copyright by pooneh hosseininoosheri 2019

Copyright

by

Pooneh Hosseininoosheri

2019

The Dissertation Committee for Pooneh Hosseininoosheri

Certifies that this is the approved version of the following dissertation:

CO2 Trapping Mechanisms Assessment Using Numerical and Analytical

Methods

Committee:

Larry W. Lake, Supervisor

Charles J. Werth, Co-Supervisor

Kamy Sepehrnoori

Polina Sela

Seyyed Abolfazl Hosseini


Methods

by

Pooneh Hosseininoosheri

Dissertation

Presented to the Faculty of the Graduate School of

The University of Texas at Austin

in Partial Fulfillment

of the Requirements

for the Degree of

Doctor of Philosophy

The University of Texas at Austin

December 2019

Dedication

To my beloved husband, Hamed, for his continuous love and support

To my lovely parents, Leyla and Hassan

And to my dear sister, Parisa

v

Acknowledgments

This research would not have been possible without the support of several

individuals who provided valuable assistance and advice throughout this study. First, I

would like to express my profound gratitude to my supervising professor, Dr. Larry Lake,

for his guidance, inspiration, support, and encouragement. He provided me with the

knowledge, support, and invaluable insights I needed to make graduate school a fulfilling

experience. I am privileged to have had an opportunity to be his student because he is not

only an amazing supervisor but also an amazing person.

I greatly appreciate Dr. Seyyed Abolfazl Hosseini, who was a mentor for me to get

through the challenges that came up in each step of the work. He is one of the most positive

and patient people I know. I feel so fortunate to have him as a mentor. I am thankful to Dr.

Charles Werth, my co-supervisor, for his continuous support and advice. I am grateful to

Dr. Kamy Sepehrnoori for his advice. I had the opportunity to be his student during my

Master’s study and he has actually built my graduate understanding. I am also thankful to

Dr. Lina Sela Perelman for her support, time, and advice. I am so fortunate to have her as

one of my role models.

Many thanks to people at Gulf Coast Carbon Center (GCCC). To Vanessa Nunez-

Lopez for her patience, guidance, and support. Vanessa’s constant encouragement and

support made this dissertation possible. To Dr. Susan Hovarka for exemplifying academic

vi

leadership. To Dr. Jean-Philippe Nicot whose professionalism and hard work is so

inspiring. To Ramon Trevino for providing advice.

I sincerely appreciate the financial support provided by National Energy

Technology Laboratory (NETL), a USA national laboratory under the Department of

Energy (DOE), under award numbers DE-FE0024433 and DEFC26-05NT42590. I also

thank and acknowledge the Gulf Coast Carbon Center of Bureau of Economic Geology at

The University of Texas at Austin for the cost sharing support.

I would like to thank the staff of Bureau of Economic Geology, Civil Architectural

and Environmental Engineering department, and Hildebrand Department of Petroleum and

Geosystem Engineering.

Special thanks to my friends, Dr. Maryam Mirabolghasemi, Mehran Mehrabi,

Alireza Sanaei, Dr. Ali Abouie, Dr. Reza Ganjedanesh, Dr. Bo Ren, Dr. Ali Goudarzi, Dr.

Hamid R. Lashgari, Dr. Mahdi Haddad, Dr. Shayan Tavassoli, Prasanna Krishnamurthy,

Dr. Reynaldi Fifariz, Dr. Ye Feng, Masoud Behzadi, Dr. Mohammad Lotfollahi, Emily

Beckham, Izaak Ruiz, Omar Ramirez Garcia, Fabio Bordeaux, Esmail Eltahan, and Sajjad

S. Neshat, for sharing ideas, laughs, and food.

Last but not least, I am thankful to my husband, Hamed, for his endless love and

support throughout my study. I am also indebted to my family without whom none of this

would have been possible.

vii


Methods

Pooneh Hosseininoosheri, Ph.D.

The University of Texas at Austin, 2019

Supervisor: Larry W. Lake

Co-Supervisor: Charles J. Werth

Carbon capture and storage (CCS) is a proven technique for reducing greenhouse

gas emissions and climate change. Although monitoring shows that CO2 can be safely

stored underground, CO2 leakage is still of concern. Therefore, understanding and

forecasting the CO2 distribution over a geological time is necessary to assess the storage

performance and related risks. To understand the CO2 distribution during or/and after a

CCS process, four main trapping mechanisms have been introduced: stratigraphic

(structural) trapping, residual trapping, solubility trapping, and mineral trapping. The

relative contribution of each mechanism in CO2 sequestration is expected to change over

time as CO2 migrates and reacts with formation rock and fluids. Although structural

trapping is the most active trapping mechanism after CO2 injection, some of the structurally

trapped CO2 dissolves into water with the rest becoming residual over time. Both the

viii

residual and dissolved CO2 then react with rock and trap some of the CO2, the process of

which is recognized as part of mineral trapping.

The relative contribution of different trapping mechanisms depends on different

parameters, such as the type of geologic sink (i.e., saline aquifers, hydrocarbon reservoirs),

and the properties of the reservoir fluids contained. Additionally, in the case of CO2-

EOR/storage the importance of different trapping mechanisms may change depending on

the CO2 injection strategy (e.g., water alternating gas, WAG; continuous gas injection,

CGI; water curtain injection, WCI). In this dissertation, I investigate the CO2 trapping

mechanisms in two CCS processes: CO2-EOR/storage and CO2 injection in dipping

aquifers.

First, I investigate the CO2 trapping mechanisms during and after a CO2-EOR

process using reservoir simulation. The main purpose is to answer questions associated

with the relationship between EOR operational strategies and CO2 utilization ratios, and to

understand the impact of the different CO2 trapping mechanisms on this relationship. To

answer these questions, I integrate three main elements of field assessment: physical field

characterization, production and pressure history, and reservoir simulation. I use this

method to model and compare two fields that represent two different reservoir settings:

Cranfield (representative of the U.S. Gulf Coast sandstone reservoirs) and SACROC

(representative of the Permian Basin carbonate reservoirs). CGI is the original operating

strategy in Cranfield and WAG is the original operating strategy applied in the SACROC

unit.

ix

Second, I investigate the impact of relative permeability on the trapping

mechanisms in a CO2-EOR process using fractional flow analysis and reservoir simulation.

I use the fractional flow theory for miscible displacement to analytically and graphically

analyze the distribution of CO2 trappings. I use the Cranfield model to show the impact of

relative permeability on field predictions. I discuss the relative permeability impact on four

different CO2 injection schemes: continuous gas injection (CGI), water alternating gas

injection (WAG), water curtain injection (WCI), and WCI+WAG.

Third, I introduce a mathematical model, derived from force balance, to predict

CO2 plume migration in dipping aquifers. This model calculates the down and up-dip

extension of CO2 plume in the absence of trapping mechanisms. The force balance shows

that there is a point in the down-dip flow where buoyancy and viscous forces are equal and

the plume cannot extend further. However, in the up-dip flow, where the direction of

viscous and buoyancy forces are the same, the plume migrates upward for an unlimited

time.

I validate the mathematical model against numerical simulation results. I introduce

an effective relative permeability correlation to capture the competition between water and

CO2. I adjust the permeability of the aquifer to validate the mathematical model against

heterogeneous cases. The results show that the heterogeneity-induced error is small if we

use the near well-bore average permeability. I also investigate the effect of local capillary

trapping on the plume shape. Using numerical simulation, I apply capillary trapping and

show how capillary forces prevent the buoyant CO2 from migrating up-dip.

x

Table of Contents

Acknowledgments ...................................................................................................... v

List of Tables .......................................................................................................... xiii

List of Figures ......................................................................................................... xiv

Chapter 1: Introduction .............................................................................................. 1

1.1 Problem Description ......................................................................... 1

1.2 Research Objectives ......................................................................... 2

1.3 Description of chapters ..................................................................... 3

Chapter 2: Background and Literature Review ........................................................... 5

2.1 Effect of CO2 Emission on the Environment ..................................... 5

2.2 Geological Carbon Capture and Storage (CCS) ................................ 7

2.3 CO2 Storage in Saline Aquifers ........................................................ 9

2.4 CO2-EOR/Storage .......................................................................... 10

2.4.1 Miscibility ........................................................................... 10

2.4.2 CO2 Injection Schemes for EOR/Storage ............................. 12

2.4.3 EOR vs. CCS ....................................................................... 15

2.4.4 Validity of CO2-EOR for Storage ........................................ 16

2.5 CO2 Trapping Mechanisms ............................................................. 17

2.6 Monitoring ..................................................................................... 21

2.7 Summary ........................................................................................ 22

Chapter 3: Modeling of CO2 Trapping in CO2-EOR/Storage Processes Using a

Conventional Reservoir Simulation ......................................................... 23

3.1 Introduction .................................................................................... 24

3.2 Simulator ........................................................................................ 25

3.3 Modeling Method and Description ................................................. 25

3.4 Modeling of Trapping Mechanisms ................................................ 27

3.4.1 Solubility Trapping .............................................................. 27

3.4.2 Residual Trapping ............................................................... 28

3.4.3 Mineral Trapping ................................................................. 29

xi

3.5 Trapping Calculations .................................................................... 32

3.6 Case Studies ................................................................................... 33

3.6.1 SACROC............................................................................. 34

3.6.2 Cranfield ............................................................................. 65

3.6.3 Comparison of SACROC and Cranfield ............................... 72

3.7 Summary and Conclusions ............................................................. 77

Chapter 4: CO2 Trapping Modeling in CO2-EOR/Storage Processes Using Fractional

Flow Analysis ......................................................................................... 79

4.1 Introduction .................................................................................... 80

4.2 The Method of Characteristics ........................................................ 81

4.3 The Concept of Coherence ............................................................. 82

4.4 Fractional Flow Application for Trapping Mechanisms .................. 82

4.5 Trappings sensitivity to relative permeability parameters ................ 87

4.5.1 Modified Brooks and Corey’s Model ................................... 87

4.5.2 Case Studies ........................................................................ 89

4.5.3 Sensitivity Analysis ............................................................. 95

4.6 Summary and Conclusions ........................................................... 101

Chapter 5: Relative Permeability Uncertainty Effect on CO2-EOR/Storage (Cranfield

Case Study) ........................................................................................... 103

5.1 Introduction .................................................................................. 104

5.2 Method ......................................................................................... 104

5.3 Measured CO2/water Relative Permeability .................................. 105

5.4 Two Sets of CO2/water Relative Permeability ............................... 106

5.5 The Effect on EOR/Storage Performance...................................... 107

5.5.1 Oil Recovery Factor........................................................... 108

5.5.2 Cumulative CO2 Storage .................................................... 109

5.5.3 Net and Gross Utilization Ratios ........................................ 110

5.6 The Effect on CO2 Trapping Contributions ................................... 114


xii

Chapter 6: CO2 Plume Migration in a Dipping Aquifer ........................................... 119

6.1 Introduction .................................................................................. 120

6.2 Mathematical Model ..................................................................... 123

6.3 Validation against Numerical Simulation ...................................... 128

6.4 Relative Permeability Effect ......................................................... 134

6.5 Lateral Heterogeneity Effect ......................................................... 136

6.6 Local Capillary Trapping .............................................................. 141


Chapter 7: Summary, Conclusions, and Recommendations..................................... 144


7.2 Recommendations ........................................................................ 148

Appendix A1 .......................................................................................................... 149

Appendix A2 .......................................................................................................... 157

Appendix A3 .......................................................................................................... 167

References ............................................................................................................. 174

xiii

List of Tables

Table 2.1 – Comparison between local capillary trapping and residual gas trapping (Ren,

2017). .................................................................................................................... 21

Table 3.1 - Mineral properties of the SACROC unit (Han et al., 2010) .......................... 31

Table 3.2 – Initial brine concentration. .......................................................................... 31

Table 3.3 - SACROC redevelopment projects 1996–2014 (Ghahfarokhi et al., 2016) .... 38

Table 3.4 – Brooks and Corey’s function parameters for liquid-gas relative permeability

curve. .................................................................................................................... 44

Table 4.1 - Corey’s parameters for the relative permeability of two designed cases. ...... 90

Table 4.2 - Required parameters for fractional flow calculation assumed to be the same

for all cases. ........................................................................................................... 91

Table 4.3 - Trapping mechanism calculation for cases 1 and 2. ...................................... 95

Table 6.1 - Basic fluid properties used for the base model. .......................................... 128

Table 6.2 - Designed cases with different dipping angle, injection rate, permeability,

thickness, and Corey's function parameters for relative permeability. ................... 129

Table 6.3 - MBC parameters for base relative permeability in Figure 6.7 and Figure 6.5.

............................................................................................................................ 135

xiv

List of Figures

Figure 2.1 - Globally averaged combined land and ocean surface temperature anomaly

(IPCC, 2014). .......................................................................................................... 6

Figure 2.2 - Globally averaged GHG concentrations (IPCC, 2014). ................................. 6

Figure 2.3 - Overview of CCS options (IPCC, 2005). ...................................................... 8

Figure 2.4 - Illustration of different sections of a typical CCS operation. ......................... 8

Figure 2.5 – A schematic of the vaporizing and condensing processes that result in multi-

contact miscibility (Verma, 2015). ......................................................................... 12

Figure 2.6 – A schematic of continuous CO2 injection scheme

(https://slideplayer.com/slide/5785915/). ............................................................... 13

Figure 2.7 – A schematic of water alternating gas injection scheme

(https://phys.org/news/2017-04-analysis-co2-sequestration-oil-recovery.html). ..... 14

Figure 2.8 – A schematic of water curtain injection scheme. .......................................... 15

Figure 2.9 - CO2 trapping mechanisms in a CCS process (Hosseininoosheri et al.,

2018(b)). ................................................................................................................ 18

Figure 2.10 - Contribution and relation of different CO2 trapping mechanisms over time.

.............................................................................................................................. 19

Figure 3.1 – A summary of our field assessment approach for SACROC and Cranfield. 26

Figure 3.2 – SACROC CO2 flood redevelopment project areas (Ghahfarokhi et al., 2016).

.............................................................................................................................. 39

xv

Figure 3.3 – Aerial view of Petrel model for the SACROC unit. (a) The colored points are

more than 2000 vertically drilled wells in the field. (b) Permeability model for the

Northern Platform and 19 wells in the study area. .................................................. 40

Figure 3.4 - Reservoir model showing formation depth and well locations (reservoir

depth varies from 3,778 to 4,612 ft). ...................................................................... 41

Figure 3.5 – Composition (mole %) of the reservoir fluid. ............................................. 42

Figure 3.6 - Water-oil relative permeability curves based on core data. .......................... 43

Figure 3.7 – History matching of average reservoir pressure. ......................................... 45

Figure 3.8- History matching of oil, gas, and water production within the study area. .... 46

Figure 3.9 - Water and CO2 injection rate in WAG scenario. ......................................... 47

Figure 3.10 - CO2 injection rate for different field development strategies. .................... 48

Figure 3.11 - Estimated total CO2 with and without hysteresis effect. ............................ 50

Figure 3.12 – Residual gas saturation distribution on 06/01/1995. ................................. 50

Figure 3.13 - The calculated amount of CO2 in the gas phase based on density and

supercritical methods. ............................................................................................ 52

Figure 3.14 – Net utilization factor for a large set of CO2-EOR projects (Lake et al.,

2018). .................................................................................................................... 54

Figure 3.15 - Evolution of gross and net CO2 utilization ratio for different field

development strategies during CO2 injection time. ................................................. 55

Figure 3.16 - Net amount of stored CO2 by the end of 2010. .......................................... 57

Figure 3.17 – CO2 retention/storage of a large set of CO2-EOR projects (Lake et al.,

2018). .................................................................................................................... 58

xvi

Figure 3.18 – CO2 storage versus HCPV/PV injected CO2. ............................................ 58

Figure 3.19 - CO2 stored by different trapping mechanisms at the end of the CO2–EOR

operation (12/2010). .............................................................................................. 59

Figure 3.20 - Contribution of different CO2 trapping mechanism during injection and

observation period in the WAG scenario. ............................................................... 62

Figure 3.21 - Contribution of different CO2 trapping mechanism during injection and

observation period in the CGI scenario. ................................................................. 62

Figure 3.22 - Cumulative volume of produced oil from 1983 to 2010 for different

scenarios. ............................................................................................................... 63

Figure 3.23 – Oil recovery factor versus injected CO2. .................................................. 64

Figure 3.24 - Structural contour map at Cranfield: (a) the black dashed line represents the

sealing fault that divides the productive zone into two compartments. (b) the

simulation model focuses on the smaller zone (north eastern) the reservoir so the rest

of the model is inactive to reduce the computational cost (Hosseini et al., 2018;

Hosseininoosheri et al., 2018 (c)). .......................................................................... 68

Figure 3.25 - Reservoir model showing formation depth and well locations. .................. 68

Figure 3.26 – Relative permeability curves used in Cranfield case study (Hosseini et al.

(2018))................................................................................................................... 69

Figure 3.27- Historical injection, production, and pressure data before starting the CO2-

EOR operation (Hosseini et al., 2018) .................................................................... 70

Figure 3.28- CO2 injection rate in WAG and CGI scenarios........................................... 71

xvii

Figure 3.29 - Contribution of different CO2 trapping mechanisms in post-injection period

for Cranfield. ......................................................................................................... 74

Figure 3.30 - Contribution of different CO2 trapping mechanisms in post-injection period

for SACROC. ........................................................................................................ 74

Figure 3.31 - Cumulative volume of produced oil for WAG and CGI. ........................... 75

Figure 3.32 - Gross and net CO2 utilization ratio for different field development strategies

during CO2 injection time (Cranfield). ................................................................... 76


during CO2 injection time (SACROC). .................................................................. 76

Figure 4.1 - Relative permeability curves for water-wet case (case 1). ........................... 89

Figure 4.2 - Relative permeability curves for the oil-wet case (case 2). .......................... 90

Figure 4.3 - CO2-EOR displacement analysis for case 1: (a) Fractional flow curves; (b)

Elution history; (c) saturation profiles at 0.25 pore volume injected; (d) Time-

distance diagram. ................................................................................................... 93


Elution history; (c) saturation profiles at 0.25 pore volume injected; (d) Time-

distance diagram. ................................................................................................... 94

Figure 4.5 - Trapping mechanisms contribution changes by changing the residual water

saturation. .............................................................................................................. 96

Figure 4.6 - Trapping mechanisms contribution changes by changing the residual gas

saturation. .............................................................................................................. 97

xviii

Figure 4.7 - Trapping mechanisms contribution changes by changing the water relative

permeability end point. .......................................................................................... 98

Figure 4.8 - Trapping mechanisms contribution changes by changing the gas relative

permeability end point. .......................................................................................... 99


permeability exponent.......................................................................................... 100


permeability exponent.......................................................................................... 100

Figure 4.11 – Tornado chart to show the sensitivity of trappings to each relative

permeability parameter. ....................................................................................... 101

Figure 5.1 - Measured relative permeability data versus the ones reported by Weaver and

Anderson (1966). ................................................................................................. 107

Figure 5.2 - Oil recovery factor for two relative permeability data sets for all four

injection schemes. ................................................................................................ 109

Figure 5.3 – Cumulative CO2 storage for two relative permeability data sets for all four


Figure 5.4 – Net utilization ratio for two relative permeability data sets for all four-


Figure 5.5 - Gross utilization ratio for two relative permeability data sets for all four-


Figure 5.6 - CO2 trapping mechanisms for two sets of relative permeability data in

continuous gas injection scheme. ......................................................................... 116

xix

Figure 5.7 - CO2 trapping mechanisms for two sets of relative permeability data in water

alternating gas injection scheme. .......................................................................... 116

Figure 5.8 - CO2 trapping mechanisms for two sets of relative permeability data in water

curtain injection scheme. ..................................................................................... 117


WAG+WCI injection scheme. ............................................................................. 117

Figure 6.1 – Schematic top view of CO2 plume migration in a dipping aquifer. ........... 124

Figure 6.2 – Schematic side view of CO2 plume migration in a dipping aquifer. .......... 125

Figure 6.3 - An example for krcross which is where the water and CO2 relative

permeabilities are equal. ...................................................................................... 127

Figure 6.4 – CO2 saturation at Xf in down-dip direction (Case 2 from Table 6.2). ........ 131

Figure 6.5 - Plume shape after increasing the injection rate in case 18 (Table 6.2). ...... 132

Figure 6.6 - Top view of CO2 saturation after 100 years of continuous injection for

selected cases (Table 6.2)..................................................................................... 133

Figure 6.7 - Numerical vs. analytical results for CO2 extension in down direction (Xf). 134

Figure 6.8 - Numerical vs. analytical results of CO2 extent in down dip direction (Xf ).136

Figure 6.9 - CO2 plume shape after hitting a sealing fault. ........................................... 137

Figure 6.10- Permeability distribution of heterogeneous cases with different coefficient of

variations. The average permeability in all of them is 20 mD. .............................. 138

Figure 6.11 - Numerical vs. analytical results for down dip extent of CO2 plume (Xf ) for

different average relative permeability areas shown in Figure 6.12. ..................... 140

Figure 6.12- Medium and small boxes for average permeability .................................. 140

xx

Figure 6.13- Two rock types based on capillary entry pressure and the CO2 plume shape

after 100 years of injection. Left figure: Red: Higher capillary entry pressure. ..... 142

1

Chapter 1: Introduction

This dissertation investigates the CO2 trapping mechanisms in carbon capture and

storage (CCS) processes using both simulation and analytical methods. This chapter briefly

explains the problem that motivated us to start this research, and then provides the

objectives and overall scopes of this dissertation. The last section of this chapter gives a

brief review of the chapters in this dissertation.

1.1 PROBLEM DESCRIPTION

It is now well documented and accepted by a majority of scientists that global

surface temperature is increasing gradually, a phenomenon called “global warming” or

“global climate change”. The increase in greenhouse gases (e.g., carbon dioxide, methane,

etc.) caused by human activity is the most cited cause of global warming. Global emissions

of carbon dioxide (CO2) exceed 35 Gt/year (IPCC, 2014) and the US contributes 6.5

Gt/year (United States Environmental Protection Agency, 2018). To reduce this number,

carbon capture and storage (CCS) has been brought to the fore as a fossil fuel emission

mitigation tool. Global CCS Institute (2018) reports that to reach Paris climate targets of 2

⁰C by 2060, CCS should contribute at least 14% to the cumulative emission reductions.

There are different options for CCS such as injection into deep saline aquifers, injection

into depleted oil reservoirs commonly for CO2–enhanced oil recovery (CO2–EOR), and

injection into coal seams. In this research, CO2-EOR/storage and CO2 injection into deep

saline aquifers are of interest. Although it has been 47 years since the first CCS project,

2

and monitoring shows that CO2 can be safely stored underground, CO2 leakage is still of

concern (CCS global status report, 2018). Therefore, understanding and forecasting the

CO2 distribution over a geological time is necessary to successfully assess the storage

performance and related risks.

1.2 RESEARCH OBJECTIVES

This PhD work aims to establish an understanding of the CO2 trapping mechanisms

in CCS. This understanding will ultimately aid in verifying that the CO2 plume remains

within the targeted area of CO2 storage. This verification is of interest to both regulators

and operators. To achieve this goal, we use both full physics computational method

(reservoir simulation) and reduced physics analytical models. This combination of

numerical and analytical techniques at field scale represents a novel approach for

investigating the CO2 flow process in CCS. The key objectives can be divided to three

categories:

1. Identifying the reservoir and operational parameters that affect the CO2

distribution during and after a CO2-EOR process: The relative contribution of the different

trapping mechanisms depends on different parameters, such as the type of geologic sink

(i.e., saline aquifers, hydrocarbon reservoirs), and the properties of the reservoir fluids

contained (Han et al., 2010; Hutcheon et al., 2016). Additionally, the importance of

different trapping mechanisms may change depending on the CO2 injection strategy (e.g.,

water alternating gas (WAG), continuous gas injection (CGI), etc.). In this dissertation we

3

aim to investigate the impact of relative permeability uncertainty and injection strategy on

the CO2 saturation changes in different phases.

2. Using fractional flow theory to analytically and graphically analyze the

distribution of CO2 trappings in a CO2-EOR flood: We use the analysis published by Walsh

and Lake (1989) on the application of fractional flow theory for miscible displacement in

the presence of an immiscible aqueous phase. We use two examples to explain the CO2-

EOR/storage displacement. Then, we calculate the CO2 trappings for several cases and

show the sensitivity of the results to relative permeability parameters based on fractional

flow calculations.

3. Developing an analytical solution to predict the lateral extent of CO2 plume in

slopping aquifers: We introduce a mathematical model, derived from a force balance, to

predict CO2 plume migration in dipping aquifers. This model calculates the down and up-

dip extension of CO2 plume in the absence of trapping mechanisms. The solution could

also be used for a thin aquifer layer or the top layer of a more complex aquifer.

1.3 DESCRIPTION OF CHAPTERS

Chapter 2 provides a background on the effect of CO2 emission on the environment

and how geological carbon sequestration plays an important role to mitigate CO2

emissions. We talk about different options for carbon capture and storage and specifically

about CO2-EOR/storage, CO2 storage in saline aquifers that are the objectives of this

research. In Chapter 3, we present a study on CO2 trapping modeling is CO2-EOR/storage

processes using CMG-GEM. We investigate the trapping mechanisms during and after

4

CO2-EOR process for two different fields: SACROC and Cranfield. SACROC is a West

Texas carbonate and Cranfield is a Gulf Coast sandstone field. Both of these fields are oil

producers. We provide a complete workflow of how we design the models and calculate

the trapping mechanism contributions. We investigate the impact of different CO2 injection

schemes on the CO2 trapping and then compare the results of two fields and conclude that

water alternating gas (WAG) is optimal for both fields by balancing the CO2 storage and

oil recovery.

Chapter 4 is devoted to fractional flow analysis. This chapter first provides a

literature review on the method of characteristics (MOC), the coherence concept, and the

MOC solution for solvent flooding. Then, we explain how we use the fractional flow

analysis to calculate the CO2 trapping mechanisms. Later in this chapter, we investigate the

effect of relative permeability on the CO2 trapping mechanism using fractional flow

analysis. We also provide the Cranfield measured data for CO2-water relative permeability

and explain how the relative permeability model from history matching was accurate

enough for CO2 trapping prediction.

Chapter 5 focuses on CO2 sequestration in deep saline aquifers. We focus on the

lateral extent of CO2 plume in dipping aquifers. We provide a simple analytical solution

that can predict the maximum downward extent of CO2 plume during and after CO2

injection. We explain how a solid trapping mechanism is required in dipping aquifers to

prevent the CO2 plume from migrating upward. Finally, Chapter 6 summarizes the results

and presents the conclusions and recommendations for future work.

5

Chapter 2: Background and Literature Review

In this chapter, I will first provide a background on the effect of excessive CO2

emission on the environment. Then, I will discuss geological carbon capture and storage

as an option to mitigate this impact. I will provide an overview of CO2-EOR/storage and

CO2 sequestration in deep saline aquifers as well as different CO2 trapping mechanisms.

Finally, I will provide a quick background on different monitoring phases and technologies.

2.1 EFFECT OF CO2 EMISSION ON THE ENVIRONMENT

Human activities contribute substantially to climate change by adding CO2 and

other heat-trapping gases to the atmosphere. These greenhouse gas emissions change the

temperature of the Earth’s surface, change the global water cycle, cause glaciers to shrink

and consequently increase the global mean sea level (IPCC, 2013). Figure 2.1 shows the

globally averaged combined land and ocean surface temperature anomaly. Many climate

science reports have detected the increased emissions of anthropogenic greenhouse gases

(e.g., CO2, CH4, and N2O) as the main cause of the observed global warming (IPCC, 2005,

2013, 2014; IEA, 2008, 2013, 2016). Figure 2.2 shows the globally averaged greenhouse

gas concentrations (IPCC, 2014). Among the various greenhouse gases, CO2 accounts for

the largest share of the anthropogenic GHG emissions (IEA, 2016). Fossil fuel combustion

and industrial processes contribute the most (about two-third) to the CO2 emissions.

6

Figure 2.1 - Globally averaged combined land and ocean surface temperature anomaly

(IPCC, 2014).

Figure 2.2 - Globally averaged GHG concentrations (IPCC, 2014).

Fossil fuels are being consumed continuously to satisfy the worldwide energy

demand. Consequently, the annual GHG emissions because of human activities are

expected to increase. Even by assuming a restricting control of GHG emissions by

government and industry, the projected CO2 emissions are forecasted to be almost two and

a half times of the current level of emission by 2050 (IEA, 2008).

7

To reduce the global CO2 emissions, mitigation technologies are necessary.

Mitigation technologies include but not limited to switching to less carbon-intensive fuels,

renewable energy, advanced bioenergy, nuclear power generation, and methods to improve

energy efficiency to reduce the produced CO2 from the source (Wu, 2018). Carbon capture

and storage (CCS) technologies are known as feasible methods to reduce the CO2 emissions

significantly and have the potential to contribute up to 14% to CO2 emissions mitigation.

2.2 GEOLOGICAL CARBON CAPTURE AND STORAGE (CCS)

Carbon Capture and Storage (CCS) is a proven safe and commercial technology to

mitigate climate change by reducing the net anthropogenic CO2 emissions into the

atmosphere (IPCC, 2005; IEA, 2008). There are different options for CO2 sequestration,

including injection into deep saline aquifers, injection into depleted oil reservoirs

commonly for CO2–enhanced oil recovery (CO2–EOR), and injection into coal seams.

Typical CCS operations are shown in Figure 2.3. Typical CCS operations include a

portfolio of technologies that involve capture, transport, storage and monitoring as shown

in Figure 2.4.

8

Figure 2.3 - Overview of CCS options (IPCC, 2005).

Figure 2.4 - Illustration of different sections of a typical CCS operation.

9

The major ongoing storage projects include the offshore Sleipner project (Norway,

1Mt CO2/yr storage in a deep saline aquifer); the Weyburn project (Canada, 1Mt CO2/yr

storage with EOR) (IPCC, 2005). These storage projects have reduced million tons of CO2

that would be emitted into the atmosphere, and no leakage was detected, which support the

feasibility of geological CO2 storage. Furthermore, the process of geological CO2 storage

is analogous to traditional operations in oil and gas industry, the technologies such as

injection and production, disposal of liquid/gas wastes, can be used directly to CO2 storage

(Bachu, 2008).

2.3 CO2 STORAGE IN SALINE AQUIFERS

Geographically, anthropogenic CO2 is distributed in many places worldwide.

Hence, it is unlikely to find oil and gas reservoirs for the purpose of CCS in all areas. The

substitution is storage in deep saline aquifers that are distributed widely. However, deep

saline aquifers are not known as much as hydrocarbon reservoirs. Many field trials have

been conducted in saline aquifers to understand the mechanisms involved in CO2 storage.

The most famous large scale CO2 storage in saline aquifer is Sleipner project in Norway

(Torp and Gale., 2004). Monitoring programs have also been conducted in Sleipner that

showed that the injected CO2 remains within the injection target zone; however, vertical

migration of CO2 plume occurs. Frio in south Texas (Hovarka et al., 2006), In Salah in Sahara

desert in Algeria, Snohvit in Barnet Sea, and Cranfield in Mississippi (Hovarka et al., 2013)

are other examples of CO2 storage in saline aquifers. The Cranfield project was a combination

of CO2-EOR/storage and CO2 injection in aquifers.

10

2.4 CO2-EOR/STORAGE

CO2 storage in hydrocarbon reservoirs occurs as a part of CO2 Enhanced Oil

Recovery (CO2-EOR) technique. Therefore, in commercial scale, CO2-EOR/storage is of

interest. Because it not only offers permanent CO2 storage, it is also a commercial

opportunity to improve oil recovery from mature oil fields (Choi et al., 2013; Kim and

Hosseini, 2015; Zhang et al., 2015; Jia et al., 2016; Ampomah et al., 2017). Additionally,

hydrocarbon reservoirs are characterized by having structural seals that offer a permanent

storage of CO2. Several CO2-EOR projects have been conducted in the past decades.

SACROC (Hawkins et al., 1996) and North Cross (Mizenko, 1992) were among the first

successful CO2-EOR projects. However, most of the CO2-EOR projects use CO2 extracted

from the natural reservoirs (Ganjedanesh, 2014).

The first field scale of CO2-EOR/storage was conducted in the Weyburn field in

Saskatchewan (Malik et al., 2000). For this project, they used CO2 from a coal-gasification

plant in North Dakota. They transported the captured CO2 from North Dakota to the

Weyburn field through a pipeline (Moberg et al., 2002).

2.4.1 Miscibility

The classical thermodynamic definition of miscibility is the condition of pressure

and temperature at which two fluids mix together in all proportions to form a single phase

fluid. Miscibility is considered the most important parameter for assessing the applicability

of any gas-EOR for an oil reservoir (Speight, 2013, Lake et al., 2014). The pressure at

which miscibility occurs is called the minimum miscibility pressure (MMP) (Lake, 1989).

11

Minimum miscibility pressure has been defined differently by different authors. Yelling

and Metcalfe (1980) has defined MMP as the pressure at which the oil recovery of injecting

1.2 PV (pore volume) of CO2 is equal to or near the maximum final recovery. Holm and

Josendal (1974) defined MMP as the pressure that results in 80% of oil recovery at CO2

breakthrough and 94% recovery at a GOR (gas-oil-ratio) of 40 MSCF/STB. Williams et al.

(1980) defined MMP to be the pressure at which an oil recovery of 90% is obtained after

1.2 HCPV (hydrocarbon pore volume) of CO2 injection.

Miscibility can be either as first-contact or multi-contact miscibility. First-contact

miscibility occurs when the injected gas mixes with the reservoir oil in all proportions and

remains one phase. This process has a very high ultimate displacement efficiency because

the residual oil saturation will be zero (Lake, 1989). Multi-contact miscibility occurs when

the injected gas develops miscibility after exchanging components with the reservoir oil in

the mixing zone of the flood front.

There are two mechanisms to help multi-contact mobility to be obtained: vaporizing

gas drive and condensing gas drive. In a vaporizing gas drive, the injected gas (e.g., CO2)

vaporized the lighter components of the in-situ oil into the gas phase. In a condensing gas

drive, the injected gas condenses into the reservoir’s oil (Merchant, 2010; Verma, 2015).

Figure 2.5 shows a schematic of vaporizing and condensing processes in a CO2-EOR

process. The mass transfer between CO2 and oil provides the condition in that the two

phases become completely miscible.

12

Figure 2.5 – A schematic of the vaporizing and condensing processes that result in multi-

contact miscibility (Verma, 2015).

2.4.2 CO2 Injection Schemes for EOR/Storage

In CO2-EOR there are three main field development strategies: continuous gas

injection (CGI), water-alternating-gas (WAG), and water curtain injection (WCI). CGI is

the process in which CO2 is injected continuously during the life of the EOR. Figure 2.6

shows a schematic of continuous CO2 injection. Gas (e.g., CO2) EOR improves the oil

recovery through different mechanisms: oil swelling, gas-oil interfacial tension (IFT)

reduction, oil viscosity reduction, and vaporization of light and intermediate hydrocarbons

(Chen et al. 2010; Tunio et al. 2011; Cao and Gu 2013). Chordia and Trivedi (2010)

investigated the specific case of CO2 injection. They showed that when CO2 contacts oil,

swelling causes the oil to expand and move towards the producing wells.

13

Figure 2.6 – A schematic of continuous CO2 injection scheme

(https://slideplayer.com/slide/5785915/).

For any secondary or tertiary oil recovery method, the objective is to improve the

overall recovery efficiency (ER). ER of a tertiary recovery is the product of an volumetric

sweep efficiency (EV) and a displacement sweep efficiency (ED) (Lake et al., 2014):

𝐸𝑅 = 𝐸𝑉𝐸𝐷 (2.1)

Mobility ratio is also an important factor that controls the gas (CO2) injection process

volumetric sweep efficiency. Mobility ratio is described as follows:

𝑀 =𝑘𝑟𝑔 𝜇𝑔⁄

𝑘𝑟𝑜 𝜇𝑜⁄ (2.2)

where krg and kro are the relative permeabilities; and 𝜇𝑔 and 𝜇𝑜 are the viscosities of gas

and oil, respectively. Mobility ratio of less than one is considered a favorable mobility

ratio; however, in the case of gas injection the viscosity of gas is much lower than the

viscosity of the oil leading to a large mobility ratio. To control the mobility ratio of the gas

https://slideplayer.com/slide/5785915/

14

injection process, water-alternating-gas injection has been proposed. Figure 2.7 shows a

schematic of WAG injection. In WAG injection water and gas is injected alternatively

through the EOR process. Alternative injection of water improves the volumetric sweep

efficiency by stabilizing the front. WAG combines the improved displacement efficiency

of the gas flooding with an improved volumetric efficiency of water flooding (Christensen

et al., 1998).

Figure 2.7 – A schematic of water alternating gas injection scheme

(https://phys.org/news/2017-04-analysis-co2-sequestration-oil-recovery.html).

Another important issue in a CO2-EOR process is maintaining reservoir pressure

within the floodable area (Davis et al., 2011). In other words, we must prevent the CO2

leak-off to be able to maximize volumetric sweep efficiency. This is accomplished by using

another injection scheme called water-curtain-injection. Figure 2.8 shows a schematic of

water curtain injection (WCI). In a WCI process, water injection wells are designed around

https://phys.org/news/2017-04-analysis-co2-sequestration-oil-recovery.html

15

the gas injection area to keep the gas/CO2 within the target area. This technique has been

applied to several fields such as the Hastings field (Davis et al., 2011), Salt Creek field

(NRDC, 2017), Monell unit, Patricj Draw field (Gaines, 2008), etc. Within the water

curtain well, the CO2 injection could be either continuous gas injection or water alternating

gas injection (Nuñez-Lopez et al., 2019).

Figure 2.8 – A schematic of water curtain injection scheme.

2.4.3 EOR vs. CCS

The main important difference between CO2-EOR and CO2 storage is the objectives

of the two. In CO2-EOR, the objective is to maximize the oil production with a low cost.

The main cost of a CO2-EOR is the purchase cost of injecting CO2. Therefore, the focus is

to minimize the amount of CO2 trapped into the reservoir. The objective in a CO2 storage

16

is to maximize the amount of CO2 stored into the reservoir. This conflict of interests

introduces an engineering challenge to CO2-EOR as a storage process. For instance, a

blowdown process is usually implemented after an EOR operation to vent the CO2 from

the reservoir; hence, the CO2 is reusable for injection in another nearby well (Bock et al.,

2003). However, to maximize the permanent storage of CO2, blowdown cannot be

implemented in a CO2-EOR/storage process. CO2-EOR/storage at Weyburn Field in

Canada is an example of which the blowdown was not implemented (Coleman, 2012).

2.4.4 Validity of CO2-EOR for Storage

Oil field operators consider the mass of trapped CO2 in the reservoir a loss that

needs to be replaced by purchased CO2 to maintain the injection rates. In cases where the

operators use anthropogenic CO2, captured from industrial facilities, the amount of CO2

loss in the subsurface could be considered as a geologically stored CO2 mass. This mass

would have been emitted to the atmosphere as a greenhouse gas had it not been captured

and utilized for CO2-EOR. For this reason, CO2-EOR technologies that use anthropogenic

CO2 are considered carbon capture, utilization, and storage (CCUS) technologies.

However, some questioned the validity of CO2-EOR as a greenhouse gas emission

reduction technology, as CO2-EOR result emissions from the energy combustion

throughout the EOR operation and form the combustion of the incremental oil recovered.

Nuñez-Lopez et al. (2019) conducted a carbon cycle analysis (LCA) assuming a gate-to-

grave CCUS system. They examined four injection schemes and showed that all four CO2

injection schemes start operating with a negative carbon footprint and at some point

17

transition into operating with positive carbon footprint. Their study provide a workflow to

design a CO2-EOR process to serve as both enhanced oil production and greenhouse gas

emission reduction technology.

2.5 CO2 TRAPPING MECHANISMS

Geological CO2 storage depends on a combination of physical and geochemical

trapping mechanisms to keep the injected CO2 securely stored underground in the porous

medium. There are four major natural trapping mechanisms: stratigraphic (structural)

trapping, residual trapping, solubility trapping, and mineral trapping (Xu et al., 2004; Riaz

and Tchelepi, 2006; Han 2008; Hosseininoosheri et al., 2018(a); Hosseini et al., 2018).

Structural trapping is the most significant trapping mechanism which traps the CO2

in the highly porous and permeable zones of the reservoir. The CO2 is trapped under the

impermeable zones of the reservoir, such as caprocks and sealing faults (Bachu et al.,

1994). Residual trapping refers to the entrapment of supercritical CO2 in pores as an

immobile phase because of the capillary pressure and relative permeability curves

hysteresis (Kumar et al., 2005; Juanes et al., 2006; Juanes and MacMinn, 2008). This

trapping mechanism is basically a post-injection process where the top and bottom of the

plume experiences two different relative permeability and capillary pressure curves

(imbibition and drainage) (Flett et al., 2004). Solubility trapping refers to the dissolution

of CO2 into brine or residual oil (Ennis-King and Paterson. 2005). Pressure, temperature

and brine salinity are the main parameters that determine the solubility of CO2 in brine and

oil. Mineral trapping happens as a post trapping mechanism after dissolution trapping. The

18

brine pH decreases by CO2 dissolution in brine; therefore, the solubility of many formation

minerals increase. The increase in solubility of minerals leads the CO2 to react directly and

indirectly with them. The reaction of CO2 with the minerals leads to the precipitation of

secondary carbonate minerals and hence geochemical binding to the rock (Gunter et al.,

1997). Figure 2.9 shows the schematic of four main mechanisms that contribute to trapping

the injected CO2 in a reservoir (Hosseininoosheri et al., 2018(b)).

Among the four main mechanisms of CO2 trapping during and after CO2

sequestration, stratigraphic trapping represents the highest risk of leakage, given that

supercritical CO2 is still mobile. Dissolution of CO2 in brine can contribute to trapping the

supercritical CO2 by increasing the convective force of brine, which leads to convective

mixing (Soltanian et al., 2016). However, convective mixing has not been reported at the

field scale yet. Mineral trapping is believed to be the safest mechanism of CO2 trapping.

Figure 2.9 - CO2 trapping mechanisms in a CCS process (Hosseininoosheri et al.,

2018(b)).

19

The relative contribution of each mechanism in CO2 sequestration is expected to

change over time as CO2 migrates and reacts with formation rock and fluids. Figure 2.10

shows a schematic of contribution of the trapping mechanisms in a saline aquifer after CO2

injection over time. Although structural trapping is the most active trapping mechanism

after CO2 injection, the structurally trapped CO2 becomes residual and dissolves into water

over time. Both the residual and dissolved CO2 then react with rock minerals and trap some

of the CO2 as mineral trapping. Figure 2.10 shows the relations between different trapping

mechanisms. The contributions of different mechanisms are specific to aquifers, and there

is no general mechanism contribution trend for the CO2–EOR case thus far.

Figure 2.10 - Contribution and relation of different CO2 trapping mechanisms over time.

Having information on the evolution of different trapping mechanisms helps to

propose different injection strategies. For example, to speed up safe storage of CO2, an

important endeavor is to accelerate the solubility and residual trappings (Ren, 2017). The

proposed injection scheme is the “inject low and let rise” approach. In this approach, CO2

Residual Trapping

Mineral Trapping

Solubility Trapping

Structural Trapping

Residual Trapping

Solubility Trapping

Mineral Trapping

After Thousands

of Years Structural

Trapping

20

is injected only into the lower part of an aquifer (Kumar et al., 2005). Another approach is

to inject the CO2 into the lower part and simultaneously inject water in the upper part of an

aquifer (Leonenko and Keith, 2008; Nghiem et al., 2009; Javaheri and Jessen, 2011;

Anchliya et al., 2012). Several other works also focused on increasing the residual trapping

(Qi et al., 2009; Na et al., 2011).

In addition to the aforementioned trapping mechanisms, local capillary trapping

was also introduced. In a buoyancy-dominated flow regime, the magnitude of buoyant

force and capillary pressure are comparable; therefore, CO2 prefers to flow through the

paths with smaller capillary entry pressures. When CO2 encounters a region with high

capillary entry pressure, it cannot move any farther so it accumulates beneath the high

capillary entry pressure region. These accumulations called local capillary trapping of CO2

(Saadatpoor, 2012; Ren, 2017). The main difference between local capillary trapping and

structural trapping is that CO2 will not escape from local capillary trapping, even if the

integrity of caprock is compromised (Saadatpoor, 2012). Table 2.1 compares local

capillary trapping with residual trapping (Ren, 2017).

21

Table 2.1 – Comparison between local capillary trapping and residual gas trapping (Ren,

2017).

Property Local Capillary Trapping Residual Trapping

Origin Intra-reservoir capillary barriers Snap-off

Porous media Heterogeneous Heterogeneous/homogenous

Flow Regime Buoyant Viscous

Displacement type Drainage Imbibition

Trapped CO2 saturation Larger than maximum residual

gas saturation (𝑆𝑔𝑟𝑚𝑎𝑥)

Smaller than 𝑆𝑔𝑟𝑚𝑎𝑥

Scale of trapping 10-2-10+2 meter µm, pore scale

Influential parameters Gas column height, capillary entry

pressure, heterogeneity

Wettability, pore structure

and connectivity

2.6 MONITORING

Monitoring the migration of the injected CO2 to ensure its containment within the

target storage area is another issue for a successful storage. Benson et al. (2005) categorized

the monitoring technologies into four distinct phases: pre-operational, operational, closure,

and post-closure.

The pre-operational phase is conducted before the injection when all the possible

data to characterize the subsurface is gathered. The data include a combination of well logs,

wellhead pressures, formation pressures, rate testing, and seismic survey. The operational

phase of monitoring starts with injection that include the measurement of wellhead

pressures, rates, and seismic survey. The closure phase begins right after CO2 injection has

22

stopped. Seismic survey with the addition of gravity and electromagnetic surveys are the

process used in closure monitoring phase. During post-closure phase 3D seismic and

monitoring wells are designed (Bhowmik, 2012).

2.7 SUMMARY

This chapter gave a background on geologic carbon storage. I explained the CO2

storage in saline aquifer and in oil reservoirs since these two are the objectives of this

dissertation. I explained different CO2 trapping mechanisms and the ambiguity in the

prediction of their evolution over time. I quickly overviewed the different monitoring

techniques too.

23

Chapter 3: Modeling of CO2 Trapping in CO2-EOR/Storage Processes

Using a Conventional Reservoir Simulation1

In this chapter, the distribution of injected CO2 in different phases during and after a

CO2-EOR/storage will be discussed. I used the General Equation-of-state Model (GEM)

developed by the Computer Modeling Group Ltd. (CMG) to simulate the CO2-EOR and

investigate the evolution of different CO2 trapping mechanisms. I will first provide an

introduction and then briefly explain the reservoir simulator. After that, I will explain the

modeling method and our approach to calculate the amount of CO2 trapped by each

trapping mechanism. I will also provide two case studies: SACROC and Cranfield. I will

provide a background on each of them and present the results of the simulation model for

1 The content in this chapter was published as the following papers. The main author of the papers is

Hosseininoosheri P. and the other authors are the supervisors.

1. Hosseininoosheri, P., Hosseini, S.A., Nuñez-López, V. and Lake, L.W., 2018. Impact of field

development strategies on CO2 trapping mechanisms in a CO2–EOR field: a case study in the

Permian Basin (SACROC unit). International Journal of Greenhouse Gas Control, 72, pp.92-104.

2. Hosseininoosheri, P., Hosseini, S.A., Nunez-Lopez, V. and Lake, L.W., 2018, April. Modeling CO2

partitioning at a carbonate CO2-EOR site: Permian Basin field SACROC Unit. In SPE Improved Oil Recovery Conference. Society of Petroleum Engineers.

3. Hosseininoosheri, P., Hosseini, S.A., Nuñez-López, V. and Lake, L., 2018, October. A comparative

study of CO2-flood displacement efficiency for different CO2 injection strategies: Permian Basin vs.

US Gulf Coast. In 14th Greenhouse Gas Control Technologies Conference Melbourne (pp. 21-26).

4. Hosseininoosheri, P., Hosseini, S.A., Nunez-Lopez, V. and Lake, L.W., 2018, April. Evolution of

CO2 utilization ratio and CO2 storage under different CO2-EOR operating strategies: a case study

on SACROC unit Permian Basin. In SPE Western Regional Meeting. Society of Petroleum

Engineers.

24

both. Finally, I will compare the results of Cranfield and SACROC and provide a

conclusion.

3.1 INTRODUCTION

In a CO2-EOR/storage process, the injected CO2 distributes into oil, gas, and brine

phases. The CO2 in the gas phase can be either free or residually trapped. The distribution

of CO2 in different phases depends on various reservoir’s static and dynamic parameters

such as reservoir heterogeneities, caprock properties, CO2-rock wettability, reservoir

pressure and temperature, brine salinity, and hydrocarbon properties. During injection, as

the amount of CO2 in the formation increases over time, the distribution of CO2 in different

phases also changes. In the post injection periods, as the CO2 mass evolves and stabilizes,

the distribution changes again. Our numerical simulations, based on SACROC and

Cranfield CO2-EOR data, demonstrate these variations are significant and mostly depend

on the operator‘s field development strategy.

Although actual operating strategy in these two fields are different (CGI in Cranfield

and WAG in SACROC), our numerical modelling results show that WAG could not only

balance the CO2 storage, incremental oil recovery, and CO2 utilization ratio but also store

the trapped CO2 with lower risk of leakage in both fields (by decreasing the amount of

structurally trapped CO2). Because of multiple alternation of CO2 and water slugs in WAG,

this approach reduces the viscous instability and therefore the efficiency of oil recovery.

Our study shows that the distribution of CO2 in different phases is different for each field.

25

The present work provides valuable insights for optimizing oil production and CO2

storage in a CO2-EOR project. Additionally, this study clearly shows the impact of

development strategies on the relative importance of different trapping mechanisms.

3.2 SIMULATOR

To simulate an enhanced oil recovery process involving gas (CO2) injection, it is

important to identify if the process is miscible or immiscible. As we discussed earlier

(section 2.4.1), miscibility depends on the composition of the injected fluid and the

reservoir oil, and the reservoir pressure and temperature. The complexity of this process

requires special handling of both thermodynamic and the fluid flow in the reservoir. In this

dissertation, we used GEM (Generalized Equation-of-state Model) developed by Computer

Modeling Group Ltd. (CMG). GEM is a finite difference based, multi-dimensional,

multiphase, and non-isothermal compositional reservoir simulator that can simulate the

important mechanisms of a miscible gas injection process. GEM runs by an adaptive

implicit formulation by default, which means for each grid block at each time step the

simulator decides whether to use fully implicit method or IMPES (Implicit Pressure

Explicit Saturation). This technique helps the simulator to run faster in comparison with

fully implicit and fully explicit methods.

3.3 MODELING METHOD AND DESCRIPTION

To address the distribution of CO2 in different phases and to suggest the most

efficient operation development strategy in SACROC and Cranfield, we integrated three

main elements of field assessment: field characterization based on measured data

26

(geocellular model), field production-pressure history performance, and reservoir

simulation (CMG-GEM). Although the results from this technique is not unique, we

assume that the integration of these three elements enables us to build a simulation model

that gives a reliable set of results.

Figure 3.1 shows the summary of our approach in modeling the SACROC and

Cranfield performances. The details of each assessment element are explained in the

following sections.

Figure 3.1 – A summary of our field assessment approach for SACROC and Cranfield.

90

High

Confidence

Field

Performance

Physical Field

Measurement (Seismic,

Logs, etc.)

Reservoir

Simulation

Model

Geocellular Model

Production-pressure

History Data

27

3.4 MODELING OF TRAPPING MECHANISMS

In this study, our main focus is on four main CO2 trapping mechanisms: structural,

residual, solubility, and mineral trappings. In the following sections, we first explain how

we find the residual, solubility, and mineral trappings. We then explain how we calculate

the structural trapping using a material balance equation.

3.4.1 Solubility Trapping

Solubility is divided into two categories: solubility in brine and solubility in oil.

Solubility in oil is calculated using the composition exchange through the Peng-Robinson

equation of estate (EOS) model (Peng and Robinson, 1976). Solubility in brine is another

important factor involved in CO2–EOR storage. In this study, Henry’s law (Henry, 1803)

was used to model the solubility of supercritical CO2 into brine. The reason that we did not

assume brine to be another component in the EOS model was to be able to model the

aquifer in the Cranfield case study (section 3.6.2). To be consistent, we used Henry’s law

for the SACROC case study (section 3.6.1) as well.

Henry’s law assumes a thermodynamic equilibrium between the gaseous phase and

aqueous phase which is based on the equality of fugacities of gas and water components:

𝑓𝑖𝑔 = 𝑓𝑖𝑤 , 𝑖 = 1, 2, … , 𝑛𝑐 (3.1)

where 𝑓𝑖𝑔 is fugacity of component 𝑖 in the gas phase, 𝑓𝑖𝑤 is fugacity of component 𝑖 in the

water phase, and 𝑛𝑐 is the number of gaseous components. 𝑓𝑖𝑔 is calculated from the

28

equation of state (EOS)—Peng and Robinson EOS in this study—and 𝑓𝑖𝑤 was calculated

using Henry’s law:

𝑓𝑖𝑤 = 𝑦𝑖𝑤𝐻𝑖 (3.2)

where 𝑦𝑖𝑤 is the mole fraction of component 𝑖 in the aqueous phase and 𝐻𝑖 is Henry’s

coefficient for component 𝑖. In this study, Henry’s coefficient was calculated as a function

of temperature, pressure, and salinity using the model provided by Harvey (1996).

3.4.2 Residual Trapping

To model the residual trapping, we used the hysteresis concept. Hysteresis refers to

a dependence of the system properties on its past; in other words, hysteresis is a path

dependency or irreversibility. Specifically, hysteresis in relative permeability depends on

saturation history. One of the main reasons for relative permeability hysteresis is trapping

of the non-wetting phase during imbibition. In a water-alternating-gas (WAG) process, the

gas phase (non-wetting phase) is trapped during water injection after a gas flood. Juanes et

al. (2006) evaluated the relevance of relative permeability hysteresis when CO2 is injected

into a saline aquifer and concluded that modeling the relative permeability hysteresis is

required to accurately estimate the amount of trapped CO2 in a saline aquifer.

As modeling CO2 sequestration in saline aquifers only requires a two-phase fluid

flow system, relative permeability hysteresis can be modeled with two-phase relative

permeability curves. However, in a CO2–EOR process, where three phases are present in

the fluid flow system, modeling the relative permeability hysteresis becomes more

complicated. Ghomian (2008) studied the effect of relative permeability hysteresis in a

29

CO2–EOR process. They also concluded that the effect of hysteresis on the amount of

trapped CO2 is significant and an accurate estimate of trapped CO2 requires the modeling

of relative permeability hysteresis. In this study, we investigate the effect of relative

permeability hysteresis in the SACROC field to determine the contribution of hysteresis in

CO2 trapping.

In this study, the Land (1968) equation is used to model the gas relative

permeability hysteresis. In this model, the residual gas saturation 𝑆𝑔𝑟 is calculated as

𝑆𝑔𝑟 =𝑆𝑔𝑖

1 + 𝐶𝑆𝑔𝑖 (3.3)

where 𝑆𝑔𝑖 is the gas saturation at flow reversal and 𝐶 is Land coefficient that is calculated

as follows:

𝐶 =1

𝑆𝑔𝑟,𝑚𝑎𝑥−

1

𝑆𝑔,𝑚𝑎𝑥 (3.4)

where 𝑆𝑔𝑟,𝑚𝑎𝑥 is the maximum residual gas saturation and 𝑆𝑔,𝑚𝑎𝑥 is the maximum gas

saturation associated with imbibition curve. Both 𝑆𝑔𝑟,𝑚𝑎𝑥 and 𝑆𝑔,𝑚𝑎𝑥 are inputs in the

simulation model. We assumed 𝑆𝑔𝑟,𝑚𝑎𝑥 = 0.35 and 𝑆𝑔,𝑚𝑎𝑥 = 0.78. Having these two

numbers, the simulator calculates the Land coefficient and use it to find the residual gas

saturation for each grid cell in each time step using equation 3.3.

3.4.3 Mineral Trapping

Minerals of the formation rock could play an important role in trapping the CO2

through mineralization. In the current study, we used CMG-GEM geochemistry option to

30

model the reactions of minerals with aqueous phase components. For SACROC case study,

Romanak and Smyth (2008) suggested the following reactions:

𝐶𝑂2 + 𝐻2𝑂 ⇄ 𝐻+ + 𝐻𝐶𝑂3− (3.5)

𝐶𝑎𝑙𝑐𝑖𝑡𝑒 + 𝐻+ ⇄ 𝐶𝑎2+ + 𝐻𝐶𝑂3− (3.6)

𝐷𝑜𝑙𝑜𝑚𝑖𝑡𝑒 + 2𝐻+ ⇄ 𝐶𝑎2+ + 𝑀𝑔2+ + 2𝐻𝐶𝑂3− (3.7)

𝑆𝑖𝑑𝑒𝑟𝑖𝑡𝑒 + 𝐻+ ⇄ 𝐹𝑒2+ + 𝐻𝐶𝑂3− (3.8)

Siderite is considered to be a secondary mineral deposited in the reservoir. CMG calculates

the mineral dissolution and precipitation rate using Transition State Theory (TST):

�̂� = �̂�0 𝑁𝑚

𝑁𝑚0 (3.9)

where �̂� and �̂�0 are the reactive surface area at the current time and at time zero,

respectively. 𝑁𝑚 and 𝑁𝑚0 are the current moles of mineral and moles of mineral at time

zero, respectively. The activity coefficients are calculated form B-dot model. Table 3.1

shows the properties of minerals used in the SACROC model. Equilibrium constants are

taken from SOLMINEQ.88 and PHREEQC (Han et al., 2010). Han (2008) calculated the

reactive surface areas assuming specific grain volumes, grain surface areas, molar volumes,

molecular weights, and average grain diameter. He assumed that the mineral grains are

spherical.

31

Table 3.1 - Mineral properties of the SACROC unit (Han et al., 2010)

Mineral Initial Volume

Fraction

Reactive Surface

Area (m2/m3)

Activation

Energy (J/mol)

Log K25

(mol/m2S)

Calcite 0.6063 585 41879 -8.8

Dolomite 0.0933 6115 41879 -9.22

Siderite 0.0 400 41870 -10.22

* K25 is the reaction rate coefficient at 25 ºC .

Additionally, the initial brine concentration plays an important role in dissolution

and precipitation of minerals after CO2 injection. Therefore, we used the initial

concentration from Han et al. (2010). The data is an average of brine chemistry data for the

SACROC unit. Table 3.2 shows the initial concentration of brine in the current model.

𝐻𝐶𝑂3− is considered to be the secondary component generated after CO2 injection.

Table 3.2 – Initial brine concentration.

Component 𝑯+ 𝑪𝒂𝟐+ 𝑴𝒈𝟐+ 𝑵𝒂+ 𝑪𝒍− 𝑭𝒆𝟐+

Initial Molality 3.981e-07 0.1314 5.7e-02 1.094 1.391 8.85e-4

After applying the reactions, we calculated the contribution of mineral trapping.

Mineralization contribution in CO2 trapping was insignificant even after 400 years of post-

injection observation. The contribution of mineralization in CO2 trapping does not exceed

0.03% for the SACROC case study. Therefore, we decided to ignore the mineral trapping

contribution effect in our study.

32

Adding geochemistry to the model generates convergence problem since the

reaction rate coefficients are so large so that the mineral volume changes because of

dissolution and precipitation occur rapidly. Consequently, the pressure and saturation

changes become too large which lead to a convergence failure. This problem becomes more

severe because of the large heterogeneity of the carbonate field (SACROC). To overcome

this issue, we changed our time steps to be very small. Han (2008) reported the same

problem for their mineralization modeling with CMG-GEM.

3.5 TRAPPING CALCULATIONS

Although simulation provides the amount of CO2 in brine, oil, and gas phases, it

does not output the amount of trapped CO2 because of mineralization. Additionally, the

simulator does not differentiate the amount of residual CO2 from mobile CO2. Therefore, I

calculate the amount of trapped CO2 in the reservoir using a material balance (mole):

𝑀𝐶𝑂2

𝐼𝑛𝑗= 𝑀𝐶𝑂2

𝑜𝑖𝑙 + 𝑀𝐶𝑂2

𝑏𝑟𝑖𝑛𝑒 + 𝑀𝐶𝑂2

𝑟𝑒𝑠𝑖𝑑𝑢𝑎𝑙 + 𝑀𝐶𝑂2

𝑚𝑜𝑏𝑖𝑙𝑒 + 𝑀𝐶𝑂2

𝑚𝑖𝑛𝑒𝑟𝑎𝑙 + 𝑀𝐶𝑂2

𝑝𝑟𝑜𝑑𝑢𝑐𝑒𝑑 (3.10)

where 𝑀𝐶𝑂2

𝐼𝑛𝑗 is the amount of injected CO2, 𝑀𝐶𝑂2

𝑜𝑖𝑙 is the amount of CO2 dissolved in oil,

𝑀𝐶𝑂2

𝑏𝑟𝑖𝑛𝑒 is the amount of CO2 dissolved in brine, 𝑀𝐶𝑂2

𝑟𝑒𝑠𝑖𝑑𝑢𝑎𝑙 is the amount of CO2 trapped

because of relative permeability hysteresis, 𝑀𝐶𝑂2

𝑚𝑜𝑏𝑖𝑙𝑒 is the amount of CO2 structurally

trapped in the reservoir, 𝑀𝐶𝑂2

𝑚𝑖𝑛𝑒𝑟𝑎𝑙 is the amount of CO2 trapped because of mineral

precipitation, and 𝑀𝐶𝑂2

𝑝𝑟𝑜𝑑𝑢𝑐𝑒𝑑 is the amount of produced CO2. 𝑀𝐶𝑂2

𝑜𝑖𝑙 and 𝑀𝐶𝑂2

𝑏𝑟𝑖𝑛𝑒 can be

33

exported directly from the simulator, but 𝑀𝐶𝑂2

𝑟𝑒𝑠𝑖𝑑𝑢𝑎𝑙 and 𝑀𝐶𝑂2

𝑚𝑜𝑏𝑖𝑙𝑒 must be calculated based

on 𝑆𝑔𝑟 based on hysteresis in each grid block as follows:

𝑀𝐶𝑂2

𝑚𝑜𝑏𝑖𝑙𝑒 = ∑ 𝑉𝑚,𝑔(𝑖) × 𝑓𝐶𝑂2(𝑖) × (𝑆𝑔(𝑖) − 𝑆𝑔𝑟(𝑖)) × 𝑃𝑉(𝑖)

𝑛

𝑖=1

(3.11)

𝑀𝐶𝑂2

𝑟𝑒𝑠𝑖𝑑𝑢𝑎𝑙 = ∑ 𝑉𝑚,𝐶𝑂2(𝑖) × 𝑓𝐶𝑂2(𝑖) × 𝑆𝐶𝑂2,𝑟(𝑖) × 𝑃𝑉(𝑖)

𝑛

𝑖=1

(3.12)

where 𝑉𝑚,𝑔 is molar density of gas phase, 𝑓𝐶𝑂2 is CO2 mole fraction, 𝑆𝑔 is gas saturation,

𝑆𝑔𝑟 is residual gas saturation, 𝑃𝑉 is net pore volume, and 𝑛 is total number of grid blocks.

As discussed in the Mineral Trapping section (3.4.3), we investigated the mineralization

contribution in CO2 trapping even after 400 years of post-injection observation. The

contribution of mineralization in CO2 trapping does not exceed 0.03% for the SACROC

case study. Therefore, we decided to ignore the mineral trapping contribution effect in our

study. Our observation agrees with previous studies (Han, 2008; Luo and Jiang, 2012;

Kempka et al., 2013).

3.6 CASE STUDIES

In this study, we model and compare two fields that represent two different

reservoir settings: Cranfield (representative of the U.S. Gulf Coast sandstone reservoirs)

and SACROC (representative of the Permian Basin carbonate reservoirs). CGI is the

original operating strategy in Cranfield and WAG is the original operating strategy applied

in the SACROC unit.

34

3.6.1 SACROC

This section presents the results of field-scale compositional reservoir flow

modeling in the SACROC (Scurry Area Canyon Reef Operators Committee) unit, Permian

Basin, to demonstrate the relative partitioning of CO2 during and after CO2 injection. The

model was developed to study the effect of structural trapping, solubility trapping, and

residual trapping on the partitioning of CO2 in oil, gas (free or residual), and brine phases

over time. Furthermore, we investigated the impact of various injection scenarios, such as

CGI (Continuous Gas Injection) and WAG (Water Alternating Gas), on the different

trapping mechanisms.

First, we used a high-resolution geocellular model, which was constructed from

wireline logs, seismic surveys, core data, and stratigraphic interpretation. As the initial

distribution of fluids plays an important role in CO2 partitioning, a comprehensive

pressure-production history matching of primary, secondary, and tertiary oil recovery was

completed. The hysteresis model was used to calculate the amount of CO2 trapped as

residual. CO2 solubility into brine was verified based on previous experiments.

The model results show a new understanding of relative CO2 distribution in

different phases in field scale porous media. Although it was believed that structural

trapping is the largest of the trapping mechanisms during CO2 injection and the first years

of post-injection, our results show that in a carbonate field like SACROC the solubility of

CO2 in oil plays a very important role, even in the first stage of CO2 injection. The reason

lies in the fact that SACROC oil has an API of around 40; therefore, the oil density is close

35

to CO2 density. When CO2 is injected into this light oil, it dissolves into CO2 very quickly

and there is no time for CO2 to reach the structure.

Running a comprehensive history matching shows the deficiency of previous

models to estimate the amount of trapped CO2 during and after the injection period. Among

the various scenarios explored, WAG seems to be a promising operational approach to

balance both storage and oil production. The present work provides valuable insights for

optimizing oil production and CO2 storage in carbonate reservoirs like SACROC unit. In

addition, this work helps decision makers to set storage goals based on optimized project

risks.

3.6.1.1 Background

The Scurry Area Canyon Reef Operators Committee (SACROC) unit in Scurry

County, West Texas, was discovered in 1948. It comprises an area of 356 km2 with an

approximate north–south length of 40 km and an east–west length of 3 km to 15 km. The

SACROC unit has 2.8 billion bbl of original oil in place and covers approximately 56,000

acres of the Kelly-Snyder field, which is the largest field along the Pennsylvanian-age

Horseshoe Atoll in the Midland Basin (Ghahfarokhi et al., 2016). The Horseshoe Atoll is

an icehouse carbonate reservoir. Icehouse carbonates are one of the least understood and

documented carbonate reservoirs because of their high heterogeneity (Isdiken, 2013).

The SACROC unit can be classified into two major reservoir zones, Canyon

and Cisco, with distinct depositional trends (Saneifar et al., 2016). The Canyon Reef

formation has limestone as the dominant mineral and some thin sections of shale that are

36

important stratigraphic markers. Shale, carbonate mudstone/wackstone, carbonate

packstone, and carbonate grainstone/boundstone are the four main lithofacies of the

Canyon formation (Ghahfarokhi et al., 2016). The heterogeneity in the Canyon formation

is because of the high-frequency cycles of sea-level change, sudden tectonic subsidence,

development of moldic and touching vug porosity, and karstification. In the Cisco

formation, karstification, fractures, and abrupt facies change are the main reasons for

heterogeneity. Geographically, the SACROC unit is divided into three major areas: the

Northern Platform, the Central Plain, and the Southwestern Region. Of the three, the

Northern Platform has the highest net-pay thickness, whereas the Southwestern Region has

the lowest net-pay thickness (Saneifar et al., 2016).

Chevron Oil Co. completed the first well at a depth interval of 6,334 to 6,414 ft.

Subsequent development was rapid, and by 1951, 1617 producing wells had been drilled

by 88 different operators. By that time, the reservoir pressure had decreased by 50%, while

the produced oil was only 5% of reservoir oil in place. Analyzing this early performance

of the reservoir revealed that solution gas drive was the primary producing mechanism of

the reservoir and no effective water drive existed. Therefore, a pressure-maintenance

program was required to improve the recovery. In 1954, water injection started along the

longitudinal axis of the crest of the reef called the “center-line” waterflood pattern in

SACROC.

Although the center-line waterflood proved to be efficient, as the waterflood

progressed to outside the flanks, it became evident that the waterflood was no longer able

to transmit enough displacement energy for oil production. Therefore, in 1968, the

37

SACROC Engineering Committee planned water-alternating-gas (WAG) injection into

202 inverted nine-spot patterns on the flanks. Because of limited CO2 supplies, three pilot

areas were selected for initial flooding. The positive results encouraged the operators to

start phase one of CO2 injection in 1972. Phase one resulted in an increase in oil production

from 30,000 BOPD to 100,000 BOPD within 18 months. Subsequently, WAG injection

was continued in two other phases.

In 2000, Kinder Morgan (KM) purchased the SACROC unit. KM installed the

Centerline Pipeline, which is delivering an additional 300 MMSCFD of CO2. KM’s

developments increased the oil production significantly; therefore, they expanded their

fully miscible CO2 flood phase-by-phase from the central area outward. These phases are

referred to as “expansion areas.” Table 3.3 summarizes the SACROC unit redevelopment

projects from 1996 to 2014. The location of different projects are shown in Figure 3.2.

More details about reservoir specifications, production history, simulation projects, and

monitoring efforts can be found in other works (Brummett et al., 1976; Dicharry et al.,

1973; Schepers et al., 2007; Han et al., 2010; He et al., 2016).

38

Table 3.3 - SACROC redevelopment projects 1996–2014 (Ghahfarokhi et al., 2016)

Year Project

1996 Center Line 1 & 2 Expansions

2001 Center Line 3

2002 Center Line 4 & 5

2003 Bull’s Eye

2004 Center Ring 1

2005 Center Ring 2

2007 Southwest Center Line 1 & 2

2008 Southwest Center Line 3, Gilligan’s Island, South Platform

2009 P1

2010 Chiquita

2011–2012 South Shore

2012–2013 P2

2013–2014 P3S

2014 Chiquita Expansion

39

Figure 3.2 – SACROC CO2 flood redevelopment project areas (Ghahfarokhi et

al., 2016).

Center Ring 2

Center Ring 1

Center

Line 5

Center

Line 1

Gilligan’s

Island

Center

Line 3

Chiquita

Southwest

Center Line

1 &2

South

Shore

SW Center

Line 3

Center

Line 2

P2

P1-A

P1-B

Bull’s Eye

P3 North

P3 South

South

Platform

40

3.6.1.2 Static Model

The Texas Bureau of Economic Geology constructed a high-resolution Petrel

model based on wire-line logs, seismic survey, core data, and stratigraphic interpretation

for the Northern Platform of the SACROC unit. Therefore, the model mimics the

heterogeneity and structure of the formations. The model consists of 221 layers and five

geological zones with a total of 9,450,623 grid blocks. In the current study, we selected a

part of the geological model shown in Figure 3.3.

Figure 3.3 – Aerial view of Petrel model for the SACROC unit. (a) The colored points are

more than 2000 vertically drilled wells in the field. (b) Permeability model for the

Northern Platform and 19 wells in the study area.

A three-dimensional corner point grid was used to model the selected study area.

The model consists of a 55×50×20 (x×y×z) Cartesian grid that has an area of 1.67 km2

(maximum grid size: 100 ft ×100 ft ×100 ft) with a maximum reservoir thickness of 0.3 km

64

Study

Area

a) SACROC Unit b) Northern Platform and study area

41

(850 ft). The area consists of 9.74E+7 STB original oil in place (OOIP). The study area

includes 19 production wells. Twelve wells have been converted to injection wells for

waterflooding. Out of these 12 wells, 10 have undergone CO2 flooding. Figure 3.4 shows

the well locations in the reservoir model. The well perforations were provided by the Texas

Bureau of Economic Geology.

Figure 3.4 - Reservoir model showing formation depth and well locations (reservoir

depth varies from 3,778 to 4,612 ft).

3.6.1.3 Phase Behavior

The Peng-Robinson equation of state (1976) was used to model the reservoir fluid

properties. The fluid model is composed of 11 different components including CO2. The

thermodynamic model and component properties were tuned based on published literature.

The composition of the components is shown in Figure 3.5 (Dicharry et al., 1973; Chaback

and Williams, 1988).

1

Depth (ft)

42

We used WINPROP from Computer Modeling Group (CMG) to model the fluid

properties: bubble point pressure, solution gas-oil ratio, formation volume factor, and fluid

viscosities (oil and gas) in this study. The Jossi-Stiel-Thodos correlation was used for oil

viscosity calculation. The bubble point pressure at reservoir temperature (130 °F) is 1820

psia, which is in agreement with the literature. Critical temperature and pressure of

reservoir fluid are 677.154 °F and 1,722.74 psia. Minimum miscibility pressure is 1640

psia which is in agreement with literature (Dicharry et al. 1973, Han 2008). We have

assumed that pure CO2 is injected and impurities from the recycle stream is not considered.

Impurities could have potentially decrease MMP and compromise performance of CO2-

EOR.

Figure 3.5 – Composition (mole %) of the reservoir fluid.

43

3.6.1.4 Relative Permeabilities

Oil-water relative permeability curves were available for two wells (Schepers et al.,

2007). However, because of the large heterogeneity of the reservoir, the data were scattered

for different core samples. The scattered data causes discontinuity in the relative

permeability data; therefore, I used Corey’s function to input a continuous set of relative

permeability into the simulator. Figure 3.6 shows the relative permeability curves matched

with the core data plotted in log scale (left) and linear scale (right).

Figure 3.6 - Water-oil relative permeability curves based on core data.

To the knowledge of the authors, there were no liquid-gas relative permeabilities

available for the SACROC unit. Thus, we used Brooks and Corey’s model (1964) for

liquid-gas relative permeability and set different parameters during history matching. Table

3.4 shows the Brooks and Corey’s function parameters used to reach the final history

match. Slr and Sgr are residual liquid and gas saturation, k0rl and k0

rg are end point relative

44

permeabilities of liquid and gas, nl and ng are liquid and gas exponents Although previous

studies have not reported the exact numbers for liquid-gas relative permeabilities, Schepers

et al. (2007) reported the ranges for different Brooks and Corey’s function parameters and

our numbers are within the same range. The liquid-gas relative permeability curve is

discussed in more details in the next section (3.6.1.5).

Table 3.4 – Brooks and Corey’s function parameters for liquid-gas relative permeability

curve.

Slr Sgr k0rl k0

rg nl ng

0.22 0.05 0.55 0.4 2 2

3.6.1.5 History matching

Although the entire historical production and injection data (1949–2016) were not

available for the study area, we could access the data for the period from 1978 to 2010. In

addition, we used the average pressure of the study area calculated by Schepers et al.

(2007). They used shut-in pressure of five wells within the study area and applied the

Peaceman’s correction (Peaceman, 1993) to calculate the average reservoir pressure. Using

this pressure data, we adjusted the production and injection data for the missing period

(1948–1978). Figure 3.7 shows the average reservoir pressure during the simulation

compared to the field data. The initial reservoir pressure was 3,122 psi at 4,300 ft.

In addition to the average reservoir pressure; oil, water, and gas production in the

study area were successfully history matched (Figure 3.8). To obtain the history match,

45

different parameters were modified and, more important, 12 pseudo-wells were introduced

to mimic the boundary condition of the study area.

Although there is no aquifer beneath the reservoir, the reservoir was under water

flooding for several years. In this research, we have focused in a section of reservoir

surrounded by several water injection wells. Schepers et al. (2007) calculated a material

balance on the edge of the study area and reported the influx of water. However, they

assumed that there is only water influx on the edges of the reservoir and they ignored oil

and gas influx on the boundary. In this study, we also assumed that it is only water influx

that controls the boundary condition, but we had to modify the water influxes to achieve

the history match. Figure 3.8 shows the history matches for oil, gas, and water production

data, respectively. In each figure, we also plotted the cumulative production. Although

history matching can always be improved, the achieved match is satisfactory for the

objectives of this project.

Figure 3.7 – History matching of average reservoir pressure.

46

Figure 3.8- History matching of oil, gas, and water production within the study area.

47

3.6.1.6 CO2 Injection Schemes

In this study, we consider two scenarios: 1) a water alternating gas (WAG) scenario,

where we assumed that the operator would have done WAG injection with the gas and

water injection rates shown in Figure 3.9; and 2) a continuous gas injection (CGI) scenario,

where we assumed that the operator would have done continuous gas injection from the

beginning of CO2 injection. The scenarios start in 1983 in which the operator had started

water and gas flooding. In 1983, the minimum oil saturation is 0.33 and 27% of initial oil

in place is still remained in the reservoir. We assumed a WAG ratio of 1 (six months of

CO2 injection followed by six months of water injection. In the last scenario, the water

injection rate is zero and the CO2 injection rate is the same as the CO2 injection rate in the

WAG scenario. In Figure 3.9 the CO2 rate is calculated using a conversion factor of

0.000328 Tonnes CO2/bbl.

Figure 3.9 - Water and CO2 injection rate in WAG scenario.

48

To design the different scenarios, we have to find a basis to choose the different

injection rates. To have a fair comparison, we decided to choose the injection CO2 and

water rates in a way that the average reservoir pressure does not change much between in

different scenarios. Therefore, reservoir pressure is a restriction in this comparison,

because if we did not have pressure restriction, then the oil production would be much

higher in continuous gas injection because of the continuous tertiary EOR technique that

we were applying to the field. The final injection patterns for different injection scenarios

are plotted in Figure 3.10. As shown in the figure (history pattern), the operator has not

injected CO2 in the study area except for a short time period. The operator implemented

water flooding for most of the time to maintain the reservoir pressure and oil production.

Figure 3.10 - CO2 injection rate for different field development strategies.

49

3.6.1.7 Hysteresis Effect

The Land (1968) equation is used to model the gas relative permeability hysteresis

by which the residual gas saturation is updated in each time step (section 3.4.2). Figure

3.11 compares the total amount of CO2 (moles) in the reservoir when the hysteresis is

included into the simulation model with the scenario in which we did not take into account

the hysteresis effect. The CO2 amount is the sum of CO2 dissolved in brine, CO2 dissolved

in oil, CO2 that exists in mobile form, and residual CO2. Hysteresis contributes to CO2

trapping significantly. In the case where we ignored the relative permeability hysteresis,

the amount of trapped CO2 is underestimated by 15%. Therefore, considering the relative

permeability hysteresis in the model is necessary to characterize the migration and final

distribution of CO2 in the reservoir.

Adding hysteresis to the simulation model increases the residual CO2 trapping.

Figure 3.12 shows the residual gas saturation distribution on 06/01/1995 for both when we

included the hysteresis into the simulation and when we did not include the hysteresis in

the simulation. This figure shows the distribution of residually trapped CO2 saturation only

in the top layer of the reservoir. In the case when we did not included the hysteresis, the

maximum amount of residually trapped CO2 is 0.05 that is the residual gas saturation in

the liquid-CO2 relative permeability curves.

50

Figure 3.11 - Estimated total CO2 with and without hysteresis effect.

1,046,000 1,047,000 1,048,000 1,049,000 1,050,000 1,051,000

1,046,000 1,047,000 1,048,000 1,049,000 1,050,000 1,051,000

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Residual Gas

Saturation

1,046,000 1,047,000 1,048,000 1,049,000 1,050,000 1,051,000

1,046,000 1,047,000 1,048,000 1,049,000 1,050,000 1,051,000

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Sg < Sgc / Hysteresis Dynamic trapped gas saturation 1996-06-01 K layer: 1

Residual Gas

Saturation

Hysteresis Not Included Hysteresis Included

Figure 3.12 – Residual gas saturation distribution on 06/01/1995.

51

3.6.1.8 Molecular Diffusion Effect

Molecular diffusion occurs because of a concentration difference between two

regions. The molecular diffusion of CO2 in brine and oil could increase the solubility

trapping. In the current study, we considered the molecular diffusion of CO2 in brine to be

2×E-9 (m2/s) (Espinoza and Santamarina, 2010) and the diffusion of CO2 in oil to be 1.8×E-

11 (cm2/s) (Guo et al., 2009). The amount of CO2 that exists in the brine, oil, and gas phases

does not change significantly when accounting for the diffusion. Grogan and Pinczewski

(1987) also concluded that molecular diffusion does not play a significant role at the field

scale.

3.6.1.9 Phase Labeling Issue

Compositional simulators sometimes label the same physical phase differently

from one time step to another time step in the same grid block. This problem is called phase

flipping. Phase flipping has been addressed by several authors (Nghiem et al., 1983; Wang

et al., 1997; Fazelipour et al., 2008; Yuan and Pope, 2012; Neshat and Pope, 2017).

Although the main issue caused by phase flipping is relative permeability discontinuities,

another problem is identified in this study. The oil density in SACROC is close to the CO2

density, and CMG-GEM labels phases based on density differences by default. Therefore,

the phase identification after CO2 injection becomes important in the SACROC unit.

In this study, we used a different method for phase labeling that determines single

phase identities based on supercritical conditions. Figure 3.13 shows the difference

between the total amounts of CO2 in the gas phase for these two methods. As can be seen

52

in the figure, there is a significant difference between the two methods, which shows the

importance of correct phase labeling in this oilfield. We choose the phase labeling method

based on supercritical conditions because in the reservoir pressure and temperature the

density of CO2 is very close to oil. Thus the phase labeling based on density difference

could not be a good option. For the case of SACROC, the density difference is even smaller

because the SACROC oil has an API of around 40.

Figure 3.13 - The calculated amount of CO2 in the gas phase based on density and

supercritical methods.

3.6.1.10 Net and Gross Utilization Ratios

Utilization ratio have the greatest import for CCS among all the performance

metrics because it is closely related to the amount of CO2 retained in the reservoir (Lake et

al., 2018). The utilization ratio is defined as the amount (MSCF) of CO2 required to produce

53

one stock tank barrel of oil. Gross utilization ratio is the amount (MSCF) of injected CO2

to produce one barrel of oil, and net gross utilization ratio is the amount of purchased CO2

to produce one barrel of oil. Figure 3.15 shows the net and gross CO2 utilization ratio for

the two scenarios that is calculated as follows:

Utilization ratios are plotted versus time and pore volume of CO2 injected (PV) in

Figure 3.15. Utilization ratios are not constant as they highly depend on the time of CO2

injection. At early times before significant oil production begins, the net utilization ratio is

large. In both the continuous gas injection and water alternating gas scenarios, the net

utilization factor becomes nearly constant with an average of around 2 MSCF/STB. Lake

et al. (2018) investigated several CO2-EOR projects and reported a range of 2 to 14

MSCF/STB for net utilization factor with an average of 5 MSCF/STB (Figure 3.14).

𝐺𝑟𝑜𝑠𝑠 𝑢𝑡𝑖𝑙𝑖𝑧𝑎𝑡𝑖𝑜𝑛 𝑟𝑎𝑡𝑖𝑜 = 𝐼𝑛𝑗𝑒𝑐𝑡𝑒𝑑 𝐶𝑂2

𝑃𝑟𝑜𝑑𝑢𝑐𝑒𝑑 𝑂𝑖𝑙 (3.13)

𝑁𝑒𝑡 𝑢𝑡𝑖𝑙𝑖𝑧𝑎𝑡𝑖𝑜𝑛 𝑟𝑎𝑡𝑖𝑜 = 𝐼𝑛𝑗𝑒𝑐𝑡𝑒𝑑 𝐶𝑂2 − 𝑃𝑟𝑜𝑑𝑢𝑐𝑒𝑑 𝐶𝑂2

𝑃𝑟𝑜𝑑𝑢𝑐𝑒𝑑 𝑂𝑖𝑙 (3.14)

54

Figure 3.14 – Net utilization factor for a large set of CO2-EOR projects (Lake et al.,

2018).

At the beginning of the project, more CO2 is required to increase the pressure but after each

cycle of injection the required net CO2 to produce each barrel of oil decreases. In

continuous gas injection scenario (CGI), the net utilization factor is larger at early time of

the project in comparison with water alternating gas (WAG) injection. The larger values in

CGI scenario suggest that more net CO2 production is occurring in CGI in comparison with

WAG.

Gross utilization factor is smaller at the beginning of the project that means to

produce each STB of oil, 10 MSCF of CO2 is required in CGI case and 5 MSCF is required

in WAG injection case. As the Figure 3.15 suggests, gross utilization ratio has a minimum.

This minimum happens after two years of CO2 injection for our cases. After two years of

55

CO2 EOR, the gross utilization ratio increases because the reservoir pressure and thus CO2

solubility in oil decreases. It suggests that after a period of time the amount of pure CO2

production increases. CGI has larger gross utilization ratio in comparison with WAG. This

difference indicates the higher performance of WAG to produce each barrel of oil. In WAG

scenario, water injection decreases the mobility ratio and thus increases the sweep

efficiency of the flood.

Figure 3.15 - Evolution of gross and net CO2 utilization ratio for different field

development strategies during CO2 injection time.

56

3.6.1.11 CO2 Storage

The contribution of CO2-EOR to CO2 storage lies in the voidage replacement

concept. Voidage replacement simply describes the contribution of the injecting fluid (e.g.,

CO2) in replacing the initial resident fluid (e.g., brine, oil) in pore space. Although the

voidage replacement depends on how much oil shrinks after production from the reservoir,

the voidage replacement of oil by CO2 is in the range of 2 to 4 MSCF/STB for typical

reservoir pressure and temperature. The voidage replacement of brine by CO2 is around 2

MSCF/STB (Lake et al., 2018). Therefore, in WAG injection, water may occupy some of

the pore space previously occupied by oil or previously injected CO2 that reduce the CO2

retention/storage. Figure 3.16 shows a comparison between the retention/storage of CGI

and WAG. As discussed above, WAG shows a smaller storage capacity. The net stored

CO2 is calculated as follows (Choi et al., 2013):

We assume there is no CO2 loss in subsurface and no vented CO2. The net CO2

storage occurs because of different trapping mechanisms that includes the amount of

mobile CO2, residual CO2, CO2 soluble/miscible in oil, and CO2 dissolved in brine.

𝑁𝑒𝑡 𝐶𝑂2 𝑠𝑡𝑜𝑟𝑎𝑔𝑒 =

𝐼𝑛𝑗𝑒𝑐𝑡𝑒𝑑 𝐶𝑂2 − 𝑅𝑒𝑐𝑦𝑙𝑐𝑒𝑑 𝐶𝑂2 − 𝐿𝑜𝑠𝑡 𝐶𝑂2 𝑖𝑛 𝑠𝑢𝑏𝑠𝑢𝑟𝑓𝑎𝑐𝑒 − Vented 𝐶𝑂2

(3.15)

57

Figure 3.16 - Net amount of stored CO2 by the end of 2010.

Lake et al. (2018) investigated the retention/storage in several CO2-EOR projects and

reported an average of 0.4 hydrocarbon pore volume (HCPV) stored CO2 after injecting

one HCPV of CO2 (Figure 3.17). We also calculate the amount of stored CO2 (PV/HCPV)

versus the amount of injected CO2 (PV/HCPV) for CGI and WAG scenarios (Figure 3.18).

In both Figure 3.16 and Figure 3.18, there are oscillations in WAG scenario. These

oscillations occur because of cyclic injection of CO2 in WAG scenario. During the water

injection period of each cycle, CO2 is produced and the amount of CO2 in the reservoir

(stored CO2) decreases.

58

Figure 3.17 – CO2 retention/storage of a large set of CO2-EOR projects (Lake et al.,

2018).

Figure 3.18 – CO2 storage versus HCPV/PV injected CO2.

59

3.6.1.12 CO2 Trapping Mechanisms Contribution

Although all trapping mechanisms are considered effective and safe for CO2

storage, capillary trapping and dissolution trapping add a degree of confidence in the

permanence of CO2 storage. Therefore, we calculated the percentage of CO2 in different

phases to show the reliability of storage for various field development strategies. Figure

3.19 shows the percentage of CO2 stored by each trapping mechanism at the end of the

CO2–EOR operation (12/2010). The contribution of residual CO2 trapping is higher in the

WAG injection scenario in comparison with CGI scheme. The reason is the frequent

hysteresis effect that happens during WAG injection because of the alternative imbibition

and drainage.

Figure 3.19 - CO2 stored by different trapping mechanisms at the end of the CO2–EOR

operation (12/2010).

Additionally, the amount of CO2 in the four main trapping mechanisms (i.e.,

residual trapping, structural trapping, CO2 miscibility trapping in oil, and CO2 solubility

58

5

26

11

47

3

43

7

0

10

20

30

40

50

60

70

Miscible in oil Dissolved in brine Mobile CO2 Residual CO2

Fra

ctio

n (

%)

WAG CGI

60

trapping in brine) are calculated. Both injection scenarios were followed by a 100-year

observation period (post-injection period). Figure 3.20 and Figure 3.21 show the CO2

partitioning in different phases and forms in the both injection and observation periods for

WAG and CGI respectively. These figures show how the contribution of different trapping

mechanisms change during the injection period and over 100 years post injection.

Comparing Figure 3.20 and Figure 3.21, WAG shows much lower mobile CO2

(structurally trapped) and higher miscible, dissolved, and residual CO2 in comparison with

CGI. As discussed earlier, WAG retains smaller amount of CO2 into the reservoir in

comparison with CGI. However, in the following two figures, we are comparing the

percentage contribution of each trapping mechanism for each individual scenario. In WAG

scenario, cyclic injection water first, induces hysteresis that increases the residual trapping

of CO2. Second, multiple contact of water and CO2 occurs that leads to a higher solubility

of CO2 into water. Third, the mobility of the flood decreases so CO2 does not breakthrough

quickly and has the chance to dissolve into oil through multi-contact mechanism.

Increasing the contribution of the above trapping mechanisms reduces the contribution of

mobile (structural) trapping mechanism.

More mobile CO2 in the CGI scenario introduces a greater risk of vertical

displacement of CO2 plume in the reservoir which increases the risk of future CO2 leakage.

Miscible CO2 increases in WAG, because the cyclic injection of water controls the mobility

ratio and stabilizes the front; therefore, the sweep efficiency of the flood increases. Higher

sweep efficiency in WAG means more CO2 in contact with oil which leads to more

miscibility trapping of CO2 in the WAG scenario. In the WAG scenario, cyclic injection of

61

water makes the total amount of present water in the reservoir higher; therefore, more water

is in contact with CO2. Since the amount of CO2-contacted brine is more in WAG, more

brine solubility trapping is an expected result in WAG in comparison with CGI scenario.

Residual trapping is also larger in WAG in comparison with CGI, especially during the

injection period and first years of post-injection, because of the frequent relative

permeability hysteresis effect during WAG injection.

In Figure 3.20 and Figure 3.21, the red lines in the injection period shows the trend

of oil miscibility trapping. Comparing the trend of oil miscibility trapping and “net

utilization ratio vs. time” in Figure 3.15, we find that net utilization ratio can be a very

good representative of oil miscibility in a CO2-EOR process.

62

Figure 3.20 - Contribution of different CO2 trapping mechanism during injection and observation period

in the WAG scenario.

92

Tim

e S

cale

Bre

ak

CGI

0

100

01/1983

27 years of Injection 100 years of Post Injection

12/2010 12/2110

Figure 3.21 - Contribution of different CO2 trapping mechanism during injection and observation

period in the CGI scenario.

91

Tim

e S

cale

Bre

ak01/1983

0

27 years of Injection 100 years of Post Injection12/2010 12/2110

WAG

63

3.6.1.13 Oil Recovery

Finally, we compared the amount of produced oil for the assumed field

development strategies. Figure 3.22 shows the cumulative oil production for the two

scenarios compared with the actual history of the field oil production. Figure 3.22 shows

that the history pattern produces 50% less oil than the CGI and WAG simulation because,

in the history pattern, the CO2 injection rate was very small and was terminated only after

a few years, and waterflooding was the main recovery technique. This figure shows that if

the operators would inject more CO2, the oil recovery could be 50% greater.

Figure 3.22 - Cumulative volume of produced oil from 1983 to 2010 for different

scenarios.

64

Comparing the CGI and WAG scenarios with the actual operating injection scheme,

we find that WAG and CGI increases the oil recovery significantly. Implementing the

assumptions in the simulations, the difference between oil recovery of WAG and CGI is

not significant. As discussed before, the utilization ratio in WAG is lower than CGI, which

suggests a lower cost in operation. In addition, CGI stores the injected CO2 mostly in the

mobile phase, which increases the risk of leakage. Therefore, our study shows that WAG

could be a balance between CO2 utilization and oil production in the most efficient way.

To show the better performance of WAG in comparison with CGI, we calculated the

recovery factor of each scenario versus the amount of injected CO2 (HCPV/PV). As shown

in Figure 3.23, although the total oil recovery factor is higher in CGI (around 43%), the

recovery factor for the same amount of injected CO2 is higher in WAG scenario.

Figure 3.23 – Oil recovery factor versus injected CO2.

65

3.6.2 Cranfield

This section presents another field-scale compositional reservoir flow modeling for

the Cranfield reservoir, Mississippi. The simulation work is completed by Hosseini et al.

(2018). I use this simulation case study for reference as a sandstone field case study. I will

compare the results of the SACROC unit simulation with the results of Cranfield in section

3.6.3. For this study, they used the public-domain data related to Denbury Onshore, LLC-

operated EOR site of Cranfield, MS. The Bureau of Economic Geology (UT-BEG) has

been conducting a research program in this area almost a decade (Hovarka et al., 2013;

Hosseini et al., 2018).

3.6.2.1 Background

The Cranfield site is located on the Adams-Franklin county line in Mississippi, east

of the town of Natchez (Weaver and Anderson, 1966). The original productive area of the

reservoir was estimated to be 31.3 km2 which comprises fluvial sandstones of Cretaceous

lower Tuscaloosa Formation at depths from 3,060 to 3,193 m which form a simple anticline

with a northwest trending crestal graben (Hovarka et al., 2011). Water drive from an active

aquifer down dip of the reservoir is the primary producing mechanism of the reservoir. The

initial reservoir temperature was reported 125°C with an initial reservoir pressure of 32.4

MPa at 3,040 m. In the northeast of part of the anticline, a sealing fault intersects the

reservoir.

66

The first oil producing well was drilled in 1944. Since then, a productive area of

about 7,750 acres has been defined by 93 producing wells. The oil wells were drilled based

on a 40-acre spacing whereas the spacing for the gas wells was 320 acres. The dome-shaped

reservoir consists of an oil ring overlain by a large gas cap. A cycling and extraction gas

plant was used to reinject the produced gas from the Cranfield and the deeper Paluxy

reservoirs into the Tuscaloosa Formation. By 1951, the injected gas had reached many of

the oil zone wells. The gas cycling continued until 1960 with dry gas sweeping the gas cap

and the oil zone. Although the gas injection plans were meant to avoid, or slow down, the

pressure depletion in the reservoir, reservoir pressure gradually fell below 27.6 MPa (4000

psi) causing water to encroach into the oil zone as the oil was produced.

By the beginning of 1960, most of the wells had either a ~100% water cut or a

GOR greater than 100,000 (SCF/STB) with an average field water cut equal to 88% and

GOR equal to 85,000 SCF/STB. The blow down of the gas cap started then. At the same

time, water was produced in large volumes to prevent the aquifer from pushing the

remaining oil into the gas cap and moving into other overlying formations. Gas injection

stopped in 1964 when the project was near its economic limit. Production from the field

was halted on 1966 and the reservoir was abandoned. This time period, from 1944 to 1966,

corresponds to the conventional historical production interval.

Over the next several decades, a strong water drive restored pressure to near-initial

levels. In 2007, CO2-EOR was initiated by Denbury Onshore, LLC to sweep the residual

oil. Between 2008 and 2015, more than half of the oil ring was developed using a semi

five-spot injection pattern with continuous CO2 injection. Development of the initial

67

patterns started in the northern part of the field and continued clockwise around the oil ring.

This time period corresponded to the historical CO2-EOR injection period. More details

about reservoir specifications, production history, simulation projects, and monitoring

efforts can be found in other works (Alfi and Hosseini, 2016; Alfi et al., 2015; Choi et al.,

2011; Hosseini et al., 2013; Hovorka et al., 2013; Weaver and Anderson, 1966).

3.6.2.2 The Cranfield Model

Cranfield’s productive zone divides into two compartments by a fault. Although

Cao (2011) reported a weak connectivity between the two productive segments, Hosseini

et al. (2018) assumed that the fault is sealing and there is minimum interaction between the

two compartments. The dashed line in

Figure 3.24 (a) shows this sealing fault. Hosseini et al. (2018) used this

characteristic and modelled only the smaller section of the Cranfield that is located in the

north eastern side of the reservoir.

They built a Cartesian grid system that consists of 124 grids in the x-direction, 149

grids in y-direction, and 20 grids in z-direction using CMG-GEM. The dimension of the

reservoir model is 7.5 km × 5.65 km × 24.4 m which corresponds to length, width, and

thickness, respectively (Hosseini et al., 2018). The permeability and porosity distribution

is obtained from detailed core and log analysis (Hosseini et al., 2013). Although the total

number of grid blocks is 369,520, only 82,559 are active located in the northeastern part

of the reservoir. The details on the reservoir model could be found (Hosseini et al., 2018).

Figure 3.25 shows the well locations in the north eastern side of the reservoir.

68

Figure 3.24 - Structural contour map at Cranfield: (a) the black dashed line represents the

sealing fault that divides the productive zone into two compartments. (b) the simulation

model focuses on the smaller zone (north eastern) the reservoir so the rest of the model is

inactive to reduce the computational cost (Hosseini et al., 2018; Hosseininoosheri et al.,

2018 (c)).

Figure 3.25 - Reservoir model showing formation depth and well locations.

69

3.6.2.3 Phase Behavior

The Peng–Robinson equation of state (1976) was used to model the reservoir fluid

properties in WINPROP from CMG. The fluid model is composed of seven components,

including CO2. The thermodynamic model and component properties were tuned based on

published literature (Weaver and Anderson, 1966).

3.6.2.4 Relative Permeability

In the Cranfield simulation model, Hosseini et al. (2018) obtained the relative

permeability curves from the data published by Weaver and Anderson (1966). They

modified the endpoint relative permeabilities and the residual saturation during the history

matchings. The final relative permeability curve they used in the simulation model is in

Figure 3.26.

Figure 3.26 – Relative permeability curves used in Cranfield case study (Hosseini et

al. (2018)).

70

3.6.2.5 History Matching

Before moving to design the different injection scenarios, Hosseini et al. (2018)

verified their simulation model by comparing the reservoir pressure; and oil, gas, and water

production with historical data (1944-19660). Figure 3.27 shows the historical injection,

production, and pressure data. In addition to the primary and secondary production history

matching, they performed a history matching for CO2-EOR period. More details on the

history matching could be found in the original paper (Hosseini et al., 2018).

Figure 3.27- Historical injection, production, and pressure data before starting the

CO2-EOR operation (Hosseini et al., 2018)

71

3.6.2.6 CO2 Injection Schemes

Although Hosseini et al. (2018) have designed four different CO2 injection

scenarios: continuous gas injection (CGI), water alternating gas (WAG), water curtain

injection (WCI), and water curtain injection with WAG patter in the middle wells, the focus

of this chapter is providing a comparison between the results of SACROC simulation

model and the Cranfield model. Therefore, we only focus on two injection schemes:

continuous gas injection (CGI) and water alternating gas injection (WAG). In the SACROC

model case, we did not investigate the water curtain scenarios because our available data

was for a middle section of the reservoir and water flux existed around the boundary of that

section. The water flux existed because of the ongoing water flooding around the area.

Figure 3.28 shows the CO2 injection rates designed for Cranfield study.

Figure 3.28- CO2 injection rate in WAG and CGI scenarios.

72

3.6.3 Comparison of SACROC and Cranfield

Water alternating gas (WAG) and continuous gas injection (CGI) are two main field

development strategies in CO2-EOR processes. Therefore, we investigated and discussed

the partitioning of CO2 among different phases (oil, gas, and brine) during and after two

well-known CO2 injection schemes using numerical multiphase flow simulations. We

compare these strategies in terms of their economic performance (from the basis of

incremental oil recovery) and in terms of their environmental performance (from the basis

of ultimate CO2 storage volumes). Within this framework, and to demonstrate the

efficiency of each strategy, we evaluate the distribution of carbon dioxide in oil, gas, and

brine phases; the amount of total CO2 stored at the end of the project; the incremental oil

recovery; and the CO2 utilization ratios. In this study, we model and compare two fields,

which represent two different reservoir settings: Cranfield (representative of the U.S. Gulf

Coast sandstone reservoirs) and SACROC (representative of the Permian Basin carbonate

reservoirs). CGI is the original operating strategy in Cranfield and WAG is the original

operating strategy applied in the SACROC unit.

3.6.3.1 Contribution of CO2 Trapping Mechanisms

Residual trapping, structural trapping, CO2 miscibility trapping in oil, and CO2

solubility trapping in brine were calculated and analyzed for both fields. Figure 3.29

summarizes the CO2 partitioning in different phases and forms in the observation period

for Cranfield. Figure 3.30 shows the CO2 trapping mechanisms’ contribution for the

SACROC unit. Both of the figures are plotted in observation period (post-injection period).

73

As can be seen in both Figure 3.29 and Figure 3.30, WAG shows much lower mobile CO2

(structurally trapped) and higher miscible, dissolved, and residual CO2 in comparison with

CGI. Higher mobile CO2 in the CGI scenario introduces a higher risk of vertical

displacement of CO2 plume in the reservoir that increases the risk of CO2 leakage in the

future.

Miscible CO2 increases in WAG, because the cyclic injection of water controls the

mobility ratio and stabilizes the front; therefore, the sweep efficiency of the flood increases.

Higher sweep efficiency in WAG means more CO2 in contact with oil that leads to more

miscibility trapping of CO2 in WAG scenario. In WAG scenario, cyclic injection of water

makes the total amount of present water in the reservoir higher; therefore, more water is in

contact with CO2. Since the amount of CO2-contacted brine is more in WAG, more brine

solubility trapping is an expected result in WAG in comparison with CGI scenario.

Residual trapping is also higher in WAG in comparison with CGI, especially during the

injection period and first years of post-injection, due to the frequent relative permeability

hysteresis effect during WAG injection.

74

Figure 3.29 - Contribution of different CO2 trapping mechanisms in post-injection period for

Cranfield.

Figure 3.30 - Contribution of different CO2 trapping mechanisms in post-injection period for

SACROC.

75

3.6.3.2 Incremental Oil Recovery

In addition to the importance of CO2 trapping mechanisms’ contributions, the effect

of each scenario on the incremental oil recovery plays an important role to decide which

of these field development strategies could be more efficient, especially from the operator’s

point of view. Therefore, we plotted the amount of produced oil for the assumed field

development strategies for both fields. Figure 3.31 shows the cumulative oil production of

WAG and CGI for Cranfield and SACROC.

Figure 3.31 - Cumulative volume of produced oil for WAG and CGI.

3.6.3.3 Utilization Ratios

In addition to oil production and the distribution of CO2 in different phases, net and

gross utilization ratios of CO2 are important factors. We plotted the net and gross utilization

ratios for both Cranfield and SACROC and compared WAG and CGI scenarios for both

fields (Figures 3.32 and 3.33).

76


during CO2 injection time (Cranfield).


during CO2 injection time (SACROC).

77

3.7 SUMMARY AND CONCLUSIONS

In this chapter, we investigated the partitioning of CO2 in different phases through

different operation development strategies. The main purpose of this study was to answer

questions associated with the relationship between EOR operational strategies and CO2

utilization ratios, and to understand the impact of the different CO2 trapping mechanisms

on this relationship. First we modelled the CO2 injection scenarios for the SACROC

reservoir. In the specific case of SACROC, and to answer these questions with high

confidence, we integrated three main elements of field assessment: physical field

characterization, production and pressure history, and reservoir simulation.

We used a geocellular model and modified the relative permeabilities and reservoir

boundary conditions of the simulation model based on field history performance. We used

the history-matched model for initialization of different development strategies. We

assumed that the average reservoir pressure of the field is the same for different

development strategies.

In summary, our results show that various field development strategies have a

greater impact on the relative contribution of different trapping mechanisms. Based on our

simulation model on SACROC, WAG shows a good balance between maximizing oil

production and CO2 storage with a lower utilization ratio compared to CGI. In addition,

WAG improves the storage security by decreasing the amount of mobile CO2 in the

reservoir. It is worth mentioning that any final decision should be made based on a cost-

benefit analysis.

78

After that, to compare the results of the SACROC simulation, we used the Cranfield

simulation model to investigate if the conclusion is different for different fields. Although

the actual operating strategy in SACROC and Cranfield are different (CGI in Cranfield and

WAG in SACROC), our numerical modelling results show that WAG could not only

balance the CO2 storage, incremental oil recovery, and CO2 utilization ratio but also store

the trapped CO2 with lower risk of leakage in both fields (by decreasing the amount of

structurally trapped CO2) in both cases. Because of the multiple alternation of CO2 and

water slugs in WAG, this approach reduces the viscous instability and therefore the

efficiency of oil recovery.

Our study shows that the distribution of CO2 in different phases is different for each

field. Because of the lower minimum miscibility pressure (MMP) and lighter initial oil

saturation in SACROC, the partitioning of CO2 in oil is much higher in SACROC than in

Cranfield. The dissolution of CO2 in brine is much higher in Cranfield because of the

presence of strong aquifer near injection wells. In summary, our results show that various

field development strategies have a greater impact on the relative contribution of different

trapping mechanisms rather than the type of the reservoir.

79

Chapter 4: CO2 Trapping Modeling in CO2-EOR/Storage Processes

Using Fractional Flow Analysis2

In this chapter, I use fractional flow analysis to investigate CO2 trapping in a CO2-

EOR process. I use the method published by Walsh and Lake (1989) to characterize the

trapping during simultaneous water and gas injection. I assume that water and gas are being

injected with the same volume fraction (i.e., WAG ratio = 1).

Before explaining how I calculated the different trapping mechanisms using the

Walsh and Lake (1989) method, I will give an introduction on why analytical investigation

of CO2 trappings is important. I also explain the method of characteristic (MOC) and the

coherence theory concept. After that, I move forward to the formulation of conservation

equation and how Walsh and Lake (1989) solved the conservation equation for a miscible

displacement using the MOC.

Relative permeability is one of the main parameters that changes the fractional flow

curves. In this chapter, I will investigate the sensitivity of the trapping mechanism

contribution by changing the relative permeability curves. I provide two cases that are the

representatives of oil-wet and water-wet relative permeability curves. I will explain how

the trapping mechanism differs in the two cases.

2 The content in this chapter was published as: Hosseininoosheri, P., Mehrabi, M., Hosseini, S.A., Nunez-

Lopez, V. and Lake, L.W., 2018. April. Impact of Relative Permeability Uncertainty on CO2 Trapping

Mechanisms in a CO2-EOR Process: A Case Study in the US Gulf Coast (Cranfield) (No. DOE-SSEB-42590-

11). In SPE Western Regional Meeting. Society of Petroleum Engineers. The main author of the paper is


80

4.1 INTRODUCTION

Besides numerical simulation models, another approach of predicting CO2

migration and trapping is analytical and semi-analytical models. Although numerical

simulation provides comprehensive solutions to multiphase flow problems, the simple

analytical solutions are of interest, as the numerical simulations do not yield explicit

expressions in terms of the model parameters. Additionally, multiphase flow simulations

are computationally intensive (Ghanbarnezhad Moghanloo, 2012).

Previously published analytical and semi-analytical models are either vertical

equilibrium (VE) models or fractional flow models (FFM). In VE models, a large aspect

ratio is assumed which provides a good vertical communication within the reservoir. The

VE assumptions can be satisfied for many reservoirs (Lake et al., 2014). In particular, the

VE assumption is valid for laterally extensive saline aquifers in sedimentary basins. By the

assumption of no capillary transition zone, the VE model reduces to a sharp interface

model. There is an extensive research on sharp-interface models (Nordbotten et al., 2005).

Further research was conducted by Hess et al. (2008) by considering the residual trapping

of CO2, MacMinn et al. (2010) by investigating the solubility trapping, Dentz and

Tartakovsky (2009) by investigating the buoyancy-dominated condition, and Vilarrasa et

al. (2010) by considering the fluid compressibility.

Although the VE and sharp interface models are useful in predicting CO2 plume

when applied within an appropriate scale (Court et al., 2010; Swickrath et al., 2016),

fractional flow models (FFM) has the advantage of accounting for the tempo-spatial

evolution of CO2 saturation (Ren, 2017). Extensive analytical research has been conducted

81

based on FFM. Burton et al. (2009) incorporated the dry region in FFM, Noh et al. (2007)

coupled geochemistry into FFM, Mijic and LaForce (2012) considered non-Darcy flow as

well as miscibility and gas compressibility (Mijic et al., 2014), Saripalli and McGrail

(2002) considered a buoyancy flow with simultaneous dissolution, and Ren et al. (2015)

accounted for buoyancy driven floating in conjunction with permeability heterogeneity.

Despite the extensive analytical research on modeling of CO2 trapping, none has

provided direct relationships of different parameters with the CO2 trapping mechanisms

during a CO2-EOR process.

4.2 THE METHOD OF CHARACTERISTICS

The method of characteristics (MOC) is a technique to solve the first-order, strictly

hyperbolic, partial differential equations (PDE) that describe multiphase flow and reactive

transport in porous media such as the mass conservation equation (Lake et al. 2014, Lake

et al. 2003). The objective is to transform the governing partial differential equations into

a set of ordinary differential equations (ODE). The ODEs will be then solved using

standard methods after incorporating the initial and boundary conditions.

MOC has been employed widely in solving fluid flow in porous media PDEs. A

notable example is the solution for immiscible displacement called the Buckley-Leverett

solution (1942). The Bucklet-Leverett solution has been verified by core flooding

experiment (Peters and Hardham, 1990). The MOC has also been used to describe the

vertical CO2 plume migration in aquifers (Silin et al. 2009, Hayek et al. 2009, Riaz and

Tchelepi 2008).

82

4.3 THE CONCEPT OF COHERENCE

The coherence concept is stated as “an arbitrary variation in the starting condition,

if embedded between sufficiently large regions of constant state, sorts itself out into simple

waves between which new regions of constant state arise” (Helfferich, 1981). In other

words, if a wave is coherent, all of the compositions of the wave travel with the same

velocity and in the same direction (Hankins et al., 2004, Ghanbarnezhad Moghanloo,

2012).

4.4 FRACTIONAL FLOW APPLICATION FOR TRAPPING MECHANISMS

We use the fractional flow analysis that is an application of a subset of the MOC,

known as coherent wave theory (Courant and Hilbert, 1954; Helfferich, 1981). It solves

the conservation and constitutive equations in one-dimensional flow. Fractional flow

theory has been used for simplifying and understanding of water flooding (Buckley and

Leverett., 1942; Craig, 1971), polymer flooding (Patton et al., 1971), carbonated

waterflooding (De Nevers, 1964), alcohol flooding (Wachmann, 1964), solvent flooding

(Welge et al., 1961; Walsh and Lake 1989), steam flooding (Shutler and Boberg, 1972),

and various types of surfactant flooding (Fayers and Perrine, 1958; ) for many years (Pope,

1980; Lake, 1989).

In this study, we use the analysis published by Walsh and Lake (1989) on the

application of fractional flow theory for miscible displacement in the presence of an

immiscible aqueous. In this method it is assumed the water and solvent (CO2) are being

injected simultaneously. We take a constant WAG ratio and apply the fractional flow

83

theory to find the CO2 distribution in gas, oil, and water. We also investigate the effect of

relative permeability on trapping mechanisms by changing the modified Brooks-Corey

(Lake, 1989; Droz, 1997; Alpak et al., 1999; Goda and Behrenburch, 2004) parameters for

relative permeability. The main assumptions in fractional flow analysis in EOR studies are

as follows (Lake, 1989; Pope, 1980; Walsh and Lake; 1989):

(1) the flow is 1D in a homogenous and isothermal porous medium

(2) rock properties are independent of pressure

(3) the fluids are in local thermodynamic equilibrium

(4) at most three components are present

(5) two phases are flowing at initial conditions

(6) gravity and capillarity are negligible

(7) dispersion/diffusion is negligible

(8) there is no adsorption

Subject to the above assumptions, the conservation equations can be written in non-

dimensional form for each component as follows:

where 𝐶𝑖 and 𝐹𝑖 are the overall concentration and fractional flow of component 𝑖, 𝑡𝐷 and

𝑥𝐷 are dimensionless time and distance, respectively (Lake, 1989). The independent

variables in the equation are dimensionless time and position. Dimensionless time is the

total volume of fluid injected up to time t divided by the medium total pore volume as

follows:

𝜕𝐶𝑖

𝜕𝑡𝐷+

𝜕𝐹𝑖

𝜕𝑥𝐷= 0 𝑖 = 1, … , 𝑁𝑐

(4.1)

84

where 𝐴 is the cross-sectional area of the 1D medium in the direction perpendicular to the

x-axis, 𝑢 is the volumetric flux or Darcy velocity, t is time, ∅ is porosity, 𝐿 is the length, and

�̅� is the average cross sectional area. Dimensionless position is defined as follows:

where 𝑥 is the position. 𝐶𝑖 and 𝐹𝑖 are defined as follows:

where 𝐶𝑖𝑗 is the volume fraction of component 𝑖 in phase 𝑗, 𝑆𝑗 is the saturation of phase 𝑗,

𝑓𝑗 is the fractional flow of phase 𝑗, 𝑁𝑐 is the total number of components, and 𝑁𝑝 is the

number of phases. The water fractional flow for water in a horizontal medium (dip angle

of zero) can be defined as follows:

where 𝑘𝑟 is relative permeability and 𝜇 is viscosity.

𝑡𝐷 =∫ 𝐴𝑢𝑑𝑡

𝑡

0

∅𝐿�̅�

(4.2)

𝑥𝐷 =∫ 𝐴𝑑𝑥

𝑥

0

𝐿�̅�

(4.3)

𝐶𝑖 = ∑ 𝑆𝑗𝐶𝑖𝑗

𝑁𝑝

𝑗=1

𝑖 = 1, … , 𝑁𝑐 (4.4)

𝐹𝑖 = ∑ 𝑓𝑗𝐶𝑖𝑗

𝑁𝑝

𝑗=1

𝑖 = 1, … , 𝑁𝑐 (4.5)

𝑓𝑤,𝑗 = (1 +𝑘𝑟𝑗𝜇𝑤

𝑘𝑟𝑤𝜇𝑗)−1 𝑗 = oil, CO2

(4.6)

85

The analysis is for the case where CO2 and water are injected simultaneously. The

initial condition (𝑡𝐷=0) is a uniform water saturation, 𝑆𝑊𝐼 , with no CO2 present initially.

The injection condition 𝐽 is some prespecified proportion of CO2 and water 𝑓𝑤𝐽 given on

CO2/water fractional flow curve. The volumetric flow-rate ratio of water to CO2 (WAG

ratio) is given by

Inverting equation 4.5, the fractional flow of water at the injection point can be written as

follows:

After writing the conservation equation for water and CO2 in oil, the specific concentration

velocity is calculated as follows:

By taking the solubility of CO2 in water (𝐶𝑔𝑤), a trapped oil saturation (𝑆𝑂𝑀), and

partitioning of CO2 into the trapped oil (𝐶𝑔𝑇) into account, the specific concentration

velocity can be calculated by a simple material balance around the miscible displacement

front as follows:

𝑊𝑅 =𝑣𝑜𝑙𝑢𝑚𝑒𝑡𝑟𝑖𝑐 𝑟𝑎𝑡𝑒 𝑜𝑓 𝑤𝑎𝑡𝑒𝑟

𝑣𝑜𝑙𝑢𝑚𝑒𝑡𝑟𝑖𝑐 𝑟𝑎𝑡𝑒 𝑜𝑓 𝐶𝑂2=

𝑓𝑤𝐽

1−𝑓𝑤𝐽

(4.7)

𝑓𝑤𝐽 =𝑊𝑅

1+𝑊𝑅

(4.8)

𝑣𝑐 =𝑓2

𝑆2

2 = oil, CO2 (4.9)

86

where 𝑣𝑐 is the specific concentration velocity, which is constant. Specific velocity of

concentration C is the differential of dimensionless position divided by the differential of

dimensionless time for constant concentration of C. It is called “specific” velocity because

it has been normalized by bulk fluid intestinal velocity (Lake et al., 2014). 𝑓𝑔 is fractional

flow of CO2, 𝑆𝑔 is CO2 saturation, 𝐶𝑔𝑤 is the volume fraction of CO2 in the water, 𝑆𝑂𝑀 is

the residual oil saturation to the miscible solvent, 𝐶𝑔𝑇 is the volume of fraction of CO2 in

the residual phase. The graphical interpretation of 𝑣𝑐 from equation 4.8 is the slope of a

straight line emanating from point (a,b) and intersecting CO2-water fractional flow curve.

By writing a similar material balance on the oil cross, the wave specific

concentration velocity is calculated as follows:

which is the slope of a straight line emanating from point (c,1) and intersecting the oil-

water fractional flow curve.

𝑣𝑐 =𝑓𝑔

𝑆𝑔=

1 − (1 − 𝐶𝑔𝑤)𝑓𝑤

𝐶𝑔𝑤𝑆𝑤 − 𝐶𝑔𝑇𝑆𝑂𝑀 + (1 − 𝑆𝑂𝑀 − 𝑆𝑤)=

𝑓𝑤 − 𝑏

𝑆𝑤 − 𝑎

(4.10)

𝑎 =1 − 𝑆𝑂𝑀 (1 − 𝐶𝑔𝑇)

1 − 𝐶𝑔𝑤

(4.11)

𝑏 =1

1 − 𝐶𝑔𝑤

(4.12)

𝑣𝑐 =𝑓𝑜

𝑆𝑜=

1 − 𝑓𝑤

1 − 𝑆𝑤 − 𝑆𝑂𝑀(1 − 𝐶𝑔𝑇)=

𝑓𝑤 − 1

𝑆𝑤 − 𝑐

(4.13)

𝑐 = 1 − 𝑆𝑂𝑀(1 − 𝐶𝑔𝑇) (4.14)

87

To apply this method to find the CO2 trapping mechanisms, we assume WAG ratio

of 1 (𝑊𝑅 = 1) for all cases and keep the solubilities and miscible residual oil saturation

constant. We use the modified Brooks Corey’s function to define the relative permeabilities

and fractional flows. We calculate the trapped CO2 as follows:

where 𝑆𝐶𝑂2

𝑝𝑢𝑟𝑒 , 𝑆𝐶𝑂2

𝑜𝑖𝑙 , and 𝑆𝐶𝑂2

𝑤𝑎𝑡𝑒𝑟 are pure CO2 saturation, saturation of CO2 dissolved in oil,

and saturation of CO2 dissolved in water, respectively. We do not take into account the

hysteresis effect so we assume that residual trapping is negligible.

4.5 TRAPPINGS SENSITIVITY TO RELATIVE PERMEABILITY PARAMETERS

In this section, I first introduce the modified Brooks and Corey function for relative

permeability. Then, I discuss the effect of relative permeability parameter on the

contribution of different CO2 trapping mechanisms in a CO2-EOR process.

4.5.1 Modified Brooks and Corey’s Model

Although no general theoretical expression exists for relative permeability, several

empirical models have been proposed for relative permeabilities (Lake, 1989). Brooks and

Corey (1964) extended Corey (1954) model for capillary pressure. Corey (1954) had

combined the predictions of a tube-bundle model with an empirical expression to find a

𝑆𝐶𝑂2

𝑝𝑢𝑟𝑒= 1 − 𝑆𝑤𝐽 − 𝑆𝑂𝑀 (4.15)

𝑆𝐶𝑂2

𝑜𝑖𝑙 = 𝑆𝑂𝑀 × 𝐶𝑔𝑇 (4.16)

𝑆𝐶𝑂2

𝑤𝑎𝑡𝑒𝑟 = 𝑆𝑤𝐽 × 𝐶𝑠𝑤 (4.17)

88

model for oil and gas relative permeabilities. The original Brooks and Corey model is the

following:

where 𝑘𝑟𝑤 and 𝑘𝑟𝑛𝑤 are the relative permeabilities of the wetting and non-wetting phases,

respectively, 𝑆𝑤 is the saturation of the wetting phase, 𝑆𝑤𝑟 is the wetting phase residual

saturation, 𝜆 is the empirical parameter. For 𝜆 = 2, Equations 4.16 and 4.17 reduce to

Corey model. We call the following exponential form of the Brooks and Corey model, the

modified Brooks and Corey model:

where, 𝑘𝑟𝑤0 and 𝑘𝑟𝑛𝑤

0 are the wetting and non-wetting end point relative permeabilities,

𝑆𝑛𝑤𝑟 is the residual saturation of the non-wetting phase, 𝑛𝑤 and 𝑛𝑛𝑤 are the relative

permeability exponents.

𝑘𝑟𝑤 = (𝑆𝑤 − 𝑆𝑤𝑟

1 − 𝑆𝑤𝑟)

2+3𝜆𝜆

(4.18)

𝑘𝑟𝑛𝑤 = (1 − 𝑆𝑤

1 − 𝑆𝑤𝑟)

2

[1 − (𝑆𝑤 − 𝑆𝑤𝑟

1 − 𝑆𝑤𝑟)

2+𝜆𝜆

] (4.19)

𝑘𝑟𝑤 = 𝑘𝑟𝑤0 (

𝑆𝑤 − 𝑆𝑤𝑟

1 − 𝑆𝑤𝑟 − 𝑆𝑛𝑤𝑟)

𝑛𝑤

(4.20)

𝑘𝑟𝑛𝑤 = 𝑘𝑟𝑛𝑤0 (

1 − 𝑆𝑤 − 𝑆𝑛𝑤𝑟

1 − 𝑆𝑤𝑟 − 𝑆𝑛𝑤𝑟)

𝑛𝑛𝑤

(4.21)

89

4.5.2 Case Studies

First, we use two examples to explain the CO2-EOR/storage displacement. Then,

we calculate the CO2 trappings for several cases and show the sensitivity of the results to

relative permeability parameters based on fractional flow calculations. We design two

cases such that case 1 is water wet and case 2 is oil wet. Figure 4.1 shows the water/oil and

water/CO2 relative permeability curve assumed for the water-wet case (case 1). Figure 4.2

shows the water/oil and water/CO2 relative permeability curve assumed for the oil-wet case

(case 2). The Corey’s parameters of the two cases are reported in Table 4.1.

Figure 4.1 - Relative permeability curves for water-wet case (case 1).

90

Figure 4.2 - Relative permeability curves for the oil-wet case (case 2).

Table 4.1 - Corey’s parameters for the relative permeability of two designed cases.

𝑺𝒘𝒓 𝒌𝒓𝒘𝟎 𝒏𝒘 𝑺𝒐𝒓 𝒌𝒓𝒐

𝟎 𝒏𝒐 𝑺𝒈𝒓 𝒌𝒓𝒈𝟎 𝒏𝒈

Case 1 0.3 0.2 2.4 0.3 1 2.5 0.3 0.2 2.5

Case 2 0.1 1 1.5 0.3 0.5 2.5 0.3 0.2 4

Table 4.2 shows the parameters that we keep constant for the two cases. These

numbers are taken from the example provided by Lake and Walsh (1989). In Table 4.1

and Table 4.2, 𝑆𝑤𝑟, 𝑆𝑜𝑟 , and 𝑆𝑔𝑟 are residual water, oil, and CO2 saturations, 𝑘𝑟𝑤0 , 𝑘𝑟𝑜

0 , and

𝑘𝑟𝑔0 are water, oil, and CO2 relative permeability endpoints, 𝑛𝑤, 𝑛0, and 𝑛𝑔 are water, oil,

and CO2 Corey’s exponents, 𝜇𝑤, 𝜇𝑜, and 𝜇𝑔 are water, oil, and CO2 viscosities, 𝑆𝑊𝐼 is

initial water saturation, 𝑊𝑅 is WAG ratio, 𝐶𝑔𝑤 is CO2 volume fraction in water, 𝐶𝑔𝑇 is CO2

91

volume fraction in trapped oil, and 𝑆𝑂𝑀 is trapped oil saturation after miscible flood. Two

cases are designed with two completely different relative permeability parameters. We

designed the cases after trying several different relative permeability sets. For the cases

with similar wettability, the sensitivity to relative permeability was negligible. Here, we

report two cases that have different wettability and show the sensitivity of trapping

mechanisms to relative permeability.

Table 4.2 - Required parameters for fractional flow calculation assumed to be the same

for all cases (Lake and Walsh, 1989).

𝝁𝒐(cP) 𝝁𝒘(cP) 𝝁𝒈(cP) 𝑺𝑾𝑰 𝑾𝑹 𝑪𝒈𝒘 𝑪𝒈𝑻 𝑺𝑶𝑴

5.0 1.0 0.05 0.7 1.0 0.1 0.2 0.15

As Figure 4.3 and Figure 4.4 show, first we calculate the fractional flow curves for

water/oil and water/CO2, based on the parameters shown above (Figure 4.3 (a) and Figure

4.4 (a)). The WAG ratio (WR) is assumed to be one for all cases; therefore, 𝑓𝑤𝐽 is calculated

using equation (4.5) which is the injection fractional flow of water. Having the injection

fractional flow, the injection water saturation (𝑆𝑤𝐽) is calculated as point J in the water/CO2

fractional flow curves. Having the injection point, we find the CO2 front velocity (equations

4.8 and 4.11). After finding the oil bank fractional flow and saturation (point OB in Figure

4.3 (a) and Figure 4.4 (a)), we can find the oil bank velocity (VOB) (Lake, 1989).

Having the CO2 and oil bank velocities, we plot the saturation profiles (Figure 4.3

(c) and Figure 4.4 (c) are plotted for 0.25 pore volume injected). As it was discussed before,

92

we assumed 15% of residual oil saturation from miscible flood (SOM = 0.15) which has

20% of partitioned CO2 (CgT = 0.2). We also account for the solubility of CO2 in water and

assume it 10% (Cgw = 0.1). Figure 4.3 (d) and Figure 4.4 (d) show the CO2 and oil bank

velocities over dimensionless time. Figure 4.3 (b) and Figure 4.4 (b) show water fractional

flow at the effluent (xD =1) over time.

Comparing Figure 4.3 and Figure 4.4, we see that by changing the relative

permeability curves, the injection point on the water/CO2 fractional flow curves changes.

Changing the injection water saturation (SwJ) results in changing the pure CO2 saturation

and the CO2 saturation in trapped oil and water. The CO2 trappings through different

mechanisms are calculated by calculating the CO2 saturation in the injection slug (Figure

4.3 (c) and Figure 4.4 (c)). Because after producing the oil bank and at the point where the

injection slug reaches the effluent (XD =1), the injection slug is trapped in the reservoir.

Table 4.3 shows the trapping mechanism calculation for case 1 and case 2. With

the same CO2 solubility in water and oil, the results show a significant difference in

trapping mechanisms contribution in CO2 storage. The contribution of oil solubility

trapping changes from almost 9% to 6%, the water solubility trapping contribution changes

from 18% to 7%, and pure CO2 contribution increases from 73% to 87%.

93


Elution history; (c) saturation profiles at 0.25 pore volume injected; (d) Time-distance

diagram.

94


Elution history; (c) saturation profiles at 0.25 pore volume injected; (d) Time-distance

diagram.

95

Table 4.3 - Trapping mechanism calculation for cases 1 and 2.

Pure CO2

(mobile + residual CO2)

CO2 partitioned in oil

(oil solubility trapping)

CO2 dissolved in water

(water solubility trapping) Total CO2

Case 1

(saturation) 1 − 𝑆𝑤𝐽 − 𝑆𝑂𝑀 = 0.47 𝑆𝑂𝑀 × 𝐶𝑔𝑇 = 0.03 𝑆𝑤𝐽 × 𝐶𝑠𝑤 = 0.038 0.538

Case 2

(saturation) 1 − 𝑆𝑤𝐽 − 𝑆𝑂𝑀 = 0.24 𝑆𝑂𝑀 × 𝐶𝑔𝑇 = 0.03 𝑆𝑤𝐽 × 𝐶𝑠𝑤 = 0.06 0.33

Case 1

(%) 72.87 8.98 18.15 100

Case 2

(%) 87.32 5.59 7.09 100

4.5.3 Sensitivity Analysis

Based on the results in the previous section, we continue to discuss the impacts of

relative permeability on the CO2 trapping mechanisms. For comparison; in all the cases,

we assume the solubilities and trapped oil saturation to be 𝐶𝑔𝑤 = 0.1, 𝐶𝑔𝑇 = 0.2, and

𝑆𝑂𝑀 = 0.15. We take case 1 as the base case; hence, the base case relative permeability

parameters are same as case 1.

We set the variation range of the relative permeability parameters such that the

fractional flow has an answer, which means in calculation of CO2 front velocity, solutions

of equations 4.8 and 4.11 be the same. Checking this condition, we change the irreducible

water saturation from 0 to 0.5, the residual CO2 saturation from 0.2 to 0.4, the water relative

permeability end point from 0.1 to 1, the CO2 relative permeability end point from 0.2 to

1, and water and the CO2 Corey exponents from 1 to 4.

96

Figure 4.5 to Figure 4.10 show the dependency of the CO2 trapping mechanisms

contribution for different relative permeability parameters. As expected, by increasing the

residual water saturation, the amount of CO2 decreases that means the contribution of

mobile CO2 decreases and the brine solubility and oil solubility trappings increase (Figure

4.5). By increasing the residual water saturation, the water fractional flow curve shifts

toward larger water saturations; therefore, for the same WAG ratio (WR = 1, fwJ = 0.5), the

injection water saturation (SwJ) increases. An increase in SwJ means a decrease in pure

injected CO2 saturation. Keeping the CO2 solubility in water constant, by increasing SwJ

the saturation of CO2 in brine increases (equation 4.14). Although the saturation of CO2 in

oil is constant (20% of SOM), the percentage of its contribution changes. By increasing SwJ,

the total CO2 saturation decreases; therefore, the contribution of oil solubility increases.

Figure 4.5 - Trapping mechanisms contribution changes by changing the residual water

saturation.

97

Figure 4.6 shows the sensitivity analysis on residual gas saturation. By increasing

the residual gas saturation, the fractional flow curve shifts toward smaller water saturations.

Therefore, for the same WAG ratio or water fractional flow, SwJ decreases and the CO2

saturation increases. A decrease in injecting water saturation leads to lower CO2 in brine.

By increasing the total CO2 saturation, the contribution of oil solubility trapping decreases.

Figure 4.6 - Trapping mechanisms contribution changes by changing the residual gas

saturation.

The same result is observed by changing the water relative permeability end point

and exponent (Figure 4.7 and Figure 4.9). Increasing the water relative permeability

endpoint and the water Corey exponent change the curvature of both water/oil and

water/CO2 fractional flow curves. The change in fractional flow curvature results in a

change in CO2 velocity (VS) and hence a change in SwJ. Increasing the water relative

permeability end point or exponent means with the same water saturation the water relative

permeability increases. By increasing the water relative permeability, the water fractional

98

flow increases for each saturation. Therefore, for the same injection fractional flow (fwJ =

0.5), the injection water saturation decreases. As explained for above Figure 4.6, the

decrease in SwJ results in an increase in pure CO2 and a decrease in oil and water solubility

trappings.


permeability end point.

99


permeability end point.

Although the CO2 relative permeability end point and exponent also change the

curvature of fractional flow, but the effect of this change is different. Increasing the CO2

relative permeability end point and exponent decrease the water fractional flow. Therefore,

a larger injection water saturation (SwJ) leads to the same WAG ratio and injection fraction

flow (fwJ). As explained before, an increase in SwJ results in less pure CO2 and more water

and oil solubility trappings contribution. Figure 4.8 and Figure 4.10 show the change in

trapping mechanism contribution by increasing the CO2 end point relative permeability and

exponent.

This sensitivity analysis show that each relative permeability parameter could

change the CO2 trapping mechanisms as well as the total amount of stored CO2. Irreducible

water saturation and residual gas saturation show the largest impact on the trapping

mechanisms. Therefore, petrophysical analysis is not only important to forecast the EOR

100

performance, but also has a significant impact on storage capacity estimations. Figure 4.11

shows a tornado chart in which we show the sensitivity of each trapping mechanism to

each relative permeability parameter.


permeability exponent.


permeability exponent.

101

Figure 4.11 – Tornado chart to show the sensitivity of trappings to each relative

permeability parameter.


This chapter provides valuable insights for evaluating the uncertainties induced by

relative permeability to CO2-EOR/storage using fractional flow analysis. We use 1D

fractional flow theory to describe the contribution of different CO2 trapping mechanisms

and explain why the relative permeability changes the distribution of the trappings.

This chapter provides a workflow to analyze CO2-EOR/storage. We use the

fractional flow theory for miscible displacement to analytically and graphically analyze the

distribution of CO2 trappings. We show the significant impact of the relative permeability

73.15

77.92

74.26

74.26

70.09

75.52

24.48

53.35

22.08

20.75

21.18

27.38

10.92

19.78

10.18

9.77

9.91

11.81

64.60

55.87

67.74

69.48

68.91

60.81

17.94

14.29

17.09

17.09

20.28

16.13

8.91

7.79

8.65

8.65

9.63

8.36

100 50 0 50 100

swr

sgr

krw0

krg0

nw

ng

Trapping Contribution (%)

CO2 in Oil (low) CO2 in Brine (low) Pure CO2 (low)

CO2 in Oil (high) CO2 in Brine (high) Pure CO2 (high)

102

on the distribution. Although fractional flow analysis is limited by several assumptions, it

at least provides qualitative relations between CO2-EOR/storage performance and reservoir

properties (i.e, relative permeability).

In this chapter, we provided two cases with different wettability (oil wet versus

water wet) and showed that the most important impact on the contribution of trapping

mechanisms occurs when the wettability of the cases are different. In the next chapter, I

will provide the Cranfield case study and show that the relative permeability experiment

was not necessary for trapping mechanism investigation.

103

Chapter 5: Relative Permeability Uncertainty Effect on CO2-

EOR/Storage (Cranfield Case Study)3

In this chapter, I focus on the impact of relative permeability on field scale

predictions using experience on the Cranfield case study. The original simulation model

was built based on an estimated relative permeability data from literature. In this chapter,

I use another set of relative permeability data that was measured by Weatherford

Laboratories for the Bureau of Economic Geology using the cores from Cranfield. I

compare the results of the two sets of simulation. The relative permeability impact will be

discussed for four different CO2 injection schemes: continuous gas injection (CGI), water

alternating gas injection (WAG), water curtain injection (WCI), and WCI+WAG.

First, I will provide a description on how the relative permeability experiment was

conducted. Then, I will discuss the effect of relative permeability on EOR performance by

investigating the oil recovery factor, cumulative CO2 storage, and utilization ratios. After

that, I will explain the effect of relative permeability on CO2 trapping mechanisms in all of

the four injection schemes. Finally, I will provide a conclusion on when the relative

permeabilities would change the predictions.

3 The content in this chapter was published as: Hosseininoosheri, P., Mehrabi, M., Hosseini, S.A., Nunez-

Lopez, V. and Lake, L.W., 2018. April. Impact of Relative Permeability Uncertainty on CO2 Trapping

Mechanisms in a CO2-EOR Process: A Case Study in the US Gulf Coast (Cranfield) (No. DOE-SSEB-42590-

11). In SPE Western Regional Meeting. Society of Petroleum Engineers. The main author of the paper is


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5.1 INTRODUCTION

The relative contribution of different trapping mechanisms in a CO2-EOR process

depends on various petrophysical properties. Relative permeability is one of the essential

petrophysical properties that describes the multi-phase flow in porous media (Peters, 2012).

However, relative permeability data is scarce for many geological regions and often cited

as a major source of uncertainty. Therefore, a CO2-displacing-water steady state relative

permeability experiment is conducted by Weatherford Laboratories for Bureau of

Economic Geology on the cores collected from Cranfield.

We used the measured relative permeability data to calculate the trapping

mechanisms contribution and compare it with our previous study (Hosseini et al., 2018)

which was based on the relative permeability curves reported by Weaver and Anderson

(1966). We used numerical simulation method to design four CO2 injection: Continuous

Gas Injection (CGI), water alternating gas (WAG), water curtain injection (WCI), and

hybrid WAG and WCI.

The simulation results show a difference not only in the trapping mechanisms

contribution, but also in the total CO2 entrapment and incremental oil recovery, WAG

seems be a promising operational approach to balance both storage and oil production for

both of the relative permeability data sets.

5.2 METHOD

To investigate the effect of relative permeability uncertainty on the prediction of

CO2-EOR/storage performance, we used the simulation model discussed in Chapter 3

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(Section 3.6.2). We ran the reservoir simulation models for two sets of relative permeability

curves; measured and estimated. We did not repeat history match because the purpose of

this study was to find out how the relative permeability could change the results of a field

scale simulations. Hence, for this objective, history matching was not necessary. In the

following, I first summarize how we obtained the measured CO2-water relative

permeabilities, and then I will report and compare the relative permeability curves used in

this study. After that, I show the results of this study.

5.3 MEASURED CO2/WATER RELATIVE PERMEABILITY

To measure the CO2 and water relative permeability data, the Bureau of Economic

Geology (BEG) extracted some samples from the same facies and the same depth (Lu et

al., 2012; Sun et al., 2016). The samples are extracted from the injection well, CFU31F-1,

located in the Cranfield site. Weatherford Laboratory measured the relative permeabilities:

1. Cleaned and vacuum dried the samples to a constant weight.

2. Measured the air permeability and porosity of the samples at 3,400 psi (net

confining pressure).

3. Prepared the composite samples based on Huppler’s method (1969).

4. Loaded the composite samples in a specific core-holder that allows penetration

by the X-rays, which monitors the saturation changes during the experiment.

5. Saturated the composite samples with 100% CO2.

6. Calculated the absolute permeability to CO2 by measuring the pressure drop of

different constant flow rates.

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7. Vacuum-saturated the composite sample with 100% brine.

8. Calculated the brine permeability by changing the flow rates.

9. Elevated the system to reservoir condition: 252 ºF and 5,000 psi.

10. Displaced the non-equilibrated brine by 100% CO2 saturated brine (equilibrated

brine) and reached 100% equilibrated brine saturation.

11. Injected equilibrated CO2 and equilibrated brine simultaneously at different

flow rates to increase the gas saturation.

12. Continued the injection until the steady state flow is established.

13. Used the measured flow rates and pressure gradients for each water-gas ratio to

calculate the steady.

5.4 TWO SETS OF CO2/WATER RELATIVE PERMEABILITY

In this study we use two sets of relative permeability data. The first set was given

bt Weaver and Anderson (1966) and the second set was the Cranfield measured data

performed by Weatherford Laboratories (Section 5.2). Figure 5.1 shows the measured CO2-

water relative permeability data, the Modified Brooks and Corey’s (MBC) relative

permeability function (Lake, 1989) fitted to the data, and the relative permeabilities

reported by Weaver and Anderson (1966). The estimated relative permeability reported by

Weaver and Anderson (1966) is very close to our measured relative permeability data. The

most significant difference is on the endpoint relative permeabilities. The measured data

show a much higher endpoint relative permabilities compared to the estimated relative

permeabilities.

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Figure 5.1 - Measured relative permeability data versus the ones reported by Weaver and

Anderson (1966).

5.5 THE EFFECT ON EOR/STORAGE PERFORMANCE

To investigate the effect of relative permeability on CO2-EOR/storage

performance, we performed compositional numerical reservoir simulation on a Cranfield

pre-existing model described in detail by Hosseini et al. (2018). We use field measured

relative permeability data to numerically calculate the CO2 trapping mechanisms for four

CO2 injection schemes. We compared the results with our previous research in which we

used relative permeability data from literature. Several other research have identified the

relative permeability as the most important factor in determining reservoir performance

(Maini and Okazawa, 1987; Pope et al., 2000). Our results also show the difference in oil

recovery factor, cumulative CO2 storage, and net and gross utilization ratios by changing

the relative permeability data.

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5.5.1 Oil Recovery Factor

We investigated the effect of relative permeability on oil recovery factor for all of

the four assumed injection schemes. As can be seen in Figure 5.2 the estimated oil recovery

factors in the simulation studies based on Weaver and Anderson relative permeabilities

(estimated kr) are up to 20% more than the simulation studies based on our measured

relative permeabilities. As can be seen in the figure, the oil recovery factor of CGI shows

the maximum sensitivity to relative permeabilities. The reason is behind the total amount

of CO2 injected into the reservoir.

In the CGI scenario, the CO2 is being injected continuously so more CO2 and less

water exist in the reservoir. Based on the relative permeability curves, in lower water

saturations, the measured CO2 relative permeability is larger than the estimated relative

permeability. However, the water relative permeability in smaller water saturations is

smaller from the measured data. Therefore, in the CGI, since less water exists (smaller

water saturation), the relative permeability difference between CO2 and water is larger in

the estimated curves. This results in larger mobility ratio and lower sweep efficiency.

That’s why in the CGI scenario, the estimated relative permeability curves overestimate

the oil recovery factor more than other scenarios.

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Figure 5.2 - Oil recovery factor for two relative permeability data sets for all four

injection schemes.

5.5.2 Cumulative CO2 Storage

The ultimate oil recovery factor is not the only measure of EOR-storage

performance; Figure 5.3 shows the effect of relative permeability uncertainty on

cumulative CO2 storage. The cumulative CO2 storage curves are plotted versus

hydrocarbon pore volume of injected CO2 (HCPV). CO2 storage is defined in Chapter 3,

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equation 3.15. The measured relative permeability curves also overestimate the amount of

CO2 storage in CGI. Because in the CGI scenario a large volume of CO2 is being injected

into the reservoir and larger mobility ratio results into earlier breakthrough of CO2. Earlier

breakthrough of CO2 causes lower amount of stored CO2 into the reservoir.

Figure 5.3 – Cumulative CO2 storage for two relative permeability data sets for all four

injection schemes.

5.5.3 Net and Gross Utilization Ratios

I calculated the net and gross utilization ratios that are the amount of CO2 stored

per incremental barrel of produced oil, and the amount of injected CO2 per incremental

barrel of produced oil, respectively. Figure 5.4 shows the net utilization versus time for

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continuous gas injection, water alternating gas injection, water curtain injection, and a

water curtain with water alternating gas injection in the middle wells for both of the relative

permeability sets. The relative permeability does not affect the net utilization ratios because

as discussed above, the higher relative permeability decreases both the incremental oil

recovery and the storage. Therefore, the ratio of the storage and oil recovery stays the same

(same net utilization ratios).

On the other hand, gross utilization ratios change by changing the relative

permeability curves (shown in Figure 5.5). Gross utilization ratio is defined as the amount

of injected CO2 per produced oil. An increase in the relative permeability of CO2 results in

lower oil recovery. Therefore, for the same amount of injected CO2, lower amount of oil is

produced so higher gross utilization ratios are expected.

To summarize, as shown in Figure 5.3, for the same average reservoir pressure, in

CGI injection, the amount of CO2 injection (HCPV) is higher than other scenarios. WCI

has the second highest injection volume and WCI+WAG has the lowest injection volume.

By increasing the amount of injected CO2 into the reservoir, the impact of relative

permeability on the cumulative oil production, cumulative CO2 storage, and utilization

ratios increases.

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Figure 5.4 – Net utilization ratio for two relative permeability data sets for all four-

injection schemes.

113

Figure 5.5 - Gross utilization ratio for two relative permeability data sets for all four-

injection schemes.

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5.6 THE EFFECT ON CO2 TRAPPING CONTRIBUTIONS

To illustrate the influence of relative permeability on CO2 trapping mechanisms,

we consider residual trapping, the amount of CO2 dissolved into oil (oil solubility), the

amount of mobile CO2 (structural), and the CO2 dissolved in the brine (brine solubility).

The trapping mechanisms contributions are calculated for both during (2008-2033) and

after CO2 injection (2033-2108) periods.

Figure 5.7 to Figure 5.9 show the comparison of two relative permeability sets

results for all the four assumed injection schemes. The percentages are all in mole fractions.

The residual trapping is zero for the results from measured relative permeability data. As

can be seen in the figures, the residual CO2 in the measured data is zero; therefore, there is

no CO2 residually trapped in the cases where we use the measured relative permeability

data. However, in the estimated relative permeability models, residual CO2 were assumed

0.01; therefore, in the cases with estimated relative permeability curves, we calculate the

amount of residually trapped CO2 as well as other trapping mechanisms.

In all scenarios for both relative permeability data, the contribution of trapping

mechanisms is the same during and after injection. The structurally trapped CO2 decreases

in the post injection periods and dissolution trapping (including brine and oil dissolution)

increases over time. By changing the scenarios from CGI to WAG, WCI, and WAG+WCI;

the oil dissolution trapping increases. The reason is mainly that larger amount of oil is

produced by the end of CGI operations in comparison with other scenarios. In the WAG

scenario, the cyclic injection of water controls the mobility ratio and stabilizes the CO2

front. Therefore, in WAG scenario the amount of structurally trapped CO2 is lower.

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The results from the Weaver and Anderson relative permeability curves show up to

8% difference in structurally trapped CO2. In WCI, the water curtain designed below the

WOC prevents the CO2 from moving to the aquifer; therefore, less CO2 is in contact with

water and CO2 dissolution in water is less in comparison with CGI. Comparing the

WAG+WCI scenario and WAG, the amount of brine solubility trapping is lower when we

have the water curtain. Comparing the results of two relative permeability sets, other than

the difference in residual trapping mechanism, the main difference is the change in CO2

dissolution in brine in all scenarios. Although the change in different scenarios are the same

for both relative permeability sets, the percentage in each scenario changes.

The highest change happens in CGI scenario and it is because of the higher amount

of injected CO2. In general, in all scenarios, the amount of brine solubility trapping

increases comparing the results of two relative permeability data sets. It is because of the

difference in the relative permeability curves. In the Cranfield measured data, the relative

permeability is higher for both water and CO2. Therefore, more CO2 will get in contact

with in situ fluids.

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water alternating gas injection scheme.

Figure 5.6 - CO2 trapping mechanisms for two sets of relative permeability

data in continuous gas injection scheme.

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water curtain injection scheme.


WAG+WCI injection scheme.

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This chapter provides valuable insights for evaluating the uncertainties induced by

relative permeability to a CO2-EOR/storage process using numerical methods. We

presented the measured water/CO2 relative permeability for Cranfield. We explained our

experience of estimating CO2-EOR/storage performances for four CO2 injection schemes

based on estimated and measured relative permeability curves. The numerical results

indicate up to 20% impact of relative permeability on not only oil recovery, but also the

CO2 storage and CO2 utilization ratios.

In the previous chapter, I used the fractional flow theory for miscible displacement

to analytically and graphically analyze the distribution of CO2 trappings. I concluded that

if the relative permeability curves are different in a way that they represent different

wettabilities, then the CO2 trapping mechanism contribution changes. In this chapter, I

provided an example in which we performed simulation studies for two sets of

permeabilities (measured versus estimated). I showed that the trapping mechanisms

contribution does not change and it is because the wettability of the rock has not been

changed. Although in some cases, the results have changed up to 20%, the difference that

the operating strategy makes is greater than the difference induced by relative permeability.

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Chapter 6: CO2 Plume Migration in a Dipping Aquifer4

In this chapter, after establishing the importance of buoyancy driven flow, I discuss

the previous models in the prediction of plume shape in CO2 sequestration and explain why

predicting the CO2 plume shape in a dipping aquifer is of interest.

I introduce a mathematical model, derived from force balance, to predict CO2

plume migration in dipping aquifers. This model calculates the down and up-dip extension

of CO2 plume in the absence of trapping mechanisms. The force balance shows that there

is a point in the down-dip flow where buoyancy and viscous forces are equal and the plume

cannot extend further. However, in the up-dip flow, where the direction of viscous and

buoyancy forces are the same, the plume migrates upward for an unlimited time, assuming

no boundary and no capillary pressure.

I validate the mathematical model against numerical simulation results and

introduce an effective relative permeability correlation to capture the competition between

water and CO2. To validate the model against heterogeneous cases, I provide a workflow

to adjust the permeability of the aquifer. The results show that the heterogeneity-induced

error is small if we use the near well-bore average permeability. Finally, to investigate the

effect of local capillary trapping on the plume shape, I apply capillary trapping in the

4 The content is under review as: Hosseininoosheri, P., Hosseini, S.A., Nunez-Lopez, V. and Lake, L.W.,

2019. An Analytical Solution to Predict the Lateral Extent of CO2 Plume in Sloping Aquifers. Scientific

Reports. The main author of the paper is Hosseininoosheri P. and the other outhors are the supervisors.

120

numerical simulation model and show how capillary forces prevent the buoyant CO2 from

migrating up-dip.

6.1 INTRODUCTION

Buoyancy-driven flow through porous media has received a considerable interest

over many decades (Dietz, 1953, Dagan 1984; Hess et al., 1992; Berkowitz et al., 2000;

Paster et al., 2013; Hinton and Woods, 2019). Buoyant flow may occur because of

concentration or temperature gradients within the same fluid or because of density

differences between two immiscible fluid phases (Hesse et al., 2007). Such flows are of

concern in many geological and engineering applications, including water and gas flooding

in hydrocarbon reservoirs (Lake et al., 2014) and carbon dioxide storage in depleted

reservoirs and deep saline aquifers.

This study is motivated by carbon capture, and storage (CCS) in deep saline

aquifers. Even if the CO2 is injected as a supercritical fluid, within the aquifers temperature

and pressure range, the density of the supercritical CO2 is less than the density of the brine

(Bachu, 2003; Flett et al., 2007; Dai et al., 2014). Therefore, the injected CO2 experiences

a buoyancy force that drives the CO2 plume upward. The buoyant CO2 thus accumulates

underneath the aquifers sealing layer and forms a gravity current. Therefore, answering the

question of "how far and how fast this gravity current will migrate?" is of interest for site

selection and subsequent monitoring methods.

Many mathematical and numerical models have been developed in different

disciplines to predict buoyancy-driven flow. Most of the mathematical models assume that

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the fluids are completely segregated and the pressure distribution in both fluids is hydro-

static. In petroleum engineering, this set of assumptions is called the vertical equilibrium

(VE) assumption (Yortsos, 1995). Dietz (1953) used this assumption to predict the "water

tongue" behavior in a water flood in a reservoir with very viscous oil. He solved the

problem using Darcy's law in xz-direction.

Hesse et al. (2007) investigated the tilting interface of CO2 in a horizontal aquifer

based on the same sets of assumptions. Riaz and Tchelepi (2008) also tried to formulate

the vertical displacement of CO2 in horizontal aquifers. Brown and Shearer (2018) used a

quasi-linear hyperbolic partial differential equation to model the CO2 migration.

Nordbotten et al. (2005) provided an analytical solution to predict the maximum extent of

CO2 plume and the shape of the overriding supercritical CO2 during injection. Nordbotten

et al. (2005) combined a step-wise method with Darcy's equation to predict the tilting

interface of CO2.

The basic phenomenon in CO2 injection is the displacement of a fluid (water and/or

oil) by CO2. Therefore, the sequestration of CO2 in the pore space depends on the relative

permeability of CO2 and brine (Batycky et al., 1981; Mo et al., 2005; Bennion and Bachu,

2006). In addition, to validate the mathematical model against numerical models, relative

permeability information is required. However, in the previous mathematical models, the

effect of relative permeability is either ignored or assumed to be constant for all of the

designed cases. For instance, Nordbotten et al. (2005) tried to validate their mathematical

model against numerical simulation results. To match their results, they assumed cubic

relative permeability functions with zero residual saturations for all of the cases.

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Beside the effect of relative permeability on the models, many other uncertainties

including heterogeneity complicate the prediction of plume migration in porous media.

None of the mathematical models has investigated the error of their model caused by

neglecting heterogeneity.

In addition, most research attempted to predict the gravity current migration in

horizontal aquifers; however, a very large potential for CO geologic storage exists in

sedimentary basins in which saline aquifers and the associated caprock formations have

significant dipping angles. The Mt. Simon aquifer in the Illinois Basin (Birkholzer et al.,

2009), the Carrizo–Wilcox aquifer in the Texas Gulf Coast Basin (Nicot, 2008), and saline

aquifers in the Alberta Basin, Canada (Bachu et al., 1994) are the most important examples

of such aquifers. A sloping aquifer has a profound influence on the characteristics and

dynamics of buoyant gravity current (Pruess and Nordbotten, 2001). In dipping reservoirs,

the down-dip migration of CO2 is important in terms of storage evaluation, and up-dip

migration is important in terms of leakage. In this study, we find an analytical solution to

describe the lateral migration of a CO2 plume in a sloping saline aquifer. We consider

viscous force, because of the CO2 injection, and buoyancy force, because of density

difference, and use a force balance to find the maximum distance that CO2 could move if

there were no preventive forces.

Although all previous models describe the vertical migration of plume and focus

on tilting angle of the CO2 plume, we investigate the lateral migration of CO2 in a 2-

dimensional sloping aquifer. In this problem, buoyancy is dominant not only because of

the large density difference, but also because of the dipping angle of the aquifer. Our

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mathematical model shows that, in the absence of trapping mechanisms, the CO2 starts

migrating up-dip before the injection stops. Using several CO2-water relative permeability

curves for several numerical realizations, we find an effective relative permeability

correlation. We later apply capillary trapping in a numerical simulation model to show how

capillary trapping prevents the buoyant CO2 from migrating further up-dip.

When CO2 injection starts in a sloping aquifer, the viscous force (imposed by

injection well) is dominant at the beginning of the injection depending on the aquifer

characteristics (e.g., permeability, size), but a competition exists between viscous and

buoyancy forces (Bryant et al., 2008). If CO2 injection continues, a point is reached when

buoyancy becomes active and gravity override starts. Our model shows that, even if we

continue the injection in a sloping aquifer, there will be a point when the buoyancy force

becomes dominant and the CO2 plume migrates up-dip.

In this study, we develop an analytical solution that finds the maximum distance

reached by the edge of the CO2 plume, based on reservoir characteristics and injection rate.

We then design heterogeneous models using numerical simulation to show how

heterogeneity affects the prediction.

6.2 MATHEMATICAL MODEL

We assume that CO2 of density 𝜌 and viscosity 𝜇 is injected into an open boundary

aquifer with dipping angle of 𝛼. The aquifer is initially filled with water of density 𝜌𝑤.The

fluid densities and viscosities are constant. The aquifer has a porosity of 𝜑, permeability

of 𝑘, and thickness of ℎ. CO2 is injected with a constant volumetric flow rate of 𝑄. We

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assume that the injection of CO2 in an aquifer is an immiscible two-phase fluid flow

process. We also assume homogeneous properties for the fluids and the aquifer. We ignore

capillary force and dissolution of CO2 in brine, and only consider buoyancy and viscous

forces. Buoyancy force is an upward force that exists because of the difference in the

density of CO2 and water. Viscous force is the force imposed by the injection well. For an

injection well, viscous force incites the fluid movement. Viscous force is reflected in the

pressure gradient by the flow through the porous medium (Dietz, 1953).

We solve the problem in two dimensions assuming a thin aquifer layer. The solution

could also be used for the top layer of a more complex aquifer. The schematic model of the

process is shown in Figure 6.1 and Figure 6.2 . Figure 6.1 shows a top view of the CO2

plume in a dipping aquifer. Figure 6.1 is a cross section of Figure 6.2. Figure 6.2 shows a

side view of the aquifer and how we write the force balance for buoyancy and viscous

forces. The force balance is written in the x-direction on AA' cross section, shown in the

figures.

Figure 6.1 – Schematic top view of CO2 plume migration in a dipping aquifer.

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Figure 6.2 – Schematic side view of CO2 plume migration in a dipping

aquifer.

To find the maximum distance that CO2 migrates in the absence of trapping

mechanisms (Xf), we use a force balance in x-direction. As can be seen in Figure 6.2,

viscous and buoyancy forces are in opposite directions in the down dip section of the

aquifer. However, the direction of these two forces is the same in the up dip section. This

suggests that in the up dip section of the aquifer, the CO2 plume tends to migrate upward

for an unlimited time if there is no trapping mechanism or barrier.

The force balance in the up and down-dip sections could be written as follows,

respectively:

126

where Fx is the total force in x-direction and FB and Fv are buoyancy and viscous forces,

respectively. The entire force balance could be divided by area (A). The buoyancy (PB) and

viscous (Pv) pressures are defined as follows; the viscous force is written based on Darcy's

law:

where Q is the CO2 injection rate, 𝜌𝑤 is the water density, 𝜌𝑔 is the CO2 density, 𝜇𝑔 is the

CO2 viscosity, g is the gravitational acceleration constant, h is the aquifer thickness, k is

the aquifer permeability, and 𝛼 is the aquifer dipping angle. 𝑘𝑟𝑒𝑓𝑓

is the effective relative

permeability which is defined based on the intersection of CO2 and water relative

permeability curves. 𝑘𝑟𝑐𝑟𝑜𝑠𝑠 is the point where CO2 and water relative permeability curves

intersect. In other words, 𝑘𝑟𝑐𝑟𝑜𝑠𝑠 is the relative permeability associated with the saturation

in which water and CO2 relative permeabilities are equal. Figure 6.3 shows an example of

our definition for 𝑘𝑟𝑐𝑟𝑜𝑠𝑠. We found the effective relative permeability based on several

𝐹𝑥𝑢𝑝−𝑑𝑖𝑝

= 𝐹𝑣 cos 𝛼 + 𝐹𝐵 sin 𝛼 (6.1)

𝐹𝑥𝑑𝑜𝑤𝑛−𝑑𝑖𝑝

= 𝐹𝑣 cos 𝛼 − 𝐹𝐵 sin 𝛼 (6.2)

𝑃𝐵 = (𝜌𝑤 − 𝜌𝑔)𝑔ℎ (6.3)

𝑃𝑣 = 𝑄𝜇𝑔 𝑘𝑘𝑟𝑒𝑓𝑓

𝑋𝑓⁄ (6.4)

𝑘𝑟𝑒𝑓𝑓

=√𝑘𝑟

𝑐𝑟𝑜𝑠𝑠

0.5

(6.5)

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simulation cases that we conducted. In the relative permeability effect part, we explain how

the results of the analytical model would change if the effective relative permeability was

not taken into account in the model.

Figure 6.3 - An example for 𝐤𝐫𝐜𝐫𝐨𝐬𝐬 which is where the water and CO2 relative

permeabilities are equal.

The goal is to find the maximum distance that the edge of the CO2 plume could

migrate down-dip and up-dip in the absence of trapping mechanisms and before buoyancy

force becomes dominant. In the up dip section, as equation 6.1 shows, buoyancy and

viscous forces are adding up in the x-direction; therefore, we cannot find a balance point

for the up dip section. However, in the down dip section, as equation 6.2 suggests buoyancy

and viscous forces act in opposite directions. Therefore, there is a point in which these

forces become equal and from that point downward buoyancy force becomes dominant. To

find the maximum distance that the CO2 plume migrates down dip (Xf) before the buoyancy

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force becomes dominant, we substitute equations 6.3 and 6.4 into equation 6.2 and make it

equal to zero and solve it for Xf :

6.3 VALIDATION AGAINST NUMERICAL SIMULATION

We used GEM from the Computer Modeling Group (GEM-CMG) to investigate

the CO2 plume migration numerically. We built a two-dimensional center point grid

consisting of 500×500×1 (x×y×z) Cartesian gird cells. The grid block size is 20 ft × 20 ft

× 10 ft for the base case. We change the thickness for different cases later. Table 6.1

summarizes the basic fluid and rock properties assumed in the model. The porosity is

assumed to be 13% for all cases. To model the open boundary aquifer in the simulation

model, we assumed a very large pore volume (~ 32,808 ft3) for the boundary grids in left

and right boundaries. No flow is assumed for the upper and lower boundaries.

Table 6.1 - Basic fluid properties used for the base model.

CO2

Density

Water

Density

CO2

Viscosity

Water

Viscosity Depth

Initial

Pressure Temperature

37.25 lb/ft3 63.16 lb/ft3 0.049 cp 0.309 cp 7,500 ft 3,500 psi 200 ⁰F

𝑄𝜇𝑔

𝑘𝑘𝑟𝑒𝑓𝑓

𝑋𝑓

cos 𝛼 − (𝜌𝑤 − 𝜌𝑔)𝑔ℎ sin 𝛼 = 0 (6.6)

𝑋𝑓 =

𝑄𝜇𝑔

𝑘𝑘𝑟𝑒𝑓𝑓 cos 𝛼

(𝜌𝑤 − 𝜌𝑔)𝑔ℎ sin 𝛼

(6.7)

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To validate the analytical solution, we built several cases with different aquifer

properties and injection rates. We find Xf, which is the maximum distance traveled down

dip by the edge of CO2 plume. We compare the results from simulation cases with the

results calculated using analytical solution. Table 6.2 summarizes the cases that we

designed in CMG-GEM.

Table 6.2 - Designed cases with different dipping angle, injection rate, permeability,

thickness, and Corey's function parameters for relative permeability.

Case # α (deg) Q (ft3/day) k (mD) h (ft) Sgr Swi ng nw 𝐤𝐫𝐰𝟎 𝐤𝐫𝐠

𝟎

1 1 30 20 10 0 0 2 2 1 1

2 2 30 20 10 0 0 2 2 1 1

3 3 30 20 10 0 0 2 2 1 1

4 4 30 20 10 0 0 2 2 1 1

5 5 30 20 10 0 0 2 2 1 1

6 30 30 20 10 0 0 2 2 1 1

7 3 10 20 10 0 0 2 2 1 1

8 3 20 20 10 0 0 2 2 1 1

9 3 50 20 10 0 0 2 2 1 1

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Table 6.2 continued.

10 3 70 20 10 0 0 2 2 1 1

11 3 100 20 10 0 0 2 2 1 1

12 3 30 10 10 0 0 2 2 1 1

13

14

3 30 50 10 0 0 2 2 1 1

14 3 30 100 10 0 0 2 2 1 1

15 3 30 20 5 0 0 2 2 1 1

16 3 30 20 20 0 0 2 2 1 1

17 3 30 20 50 0 0 2 2 1 1

18 3 30 20 100 0 0 2 2 1 1

19 3 30 20 10 0.2 0 2 2 1 1

20 3 30 20 10 0 0.3 2 2 1 1

21 3 30 20 10 0 0 4 2 1 1

22 3 30 20 10 0 0 2 4 1 1

23 3 30 20 10 0 0 2 2 0.8 1

24 3 30 20 10 0 0 2 2 1 0.6

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Figure 6.6 shows the plume shape for cases 3, 10, 11, and 18 (case numbers are

based on Table 6.2) after 100 years of CO2 injection. The figure shows the top view of the

plume extension that means it is plotted in x-y coordination. As can be seen in the figure,

Xf changes from 10 to 400 ft for the different cases depending on the aquifer and injection

properties. All cases are showing a tongue on the up dip section of the plume. This shape

develops after the CO2 plume reaches its maximum distance in down-dip direction and it

grows over time. Figure 6.4 shows the CO2 saturation profile over 100 years of continuous

injection for case 2 in Table 6.2. After 2040, the saturation profile reaches the residual CO2

saturation. This time is associated with the time that the tongue starts developing in the up-

dip section of the plume.

Figure 6.4 – CO2 saturation at Xf in down-dip direction (Case 2 from Table 6.2).

Case 18 shows more directional shape than do the others. This happens because of

the higher thickness of the aquifer assumed for this case in comparison with other cases

132

(100 versus 10 ft). As equation 6.7 suggests, there is a direct relationship between buoyancy

force and the thickness of the aquifer. Therefore, in case 18, the buoyancy force is much

higher than the viscous force so it does not let the viscous force develop enough. If we

increase the injection rate, which increases viscous force, we will get the same shape and

be able to store more CO2 down dip. Figure 6.5 shows the plume shape of case 18 after

increasing the injection rate from 30 to 150 ft3/day.

Figure 6.5 - Plume shape after increasing the injection rate in case 18 (Table 6.2).

133

Figure 6.6 - Top view of CO2 saturation after 100 years of continuous injection for

selected cases (Table 6.2).

After designing the different cases, we compared the calculated Xf with the one

from the simulation cases (Figure 6.7). The results in include cases with different other

combinations of relative permeability parameters. As can be seen in the figure, the

analytical solution predicts the down dip extension of the CO2 plume very well, compared

with the results from numerical simulation cases.

134

Figure 6.7 - Numerical vs. analytical results for CO2 extension in down direction

(Xf).

6.4 RELATIVE PERMEABILITY EFFECT

In a hydrocarbon reservoir, it is possible to have two or three fluids flowing at the

same time. Injection of CO2 in a saline aquifer is also a multi-phase flow problem in which

CO2 and water are present and can flow simultaneously. In petroleum engineering, we

extend Darcy's law to multi-phase by adding relative permeability to the equation (Peters,

2012). In the petroleum industry, a commonly used model for relative permeability is the

modified Brooks and Corey (MBC) model (Droz, 1997; Alpak et al., 1999; Goda and

Behrenburch, 2004; Lake et al., 2014). This model is a modified version of Corey's original

model (Corey, 1954) and Brooks and Corey model (Brooks and Corey, 1964) or MBC.

Based on the MBC model, CO2 and water relative permeabilities are defined as follows:

135

where 𝑘𝑟𝑔 and 𝑘𝑟𝑤 are CO2 and water relative permeabilities, 𝑘𝑟𝑔0 and 𝑘𝑟𝑤

0 are CO2 and

water end point relative permeabilities, 𝑆𝑤 is water saturation, 𝑆𝑤𝑖 is irreducible water

saturation, 𝑆𝑔𝑟 is residual CO2 saturation, and 𝑛𝑔 and 𝑛𝑤 are Corey exponents for CO2 and

water.

In Figure 6.8, we compare two versions of the mathematical model with the

simulation results. The first version corresponds to the mathematical model without taking

the relative permeability into account (Figure 6.8 (a)), that means assuming 𝑘𝑟𝑒𝑓𝑓

= 1 in

equation 6.7. To match this version of the analytical model with simulations, we define a

base relative permeability (base kr) using the MBC relative permeability model for the

simulation cases. The base relative permeability parameters are summarized in Table 6.3.

Table 6.3 - MBC parameters for base relative permeability in Figure 6.10 and Figure 6.8.

MBC Parameters Sgr Swi ng nw 𝒌𝒓𝒘𝟎 𝒌𝒓𝒈

𝟎

Values 0 0 2 2 1 1

𝑘𝑟𝑔 = 𝑘𝑟𝑔0 (

1 − 𝑆𝑤 − 𝑆𝑔𝑟

1 − 𝑆𝑤𝑖 − 𝑆𝑔𝑟)

𝑛𝑔

(6.8)

𝑘𝑟𝑤 = 𝑘𝑟𝑤0 (

𝑆𝑤 − 𝑆𝑤𝑖

1 − 𝑆𝑤𝑖 − 𝑆𝑔𝑟)

𝑛𝑤

(6.9)

136

Figure 6.8 - Numerical vs. analytical results of CO2 extent in down dip direction

(Xf ).

The square points are the cases with MBC model parameters other than the base

relative permeability model in the simulation. As Figure 6.8 (a) shows, having various

relative permeability parameters in the simulation changes the down dip extent of CO2

plume significantly. Therefore, using several simulation cases, we found a correlation for

effective relative permeability (equation 6.5). Figure 6.8 (b) shows the results of having

effective relative permeability in the mathematical model. In this figure, the analytical

model is modified based on the defined effective relative permeability (equation 6.5).

6.5 LATERAL HETEROGENEITY EFFECT

To evaluate the application of the developed analytical model in the field scale, we

used Builder from Computer Modeling Group (CMG) and designed three different

heterogeneous permeability distributions using sequential Gaussian method. Although,

there are limitations such as stationary in the population of permeability using 2-point

137

statistics should be enough for the purpose of this study. Having natural fractures, fault, or

thief zones change the results.

Although we did not investigate fractured reservoirs for this study, we show the

impact of a fault or a thief zone with two simple cases shown in Figure 6.9. Case 1 is a case

with a sealing fault. In this case, as it is shown in the figure, the CO2 plume stops migrating

upward hitting the fault and it returns back or basically is trapped because of the sealing

fault. Case 2 is a case that includes a sealing fault and a thief zone. Case 2 shows that after

reaching the fault, a fraction of CO2 passes through the thief zone and builds a new plume

with the same shape. Therefore, it is a valid argument that the analytical model is not

capable of capturing this kind of heterogeneity without modification. The same will happen

about the fractured reservoir. CO2 plume will definitely choose the fracture to go through.

Figure 6.9 - CO2 plume shape after hitting a sealing fault.

138

In this study, we designed three homogeneously heterogeneous cases with different

coefficient of variation of logarithm of permeability (CV). CV is defined as follows:

Using the numerical model explained in section 6.3 and assuming the average

permeability of the aquifer to be the same as the one in base case which was 20 mD. We

generated three realizations of permeability with different CV of logarithm of permeability

and average of 20 mD in CMG. We assume that permeabilities in x and y directions are

equal. Figure 6.10 shows the top view of the heterogeneous models.

Applying the heterogeneity to all the simulation cases, we quantified the effect of

the heterogeneity. As can be seen in Figure 6.11, heterogeneity introduces a significant

error to the analytical solution. The error is because of the assumption of using the average

𝐶𝑉 = 𝑆𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 log (𝑘)

𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑜𝑓 log (𝑘) (6.10)

Figure 6.10- Permeability distribution of heterogeneous cases with different coefficient of variations.

The average permeability in all of them is 20 mD.

139

permeability of the entire reservoir (20 mD). To overcome this issue, we chose two boxes

in the near well-bore region to update the average permeability. The smaller box has a size

of 200 ft × 200 ft with average permeability of 27 mD and the medium box has a size of

500 ft × 500 ft and average permeability of 18 mD. The boxes can be seen in Figure 6.12.

This figure shows the heterogeneity model of the case with CV=0.7 as a sample, the box

size for the two other heterogeneous models is the same.

As shown in Figure 6.11, the error decreases significantly when we take the average

permeability of a small box. Therefore, the mathematical model well predicts the down-

dip migration of CO2 plume by using the near-wellbore average permeability. The

analytical model predicts the down-dip plume migration accurately if we use the near-

wellbore permeability, which is basically current in practice. The reason behind this goes

back to the interplay of viscous and buoyancy forces. Near-wellbore permeability controls

the CO2 flow as it first enters the reservoir. This is of significant important because near-

wellbore permeability will dictate whether the flow will be dominated by viscous or

buoyancy force. However, if we increase the injection rate, the viscous force will increase;

therefore, we must have the average permeability of a wider region.

140

Figure 6.12- Medium and small boxes for average permeability

Figure 6.11 - Numerical vs. analytical results for down dip extent of CO2 plume (Xf ) for different average

relative permeability areas shown in Figure 6.12.

141

6.6 LOCAL CAPILLARY TRAPPING

In the absence of trapping mechanisms, the CO2 plume tends to migrate up-dip for

an unlimited time. As explained before, this happens because buoyancy and viscous forces

are in the same direction in the up-dip direction (equation 6.1). Therefore, the only way to

predict the plume stability point up-dip is applying at least one trapping mechanism into

the model. To investigate local capillary trapping, we used the numerical model (Case 3

from Table 6.2). In the heterogeneous model with CV coefficient of 0.7, we divided the

reservoir into two different rock types according to capillary pressure curves.

Figure 6.13 shows the rock types and CO2 accumulation after 100 years of

continuous injection. The left figure in Figure 6.13 shows two types of rock with two

capillary entry pressures. The difference between the capillary entry pressures of the two

rock types is 50 psi. We chose the huge difference between capillary pressures to show the

phenomenon. The red rock type is the rock type with higher capillary entry pressure. The

right figure shows the plume shape (CO2 saturation) that is the plume shape developed in

the black box. As can be seen, when the plume reaches the rock type with higher capillary

entry pressure (red areas), the CO2 can no longer migrate and it is trapped in those areas

(higher saturation). The higher saturation in these areas indicate the CO2 trapping because

of capillary entry pressure difference (local capillary trapping). This effect was investigated

in previous studies (Li et al., 2013; Ren et al., 2014) in detail.

142


This study modeled the viscous-buoyancy flow of injecting CO2 into dipping

aquifers. We used a simple force balance calculation to derive an analytical solution. We

introduced a correlation for effective relative permeability to capture the effect of relative

permeability in the mathematical model. We then validated the results of the mathematical

model against numerical simulation results. Our mathematical and numerical investigation

shows:

1. In the absence of trapping mechanisms, there is a competition between

buoyancy and viscous forces. After some period of time, even if we continue

with the same injection rate, buoyancy force becomes dominant and CO2 plume

will not move further down dip.

Figure 6.13- Two rock types based on capillary entry pressure and the CO2 plume shape after 100

years of injection. Left figure: Red: Higher capillary entry pressure.

143

2. The force balance in the down-dip and up-dip sections of a dipping aquifer is

different. In the down-dip section, buoyancy and viscous forces are in opposite

directions; however, in the up-dip section, these two forces are in the same

direction.

3. The opposite directions of viscous and buoyancy forces give us the opportunity

of calculating a stability point (at which buoyancy and viscous forces are equal)

in the down-dip section (Xf). We can now calculate the down-dip extent of the

CO2 plume by simple force balance calculations.

4. The main assumptions to derive the analytical model are: constant fluid

properties, open boundary aquifer, homogeneous rock properties, constant

volumetric flow rate, immiscible fluid flow, and negligible capillarity and

dissolution.

5. Based on the mathematical model, the CO2 plume extent depends on injection

rate, CO2 viscosity, permeability, relative permeability, fluid densities,

thickness, and dipping angle.

6. In the absence of trapping mechanisms, the injected CO2 tends to migrate up-

dip for an unlimited time.

7. After adding local capillary trapping to the simulation model, we showed how

a trapping mechanism could eventually stop the migration of the CO2 plume

up-dip.

144

Chapter 7: Summary, Conclusions, and Recommendations

In this chapter, we first present summary and conclusions of this thesis. Then we

conclude this work by providing recommendations for future study.


We investigated the distribution of CO2 in different phases through different

operation development strategies. The main purpose was to answer

questions associated with the relationship between EOR operational

strategies and CO2 utilization ratios, and to understand the impact of the

different CO2 trapping mechanisms on this relationship.

We modelled the CO2 injection scenarios for the SACROC reservoir. In the

specific case of SACROC, we used a geocellular model and modified the

relative permeabilities and reservoir boundary conditions of the simulation

model based on field history performance. We used the history-matched

model for initialization of different development strategies. We assumed

that the average reservoir pressure of the field is the same for different

development strategies.

The results show that various field development strategies have a great

impact on the relative contribution of different trapping mechanisms. Based

on our simulation model on SACROC, WAG shows a good balance

between maximizing oil production and CO2 storage with a lower utilization

145

ratio compared to CGI. In addition, WAG improves the storage security by

decreasing the amount of mobile CO2 in the reservoir.

We compared the results of the SACROC simulation with the Cranfield

simulation model to investigate if the conclusion is different for different

fields.

Although the actual operating strategy in SACROC and Cranfield are

different (CGI in Cranfield and WAG in SACROC), our numerical

modelling results show that WAG could not only balance the CO2 storage,

incremental oil recovery, and CO2 utilization ratio but also store the trapped

CO2 with lower risk of leakage in both fields (by decreasing the amount of

structurally trapped CO2) in both cases. Because of the multiple alternation

of CO2 and water slugs in WAG, this approach reduces the viscous

instability and therefore the efficiency of oil recovery.

The study shows that the distribution of CO2 in different phases is different

for each field. Because of the lower minimum miscibility pressure (MMP)

and lighter initial oil saturation in SACROC, the partitioning of CO2 in oil

is much higher in SACROC than in Cranfield. The dissolution of CO2 in

brine is much higher in Cranfield because of the presence of strong aquifer

near injection wells.

Our results show that various field development strategies have a greater

impact on the relative contribution of different trapping mechanisms rather

than the type of the reservoir.

146

I used the fractional flow theory for miscible displacement to analytically

and graphically analyze the distribution of CO2 trappings. I concluded that

if the relative permeability curves are different in a way that they represent

different wettabilities, then the CO2 trapping mechanism contribution

changes.

I provided an example in which we performed simulation studies for two

sets of permeabilities (measured versus estimated). I showed that the

trapping mechanisms contribution does not change and it is because the

wettability of the rock has not been changed.

Although in some cases, the results have changed up to 20%, the difference

that the operating strategy makes is greater than the difference induced by

relative permeability.

We modeled the viscous-buoyancy flow of injecting CO2 into dipping

aquifers. We used a simple force balance calculation to derive an analytical

solution. We introduced a correlation for effective relative permeability to

capture the effect of relative permeability in the mathematical model. We

then validated the results of the mathematical model against numerical

simulation results.

In the absence of trapping mechanisms, there is a competition between

buoyancy and viscous forces. After some period of time, even if we

continue with the same injection rate, buoyancy force becomes dominant

and CO2 plume will not move further down dip.

147

The force balance in the down-dip and up-dip sections of a dipping aquifer

is different. In the down-dip section, buoyancy and viscous forces are in

opposite directions; however, in the up-dip section, these two forces are in

the same direction.

The opposite directions of viscous and buoyancy forces give us the

opportunity of calculating a stability point (at which buoyancy and viscous

forces are equal) in the down-dip section (Xf). We can now calculate the

down-dip extent of the CO2 plume by simple force balance calculations.

The main assumptions to derive the analytical model are: constant fluid

properties, open boundary aquifer, homogeneous rock properties, constant

volumetric flow rate, immiscible fluid flow, and negligible capillarity and

dissolution.

Based on the mathematical model, the CO2 plume extent depends on

injection rate, CO2 viscosity, permeability, relative permeability, fluid

densities, thickness, and dipping angle.

In the absence of trapping mechanisms, the injected CO2 tends to migrate

up-dip for an unlimited time.

After adding local capillary trapping to the simulation model, we showed

how a trapping mechanism could eventually stop the migration of the CO2

plume up-dip.

148

7.2 RECOMMENDATIONS

The recommendations for further studies are presented as follows:

Investigate different WAG ratios in the simulation model and for different

field and provide a workflow to find the optimum WAG ratio.

In our models, we kept the average reservoir pressure the same for different

CO2 injection schemes. We recommend to increase the reservoir pressure

by constraining the well pressure by fracture pressure instead of observed

reservoir pressure; therefore, higher injection rates will be possible and the

reservoir could produce the oil below the water-flood residual oil saturation.

We recommend to perform the fractional flow analysis for continuous gas

injection as well as different WAG ratios and compare with each other.

In our analytical solution for CO2 plume migration in a dipping aquifer,

although we investigated the local capillary trapping in the numerical

model, we did not include the capillary force. We recommend to add the

capillary force into the force balance and find the distance in the up-dip

section. To add the capillary force, an assumption on rock types should be

made.

149

A.1 SAMPLE INPUT DATA FOR SACROC CONTINUOUS GAS INJECTION

SIMULATION MODEL (CMG)

RESULTS SIMULATOR GEM 201510

*FILENAMES *OUTPUT 'CGI.out'

*FILENAMES *RESTARTIN 'WAG.rst'

*FILENAMES *INDEX-IN 'WAG'

*RESDATE 1982 12 01

RANGECHECK ON

*INUNIT *FIELD

*DIM MDJCS 200

*INTERRUPT *INTERACTIVE

*XDR *ON

*MAXERROR 20

*WRST 10

*WPRN *WELL *TIME

*WPRN *GRID *TIME

*WPRN *ITER *NONE

*WSRF *WELL *TIME

*WSRF *GRID *TIME

*DIARY *CHANGES

*OUTPRN *RES *ALL

*OUTPRN *GRID *NONE

*OUTSRF *GRID DENG RHOG MWG FRG SG DENO RHOO PCG PCW SO DENW

SW KRG SGHYS SGDTHY SGRHYS VISG MWO KRO VISO PRES KRW XALL

YALL ZALL WALL PERM PERMEFF

K 'CO2' Z 'CO2' Y 'CO2' X 'CO2'

*OUTSRF *RES *ALL

**--------------------------------------------------------------------**

** RESERVOIR DATA

**--------------------------------------------------------------------**

INCLUDE 'grid20.GRDECL'

*NULL *IJK

150

1:4 1:50 1:20 0

46:55 1:50 1:20 0

1:55 1:2 1:20 0

1:55 46:50 1:20 0

INCLUDE 'por20.GRDECL'

INCLUDE 'permi20.GRDECL'

PERMJ *EQUALSI

PERMK *EQUALSI * 0.1

PINCHOUTARRAY CON 1

*CPOR 5.0E-06

*PRPOR 14.7

*AQUIFER *BOTTOM

*AQLEAK *ON

**--------------------------------------------------------------------**

** FLUID COMPONENT DATA

**--------------------------------------------------------------------**

*MODEL *PR

*NC 11 11

*PHASEID *CRIT

*TRES 130.000

*COMPNAME

'CO2' 'N2' 'CH4' 'C2H6'

'C3H8' 'IC4' 'NC4' 'IC5'

'NC5' 'FC6' 'C7+'

*SG 8.1800000E-01 8.0900000E-01 3.0000000E-01 3.5600000E-01

5.0700000E-01 5.6300000E-01 5.8400000E-01 6.2500000E-01

6.3100000E-01 6.9000000E-01 8.4100000E-01

*TB -1.0921000E+02 -3.2035000E+02 -2.5861000E+02 -1.2757000E+02

-4.3690000E+01 1.0670000E+01 3.1190000E+01 8.2130000E+01

9.6890000E+01 1.4693000E+02 5.1707482E+02

*PCRIT 7.2800000E+01 3.3500000E+01 4.5400000E+01 4.8200000E+01

4.1900000E+01 3.6000000E+01 3.7500000E+01 3.3400000E+01

3.3300000E+01 3.2460000E+01 1.9300000E+01

*VCRIT 9.4000000E-02 8.9500000E-02 9.9000000E-02 1.4800000E-01

151

2.0300000E-01 2.6300000E-01 2.5500000E-01 3.0600000E-01

3.0400000E-01 3.4400000E-01 7.8004404E-01

*TCRIT 3.0420000E+02 1.2620000E+02 1.9060000E+02 3.0540000E+02

3.6980000E+02 4.0810000E+02 4.2520000E+02 4.6040000E+02

4.6960000E+02 5.0750000E+02 7.3117417E+02

*AC 2.2500000E-01 4.0000000E-02 8.0000000E-03 9.8000000E-02

1.5200000E-01 1.7600000E-01 1.9300000E-01 2.2700000E-01

2.5100000E-01 2.7504000E-01 5.7512768E-01

*MW 4.4010000E+01 2.8013000E+01 1.6043000E+01 3.0070000E+01

4.4097000E+01 5.8124000E+01 5.8124000E+01 7.2151000E+01

7.2151000E+01 8.6000000E+01 1.9740000E+02

*HCFLAG 0 0 0 0

0 0 0 0

0 0 0

*BIN

0.0000000E+00

1.0500000E-01 2.5000000E-02

1.3000000E-01 1.0000000E-02 2.6890022E-03

1.2500000E-01 9.0000000E-02 8.5370405E-03 1.6620489E-03

1.2000000E-01 9.5000000E-02 1.5715316E-02 5.4857876E-03

1.1165976E-03

1.1500000E-01 9.5000000E-02 1.4748531E-02 4.9143360E-03

8.6625350E-04 1.5903506E-05

1.1500000E-01 1.0000000E-01 2.0878892E-02 8.7338646E-03

2.8007353E-03 3.8207590E-04 5.5378054E-04

1.1500000E-01 1.1000000E-01 2.0640839E-02 8.5779330E-03

2.7121325E-03 3.4971119E-04 5.1467786E-04 7.1665797E-07

1.1500000E-01 1.1000000E-01 2.5345101E-02 1.1747825E-02

4.6198099E-03 1.2003051E-03 1.4920539E-03 2.2833006E-04

2.5462307E-04

0.0000000E+00 0.0000000E+00 6.7288351E-02 4.4449725E-02

2.9507614E-02 1.9402368E-02 2.0502723E-02 1.4430364E-02

1.4631002E-02 1.1075118E-02

*VSHIFT 7.5500000E-02 -1.9270000E-01 -1.5950000E-01 -1.1340000E-01

-8.6300000E-02 -8.4400000E-02 -6.7500000E-02 -6.0800000E-02

-3.9000000E-02 -5.9167861E-02 1.3844670E-01

152

*VISCOR *HZYT

*MIXVC 1.0000000E+00

*VISVC 9.4000000E-02 8.9500000E-02 9.9000000E-02 1.4800000E-01

2.0300000E-01 2.6300000E-01 2.5500000E-01 3.0600000E-01

3.0400000E-01 3.4400000E-01 7.8004404E-01

*VISCOEFF 1.0230000E-01 2.3364000E-02 5.8533000E-02 -4.0758000E-02

9.3324000E-03

*OMEGA 4.5723553E-01 4.5723553E-01 4.5723553E-01 4.5723553E-01

4.5723553E-01 4.5723553E-01 4.5723553E-01 4.5723553E-01

4.5723553E-01 4.5723553E-01 4.5723553E-01

*OMEGB 7.7796074E-02 7.7796074E-02 7.7796074E-02 7.7796074E-02

7.7796074E-02 7.7796074E-02 7.7796074E-02 7.7796074E-02

7.7796074E-02 7.7796074E-02 7.7796074E-02

*PCHOR 7.8000000E+01 4.1000000E+01 7.7000000E+01 1.0800000E+02

1.5030000E+02 1.8150000E+02 1.8990000E+02 2.2500000E+02

2.3150000E+02 2.5010880E+02 5.4047513E+02

*ENTHCOEF

9.6880000E-02 1.5884300E-01 -3.3712000E-05 1.4810500E-07

-9.6620300E-11 2.0738320E-14

-6.5665000E-01 2.5409800E-01 -1.6624000E-05 1.5302000E-08

-3.0995000E-12 1.5167000E-16

-2.8385700E+00 5.3828500E-01 -2.1140900E-04 3.3927600E-07

-1.1643220E-10 1.3896120E-14

-1.4220000E-02 2.6461200E-01 -2.4568000E-05 2.9140200E-07

-1.2810330E-10 1.8134820E-14

6.8715000E-01 1.6030400E-01 1.2608400E-04 1.8143000E-07

-9.1891300E-11 1.3548500E-14

1.4595600E+00 9.9070000E-02 2.3873600E-04 9.1593000E-08

-5.9405000E-11 9.0964500E-15

7.2281400E+00 9.9687000E-02 2.6654800E-04 5.4073000E-08

-4.2926900E-11 6.6958000E-15

1.7694120E+01 1.5946000E-02 3.8244900E-04 -2.7557000E-08

-1.4303500E-11 2.9567700E-15

9.0420900E+00 1.1182900E-01 2.2851500E-04 8.6331000E-08

-5.4464900E-11 8.1845000E-15

0.0000000E+00 -1.6543463E-02 4.1169069E-04 -5.7742757E-08

153

0.0000000E+00 0.0000000E+00

0.0000000E+00 -3.8692788E-02 4.1661875E-04 -6.2160159E-08

0.0000000E+00 0.0000000E+00

*SOLUBILITY

*HENRY-CORR-CO2 ** Use Harvey's correlation for Hen Law const.

NC-AQUEOUS 1

COMPNAME-AQUEOUS

'NaCl'

SALINITY PPMVOL 159000

*DERIVATIVEMETHOD *NUMERALL

*AQUEOUS-DENSITY *ROWE-CHOU

*AQUEOUS-VISCOSITY *KESTIN

**PHASEID *DEN

**Water phase denser than oil phase will cause water phase to dissapear and

**the system will become two-phase: oil-gas

**DENW 63.2

**--------------------------------------------------------------------**

** ROCK FLUID

**--------------------------------------------------------------------**

*ROCKFLUID

RPT 1 DRAINAGE SCALING-OLD

*HYSKRG 0.35

*SWT

**Data from DOE Report

** Sw Krw Krow Pcow

0.22000 0.00000 0.55000

0.24650 0.02334 0.44798

0.27300 0.05363 0.36086

0.29950 0.08724 0.28710

0.32600 0.12321 0.22528

0.35250 0.16104 0.17402

0.37900 0.20043 0.13206

0.40550 0.24116 0.09818

0.43200 0.28307 0.07128

154

0.45850 0.32604 0.05033

0.48500 0.36998 0.03438

0.51150 0.41481 0.02255

0.53800 0.46047 0.01408

0.56450 0.50689 0.00825

0.59100 0.55403 0.00446

0.61750 0.60186 0.00215

0.64400 0.65032 0.00088

0.67050 0.69939 0.00028

0.69700 0.74905 0.00005

0.72350 0.79926 0.00000

0.75000 0.85000 0.00000

*SLT

** oil/gas

**Sl krg krog Pcog

0.22000 0.40000 0.00000

0.25650 0.36100 0.00138

0.29300 0.32400 0.00550

0.32950 0.28900 0.01238

0.36600 0.25600 0.02200

0.40250 0.22500 0.03438

0.43900 0.19600 0.04950

0.47550 0.16900 0.06738

0.51200 0.14400 0.08800

0.54850 0.12100 0.11138

0.58500 0.10000 0.13750

0.62150 0.08100 0.16638

0.65800 0.06400 0.19800

0.69450 0.04900 0.23238

0.73100 0.03600 0.26950

0.76750 0.02500 0.30938

0.80400 0.01600 0.35200

0.84050 0.00900 0.39738

0.87700 0.00400 0.44550

0.91350 0.00100 0.49638

0.95000 0.00000 0.55000

155

**--------------------------------------------------------------------**

** INITIAL CONDITIONS

**--------------------------------------------------------------------**

*INITIAL

*VERTICAL *DEPTH_AVE *WATER_OIL_GAS

** 'CO2' 'N2' 'CH4' 'C2H6' 'C3H8' 'IC4' 'NC4' 'IC5' 'NC5' 'FC6' 'C7+'

*ZOIL

0.32 0.83 28.65 11.29 12.39 1.36 6.46 1.98 2.51 4.06

30.15

*ZGAS

0.47 2.35 69.03 15.55 8.917 0.56 2.14 0.35 0.37 0.26

0.003

REFPRES

3122

REFDEPTH

4300

DWOC

4450

DGOC

3000

*SALINR *PPMVOL 159000

**--------------------------------------------------------------------**

** NUMERICAL METHODS CONTROL

**--------------------------------------------------------------------**

*NUMERICAL

*DTMAX 5

*DTMIN 1.E-06

*NORM *PRESS 2000

*MAXCHANGE *GMOLAR 0.2

*MAXCHANGE *SATUR 0.2

*AIM *STAB 1

*CONVERGE *PRESS 0.15

*MAXSTEPS 1000000

156

**--------------------------------------------------------------------**

** WELL DATA

**--------------------------------------------------------------------**

*INCLUDE 'WellData-CGI.inc'

157

A.2 SAMPLE INPUT DATA FOR CRANFIELD CONTINUOUS GAS INJECTION

SIMULATION MODEL (CMG)

RESULTS SIMULATOR GEM 201401

REWIND 4

*MAINRESULTSIN

*INUNIT *FIELD

*DIM MDJCS 200

*DIM *MDGRID 50

*INTERRUPT *INTERACTIVE

*XDR *ON

*MAXERROR 20

RANGECHECK ON

*WPRN *WELL TIME***TIME

*WPRN *GRID 0**TIME

*WPRN *ITER *MATRIX

*WSRF *WELL *TIME

*WSRF *GRID *TIME

**RESTART 1

*DIARY *WELL-INFO

*DIARY2 *CHANGES-UNCONV

*OUTPRN *RES NONE **ALL

RANGECHECK ON

*OUTPRN *WELL ALL **BRIEF **ALL **BRIEF **NONE **ALL

*OUTPRN *GRID NONE **DENG RHOG MWG FRG KRG SG SIG VISG

*OUTPRN *RES NONE **ALL

*OUTSRF *GRID *DENG RHOG MWG FRG SG DENO RHOO PCW SO DENW

SW KRG VISG MWO KRO VISO PRES KRW XALL YALL ZALL WALL

PERM PERMEFF

*OUTSRF *RES *ALL

**--------------------------------------------------------------------**

** RESERVOIR DATA

**--------------------------------------------------------------------**

*INCLUDE 'Grid.inc'

158

*INCLUDE 'Kx.cmg'

*INCLUDE 'Poro.cmg'

*INCLUDE 'NTG.cmg'

*NULL *IJK

1:124 92:149 1:20 0

1:101 91 1:20 0

1:101 90 1:20 0

1:101 89 1:20 0

1:100 88 1:20 0

1:100 87 1:20 0

1:99 86 1:20 0

1:99 85 1:20 0

1:99 84 1:20 0

1:98 83 1:20 0

1:98 82 1:20 0

1:97 81 1:20 0

1:96 80 1:20 0

1:95 79 1:20 0

1:94 78 1:20 0

1:93 78 1:20 0

1:92 77 1:20 0

1:91 76 1:20 0

1:90 75 1:20 0

1:89 74 1:20 0

1:89 73 1:20 0

1:88 73 1:20 0

1:88 72 1:20 0

1:88 71 1:20 0

1:87 70 1:20 0

1:87 69 1:20 0

1:86 68 1:20 0

1:86 67 1:20 0

1:85 66 1:20 0

1:85 65 1:20 0

1:84 64 1:20 0

1:84 63 1:20 0

1:84 62 1:20 0

1:83 61 1:20 0

1:82 60 1:20 0

1:82 59 1:20 0

1:82 58 1:20 0

159

1:81 58 1:20 0

1:80 58 1:20 0

1:80 57 1:20 0

1:80 56 1:20 0

1:79 55 1:20 0

1:78 54 1:20 0

1:77 53 1:20 0

1:76 52 1:20 0

1:76 51 1:20 0

1:75 50 1:20 0

1:75 49 1:20 0

1:74 48 1:20 0

1:74 47 1:20 0

1:73 46 1:20 0

1:73 45 1:20 0

1:73 44 1:20 0

1:72 43 1:20 0

1:72 42 1:20 0

1:72 41 1:20 0

1:71 40 1:20 0

1:71 39 1:20 0

1:71 38 1:20 0

1:70 37 1:20 0

1:70 36 1:20 0

1:70 35 1:20 0

1:70 34 1:20 0

1:70 33 1:20 0

1:69 1:32 1:20 0

PERMJ EQUALSI

PERMK EQUALSI * 0.05

PINCHOUTARRAY CON 1

CPOR MATRIX 40e-6

PRPOR MATRIX 14.7

PVCUTOFF 1000.

**INCLUDE 'BGs.cmg'

**-------------------------------------------------------------------

** Aquifer definition

**-------------------------------------------------------------------

*AQUIFER *BOUNDARY

160

*AQPROP 20 0.1 25 0 0 10000

*AQMETHOD *CARTER-TRACY

*AQLEAK *ON

**--------------------------------------------------------------------**

** FLUID COMPONENT DATA

**--------------------------------------------------------------------**

MODEL PR

NC 8 8

COMPNAME 'CO2' 'CH4' 'C2H6' 'C3H8' 'NC4' 'NC5' 'FC20' 'TR'

TRES 252

VISCOR MODPEDERSEN

MIXVC 1

PVC3 1.2

VISCOEFF

0.00015648 2.5070 0.0059024 2.3576 0.38184

MW

44.01 16.043 30.07 44.097 58.124 72.151 272.79466 16.043

AC

0.225 0.008 0.098 0.152 0.193 0.251 0.816053 0.008

PCRIT

72.8 45.4 48.2 41.9 37.5 33.3 14.36 45.4

VCRIT

0.094 0.099 0.148 0.203 0.255 0.304 1.027 0.099

TCRIT

304.2 190.6 305.4 369.8 425.2 469.6 782.9 190.6

PCHOR

78.0 77.0 108.0 150.3 189.9 231.5 710.475 77.0

SG

161

0.818 0.3 0.356 0.507 0.584 0.631 0.866 77.0

TB

-109.21 -258.61 -127.57 -43.69 31.19 96.89 641.93 -258.61

OMEGA

0.457235528921 0.457235528921 0.457235528921 0.457235528921 0.457235528921

0.457235528921 0.457235528921 0.457235528921

OMEGB

0.0777960739039 0.0777960739039 0.0777960739039 0.0777960739039

0.0777960739039 0.0777960739039 0.0777960739039 0.0777960739039

VSHIFT

-0.0817 -0.1595 -0.1134 -0.0863 0.0 -0.039 0.30222771 -0.1595

HEATING_VALUES

0.0 844.290010539 1478.46001529 2105.16002783 2711.54003814 3353.66003806

12717.0002077 844.290010539

VISVC

0.094 0.099 0.148 0.203 0.255 0.304 1.027 0.099

BIN

0.103

0.13 0.002689002

0.135 0.008537041 0.001662049

0.115 0.01474853 0.004914336 0.0008662535

0.125 0.02064084 0.008577933 0.002712132 0.0005146779

0.115 0.08513851 0.05963522 0.04235822 0.031552 0.02423371

0.103 0.0 0.0 0.0 0.0 0.0 0.0

HCFLAG

0 1 1 1 1 1 1 1

PHASEID TCMIX

SOLUBILITY

*HENRYC

98000 885965 0 0 0

0 0 0

*VINFINITY

162

0.04147 0.036693143 0.072727308 0.1370383 0.23672987

0.40815068 0.54636225 0.019069178

*REFPH

1000 1000 0 0 0 0

0 0

NC-AQUEOUS 1

COMPNAME-AQUEOUS

'NaCl'

SALINITY PPMVOL 150000

*DERIVATIVEMETHOD *NUMERALL

*AQUEOUS-DENSITY *ROWE-CHOU

*AQUEOUS-VISCOSITY *KESTIN

TRACE-COMP 8

**--------------------------------------------------------------------**

** ROCK FLUID

**--------------------------------------------------------------------**

*ROCKFLUID

** SAND

RPT 1 DRAINAGE SCALING-OLD

SWT

0.45 0 0.5

0.454482759 0.000544279 0.46447899

0.458965517 0.001539455 0.430326522

0.463448276 0.002828159 0.397537626

0.467931034 0.004354236 0.366107164

0.472413793 0.006085229 0.336029818

0.476896552 0.007999241 0.307300074

0.48137931 0.010080196 0.279912207

0.485862069 0.012315638 0.253860264

0.490344828 0.014695545 0.229138043

0.494827586 0.017211627 0.205739069

0.499310345 0.019856878 0.18365657

0.503793103 0.022625271 0.162883444

0.508275862 0.025511557 0.143412225

0.512758621 0.028511101 0.125235038

0.517241379 0.031619778 0.108343555

0.521724138 0.034833884 0.09272893

0.526206897 0.038150068 0.078381727

0.530689655 0.041565278 0.065291831

163

0.535172414 0.045076722 0.053448338

0.539655172 0.048681833 0.04283941

0.544137931 0.052378236 0.033452084

0.54862069 0.056163731 0.025272028

0.553103448 0.060036267 0.018283184

0.557586207 0.063993931 0.012467266

0.562068966 0.06803493 0.007802975

0.566551724 0.072157579 0.004264704

0.571034483 0.076360291 0.001820108

0.575517241 0.08064157 0.000424555

0.58 0.085 0

SLT

0.72 0.45 0

0.729310345 0.423940171 0.001165879

0.73862069 0.398523849 0.004059828

0.747931034 0.373758096 0.008423098

0.757241379 0.349650322 0.014137141

0.766551724 0.326208316 0.021125141

0.775862069 0.303440286 0.029330932

0.785172414 0.281354895 0.038710616

0.794482759 0.259961311 0.049228385

0.803793103 0.239269262 0.060854139

0.813103448 0.219289097 0.073562014

0.822413793 0.200031861 0.087329393

0.831724138 0.181509384 0.102136237

0.841034483 0.163734383 0.117964584

0.850344828 0.146720588 0.134798194

0.859655172 0.130482893 0.152622258

0.868965517 0.115037548 0.171423192

0.878275862 0.100402386 0.191188456

0.887586207 0.086597127 0.211906421

0.896896552 0.073643754 0.233566251

0.906206897 0.061567027 0.256157809

0.915517241 0.050395168 0.279671582

0.924827586 0.040160821 0.304098609

0.934137931 0.030902459 0.32943043

0.943448276 0.022666524 0.355659033

0.952758621 0.015510932 0.382776814

0.962068966 0.009511348 0.410776542

0.97137931 0.004774049 0.439651322

0.980689655 0.001469386 0.469394573

0.99 0 0.5

164

SWT

0.45 0 0.5

0.455 0.000133189 0.463648834

0.46 0.000285498 0.42866941

0.465 0.000445968 0.395061728

0.47 0.000611978 0.362825789

0.475 0.000782234 0.331961591

0.48 0.000955952 0.302469136

0.485 0.001132603 0.274348422

0.49 0.001311804 0.247599451

0.495 0.001493264 0.222222222

0.5 0.001676756 0.198216735

0.505 0.001862095 0.17558299

0.51 0.002049129 0.154320988

0.515 0.002237729 0.134430727

0.52 0.002427788 0.115912209

0.525 0.00261921 0.098765432

0.53 0.002811913 0.082990398

0.535 0.003005825 0.068587106

0.54 0.003200882 0.055555556

0.545 0.003397026 0.043895748

0.55 0.003594205 0.033607682

0.555 0.003792373 0.024691358

0.56 0.003991488 0.017146776

0.565 0.00419151 0.010973937

0.57 0.004392404 0.00617284

0.575 0.004594136 0.002743484

0.58 0.004796678 0.000685871

0.585 0.005 0

SLT

0.72 0.035 0

0.725 0.033698453 0.000235345

0.73 0.032418873 0.00081952

0.74 0.029925997 0.002853736

0.75 0.027522162 0.005920768

0.76 0.025208198 0.009937285

0.77 0.022984989 0.014849293

0.78 0.020853469 0.020617311

0.79 0.018814638 0.027210483

0.8 0.016869561 0.034603637

165

0.81 0.015019382 0.042775618

0.82 0.013265337 0.051708242

0.83 0.01160876 0.061385614

0.84 0.010051111 0.071793647

0.85 0.008593986 0.082919716

0.86 0.007239154 0.094752404

0.87 0.005988586 0.107281303

0.88 0.004844509 0.120496863

0.89 0.003809468 0.134390272

0.9 0.002886424 0.148953353

0.91 0.002078901 0.164178489

0.92 0.00139122 0.180058557

0.93 0.000828907 0.196586868

0.94 0.000399523 0.213757125

0.945 0.000238041 0.222581111

0.95 0.000114733 0.231563379

0.96 0 0.5

***HYSKRG 0.30

*KROIL *STONE2 *SWSG

**RTYPE *CON 1

*INCLUDE 'Facies.cmg'

**--------------------------------------------------------------------**

** INITIAL CONDITIONS

**--------------------------------------------------------------------**

*INITIAL

*USER_INPUT

*INCLUDE 'init_Sw.cmg'

*INCLUDE 'init_pressure.cmg'

*INCLUDE 'TR.cmg'

*INCLUDE 'CO2_NO_initial.cmg'

*INCLUDE 'CH4.cmg'

*INCLUDE 'C2H6.cmg'

*INCLUDE 'C3H8.cmg'

*INCLUDE 'NC4.cmg'

*INCLUDE 'NC5.cmg'

*INCLUDE 'FC20.cmg'

166

*SALINR *PPMVOL 150000

**--------------------------------------------------------------------**

** NUMERICAL METHODS CONTROL

**--------------------------------------------------------------------**

*NUMERICAL

DTMIN 1e-8

*NORM *PRESS 500.

*NORM *SATUR 0.10

*NORM *GMOLAR 0.05

*MAXCHANGE *PRESS 5000

*MAXCHANGE *SATUR .5

*MAXCHANGE *GMOLAR .5

*CONVERGE *MAXRES 1.E-04

**CONV-RESONLY *ON

*ITERCER 5

DTMAX 5

**--------------------------------------------------------------------**

** WELL DATA

**--------------------------------------------------------------------**

*INCLUDE 'WellData_1_corrected_47-

1_29F1_31F4_lowinj32F4_lowBHP2_modoilR_32F3_mdfperf28F2_oil31F-

4_lowperf31F4-Extended.inc'

167

A.3 SAMPLE INPUT DATA PLUME MIGRATION (CASE 2 FROM TABLE 6.2)

*RESULTS *SIMULATOR *GEM

*FILENAMES *OUTPUT *SRFOUT *RESTARTOUT *INDEX-OUT

*MAINRESULTSOUT

*TITLE1 'CO2 Sequestration into an Aquifer'

*CASEID 'CASE 1'

*INUNIT *FIELD

*WPRN *WELL *TIME

*WPRN *GRID *TIME

*WPRN *ITER *NONE

*WSRF *WELL *TIME

*WSRF *GRID *TIME

*DIARY *CHANGES

*OUTPRN *RES *ALL

*OUTPRN *GRID *NONE

*OUTSRF *GRID *OUTSRF *GRID DENG RHOG MWG FRG SG DENO RHOO

PCG PCW SO DENW SW KRG VISG MWO KRO VISO PRES KRW XALL YALL

ZALL WALL PERM PERMEFF

*Z 'CO2' *W 'CO2'

**--------------------------------------------------RESERVOIR DATA------

*GRID *CART 500 500 1

*KDIR *DOWN

*DI *CON 20

*DJ *CON 20

*DK *CON 10

*DEPTH *TOP 1 1 1 7425.00

*DIP -3 0.0

*POR *CON 0.13

*VOLMOD *IJK

1 1:500 1 32808

500 1:500 1 32808

1:500 1 1 32808

1:500 500 1 32808

168

*PERMI *CON 20

*PERMJ *EQUALSI

*PERMK *EQUALSI

*CPOR 4.0E-06

*PRPOR 3550.0

**--------------------------------------------------FLUID COMPONENT DATA

*MODEL *PR

*NC 2 2

*TRES 200.000

*PVC3 1.2000000E+00

*COMPNAME

'CO2' 'C1'

*SG 8.1800000E-01 3.0000000E-01

*TB -1.0921000E+02 -2.5861000E+02

*PCRIT 7.2800000E+01 4.5400000E+01

*VCRIT 9.4000000E-02 9.9000000E-02

*TCRIT 3.0420000E+02 1.9060000E+02

*AC 2.2500000E-01 8.0000000E-03

*MW 4.4010000E+01 1.6043000E+01

*HCFLAG 0 0

*BIN

1.0300000E-01

*VSHIFT 0.0000000E+00 0.0000000E+00

*VISCOR *HZYT

*MIXVC 1.0000000E+00

*VISVC 9.4000000E-02 9.9000000E-02

*VISCOEFF 1.0230000E-01 2.3364000E-02 5.8533000E-02 -4.0758000E-02

9.3324000E-03

*OMEGA 4.5723553E-01 4.5723553E-01

*OMEGB 7.7796074E-02 7.7796074E-02

*PCHOR 7.8000000E+01 7.7000000E+01

*HENRYC 0. 0.

*REFPH 3.5500000E+03 3.5500000E+03

*VINFINITY 3.6023289E-02 3.6176602E-02

*ENTHCOEF

4.7780500E+00 1.1443300E-01 1.0113200E-04 -2.6494000E-08

3.4706000E-12 -1.3140000E-16

-5.5811400E+00 5.6483400E-01 -2.8297300E-04 4.1739900E-07

-1.5255760E-10 1.9588570E-14

*TRACE-COMP 2

169

**--------------------------------------------------ROCK FLUID----------

*ROCKFLUID

*RPT

*SGT

0.005 0 0.00000

0.04675 0.001450584 0.00000

0.0885 0.006581123 0.00000

0.13025 0.015939632 0.00000

0.172 0.029857754 0.00000

0.21375 0.048583155 0.00000

0.2555 0.072316174 0.00000

0.29725 0.101226274 0.00000

0.339 0.135461002 0.00000

0.38075 0.175151452 0.00000

0.4225 0.220415869 0.00000

0.46425 0.271362155 0.00000

0.506 0.32808969 0.00000

0.54775 0.390690697 0.00000

0.5895 0.4592513 0.00000

0.63125 0.533852349 0.00000

0.673 0.614570096 0.00000

0.71475 0.701476732 0.00000

0.7565 0.794640842 0.00000

0.79825 0.894127783 0.00000

0.84 1 0.00000

*SWT

0.160 0.0 0.

0.200 0.002 0.

0.240 0.010 0.

0.280 0.020 0.

0.320 0.033 0.

0.360 0.049 0.

0.400 0.066 0.

0.440 0.090 0.

0.480 0.119 0.

0.520 0.150 0.

0.560 0.186 0.

0.600 0.227 0.

0.640 0.277 0.

0.680 0.330 0.

0.720 0.390 0.

0.760 0.462 0.

170

0.800 0.540 0.

0.840 0.620 0.

0.880 0.710 0.

0.920 0.800 0.

0.960 0.900 0.

0.995 1.0 0.

**--------------------------------------------------INITIAL CONDITION---

*INITIAL

*VERTICAL *DEPTH_AVE *WATER_GAS

*REFPRES 3550.0

*REFDEPTH 7500.0

*DWGC 100.0

*ZGAS 0.0001 0.9999

*SEPARATOR

14.70000 60.00000

**--------------------------------------------------NUMERICAL-----------

*NUMERICAL

*NORM *PRESS 50.

*NORM *SATUR 0.005

*NORM *GMOLAR 0.005

*CONVERGE *PRESS 1.E-04

*CONVERGE *HC 5.E-05

*CONVERGE *WATER 5.E-05

*MAXCHANGE *GMOLAR 0.8

*MAXCHANGE *SATUR 0.8

*CONVERGE *MAXRES 1.E-04

*NORTH 60

*DTMIN 1.E-06

*DTMAX 182.5

**--------------------------------------------------WELL DATA-----------

*RUN

*DATE 2000 1 1

*DTWELL 0.01

*AIMWELL *WELLNN

*WELL 1 'INJ'

171

*INJECTOR 1

*INCOMP *SOLVENT 1. 0.

*OPERATE MAX BHG 30 CONT

*GEOMETRY *K 1.0 0.34 1.0 0.0

*PERF *GEO 1

250 250 1 1

*DATE 2000 2 1

*DATE 2000 3 1

*DATE 2000 4 1

*DATE 2000 5 1

*DATE 2000 6 1

*DATE 2000 7 1

*DATE 2000 8 1

*DATE 2000 9 1

*DATE 2000 10 1

*DATE 2000 11 1

*DATE 2000 12 1

*DATE 2001 1 1

*DATE 2002 1 1

*DATE 2003 1 1

*DATE 2004 1 1

*DATE 2005 1 1

*DATE 2006 1 1

*DATE 2007 1 1

*DATE 2008 1 1

*DATE 2009 1 1

*DATE 2010 1 1

*DATE 2011 1 1

*DATE 2012 1 1

*DATE 2013 1 1

*DATE 2014 1 1

*DATE 2015 1 1

*DATE 2016 1 1

*DATE 2017 1 1

*DATE 2018 1 1

*DATE 2019 1 1

*DATE 2020 1 1

*DATE 2021 1 1

*DATE 2022 1 1

*DATE 2023 1 1

*DATE 2024 1 1

*DATE 2025 1 1

172

*DATE 2026 1 1

*DATE 2027 1 1

*DATE 2028 1 1

*DATE 2029 1 1

*DATE 2030 1 1

*DATE 2031 1 1

*DATE 2032 1 1

*DATE 2033 1 1

*DATE 2034 1 1

*DATE 2035 1 1

*DATE 2036 1 1

*DATE 2037 1 1

*DATE 2038 1 1

*DATE 2039 1 1

*DATE 2040 1 1

*DATE 2041 1 1

*DATE 2042 1 1

*DATE 2043 1 1

*DATE 2044 1 1

*DATE 2045 1 1

*DATE 2046 1 1

*DATE 2047 1 1

*DATE 2048 1 1

*DATE 2049 1 1

*DATE 2050 1 1

*DATE 2051 1 1

*DATE 2052 1 1

*DATE 2053 1 1

*DATE 2054 1 1

*DATE 2055 1 1

*DATE 2056 1 1

*DATE 2057 1 1

*DATE 2058 1 1

*DATE 2059 1 1

*DATE 2060 1 1

*DATE 2061 1 1

*DATE 2062 1 1

*DATE 2063 1 1

*DATE 2064 1 1

*DATE 2065 1 1

*DATE 2066 1 1

*DATE 2067 1 1

*DATE 2068 1 1

173

*DATE 2069 1 1

*DATE 2070 1 1

*DATE 2071 1 1

*DATE 2072 1 1

*DATE 2073 1 1

*DATE 2074 1 1

*DATE 2075 1 1

*DATE 2076 1 1

*DATE 2077 1 1

*DATE 2078 1 1

*DATE 2079 1 1

*DATE 2080 1 1

*DATE 2081 1 1

*DATE 2082 1 1

*DATE 2083 1 1

*DATE 2084 1 1

*DATE 2085 1 1

*DATE 2086 1 1

*DATE 2087 1 1

*DATE 2088 1 1

*DATE 2089 1 1

*DATE 2090 1 1

*DATE 2091 1 1

*DATE 2092 1 1

*DATE 2093 1 1

*DATE 2094 1 1

*DATE 2095 1 1

*DATE 2096 1 1

*DATE 2097 1 1

*DATE 2098 1 1

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