. The results

for a high permeability and porosity case show that 3 Mt/yr of CO2 can be injected with 3.6%

increase in initial pressure and a maximum plume migration of 4.6 km at 50 years of injection and

7.6 km at 1,100 years of shut-in. A low permeability and porosity case requires additional wells to

achieve the target rate of 3 Mt/yr of CO2. Multiple well scenarios under a field rate constraint

achieve the target rate with a pressure buildup of 4.4% from initial reservoir pressure. Plume

vi

migrations from different wells interfered with each other to achieve maximum coverage of the grid

area, 16 by 16 km.

7

Acknowledgments

My sincerest gratitude goes to my advisor, Dr. Sally Benson, whose guidance and support

provided the foundation of my research. Her unlimited patience and gentle advice helped me through the

many tasks associated with research and classes.

Thanks to Rani Calvo (Geological Survey of Israel) for providing a detailed geologic description

of the Powder River Basin. I also want to recognize Anshul Agarwal (Director of the Stanford Center for

Carbon Storage) for her direct contribution to this research and I hope that her continuation of the

project will be interesting and fun. Also, thanks to all the participants in the Two Elk Energy Park

project who worked hard to provide a model used in this research.

I want to thank the members of the Benson Lab who provided feedback on presentations about

my work. I especially want to acknowledge Christin Strandli for openly discussing research ideas with

me these last two years. Also, my appreciation goes to Sam Krevor and Ronny Pini for providing lab

data used in my research.

I am blessed to have my parents, Ben and Stephanie, as role models. Their trust and support is

invaluable and greatly appreciated. Without their influence I would not be driven to continue learning

and improving. Also, thanks to my friends, both at Stanford and back in Texas, for their role in keeping

my life fun and interesting.

My research is funded by the US Department of Energy, grant number DE-FE0001997 awarded

to North American Power Group Ltd.

8

Contents Abstract ...................................................................................................................................................................... v

Acknowledgments ...................................................................................................................................................... 7

Contents ...................................................................................................................................................................... 8

List of Tables .............................................................................................................................................................. 9

List of Figures .......................................................................................................................................................... 10

Chapter 1—Introduction and Thesis Scope of Work ............................................................................................... 13

1.1 Motivation .................................................................................................................................................... 13

1.2 Introduction .................................................................................................................................................. 13

1.3 CO2 Injection Modeling Basics .................................................................................................................... 14

Trapping Mechanism ........................................................................................................................................ 14

CO2-Fluid-Rock Interactions ............................................................................................................................ 14

Plume Migration ............................................................................................................................................... 15

Pressure Influence ............................................................................................................................................ 15

Storage Ability and Capacity ............................................................................................................................ 16

1.4 Analytical Models ........................................................................................................................................ 16

1.5 Numerical Models ........................................................................................................................................ 19

Chapter 2—Semi-Analytical Modeling of Carbon Dioxide Sequestration .............................................................. 21

2.1 Original Semi-Analytical Model .................................................................................................................. 21

Description of the three regions of the semi-analytical model ......................................................................... 22

Pressure Treatment ........................................................................................................................................... 22

Explanation of Front Movement....................................................................................................................... 23

Semi-Analytical Model Assumptions and Parameters ..................................................................................... 23

The Algorithm Proposed in the Original Semi-Analytical Model .................................................................... 24

2.2 Semi-Analytical Heterogeneous CO2 (SAHCO2) Injection Model ............................................................. 26

SAHCO2 Injection Model Improvements ........................................................................................................ 26

Well Pressure Initialization .............................................................................................................................. 27

Well Pressure at time t ...................................................................................................................................... 27

2.3 Simple Example Results Comparing the Semi-Analytical and a Comparable TOUGH2/ECO2N Simulation

Model .................................................................................................................................................................... 28

Example Problem Conditions ........................................................................................................................... 28

Verification Results .......................................................................................................................................... 29

Chapter 3—Powder River Basin Geological Description ........................................................................................ 32

3.1 Powder River Basin (PRB) CCS Opportunities ........................................................................................... 32

9

3.2 Powder River Basin Geology ....................................................................................................................... 33

3.3 Two Elk Energy Park (TEEP) Geologic Units for Carbon Sequestration .................................................... 36

Minnelusa-Madison/Goose Egg ....................................................................................................................... 36

Spearfish-Hulett/Sundance ............................................................................................................................... 36

Morrison-Lakota/Fuson .................................................................................................................................... 37

Dakota Reservoir .............................................................................................................................................. 38

3.4 Reservoir Data .............................................................................................................................................. 38

3.5 Petrel Static Geologic Model Description .................................................................................................... 39

Chapter 4—Two Elk Energy Park Carbon Sequestration Study Results ................................................................. 43

4.1 TEEP Semi-Analytical Heterogeneous CO2 Injection Model ...................................................................... 43

Input Data ......................................................................................................................................................... 43

SAHCO2 Injection Model Results ................................................................................................................... 45

4.2 TEEP Reservoir Simulation Model .............................................................................................................. 48

Geological Model Case Descriptions ............................................................................................................... 49

Simulation Initialization Data ........................................................................................................................... 49

Well Completions ............................................................................................................................................. 50

High Case Simulation Results .......................................................................................................................... 52

Low Case Simulation Results ........................................................................................................................... 55

CO2 Trapping Mechanisms .............................................................................................................................. 62

Chapter 5—Conclusions ........................................................................................................................................... 63

Future Work...................................................................................................................................................... 63

Nomenclature ........................................................................................................................................................... 64

References ................................................................................................................................................................ 66

Appendix 1 ............................................................................................................................................................... 69

Appendix 2 ............................................................................................................................................................... 70

Appendix 3 ............................................................................................................................................................... 72

Appendix 4 ............................................................................................................................................................... 74

Appendix 5 ............................................................................................................................................................... 77

List of Tables

Table 1—List of codes used in the Code Intercomparison Study (Pruess, et al., 2002). .......................... 20 Table 2—Code intercomparison on problems and results (Pruess, et al., 2002). ..................................... 21 Table 3—Input Parameters for the SAHCO2 injection model and TOUGH2/ECO2N. .......................... 29 Table 4—Pressure buildup comparison between the SAHCO2 and simulation model............................ 30

10

Table 5—Layer properties from well log analysis including capacity calculations (Calvo, 2011). ......... 39

Table 6—Average layer thickness and number of grid blocks per formation layer. ................................ 41 Table 7—Formation property statistics for the High Case and Low Case. .............................................. 42 Table 8—SAHCO2 injection model TEEP reservoir data inputs. ............................................................ 44

Table 9—SAHCO2 injection model TEEP formation properties............................................................. 44 Table 10—SAHCO2 injection model maximum zone radii results for 1, 10, 25, and 50 years. ............. 46 Table 11—Summary of CO2 injection rates at surface conditions with a CO2 density of 1.98 kg/m

3. The

volumetric rates per well for cases with multiple wells are also provided. .............................................. 53 Table 12—Summary of field pressure increases for Low Case scenarios. ............................................... 59

Table 13—SAHCO2 injection model maximum zone radii results for 1, 10, 25, and 50 years in field

units. .......................................................................................................................................................... 74 Table 14—Relative permeability and capillary pressure data used in the E300 simulation model. ........ 77

List of Figures

Figure 1—CO2 density and viscosity at subsurface conditions, surface temperature is 15 C, 30 C/km and

10 MPa/km (Ennis-King & Peterson, 2002) ............................................................................................. 17 Figure 2—(Left) Typical profile of CO2 region denoted by b(r,t). (Right) Piecewise approximation used

to represent the invading CO2 front. Notice that bN is constrained to equal the total formation thickness

B. (Nordbotten, Celia, & Bachu, 2005). ................................................................................................... 18

Figure 3—Cartoon depicting the CO2-brine interface, denoted by h(x,t), and the location of the centroid

for a typical sloping aquifer (Gasda, Celia, & Nordbotten, 2006). ....................................................... 19 Figure 4—Diagram showing the three regions described in the semi-analytical models. ........................ 22 Figure 5—Pressure profile for the well and formation. In a homogenous reservoir, the injection rate will

be greatest at the top of the injection zone due to the larger pressure difference. .................................... 22

Figure 6—Fractional flow diagram with the inclusion of the D factors (Burton, Kumar, & Bryant, 2008)

................................................................................................................................................................... 23 Figure 7—Schematic showing the heterogeneous layers and arrows indicate potential amount of CO2

injection in the layer.................................................................................................................................. 26 Figure 8—Relative permeability of CO2 and brine used in the updated semi-analytical model and

numerical TOUGH2/ECO2N model. ........................................................................................................ 28

Figure 9—Reservoir pressure distribution in the aquifer compared to the pressure influence radius

calculated by the SAHCO2 injection model. ............................................................................................ 30 Figure 10—Reservoir pressure on a semi-log axis showing how the extrapolation of the linear portion to

the initial pressure compares to the SAHCO2 pressure influence radius. ................................................ 31

Figure 11—Saturation front comparison between the SAHCO2 and simulation model. ......................... 31 Figure 12—The major geologic basins in Wyoming with locations of major oil fields and enhanced oil

recovery operations using CO2 (De Bruin, 2001). .................................................................................... 32 Figure 13—CO2 emission sources locations for the northwest area of the United States (BSCSP, 2010).

................................................................................................................................................................... 33 Figure 14—East-West cross section of the PRB (Anna, 2009). ............................................................... 34 Figure 15—Corrected bottom-hole temperature measurements for the southern PRB (McPherson &

Chapman, 1996). ....................................................................................................................................... 34 Figure 16—PRB stratigraphic map showing both the east and west locations (Dolton & Fox). ............. 35 Figure 17—Diagram of well locations relative to the TEEP well site in the geologic model used for the

simulation study. ....................................................................................................................................... 36

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Figure 18—Stratigraphic cross section of the PRB showing four distinct reservoir/seal units (Calvo,

2011). ........................................................................................................................................................ 37 Figure 19—Log porosity versus permeability cross plot from the Minnelusa formation (Butsch, 2011).39 Figure 20—Wyoming county outlines in red with the 188 by 201 km basin model outline in purple, 40

by 40 km detailed model in dark blue, and 16 by 16 km TEEP section model in light blue. The

petrophysical wells used for property modeling are shown on the map, with the location on the left side

of the name. ............................................................................................................................................... 40 Figure 21—Simplified stratigraphic column of the PRB showing the breakdown of the formations in the

Petrel static geological model (Trigilio, Mills, J., & Brown, 2011). ........................................................ 40

Figure 22—16 by 16 km section of Petrel static geologic model looking from the SW corner. Z-axis is

scaled by 10X. A well is placed in the middle of the model. ................................................................... 41 Figure 23—Relative permeability curve for SAHCO2 injection model .................................................. 45 Figure 24—Modified fractional flow curve with dimensionless velocities for SAHCO2 injection model

................................................................................................................................................................... 45 Figure 25—Zone radius migration for 1, 10, 25, and 50 years on a linear scale. ..................................... 46

Figure 26—Zone radius migration for 1, 10, 25, and 50 years on a logarithmic scale. ........................... 47 Figure 27—Comparison of zone radii as a function of time. ................................................................... 47

Figure 28—Pressure profile of the well compared to the aquifer reservoir pressure as a function of time.

................................................................................................................................................................... 48 Figure 29—Pressure buildup plots showing a 14.3% pressure increase from initial reservoir pressure

after 50 years of constant injection. .......................................................................................................... 48 Figure 30—CO2-water relative permeability curves for the Arqov sample used in the TEEP simulations

(Pini, Krevor, & Benson, 2012). ............................................................................................................... 50 Figure 31—Scaled CO2 capillary pressure curves for the Arqov sample, Minnelusa/Madison, and

Opeche formations using the Leverett J-function (Pini, Krevor, & Benson, 2012), (Leverett, 1941). .... 50

Figure 32—Pseudo Well High Case completion information showing formation tops and pseudo well-

log permeability and porosity values. Depth units are subsurface depths in feet. Permeability is in mD. 51 Figure 33—High Case permeability and porosity map for the J-slice through the center well. Z-scale is

5X and the thickness is 1,807 ft. ............................................................................................................... 52

Figure 34—(Left) Field cumulative CO2 injection vs. time. (Right) Field pressure vs. time (in years) for

all the High Case scenarios. The 3 Mt/yr cases have the same pressure buildup of 199 psi (1.37 MPa).

The 1 Mt/yr case has a pressure buildup of 67 psi (0.46 MPa). ............................................................... 52 Figure 35—(Left) BHP vs. time (in years) for the High Case scenarios with 3 Mt/yr CO2 injection rate.

The early spike reaches a BHP of 8,474 psi (58.4 MPa) but is reduced once CO2 is introduced into the

system. (Right) CO2 field injection rate vs. time (in years) confirms target CO2 rate is met. .................. 53 Figure 36—CO2 saturation maps for High Case base case. (Left) Plume migration after 50 years of

injection with maximum plume distance of 15,000 ft (4.57 km) (Right) Plume migration after 1,100

years of shut-in time with maximum plume distance of 25,000 ft (7.62 km). Z-scale in I and J slice is 5X

and thickness is 1,807 ft (551 m). ............................................................................................................. 54 Figure 37—Low Case permeability and porosity map for the J-slice through the center of the grid. Z-

scale is 5X and the thickness is 1,807 ft (551 m). ..................................................................................... 55 Figure 38—Cartoon of approximate well locations used in Low Case simulations................................. 55 Figure 39—Low Case Base Case: (Left) BHP vs. time in the Pseudo Well High Case shows a constant

BHP at the maximum of 8,702 psi. (Right) CO2 injection rate vs. time for the Pseudo Well High Case

showing the varying rate due to the BHP constraint. ................................................................................ 56

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Figure 40—Low Case, three well with small casing: (Left) BHP vs. time for the Pseudo Well High Case

and Pseudo2 shows a constant BHP at the maximum of 8,702 psi. Pseudo3 well has a lower BHP and is

able to reach the maximum rate for the well. (Right) CO2 injection rate vs. time for the Pseudo Well

High Case and Pseudo2 shows the varying rate due to the BHP constraint. A constant rate is reached for

Pseudo3. .................................................................................................................................................... 56 Figure 41—Low Case, three well with large casing: (Left) BHP vs. time for the Pseudo Well High Case

and Pseudo2 shows a constant BHP at the maximum of 8,702 psi (60 MPa). Pseudo3 well has a lower

BHP and is able to reach the maximum rate for the well. (Right) CO2 injection rate vs. time for the

Pseudo Well High Case and Pseudo2 shows the varying rate due to the BHP constraint. ...................... 57

Figure 42—Low Case, four wells with large casing: (Left) BHP vs. time for four wells in the model.

Two wells reach the BHP limit and switch to BHP control. (Right) CO2 injection rate vs. time for the

four wells shows reduced injection rate for two wells due to the BHP control. ....................................... 58 Figure 43—Low Case with five wells: (Left) BHP vs. time showing P1, P2, and P4 at the maximum

BHP limit. (Right) CO2 injection rate vs. time for all wells where P3 and P5 can meet the well specified

rate............................................................................................................................................................. 58

Figure 44—Low Case scenarios: (Left) Cumulative CO2 injection vs. time for all Low Case scenarios.

(Right) Average field pressure vs. time for all Low Case scenarios. ....................................................... 59

Figure 45—Low Case with three wells on group rate constraint: (Left) BHP vs. time for three wells.

(Right) CO2 injection rate vs. time for three wells showing Pseudo3 contributing most of the rate. ...... 60 Figure 46—Low Case with four wells on group rate control: (Left) BHP vs. time for four wells. (Right)

CO2 injection rate vs. time for four wells. ................................................................................................ 60 Figure 47—Low Case with five wells on group rate control: (Left) BHP vs. time for the five wells.

(Right) CO2 injection rate vs. time for the five wells. .............................................................................. 61 Figure 48—Low Case with five wells: CO2 saturations maps (Left) Saturation map with the upper right

well (Pseudo5) having the largest plume extent after 50 years of injection. (Right) Saturation map

showing the total plume migration after 1,100 years of shut-in. The CO2 from the wells have interfered

with other plume migrations. .................................................................................................................... 62 Figure 49—Trapping mechanism plot showing the percentage of trapping by mechanism. The one

capillary pressure curve scenario has higher residual trapping than the two capillary pressure curves

scenario. The time scale starts at the end of the 50 year injection period and extends to the end of the

1,100 years of shut-in time........................................................................................................................ 62

Figure 50—188 by 201 km static geological model. Z-scale is 10X........................................................ 72 Figure 51—40 by 40 km static geological model. Z-scale is 10X............................................................ 72

Figure 52—16 by 16 km static geological model. Z-scale is 10X............................................................ 73 Figure 53—Zone radius migration for 1, 10, 25, and 50 years on a linear scale in field units. ................ 74 Figure 54—Zone radius migration for 1, 10, 25, and 50 years on a logarithmic scale in field units. ...... 75 Figure 55—Comparison of zone radii as a function of time in field units. .............................................. 75 Figure 56—Pressure profile of the well compared to the aquifer reservoir pressure as a function of time

in field units. ............................................................................................................................................. 76 Figure 57—Pressure buildup plots showing a 14.3% pressure increase from initial reservoir pressure

after 50 years of constant injection in field units. ..................................................................................... 76 Figure 58—Trapping plots for the Low Case Scenarios. ......................................................................... 78

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Chapter 1—Introduction and Thesis Scope of Work

1.1 Motivation The Two Elk Energy Park (TEEP), located in the Powder River Basin (PRB) in Wyoming, is an

integrated energy park with the potential for multiple power generating and carbon capture facilities

with carbon sequestration. The TEEP is being developed by North American Power Group, Ltd.

(NAPG) (North American Power Group, Ltd). The work for this thesis is to assess the injectivity and

capacity of the PRB geologic formations near the TEEP.

The heterogeneity and large thicknesses of the targeted formations for carbon sequestration

created a need for a simple semi-analytical model that can quickly screen potential formations that

contain these characteristics. This research develops an extended semi-analytical model from the work

by Kumar and Bryant (2009) that has the ability to include layered heterogeneity of permeability and

porosity, analyze the difference in well and formation pressure gradients in long intervals, and determine

the extent of the CO2 plume migration including a dry-out zone (Kumar & Bryant, 2009). The extended

semi-analytical model, named the SAHCO2 injection model, is verified with a simple numerical model

with good correlation for pressure buildup and phase front movement. The SAHCO2 model is then

applied to the TEEP region in the PRB.

Further analysis utilizes a reservoir simulation study of the TEEP region. A three-dimensional

basin-wide geological model based on well information and geostatical analysis using the Schlumberger

developed industrial software Petrel is used as the basis for this analysis (Schlumberger Information

Systems, 2010). The Eclipse compositional reservoir simulator, E300, is used to perform analysis of

carbon sequestration in the targeted PRB formations with the CO2STORE option (Schlumberger

Information Systems, 2010).

1.2 Introduction Carbon capture and sequestration (CCS) is part of the solution for reducing carbon dioxide

emissions into the atmosphere. Carbon sequestration is the process of taking a stream of CO2 and

injecting it into a rock formation in the earth for long-term storage. Depleted oil and natural gas

reservoirs, coal bed methane reservoirs, and deep saline aquifers are the potential options for carbon

storage and the focus of most research today. Extensive ongoing research ranges from CO2-fluid

interactions, CO2-rock interactions, CO2 migration, CO2 monitoring, and CCS optimization.

Natural gas has been injected into geologic formations for interim storage proving by analogy,

that CO2 can be treated in the same manner. Oil and gas accumulations have been in place for long

geologic times and have been trapped in structural formations which proves the ability of geologic

formations to provide long term storage of CO2 (IPCC, 2005). The unique characteristics of CO2 flow in

porous media for the purpose of long term storage require further analysis.

An important part of modeling carbon sequestration is creating mathematical solutions to model

CO2 injection into rock formations. Historically, porous media modeling research has focused on oil and

gas reservoirs. Enhanced oil recovery (EOR) and enhanced gas recovery (EGR) operations using CO2

flooding have helped add to our knowledge of CO2 injection behavior and injection modeling; especially

in CO2 displacement processes and injection strategies (Ennis-King & Peterson, 2002). Production from

naturally occurring CO2 accumulations gives unique information about geochemistry of CO2 in porous

media. Most recently, those models have been applied to carbon sequestration. Analytical models and

14

numerical simulators have been developed and are discussed here in the context of CO2 sequestration.

Most of the models are developed for deep saline aquifers but many of the same ideas are applied to the

other storage reservoir types.

The important considerations with CO2 injection include, but are not limited to, trapping

mechanisms, CO2-fluid interactions, CO2-rock interactions, plume migration, pressure influence, and

total storage ability and capacity.

1.3 CO2 Injection Modeling Basics Trapping Mechanism

Four trapping mechanisms occur during CO2 injection and storage (IPCC, 2005). The first is

structural and stratigraphic trapping, where CO2 is trapped in the pore space and is kept from escaping

the storage reservoir by a sealing structure. This type of trapping is straightforward to model in

analytical and numerical models since the only important necessary components are porosity,

permeability, and saturations in the formation and the geologic structure geometry of the reservoir.

Capillary entry pressure of the seal is important as well but analytical models lack the ability to include

its affects.

The other three trapping mechanisms are considered secondary. Residual gas trapping is the

second form of CO2 trapping where CO2 will reside permanently in the pore space by capillary forces,

regardless of external forces that will try to displace it. The third trapping mechanism is solution

(solubility) trapping. Solution trapping is described by the dissolution of CO2 into the in-situ fluid.

Several analytical models have attempted to model the effects of solution trapping via dissolution but

ultimately numerical modeling with full compositional simulators is needed to explain this process.

Mineral trapping is the fourth form of trapping and is considered the most permanent form of trapping.

Mineral trapping describes the reaction of CO2 with the rock and fluids to form solid materials and

permanently keeps CO2 in place. Both analytical and numerical models for mineral trapping require

additional development because of the complexity of the mineral-fluid reactions. Research is ongoing to

improve modeling the effects of mineral trapping; results are being incorporated into numerical models.

CO2-Fluid-Rock Interactions

Carbon dioxide is typically injected as a supercritical fluid, where the density is liquid-like and

the viscosity is gas-like. This state is preferred because more CO2 can be stored with a higher density

and the CO2 is easier to inject with a low viscosity. This limits the depths of injection to greater than 800

meters below the earth’s surface in order to have the desired pressure and temperature conditions for

supercritical CO2. In oil reservoirs and deep saline aquifers, CO2 will have a lower density than the in-

situ fluid, meaning that gravitational effects will need to be considered for a complete model.

Solution trapping is a CO2-fluid interaction and happens through dissolution. Dissolution occurs

over long time scales of hundreds to thousands of years and three mechanisms contribute to it; gravity

segregation and buoyancy lets CO2 contact fresh brine (or in-situ fluid), dispersion further allows

mixing, and convective mixing (Ennis-King & Peterson, 2002). During injection the dissolution of CO2

into the brine happens very slowly and the proportion of single phase CO2 and dissolved CO2 in brine

stays constant (Ennis-King & Peterson, 2002). Relative permeability, mainly residual water saturation,

will affect the proportion of CO2 that will dissolve during injection. More brine will come into contact

with CO2 due to convective mixing.

15

Four zones are defined in the reservoir during CO2 injections into an aquifer: pure CO2, brine

saturation CO2, CO2 saturated brine, and pure brine. The pure CO2 will flow upwards by gravity forces,

and the CO2 and water mixture (which is roughly 1% denser than brine) will sink, leaving pure brine to

continue to contact the pure CO2 and increasing the dissolution rate (Ennis-King & Peterson, 2002). If

the sequestration site is an open reservoir with no containing boundaries, then dissolution will be

important and will help limit the distance for plume migration.

The mineralogy of the rock that composes the storage reservoir can cause reactions with CO2.

With residual CO2 trapping, the type of rock surface that encounters CO2 will partially determine how

much CO2 will reside in the pore space. Mineral trapping describes the reactions of CO2 with rock

minerals and fluids to create solid material, or new rock material. Mineral trapping, while a very long

term process, can affect CO2 mobility (possibly injection), storage capacity, and storage security.

Plume Migration

CO2 sequestration modelers are interested in the extent of the CO2 plume migration. Structural

trapping mechanisms, such as sealing formations and faults, will prevent CO2 migration into unwanted

areas. However, there can be conduits, such as faults, spill points, or leaking wells, CO2 can use as

escape from the storage reservoir. A complete geologic description will help locate potential for CO2

leakage into unwanted areas. Predicting the plume migration distance provides a means of understanding

the potential risk of CO2 reaching potential leakage pathways. The plume migration is dependent upon

many factors including gravity over-ride, CO2-fluid and CO2-rock interactions, pressure, and physical

rock properties.

Plume migration monitoring is important during injection and post-injection. During injection,

the dominating factors that affect how CO2 migrates are relative permeability, permeability anisotropy,

capillary forces, and gravity segregation (Ennis-King & Peterson, 2002). Post-injection, when there is no

longer a lateral pressure force from the injection well, gravity segregation and establishing gravity-

capillary equilibrium begin to dominate (if not already) CO2 migration. During this time vertical

permeability and flow path barriers (faults, shales, etc.) become more important (Ennis-King &

Peterson, 2002).

Free gas migration will be limited because of dissolution and trapped residual gas (Ennis-King &

Peterson, 2002). Higher residual gas saturation will trap more CO2 in the free pore spaces.

Understanding the relative permeability, especially for imbibition, will provide insight into how much

residual gas will be trapped.

Analytical modeling efforts attempt to estimate the migration of CO2 in storage reservoirs.

Further investigation in plume migration calculations is given in the Analytical Models section below.

Pressure Influence

Pressure buildup will depend on the type of boundary condition that is present. A closed

reservoir will result in a higher pressure buildup than an open reservoir (Economides & Ehlig-

Economides, 2009). Injection of CO2 into a closed volume, which is representative of come

underground reservoirs, will cause the pressure to increase in proportion to the ratio between the

injection volume and reservoir volume. Injectivity of CO2 is limited by the pressure buildup limit of the

storage reservoir. Foremost, the fracture pressure, if exceeded, poses a risk of damaging the reservoir

seal. The fracture pressure limit should be carefully monitored. A maximum pressure limit well below

the fracture pressure should be set in a closed reservoir during CO2 injection. In a truly open reservoir,

such as those that outcrop, the pressure has a means of escape, thus the pressure buildup is considerably

16

less than a closed system. Some situations, such as large, laterally extensive reservoirs with unknown

boundaries, may be amenable to an open boundary representation.

Storage Ability and Capacity

The ability to permanently store CO2 is the most important aspect of selecting a CO2

sequestration site. Adequate space is needed to hold CO2 and proper structural or secondary traps are

needed to prevent CO2 flow into unwanted areas. Capacity estimations can be calculated using Eq. 1-1

(U.S. Department of Energy, 2010). A depth greater than 800 m is considered to be deep enough for

sequestration sites with supercritical CO2 and sufficient groundwater aquifer separation (Benson & Cole,

2008).

……………………………………………………………………..…..………. Eq. 1-1

The seal should be properly analyzed to ensure long term storage of CO2 without vertical

leakage. Two important characteristics to study in a sealing layer are capillary entry pressure

characteristics and permeability; high entry capillary pressure and low permeability are ideal sealing

properties (Ennis-King & Peterson, 2002). Analysis of faults and fractures is important because the

potential for leakage is higher near these geologic features.

1.4 Analytical Models Many analytical models developed to help address some of the unique processes with CO2 injection

share these assumptions:

Homogeneous formation properties

Isothermal properties

Immiscible and incompressible fluids

Horizontal flow

Horizontal formation

Line source injection

Other assumptions also apply, particularly certain boundary conditions, which can change

according to the specific analytical model. Overall, analytical models must be used with caution because

research has shown that gravitational forces and geological heterogeneity can dominate CO2 flow which

is best modeled with numerical simulators (Ennis-King & Peterson, 2002). Analytical models are useful

for estimations of CO2 injectivity and plume migration. Several models are described here, though many

other analytical models have also been developed. Also, analytical models for different types of storage

reservoirs (depleted oil and gas reservoirs, deep saline aquifers, coalbed methane reservoirs, etc.) may

change accordingly with fluid and rock types.

The physical properties of CO2, namely density and viscosity, in analytical models, are taken as

constants. This is generally a good approximation because they do not change significantly with

temperature and pressure at injection conditions (Figure 1). The immiscible, incompressible fluid and

homogeneous layer assumptions allow saturation profiles to be estimated by Buckley-Leverett flow

theory. Some models attempt to account for a dry-out zone and a two-phase CO2 and brine zone, which

is discussed further in Chapter 2 (Noh M. , Lake, Bryant, & Araque-Martinez, 2004).

17

Figure 1—CO2 density and viscosity at subsurface conditions, surface temperature is 15 C, 30 C/km and 10

MPa/km (Ennis-King & Peterson, 2002)

For a specified pressure buildup, the flow rate of CO2 is calculated using the multiphase flow

extension of Darcy’s flow equation

. Use of this equation requires knowing the properties of

both the fluid and the formation. Many analytical CO2 injection models are developed using a varying

form of Darcy’s flow equation (Kumar & Bryant, 2009), (Okwen, Stewart, & Cunningham, 2011).

Kumar and Bryant (2009) provides an algorithm to solve a time-dependent flow equation for CO2

injection. In this model they include the effects of a dry-out zone and dissolution during injection

(Kumar & Bryant, 2009). This algorithm can be applied to numerous equations that are not discussed in

their model; such as early transient flow, steady-state flow, and pseudo-steady state flow equations. The

equation that is used for CO2 flow is dependent on the size of the storage reservoir and the time of

injection. Okwen et al. solves the partial differential equation for pressure using Dirichlet boundary

conditions. This model is good at approximating the pressure boundary but is inefficient at including the

dry-out effect (Okwen, Stewart, & Cunningham, 2011).

Nordbotten et al. (2005) describes an analytical solution for CO2 injection into deep saline

aquifers. The model uses a simple viscous-based solution which addresses a nonzero residual saturation,

CO2 dissolution into brine, and water evaporation into the CO2 (Nordbotten, Celia, & Bachu, 2005).

Two zones are defined, a CO2 zone and brine solution. The radial influence of the system expands as a

function of t1/2

and a method for determining the advancement of the CO2 front is included in the

analytical model. The solution neglects capillary pressure, uses the Buckley-Leverett approach to two

phase front movement, and assumes vertical equilibrium. A steady-state flow equation with a moving

boundary is used to calculate the pressure buildup and plume migration for CO2. A visual description of

the system is shown in Figure 2 (Nordbotten, Celia, & Bachu, 2005). Since analytical models are not

able to directly account for gravity forces, this solution uses a stepwise approach to mimic vertical

migration of CO2.

18

Figure 2—(Left) Typical profile of CO2 region denoted by b(r,t). (Right) Piecewise approximation used to

represent the invading CO2 front. Notice that bN is constrained to equal the total formation thickness B.

(Nordbotten, Celia, & Bachu, 2005).

A second analytical solution described by Nordbotten et al. (2009), describes a case where a well

penetrates a series of layered, homogeneous aquitards, which have different rock properties (Nordbotten,

Kavetski, Celia, & Bachu, 2009). This case focuses on the pressure and buoyancy forces that govern

flow and ignores dissolution and geochemical processes. Similar to the previous analytical solution, this

model ignores capillary pressure and has two zones, a CO2-rich phase and brine.

An analytical model to estimate conditions during CO2 injection in a real reservoir should be

used with caution. Real systems will be subjected to heterogeneity in the rock properties and features.

Many analytical models assume that the reservoir is perfectly horizontal and homogeneous, which is not

the case in real reservoirs. Many formations are dipping, including the Powder River Basin formations,

which can influence CO2 plume migration due to buoyancy forces. A study by Gasda et al. analyzes the

effect of a sloping aquifer using the analytical model developed by Nordbotten et al. (Gasda, Celia, &

Nordbotten, 2006). Figure 3 shows a slightly dipping formation, where the plume migration is further on

the updip side. In large scale modeling, a sloping nature will decrease the “lateral symmetry of the

injected plume” (Gasda, Celia, & Nordbotten, 2006). A one-dimensional and two-dimensional analytical

model with a slope is compared to numerical simulation models. The conclusion of this study is that the

inclusion of a dipping formation between 0.1° and 1° is insignificant for typical conditions in North

American sedimentary basins. The centroid of the plume only moved a small fraction further than in a

horizontal aquifer over 30 years, although, the effect of highly permeable layers can exaggerate the

buoyancy forces and increase plume migration updip (Gasda, Celia, & Nordbotten, 2006). The

timeframe for this study was for 30 years of injection in slightly dipping aquifers. An increase in time of

injection, slope, and permeability will make the nonsymmetry of the plume migration greater.

Overall these models provide reasonably accurate qualitative estimates for injectivity of CO2. In

Chapter 2, a semi-analytical model is developed that takes advantage of the Kumar and Bryant (2009)

semi-analytical model and includes a layered aquifer system similar to the scenario described by

Nordbotten et al. (2009).

19

Figure 3—Cartoon depicting the CO2-brine interface, denoted by h(x,t), and the location of the centroid for a typical sloping aquifer (Gasda, Celia, & Nordbotten, 2006).

1.5 Numerical Models Using numerical models enables the ability to include gravitational effects, heterogeneity and

compressibility, unlike analytical models. Once a geologic model is built and a sequestration site is

chosen, a numerical simulator should be used to aid the decision for the potential success of CO2 storage

into a formation. Commonly used general purpose commercial interfaces and simulators that are used in

industry include (but are not limited to) PetraSim with TOUGH2, Eclipse with CO2STORE, and CMG

STARS compositional simulator. These simulators are unique and have their own advantages and

disadvantages for CO2 sequestration modeling.

The equations that govern fluid transport of p phases of c components in isothermal porous

media are conservation of mass (Eq. 1-2) and Darcy’s Law (Eq. 1-3) (Aziz & Settari, 1979).

………………………………………………………………..……...… Eq. 1-2

……………………………………………..………...………… Eq. 1-3

These equations can be manipulated to include forces and reactions that are important for CO2

sequestration and are the backbone of the codes in reservoir simulators used today.

A comparison between common simulations codes has been performed by Pruess et al. (Pruess,

et al., 2002). In this study, ten groups submitted results for eight problems using their own variation of a

numerical model. Saline aquifers, oil reservoirs and gas reservoirs were the focus of this study. Table 1

provides the codes that are used for the problems. Table 2 provides a brief description of the problems

and the results. Overall, the conclusion of this study was general agreement among the numerical model

predictions although the discrepancies in some results can be traced back to fluid property description

differences (Pruess, et al., 2002).

Another study was performed to compare the analytical results and numerical simulation results

using a modified version of TOUGH2 (Ennis-King & Peterson, 2002). In this study, agreement was

found between theory and simulation for the front location for high injection rates. Low injection rates

see the effects of gravity more strongly which analytical models cannot capture. Another conclusion is

20

that finite grid block sizes lead to an overestimation of amount of dissolved CO2; hence more

discrepancy will occur with coarser grid block sizes. It was observed that for coarse grid blocks, a

reduction of solubility up to 25% of solubility in fine grids can enhance the matching ability of

saturation distribution. Much of the discussion about dissolution, saturation, and other reactions in

previous sections is confirmed in this study. Also, this study outlines the need for more research in the

coupling of convective mixing and rock/water reactions over a long time scale (Ennis-King & Peterson,

2002).

Table 1—List of codes used in the Code Intercomparison Study (Pruess, et al., 2002).

Numerous other numerical CO2 injection studies have been performed to assess the feasibility of

CO2 injection into underground storage reservoirs. Today, analytical and numerical models are sufficient

for providing predictions of the processes involved in CO2 sequestration although much more work is

needed to improve these mathematical models. However, with so many unknowns there is an inherent

risk associated with CO2 sequestration, and more research into CO2 sequestration modeling will help

define these risks.

21

Table 2—Code intercomparison on problems and results (Pruess, et al., 2002).

Chapter 2—Semi-Analytical Modeling of Carbon Dioxide

Sequestration

Prior to spending time and effort on building a complex three-dimensional geological model and

running simulations to predict CO2 injection scenarios, the simple two-dimensional semi-analytical

model can be utilized to help gauge the feasibility of CO2 injection into the TEEP reservoirs. The semi-

analytical model presented here was originally developed by Kumar and Bryant (2009) (Kumar &

Bryant, 2009). The updated semi-analytical model developed in this chapter introduces added capability

to the approach outlined by Kumar and Bryant (2009) including the addition of layer heterogeneity in

stacked formations and a more realistic boundary condition. This model is named the SAHCO2 injection

model for “Semi-Analytical Heterogeneous CO2 injection model”.

2.1 Original Semi-Analytical Model Kumar and Bryant (2009) provides an algorithm that calculates the wellbore injection pressures

needed to inject a constant rate of CO2 (Kumar & Bryant, 2009). It also calculates the movement of a

dry-out zone and a two-phase zone. The model assumes that CO2 is incompressible, formation properties

22

are constant, gravity effects are ignored in the reservoir but are reflected in the well pressure calculation,

and assumes a small solubility of brine into supercritical CO2 which creates a dry out area near the

wellbore. It also considers dissolution of CO2 into the brine into the two-phase zone. Their study focuses

on improving trapping and reducing leakage potential by optimizing the perforation interval.

Description of the three regions of the semi-analytical model

The semi-analytical model recognizes three regions, the dry-out, two-phase, and single phase

brine regions, shown in Figure 4. When CO2 is injected into a water saturated reservoir, a two-phase

zone develops where CO2 vaporizes water into a gas phase and becomes H2O saturated CO2. Also, CO2

dissolves into the water and becomes CO2 saturated H2O. These two phases exist in equilibrium in the

two-phase zone. As CO2 is continuously injected, the CO2 will vaporize all the water near the wellbore

where the CO2 saturation will become 100%, creating the dry-out zone (Kumar, 2008). In this

representation, the reservoir boundary, , is fixed.

Figure 4—Diagram showing the three regions described in the semi-analytical models.

Pressure Treatment

An advantage of the Kumar and Bryant (2009) model is the treatment of the well pressure and

reservoir pressure. The pressure profile of the well will change as a function of depth due to the density

of CO2 and similarly in the reservoir with the brine density (Figure 5). This is important when modeling

long perforation intervals, or very thick reservoirs such as in the PRB. For a constant injection rate of

CO2, the well pressure must adjust to achieve the constant rate as time moves forward due to changes in

the reservoir by CO2. The reservoir pressure will remain constant at the boundary.

Figure 5—Pressure profile for the well and formation. In a homogenous reservoir, the injection rate will be

greatest at the top of the injection zone due to the larger pressure difference.

23

Explanation of Front Movement

The saturation front velocity of the two regions is determined by modifying Buckley-Leverett

fractional flow theory with the additional retardation factor, D (Noh M. , Lake, Bryant, & Araque-

Martinez, 2004), (Buckley & Leverett, 1942). Noh et al. explains that ignoring the dry-out zone has a

major effect on how the model will predict the injection pressure inside the wellbore (Noh M. , Lake,

Bryant, & Araque-Martinez, 2004). The D factor is determined from concentrations of dissolved CO2 in

water as well as aqueous CO2 in water. It is incorporated into the fractional flow theory by extending

the axis of the fractional flow plot shown in Figure 6. The dry-out zone velocity, , and the two-

phase zone velocity, , are defined as the slope to the tangents for the fractional flow curves extending from the D factors (Eq. 2-1 and Eq. 2-2) (Noh, Lake, & Araque-Martinez, 2007), (Burton, Kumar, &

Bryant, 2008). The dimensionless velocities are constant through the life of injection.

………………………………………………….…….. Eq. 2-1

……………………………………….………………… Eq. 2-2

Figure 6—Fractional flow diagram with the inclusion of the D factors (Burton, Kumar, & Bryant, 2008)

Semi-Analytical Model Assumptions and Parameters

The following lists outline the semi-analytical model assumptions and the parameters that must

be supplied. Most of the assumptions and parameters are the same for the original model and updated

model that is explained in later sections.

Model Assumptions

Slightly compressible fluid

are independent of pressure fluctuations Uniform layer properties

One dimensional horizontal flow

Well fully penetrates and is perforated in the entire thickness

Boundary conditions

24

o Constant pressure boundary o Line source o Constant injection rate Q

Model Parameters

Reservoir pressure at the top of the perforations, Relative Permeability Parameters (Brooks-Corey Correlations), , ,

Irreducible water saturation, Retardation factors, ,

Depth to top of perforation, Thickness of perforations and formations, Layer permeability, Layer porosity, Fluid densities, and

Fluid viscosities, and

Target total flow rate, Reservoir radius,

The Algorithm Proposed in the Original Semi-Analytical Model

The algorithm used to calculate the well injection pressure for the original semi-analytical model

is provided here. The same algorithm process is used in the updated semi-analytical model explained in

later sections.

Semi-Analytical Model Algorithm

1. Assume an initial well pressure at the top of the perforations, , greater than the reservoir pressure at the top of the perforations, .

2. Calculate the pressure profiles with Eq. 2-3 through Eq. 2-5.

………………………………………………………….……..… Eq. 2-3

…………………………………………………………..…….…… Eq. 2-4

…………………………………….……...……………………….…. Eq. 2-5

3. Calculate the average mobility, .

a. During initial injection the average mobility is equal to the brine mobility, . b. After initial injection, the next time steps use Eq. 2-6 through Eq. 2-9.

…………...…………..……..… Eq. 2-6

.…………………….………………………………………. Eq. 2-7

25

…………………………………………………..………….…. Eq. 2-8

………………………………………...………………………….…….. Eq. 2-9

4. Calculate the total flow rate by summing the steady-state flow equation for the layers, Eq. 2-10 and Eq. 2-11.

……………………..…………..…………..…… Eq. 2-10

……………………………………….………………..……….……… Eq. 2-11

a. If then change and repeat steps 1 through 4.

b. If , increase

c. If , decrease

5. When , a solution has been achieved.

In the original model, the advancement of the solution through time uses the following equations

(Eq. 2-12 through Eq. 2-24) to find the radius of the different regions. This is where the D factor is

introduced into the model (Kumar & Bryant, 2009).

…………………….…………………………………………………. Eq. 2-12

…………………………………….……………...……………. Eq. 2-13

…………………………………………………….…………..…. Eq. 2-14

………………………………………………………..………………….………… Eq. 2-15

….……………………………………………..………….………….. Eq. 2-16

………………………………………………………….…..………….. Eq. 2-17

……………………………………………………………….…………..…………. Eq. 2-18

………………………………………...……………………….....…………… Eq. 2-19

……………………………………….………… Eq. 2-20

…………………………………………………….……………………………. Eq. 2-21

……………………………………………………….…..…….…………………. Eq. 2-22

26

………………………………..…………………….………………………... Eq. 2-23

…………………………………………………….…….…………………. Eq. 2-24

2.2 Semi-Analytical Heterogeneous CO2 (SAHCO2) Injection Model

The algorithm presented here is based on the semi-analytical model from Kumar and Bryant

(2009) The changes in assumptions and equations make this an “extended semi-analytical model.” The

model developed by Kumar and Bryant (2009) is limited to a single homogeneous reservoir with a

constant pressure boundary at a fixed reservoir radius. In most locations, and in particular for the PRB

setting, these assumptions are too limited. The SAHCO2 injection model addresses these issues.

SAHCO2 Injection Model Improvements

Improvements to the model are as follows. First, the boundary of the reservoir is infinite and the

constant pressure boundary, , expands as a function of time. Second, the early transient flow equation is used and assumed applicable to CO2 injection. In the original model, the initialization of the model

uses the steady state flow equation and is dependent on a defined reservoir radius. Now that the constant

pressure boundary is a function of time, this equation is not suitable. The early transient flow equation is

useful because it does not depend on the reservoir radius and is applicable to initial flow rates in a

reservoir. Lastly, heterogeneity between layers is included in the model, where the injection zone now

looks like Figure 7.

An appropriate situation where this model will work well is in highly stratified rock formations

with interbedded shale or very low permeable layers. The layers would be thin enough where gravity

forces would not be a large influence on vertical migration of the CO2 plume.

Figure 7—Schematic showing the heterogeneous layers and arrows indicate potential amount of CO2

injection in the layer.

27

Well Pressure Initialization

The initial well pressure is calculated and the flow rates in each layer are determined. This

solution requires the early transient flow equation because there is a change in flow rate (from zero to a

constant rate) around the well and the pressure needs to begin to propagate into the reservoir. Initially,

the reservoir is brine-saturated so the mobility is provided by brine mobility in Eq. 2-7. The process is

iterative and the algorithm is provided by steps 1 through 4, which are similar to the algorithm provided

in the original semi-analytical model (Kumar & Bryant, 2009).

Initialization Algorithm:

1. Assume an initial well pressure at the top of the perforations, , greater than the reservoir pressure at the top of the perforations, .

2. Calculate the pressure profiles with Eq. 2-3 through Eq. 2-5. 3. Calculate the total flow rate using the early transient flow equation at a small time step

using Eq. 2-25 and Eq. 2-11.

………………………………..……….…………………… Eq. 2-25

If then change and repeat steps 1 through 4.

o If , increase

o If , decrease

Note: A convergence value of 1.0% error is used for the updated semi-analytical model.

4. When , a solution has been achieved.

Well Pressure at time t

This section describes the process to determine the well pressure as a function of time. The

reservoir boundary, or pressure influence radius, grows with time. The semi-log approximation of the

flow equations is used to calculate the effective radius of the pressure buildup zone (Eq. 2-26). The

derivation of Eq. 2-26 is from the Theis solution and the full derivation is shown in Appendix 1 (Theis,

1935).

.......................................................................................................................... Eq. 2-26

The fronts move according to the amount of CO2 injected up to time, t, and is determined by

mass balance and the front dimensionless velocity relationships, which accounts for mutual solubility

(Burton, Kumar, & Bryant, 2008). The dry-out zone and two-phase zone radii are determined by Eq. 2-

27 and Eq. 2-28. The derivation is provided in Appendix 2. This addresses the third assumption.

…………………………….…………..…….. Eq. 2-27

……………………………….……...……..… Eq. 2-28

28

The algorithm in steps 1-4 from the initialization process is followed to determine the well

pressure. However, the flow equation has changed. Since the assumption is an infinite radial extent

( ) the steady-state flow equation is appropriate and provided in Eq. 2-10.These steps can be repeated for as many time values as desired.

2.3 Simple Example Results Comparing the Semi-Analytical and a Comparable TOUGH2/ECO2N Simulation Model

The SAHCO2 injection model is verified with a numerical solution using TOUGH2/ECO2N.

The pressure buildup estimation and front movements have been compared to results of a simple radial

model and provide confidence that the updated semi-analytical is appropriate for the conditions of the

aquifer.

Example Problem Conditions

The example problem was kept very simple so the solutions for both models are easily

compared. Table 3 provides the input parameters for the models. Figure 8 shows the relative

permeability of the CO2-brine system used in the two models.

The D-factor for the dry-out zone reported in Burton et al. did not match simulation results so a

different approach at approximating these values was used (Burton, Kumar, & Bryant, 2008). Eq. 2-29

and Eq. 2-30 use a simplified approach assuming a 5% CO2 mass solubility in water to approximate the

D-factors; however, the dry-out zone D-factor was still too high causing the dry-out zone radius to

increase much faster than simulation results. A trial and error approach was used to determine an

appropriate value for the dry-out zone D-factor.

…………………………………………….……………………….…… Eq. 2-29

……………………………………….………………….……………..… Eq. 2-30

Figure 8—Relative permeability of CO2 and brine used in the updated semi-analytical model and

numerical TOUGH2/ECO2N model.

29

Table 3—Input Parameters for the SAHCO2 injection model and TOUGH2/ECO2N.

Verification Results

The well pressure calculated by the SAHCO2 injection model is compared to the well block

pressure from the simulation model. Table 4 shows the percent difference and percent error for the well

pressures at each time step and the pressure buildup from the initial pressure. By comparing the

individual pressures at each time step, the percent difference is just over 1% for all time steps. The

pressure buildup, which is the current pressure less the initial pressure, ranges between 5% and 8%. A

reasonable comparison between the two models is concluded based on these results, particularly in light

of the many simplifying assumptions in the SAHCO2 injection model.

The pressure influence radius is compared graphically in Figure 9 and Figure 10. In Figure 9,

the dots represent the location of the reservoir radius from the semi-analytical model, calculated by Eq.

2-26. It may seem by this scale that the two models are not comparable; however, when the data is

represented on a different scale in Figure 10, the linear portion of the simulation data can be

extrapolated to the initial pressure and the two models indeed compare reasonably well. The pressure

tail that is present in the simulation model is the result of the compressibility of the formation and pore-

filling fluids. The pressure tail is expected based on the fully transient form of the Theis solution.

30

Table 4—Pressure buildup comparison between the SAHCO2 and simulation model.

Figure 9—Reservoir pressure distribution in the aquifer compared to the pressure influence radius

calculated by the SAHCO2 injection model.

Time (years)

Semi-Analytical Well

Pressure (Pa)

Simulation Well Block

Pressure (Pa)

Pressure Difference

(Pa)

Average Pressure of

Models (Pa) % difference % error

Initial 16033366 15811214 222152 15922290 1.40% 1.41%

1 16682706 16512509 170197 16597607 1.03% 1.03%

10 16721934 16539006 182928 16630470 1.10% 1.11%

25 16737667 16553780 183887 16645723 1.10% 1.11%

50 16749556 16565804 183752 16657680 1.10% 1.11%

Time (years)

Semi-Analytical Model

Pressure Buildup from

Initial (Pa)

Simulation Model

Pressure Buildup from

Initial (Pa)

Pressure Buildup

Difference (Pa)

Average Pressure

Buildup of Models (Pa) % difference % error

1 649340 701295 51955 675318 7.69% 7.41%

10 688568 727792 39224 708180 5.54% 5.39%

25 704301 742566 38265 723433 5.29% 5.15%

50 716190 754590 38400 735390 5.22% 5.09%

31

Figure 10—Reservoir pressure on a semi-log axis showing how the extrapolation of the linear portion to the

initial pressure compares to the SAHCO2 pressure influence radius.

The front movement of the dry-out zone and two-phase zone for both models is shown in Figure

11. A visual comparison of the results shows that the dry-out zone agrees reasonably well between the

two models. The two-phase zone radius of the SAHCO2 injection model lags behind the simulation

results, although the lag is due to the treatment of two-phase flow between the two models, where the

SAHCO2 injection model assumes Buckley-Leveret saturation treatment.

Figure 11—Saturation front comparison between the SAHCO2 and simulation model.

32

Chapter 3—Powder River Basin Geological Description

3.1 Powder River Basin (PRB) CCS Opportunities Seven major geological basins are present in Wyoming, including the PRB, shown in Figure 12

(De Bruin, 2001). Within this basin, many stationary CO2 emitting sources, enhanced oil recovery

(EOR) projects using CO2, and potential geological storage formations are present, providing an

opportunity for better management of CO2 emissions into the atmosphere. The main CO2 sources in the

PRB are from electricity generating power plants and petroleum and natural gas processing (Figure 13)

(BSCSP, 2010). Potentially, the EOR projects and geologic storage formations will use the captured

CO2 from the stationary CO2 sources for improving oil recovery and for CO2 sequestration. The

geologic CO2 storage opportunities include depleted oil fields, deep unmineable coal seams, deep saline

aquifers, and mafic volcanic formations (BSCSP, 2010). The simulation study focuses on CO2 storage in

a deep saline aquifer of the PRB as part of the Two Elk Energy Park (TEEP) project developed by the

North American Power Group, Ltd. (North American Power Group, Ltd).

Figure 12—The major geologic basins in Wyoming with locations of major oil fields and enhanced oil

recovery operations using CO2 (De Bruin, 2001).

33

Figure 13—CO2 emission sources locations for the northwest area of the United States (BSCSP, 2010).

3.2 Powder River Basin Geology The Powder River Basin, formed during the Laramide orogeny, is located in southeastern

Montana and northeastern Wyoming and is approximately 400 km long and 160 km wide (Robertson,

2008). The basin covers approximately 88,000 km2. The Bighorn Mountains bound the PRB in the west,

the Hartville uplift in the southeast, the Casper-Arch-Laramie Range in the southwest, the Black Hills in

the east, and Miles City arch in the northeast.

Figure 14 provides an East-West cross section of the PRB. The PRB is an asymmetric, synclinal,

structural basin with its axis on the western side in the NW-SE direction; the eastern flank dips to the

east at roughly 20-25° (Ross, Hagin, & Zoback, 2009). In the central region, particularly in the TEEP

site area, the basin dips less than 2° to the southwest. TEEP is located in the eastern vicinity of Figure

14 where the basin dip is smaller.

Faulting in the region has been mapped in the eastern margin and basement reverse faults have

been recorded in the western and southern edges (Ross, Hagin, & Zoback, 2009). The central region

including the TEEP site is not known to have significant faulting (Ross, Hagin, & Zoback, 2009). The

uncomplicated structural geology in the PRB makes the region a desirable location for carbon

34

sequestration. The deep saline aquifers that are part of this study are Lower Cretaceous and Paleozoic in

age.

The aquifer water for the deep saline aquifers is recharged from the Black Hills uplift area in the

East (McPherson & Cole, 2000). A thermal analysis of the PRB region using bottom-hole temperature

logs yielded an average geothermal gradient of 29°C/km and a corrected plot of temperature versus

depth is given in Figure 15 (McPherson & Chapman, 1996). A detailed stratigraphic column for the

PRB is provided in Figure 16, where both the east and west areas of the PRB are described.

Figure 14—East-West cross section of the PRB (Anna, 2009).

Figure 15—Corrected bottom-hole temperature measurements for the southern PRB (McPherson &

Chapman, 1996).

35

Figure 16—PRB stratigraphic map showing both the east and west locations (Dolton & Fox).

36

3.3 Two Elk Energy Park (TEEP) Geologic Units for Carbon Sequestration

The geologic characterization of the four distinct formations in the TEEP study area is based on

literature and on data from two wells that penetrate the formations of interest (Calvo, 2011). Rudesill

w—10 well is located 10 km to the south and Rattlesnake—1 well is 40 km northwest of the proposed

TEEP site, shown in Figure 17. The sedimentary units identified for potential CO2 sequestration are

divided into four sections, each one having its own sealing unit. A stratigraphic cross section is provided

in Figure 18 and identifies the four distinct reservoir/sealing units (Calvo, 2011).

Figure 17—Diagram of well locations relative to the TEEP well site in the geologic model used for the

simulation study.

Minnelusa-Madison/Goose Egg

The Minnelusa formation, created in the Paleozoic era, is part of an alternating deep marine,

shallow shelf, and lagoon sedimentary sequence. The sedimentary units are composed of anhydrite,

dolomite, shale, and sandstone. The Minnelusa is 256 m thick with 40% net sand, 8% log-porosity, and

an estimated average permeability of 7 mD. The Madison limestone formation lies below the Minnelusa

and has similar properties to the Minnelusa.

The Goose Egg formation is the sealing structure for the Minnelusa, consisting of eight units

including the Opeche and Minnekahta formations. At 114 m thick, it is composed mainly of marine

shale, halite, and dolomite and was formed in a shallow marine environment during the late Permian and

early Triassic times. The average permeability of these sediments is estimated to be 0.01 mD and have

very low porosity.

Spearfish-Hulett/Sundance

Above the sealing Goose Egg formation is the Spearfish formation which is 138 m thick at the

TEEP site. This formation is characterized by alternating shale and sandstone formations with about

30% net sandstone. The sandstone layers are about 2 m thick and the shale layers are up to 6 m with two

thicker layers at 15 and 30 m. The average permeability is 7 mD and porosity is 7%.

In the late Triassic time a large uplift occurred, creating an unconformity, followed by three

transgression-regression sea cycles that deposited the Hulett and Sundance formation. The Hulett

16 km1

6 k

m

40 km

40

km

Geological Model Area

37

formation is 62 m thick with 65% net sandstone. This formation is mainly repeated sandstone and shale

layers. The estimated average horizontal permeability is 105 mD and porosity is 15%.

The Sundance formation acts as the sealing unit for the Spearfish and Hulett formations. It is 19

m of 90% marine shale, has an estimated permeability of 0.01 mD and very low porosity.

Figure 18—Stratigraphic cross section of the PRB showing four distinct reservoir/seal units (Calvo, 2011).

Morrison-Lakota/Fuson

The Morrison formation located above the Sundance formation is a terrestrial depositional

environment. The formation is not homogeneous laterally. In the TEEP study area the Morrison

formation is 39 m thick with 49% net sandstone. The estimated average permeability is 20 mD and log-

porosity average is 10%.

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The Lakota formation is 37 m of more than 92% sandstone. The Lakota has the same average

rock properties as the Morrison.

The Fuson formation, located between the Lakota and Dakota formations, is the main sealing

unit for the Morrison-Lakota reservoir. This formation is 12 m of marine shale and was formed during

the mid-Cretaceous time when a large seaway covered the area and marine shale was deposited in the

deep basin (Fuson, Skull, Mowry, and Niobrara formations). During the regression periods, deltaic

sandstones were deposited in the basin (Dakota, Muddy, Frontier, and Mesaverde and Lance

formations). The estimated average permeability is 0.01 mD and very low porosity.

Dakota Reservoir

The Dakota formation, a lower clastic unit, was deposited during the regression periods of the

mid-Cretaceous seaway. This is the main alternating sandstone-shale structure for this reservoir and is

11 m thick with 64% net sandstone. The average permeability is 80 mD and log-porosity is 12%.

The sealing units above the Dakota formation are a total of 1,500 m thick consisting of mostly

shale units. These units include the Skull, Muddy, Mowry, Carlile, Turner, Niobrara, Sussex, Teapot and

Lewis formations.

The four reservoirs and their sealing units are of current interest for the TEEP study. Table 5

provides a summary of the layer properties discussed above. The 1,500 m sealing units above the Dakota

formation are believed to be capable of preventing CO2 from escaping vertically for the foreseeable

future. No known sealing units or geologic structures are present to prevent lateral CO2 migration. As

part of the TEEP study, the trapping of CO2 will be analyzed to evaluate the extent of lateral migration

for risks this poses to drinking water or for atmospheric release of CO2.

3.4 Reservoir Data Reservoir information for the formation of interest is not readily available. Well log correlations

are from wells far from TEEP (Figure 17). Information given here is used in Chapter 4 for the semi-

analytical model.

Layer properties for the four reservoir/seal units are provided in Table 5 and are obtained from

the geological description and log analysis (Calvo, 2011). Layer permeability is estimated from Figure

19 using the log porosity for each layer (Butsch, 2011). Figure 19 is used for all the formations to

determine an estimated permeability due to the lack of data. The reservoir pressure is assumed to be at

hydrostatic pressure. The formation compressibility is calculated as

using Eq. 3-1 for

consolidated limestone and Eq. 3-2 for consolidated sandstone (Horne, 1995). The average between the

two compressibility values is used since the formations consist of a mix of limestone and sandstone.

…………………...…………………….…… Eq. 3-1

…………………...………………….…..….. Eq. 3-2

The target CO2 injection rate for TEEP is 3 Mt per year for 50 years. Capacity estimations for the

four reservoir/seal units are provided in Table 5, where the total CO2 capacity is 0.393 Mt/km2. For a 16

by 16 km region, the total estimated capacity is 101 Mt. Based on this estimation, the formations would

not be able to hold the 150 Mt; however, the large uncertainties and limits on reservoir data allows for a

large error range in the capacity estimation.

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Table 5—Layer properties from well log analysis including capacity calculations (Calvo, 2011).

Figure 19—Log porosity versus permeability cross plot from the Minnelusa formation (Butsch, 2011).

3.5 Petrel Static Geologic Model Description A “first-pass” static geologic model was created in Petrel 2010.2 using correlations between well

logs, in