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Optimization of coupled CO₂ sequestration and enhanced oil recovery
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Optimization of coupled CO₂ sequestration and enhanced oil recovery
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Content
OPTIMIZATION OF COUPLED CO
2
SEQUESTRATION AND ENHANCED
OIL RECOVERY
by
Hamid Reza Jahangiri
A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(PETROLEUM ENGINEERING)
May 2012
Copyright 2012 Hamid Reza Jahangiri
ii
In the name of God, The Most Gracious, The Most Merciful
Dedication
To my mother and father, Nahid and Rahim, who have always provided me with
their continuous support, endless encouragement and unconditional love, and to
my divine wife, Layla.
iii
Acknowledgments
First and foremost, I would like to thank my parents, Nahid and Rahim, who
have provided for and supported me far more generously than typical parents. I
would also like to thank my sister Shima who has always encouraged me as long
as I can remember. I wish them the best.
I would like to express special appreciation to my advisor, Dr. Zhang, for his
invaluable support, guidance, patience and valuable suggestions throughout my
PhD work at USC. I am very grateful for his contributions to my professional
accomplishments. I would like to especially thank Dr. Ershaghi, the director of
Petroleum Engineering program at USC, for all the support and guidance he
provided for my academic and professional development.
I appreciate all the guidance and comments I received from my supervising
committee members, Dr. Jessen, Dr. Aminzadeh and Dr. Mendel.
I would like to thank John Bolling and Jerry Hale for providing internship
opportunities at Occidental Petroleum and Chevron Corporation, giving me
industrial and field experience.
I am also extremely thankful to David Simmons, Jitendra Mouhan and Ehsan
Tajer, my supervisors and mentor at OXY and Chevron who helped me develop
my professional skills through the summer internship programs. I also need to
thank Mork Family Department, Global Climate and Energy Project (GCEP) at
iv
Stanford University via a grant to University of Southern California, Peking
University, and China University of Geosciences at Wuhan for providing funding
throughout my PhD studies at USC.
I would like to thank my dearest uncle, Bahman and his lovely wife, Mahnaz
who are my only relatives in the US. Their care and support have been
outstanding.
Many thanks to my fellow student friends in the Petroleum Engineering
Department at USC: Parham Ghods, Abdollah Orangi, Mohsen Heydari, Nelia
Jafroodi, Ehsan Tajer, Dalad, Amir Nejad, Mohammad Javaheri, Farnaz Khalaj,
Hamed Haddadzadegan, Tayeb Ayatollahi, Mohammad Evazi, Hassan Shojaei,
Asal Rahmani, Shahram Farhadi and Arman Khodabakhshnejad. Thank you for
providing such a wonderful environment to work and grow in.
Last, but far from least, I want to express my deep appreciation, gratitude,
and love for my wife Layla who helped me tremendously in writing this
dissertation with her patience, persistent support, and love. I am forever indebted
to her.
v
Table of Contents
Dedication ............................................................................................................. ii
Acknowledgments ................................................................................................ iii
List of Tables ...................................................................................................... vii
List of Figures .................................................................................................... viii
Abstract ............................................................................................................ xvii
Chapter 1: Introduction .................................................................................... 1
1.1 Literature review ................................................................................10
1.2 Research objectives and tasks .............................................................25
Chapter 2: Evaluation of CO
2
Sequestration and Enhanced Oil Recovery .......29
2.1 Introduction ........................................................................................29
2.2 Reservoir description ..........................................................................31
2.3 Injection scenarios ..............................................................................35
2.4 Evaluation of scenarios .......................................................................36
2.5 Results and discussion ........................................................................39
2.6 Conclusions .........................................................................................47
Chapter 3: Investigation on Economics of CO
2
Sequestration and EOR ..........50
3.1 Introduction ........................................................................................50
3.2 Net present value of CO
2
EOR and sequestration ..............................53
3.3 Reservoir description ..........................................................................57
3.4 Results and discussion ........................................................................58
3.4.1 Immiscible case ........................................................................60
3.4.2 Miscible case ............................................................................68
3.5 Conclusion ..........................................................................................75
vi
Chapter 4: Ensemble-Based Co-optimization of CO
2
Sequestration and
Enhanced Oil Recovery ...............................................................................78
4.1 Introduction ........................................................................................78
4.2 Methodology .......................................................................................84
4.2.1 Ensemble-based optimization ...................................................84
4.3 Reservoir description ..........................................................................88
4.4 Results and discussion ........................................................................89
4.4.1 Scenario (a) ..............................................................................90
4.4.2 Scenario (b) ............................................................................ 101
4.4.3 Scenario (c) ............................................................................ 107
4.4.4 Effect of oil price and tax credit ............................................ 111
4.5 Conclusion ........................................................................................ 115
Chapter 5: Closed Loop Ensemble-Based Co-optimization of CO
2
Sequestration
and Enhanced Oil Recovery ...................................................................... 117
5.1 Introduction ...................................................................................... 117
5.1.1 Ensemble Kalman Filter ........................................................ 118
5.1.2 Production optimization algorithm ........................................ 123
5.2 Mathematical model and methodology ............................................. 127
5.2.1 Ensemble Kalman filter .......................................................... 127
5.2.2 Ensemble optimization with uncertain reservoir description .. 130
5.3 Implementation of ensemble-based closed-loop co-optimization ........ 135
5.4 Reservoir description ........................................................................ 137
5.5 Results and discussion ...................................................................... 144
5.5.1 Scenario (a) ............................................................................ 144
5.5.2 Scenario (b) ............................................................................ 177
5.5.3 Scenario (c) ............................................................................ 193
5.6 Conclusion ........................................................................................ 208
Chapter 6: Summary, Conclusions and Recommendations ............................. 210
6.1 Summary and conclusions ................................................................. 210
6.2 Recommendations and future work .................................................. 214
Bibliography ...................................................................................................... 217
vii
List of Tables
Table 1-1. Estimated Storage Capacities of Geologic Formations (Gt CO
2
) ......... 3
Table 2-1. Compositional description of oil ..........................................................34
Table 2-2. Injection rate of optimized case for different injection schemes ..........46
Table 3-1. Oil composition for miscible flooding ..................................................60
Table 4-1. Share of each injector from the total CO
2
injection in scenario
(a) ...........................................................................................................96
Table 4-2. Share of each injector from the total CO
2
and water in scenario
(b) and (c) ............................................................................................ 106
Table 4-3. Share of each injector from the total CO
2
injection for different
economic parameters ............................................................................. 114
Table 5-1. Share of each injector from the total CO
2
injection for
immiscible flooding in scenario (a) ........................................................ 150
Table 5-2. Average data mismatch for immiscible case in scenario (a) .............. 161
Table 5-3. Share of each injector from the total CO
2
injection for miscible
flooding in scenario (a).......................................................................... 167
Table 5-4. Average data mismatch for miscible case in scenario (a) .................. 175
Table 5-5. Share of each injector from the total CO
2
and water in scenario
(b) ......................................................................................................... 183
Table 5-6. Average data mismatch for immiscible case in scenario (b) .............. 191
Table 5-7. Share of each injector from the total CO
2
and water in scenario
(c) ......................................................................................................... 197
Table 5-8. Average data mismatch for immiscible case in scenario (c) .............. 206
viii
List of Figures
Figure 1-1. Concentrations of greenhouse gases in the atmosphere (Orr Jr.
2004) ........................................................................................................ 2
Figure 2-1. Permeability distribution of reference model .....................................31
Figure 2-2. Porosity distribution of reference model ............................................32
Figure 2-3. Top view of reference model and well location ..................................33
Figure 2-4. Two-phase relative permeability relationship: (a) water and oil
and (b) oil and gas ..................................................................................35
Figure 2-5. (a) Cummulative oil production, (b) Recovery factor, (c) Mass
of CO
2
stored, and (d) Mass of CO
2
storage factor of different
injection schemes in reference case ..........................................................40
Figure 2-6. Comparison of objective function of different injection schemes
in reference case ......................................................................................41
Figure 2-7. (a) Cumulative oil production, (b) Recovery factor, (c) Mass of
CO
2
stored, and (d) Mass of CO
2
storage factor of different
injection schemes in optimized BHP of production wells ........................43
Figure 2-8. Comparison of objective function of different injection schemes
in optimized BHP of production wells and reference case .......................44
Figure 2-9. Comparison of (a) Cumulative oil production, (b) Recovery
factor, (c) Mass of CO
2
stored, and (d) Mass of CO
2
storage factor
of different injection schemes in optimized rate of injection wells
and reference case ...................................................................................45
Figure 2-10. Comparison of objective function of different injection
schemes in optimized rate of injection wells and reference case ..............47
Figure 3-1. Top view of reference model and well location ..................................58
Figure 3-2. (a) Cumulative oil production, (b) Recovery factor storage, (c)
Mass of CO
2
stored, and (d) Mass of CO
2
storage factor for
different injection schemes of immiscible flooding ...................................61
ix
Figure 3-3. (a) Objective function, and (b) Net Present Value for different
injection schemes of immiscible flooding .................................................62
Figure 3-4. Effect of tax credit on NPV for immiscible flooding ..........................64
Figure 3-5. (a) Cumulative oil production, (b) Recovery factor, (c) Mass of
CO
2
stored, and (d) Mass of CO
2
storage factor at different CO
2
injection timing for immiscible flooding ..................................................65
Figure 3-6. (a) Objective function, and (b) Net Present Value for different
injection schemes of immiscible flooding .................................................66
Figure 3-7. Comparison of (a) Cumulative oil production, (b) Recovery
factor, (c) Mass of CO
2
stored, and (d) Mass of CO
2
storage factor
for the optimized and base cases of immiscible flooding .........................67
Figure 3-8. (a) Objective function, and (b) Net Present Value for the
optimized and base cases of immiscible flooding .....................................68
Figure 3-9. (a) Cumulative oil production, (b) Recovery factor storage, (c)
Mass of CO
2
stored, and (d) Mass of CO
2
storage factor for
different injection schemes of miscible flooding .......................................69
Figure 3-10. (a) Objective function, and (b) Net Present Value for
different injection schemes of miscible flooding .......................................70
Figure 3-11. Effect of tax credit on NPV for miscible flooding ............................71
Figure 3-12. (a) Cumulative oil production, (b) Recovery factor, (c) Mass
of CO
2
stored, and (d) Mass of CO
2
storage factor at different CO
2
injection timing for miscible flooding ......................................................72
Figure 3-13. (a) Objective function, and (b) Net Present Value for
different injection schemes of miscible flooding .......................................73
Figure 3-14. Comparison of (a) Cumulative oil production, (b) Recovery
factor, (c) Mass of CO
2
stored, and (d) Mass of CO
2
storage factor
for the optimized and base cases of miscible flooding .............................74
Figure 3-15. (a) Objective function, and (b) Net Present Value for the
optimized and base cases of miscible flooding .........................................75
x
Figure 4-1. Comparison of (a) Cumulative oil production and (b) Mass of
the stored CO
2
for the optimized and base cases of immiscible
flooding in scenario (a)............................................................................92
Figure 4-2. Comparison of Dimensionless Net Present Value for the
optimized and base cases of immiscible flooding in scenario (a) .............93
Figure 4-3. The change of the NPV with iteration ..............................................94
Figure 4-4. The change of the controls for different injectors for immiscible
flooding in scenario (a)............................................................................95
Figure 4-5. Comparison of (a) Cumulative oil production and (b) Mass of
CO
2
stored for the optimized and base cases of miscible flooding in
scenario (a). ............................................................................................98
Figure 4-6. Comparison of Dimensionless Net Present Value for the
optimized and base cases of miscible flooding in scenario (a). ................99
Figure 4-7. The change of the controls for different injectors for miscible
flooding in scenario (a).......................................................................... 100
Figure 4-8. Comparison of (a) Cumulative oil production and (b) Mass of
CO
2
stored for the optimized and base cases of immiscible flooding
in scenario (b) ....................................................................................... 103
Figure 4-9. Comparison of Dimensionless Net Present Value for the
optimized and base cases of immiscible flooding in scenario (b). .......... 104
Figure 4-10. The change of the controls for different injectors for
immiscible flooding in scenario (b) ........................................................ 106
Figure 4-11. Comparison of (a) Cumulative oil production and (b) Mass of
CO
2
stored for the optimized and base cases of immiscible flooding
in scenario (c). ...................................................................................... 108
Figure 4-12. Comparison of Dimensionless Net Present Value for the
optimized and base cases of immiscible flooding in scenario (c). ........... 109
Figure 4-13. The change of the controls for different injectors for
immiscible flooding in scenario (c). ....................................................... 110
xi
Figure 4-14. Comparison of Dimensionless Net Present Value for the
optimized and base cases for three different oil prices and CO
2
tax
credit (oil price, $/bbl - CO
2
tax credit, $/ton). ................................... 112
Figure 4-15. The change of the controls for different injectors for three
different oil prices and CO
2
tax credit (oil price, $/bbl - CO
2
tax
credit, $/ton). ....................................................................................... 113
Figure 5-1. Mean of the initial permeability ensemble ....................................... 142
Figure 5-2. True horizontal permeability of the reservoir .................................. 143
Figure 5-3. Comparison of (a) Cumulative oil production and (b) Mass of
the stored CO
2
for the optimized cases with known geology and
unknown geology and the base case of immiscible flooding in
scenario (a) ........................................................................................... 147
Figure 5-4. Comparison of Dimensionless Net Present Value for the
optimized cases with known geology and unknown geology and
base case of immiscible flooding in scenario (a) .................................... 149
Figure 5-5. The change of the controls for different injectors for immiscible
flooding in scenario (a) for optimized cases with known and
unknown geology ................................................................................... 150
Figure 5-6. Data match from the initial and updated ensemble for
immiscible flooding in scenario (a). The solid red line is the
reference oil production profile, the dark black represents the
responses from the updated ensemble and gray represents the
responses from the initial ensemble ....................................................... 153
Figure 5-7. Data match from the initial and updated ensemble for
immiscible flooding in scenario (a). The solid red line is the
reference gas-oil ratio profile, the dark black represents the
responses from the updated ensemble and gray represents the
responses from the initial ensemble ....................................................... 154
Figure 5-8. Data match from the initial and updated ensemble for
immiscible flooding in scenario (a). The solid red line is the
reference bottom-hole pressure, the dark black represents the
responses from the updated ensemble and gray represents the
responses from the initial ensemble ....................................................... 155
xii
Figure 5-9. Data match from the initial and updated ensemble for
immiscible flooding in scenario (a). The solid red line is the
reference CO
2
liquid mole fraction, the dark black represents the
responses from the updated ensemble and gray represents the
responses from the initial ensemble ....................................................... 156
Figure 5-10. Data match from the initial and updated ensemble for
immiscible flooding in scenario (a). The solid red line is the
reference CO
2
gas mole fraction profile, the dark black represents
the responses from the updated ensemble and gray represents the
responses from the initial ensemble ....................................................... 157
Figure 5-11. RMSE performance metrics for immiscible case in scenario (a) ..... 159
Figure 5-12. SPREAD performance metrics for immiscible case in scenario
(a) ......................................................................................................... 160
Figure 5-13. Mean of updated ensemble horizontal permeability of the
reservoir for immiscible case in scenario (a) .......................................... 162
Figure 5-14. Comparison of (a) Cumulative oil production and (b) Mass of
the stored CO
2
for the optimized cases with known geology and
unknown geology and the base case of miscible flooding in scenario
(a) ......................................................................................................... 164
Figure 5-15. Comparison of Dimensionless Net Present Value for the
optimized cases with known geology and unknown geology and
base case of miscible flooding in scenario (a) ........................................ 165
Figure 5-16. The change of the controls for different injectors for miscible
flooding in scenario (a) for optimized cases with known and
unknown geology ................................................................................... 166
Figure 5-17. Data match from the initial and updated ensemble for
miscible flooding in scenario (a). The solid red line is the reference
oil production profile, the dark black represents the responses from
the updated ensemble and gray represents the responses from the
initial ensemble ..................................................................................... 168
xiii
Figure 5-18. Data match from the initial and updated ensemble for
miscible flooding in scenario (a). The solid red line is the reference
gas-oil ratio profile, the dark black represents the responses from
the updated ensemble and gray represents the responses from the
initial ensemble ..................................................................................... 170
Figure 5-19. Data match from the initial and updated ensemble for
miscible flooding in scenario (a). The solid red line is the reference
bottom-hole pressure, the dark black represents the responses from
the updated ensemble and gray represents the responses from the
initial ensemble ..................................................................................... 171
Figure 5-20. Data match from the initial and updated ensemble for
miscible flooding in scenario (a). The solid red line is the reference
CO
2
liquid mole fraction, the dark black represents the responses
from the updated ensemble and grays represent the responses from
the initial ensemble ............................................................................... 172
Figure 5-21. Data match from the initial and updated ensemble for
miscible flooding in scenario (a). The solid red line is the reference
CO
2
gas mole fraction profile, the dark black represents the
responses from the updated ensemble and gray represents the
responses from the initial ensemble ....................................................... 173
Figure 5-22. RMSE performance metrics for miscible case in scenario (a) ......... 174
Figure 5-23. SPREAD performance metrics for miscible case in scenario
(a) ......................................................................................................... 175
Figure 5-24. Mean of updated ensembles of horizontal permeability of the
reservoir for miscible case in scenario (a) .............................................. 176
Figure 5-25. Comparison of (a) Cumulative oil production and (b) Mass of
the stored CO
2
for the optimized cases with known geology and
unknown geology and the base case of immiscible flooding in
scenario (b) ........................................................................................... 179
Figure 5-26. Comparison of Dimensionless Net Present Value for the
optimized cases with known geology and unknown geology and
base case of immiscible flooding in scenario (b) .................................... 180
xiv
Figure 5-27. The share of CO
2
injection for different injectors for
immiscible flooding in scenario (b) for optimized cases with known
and unknown geology ............................................................................ 182
Figure 5-28. The share of water injection for different injectors for
immiscible flooding in scenario (b) for optimized cases with known
and unknown geology ............................................................................ 183
Figure 5-29. Data match from the initial and updated ensemble in scenario
(b). The solid red line is the reference oil production profile, the
dark black represents the responses from the updated ensemble
and gray represents the responses from the initial ensemble ................. 184
Figure 5-30. Data match from the initial and updated ensemble in scenario
(b). The solid red line is the reference water production profile,
the dark black represents the responses from the updated
ensemble and gray represents the responses from the initial
ensemble ............................................................................................... 185
Figure 5-31. Data match from the initial and updated ensemble in scenario
(b). The solid red line is the reference gas-oil ratio profile, the
dark black represents the responses from the updated ensemble
and gray represents the responses from the initial ensemble ................. 186
Figure 5-32. Data match from the initial and updated ensemble in scenario
(b). The solid red line is the reference bottom-hole pressure, the
dark black represents the responses from the updated ensemble
and gray represents the responses from the initial ensemble ................. 187
Figure 5-33. Data match from the initial and updated ensemble in scenario
(b). The solid red line is the reference CO
2
liquid mole fraction,
the dark black represents the responses from the updated
ensemble and gray represents the responses from the initial
ensemble ............................................................................................... 188
Figure 5-34. Data match from the initial and updated ensemble in scenario
(b). The solid red line is the reference CO
2
gas mole fraction
profile, the dark black represents the responses from the updated
ensemble and gray represents the responses from the initial
ensemble ............................................................................................... 189
Figure 5-35. RMSE performance metrics for immiscible case in scenario (b) ..... 190
xv
Figure 5-36. SPREAD performance metrics for immiscible case in scenario
(a) ......................................................................................................... 191
Figure 5-37. Mean of updated ensembles of horizontal permeability of the
reservoir for immiscible case in scenario (b) .......................................... 192
Figure 5-38. Comparison of (a) Cumulative oil production and (b) Mass of
the stored CO
2
for the optimized cases with known geology and
unknown geology and the base case of immiscible flooding in
scenario (c) ........................................................................................... 194
Figure 5-39. Comparison of Dimensionless Net Present Value for the
optimized cases with known geology and unknown geology and
base case of immiscible flooding in scenario (c) .................................... 195
Figure 5-40. The share of CO
2
injection for different injectors for
immiscible flooding in scenario (c) for optimized cases with known
and unknown geology ............................................................................ 196
Figure 5-41.The share of water injection for different injectors for
immiscible flooding in scenario (c) for optimized cases with known
and unknown geology ............................................................................ 197
Figure 5-42. Data match from the initial and updated ensemble in scenario
(c). The solid red line is the reference oil production profile, the
dark black represents the responses from the updated ensemble
and gray represents the responses from the initial ensemble ................. 199
Figure 5-43. Data match from the initial and updated ensemble in scenario
(c). The solid red line is the reference water production profile, the
dark black represents the responses from the updated ensemble
and gray represents the responses from the initial ensemble ................. 200
Figure 5-44. Data match from the initial and updated ensemble in scenario
(c). The solid red line is the reference gas-oil ratio profile, the dark
black represents the responses from the updated ensemble and
gray represents the responses from the initial ensemble ........................ 201
Figure 5-45. Data match from the initial and updated ensemble in scenario
(c). The solid red line is the reference bottom-hole pressure, the
dark black represents the responses from the updated ensemble
and gray represents the responses from the initial ensemble ................. 202
xvi
Figure 5-46. Data match from the initial and updated ensemble in scenario
(c). The solid red line is the reference CO
2
liquid mole fraction,
the dark black represents the responses from the updated
ensemble and gray represents the responses from the initial
ensemble. .............................................................................................. 203
Figure 5-47. Data match from the initial and updated ensemble in scenario
(c). The solid red line is the reference CO
2
gas mole fraction
profile, the dark black represents the responses from the updated
ensemble and gray represents the responses from the initial
ensemble ............................................................................................... 204
Figure 5-48. RMSE performance metrics for immiscible case in scenario (c) ..... 205
Figure 5-49. SPREAD performance metrics for immiscible case in scenario
(b) ......................................................................................................... 205
Figure 5-50. Mean of updated ensembles of horizontal permeability of the
reservoir for immiscible case in scenario (c) .......................................... 207
xvii
Abstract
Sequestration of carbon dioxide (CO
2
) in depleted or partially depleted oil
reservoirs is a plausible option to reduce CO
2
emissions into the atmosphere.
Carbon dioxide has been used as the injection fluid in Enhanced Oil Recovery
(EOR) operations. The goal of such projects is to improve the profitability by
maximizing the oil production (to increase the revenue) and minimizing the CO
2
injection (to decrease the costs). However, in sequestration projects, subsurface
storage of the injected CO
2
needs to be maximized.
The objective of this study is to develop a framework to co-optimize oil
extraction and CO
2
sequestration. In the proposed framework, the net present
value (NPV) of the project is selected as the optimization objective function. In
my work, factors such as the cost of capturing the produced CO
2
, CO
2
transportation and recycling are taken into account. A number of simulations are
studied to achieve comprehensive understanding of the financial performance of
the coupled CO
2
sequestration and EOR projects. The simulations show that the
projects would be unprofitable for immiscible cases when using current typical
costs of CO
2
capture from power plants unless there is some form of credit for
storage. In contrast, in miscible cases, the projects may be profitable even
without considering any CO
2
credits, and their profitability is further enhanced
with possible carbon credits.
xviii
With the advances in smart well technology, maximizing net present value of
oil recovery and CO
2
storage can be achieved substantially by managing the
operation intelligently in a closed-loop optimization framework. Closed-loop
optimization consists of two parts: data assimilation and NPV optimization. Data
assimilation adjusts the reservoir geological model to honor the production data
and reduces the uncertainty of the estimate of reservoir geological properties.
NPV optimization modifies the operational strategy based on the updated
geological model.
The Ensemble-based Optimization (EnOpt) algorithm has been selected as
the optimization algorithm and the well-injection patterns and rates as the
controlling variables. EnOpt can be easily combined with the ensemble-based
data-assimilation methods to form an ensemble-based closed-loop optimization
framework. The production rate data are assimilated in real-time by an ensemble
Kalman filter for characterization of the reservoir. Simultaneously, EnOpt
optimizes the expectation of net present value based on the up-to-date reservoir
models. Several cases are used to demonstrate the applicability of the developed
technique. Our results show that the oil recovery and the NPV can be increased
significantly. The proposed methodology is fairly robust, does not require adjoint
programming and can be readily used with any reservoir simulator. The workflow
presented in this work can be used to design and co-optimize the coupled CO
2
sequestration and EOR projects.
1
Chapter 1: Introduction
In recent years, the concentration of greenhouse gases, such as carbon dioxide,
has drastically increased in the atmosphere and caused some concerns about
climate change. The concentrations of the major greenhouse gases (CO
2
, methane
(CH
4
), and nitrous oxide (N
2
O)) are shown in Figure 1-1 (Houghton, et al. 1996),
with a sharp rise starting in the late 1800s. Natural sources of atmospheric
carbon dioxide include volcanic outgassing, the combustion of organic matter,
and the respiration processes of living aerobic organisms. Anthropogenic sources
of carbon dioxide include the burning of fossil fuels for heating, power
generation and transportation, as well as some industrial processes, such as
cement making. CO
2
concentration which is emitted to the atmosphere as a result
of burning of fossil fuels, clearing of forests, and manufacturing of cement, has
increased by approximately a third from 280 ppm in the pre-industrial times to
370 ppm today (Houghton, et al. 1996).
Emissions of CO
2
are approximately 24×10
9
tons/yr (24 Gt/yr), or
approximately 6.5 Gt/yr of carbon. Current emissions exceed the capacity of the
natural systems to absorb them because amounts of CO
2
emitted annually
resulting from human activities are much higher compared to the large natural
cycles that exchange CO
2
between the atmosphere, oceans, and terrestrial
biosphere, leading to the accumulation of CO
2
in the atmosphere (Orr Jr. 2004).
2
Figure 1-1. Concentrations of greenhouse gases in the atmosphere (Orr Jr. 2004)
Estimates of economic growth, energy consumption, and CO
2
emissions
associated with them suggest that the concentration of CO
2
in the atmosphere
will continue to grow during this century unless significant steps are taken to
reduce the release of CO
2
into the atmosphere (Orr Jr. 2004).
3
Several suggestions have been proposed to control the problem of increasing
CO
2
emissions in the air. It is possible to decrease CO
2
emissions by increasing
energy production efficiency which means production of less CO
2
per specified
amount of produced energy. CO
2
emissions can also be reduced by increasing the
share of renewable energy. Because 85% of the primary power is supplied by
fossil fuels now, creating this new supply will be a very big challenge. The most
promising scenario is long-term sequestration of CO
2
in geological formations.
Geological sequestration is injecting CO
2
into underground porous reservoirs and
isolating it from the atmosphere.
At least three options exist for geologic storage of CO
2
(Orr Jr. 2004): oil and
gas reservoirs, deep saline aquifers, and unmineable coalbeds. Table 1-1
summarizes estimates of the capacity of the three storage options (Parson and
Keith 1998, Gale 2003).
Table 1-1. Estimated Storage Capacities of Geologic Formations (Gt CO
2
)
Storage Option (Parson and Keith 1998) (Gale 2003)
Oil and gas reservoir 740 to 1850 920
Deep saline aquifers 370 to 3700 400 to 10,000
Coalbeds 370 to 1100 40
Natural gas and oil have been stored in underground reservoirs for millions of
years. The depleted oil and natural gas fields have the capacity and structural
trap that can contain gases and liquids safely. Impermeable cap rocks can
4
prevent the leakage of gas. Thus, it is possible to use underground depleted
reservoirs to store carbon dioxide because they are known to have a geologic seal
that traps hydrocarbons. Thus, as long as oil production operations have not
damaged that seal, the reservoir should be able to hold injected CO
2
.
Considerable experience with CO
2
injection into oil reservoirs has been
obtained during the last three decades. The motivation of this is enhanced oil
recovery (EOR). The number of EOR projects that use CO
2
worldwide has been
limited by the availability of injection gas at low costs. If CO
2
is widely available,
either because the cost of capture is reduced or because incentives for CO
2
storage are in place, many oil reservoirs would be suitable candidates for CO
2
injection.
Oil and gas reservoirs are not uniformly distributed geographically, and
anthropogenic CO
2
is generated in many locations that are not close to potential
storage sites of oil or gas reservoirs. However, deep formations containing salt
water are widely distributed. Water in these deep aquifers is not suitable for
drinking or for agricultural use, mainly due to its high salinity. There are large
volumes of useless aquifers in the depths of sedimentary basins in the world. In
this setting, injected CO
2
would flow more easily through high-permeability
paths, but the flow may not be dominated by the pressure gradients imposed by
injection and production wells. Gravity segregation caused by the density
difference between the injected CO
2
and brine will cause preferential flow at the
5
top of the aquifer, though injection of the CO
2
well below the top of the aquifer
can mitigate this gravity segregation to some extent (Orr Jr. 2004). Aquifers with
large volumes, reasonable permeability and thickness, and good pressure
communication over long distances will be most attractive, in that large volumes
could be injected without raising aquifer pressure significantly. The injected CO
2
will dissolve into brine, and the resulting brine/CO
2
mixture will be slightly
denser than the brine alone (Ennis-King and Paterson 2003). Slow vertical flow of
the denser brine will cause further dissolution, as fresh brine is brought in contact
with the CO
2
phase. Trapping of a separate CO
2
phase by brine also can act to
immobilize CO
2
as a residual phase (Orr Jr. 2004).
Estimates of the time scales for dissolution and the resulting vertical
convection suggest that hundreds to thousands of years will be required to
dissolve all the CO
2
(Ennis-King and Paterson 2003), but by that time, much of
the CO
2
will exist in a trapped residual phase. Relatively slow chemical reactions,
depending on the chemical composition of the brine and the minerals present in
the aquifer, may then sequester some of the CO
2
as minerals (Orr Jr. 2004).
Key questions for aquifer-related projects involve aquifer characterization. It
is likely that much less information is available to delineate aquifers compared to
the data that is available for oil and gas reservoirs. Structural traps may or may
not exist; therefore, an understanding of the aquifer’s regional setting may be
6
needed, as well as an understanding of barriers to vertical flow, faults, and other
potential pathways for vertical migration.
A large-scale and practical CO
2
sequestration project in the North Sea at the
Sleipner gas field has already been initiated and has shown the feasibility of
performing large-scale projects. Because it is a high-permeable aquifer with
relatively high porosity, it is an especially favorable application of aquifer
injection (Torp and Gale 2003). Approximately 1×10
6
tonnes of CO
2
, separated
from produced natural gas, are injected each year into an overlying aquifer. The
injected CO
2
appears to be contained within the sand in which the CO
2
is
injected, although there is evidence of vertical migration within the aquifer (Torp
and Gale 2003). Jahangiri and Zhang (2011) have investigated the effect of
aquifer heterogeneity on plume migration and dilution with the method of Monte
Carlo simulation. This study presented results of modeling long-term CO
2
storage
in a deep saline aquifer with a reservoir simulator. They focused on the first and
second spatial moments of the plume and the dilution index for various reservoir
parameters, including average permeability, vertical to horizontal permeability
ratio (k
v
/k
h
), and variance and correlation-length ratio of heterogeneity. A
relative dispersion framework used to analyze the Monte Carlo simulations gives
a more reasonable estimation of the plume distribution, dilution index, and
spatial moments than does the commonly used absolute dispersion framework.
7
The impact of the injection completion interval and its location have also been
studied.
CO
2
sequestration in coal is another possibility. CO
2
injected in a coalbed may
have the dual benefits of CO
2
disposal and enhanced coalbed methane recovery.
CO
2
injection could improve methane recovery and help maintain reservoir
pressure. While, in oil and gas reservoirs and aquifers, injected CO
2
occupies the
pore space as a separate phase or is dissolved in water and oil as a storage
mechanism, there is a different storage mechanism in deep, unmineable coalbeds,
which are the source of coalbed methane, where CO
2
can be injected. Such gases
as CH
4
or CO
2
adsorb on the surfaces of coal particles at high pressure.
Significantly more CO
2
adsorbs on coal at a given pressure and temperature than
does CH
4
or N
2
. In addition, the adsorption curve hysteresis suggests that once
CO
2
is adsorbed, much of it will remain adsorbed even if the pressure decreases
at a later time. Ohga, et al. (2003) reported the results of adsorption experiments
in which approximately three times as much CO
2
adsorbed on a coal sample as
did CH
4
at a given pressure, while approximately half as much N
2
adsorbed as
did CH
4
.
Flow in coalbeds occurs primarily in the fracture network and cleats. Injected
CO
2
will flow through the cleats, diffusing into matrix blocks and replacing
adsorbed CH
4
(Ohga, et al. 2003). Thus, CO
2
can be used to enhance CH
4
recovery. This displacement process is similar to adsorption chromatography.
8
Because CO
2
adsorbs more strongly than either CH
4
or N
2
, it should be possible
to use the coalbed to separate a mixture of N
2
and CO
2
(Orr Jr. 2004), but at the
cost of compression of the N
2
in addition to the CO
2
and separation of N
2
from
produced CH
4
. There is evidence that coal permeability changes with the amount
of adsorbed gas. Typically, as CH
4
is removed from coal, permeability increases,
and as CO
2
adsorbs, permeability decreases (Orr Jr. 2004). Thus, displacement
processes in coalbeds involves a complex interplay of flow in the cleat system,
and changes in permeability, diffusion, and adsorption.
Field experience with CO
2
injection into coalbeds is limited (Stevens, Spector
and Riemer 1998, Reeves 2001), although field tests are planned or are being
conducted in the U.S., Canada, Poland, Australia, and Japan. Here, again, the
motivation is enhanced recovery of coalbed methane. Production of CH
4
shows a
clear response to CO
2
adsorption (Stevens, Spector and Riemer 1998), an
observation that is consistent with the idea that CO
2
can replace adsorbed CH
4
and make it available for production. The experience gained in this and other
field tests provides useful guidance for future CO
2
-storage projects. Results to
date show minimal breakthrough of injected CO
2
, which is consistent with the
idea that the injected CO
2
is being adsorbed on the coal.
Out of the three options for geologic storage presented here, coalbeds are the
least well understood. The complex physical mechanisms and flows offer
challenges as well as opportunities. The combination of physical mechanisms and
9
the potential for offsetting costs of CO
2
storage by CH
4
recovery suggest that
more investigation of this approach is warranted.
Deep saline aquifers typically have no economic value, are separated from
potable aquifers, which are much shallower, and are often located close to large
CO2-emission sources such as electric power plants. Mature oilfields also are one
of the most favorable targets for the CO2 sequestration. Injecting CO2 into these
reservoirs can increase the amount of oil produced, offsetting some of the CO2
storage costs. Most of the CO2 injection aspects into the reservoirs for the
purpose of Enhanced Oil Recovery (EOR) have been known for decades. But
there are some differences between injecting CO2 for the purpose of pure EOR
projects and for the purpose of both CO2 sequestration and EOR projects. In
EOR projects, the goal is to maximize profit by minimizing the total amount of
CO2 injected per each barrel of oil produced. The economics and incentives for
combined EOR and sequestration are less clear at this time, but a first step in
the development process should be to do studies to investigate ways to both
produce oil efficiently and maximize storage of the carbon dioxide.
The next section includes an extensive literature survey. Research papers are
reviewed on CO
2
flooding projects and processes as well as on the limited studies
on coupled CO
2
sequestration and EOR.
10
1.1 Literature review
Carbon dioxide (CO
2
) flooding for increasing oil recovery has been used since
the 1950s. First, the CO
2
was considered a solvent for crude oil or as a carbonate
water flood. Since that time several schemes have been suggested, namely
continuous CO
2
gas injection, carbonated water injection, CO
2
gas or liquid slug
followed by water, CO
2
gas or liquid slug followed by alternate water and CO
2
gas injection, or water-alternating-gas (WAG) (Klins 1984).
CO
2
sequestration studies started almost a decade ago (Bradshaw, et al. 2004,
Chadwick, et al. 2004). Despite this fact, still vast areas of research have not
been covered in detail in the area of coupled enhanced oil recovery and
sequestration.
Considerable engineering effort has gone into minimizing the amount of CO
2
required to recover oil in EOR projects. If the objective is also to increase storage
of CO
2
, then changing injection horizons, injection of CO
2
into an aquifer below
the reservoir, or injection into the capillary transition zone may also be useful
(Jessen, et al. 2004). While many of the specific actions taken to increase CO
2
storage will depend on the details of the particular reservoir setting, it is
apparent that many opportunities exist for developing the design of CO
2
-injection
projects in a way that increases storage substantially over the amounts stored in
EOR projects.
11
The first project specifically aimed at CO
2
sequestration in an oil reservoir is
being conducted at the Weyburn field in Saskatchewan (Malik and Islam 2000,
Moberg, Stewart and Stachniak 2003). The CO
2
generated at a coal-gasification
plant in Beulah, North Dakota, is transported by pipeline to Weyburn, where a
combined EOR and CO
2
-sequestration project is under way. Malik and Islam
(2000) have investigated different scenarios for the Weyburn field that could
result in maximum oil recovery or maximum storage. Based on their results,
injecting CO
2
into the producing formation will give higher storage and higher
recovery, whereas in reservoirs with bottom water, injecting CO
2
into the bottom
water will result in higher mobilized oil in the transition zone and therefore
higher oil recovery (Perry 1982). In addition, because of utilizing the aquifer
volume and formation of dissolved CO
2
in water, the CO
2
storage will increase
significantly. It should be mentioned that in some cases CO
2
flooding could be
done after primary production, leading to a huge difference in terms of oil
recovery and CO
2
sequestration.
CO
2
injection into gas reservoirs has been proposed by several researchers
(Oldenburg and Benson 2002, Oldenburg, Stevens and Benson 2004) but has not
been attempted yet. CO
2
could be used for pressure maintenance or for
condensate vaporization (Seto, Jessen and Orr 2003), but the cost of purchasing
CO
2
has made these applications uneconomical in the absence of incentives for
CO
2
storage. In reservoirs that contain some condensate, CO
2
can vaporize the
12
light hydrocarbons that make up the condensate quite efficiently, and it is even
possible for CO
2
to develop multi-contact miscibility with two-phase gas and
condensate mixtures (Jessen and Orr 2003). If CO
2
sequestration is undertaken in
large scales, gas reservoirs would be good candidates for storage, with the benefit
of a known geologic seal capable of holding gas indefinitely.
An extensive monitoring program aimed at detecting leakage of injected CO
2
is planned (Moberg, Stewart and Stachniak 2003). The Weyburn project is a
good example of why oil reservoirs are attractive early candidates for subsurface
CO
2
storage. A detailed reservoir description is available, based on seismic
surveys, cores, well logs, and the experience from operating the field. The CO
2
-
injection project will extend the producing life of the field significantly. The
Canadian authorities that issue permits for subsurface gas injection are well
acquainted with the permitting issues, and there is a well-defined regulatory
structure that can accommodate the CO
2
-sequestration project. Also, additional
hydrocarbon recovery might offset at least a portion of the costs of transporting
and storing the CO
2
.
While there is considerable experience from CO
2
-EOR projects to guide future
CO
2
-storage projects, there is a need to extend the range of reservoirs
investigated and to develop the design considerations that will allow efficient CO
2
storage in addition to EOR. An example of a site where detailed investigations of
issues related to CO
2
storage may be pursued is the Teapot Dome field, which
13
was designated by the U.S. Dept. of Energy (DOE) as a possible field laboratory
for CO
2
sequestration (Orr Jr. 2004). The field includes multiple stratigraphic
elements that could be used to test injection and monitoring strategies.
Candidate reservoirs for CO
2
-EOR and sequestration projects have diverse
geology and characteristics. For example, reservoirs near the U.S. Gulf coast
overlie salt domes, and tertiary oil exists in a series of steeply dipping sandstone
layers in several different fault blocks located on the flanks of a salt dome (Nute
1983). These reservoirs are highly heterogeneous with very high permeability and
porosity. In contrast, some of the reservoirs suitable for CO
2
flooding, e.g.
Weyburn, are almost horizontal carbonate reservoirs with low permeability and a
different type of heterogeneity (Elsayed, et al. 1993). Also, some studies have
been reported on CO
2
flooding and sequestration in fractured carbonate reservoirs
(Schechter, et al. 2001).
Since the inception of CO
2
injection for enhanced oil recovery in the 1970s,
significant reservoir engineering effort has gone into reducing the volume of CO
2
required to recover a barrel of oil. The objective of combined EOR and CO
2
sequestration, however, is to increase the amount of CO
2
left behind when the
reservoir is abandoned; thus, the engineering design objective is significantly
different.
Kovscek (2002) believes that there are three principal mechanisms by which
CO
2
may be sequestered within an oil reservoir. The first is physical containment
14
or so-called hydrodynamic trapping of CO
2
as a gas or supercritical fluid beneath
a cap rock (Law and Bachu 1996). Next, CO
2
can dissolve directly in the water
and oil phases. This is sometimes called solubility trapping (Reichle, Houghton
and Benson 1999). Lastly, CO
2
can react either directly or indirectly with
reservoir minerals and organic matter and be converted into a solid phase
(Bachu, Gunter and Perkins 1994). This process may be rather slow. Kovscek did
not mention capillary trapping as residual gas saturation, which has been shown
by Kumar et al. (2004) to be still another way to store CO
2
and is the one that
has significant advantages over hydrodynamic trapping.
The optimal operating conditions for higher oil recovery and for higher CO2
storage will not in general be the same. Some aspects of oil reservoirs that should
be considered for combined EOR and CO
2
sequestration include reservoir depth,
oil density, storage capacity, water and oil volumes in place, and formation
thickness. Usually CO
2
-injection projects in oil reservoirs have focused on oil with
densities between 29 and 48 °API (855 to 711 kg/m3) and reservoir depths from
760 to 3700 m (2500 to 12,000 ft) below ground surface (Taber, Martin and
Seright 1997a). Formation type and thickness are not main factors that affect oil
recovery, but formation thickness is a key factor in the process of storage. On the
other hand, CO
2
density is also one of the main issues; it increases with depth
(Hendriks and Block 1993), but it has been shown that the density of pure CO
2
will be greatest at a given depth in a reservoir where the fluid pressure gradient
15
is largest while the geothermal gradient is the least. Therefore, geothermal
gradients reduce the CO
2
density significantly (Kovscek 2002). The result is that
in the absence of a geothermal gradient, CO
2
phase density exceeds water density
at a depth of roughly 2750 m ( ≈ 9450 ft). Thus, the CO
2
would tend to migrate
downward rather than upward for depths greater than 2750 m. With the
inclusion of the geothermal gradient, CO
2
will not approach water density even at
depth of 4000 m. This is a deterministic issue in the aquifer storage of CO
2
.
Screening criteria for oil reservoirs that might be candidates for CO
2
storage
have been suggested by Kovscek (2002) and by Shaw and Bachu (2002). There
are two kinds of displacement that can be found when oil is displaced by CO
2
; it
can be miscible or immiscible. The nature of displacement behavior depends on
reservoir pressure, reservoir temperature and oil composition. When the reservoir
pressure is near or above the minimum miscibility pressure (MMP), CO
2
can
displace oil quite efficiently in the invaded zones of the reservoir. The MMP is
the pressure at which the oil and CO
2
are miscible with no mixing in the
reservoir. Oil can dissolve more CO
2
as pressure increases and both fluids will
become miscible at some pressure. Carbon dioxide swells the oil and reduces its
viscosity, when CO
2
is injected above the MMP. In an immiscible displacement
the residual oil saturation is not affected at all, but this swelling effect can cause
some of the residual oil to become mobile (Jarrel, Fox and Stein 2002). If gas is
injected above the pressure that miscibility is achieved, then a higher fraction of
16
residual oil can be displaced from the pores. MMP is a direct function of oil and
injected gas composition (Stalkup 1983, Lake 1989). Injected gas composition
should be designed in a way that MMP can be achieved. Nute (1983) used
methane as an additive to lighten the injected CO
2
in the Bay St. Elaine field. He
showed that the addition of methane to CO
2
tends to increase the MMP. To
prevent the loss of miscibility, he found out that the CO
2
-methane mixture could
be enriched with n-butane to reduce the MMP to the original design conditions.
Guler et al. (2001) also studied employing CO
2
and natural gas liquids (NGL)
mixtures as a method to enhance oil recovery. Zhang et al. (2004) have shown
that MMP for their oil samples increased as the N
2
or CH
4
concentration
increased in the CO
2
stream. Based on their study, CO
2
containing 37% moles of
propane reduced the pure CO
2
MMP by 45%.
Many MMP correlations that take into account oil and injection-gas
composition have been proposed (Yuan, et al. 2004), but a simple estimate of the
MMP is given by the extrapolated vapor pressure of CO
2
. If the temperature is
less than the critical temperature of CO
2
(31°C), the vapor pressure gives the
pressure above which the CO
2
is a liquid. The following expression can be used to
calculate the vapor pressure for temperatures below 31°C, and it can be used to
estimate the pressure at which the density of CO
2
climbs steeply for temperatures
above 31°C (Orr Jr. 2004).
17
exp 2015
273.15 10.91 ( 1-1)
This pressure is a reasonable estimate of the MMP; it is most accurate for
light oils at relatively low temperatures, below 50°C, and it also is a useful
estimate for sequestration because efficient use of the pore space requires that
relatively dense CO
2
be stored.
A multiple-contact miscible process is the mechanism in which oil is miscibly
displaced by CO
2
; carbon dioxide extracts part of the C
5
-C
30
hydrocarbon
fraction. Medium to high API gravity oils have a suitable quantity of extractable
hydrocarbon, in general those oils can be found in deep reservoirs, in which the
displacement pressure is above the MMP (Holm and O'Brein 1986). The pressure
required for multiple-contact miscible displacement depends on the reservoir
temperature and the composition of the oil.
Reservoir capacity is another criterion for the candidate reservoirs. For this,
the specific capacity or the mass of CO
2
per volume of rock is a good measure to
differentiate sequestration potential among reservoirs (Kovscek 2002). Of course,
over-injecting of CO
2
into the reservoir, based on reservoir capacity and rock and
fluid compressibility, is detrimental to the reservoir integrity. A conservative idea
is that reservoir pressure should not exceed greatly the initial reservoir pressure.
Over-pressurization of fluids within the reservoir pore space can cause a breach of
any type of barrier which will lead to either the natural hydraulic fracturing of
the seal or slip of sealing faults or both.
18
CO
2
-injectivity issues for sequestration have been addressed in the context of
aquifers (Law and Bachu 1996, Gupta, et al. 1999); they have stated that in the
aquifer-storage process, the high-permeability pathways increase the injectivity
and a high volume of CO
2
can be stored. But the heterogeneous, high-
permeability paths are a negative factor for the CO2-flooding process; because
they result in lower sweep efficiency causing lower oil recovery and early
breakthrough. In the reservoirs connected to an aquifer, the bottom-water aquifer
is either active or inactive. Injectivity is an important issue in the oil reservoirs
with bottom water. Bachu (2000) believes that reservoirs with inactive bottom
aquifers (so-called closed reservoirs) might be the most attractive targets for CO
2
injection because there is no need to displace water that invaded from an aquifer.
Also, the initial oil saturation is likely larger compared to reservoirs with water
influx, and thus the potential for incremental recovery is larger.
Since CO
2
sources are rarely pure and costs for separation of impurities from
CO
2
are very expensive, existence of impurities in the injected stream and their
role in the process of CO
2
flooding are very important and deserve a broad study.
In general, most designs considered the injection of pure CO
2
into the reservoir,
but it may have some impurities that change the oil-recovery efficiency. Malik
and Islam (2000) have investigated the effect of nitrogen contamination in the
gas stream in the Weyburn field. They believe that the presence of contaminants
decreases the solubility and diffusivity of carbon dioxide into the oil,
19
consequently leading to reduction in swelling of oil by carbon dioxide. The
molecular diffusion of carbon dioxide into the oil is considered to be a controlling
mechanism in the carbon dioxide flood. An impure CO
2
gas stream affects the
diffusion rate. The negative impact on production is due to the presence of the
nitrogen content that tends to form a stagnant phase between the oil and carbon
dioxide, through which carbon dioxide has to diffuse before contacting oil. The
presence of nitrogen also increases the viscosity of the carbon dioxide-oil mixture,
resulting in an inefficient displacement from the pores.
Due to low viscosity, CO
2
has a high mobility, which is a major issue in
optimizing the oil recovery and sequestration. High mobility causes lower
reservoir sweep and early production of CO
2
, which can lead to lower oil recovery
and lower storage. Continuous injection is usually replaced by the injection of
slugs of CO
2
which is displaced by a cheaper chase fluid such as water, or by
injecting small volumes of CO
2
and water, alternating them until the desired
volume of CO
2
has been injected; this scheme is called the water-alternating-gas
(WAG) process. The WAG process increases microscopic displacement efficiency,
improving oil recovery by combining better mobility ratio with contacting
unswept zones. To obtain the best possible displacement efficiency, the amount of
water and gas should be adjusted; too much water will turn out in poor
microscopic displacement, and too much gas will result in poor vertical and
horizontal sweep (Christensen, Stenby and Skauge 2001). The first reported
20
WAG injection was in 1957 in Canada. Since then several WAG-injection
processes have been performed, especially in the United States. Christensen,
Stenby and Skauge (2001) have reported that most WAG field applications have
been performed as a miscible displacement (around 79%) in sandstone reservoirs
(around 57%). The economy and project goal will play a main role in the WAG-
ratio design in the process of both recovery and sequestration. Ghomian, Pope
and Sepehrnoori (2008) studied optimized WAG-flood design for coupled CO
2
sequestration and EOR in two- and three-dimensional heterogeneous reservoirs.
They optimized project profit as $/bbl of oil and amount of stored CO
2
using
response surface and experimental design methodology. The simultaneous flow of
gas and water yields, generally, a net mobility that is less than that of the
injection gas alone.
Flood pattern and design strategy should be implemented based on the
economics and oil recovery point of view along with the sequestration objective.
Different designs and strategies should be employed for different reservoirs
considering various objectives. For instance, as one of the initial steps, if the
reservoir pressure is less than the MMP, the main challenge would be to return
the reservoir pressure back to its original one to provide the MMP (Kleinstelber
1990).
Employing horizontal or a combination of horizontal and vertical wells
depending on the project conditions can help to optimize recovery and storage
21
(Lim, Pope and Sepehrnoori 1994). The application of CO
2
flooding using
horizontal wells significantly shortens project life, thus substantially improving
project economics. For very tight reservoirs where CO
2
and brine injectivities
strongly affect project economics, the use of horizontal injectors may be a more
attractive alternative than vertical wells. The use of horizontal injectors in
conjunction with vertical producers in tertiary CO
2
-WAG flooding generally
resulted in oil recovery that was as good or better than using both horizontal
injector and producer, and always higher than using all vertical wells (Lim,
Khan, et al. 1992). The injectivity of CO
2
and brine using horizontal wells, and
hence the oil recovery in a reasonable project life, is very sensitive to the
permeability in the vicinity of the wells.
Malik and Islam (2000) believe that in the Weyburn field, horizontal injection
wells have proved to be efficient for the CO
2
-flooding process to improve recovery
while increasing the storage of CO
2
. Besides employing horizontal wells, applying
different well-control techniques, including partial completion of both injection
and production wells, can improve the amount of injected and stored CO
2
as well
as oil recovery (Jessen, et al. 2004).
Kovscek and Cakici (2004) have introduced an objective function combining
dimensionless oil recovery and reservoir utilization as follows:
22
( 1-2)
where (0 1
1 ) and (1 ) are weights and
is the volume
of CO
2
stored in the reservoir and is the volume of pore space of the reservoir.
Also OIP is the volume of the oil in place at the start of CO
2
injection and is
the net production of oil. The design objective will be the maximizing of this
function with respect to the specified set of weights. If the main aim is to
maximize oil recovery, is taken as 1, whereas if the goal is to maximize CO
2
storage, is taken as 1. The regulatory and tax structure for sequestration
remains unclear and likely will vary from nation to nation. In practice, weights
will be chosen based on the revenue produced by both oil recovery and CO
2
sequestered.
It is better to allow some volume of gas to cycle through the reservoir as a
means of obtaining maximum CO
2
storage. Any produced gas, however, must be
recompressed to injection pressure before it can be reinjected into the reservoir.
That is, there is an energy penalty associated with gas cycling. To allow the
possibility of gas cycling but also account for the energy penalty, the net
cumulative oil recovery is defined as:
23
( 1-3)
where is the cumulative oil recovery. The second term on the right is the
energy needed, in oil-equivalent units, to compress the produced injection gas to
injection pressure. It is expressed as:
7
3.1815 10
1
out
in in
in
P
EPQ t
P
γ
γ
− ⎡ ⎤
⎛⎞ ×
⎢ ⎥
=−
⎜⎟
⎢ ⎥
⎝⎠
⎣ ⎦
( 1-4)
where γ is the compressibility factor (0.23 for CO
2
), P is pressure (lbf/ft
2
), Q is
flow rate (ft
3
/min), and the subscripts in and out refer to the low- and the high-
pressure sides of the compressor. In Equation ( 1-4), E is in units of barrels of oil
and t is in days. Thus, is the net production of oil discounted by the amount
of energy needed to cycle gas.
Qi et al. (2007) studied the design of CO
2
storage in aquifers and have
recommended an injection strategy in which CO
2
and brine are injected
simultaneously followed by chase brine injection to render more than 85% of
injected CO
2
immobile in a very short period. They extended their study of the
design of carbon dioxide storage in aquifers to oilfields. They demonstrated that
pore-scale capillary trapping is an effective and rapid mechanism to render the
CO
2
immobile in oil reservoirs. They studied field-scale oil production and CO
2
storage using a streamline-based simulator that captures dissolution, dispersion,
gravity and rate-limited reactions in three dimensions. While injecting at the
optimum WAG ratio gives the fastest oil recovery, this allowed CO
2
to channel
24
through the reservoir, leading to rapid CO
2
breakthrough and extensive recycling
of the gas (Qi, LaForce and Blunt 2008). They proposed to inject more water
than optimum. This allows the CO
2
to remain in the reservoir, increases the field
life and leads to improved storage of CO
2
as a trapped phase.
Ghomian, Sepehrnoori and Pope (2008) have modeled the storage of CO
2
in a
Frio brine pilot, as the first US pilot study. They compared the results from a
simulation model with the actual field data and validated the simulation model
with high accuracy. Scharf and Clemens (2006) have evaluated the potential for
CO
2
storage in eleven of the largest oil and thirteen of the largest gas fields in
Austria and have found huge potential for CO
2
storage in these fields. Bank,
Riestenberg and Koperna (2007) have performed reservoir simulation using
detailed, representative data from major oilfields throughout the Appalachian
basin and indicated that 1,230 million barrels may become technically
recoverable, which will provide huge potential for CO
2
storage in this basin. This
of course depends on future oil prices and CO
2
costs. CO
2
injection into a North
Sea chalk field was studied using a compositional reservoir simulator by Forooghi,
Hamouda and Eilertsen (2009). They have investigated the effects of six
parameters including injection scheme, injector and producer well type, well
control mode, slug size and the WAG ratio on the coupled CO
2
-EOR and
sequestration process. In the case studied, the results show that the water-
25
alternating-gas injection scheme using a mixture of CO
2
and hydrocarbon gas is
the optimum case (EOR and sequestration process).
1.2 Research objectives and tasks
The goal of this research is to better understand the potential for both
enhanced oil recovery and storage of CO
2
in mature oil reservoirs over a wide
range of conditions. A compositional simulator was used to investigate these
combined processes, but statistical analysis was also utilized for this purpose.
This research has mainly focused on co-optimization of coupled CO
2
-EOR and
sequestration processes.
The objective in this research is to develop a framework and study effective
strategies leading to co-optimization of the oil recovery and the amount of stored
CO
2
. These strategies include employing different injection and production
schemes, applying various well-control techniques, as well as different mobility-
control technologies such as WAG to delay early CO
2
breakthrough at production
wells and optimize the flood design for the coupled CO
2
sequestration and EOR
process. Owing to the fact that the financial aspect is one of the major factors for
coupled CO
2
EOR and sequestration projects, these projects should be evaluated
in terms of their net present values (NPVs), which are calculated using their
revenues and costs. In our work, factors such as the cost of capturing the
produced CO
2
, CO
2
transportation and recycling are taken into account. The goal
26
of this dissertation is to co-optimize the coupled CO
2
sequestration and enhanced
oil recovery by taking into account the economics of the sequestration projects.
In this dissertation, we introduce an ensemble-based optimization (EnOpt) as
the optimization algorithm and the well-injection patterns and rates as the
controlling variables. The use of EnOpt with a single reservoir model and with
multiple reservoir models is illustrated with examples. Compared to the existing
optimization methods, EnOpt has two distinct features. First, similar to the
ensemble-based data-assimilation methods, the search direction used in the
production optimization is approximated from an ensemble. Second, EnOpt can
achieve robust optimization with the consideration of the uncertainty in the
estimate of reservoir properties. We also introduce an ensemble-based closed-loop
optimization that combines the ensemble-based data-assimilation methods, for
example, Ensemble Kalman filter (EnKf), with the EnOpt. An ensemble of
reservoir models is updated by EnKf and this ensemble provides the best
estimate of the reservoir properties and the associated uncertainty. EnOpt
performs a robust optimization through a coupled ensemble of control parameters
and reservoir models to maximize the expectation of the net present value of
CO
2
-EOR and sequestration. In the ensemble-based closed-loop optimization,
data assimilation and NPV optimization share the same ensemble-based feature.
The use of the ensemble greatly reduces the dimensionality of both data-
assimilation and NPV-optimization problems and makes the ensemble-based
27
closed-loop optimization suitable for large-scale problems. The ensemble concept
also makes this closed-loop optimization method independent of the reservoir
simulator and the economic model and so is very straightforward to implement.
This dissertation is divided into six chapters. Chapter 2 explains the
evaluation of coupled oil recovery and CO
2
storage. Different flood-design
parameters such as different injection and production schemes, various well-
control techniques, and different mobility-control methods including WAG were
considered to optimize the flood design for coupled CO
2
-sequestration and EOR
processes. Chapter 3 discusses the exploratory economic analysis based on
systematic compositional simulations to understand and optimize the coupled
CO
2
sequestration and enhanced oil recovery by taking into account the
economics of the sequestration projects by considering their major costs and
revenues. We explore the impact of some sort of incentives in the form of
accelerated depreciation or direct tax credits in order to support large-scale
sequestration projects in different conditions. Chapter 4 introduces the EnOpt
method for modeling, updating and optimizing reservoir models and shows the
use of EnOpt on a single reservoir model, without considering the uncertainty in
reservoir description. This chapter begins with a literature review of the
optimization algorithms in general, and EnOpt techniques. The EnOpt
methodology and formulation are all described in this chapter in some detail in
the context of our problem. The ensemble-based optimization is tested based on a
28
commonly used example for testing co-optimization of the coupled CO
2
storage
and EOR optimization. Chapter 5 illustrates the use of EnOpt, considering the
uncertainty in the estimation of the reservoir properties. Chapter 6 summarizes
the results and presents conclusions of the research work and recommendations
for future work.
29
Chapter 2: Evaluation of CO
2
Sequestration and Enhanced Oil
Recovery
2.1 Introduction
Carbon dioxide emissions will account for about two-thirds of potential global
warming, which is mainly caused by the combustion of fossil fuels for energy
production. More than 85 percent of the world’s energy needs are supplied by
fossil fuels, and demand for fossil fuels is increasing (Herzog, Eliasson and
Kaarstad 2000). Many analysts believe that the only way to resolve the growth in
the use of fossil fuels with limits on carbon dioxide emissions is through the
deployment of carbon sequestration. Oil and gas reservoirs are good candidates
for sequestration because industrial experiences already exist for CO
2
injection.
Carbon dioxide has been injected in EOR processes since the 1970s. One of the
major factors on the efficiency of EOR with CO
2
injection is the miscibility of
CO
2
in the oil phase (Orr Jr. and Taber 1984, Blunt, Fayers and Orr Jr. 1993). At
pressures greater than minimum miscibility pressure (MMP), oil and CO
2
are
mutually soluble. The dissolved CO
2
reduces the viscosity of the oil and causes
swelling of the oil phase, improving its ability to flow through the reservoir rock.
30
Screening criteria have been proposed for selecting suitable reservoirs where CO
2
may sustain or increase the oil production. To date, CO
2
-injection projects have
focused on oil with densities ranging from 29 to 48 °API (855 to 711 kg/m
3
) and
reservoir depths from 760 to 3700 m (2600 ft to 12,000 ft) (Taber, Martin and
Seright 1997a). The estimation was that if the only considerations are depth and
gravity, 80% of the world's reservoirs might be suitable for CO
2
injection, only
based upon EOR (Taber, Martin and Seright 1997a, Taber, Martin and Seright
1997b).
Carbon dioxide injection in mature or partially depleted oil and gas reservoirs
has environmental benefits since large amounts of CO
2
could be sequestrated
away from the atmosphere. To date, injection processes have been designed to
minimize the amount of CO
2
injected per barrel of oil produced, thereby
minimizing the purchase cost of CO
2
. However, when the goal is to store carbon
dioxide, the design question changes significantly (Kovscek 2002). Oil-recovery
processes need to be modified to leave the maximum amount of CO
2
in the
reservoir as well as maximizing oil recovery.
In this chapter, our main goal is to develop carbon dioxide-injection strategies
leading to co-optimization of coupled CO
2
EOR and sequestration. The focus here
is developing the appropriate function that evaluates CO
2
storage and oil recovery
for a given reservoir and fixed-well placement. It is assumed that sequestration
services provide significant revenue. The reservoir model and fluids are
31
summarized in the next section. Then, we focus on developing CO
2
-injection
scenarios leading to co-optimization, and results of the various injection schemes
and optimization of them are presented. These results are obtained using a
compositional, reservoir flow simulator. At the end, the conclusions are given.
2.2 Reservoir description
A synthetic reservoir description is chosen that is based on an actual
producing field. The PUNQ-S3 test case is described in detail (Floris, et al. 2001,
TNO PUNQ-S3 n.d.) and the geostatistical data are available electronically
(TNO PUNQ-S3 n.d.). The permeability and porosity maps of the model are
shown in Figure 2-1 and Figure 2-2. Initial reservoir pressure is 253 bars.
Figure 2-1. Permeability distribution of reference model
32
Figure 2-2. Porosity distribution of reference model
The depth of the top of the reservoir is about 2340 meters. Mean reservoir
thickness is 28 m. An average horizontal permeability is on the order of 100 md
and a sand porosity of roughly 0.20. The ratio of average horizontal to vertical
permeability is about 3. Additionally, the reservoir pore volume is a relatively
small 3 10
m
3
, whereas the initial average oil saturation is 0.60. The model
contains 19×28×5 grid blocks of which 1761 blocks are active. The x and y
dimensions of each grid block are 180 m. The model is divided into 5 layers
vertically and named 1 to 5 from top to bottom. The average thickness of the five
layers is 2.7, 4.8, 6.7, 6.7 and 6.7 meters for layers 1 to 5, respectively (Kovscek
and Cakici 2004).
33
There are four producer and four injector wells. The locations of these wells
are shown in Figure 2-3. These wells are completed to flow at the third, fourth
and fifth layers of the reservoir. A North Sea crude oil is selected as the reservoir
fluid, because it exhibits black-oil properties similar to those given with PUNQ-
S3 in a previous study (Kovscek and Cakici 2004).
Figure 2-3. Top view of reference model and well location
Table 2-1 shows the composition of the reservoir fluid (Kovscek and Cakici
2004). It is a moderately heavy (24 ºAPI, 910 kg/m3) crude oil. Pure CO
2
and
the reservoir fluid are not mutually miscible at reservoir pressure. The minimum
miscibility pressure (MMP) of pure CO
2
is estimated to be in excess of 608 bars
using the rapid estimation technique of Wang and Orr (Wang and Orr Jr. 1997).
34
On the other hand, the initial reservoir pressure is 253 bars. Thus, the reservoir is
not a good candidate for CO
2
EOR. Due to displacement efficiency, solvent
injection is recommended as a means of oil recovery.
Table 2-1. Compositional description of oil
Component Mole fraction
Molecular weight
(kg/mole)
T
c
(K) P
c
(bar)
CO
2
0 0.04401 304.2 72.9
CH
4
0.4383 0.01604 190.6 45.4
C
2
H
6
0.04262 0.03007 305.4 48.2
C
3
H8 0.009153 0.04410 369.8 41.9
i-Butane-C
4
H
10
0.005824 0.05812 408.1 36.0
n-Butane-C
4
H
10
0.005395 0.05812 425.2 37.5
i-Pentane-C
5
H
12
0.006771 0.07215 460.4 33.4
n-Pentane-C
5
H
12
0.003081 0.07215 469.6 33.3
C
6
0.01063 0.08617 507.4 29.3
C
7
0.2359 0.1355 623.9 30.4
C
8
-C
15
0.1189 0.2489 708.6 20.4
C
16
-C
23
0.07894 0.3812 795.7 16.5
C
24+
0.04456 0.6322 947.9 14.5
The solvent is designed to contain 66.7% of CO
2
with 2.5% of ethane (C
2
) and
propane (C
3
) and 8.3% butane (C
4
) that allow miscibility to develop. The relative
permeability data employed in this study are shown in Figure 2-4. In addition,
for simplicity, capillary pressures among oil, water, and gas phases are taken as 0.
35
Figure 2-4. Two-phase relative permeability relationship: (a) water and oil and (b)
oil and gas
2.3 Injection scenarios
A variety of schemes were tested (Kovscek and Cakici 2004) that are
summarized as:
• continuous gas injection
• gas injection after water flooding (GAW)
• water-alternating-gas drive (WAG)
The first scenario is simulated twice using pure CO
2
and solvent injection
fluid; the other cases are simulated with pure CO
2
. For a reference case,
36
production wells operate at a fixed pressure of 175 bars. Gas is injected at a rate
of 400,000 m
3
/day per well (at standard conditions). Gas injection after water
flooding is used where water is used to maintain pressure and drive oil from the
reservoir. After some volume of water injection, the injection is switched to gas
injection as a means of sequestering CO
2
. Again, production wells operate at a
fixed pressure of 175 bars. Water is injected at a rate of 1000 m
3
/day per well
until injection is switched to CO
2
at 400,000 m
3
/day (at standard conditions).
The WAG scheme injects water and CO
2
in alternating slugs. WAG processes
were developed to overcome having low viscosity of gas injection compared to oil.
In this procedure, gas is trying to displace oil in the upper part of the reservoir
and water invades the lower parts. The combined effect is giving overall better
vertical sweep efficiency. Equal volumes of water and gas are injected during each
slug because the optimal WAG ratio (volume of water to that of gas in a slug) is
approximately 1 for our reservoir and fluid models (Cakici 2003). Production
wells operate at a fixed pressure of 175 bars. The injection rate of water is 1000
m
3
/day, whereas that of CO
2
or a solvent is 400,000 m
3
/day (at standard
conditions).
2.4 Evaluation of scenarios
Our main goal is to find injection scenarios leading to maximum oil recovery
with simultaneous maximum emplacement of CO
2
in the reservoir. To achieve
37
this goal, reservoir simulations are performed with ECLIPSE 300 (GeoQuest
2008), a fully compositional, finite difference-based reservoir simulator.
In a co-optimization procedure, we need to evaluate the performance of
different scenarios; the objective function was defined by Kovscek and Cakici
(2004) as Equation ( 1-2). Because the volume of CO
2
is a dynamic parameter and
depends on the pressure and temperature of the reservoir and it differs this
parameter whether CO
2
is stored as a liquid or gas phase, it seems that the
second term cannot be a good representation for reservoir utilization of CO
2
.
Hence, instead of defining the volume ratio of CO
2
stored in the reservoir, we
have introduced the storage factor by using mass of CO
2
stored in the reservoir
over total capacity of the reservoir, which can store CO
2
in mass in the ideal
case, as this factor is independent of knowing how much CO
2
is stored in the
reservoir as a liquid or gas phase. We can rewrite the objective function as:
2
12
2
P
NMassofCOstored
fw w
OOIP Total capacity of CO
=+
( 2-1)
where Np is the cumulative oil recovery, and OOIP is the original oil in place and
0 1 and 1– , are weights. This equation combines
parameters that we want to optimize. The first term on the right is a
dimensionless oil-recovery factor and the second term is a dimensionless CO
2
-
storage factor. The weights for both terms are chosen with respect to the goals of
the recovery process. Equal weighting
0.5 places equal emphasis
38
on oil recovery and CO
2
storage. If the aim is to maximize oil recovery, w
1
is
taken as 1, whereas if the goal is to increase CO
2
storage, w
2
is taken as 1. The
relative prices of oil and gas cycling and injection determine the weight of each
term. In this study, an equal weighting was used. A scenario that injects, for
instance, a large volume of water, has less , for non-zero , because the second
term on the right of Equation ( 2-1) is not maximized. The design equation for co-
optimization is thus stated as:
max
( 2-2)
We implement the optimization algorithm such that the performance of the
reservoir for a particular set of settings can be determined via forward
simulations. In the co-optimization of CO
2
-EOR and sequestration problem, the
control parameters may be injection rate, fluid-production rate and bottom-hole
pressure of production wells. In this study, the injectors are controlled by
injection rate and the producers are controlled by bottom-hole pressure. In this
chapter, we use a Differential Evolution (DE) algorithm (Storn and Price 1995,
Storn and Price 1997) for optimization of objective function during the reservoir
life. DE optimizes a problem by maintaining a population of candidate solutions
and creating new candidate solutions by combining existing ones according to its
simple formulae, and then keeping whichever candidate solution has the best
score or fitness on the optimization problem at hand. In this way the
optimization problem is treated as a black box that merely provides a measure of
39
quality given a candidate solution, and the gradient is therefore not needed. The
optimizer, developed in MATLAB, drives ECLIPSE 300, which acts as the
objective function evaluator. An interface establishes communication between the
optimization routines and the simulator. We implement the optimization
algorithm such that the performance of the reservoir for a particular set of
settings can be determined via forward simulations. Our computer code uses the
reservoir simulator model to evaluate objective function for all population
members. It generates simulation input files (schedule data files) for each
individual member. These input files are data files containing the updated
bottom-hole pressures or rates after each iteration process. For the first
generation these profiles are generated randomly. The output files are the files
containing oil and gas production rates and cumulative production. The objective
function is calculated by a subroutine using these data. These values are
computed from the oil and gas flow rates at the various time steps. The rates and
cumulative productions are read from the ECLIPSE 300 run summary output
file.
2.5 Results and discussion
As we discussed earlier, in the base case used for comparison, the total water
injection rate is equally distributed among the injectors and all producers operate
at the same condition, so all the injectors are controlled by the water injection
40
rate of 1000 m
3
/day and gas rate of 400,000 m
3
/day, and all the producers are
controlled by the bottom-hole pressure of 175 bars. This reference case reflects
similarities to previous works (Wang and Orr Jr. 1997, Cakici 2003). They also
served as initial guesses for the optimal control function in the optimization
procedure. Figure 2-5 summarizes the performance of the continuous pure CO
2
and solvent injection, GAW and WAG schemes discussed above in the reference
case.
Figure 2-5. (a) Cummulative oil production, (b) Recovery factor, (c) Mass of CO
2
stored, and (d) Mass of CO
2
storage factor of different injection schemes in reference
case
41
In terms of oil recovery, it can be seen that solvent injection is the best
scheme because of miscibility of injection gas and oil. WAG scenario has the
second rank because the denser phase, water, sweeps the lower portion of the
reservoir while the gas sweeps the upper portion. As seen in the figure, of all the
cases, WAG performs the worst among all methods in CO
2
sequestration. This is
caused by the injection of water through the production period, which results in
limited reservoir pore-volume utilization for CO
2
storage. Here the pure CO
2
injection performs better than solvent injection because only two-thirds of the
injected gas is CO
2
.
Figure 2-6. Comparison of objective function of different injection schemes in
reference case
42
The objective function which is defined before in Equation ( 2-1) is depicted in
Figure 2-6. Equal weight is given to oil recovery and reservoir utilization. The
solvent-injection scheme performs much better than WAG and pure CO
2
injection. However, results from continuous gas injection processes both for
CO
2
and solvent are almost 70% higher than WAG due mainly to less
CO
2
storage during WAG processes in the second term of Equation ( 2-1). The
greatest value for objective function is obtained for a solvent in which the
miscibility increases oil recovery; gas injection focuses on the storage goal.
Figure 2-7 shows the results of all scenarios after calculating the optimal
bottom-hole pressure which is 215 bars by the DE algorithm. The result indicates
that we have improvement up to 16% in recovery factor and 25% in CO
2
storage
compared to reference cases.
43
Figure 2-7. (a) Cumulative oil production, (b) Recovery factor, (c) Mass of CO
2
stored, and (d) Mass of CO
2
storage factor of different injection schemes in
optimized BHP of production wells
Figure 2-8 shows the results for optimized bottom-hole pressure of the
production well in different schemes. For all cases considered, an improvement in
NPV with respect to the reference case was found, ranging from15–20%.
44
Figure 2-8. Comparison of objective function of different injection schemes in
optimized BHP of production wells and reference case
In this case, we optimized the CO
2
EOR-SEQ by controlling the injection rate
of injectors. Hence, we have four wells and four control parameters. The
optimization was done for solvent and pure-CO
2
injection scenarios. For each
reservoir the optimized results are compared with results from the corresponding
reference case.
45
Figure 2-9. Comparison of (a) Cumulative oil production, (b) Recovery factor, (c)
Mass of CO
2
stored, and (d) Mass of CO
2
storage factor of different injection
schemes in optimized rate of injection wells and reference case
Results for reference case and optimized case are presented in Figure 2-9.
Total injection rates are constant and equal to 1,600,000 m
3
/day, and upper limit
and lower limit of injection rate of each well are 600,000 m
3
/day and 200,000
m
3
/day, respectively. Best values for these parameters after optimization are
given in Table 2-2.
46
Table 2-2. Injection rate of optimized case for different injection schemes
Well
Injection rate (m
3
/day)-
Solvent Injection
Injection rate (m
3
/day)-
Pure-CO
2
Injection
Injector 1 586,530 577,860
Injector 2 229,450 232,590
Injector 3 583,130 588,330
Injector 4 200,890 201,220
It can be depicted that the best results happen when injection wells Injector 1
and Injector 3 inject at their maximum injection rate and Injector 2 and Injector
4 are approximately operated at minimum rate. As we can see in Figure 2-9, for
all cases considered, an improvement in recovery factor and storage factor with
respect to the reference case was found, ranging from 10–35%.
It can be observed that if we controlled the injection rate of each well, we
could get better results even though the number of control parameters increases
and run time of optimization increases.
Figure 2-10 compares the objective function of solvent and CO
2
injection in
the reference case and optimized case. The increase in objective function resulted
from a slight to moderate increase in oil production combined with an increase in
CO
2
storage.
The increase in cumulative oil production is due to keeping the injection rate
of wells located in the high-permeability zone in a lower limit and maximizing the
47
rate of wells located in the low-permeability zone. Gas production is also delayed
and also considerably reduced. As a result, total CO
2
stored is enlarged.
Figure 2-10. Comparison of objective function of different injection schemes in
optimized rate of injection wells and reference case
2.6 Conclusions
Oil fields are likely to be one of the first options where carbon dioxide is
injected for sequestration because the oil industry has considerable experience in
the use of CO
2
for enhanced oil recovery. Successful CO
2
-EOR processes have
minimized the mass of CO
2
needed to recover a barrel of oil. Maximizing the
sequestration of carbon dioxide and oil recovery rate from an oil reservoir is
48
different from the goals of traditional enhanced oil recovery. We have modified
the objective function compared to prior works to analyze better the EOR-
sequestration process. An effective process for co-optimization of CO
2
sequestration and oil recovery is a kind of well control that constrains the rate of
injection and production to maximize the objective function. Results of different
scenarios indicate that adjusting injection gas composition to maximize CO
2
concentration while maintaining an appropriate MMP is needed. The
optimization process designed a strategy to create injection profiles that reduce
the adverse effects of preferential flow of injected gas through high-permeability
zones.
The optimization process showed remarkable improvement in objective
function value of up to 10% from the initial base case as well as an improvement
of cumulative production of up to 8% from the base case. It should be noted that
more data, or sophisticated decision-making procedures, will be required prior to
the deployment of instrumented wells in cases with high degrees of uncertainty.
This approach has been applied to a simple 3-D heterogeneous reservoir with
known geology.
The regulatory and economic structure for CO
2
injection and sequestration
remains unclear and likely will vary from nation to nation. In practice, weight of
objective function should be chosen based on the revenue produced by both oil
recovery and CO
2
sequestrated. The next chapter will focus on finding a better
49
objective function to represent and optimize the coupled CO
2
-EOR and
sequestration. Further work can be carried out on reservoir geology while
considering uncertainties in the reservoir-model parameters and also on large-
scale field examples. Another complication left for future work concerns the effect
of rising oil prices and carbon taxes on both the optimal management of a CO
2
injection and the decision to initiate such a process. Geologically, projects will
make the switch at different prices, thereby shifting out the sequestration versus
EOR process over time.
50
Chapter 3: Investigation on Economics
of CO
2
Sequestration and EOR
3.1 Introduction
CO
2
concentration in the atmosphere has drastically increased over the past
250 years from 280 to 380 ppm (Bryant 1997). The major cause of increasing CO
2
emissions into the air has been recognized as the dramatic increase in the fossil
fuel consumption for energy production. Increasing concentrations of CO
2
lead to
climate change by enhancing the natural greenhouse effect.
Several measures have been suggested to control the problem of increasing
CO
2
emissions in the air. One of such measures is to decrease carbon intensity of
energy production, which means less CO
2
per specified amount of produced
energy (Forooghi, Hamouda and Eilertsen 2009). CO
2
emissions can also be
reduced by increasing the share of renewable energies in the energy consumption
portfolio. The most promising, immediate option for reducing a large amount of
CO
2
is, however, the long-term sequestration of CO
2
in geological formations.
Depleted or mature oil and gas reservoirs, deep saline formations, and unmineable
coalbeds are usually considered as the most applicable CO
2
-sequestration
formations (Bachu 2003).
51
Geological CO
2
storage as the effective option to mitigate atmospheric CO
2
emissions has been considered since the 1990's and has been implemented at a
large scale for the first time in Norway (Moritis 2002). Oil and gas reservoirs are
good candidates for sequestration because industrial experiences already exist for
CO
2
injection. Regarding economic aspects of the sequestration process, coupled
enhanced oil recovery (EOR) and sequestration processes have advantages since
the increased oil recovery will offset some of the costs of the CO
2
sequestration
process. The Weyburn CO
2
sequestration and EOR project is an example of a
commercial coupled CO
2
-EOR and sequestration process, which has shown great
success in terms of both objectives of the project (Malik and Islam 2000). In this
project, carbon dioxide is transported from the North Dakota coal-gasification
plant through pipelines and is injected into the Weyburn oil field.
A number of studies have been completed to investigate several aspects of
CO
2
injection for enhanced oil recovery and enhanced gas recovery (G. C. Wang
1984, Khan 1992, Lim, Pope and Sepehrnoori 1994, Guler, et al. 2001). As we
discussed earlier in the last chapter, there are fundamental differences between
the goals of EOR projects and those of the coupled EOR and sequestration
projects. To date, the injection processes have been designed to minimize the
amount of CO
2
injected per barrel of oil produced, thereby minimizing the
purchase cost of CO
2
. This objective has been set to reduce the high cost of
purchased CO
2
, while in coupled CO
2
-EOR and sequestration projects we aim at
52
maximizing both enhanced oil recovery and CO
2
storage at the end of the
flooding period (Kovscek 2002). Thus, new strategies are needed for achieving
both the objectives of maximizing the amounts of CO
2
in the reservoir and
recovering oil.
There are two main issues in coupled CO
2
-EOR and sequestration projects
(Ghomian, Urun, et al. 2008). First, the produced gas streams from
anthropogenic sources have some type of impurities, which should be removed
because most of them have negative impacts on the miscibility of CO
2
within the
reservoir oil. This can result in a significant cost for capture and separation.
Secondly, in some cases the CO
2
sources are located far from candidate oil
reservoirs. Therefore, CO
2
must be transported by pipelines to the injection site
and compressed to maintain the required CO
2
pressure for injection. This can also
increase the costs significantly.
Due to the high CO
2
prices, some sort of incentives in the form of accelerated
depreciation or direct tax credits should be defined by regulatory sectors in order
to support large-scale sequestration projects (Ghomian, Urun, et al. 2008).
Considering additional costs of capture, transportation, and monitoring, without
any tax credits, sequestration projects may not be profitable. Taxes can have a
large effect on the economics of these projects. An example of the effect of carbon
tax regulations on project economics is the Sleipner project. In this project,
rather than paying Norway's hefty carbon emissions tax of $50/t CO
2
(H. Herzog
53
2001), Statoil has been compressing and injecting one million tons of the captured
CO
2
annually into an aquifer below the ocean floor. With $80 million dollars of
incremental investment cost, Statoil has saved almost $50 million dollars in
annual carbon tax (Anderson and Newell 2004).
The goal of this chapter is to understand and optimize the coupled CO
2
sequestration and enhanced oil recovery by taking into account the economics of
the sequestration projects by considering their major costs and revenues. The
focus of this chapter is on developing an effective method that evaluates and co-
optimizes CO
2
storage and oil recovery for a given reservoir by maximizing the
net present value. This methodology is presented in the next section. The
reservoir model and fluids are summarized in the next section. Then, we focus on
developing CO
2
-injection scenarios leading to co-optimization and present the
optimization results of the various injection schemes. These results are obtained
using a compositional, reservoir flow simulator. At the end, some conclusions are
given.
3.2 Net present value of CO
2
EOR and sequestration
In EOR projects, the goal is to maximize profit by minimizing the total
amount of CO
2
injected per barrel of oil produced. This objective has been set to
reduce the high cost of purchased CO
2
, while in coupled CO
2
-EOR and
54
sequestration projects we aim at maximizing both enhanced oil recovery and CO
2
storage at the end of the flooding period.
Kovscek and Cakici (2004) have introduced an objective function combining
dimensionless oil recovery and reservoir utilization as Equation ( 1-2). The design
objective will be to maximize this function with respect to the specified set of
weights. Instead of defining the volume ratio of CO
2
stored in a reservoir,
Jahangiri and Zhang (2010) have introduced the storage factor by using the mass
of CO
2
stored in a reservoir over the total capacity of that reservoir, as this factor
is independent of knowing how much CO
2
is stored in the reservoir as a liquid or
gas, or dissolved in another fluid (Equation ( 2-1)).
Neither of these functions considers the costs of CO
2
. As previously
mentioned, there are several components corresponding to the major costs of
storing CO
2
, which can be categorized as capture, compression, transportation,
injection, and monitoring. In general, costs of the CO
2
sequestration are in the
range of $40 to $60 per ton of CO
2
stored (Ghomian, Urun, et al. 2008), which
depends on capture process applied, volume of CO
2
, distance from source to sink,
and some other site-specific characteristics.
If proper regulations are set with carbon credits, sequestration costs could be
fully or partially offset so that these types of projects would become more
attractive. Because the financial aspect is one of the major factors for coupled
CO
2
-EOR and sequestration projects, it makes sense to evaluate these projects in
55
terms of the Net Present Value (NPV). The NPV of each project is calculated
using the revenue owing to the oil recovery based on oil price and considering all
the cost items outlined above.
The NPV is computed as:
0
1
(1 )
T
t
t
C
NPV C
r
=
= −
+
∑
( 3-1)
where is the time step, is the cash inflow for the time step of , is the
annual or periodic discount rate, is the cumulative investment or production
period, and is the initial investment.
The cash inflow for time step period is given by,
2
($/)($/ )( $/ )
( $ / ) ( $ / )
CFOPT bbl FICIT Ton FIWIT wat
FWPT dwat FCO STR TAX Ton
=× − × − ×
−× + ×
(3-2)
where,
C = cash inflow over time step, $
$/bbl = Price of Oil per bbl, $
$/Ton = Cost of CO
2
injection per ton, $
$wat = Cost of water injection per bbl, $
$dwat = Cost of water disposal per bbl, $
$ TAX /Ton = Tax credit of CO
2
stored per ton, $
FOPT = Cumulative oil production over time step, stb
56
FWPT = Cumulative water production over time step, stb
FICIT = Cumulative CO
2
injection over time step, ton
FWIT = Cumulative water injection over time step, stb
FCO
2
STR = Cumulative CO
2
stored over time step, ton
A conservative annual discount rate of 10% is used arbitrarily in this study in
the estimation of the present value of money. Cash inflow is calculated from the
oil, CO
2
and water productions of the reservoir. The price of oil is considered as
$70 per barrel for the entire 50-year production period while the cost of water
disposal is $1.50 per barrel of produced water. The cost of water injection is $0.25
per barrel and the cost of CO
2
injection (including capturing, transporting and
recycling) is assumed to be $60 per ton of CO
2
. The production wells are
operated at a fixed bottom-hole pressure and the injector is set at constant rates
of gas and water injection.
In this chapter, again we use a Differential Evolution (DE) algorithm for
optimization of objective function during the reservoir life. More specifically,
NPV is selected as the objective function. The controlling variables are chosen to
be BHP at the producers. We implement the optimization algorithm such that
the performance of the reservoir for a particular set of settings can be determined
via forward simulations. DE is a method that optimizes a problem by iteratively
trying to improve a candidate solution with regard to a given measure of quality.
57
It is implemented as a computer simulation in which a population of abstract
representations of candidate solutions to an optimization problem evolves
towards its global optimum.
3.3 Reservoir description
In this study, we use a compositional simulation model, an ECLIPSE 300
simulator, to analyze the performance of a CO
2
-injection project. A synthetic
reservoir model of PUNQ-S3 is chosen that is based on an actual producing field.
The PUNQ-S3 test case is described in detail in the literature in previous
chapters. Due to well spacing, a new 5-spot pattern has been applied in PUNQ-
S3 with the same permeability and porosity distribution. There are four
producers and one injector. The locations of these wells are shown in Figure 3-1.
58
Figure 3-1. Top view of reference model and well location
These wells are completed to flow at the third, fourth and fifth layers of the
reservoir. The relative permeability data employed in this study are similar to
that which was shown in Figure 2-4. Similar to previous cases, for simplicity the
capillary pressures among oil, water, and gas phases are taken as 0.
3.4 Results and discussion
A variety of schemes are tested that are summarized as:
• Continuous CO
2
injection
• Water-alternating-gas drive (WAG)
• Gas injection after water flooding (GAW)
59
All of the scenarios above are simulated twice using different reservoir oil
compositions and conditions: Immiscible and Miscible cases. For these two cases,
the reservoir oil compositions are given in Table 2-1 (Kovscek and Cakici 2004)
and Table 3-2 (Rastegar and Jessen 2009), respectively. This is of particular
importance because the oil recovery is a critical function of the miscibility of oil
with CO
2
. In addition to the reservoir type and injection scheme (WAG or
continuous CO
2
), the time of CO
2
injection and the CO
2
incentive are considered
as other parameters, which affect economic performance of the CO
2
-flooding
projects. The first scheme listed above is used to maximize the CO
2
storage in a
reservoir. Since the gas injection is continuous, CO
2
injection time is maximized
and there is no other injection fluid occupying volume in the reservoir. The
second and third schemes resemble conventional oil recovery methods. Gas
injection after water flooding represents a project where water is used to
maintain pressure and drive oil from the reservoir. After a certain volume of
water injection, the project is converted to gas injection as a means of
sequestering CO
2
.
60
Table 3-1. Oil composition for miscible flooding
Component
Mole fraction
Molecular weight
(kg/mole)
T
c
(K) P
c
(bar)
N
2
- CH
4
0.362091 0.0160 190.580 45.998
CO
2
0.007749 0.0440 304.269 73.882
C
2
H
6
0.097348 0.0301 305.400 48.839
C
3
H
8
- C
4
H
10
0.117027 0.0500 392.087 40.169
C
5
H
12
-C
6
H
14
0.071831 0.0786 485.533 31.728
C
7
-C
16
0.234095 0.1395 623.023 27.044
C
17+
0.109858 0.3916 764.082 17.644
3.4.1 Immiscible case
In the case shown in Table 2-1, the initial reservoir pressure is 253 bars; the
oil is relatively heavy (24
0
API) and, consequently, the MMP for pure CO
2
(608
bars) exceeds the initial reservoir pressure significantly so that the CO
2
flooding
is immiscible. Moreover, the relatively small reservoir size, moderate
permeability, and fairly large angle of inclination to each side of the crest suggest
that water flooding should be relatively efficient (Kovscek and Cakici 2004).
Thus, the given reservoir and fluid combination is not ideal for CO
2
-EOR.
61
Figure 3-2. (a) Cumulative oil production, (b) Recovery factor storage, (c) Mass of
CO
2
stored, and (d) Mass of CO
2
storage factor for different injection schemes of
immiscible flooding
Figure 3-2 summarizes the performance of four production scenarios: primary
production, production with water flooding, WAG and pure CO
2
injection. For
these simulations, production wells operate at a fixed bottom-hole pressure of 175
bars. Injection rates of CO
2
and water are 800,000 and 1,000 m
3
/day,
respectively. The recovery from EOR with CO
2
is shown in two different ways:
cumulative oil recovery and oil recovery factor. The results show that the
recovery with the help of WAG is somewhat larger than the recovery with pure
CO
2
injection. The most important conclusion from this result is that EOR with
62
CO
2
must be carefully designed for this reservoir. Immiscible CO
2
injection may
not be the preferred method for this reservoir, based on oil recovery criteria
alone. In terms of CO
2
sequestration, pure CO
2
injection performs better than
WAG because the latter reduces the amount of stored CO
2
by injecting water.
Figure 3-3. (a) Objective function, and (b) Net Present Value for different
injection schemes of immiscible flooding
Figure 3-3 compares the objective function, which has been defined in
Equation ( 2-1) with equal weighting (
0.5 ), and the net present value
for different schemes. In this case, a tax credit of $40 per ton of CO
2
stored is
assumed. It can be seen how the net present value differs from the previously
defined function. Unlike NPV, the maximum value of objective function is
63
obtained for a pure CO
2
injection. The WAG process sequesters less than half of
the CO
2
, as does the pure CO
2
injection. Thus, the injection of water for mobility
control reduces the amount of CO
2
stored. On the other hand, in terms of NPV,
water flooding and WAG perform much better than the pure CO
2
injection. In
this case, when the recovery of oil is not large enough, the cost of CO
2
injection
will play an important role. Thus, without governmental or regulatory incentives,
the coupled CO
2
storage and EOR projects may become less attractive than their
EOR counterparts.
We next look at the effects of different carbon taxes on the economics of the
model. Such taxes may offset the costs of injection and recycling of CO
2
. Figure
3-4 shows how the project NPV changes as the CO
2
tax credit level is raised from
$0 to $120/ton. For reference, we also plot the NPV for the pure water-flooding
scenario. The results indicate that compared to pure water flooding, the coupled
CO
2
storage and EOR project becomes more profitable at early stages and may
lessen the advantage at a later time. This can be seen clearly at no or low tax
credit. For instance, without any tax credit the process has much lower profit
compared to water flooding. However, the net present value increases
significantly with the increase of the CO
2
tax credit up to $120 per ton.
64
Figure 3-4. Effect of tax credit on NPV for immiscible flooding
Because the reservoir pressure is below the minimum miscibility pressure, the
main difference between the pure CO
2
injection and water-flooding processes is
the greater mobility of CO
2
than water. An approach to reduce this effect is to
water flood the reservoir for a certain time and then to start gas injection after
water flooding. In short, this process will be referred to as GAW. Four different
scenarios are simulated for CO
2
injection up to 18,000 days. Gas injection starts
after 600, 1200, 2400 and 6000 days of water injected into the reservoir,
respectively. Figure 3-5 summarizes the performance of the different timing of
CO
2
injection in terms of oil recovery and CO
2
storage. The results indicate that
65
by delaying CO
2
injection and using water flooding, the total oil production is
slightly increased while the storage of CO
2
is decreased significantly. The results
indicate that the later the start of the CO
2
injection, the higher is the ratio of
recovered oil to OIP. However, this increase is relatively small. As expected, the
storage is greater for a longer period of CO
2
injection.
Figure 3-5. (a) Cumulative oil production, (b) Recovery factor, (c) Mass of CO
2
stored, and (d) Mass of CO
2
storage factor at different CO
2
injection timing for
immiscible flooding
Figure 3-6 compares the f function and NPV for different injection timing. In
terms of the objective function, because of a similar trend of recover factors for
all cases, it seems that all the cases have a similar behavior as the CO
2
storage
66
factor. On the other hand, in terms of NPV, the results indicate that delaying the
CO
2
injection results in increasing the NPV due to reducing CO
2
production and
hence the cost of CO
2
recycling. The peak point of profit is reached earlier
compared to those cases in which CO
2
injection starts later, especially in the last
case when the reservoir has 20 years of water flooding before the injection switch
to CO
2
. In this case, the greatest values are obtained when injection starts after
1200 or 2400 days.
Figure 3-6. (a) Objective function, and (b) Net Present Value for different
injection schemes of immiscible flooding
Finally, we optimize the CO
2
EOR-sequestration process by controlling the
BHP of producers. The optimization is done for the pure CO
2
-injection scenario.
67
For each reservoir, the optimized results are compared with results from the
corresponding reference case (Figure 3-7). Figure 3-8 compares the objective
function and NPV of CO
2
injection in the reference and optimized cases. The
trends for the objective function and NPV were similar for the optimized case.
The increases in both functions result from the increase in oil production
combined with the increase in CO
2
storage.
Figure 3-7. Comparison of (a) Cumulative oil production, (b) Recovery factor, (c)
Mass of CO
2
stored, and (d) Mass of CO
2
storage factor for the optimized and base
cases of immiscible flooding
68
Figure 3-8. (a) Objective function, and (b) Net Present Value for the optimized
and base cases of immiscible flooding
3.4.2 Miscible case
In the case shown in Table 3-1, the initial reservoir pressure is set at 175 bars
and the oil composition is assumed to allow miscibility to develop at pressure
below 175 bars. For the fluid compositions given in Table 3-1, the MMP for pure
CO
2
is estimated at 173 bars (Rastegar and Jessen 2009). Figure 3-9 shows the
performance of different scenarios of injection. In this case, the production wells
operate at a fixed bottom-hole pressure of 123 bars. Pressure higher than MMP
yields a better CO
2
storage and oil recovery potential. In the miscible case, the
69
amount of CO
2
stored is not greatly affected in the long run while the cumulative
oil recovery increases significantly compared to the immiscible case.
Figure 3-9. (a) Cumulative oil production, (b) Recovery factor storage, (c) Mass of
CO
2
stored, and (d) Mass of CO
2
storage factor for different injection schemes of
miscible flooding
Recovery is greatest when pure CO
2
is injected. After 18,000 days, the net
cumulative recovery approaches 65% of the oil in places. With the miscibility
condition, the local displacement efficiency approaches unity, and recovery is
maximized. Figure 3-9 c and d contrast the injection scenario with respect to CO
2
storage. In terms of CO
2
sequestration, WAG performs worse than the pure CO
2
70
injection. This is caused by the injection of water through the production period,
which results in reduced reservoir pore volume utilization for CO
2
storage.
Figure 3-10. (a) Objective function, and (b) Net Present Value for different
injection schemes of miscible flooding
The f function and NPV are compared in Figure 3-10. In this case, we assume
no tax credit for CO
2
stored. Both of these parameters show the similar trend.
The pure CO
2
-injection scheme performs better than WAG and water flooding.
The maximum values for f function and NPV are obtained for a pure CO
2
injection in which the miscibility increases oil recovery and gas injection enhances
carbon storage. Continuous CO
2
injection has the largest NPV due to accelerated
oil production in early periods after considering the annual discount of revenue.
71
Figure 3-11. Effect of tax credit on NPV for miscible flooding
For better understanding of the effect of CO
2
incentive, we have compared the
effect of tax credits on NPV. Based on Figure 3-11, it can be concluded that the
oil price dominates the economics of CO
2
EOR and storage in the miscible case.
There is no need to have a CO
2
tax credit for this project to profit. The more
obvious point to take away from this figure is that the CO
2
EOR and
sequestration projects are far less sensitive to the carbon tax compared to the
immiscible case.
Figure 3-12 gives the results for water flooding followed by CO
2
injection. The
results show that by delaying CO
2
injection and using water flooding, the CO
2
72
recovers oil more slowly. The ultimate recoveries and storage of CO
2
in all cases
are identical. However, the main difference between these four scenarios is found
during the intermediate times lying between 2,000 and 10,000 days.
Figure 3-12. (a) Cumulative oil production, (b) Recovery factor, (c) Mass of CO
2
stored, and (d) Mass of CO
2
storage factor at different CO
2
injection timing for
miscible flooding
According to Figure 3-13, a later start of the CO
2
injection results in a lower
value of f function and NPV. At the end of 50 years the f values are nearly the
same for all the cases. On the other hand, in terms of NPV, the oil revenue is the
dominant factor compared to CO
2
cost even without CO
2
incentives. The result
indicates that delaying the CO
2
injection is decreasing the NPV in miscible cases.
73
The greatest NPV is obtained when the injection starts sooner due to larger oil
production in the early periods of production.
Figure 3-13. (a) Objective function, and (b) Net Present Value for different
injection schemes of miscible flooding
Finally, an option of optimizing CO
2
injection is tested. Results for the
reference and optimized cases are presented in Figure 3-14 and 15. As we can see,
an improvement in recovery factor at initial reservoir life with respect to the
reference case is found, ranging from 2–5%. On the other hand, there is a huge
decrease (up to 50%) in the CO
2
-storage factor. The decrease in objective
function results from the significant decrease of CO
2
-storage term. However, in
terms of NPV, the larger value of oil production dominates the lack of CO
2
stored
74
during the reservoir life (Figure 3-15), and the NPV is mainly affected by the
improvement in oil recovered.
Figure 3-14. Comparison of (a) Cumulative oil production, (b) Recovery factor,
(c) Mass of CO
2
stored, and (d) Mass of CO
2
storage factor for the optimized and
base cases of miscible flooding
75
Figure 3-15. (a) Objective function, and (b) Net Present Value for the optimized
and base cases of miscible flooding
3.5 Conclusion
Injection of carbon dioxide in hydrocarbon reservoirs can substantially
improve the hydrocarbon recovery and reduce the amount of CO
2
in the
atmosphere. In this study, the objective is to co-optimize the CO
2
-EOR and
sequestration process. We aim at maximizing the NPV. It takes into
consideration the costs associated with CO
2
production and injection as well as
the revenues from oil production and carbon credits. Although previous studies
defined objective function to aim at maximizing extra oil recovery and
76
maximizing the CO
2
storage capacity of the reservoir simultaneously, these
functions did not take into account the costs of CO
2
injection factors such as
capture and transportation costs. In this study, we aimed to maximize the
profitability of the project by considering factors such as flood performance and
CO
2
incentives. In order to carry out this study, two comparative cases (miscible
and immiscible cases) were developed.
Incentives in the form of tax credits are needed to support carbon capture and
storage (CCS) projects under immiscible conditions. However, under miscible
conditions, coupled EOR and sequestration projects may be profitable even
without carbon incentives and they could become more profitable with such
incentives. Different injection schemes, including WAG, pure continuous CO
2
injection and GAW schemes are considered. In addition, the effects of well
controls on the NPV to optimize the coupled CO
2
-EOR and sequestration process
were studied. An exploratory analysis based upon systematic compositional
simulations of CO
2
EOR was performed to investigate when CO
2
injection should
begin and how much economic incentives might be needed to promote storage of
CO
2
in oil reservoirs. Of the various cases tested, the results showed that the
WAG-injection scheme created the highest NPV, especially in immiscible cases.
This may be attributed to the better mobility control provided by water slugs,
hence better macroscopic sweep efficiency. The optimization process showed
remarkable improvement in the NPV up to 10% and 25% as well as an
77
improvement of the cumulative production up to 2% and 5% for miscible and
immiscible cases, respectively, compared to the base case by adjusting the
bottom-hole pressure of producers.
Generally, the stochastic methods (such as DE used in this chapter) are
capable of finding the global optimum in a theoretical sense, but they require a
large number of forward model evaluations and are not able to guarantee
monotonic minimization or maximization of the objective function. Hence in the
next chapter we will introduce an efficient framework to maximize the NPV of
the CO
2
EOR and sequestration.
78
Chapter 4: Ensemble-Based Co-
optimization of CO
2
Sequestration and
Enhanced Oil Recovery
4.1 Introduction
The combustion of fossil fuels for energy production and other industrial
activities is the major source of anthropogenic CO
2
and will likely continue to
increase over the next century. High CO
2
concentration in the atmosphere can
lead to climate changes by increasing the natural greenhouse effects.
Several approaches have been proposed to control the increasing CO
2
concentrations in the atmosphere. One of the proposed solutions is to increase the
energy efficiency and decrease the carbon intensity of energy production; that is,
to emit less CO
2
per specified amount of produced energy (Bachu 2003). CO
2
emissions can also be reduced by increasing the share of renewable energies in the
energy consumption portfolio. Given the projected increase in the world
population and expanded use of energy in the developing economies, CO
2
emissions will continue to increase in the future and, without reliable techniques
for capturing and storing CO
2
, the sustainability of the environment would be
endangered. The most promising, immediate option to reduce significant amounts
79
of CO
2
emissions is the long-term sequestration of carbon dioxide by capturing,
separating and diverting it into geological underground formations. Depleted or
mature oil and gas reservoirs, deep saline formations, and unmineable coalbeds
are usually considered as the most suitable candidates for CO
2
sequestration
(Bachu 2003).
Oil and gas reservoirs are promising candidates for CO
2
sequestration due to
the availability of several field experiences on CO
2
injection, aimed to increase the
recovery of residual oil. Incremental profitability of such projects due to increased
oil production helps to offset the cost of CO
2
sequestration. As we discussed
earlier, one of the major factors controlling the efficiency of CO
2
-assisted
enhanced oil recovery is the miscibility of the CO
2
in the liquid phase. CO
2
flooding can either be miscible or immiscible depending on the reservoir
Minimum Miscible Pressure (MMP), the pressure below which CO
2
is immiscible
in the liquid phase. During immiscible flooding, CO
2
does not form a single-phase
solution with the hydrocarbons in the reservoir. On the other hand, in miscible
flooding, a single-phase solution is formed. The dissolved CO
2
reduces the
viscosity of the oil and causes the oil phase to swell, improving ability of the
hydrocarbons to flow through the reservoir rock.
Contrary to commercial CO
2
-EOR projects, in which the main purpose is to
maximize the oil recovery with the minimum amount of CO
2
injection because of
80
the high cost of purchased CO
2
, coupled CO
2
-EOR and storage projects are aimed
at simultaneous maximization of oil production and CO
2
storage.
Few studies have been reported on co-optimization of CO
2
sequestration and
EOR projects. Malik and Islam (2000) have reported that in the Weyburn field in
Canada, horizontal injection wells have proved to be efficient for CO
2
-flooding
processes to improve the oil recovery and increase the CO
2
storage. Kovscek and
Cakici (2004) and Jahangiri and Zhang (2010) have introduced an objective
function combining dimensionless oil recovery and reservoir storage utilization.
They have compared the performance of different field operation scenarios using
this objective function. Although the objective functions have been aimed to
maximize the incremental oil recovery and the CO
2
-storage capacity of the
reservoirs simultaneously, they did not take into account the costs of storing CO
2
categorized as capture, compression, transportation, injection, and monitoring.
The cost of CO
2
sequestration has been reported in the range of $40 to $60 per
ton of CO
2
stored (Ghomian, Urun, et al. 2008) and depends on the applied
capturing process, the amount of injected CO
2
, distance from the source to the
sink, and some other site-specific characteristics. Jahangiri and Zhang (2011)
have studied the maximization of the profitability of the project based on factors
such as flood performance and CO
2
incentives.
Owing to the fact that the financial aspect is one of the major factors for
coupled CO
2
-EOR and sequestration projects, these projects should be evaluated
81
in terms of the their NPV. The NPV of each project is calculated using the
revenues and the cost of the project. The goal of this chapter is to co-optimize
the coupled CO
2
sequestration and enhanced oil recovery by taking into account
the economics of the sequestration projects, their major costs and revenues. Early
CO
2
breakthrough due to its high mobility and reservoir heterogeneity, can
greatly affect the economics of the project. Employing different injection and
production schemes, and applying various well-control techniques and mobility-
control technologies (e.g., WAG used to delay early CO
2
breakthrough at
production wells) are different techniques to optimize the simultaneous enhanced
oil recovery and CO
2
storage.
Optimization algorithms that are available in the literature can be categorized
into gradient-based (Asheim 1988, Ramirez, Fathi and Cagnol 1984a, Fathi and
Ramirez 1984b) and stochastic algorithms. Gradient-based algorithms require
efficient techniques for calculating the gradient of the objective function with
respect to the control variables such as the injection rates or the bottom-hole
pressure of the producers. The number of the control variables can be very large
even for simple reservoir models with a small number of wells and control steps,
making the gradient–based optimization techniques very tedious. The other
major drawback of the gradient-based methods using adjoint equations is that
the explicit knowledge of the simulation model equations describing the
dynamical system is required. The process is further complicated by the
82
uncertainties in the description of the reservoir. Such uncertainties may be
reduced by incorporating the observed production data. Closed-loop optimization
methodologies have been introduced and applied in the past few years to
simultaneously reduce the degree of uncertainty of the reservoir models and
optimize the economics of the project (Brouwer, et al. 2004, Sarma, Aziz and
Durlofsky 2005a, Wang, Li and Reynolds 2007). Owing to the nonlinearity of the
multiphase flow problems, the gradient-based techniques should be used
iteratively and require extensive computational resources. On the other hand, the
stochastic algorithms such as genetic programming (Tavakkolian, Jalali and
Amadi 2004, Harding, Radcliffe and King 1998) require many forward model
evaluations but are better suited for finding the global optimum at the expense of
large numbers of simulation runs. Unlike the gradient-based algorithms, they do
not require explicit gradient estimations because the relationship between the
objective function and the control variables is obtained from several forward
simulations. These techniques become inefficient when the number of the
variables is large.
Benefiting from both methodologies, an ensemble-based technique can be used
to compute the gradient of the objective function through Monte Carlo
evaluation over an ensemble of the states corresponding to the uncertainties in
the description of the model. Ensemble techniques were introduced by Evensen
(2003) as Ensemble Kalman filter (EnKf) for sequential data assimilation in
83
large-scale nonlinear dynamical systems. EnKf has been used in reservoir
modeling history-matching problems since 2003 (Nævdal, Johnsen, et al. 2005,
Gu and Oliver 2007, Zhang, Lu and Chen 2007, Haugen, et al. 2008). Chen,
Oliver and Zhang (2008) proposed using ensemble-based closed-loop optimization
(EnOpt) in which an ensemble of realizations is used to approximate the system
for characterization and production optimization. EnOpt is non-intrusive and can
be used with any commercial reservoir simulation.
The purpose of this chapter is to engineer carbon dioxide-injection strategies
leading to co-optimization of the coupled EOR and sequestration projects and to
develop the corresponding work flow. In this chapter, an ensemble-based
optimization approach is applied for this purpose. The focus of this chapter is to
co-optimize the CO
2
storage and oil recovery in an oil reservoir with fixed well
placement based on net present value of the project. Our methodology is built
upon previous work by Chen, Oliver and Zhang (2008) that uses an ensemble of
realizations to maximize the NPV of a reservoir model by efficiently allocating
the injection rates between different wells. In this study, we use a single
realization of the reservoir model and an ensemble of control variables. The NPV
of the coupled CO
2
-EOR and sequestration project is used as the objective
function for the optimization technique. In the following sections, we first provide
a brief mathematical description of the EnOpt procedure. The reservoir model
and fluids are summarized in the next section. Then, we focus on developing CO
2
-
84
injection scenarios used for co-optimization. The results of the various optimized
scenarios are presented in the later parts of this chapter. The results are obtained
using a compositional, reservoir flow simulator. At the end, we summarize the
conclusions of our results.
4.2 Methodology
The NPV is used as the objective function for the optimization of coupled
CO
2
EOR and sequestration and is calculated using Equation ( 3-1).
Equation ( 3-1) can be easily modified to accommodate temporarily varying
fluid prices and costs. In this study the goal is to maximize the NPV of the
EOR/Sequestration process. It should be noted that the optimization algorithm
applied is not limited to using this form of objective function.
4.2.1 Ensemble-based optimization
In this section, we briefly describe the mathematical model and formulation of
the EnOpt algorithm used in our study. A more elaborate description may be
found in Chen et al. (2008). Optimization control variables are stored as an
ensemble: Let x be a vector describing the control variables including well
constraints at all control steps,
85
,
,
,….
( 4-1)
where is the total number of the control variables and is equal to the product
of the number of wells and the number of control steps. These controls could be
choke settings, flow rates, bottom-hole pressures, etc.
The set of optimized control settings can be obtained by minimizing S(x), as
in the following equation,
2
( 4-2)
where is the optimization objective function (NPV), is a weighting factor,
x is the new set of the control variables, is the prior set of the control
variables, and is the covariance matrix of the new set of controls. The solution
to this optimization problem using a Newton Raphson (Nwaozo 2006) approach
can be obtained using the following equation,
1
( 4-3)
where denotes the optimization iteration step, is a tuning parameter that
determines the step size and represents the matrix of the derivatives of the
objective function with respect to the control variables and is a measure of how x
affects . is determined by first generating number of realizations of
control variables, and corresponding NPVs. The matrix is then formed using
the following equation,
86
( 4-4)
The covariance matrix of Y is calculated using the following expressions,
, 1
,
, ( 4-5)
1
,
1
,
( 4-6)
where
, is an ensemble of perturbed values of the control variable x of size
and covariance . We use a correlated Gaussian random field with zero mean to
generate perturbations for
. At each iteration, is linearized at using
and . Hence,
the product of can be approximated by:
,
( 4-7)
Substituting Equation ( 4-7) into Equation ( 4-3), using as a smoothing
matrix, and applying the steepest ascent method leads to the following equation
for determining the control variables,
87
1
,
( 4-8)
Using the notation we just introduced, the EnOpt procedure can be represented
in a simplified form. The stopping criteria typically include a maximum number
of optimization steps or an unsuccessful search for the tuning parameter .
1. Generate initial control variables and initial ensemble of control
variables
, , j = 1, 2, . . . , .
• ,
is generated in two steps. First, the mean control is sampled from a
uniform distribution with suitable upper and lower bounds. Second, the
control mean is perturbed by adding some random number generated from
N(0, ). ∑ ,
2. If 1 , , is generated by adding random samples from N(0, ) to control
variables .
3. Run the simulator and compute
,.
4. Compute the cross covariance , using Equation ( 4-5).
5. Compute the updated control variables using Equation ( 4-8).
6. Evaluate the net present value
.
7. If
, update by and let 1 , otherwise
increase and go to step 5.
88
8. Check if the stopping criteria are satisfied. If not, go to step 2, otherwise set
and exit the optimization loop.
4.3 Reservoir description
In this study we performed synthetic detailed compositional simulations
utilizing an ECLIPSE 300 (GeoQuest 2008) simulator. A synthetic reservoir
description is chosen that is based on an actual producing field. The PUNQ-S3
test case was described in detail in earlier chapters.
There are four producer and four injector wells. The locations of these wells
are shown in Figure 2-3. All the wells are completed between the third and fifth
layers. The relative permeability data employed in this study are shown in Figure
2-4. For simplicity, capillary pressure effects are neglected.
A conservative annual discount rate of 10% is used in this study in the
estimation of the NPV. Cash inflow is calculated based on the oil revenue, the
cost of CO
2
, the cost of water production, and the carbon credit. The price of oil
is considered to be $70 per barrel for the entire production period while the cost
of water disposal is $1.50 per barrel of produced water. The cost of water
injection is $0.25 per barrel and the cost of CO
2
injection (including capturing,
transporting and recycling) is assumed to be $60 per ton of CO
2
. The carbon tax
credit of $40 per ton is assumed in the base case and is varied in the sensitivity
studies. However, in this approach the assumption of fixed costs and incomes can
89
be relaxed and easily accommodated if such variation in the future pricing can be
reasonably predicted.
4.4 Results and discussion
In this section, we evaluate EnOpt methodology for a synthetic reservoir. We
proceed with three different scenarios. We use an EnOpt framework with the
assumption that all the reservoir geologic parameters are known to focus solely
on optimizing injection profiles in order to increase the NPV. A variety of
scenarios tested are summarized as:
¾ Scenario (a): Pure CO
2
injection with the constraint of total CO
2
injection
for Immiscible and Miscible cases
¾ Scenario (b): CO
2
and water injection with the constraint of total liquid
injection for the Immiscible case
¾ Scenario (c): CO
2
and water injection with the constraint of total CO
2
injection for the Immiscible case
Changing the injection rates at each time step in turn changes the dynamic
state of the system (pressures and saturations). These changes subsequently
impact the cumulative oil and CO
2
production and hence the objective function
(NPV). The controls, x, are also subject to other constraints such as surface
production facilities, choke sizes, fracture limits, and minimum allowable bottom-
hole pressures, and these constraints determine feasible values of the controls.
90
These additional constraints complicate the solution of the optimization process
and require modifications to the original EnOpt algorithm.
The timeframe for the NPV optimization is 15,120 days, and the control
settings are modified every six months, so the number of control steps is 84.
Thus, the total number of control parameters is 336, which is the product of the
number of injectors and the number of control steps. Fifty realizations of control
variables are used in this study.
4.4.1 Scenario (a)
In the first case study, the CO
2
injection rate is constrained to be equal to
4000 m
3
/day in the liquid phase (at temperature of 20
and pressure of 60
bars). We use two different oil compositions and conditions for simulation:
Immiscible and Miscible cases. For the two cases, the reservoir oil compositions
can be found in Table 2-1 (Kovscek and Cakici 2004) and Table 3-1 (Rastegar
and Jessen 2009), respectively. The miscibility of the CO
2
in the liquid phase is
of great importance due to its effects on the oil recovery. To provide a
benchmark for the performance of the EnOpt, we use a reference case scenario
where the total CO
2
-injection rate is equally distributed among the injectors and
all the injectors are controlled by the CO
2
injection rate of 1000 m
3
/day of the
liquid phase, and all the producers are controlled by their bottom-hole pressures.
91
The objective of the optimization is to find the best allocated injection rates
among the four injectors in order to achieve a larger NPV.
4.4.1.1 Immiscible case
In the immiscible case study shown in Table 2-1, the initial reservoir pressure
is 253 bars, the oil gravity is 24
0
API, the MMP for pure CO
2
(608 bars) exceeds
the initial reservoir pressure significantly due to the low oil API gravity, making
the CO
2
flooding immiscible. In this case study, production wells operate at a
fixed bottom-hole pressure of 175 bars. Jahangiri and Zhang (2011) have shown
that the EOR/Sequestration projects are not profitable for immiscible cases
under current typical CO
2
-capture costs from power plants where no form of
incentives and/or credits are available for CO
2
storage. In order to show the
applicability of our proposed methodology in this case study, a tax credit of $40
per ton of CO
2
stored is assumed.
92
Figure 4-1. Comparison of (a) Cumulative oil production and (b) Mass of the
stored CO
2
for the optimized and base cases of immiscible flooding in scenario (a)
The cumulative oil production and stored CO
2
in the base case and the
optimized case are shown and compared in Figure 4-1. The cumulative oil
production and the CO
2
storage are higher in the optimized case than that in the
base case. The optimization results indicate that approximately 440,000 tons of
incremental CO
2
are stored in the optimized case compared to the base case. This
is a significant improvement compared to the results obtained for the base case.
Along with this storage, approximate oil production is 588,664 Sm
3
higher than
that of the base case. The increase in the cumulative oil production is due to
keeping the injection rates of the wells that are located in the high-permeability
93
zones at lower values and increasing the injection rates of the wells that are
located in the low-permeability zones. Furthermore, gas production is also
delayed and considerably reduced. As a result, total stored CO
2
is increased.
Figure 4-2. Comparison of Dimensionless Net Present Value for the optimized and
base cases of immiscible flooding in scenario (a)
In order to assess the capability and performance of a CO
2
-flooding project
(for enhanced oil recovery and sequestration), the NPV is changed to
dimensionless format by dividing by the base case NPV. Figure 4-2 compares the
dimensionless form of net present value for the reference and optimized cases. An
improvement in NPV of about 30% with respect to the base case is observed
after 10 iterations. The major contribution of the optimization algorithm in this
94
case is reducing CO
2
production while maintaining relatively high oil production
by more efficient allocation of the injection targets. Figure 4-3 shows the change
of the NPV with respect to the number of the iterations. The total number of
iterations is equal to ten in this case study. The procedure is terminated when
the rate of the increase of the NPV drops below 0.01%.
Figure 4-3. The change of the NPV with iteration
In EnOpt, the control variables (injection rates) are altered (updated) using
the gradient in the direction of increasing NPV. Figure 4-4 shows the CO
2
injection rates at different injectors for the optimized solution. The control
settings at the first iteration are similar to those used in the base case and are
95
changed gradually by the EnOpt. The total CO
2
injection rate is allocated
between the injection wells in order to maximize the NPV of the project. The
amount of the increase of the NPV and the optimized control settings depend on
the choice of the parameters used in the calculation of the NPV.
Table 4-1 shows the share of each injector from the total injected CO
2
during
the reservoir lifetime. Overall, all the injectors are mostly assigned with equal
total amounts of injected CO
2
; however, each injector daily CO
2
-injection rate is
changing over time. As shown in Figure 4-4, the injection profiles of all the
injectors are pulse-shaped.
Figure 4-4. The change of the controls for different injectors for immiscible
flooding in scenario (a)
96
Table 4-1. Share of each injector from the total CO
2
injection in scenario (a)
Injector 1 Injector 2 Injector 3 Injector 4
Immiscible case 27.35% 22.85% 25.93% 23.87%
Miscible case 30.40% 22.43% 28.96% 18.21%
An ideal way of optimizing the sweep efficiency of a CO
2
-EOR project
depends on its capability to control the CO
2
mobility. Such a method is only
achievable by shutting in the wells to establish mobility control, especially under
conditions where water injection is not possible. One major problem encountered
in continuous CO
2
injection is the formation of the viscous fingers that propagate
through the displaced fluid, leaving behind a large amount of residual
hydrocarbon. This phenomenon occurs because of the lower viscosity of CO
2
compared to oil, which results in an adverse mobility ratio. In reservoirs with
considerable vertical permeability, a significant amount of cross-flow of mobilized
oil occurs as a result of fluid-pressure gradients and the buoyancy effects. Because
of the disadvantages of the continuous CO
2
floods, the CO
2
-injection profile is
automatically chosen to be pulse-shaped by the EnOpt for all the injectors. To
obtain pulse-shaped injection profiles, the well is shut-in for some period of time
during which the pressure dissipation and fluid diffusion dominate the fluid-flow
processes behind the flood front and lead to more efficient displacement of the oil.
The optimum injection rates show that injection switches frequently from one
(group of) injector(s) to another, especially at the early stage. The switching
97
frequency may vary with the type of heterogeneity. In the real world, this
switching frequency might be limited to choke size and minimum allowable
bottom-hole pressures. It depends on how fast and how low we can change the
injection rate.
4.4.1.2 Miscible case
In the case shown in Table 3-1, the initial reservoir pressure is set at 175 bars
and the oil composition is chosen in such a way to allow the miscibility of CO
2
in
the oil phase at pressures below 175 bars. For the fluid compositions given in
Table 3-1, the MMP for pure CO
2
is estimated to be 173 bars (Rastegar and
Jessen 2009). The bottom-hole pressures of the producing wells are set at 123
bars. In miscible CO
2
-EOR cases, the projects are profitable even without any
CO
2
credits. The profitability of such projects is further improved with carbon
credits (Jahangiri and Zhang 2011). Similar to the immiscible case, a tax credit of
$40 per ton of CO
2
stored is assumed.
Figure 4-5 compares the cumulative oil production and the stored CO
2
in the
base and optimized scenarios. The miscible case shows a similar trend as the
immiscible case in terms of oil recovery and CO
2
storage. The cumulative oil
production and CO
2
storage are improved and the CO
2
storage is much larger in
the optimized scenario than that of the base scenario. Figure 4-6 compares the
dimensionless NPV for the base and optimized scenarios. Approximately, a 16%
improvement in the NPV is observed between the optimized and the base
98
scenarios. Both cases initially showed a similar trend of increasing profit. Then,
due to gas breakthrough and decreased oil plateau production and hence reduced
revenue, the CO
2
-injection cost plays an important role in the decline of NPV.
The peak NPV is reached almost at the same time for the two cases while the
decline is more rapid in the base case.
Figure 4-5. Comparison of (a) Cumulative oil production and (b) Mass of CO
2
stored for the optimized and base cases of miscible flooding in scenario (a).
99
Figure 4-6. Comparison of Dimensionless Net Present Value for the optimized and
base cases of miscible flooding in scenario (a).
Figure 4-7 shows the injection profiles of the injectors in the optimized
scenario. Implications and applications of the EnOpt optimization modeling
methodology on co-optimizing on multiple variables over time can easily be
found. The results indicate two important findings: Firstly, similar to the
immiscible scenario, all the injectors are showing pulse-shaped behavior that
leads to better sweep efficiency. Secondly, the largest share of the total injection
belongs to the first injectors located in the lower permeability zone (Table 4-1).
Similar to the immiscible case, the increase in the cumulative oil production is
due to reducing the injection rates of the wells that are located in the high-
100
permeability zones and increasing the injection rates of the wells that are located
in the low-permeability zones. Furthermore, the gas production is also delayed
and considerably reduced. As a result, the total stored CO
2
is increased. Clearly,
injectors 1 and 3 that are close to the lower permeability regions are allocated
with higher shares of CO
2
-injection rates.
Figure 4-7. The change of the controls for different injectors for miscible flooding
in scenario (a).
101
4.4.2 Scenario (b)
Problems with viscous fingering and poor volumetric sweep efficiency in pure
CO
2
flooding have often been improved by simultaneous water and CO
2
injection.
Such a technique provides better sweep efficiency and thus results in less viscous
fingering and gravity segregation. Water Alternating Gas (WAG) is a common
technique that has been used for a long time for mobility control of CO
2
because
the simultaneous flow of water with the gas lowers the total mobility of the
displacing fluid and thus improves the sweep efficiency. The flow rate and the
slug size of the injected phase are two important design variables used for
optimization of the oil recovery. It should be noted that the injecting water into
the reservoir decreases the total volume of the CO
2
that could be injected as a
continuous slug and reduces the CO
2
-injection rate. This case study addresses the
need to co-optimize the oil recovery and the CO
2
storage by employing the
optimum injection process specifications such as water or CO
2
rate and the
injection period for each of the phases.
An ensemble-based optimization approach was utilized to identify the
optimum injection configuration that maximizes the NPV of the coupled CO
2
-
EOR and sequestration project. A two-phase injection is used in this case where
the phase distribution can be described by level set functions, (Chang,
Zhang and Lu 2010). The control parameters are the injection phase (water or
CO
2
) and the rate of the injection of each fluid. All control variables are assumed
102
to be Gaussian random variables. The control variables contain flow rate (Q) and
level function ( ) for all the time steps. Thus, the total number of control
parameters is 2×336=672. The process configuration is represented by the control
vector x in the following equation,
,
( 4-9)
We define an indicator function that satisfies the following properties:
0
0
( 4-10)
The standard deviation of the level set of Gaussian variables is set at 0.5. The
standard deviation of these variables should not be too large because otherwise,
some of the generated random numbers may be far away from zero, and changing
the sign of the variables after updating is not an easy task for the EnOpt.
Furthermore, if the standard deviation were too small, the injection phase would
have quickly changed with small variations.
The reservoir oil composition and setting in this case study are similar to the
immiscible case of scenario (a). The relatively small reservoir size, moderate
permeability, and fairly large angle of inclination suggest that water flooding
should be relatively efficient (Kovscek and Cakici 2004). In this case, the
optimization is constrained to the constant total liquid injection rate (CO
2
or
water) of 4000 m
3
/day (at temperature of 20
o
C and pressure of 60 bars). The
optimization sought in this study involves finding the optimum configuration of
103
control variables for an injection scheme of 15,120 days that leads to the largest
NPV. Obviously, the highest oil recovery is achieved by maximizing the
macroscopic sweep efficiency through the optimum combination of the injection
rates and phases.
Figure 4-8. Comparison of (a) Cumulative oil production and (b) Mass of CO
2
stored for the optimized and base cases of immiscible flooding in scenario (b)
Figure 4-8 shows the results for the optimized total cumulative oil production
and CO
2
storage. The results are compared with the results of a base case in
which all injection rates are fixed at 1000 Sm
3
/day of pure CO
2
. The results
clearly demonstrate a higher cumulative oil production and a lower CO
2
storage
at the end of the optimization. Gas breakthrough is delayed significantly and the
104
oil production rates are increased for most of the production period. In terms of
CO
2
sequestration, the optimized case of the simultaneous water and CO
2
injection performs worse than the optimized case of the pure CO
2
injection. This
is caused by the injection of water through the production period, which results
in a reduced amount of injected CO
2
and smaller reservoir pore-volume
utilization for CO
2
storage.
Figure 4-9. Comparison of Dimensionless Net Present Value for the optimized and
base cases of immiscible flooding in scenario (b).
An improvement in the NPV of about 138% with respect to the base case is
obtained in this case study. This is a significant improvement compared to the
results from the optimized scenario (a). The increased profits due to larger oil
105
production surpass the decrease of the credits received because of stored CO
2
during the reservoir life. The NPV is mainly affected by the improvements in the
oil recovery (Figure 4-9).
Figure 4-10 depicts the injection rates vs. the control steps for the optimized
case. The optimized injection configuration indicates that the best results were
obtained by switching the injection phase and the repeated startup and shutdown
of the injectors. In all the injectors, the water is used to maintain the pressure
and drive the oil from the reservoir. After some water injection, EnOpt converts
the project into gas injection in order to increase the NPV by sequestrating the
CO
2
and improving the displacement efficiency. This control strategy results in
delaying the CO
2
breakthrough at the producers. As can be seen in Figure 4-10,
the EnOpt methodology results in pulse-shaped injection profiles and keeps the
oil production rates at relatively higher values. Clearly, injectors 1 and 3 show a
larger share of CO
2
and water injection rates, whereas injection wells 2 and 4
show a smaller allocated CO
2
rate. This suggests setting and lower
than the rest of the injection rates (Table 4-2). This can be explained by the
higher permeability regions around injection wells 2 and 4. In order to obtain a
higher NPV, the injection rates near the higher permeability regions need to be
reduced to allow for uniform sweep efficiency throughout the reservoir.
106
Figure 4-10. The change of the controls for different injectors for immiscible
flooding in scenario (b)
Table 4-2. Share of each injector from the total CO
2
and water in scenario (b) and
(c)
Scenario (b) Scenario (c)
Share of CO
2
Share of water Share of CO
2
Share of water
Injector 1 30.67% 30.03% 39.87% 17.57%
Injector 2 25.03% 22.19% 17.38% 31.18%
Injector 3 28.48% 25.76% 29.97% 25.08%
Injector 4 15.81% 21.03% 12.78% 26.17%
107
4.4.3 Scenario (c)
This case is similar to the second case study. The difference is in the
constraints that are imposed on the total CO
2
-injection rate. The total CO
2
-
injection rate is constant and equal to 4,000 Sm
3
/day (at a temperature of 20
o
C
and pressure of 60 bars). The maximum water injection rate for each of the
injectors is 1000 Sm
3
/day. This case may reflect the situation where the total of
CO
2
to be injected is mandated and the amount of water available is limited.
As discussed in the previous sections, viscous fingering and poor volumetric
sweep in continuous CO
2
flooding can be improved by the simultaneous injection
of water and CO
2
. The water slugs provide more favorable mobility ratios than
does a pure CO
2
injection.
Figure 4-11 compares the total cumulative oil production and CO
2
storage
obtained in the optimized case with those obtained in the base case. One can
observe that the cumulative oil production in scenario (c) is significantly higher
than that of the base case and the optimized case of scenario (a). The total
recovered oil is lower in this case study compared to the cumulative oil
production of the optimized case in scenario (b) due to the imposed constraints
on the total CO
2
injection. It can be seen that the total amount of stored CO
2
in
this case is somewhere between the other two cases.
108
Figure 4-11. Comparison of (a) Cumulative oil production and (b) Mass of CO
2
stored for the optimized and base cases of immiscible flooding in scenario (c).
The optimization results indicate that the NPV of the project doubles during
the optimization process (Figure 4-12). This is a significant improvement
compared to the results obtained in scenario (a). Although in this case study the
total amount of stored CO
2
is slightly lower than that of the base case, the
increase in NPV is due to the large increase in the oil production. If the cost of
the CO
2
separation and re-injection is much higher than the one used in this case
study, the optimized control settings should lead to reduction of the CO
2
production and increase in the NPV.
109
Figure 4-12. Comparison of Dimensionless Net Present Value for the optimized
and base cases of immiscible flooding in scenario (c).
Figure 4-13 shows the variation of the injection rates over time obtained by
the EnOpt procedure. Similar to the previous cases, the EnOpt method is able to
make drastic changes in the control. Note that the decreasing/increasing trends
in various injection wells are in general agreement with those of scenario (b) as
required to be reduced/increased for an even sweep of the reservoir and higher
NPV. These results indicate that the optimization method leads to increasing
CO
2
-injection rates for Injector 1 in the very early stages of the injection. The
NPV is maximized by switching the injection phase from water to CO
2
and vice
versa. Water as the displacing fluid improves the horizontal sweep efficiency by
110
controlling the mobility ratio, and CO
2
affects the vertical sweep efficiency, and
thus their simultaneous injections maximize the total sweep efficiency of the
reservoir. With the level set function, the EnOpt methodology is able to make
rapid changes to the control parameters as can be observed in Figure 4-13. As
mentioned earlier, injectors 1 and 3 are closest to the low-permeability zone. As
can be seen in Table 4-2, in order to delay the gas breakthrough, injectors 2 and
4 are injected with the largest amount of water in the optimized case scenario
while injectors 1 and 3 are allocated with the greatest share of the total injected
CO
2
.
Figure 4-13. The change of the controls for different injectors for immiscible
flooding in scenario (c).
111
4.4.4 Effect of oil price and tax credit
In addition to technical factors, different economic parameters such as oil
prices and CO
2
-injection costs have a great impact on the project economics.
Neither CO
2
price nor oil price will remain static over 40 years. Combinations of
economic factors are studied to achieve understanding of the financial
performance of the coupled CO
2
-sequestration and EOR projects. In this section,
we compare the effects of oil price and tax credit by examining three different
scenarios in the immiscible case of scenario (a). Figure 4-14 compares the
dimensionless NPV for the base and optimized cases of the three different
scenarios (oil prices of $70 and $140 per barrel, tax credit of $40 and $100 per ton
of CO
2
stored). We plot only the dimensionless NPV as the oil price and tax
credit do not significantly affect the total cumulative oil production and CO
2
storage obtained in the optimized case. However, the trend of NPV changes
significantly with the economic parameters.
112
Figure 4-14. Comparison of Dimensionless Net Present Value for the optimized
and base cases for three different oil prices and CO
2
tax credit (oil price, $/bbl - CO
2
tax credit, $/ton).
The base and optimized cases for different economic conditions show a similar
trend of NPV. The increasing oil price enhances the revenue of oil production and
makes the project more profitable. The peak point of NPV is reached at a later
time and the plateau of NPV is extended. However, the improvement of
dimensionless NPV compared to its base case is reduced. On the other hand, with
the same oil price, raising the CO
2
tax credit level from $40 to $100/ton changes
the trend of NPV. Since the revenue of oil production reaches its plateau due to
gas breakthrough, the cost of CO
2
injection has a more important role. A larger
113
amount of tax credit can compensate the project cost much better. Hence, the
decline of NPV is slowed down.
Figure 4-15 shows the variation of the injection rates over time obtained by
the EnOpt procedure for different economic parameters. Table 4-3 shows the
share of each injector from the total injected CO
2
during the reservoir lifetime. As
shown in Figure 4-15, the injection profiles of all the injectors are pulse-shaped.
Figure 4-15. The change of the controls for different injectors for three different
oil prices and CO
2
tax credit (oil price, $/bbl - CO
2
tax credit, $/ton).
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Table 4-3. Share of each injector from the total CO
2
injection for different
economic parameters
Injector 1 Injector 2 Injector 3 Injector 4
Oil price = $70/bbl
CO
2
tax credit=$40/ton
27.35% 22.85% 25.93% 23.87%
Oil price = $140/bbl
CO
2
tax credit=$40/ton
28.38% 23.31% 26.48% 21.83%
Oil price = $70/bbl
CO
2
tax credit=$100/ton
29.32% 22.55% 25.42% 22.71%
The NPV is greatly affected by the recovery factor when the oil prices are
high. Hence, the improvement of the sweep efficiency is due to reducing the
injection rates of the wells that are located in the high-permeability zones (such
as injector 2) and increasing the injection rates of the wells that are located in
the low-permeability zones (such as injector 1). Given a larger value for the CO
2
tax credit with the same oil price, after certain times the revenue of oil
production has reached its plateau, the objective function being dominated by
CO
2
storage. In order to increase the total amount of CO
2
stored, the gas
production is delayed and considerably reduced. Clearly, injectors 1 and 3 that
are close to the lower permeability regions are allocated with higher shares of
CO
2
-injection rates.
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4.5 Conclusion
Injection of carbon dioxide in hydrocarbon reservoirs can substantially
improve the hydrocarbon recovery and reduce the amount of CO
2
in the
atmosphere. Carbon dioxide has been already injected into a number of reservoirs
for enhanced oil recovery; however, an optimized engineering design is required
for simultaneous oil recovery and CO
2
storage. In this study, the objective is to
co-optimize the CO
2
-EOR and sequestration process by maximizing the Net
Present Value (NPV). We did so by controlling the injection patterns.
A new co-optimization framework, EnOpt, developed on the basis of the
Ensemble Kalman Filter for continuous model updating, was applied to coupled
CO
2
-EOR and sequestration projects. The advantage of the EnOpt methodology
over the adjoint-based methods is that it does not require explicit knowledge of
the simulator-flow equations and thus is computationally less demanding. A
commercial simulator can be easily incorporated into this optimization technique
without tampering with its source code.
Our proposed methodology has been applied to a simple 3-D heterogeneous
reservoir with known geology. We have validated the EnOpt procedure using
three different case studies, each with known geology but with a different set of
optimization constraints. The optimization process has shown remarkable
improvements in the NPV and the cumulative oil production. Our results
indicate that for better efficiency, pulse-shaped injection profiles should be used
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in a CO
2
-only flood. Pulse-shaped gas injection profiles are found to provide a
method for mobility control in the CO
2
-EOR and sequestration processes when
water injection is not feasible. Optimization of alternating CO
2
and water
injection for sequestration and EOR processes is important and has been shown
to predict significant improvements in NPV and oil production compared to the
initial configuration. We have done some sensitivity analyses of economic
parameters such as oil price and CO
2
tax credit. The results indicate that
different economic conditions affect the NPV of the project and optimized
injection profile.
The present study was conducted using a relatively small and simple reservoir
model but it is clear that optimization of a CO
2
-EOR and sequestration process
can lead to significant improvement in the quantity of NPV of projects. It may
be postulated that it is even more important to carefully design and optimize the
process in complex reservoir systems.
In this chapter, the co-optimization framework was demonstrated in cases
with known geology, and although often assumed, it is clearly not true for real-
world applications. The next chapter extends the methodology to cases with
uncertain reservoir geology properties.
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Chapter 5: Closed Loop Ensemble-
Based Co-optimization of CO
2
Sequestration and Enhanced Oil
Recovery
5.1 Introduction
Ensemble-based co-optimization offers the potential to substantially increase
net present value by developing an improved operating plan for a particular
reservoir of interest for CO
2
-EOR Sequestration. But it relies on a reservoir
model to simulate the future performance of the actual reservoir. Due to the
limited access to a reservoir, the reservoir geological model is always subject to
high uncertainty. In order to obtain a suitable injection strategy, co-optimization
needs to be combined with a parameter-estimation method that reduces the
uncertainty of the geology of the reservoir with available observations.
Closed-loop optimization (Brouwer, et al. 2004, Sarma, Durlofsky and Aziz
2005b, Wang, Li and Reynolds 2007) combines production optimization with
data assimilation to form real-time reservoir management. Typically the work
flow of a closed-loop co-optimization is as follows: An initial geological model is
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built using the prior knowledge of the reservoir, and an initial production
strategy is chosen based on the prior knowledge. Subsequently, at each data
assimilation step, the reservoir model is updated using available observation and
production data, and the updated geological model provides a basis for a better
prediction of the true reservoir behavior. The injection strategy is then co-
optimized based on the newly updated reservoir model, and the optimized
controls are used to operate the real field and to run the simulation. The process
can be repeated whenever there are new observed data available and the reservoir
management is kept up-to-date.
In this chapter, we first provide a brief literature review and background on
ensemble Kalman filter (EnKf) methodology with a focus on reservoir-
characterization studies. We then focus on closed-loop EnOpt. We provide the
mathematical terminology and a basic description of EnKf and EnOpt procedures
in the context of closed–loop co-optimization of coupled CO
2
-EOR and
sequestration processes.
5.1.1 Ensemble Kalman Filter
History matching in reservoir simulation concerns adjusting geological
parameters such as permeabilities and porosities in such a way that the difference
between the calculated and actual measurements is minimized. History matching
is now automated to a large extent and can be performed during a multi-phase
119
flow simulation by applying closed-loop optimization. This automated process is
our main focus in this chapter and throughout this thesis in general.
The Kalman filter is a mathematical method that produces estimates of the
true values of measurements and their associated calculated values by predicting
a value, estimating the uncertainty of the predicted value, and computing
a weighted average of the predicted value and the measured value (Gelb 2002).
The ensemble Kalman filter (EnKf) uses the Monte Carlo method in which an
ensemble of reservoir state models is generated initially and evolves in time. At
each estimation step, the parameters in each ensemble member are updated by
comparison with the observation data in such a way that the statistical
properties of the ensemble match the uncertainty at that step and the conditions
of the observables. In the application of this method all the variables of interest
are sampled in a state vector. The probability distribution of the state vector is
represented empirically by an ensemble of realizations. This ensemble
approximation reduces the dimension of the inverse problem from the number of
variables in the state vector to the number of realizations, and in the basic
formulation the solution is sought in the space spanned by these realizations. In a
petroleum engineering field, the state vector usually consists of both model
parameters and dynamic variables.
There are two major steps in EnKf. In the first step, the dynamic variables
are propagated forward (forecast step) based on the model dynamics to the time
120
when observations are to be assimilated. In the second step, the ensemble of the
state vector is updated to honor the observations using sensitivity information
obtained from the ensemble. This is called the analysis step. Because EnKf avoids
the linearization of the nonlinear model dynamics and uses a reduced order
approximation of the covariance matrix, it is more suitable for large-scale
nonlinear problems than the extended Kalman filter.
EnKf was first introduced by Evensen (1994) to a fluid dynamical problem
with a high degree of nonlinearity and a large number of parameters. In the work
by Nævdal, Mannseth and Vefring (2002), EnKf was indeed used for updating
the static parameters near well reservoir models with promising results. This was
followed in Nævdal, Johnsen, et al. (2005) where a constructive model for
permeability was presented and the EnKf procedure was shown to successfully
reduce reservoir uncertainties resulting in a successful history matching. Gu and
Oliver (2005) used EnKf for parameter estimation with a fairly small ensemble
size and observed issues related to overshooting the problem of permeability and
porosity. Gao, Zafari and Reynolds (2006) pointed out similarities between the
EnKf and randomized maximum likelihood in reservoir parameter estimation
problems. Liu and Oliver (2005) used EnKf for facies estimation in reservoir
models. In particular, the reservoir used in their work included large
nonlinearities in the permeability and porosity distributions based on a multi-
modal probability density function (PDF) for the petrophysics parameters. They
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represented the facies distribution as a two-normal Gaussian field adapted to be
solved using EnKf. They showed that EnKf can fail when used with multi-modal
distributions and there might be no systematic way to apply EnKf for such
problems. Wen and Chen (2005) used EnKf for permeability estimation in a 2D
reservoir problem where the effect of the ensemble size on the parameter
estimation problem was analyzed. Zafari and Reynolds (2007) investigated the
validity of the linear updating algorithm of EnKf with simple but highly
nonlinear models and also reported that EnKf cannot be used with the resulting
multi-modal distributions where simple average and variance do not effectively
characterize the distribution. Their results nonetheless showed a clear
improvement as the nonlinearity of the model was reduced. Other applications of
EnKf for parameter estimation can be found in Refs. (Lorentzen, Nævdal and
Lage. 2003, Kivman 2003, Annan and Hargreaves 2004, Annan, Hargreaves and
Edwards, et al. 2005, Moradkhani, et al. 2005).
EnKf has recently gained great popularity due to its simplicity in
implementation and the flexibility in handling errors in initialization and
evolution of the model state. Furthermore, the “Monte Carlo” nature of EnKf
makes it directly suitable for running on parallelized computing resources.
Utilizing EnKf in high-dimensional problems is not straightforward as EnKf
requires an ensemble of model states that approximates a posterior PDF, and
obtaining an accurate PDF in high-dimensional problems may produce undesired
122
redundancy and extreme uncertainties. By nature, EnKf locates the “mean”
solution as opposed to the “mode” and is limited in a search space spanned by the
initial ensemble. Even more problematic are emerging non-Gaussian distributions
in the course of the dynamics. More explicitly, the forecasting step in the EnKf
propagates the probability distribution fully whereas the updated part solely
deals with the mean and variance of the model state. The Gaussian assumption
makes the updated part relatively easy to perform numerically but can carry
large statistical mismatches when the model variables are non-Gaussian. An
important example of a non-Gaussian behavior is the variation in water
saturation at the fluid front. Several methods have been introduced to deal with
the non-Gaussianity problem. For example, a re-parametrization of saturation
values near the front was used by Chen, Oliver and Zhang (2009), where the
emergent time of the front at a specific saturation value is designated as a new
variable and is updated along with the rest of the model variables. The
saturation values near the front are then continuously dropped from the model
state to ensure that the parameters in the model state remain approximately
Gaussian. It was shown that using the time of front arrival instead of saturations
near the front area improves EnKf considerably. Focusing on the front
saturations, Gu and Oliver (2007) proposed a new method of reducing the non-
Gaussian distribution of the saturation values at the front area by utilizing the
normal score transformation of the saturation values at the margins. Even after
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the back-transformation, the saturation values showed large variations. This
required using the location of the front instead of the front saturations in the
update step. This approach works well with EnKf in one dimension but is yet to
be fully implemented for two- and three-dimensional problems where the location
of the front is difficult to define.
Ghods and Zhang (2010) proposed using a combination of methodologies for
fracture characterization and simulation in tight gas reservoirs. In this study,
EnKf was used for the estimation purposes. They tested on several synthetic 2D
reservoir models containing a number of fractures, some intersecting the wells.
5.1.2 Production optimization algorithm
In the literature, various methods of history matching and production
optimization have been combined to form the closed-loop optimization
framework. Brouwer, et al. (2004) used an adjoint method for production
optimization and EnKf for model updating. Sarma and Durlofsky, et al. (2005c)
used an adjoint method for both model updating and production optimization.
Karhunen-Loeve decomposition was used to represent the permeability field to
reduce the number of unknown parameters and to preserve two-point
geostatistics. Wang, Li and Reynolds (2007) combined EnKf with three
optimization methods using a small reservoir model. They concluded, based on
their computational experiments, that the steepest ascent method with gradients
124
provided by numerical perturbation gave better results than those with gradients
provided by either an ensemble or simultaneous perturbation stochastic
approximation.
The uncertainty of the reservoir, however, cannot be completely removed even
with the assimilation of the observations. Uncertainty has gained more and more
attention in field-development processes. Production prediction is usually given
with an uncertainty band. Multiple reservoir models are used to represent
different possible realizations of the actual reservoir. Since production
optimization depends on the prediction from the reservoir model, it is important
that the uncertainty of this prediction is appropriately considered. In the closed-
loop optimization work of Brouwer et al. (2004), Sarma, Aziz and Durlofsky
(2005a), Wang, Li and Reynolds (2007), the optimization is only done based on a
single field, either the mean or the central model, and the uncertainty of the
estimation is ignored. Yeten et al. (2004) studied the effects of the uncertainty in
reservoir description and equipment reliability and concluded that the level of
improvement attainable using inflow-control devices varies with both the valve
reliability and the geological realization. There are several studies that have
attempted to consider the uncertainty of the reservoir model in the production
optimization. By taking into account the uncertainty of the estimated geological
model, the optimization becomes more robust with respect to the uncertain
reservoir description. Sarma, Durlofsky and Aziz (2005b) used the adjoint method
125
to maximize the expectation of the net present value with respect to the controls,
and the uncertainty of the reservoir description is propagated using the
probability collocation method. Van Essen et al. (2006) also considered using the
expectation of the net present value as the objective function with the
uncertainty of the geological model represented by an ensemble of reservoir
models. The adjoint system of equations is solved for every geological model to
compute the gradient of the net present value with respect to the control
parameters. The average of the resulting gradients is considered as the gradient
of the expected net present value with respect to the controls. Both of the
methods require the solution of the adjoint equations.
The EnOpt can be coupled with the ensemble-based data-assimilation
methods, for example EnKf, to form a closed-loop EnOpt (Chen, Oliver and
Zhang 2008). They proposed the concept of a closed-loop EnOpt in which an
ensemble of model systems is used for both characterization and production
optimization and can be used with essentially any reservoir simulation/modeling
mechanism. They concluded that EnOpt has two distinct features. First, the
search direction used in the optimization scenario can be obtained using an
ensemble. Secondly, EnOpt focuses on maximizing the expectation of the NPV
instead of maximizing the NPV over a single reservoir model. This leads to the
robustness of EnOpt with respect to uncertainties of the reservoir geologic model.
Jafroodi and Zhang (2011) have proposed a methodology for modeling, updating,
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and optimizing large water-flooding operations that base the ensemble closed-loop
production optimization upon the capacitance resistive model (CRM) as the
underlying dynamical system. They used observation data from the production
wells to characterize and forecast the reservoir response and further use them to
control the injection wells to maximize the reservoir production. Basing the
EnOpt method on CRM (an approximate model) the reservoir simulations allow
a much quicker computational response and ultimately can be helpful in cases
where geological data is scarce and/or the operation involves a large number of
wells.
For robust optimization with the consideration of the uncertain reservoir
description, we also use the expectation of the net present value as the objective
function in which case the sensitivity of the expected net present value to the
control variables is obtained from a coupled ensemble of controls and ensemble of
geological models. Since the sensitivity calculation does not require the adjoint
code, the closed-loop co-optimization is fairly flexible in terms of the choice of the
control variables and the choice of the objective function. In addition, existing
reservoir simulators with complicated well models can be readily used. It is
possible to include any function in the objective function; the change of the form
of the objective function will not change the existing algorithm. In this
dissertation, however, only the expectation of the net present value of coupled
CO
2
-EOR and sequestration projects is used as the objective function. In this
127
chapter, the mathematical terminology and a basic description of EnKf and
EnOpt procedures in the context of reservoir characterization is shown first.
Then the procedure of the closed-loop co-optimization is outlined. Finally, 3
different scenarios that have been used to test closed-loop optimization methods
are used as illustrative examples. The results of the closed-loop co-optimization
are compared with those obtained from other possible reservoir operation
scenarios, such as wells with no controls and optimization with known geology.
5.2 Mathematical model and methodology
5.2.1 Ensemble Kalman filter
The Ensemble Kalman filter (EnKf) is usually used as a joint parameter
(static parameters) and state (dynamic variables) estimation method in
petroleum engineering applications. The EnKf is essentially a Monte Carlo
generalization of the Kalman Filter. An ensemble of realizations is used to
describe the probability distribution of the model state. The model state contains
both the static and dynamic variables as well as the observation values. In EnKf,
the model state is updated based on a weighted covariance function between the
measurements and the evaluated values of the observables from the model
variables at each time of measurement. Algorithmically, EnKf consists of two
parts: a forecast step and an analysis step. In the forecast step, the model
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variables for all ensemble members are propagated forward in time based on the
model dynamics through simulation. The analysis step modifies the state
variables in all ensemble members based on comparison with the observation
values obtained at each assimilation time with a weight given by the Kalman
gain matrix, .
The state vector in general contains variables that are not known precisely
and need to be estimated. We also typically include a set of observables in the
state vector for convenience. The state vector y at each time consists of model
variables m (reservoir properties such as porosity, permeability and dynamic
variables such as saturations, pressures, etc. at the grid coordinates) and
observation variables d (e.g., well production rates, well bottom-hole pressures,
gas-oil ratios, etc.). The variables of interest are collected into a state vector y
that can be written as:
( 5-1)
A typical state vector of CO
2
injection problems is composed of porosity (Φ),
permeability (k), pressure (P) and gas saturation (S
g
) at each grid block and all
the predicted production data (d), which usually includes bottom-hole pressure
(BHP), gas production rate (GPR) and oil production rate (OPR),
,,,
,, ( 5-2)
The components of the state vector y are column vectors containing either the
model parameters or dynamic variables at all the grid blocks or predicted
129
production data at all the wells. For the EnKf application, realizations of the
state vector are stored in a matrix Y to form an ensemble:
,
,
,…
( 5-3)
where is the total number of the ensemble members. At the analysis step,
every ensemble member is updated using
, ( 5-4)
where j indexes the individual ensemble member and , are perturbed
observations for each ensemble member. The ensemble ,
,
,…,
indicates the updated ensemble while ,
,
,…,
indicates the
forecasted ensemble member states from the reservoir simulator. Matrix is the
covariance of the measurement noise and is the covariance matrix of the state
vector defined by
1
1
( 5-5)
where denotes the mean of the state vector after the forecast step and before
the analysis step. H is a matrix operator that projects the observed variables (d
in Equation ( 5-1)) from the state vector. In many cases measurements are not
linearly related to the components of the state vector, yet by including the
observables along with the variables in the state vector we can still conveniently
relate the observables to the state vector by the matrix H. Since observation
130
values are part of the state vector, the matrix H will only consist of 0’s and 1’s.
More specifically:
0| ( 5-6)
where 0 denotes an
matrix with all zero entries and I is the
identity matrix.
The product is the cross-covariance between all the state variables and
the predicted observations, and
is the auto-covariance of the predicted
observations.
5.2.2 Ensemble optimization with uncertain
reservoir description
In Chapter 4, EnOpt was applied to a single reservoir model, for example, the
best estimate of the reservoir. In this section, we show that EnOpt can be used to
co-optimize the expectation of the net present value with the uncertain reservoir
description represented by an ensemble. When used in the ensemble-based closed-
loop optimization, EnOpt is applied to the geological model ensemble updated by
EnKf to seek the control setting that is the best on average. As opposed to the
objective function used in the Chapter 4 Equation ( 4-1), the expectation of the
net present value over the uncertain reservoir properties is chosen to be the
objective function. Since this uncertainty is represented by an ensemble of
reservoir models, the objective function becomes:
131
1
,
( 5-7)
where are the control variables, are reservoir model realizations, is the
total number of these reservoir model realizations and .,. computes the net
present value as defined in Equation ( 3-1). The subscript in indicates
that the expectation is taken with respect to the PDF of the geological model.
Because the ensemble is not modified during the production optimization,
is considered as a function of control variables only.
As in Chapter 4, the steepest ascent method is used
1
( 5-8)
in Equation ( 5-8) are the gradient and the sensitivity of the objective function
with respect to the control variables , respectively. Other symbols are the
same as those in Equation ( 4-3). Considering the Monte Carlo approximation in
Equation ( 5-7), the gradient of to the control variables can be written as:
132
1
,
1
( 5-9)
where is the gradient of the net present value, ,, to the control
variables with the underlying geological model fixed as . The sensitivity of
the expected net present value, , is simply approximated by the average of the
individual sensitivities .
As shown in Chapter 4, the product of the sensitivity to control variables
with a covariance of control variables can be estimated from an ensemble of
controls:
,,
( 5-10)
The sub-index in and ,, indicates that they are the sensitivity
and cross-covariance based on , respectively.
Using Equation ( 5-9) and Equation ( 5-10), the product in Equation
( 5-8) can be approximated as:
133
1
1
1
,,
( 5-11)
We now substitute the Monte Carlo approximation of ,, into
Equation ( 5-11):
1
,
, ( 5-12)
with
1
, 1
,
( 5-13)
In this formulation, the computation of the cross-covariance needed for
optimization can be thought of as resulting from an ensemble that is similar to
the one in Equation ( 4-4). With the iteration index included, the ensemble Z is
as follows:
134
,
,
,….
, ,,
, ,
, ,
, ,
,
, ,
( 5-14)
where , are realizations of the control variables. These realizations are
generated in the same way as in Chapter 4 and are realizations of the
geological model that represent the uncertain geological properties of the
reservoir. As shown in Equation ( 5-14), each control realization, , , is combined
with each of the reservoir models, . Basically, each realization of the control
variables , is applied to one geological model
, and the net present value,
, ,
, is computed based on the simula tion results. The construction of
the state vectors thus involves simulation runs. We denote the
approximation of using Equation ( 5-12) by ,, .
As in Chapter 4, is used as a filtering (smoothing) matrix, and the final
iterative formula becomes:
,,
( 5-15)
,
∑
,
, ,
,
( 5-16)
Since the cross-covariance in Equation ( 5-16) is approximated using the
Monte Carlo method, it is expected that the approximation gets better as the
joint PDF gets narrower. In the closed-loop co-optimization, the uncertainty of
the geological model is generally largely reduced with the assimilation of the
135
data. In addition, increasing the sampling points could further improve the
approximation of the cross-covariance.
5.3 Implementation of ensemble-based closed-loop
co-optimization
The procedure for ensemble-based closed-loop co-optimization is summarized
in this subsection. is the index for data times; indicates the ensemble of
geological models updated at the
data time; is the vector of control
variables that is used to produce the real reservoir; is the iteration index of the
EnOpt; are the control variables at the
iteration; , are realizations of
control variables used to approximate ; is the number of control
realizations and the number of geological model realizations and is the
covariance matrix of the control variables . The stopping criteria typically
include a maximum number of optimization steps or an unsuccessful search for
the tuning parameter .
1. Initialize ensemble and control variables and set 0 .
2. Integrate ensemble with well constraints from to using a reservoir
simulator.
3. Use EnKf (Equation ( 5-4)) to update and set 1 .
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4. Start optimization at l = 1, and initialize the control variables and
ensemble of control variables
, 1,2,...,
.
• If this is the first time step, ( 1 )
,
is generated in two steps. First,
mean control is sampled from a uniform distribution with suitable upper
and lower bounds. Secondly, the control mean is perturbed by adding
some random number generated from N(0, ). ∑ ,
• If this is not the first time step ( 1 ), then and samples from
N(0, ) are added to the control variables for form , .
5. If 1 , , is generated by adding random samples from N(0, ) to control
variables .
6. Run the simulator from current time to the end of the field life and
compute
, ,
using Equation ( 3-1).
7. Compute the cross-covariance , using Equation ( 5-16).
8. Compute the updated control variables using Equation ( 5-15).
9. Evaluate the net present value
using Equation ( 5-7) which only
needs simulation runs.
10. If
, update by and let 1 ; otherwise
increase and go to step 8.
137
11. Check if the stopping criteria are satisfied. If not, go to step 2; otherwise set
and exit the optimization loop.
12. Repeat from step 2 up to the end of the data-assimilation time. Otherwise
repeat from step 5.
The stopping criteria used in our work are (i) the relative increase of the net
present value had been less than 0.01%, (ii) the change in the control variables at
two previous times had been less than 1%, and (iii) we were not forced to
increase the tuning parameter more than twice.
In the case where EnOpt is formed based on a single reservoir model, the
procedure is much simplified (situation considered in Chapter 4). The EnKf loop
can be eliminated since the geological model is deterministic. The s appearing
in the EnOpt loop are equal to the known reservoir model
. Computing
sensitivity, step (6) and step (7), still requires simulation runs to obtain
, ,
, but the evaluation of the objective function, step (9), only
requires a single simulation run to compute
,
.
5.4 Reservoir description
In this section we consider a reservoir that was described in detail earlier in
Chapters 3 and 4. We assume that permeability is the only uncertain geological
property to be estimated by incorporating the production data. The permeability
field, used to generate the synthetic production data is shown in Figure 2-1.
138
There are four producer and four injector wells. The locations of these wells are
shown in Figure 2-3. The compositional suite from a commercial reservoir
simulator, ECLIPSE 300 (GeoQuest 2008), is used for the forward modeling of
flow and transport.
The simulation lasts 3,600 days. The objective is to maximize the net present
value by the end of the 3,600 days. All the economic parameters such as oil price
and the cost of CO
2
injection rate are similar to the cases described in chapter 4.
The control settings are modified every two months for the first 720 days and
then updated every 6 months, so the number of control steps is 38. Thus, the
total number of control parameters is 152. The production data are assumed to
be available every couple of months up to 720 days. EnKf is used for assimilating
the data, and 50 realizations are used. Measurements used in the data
assimilation include oil production rate, producing gas-oil ratio (GOR), bottom-
hole pressure of injectors, gas-phase CO
2
mole fraction at the producer, and
liquid-phase CO
2
mole fraction at the producer. The noise associated with the
production data is sampled from a normal distribution with a mean of 0 and
standard deviation which varies by type of observation. We compare three
different control scenarios in this example:
1. No-control: Total CO
2
injection rate is equally distributed among the
injectors.
139
2. Optimization with known geology: The reservoir’s geological properties
are assumed to be known without uncertainty, and the production
optimization is done based on the true reservoir.
3. Closed-loop optimization: The reservoir grid block permeability is
assumed to be uncertain. EnKf is used to adjust the permeability fields
to honor the production data. The injection rates are optimized under
the uncertain reservoir description using EnOpt.
The first scenario serves as base cases. The no-control case represents the
situation where individual control valves are not available. The second case,
optimization with known geology, represents the situation where the reservoir
properties are assumed to be known without uncertainty. The optimization with
the no-control case serves as a reference, to which we can compare the results of
the closed-loop optimization. Closed-loop optimization is the focus of this
chapter. The permeability fields are adjusted using EnKf, and the injection rates
are optimized using EnOpt based on the latest estimate of the permeability field.
We could expect that the net present value from a successful closed-loop
optimization should be similar to that from optimization with known geology. In
the closed-loop optimization, initially all the injection rates are equally
distributed, and the production optimization starts after the assimilation of the
first set of production data at day 60. The production optimization is repeated
after each update of the geological model and the optimized control settings are
140
expected to be more appropriate for the true reservoir with better prediction of
the reservoir responses provided by the updated reservoir models.
Figure 5-1 and Figure 5-2 show the mean of the initial k ensemble and the
true horizontal permeability field, respectively. The initial k realizations are
generated using Geostatistical Software Library (GSLIB) software (Deutsch and
Journel 1998). Data assimilation is influenced by the process of production
optimization and becomes more complicated, since some extreme control settings,
for example some injectors being fully closed, make the geological feature of those
regions not sensitive to the production data. Although using iterations increases
the computational cost, a good estimate of the geological properties of the
reservoir is beneficial to the production optimization and improves the entire
closed-loop optimization process.
At each time, we propagate each ensemble member ( ) from the current time
to the next available data-assimilation step using the reservoir simulator and
compare the results of the forecast with perturbed real observable data. We
subsequently use Equation ( 5-4) for updating each member of the ensemble
before proceeding to the next step. Notice that the matrix H is a linear projection
and produces the observations from each model state vector. The updated values
of the state vector are then used to propagate the realizations forward in time
up until the next data-assimilation step. At each time, the average of the
ensemble over the state vectors describes our best estimate of the system
141
including the phenomenological parameters. The variance over the ensemble
measures the current uncertainty/error in describing the system.
For optimization, we have parameterized the injection rates as a control
vector x. In the EnOpt setup at each step, once the state vectors in the ensemble
(Equation ( 5-4)) are determined, we optimize x, through the algorithm in
Chapter 5, Sec. 5.3. The control vector is based on a discretization of the
“lifetime” of the reservoir into steps. We assume that the injection rate is
constant during each such step and only apply the optimization procedure at the
beginning of each optimization step. In the actual implementation of the
algorithm, only the forthcoming “future” values of the injection rate are fixed so
that the past history is shared and unaltered. This amounts to a control vector
that has 4
elements for the 4 injection wells. The optimization algorithm
in turn requires an ensemble of control vectors X:
,
,
, ,
where is the number of realizations (taken to be the same as the ensemble size
for Y). We assume that the only operational constraints are on the injection rates
and thus on the vector x itself. We also assume that there is a maximum and
minimum operating injection rate associated with each well.
At the beginning of the simulation, the control vector needs to be initialized:
we pick the mean control from the uniform distribution bounded by the
minimum and maximum possible well constraints for each realization of each
142
well. At later stages of the optimization algorithm, a temporally correlated
Gaussian random field with zero mean is added to the mean control vector. By
using proper regularization, we explicitly enforce the well constraints on the
perturbed control vector. Calculation of the objective function for each
control/state vector pair requires running the simulation model from the current
time to the supposed final time of the simulation. This in general, is the most
time-consuming numerical step of the procedure.
Once the control vector is determined at the end of the optimization
algorithm, we use it as the “true” driving term for the ensemble models and the
actual reservoir and continue with characterization and propagation of the
system until the next control step comes up. The results of this combined
procedure for various synthetic cases appear next.
Figure 5-1. Mean of the initial permeability ensemble
143
Layer 1 Layer 2
Layer 3 Layer 4
Layer 5
Figure 5-2. True horizontal permeability of the reservoir
144
5.5 Results and discussion
We shall cover a series of synthetic cases for which we implement EnKf and
EnOpt. We use these cases to analyze the effectiveness and the sensitivity of our
numerical procedures for a variety of situations. As we shall see, while more
complex reservoirs with a high degree of heterogeneities might not immediately
satisfy the geological requirements, it is still possible to at least partially
characterize and even optimize the oil production and CO
2
storage in such cases
using EnKf and EnOpt procedures. A brief summary of the cases studied follows:
¾ Scenario (a): Pure CO
2
injection with the constraint of total CO
2
injection
for Immiscible and Miscible cases
¾ Scenario (b): CO
2
and water injection with the constraint of total liquid
injection for an Immiscible case
¾ Scenario (c): CO
2
and water injection with the constraint of total CO
2
injection for an Immiscible case
5.5.1 Scenario (a)
In the first case study, similar to the previous chapter, the total CO
2
injection
rate is constrained to 4000 m
3
/day in the liquid phase (at a temperature of 20
o
C
and pressure of 60 bars). We use two different oil compositions and conditions for
simulation: Immiscible (Kovscek and Cakici 2004) and Miscible cases (Rastegar
145
and Jessen 2009). All the injectors are controlled by a CO
2
injection rate of 1000
m
3
/day of the liquid phase, and all the producers are controlled by their bottom-
hole pressures.
5.5.1.1 Immiscible case
In the immiscible case study shown in Table 2-1, the initial reservoir
condition and economic parameters are similar to Chapter 4, section 4.4.1. The
production wells operate at a fixed bottom-hole pressure of 175 bars.
If all the injectors are fully open, in the no-control case, CO
2
flows through
the high-permeability streak very quickly and a lot of oil is left behind after
injecting of CO
2
. The injectors near the high-permeability streak are shut in at a
later time, and this allows the injected water to better sweep the rest of the
reservoir. Both closed-loop optimization and optimization with known geology,
however, show much higher sweep efficiency. By optimizing the net present value
at the end of reservoir life, we are able to adjust the control settings intelligently
before the presence of CO
2
at the production side. For example, by gradually
shutting in the injectors near the high-permeability streak after the CO
2
breakthrough, the reservoir is better swept in the optimized cases compared to
the no-control case.
The cumulative oil production and stored CO
2
in the base case and the
optimized cases with known and unknown geology are shown and compared in
Figure 5-3. Different curves are introduced in the figure legend. The advantages
146
of the model-based optimization technique can be more obviously seen in these
plots. The cumulative oil production and the CO
2
storage are higher in the
optimized case than that of the base case. The gas production is largely reduced
after the presence of high CO
2
production in the optimized cases by closing the
corresponding control valves. The optimized cases can, however, prevent early
CO
2
production by adjusting the settings of the control valves, which eventually
result in better sweep efficiency.
The production profiles of the no-control case and the optimized cases overlap
each other before the gas breakthrough. After the CO
2
breakthrough, the
optimized cases show higher oil production and lower CO
2
production compared
to the no-control case. The closed-loop optimization case and the case of
optimization with known geology exhibit very similar behavior (although the
contribution from different injectors is somewhat different between these two
cases as shown in Table 5-1), and both show much higher oil production at a
later time than the no-control case. The closed-loop optimization results indicate
that approximately 880,000 tons of incremental CO
2
are stored in the closed-loop
optimization case compared to the base case. This is a significant improvement
compared to the results obtained for the base (no-control) case. Along with this
storage, approximate oil production is 1,182,503 Sm
3
higher than that of the base
case. The increase in the cumulative oil production is due to keeping the injection
rates of the wells that are located in the high-permeability zones at lower values
147
and increasing the injection rates of the wells that are located in the low-
permeability zones. Furthermore, gas production is also delayed and considerably
reduced. As a result, total stored CO
2
is increased.
Figure 5-3. Comparison of (a) Cumulative oil production and (b) Mass of the
stored CO
2
for the optimized cases with known geology and unknown geology and
the base case of immiscible flooding in scenario (a)
Figure 5-4 compares the dimensionless form of net present value for the
reference and optimized cases by applying controls optimized at the twelve data-
assimilation times to the reference field. The net present value earned in the
closed-loop optimization case increased by 18% from the no-control case. With
the assimilation of the production data, the controls optimized based on the
148
ensemble of reservoir models become more and more suitable for the true field.
The largest improvement, however, happened after the assimilation of the initial
set of data since the feature of this reservoir is relatively simple and with
iterations, the main feature of the field has been captured at the initial data time.
In both optimized cases, the major contribution of the optimization algorithm in
this case is reducing CO
2
production while maintaining relatively high oil
production by more efficient allocation of the injection targets. The optimized
control settings at each data time vary in the closed-loop optimization since the
optimization is performed based on the geological models updated at different
data times, and the production profiles show some sudden changes at the data-
assimilation time due to the change of the well constraints. In general the closed-
loop optimization performed well and the results are comparable with the case
where the geological properties are assumed to be known.
149
Figure 5-4. Comparison of Dimensionless Net Present Value for the optimized
cases with known geology and unknown geology and base case of immiscible flooding
in scenario (a)
Figure 5-5 shows the control settings optimized based on the reference field
and from the closed-loop optimization. In the case of the closed-loop
optimization, all the injectors are equally operated before the first data-
assimilation time, day 60, and the first optimization is done after the data
assimilation at day 60. Controls are re-optimized at every later data assimilation
time, where the ensemble of reservoir models are supposed to be a better
representation of the actual reservoir, so the optimized controls at the later data-
assimilation time should perform better on the reference field than the controls
optimized at the earlier data time.
150
Figure 5-5. The change of the controls for different injectors for immiscible
flooding in scenario (a) for optimized cases with known and unknown geology
The total CO
2
-injection rate is allocated between the injection wells in order
to maximize the NPV of the project. The amount of the increase of the NPV and
the optimized control settings depends on the choice of the parameters used in
the calculation of the NPV.
Table 5-1. Share of each injector from the total CO
2
injection for immiscible
flooding in scenario (a)
Injector 1 Injector 2 Injector 3 Injector 4
Known Geology 43.2% 15.1% 25.4% 16.3%
Unknown Geology 47.8% 11.7% 27.9% 12.6%
151
Table 5-1 shows the share of each injector from the total injected CO
2
during
the reservoir lifetime. Overall, all the injectors in both cases are mostly assigned
with equal total amounts of injected CO
2
; however, each injector’s daily CO
2
-
injection rate is changing in time. As shown in Figure 5-5, the injection profiles of
all the injectors are pulse-shaped. Because of the disadvantages of the continuous
CO
2
floods, the CO
2
-injection profile is automatically chosen to be pulse-shaped
by the EnOpt for all the injectors. To obtain pulse-shaped injection profiles, the
well is shut-in for some period of time during which the diffusion processes
dominate the fluid flow processes behind the flood front and lead to more efficient
displacement of the oil.
To show the quality of the estimate of the permeability field, we compared
the production responses using the optimized controls with the initial
permeability ensemble and the permeability ensemble updated at day 720, the
last data time. Production responses from the initial reservoir ensemble and the
corresponding production responses from the ensemble updated at day 720 are
shown in Figure 5-6, Figure 5-7, Figure 5-8, Figure 5-9 and Figure 5-10. At the
end of the first data-assimilation step, the values of all state variables are
updated and returned to the reservoir simulator. The predictions from the initial
ensemble are generally very different from the reference production responses and
show very high uncertainty. The predictions from the updated permeability
ensemble show better matches to the data (observations were only available at
152
every couple of months up to 720 days) and better predictability, although the
uncertainty of the prediction might be somewhat underestimated.
Figure 5-6 depicts the results of EnKf matching of the oil production rate of
different producers. The red curve shows the actual observed data and the black
curves depict the results of 50 ensemble realizations. Clearly, the ensemble
members converge to the actual observation data once EnKf is switched on after
day 60. Also note that after day 720 when EnKf is switched off, the state vectors
of the ensemble still closely follow the observed data until day 3600. The results
for the oil production rate obtained from the EnKf show bias in the early
production period where most of the ensemble members produce significantly less
amounts of oil than the observations (especially in Figure 5-6b).
153
Figure 5-6. Data match from the initial and updated ensemble for immiscible
flooding in scenario (a). The solid red line is the reference oil production profile, the
dark black represents the responses from the updated ensemble and gray represents
the responses from the initial ensemble
The results of the production data match for the producing gas-oil ratio
(GOR) of different producers are shown in Figure 5-7. The results for the gas-oil
ratio obtained from the EnKf method do not match completely the historical
injection-rate data. Even though the ensemble obtained from the EnKf appears
to cover the observations from the reference model, the spread of the ensemble
members around the measurements is greater in this case.
154
Figure 5-7. Data match from the initial and updated ensemble for immiscible
flooding in scenario (a). The solid red line is the reference gas-oil ratio profile, the
dark black represents the responses from the updated ensemble and gray represents
the responses from the initial ensemble
The EnKf method generally performed better in terms of matching the
observations of the gas-oil ratio for producers P1 and P3. Similar results were
observed for bottom-hole pressure of injectors.
Figure 5-8 shows the production-data match for bottom-hole pressure for
injectors I1, I2, I3 and I4 from the application of the closed-loop optimization.
The EnKf performed better in terms of matching the bottom-hole pressures
compared to the other production parameters. The ensemble obtained from the
155
EnKf appears to have enough variability in the prediction phase, which is
important for assimilating additional production data in the future.
Figure 5-8. Data match from the initial and updated ensemble for immiscible
flooding in scenario (a). The solid red line is the reference bottom-hole pressure, the
dark black represents the responses from the updated ensemble and gray represents
the responses from the initial ensemble
The results for the history match of the liquid-phase CO
2
mole fraction
(WXMF) and gas-phase CO
2
mole fraction (WYMF) data are shown in Figure
5-9 and Figure 5-10, respectively. The results indicate that the liquid phase
resulted in a better match to the measurements, compared to the gas phase.
However, due to high sensitivity of CO
2
concentration to horizontal and vertical
156
permeability, liquid and gas mole fractions of CO
2
don’t have a good match to
the reference case compared to the other production parameters.
Figure 5-9. Data match from the initial and updated ensemble for immiscible
flooding in scenario (a). The solid red line is the reference CO
2
liquid mole fraction,
the dark black represents the responses from the updated ensemble and gray
represents the responses from the initial ensemble
157
Figure 5-10. Data match from the initial and updated ensemble for immiscible
flooding in scenario (a). The solid red line is the reference CO
2
gas mole fraction
profile, the dark black represents the responses from the updated ensemble and gray
represents the responses from the initial ensemble
To analyze the performance of the methodology, a couple of performance
metrics are defined and considered. Although Figure 5-6 through Figure 5-10
show the applicability of the proposed methodology, to analyze and quantify the
performance of the algorithm, two metrics are defined as follows.
1. Root mean square error (RMSE) as shown in the following equation is an
indication of the match between the values of the properties of the
reservoir that were estimated and those of the reference model:
158
1
( 5-17)
where operator is the expectation on the ensemble and is the
estimated mean. represents the reference field, and is the
number of the estimated parameters (Ghods and Zhang 2010). Clearly,
RMSE decreases when increasing the ensemble size. Increasing the
ensemble size allows for smoother and finer variations among the ensemble
members. Notice, however, that practically, the improvement by
increasing the ensemble population is limited.
2. SPREAD shows the variance of the ensemble around the ensemble mean,
representing the degree of uncertainty that resides in the estimation of the
parameters in the updated ensemble at the end of the history-matching
period.
1
( 5-18)
The following figures show the RMSE and SPREAD for this case study. The
decreasing trends are indicative of the good performance of the proposed
approach.
159
Figure 5-11. RMSE performance metrics for immiscible case in scenario (a)
In real applications, the true properties of a reservoir are always unknown,
which leads us into defining another metric to measure the performance of our
proposed algorithm. Average data mismatch (ADM) is representative of the
average difference between the estimations of the production data at the end of
the history matching, and the reference, and is calculated as follows (Ghods and
Zhang 2010):
160
Figure 5-12. SPREAD performance metrics for immiscible case in scenario (a)
1
( 5-19)
where represent the number of the wells and the number of the time steps,
and the number of the realizations, respectively. is the production
observation at the
time step. The following table shows the average data
mismatch calculated for this case study for both the oil production rates and
GOR. The improvements from the initial to the final ensemble are obvious.
161
Table 5-2. Average data mismatch for immiscible case in scenario (a)
Initial Ensemble Final Ensemble
Oil production rate (STB/D) 31.00 7.74
GOR(MSCf/STB) 192.28 67.68
BHP(psia) 2.31 1.59
Figure 5-13 shows the mean of the updated ensemble of horizontal
permeability for layers 1 through 5. Compared with the truth, the realizations
exhibit on average greater grid block values of horizontal permeability and as
expected, do not have the exact permeability values in the correct place.
162
Layer 1 Layer 2
Layer 3 Layer 4
Layer 5
Figure 5-13. Mean of updated ensemble horizontal permeability of the reservoir
for immiscible case in scenario (a)
163
5.5.1.2 Miscible case
Similar to chapter 4, section 4.4.1.2, in this case the initial reservoir pressure
is set as 175 bars and the oil composition (Table 3-1) is chosen in such a way as
to allow the miscibility of CO
2
in the oil phase at pressures below 175 bars. The
log-permeability fields for the reference model and the initial ensemble are
generated using the GSLIB with a correlation coefficient of 0.75. An ensemble of
50 realizations is conditioned to values of permeability at well locations from the
reference model. The state vector includes static model parameters such as log
permeability along with dynamic state variables such as pressure, CO
2
concentration, and gas saturation. The simulated production data, including oil
production rate, producing gas-oil ratio, bottom-hole pressure, and gas and liquid
phases of CO
2
-production rate, are used in the data assimilation. The
measurement noise associated with the production data is sampled from a normal
distribution with a mean of 0 and a standard deviation which varies by type of
observation.
Figure 5-14 compares the cumulative oil production and the stored CO
2
in the
base and the optimized scenarios with known and unknown geology. The miscible
case shows a similar trend as the immiscible case in terms of oil recovery and
CO
2
storage. Figure 5-15 compares the dimensionless NPV for the base and
optimized cases. Approximately, a 9% improvement in the NPV is observed
between the closed-loop optimized case and the base scenarios. All cases initially
164
showed a similar trend of increasing profit. Then, due to gas breakthrough and
decreased oil plateau production and hence reduced revenue, the CO
2
-injection
cost plays an important role in the decline of NPV. The peak NPV is reached
almost at the same time for the two optimized cases while the plateau is more
rapid in the base case. The cumulative oil production and CO
2
storage are
improved and the CO
2
storage is much larger in the optimized scenario than that
of the base scenarios.
Figure 5-14. Comparison of (a) Cumulative oil production and (b) Mass of the
stored CO
2
for the optimized cases with known geology and unknown geology and
the base case of miscible flooding in scenario (a)
165
Figure 5-15. Comparison of Dimensionless Net Present Value for the optimized
cases with known geology and unknown geology and base case of miscible flooding in
scenario (a)
Figure 5-16 shows the injection profile of the injectors of the optimized case
based on the reference field and from the closed-loop optimization in the
optimized scenario. Similar to the immiscible scenario, all the injectors are
showing pulse-shaped behavior that leads to better sweep efficiency.
Similar to the immiscible case, the closed-loop optimization case and the case
of optimization with known geology exhibit very similar behaviors; all the
injectors are showing pulse-shaped behaviors that lead to better sweep efficiency.
The largest share of the total injection belongs to the third injectors located in
166
the lower permeability zone (Table 5-3). Similar to the immiscible case, the
increase in the cumulative oil production is due to keeping the injection rates of
the wells that are located in the high-permeability zones at lower values and
increasing the injection rates of the wells that are located in the low-permeability
zones. Clearly, injectors 1 and 3 which are close to the lower permeability regions
are allocated with higher shares of CO
2
-injection rates.
Figure 5-16. The change of the controls for different injectors for miscible flooding
in scenario (a) for optimized cases with known and unknown geology
167
Table 5-3. Share of each injector from the total CO
2
injection for miscible flooding
in scenario (a)
Injector 1 Injector 2 Injector 3 Injector 4
Known Geology 38.1% 19.8% 21.2% 20.9%
Unknown Geology 27.9% 20.2% 33.2% 18.7%
In the second case study, the same reference model in the first case study is
used. Data for both the history-matching period (the first 720 days) and the
subsequent 2880-day predictions are shown in Figure 5-17, Figure 5-18, Figure
5-19, Figure 5-20 and Figure 5-21.
Figure 5-17 shows the oil production rates of each of the producers along with
their reference values. One can observe that using our proposed methodology, the
uncertainty in estimating those rates has decreased. The predictions from the
updated permeability ensemble show better matches to the data and better
predictability. As a result, the updated models are better predictively for
simulation purposes. The ensemble members converge to the actual observation
data by using EnKf. Also note that once EnKf is switched off after day 200, the
production response of the ensemble still very closely follows the observed data.
168
Figure 5-17. Data match from the initial and updated ensemble for miscible
flooding in scenario (a). The solid red line is the reference oil production profile, the
dark black represents the responses from the updated ensemble and gray represents
the responses from the initial ensemble
Figure 5-18 and Figure 5-19 show the producing GOR and bottom-hole
pressure in different producers generated by Eclipse for the true model and all 50
initial and updated ensemble members. The red curves represent data from the
true model. The gray curves show the results from the initial ensemble and dark
black curves the final ensemble during both the data-assimilation period and the
subsequent prediction period. It can be observed that the updated values better
estimate the reference properties.
169
In Figure 5-18 the average of GOR data from the 50 members of the ensemble
is somewhat lower than the truth for some time after switching off the EnKf, but
before the last GOR datum is assimilated, the average GOR of the ensemble
becomes quite close to the truth. The average bottom-hole pressure is in good
agreement with the true data until the later part of the prediction period when
the average of all ensemble bottom-hole pressures falls below the truth. However,
the true bottom-hole pressure always is encompassed reasonably near the center
of predictions from the ensemble.
The results for gas-oil ratio and bottom-hole pressure obtained from the EnKf
method do not completely match the historical data. Even though the ensemble
obtained from the EnKf appears to cover the observations from the reference
model, the spread of the ensemble members around the measurements is greater
in this case.
170
Figure 5-18. Data match from the initial and updated ensemble for miscible
flooding in scenario (a). The solid red line is the reference gas-oil ratio profile, the
dark black represents the responses from the updated ensemble and gray represents
the responses from the initial ensemble
Note that the BHP of injector 4 is best estimated compared to other injectors.
The estimation of the properties of the other producers does not show the same
performance.
171
Figure 5-19. Data match from the initial and updated ensemble for miscible
flooding in scenario (a). The solid red line is the reference bottom-hole pressure, the
dark black represents the responses from the updated ensemble and gray represents
the responses from the initial ensemble
Figure 5-20 and Figure 5-21 show the estimated CO
2
-mole fraction in liquid
and gas phases of the production in the initial ensemble, final ensemble, and the
reference model. It can be seen that after the application of EnKf, the updated
values of the estimated properties show a better match to those of the reference
model. Before gas breakthrough occurs for the true model, breakthrough occurs
for some of ensemble members, but when the first CO
2
-mole fraction is
assimilated, almost all the ensemble members give a close match of these
172
parameters, and hence the early difference in the CO
2
-mole fraction data is
diminished towards zero.
Figure 5-20. Data match from the initial and updated ensemble for miscible
flooding in scenario (a). The solid red line is the reference CO
2
liquid mole fraction,
the dark black represents the responses from the updated ensemble and grays
represent the responses from the initial ensemble
173
Figure 5-21. Data match from the initial and updated ensemble for miscible
flooding in scenario (a). The solid red line is the reference CO
2
gas mole fraction
profile, the dark black represents the responses from the updated ensemble and gray
represents the responses from the initial ensemble
During the prediction period, the average CO
2
-mole fraction for the ensembles
is very close to the truth. The EnKf performed better in terms of matching the
liquid and gas phases of CO
2
-mole fractions compared to the previous case. The
ensemble obtained from the EnKf appears to have enough variability in the
prediction phase, which is important for assimilating additional production data
in the future.
To quantify the performance of the methodology in the second test case we
have summarized the RMSE, SPREAD, and ADM in the following two figures
174
and table. As in the immiscible case, the performance of the miscible case is
found to be acceptable.
Figure 5-22. RMSE performance metrics for miscible case in scenario (a)
175
Figure 5-23. SPREAD performance metrics for miscible case in scenario (a)
Table 5-4. Average data mismatch for miscible case in scenario (a)
Initial Ensemble Final Ensemble
Oil production rate (STB/D) 69.52 21.84
GOR(MSCf/STB) 276.08 103.52
BHP(psia) 0.61 0.29
Figure 5-24 shows the average permeability distribution after data
assimilation at 720 days. Comparing Figure 5-24 to the true permeability
distribution in Figure 5-2, we see that the average permeability distribution after
data assimilation with the EnKf captures the main geological features.
176
Layer 1 Layer 2
Layer 3 Layer 4
Layer 5
Figure 5-24. Mean of updated ensembles of horizontal permeability of the
reservoir for miscible case in scenario (a)
177
5.5.2 Scenario (b)
The difference between scenario (a) and scenario (b), as stated in the previous
sections, is that we have the option of injecting water into the reservoir. For the
first 720 days, we have applied EnKf for history matching and used the updated
models to predict and optimize the reservoir performance until the 3600th day.
Similar to Chapter 4, section 4.4.2, the reservoir oil composition and setting in
this case study are similar to the immiscible case of scenario (a). The relatively
small reservoir size, moderate permeability, and fairly large angle of inclination
suggest that water flooding should be relatively efficient. In this case, the
optimization is constrained to constant total liquid injection rate (CO
2
or water)
of 4000 m
3
/day (at a temperature of 20
and pressure of 60 bars). The
optimization sought in this study involved finding the optimum configuration of
control variables for an injection scheme of 3600 days that leads to the largest
NPV. The wells are operated by constraining their bottom-hole pressures, and
the oil, water and gas production rates are measured and reported. A two-phase
injection is used in this case where the phase distribution can be described by
level set functions, . In the generation of the initial ensemble, the 50
realizations are randomly generated by associating uncertainty with the
permeability heterogeneity. The control parameters are the injection phase (water
or CO
2
) and the rate of the injection of each fluid. All control variables are
assumed to be Gaussian random variables. The control variables contain flow
178
rate (Q) and level function ( ) for all the time steps. Thus, the total number
of control parameters is 2×4×28=224. The process configuration is represented
by the control vector x (Equations ( 4-9) and ( 4-10)).
Figure 5-25 shows cumulative oil production and stored CO
2
in the base case
and the optimized cases with known and unknown geology. The results are
compared with the results of a base case in which all injection rates are fixed at
1000 Sm
3
/day of pure CO
2
. The advantages of the model-based optimization
technique can be more obviously seen in these plots. The results clearly
demonstrate a higher cumulative oil production and a lower CO
2
storage at the
end of the optimization. Gas breakthrough is delayed significantly and the oil
production rates are increased for most of the production period. The total oil
production profiles of the known geology optimized case and the unknown
geology case overlap each other. The closed-loop optimization case and the case
of optimization with known geology exhibit very similar behaviors (although the
total CO
2
-storage contributions are different from the other cases as shown in
Figure 5-25), and both show much higher oil production at early times than the
no-control cases. In terms of CO
2
sequestration, the optimized cases of the
simultaneous water and CO
2
injection perform worse than the optimized case of
the pure CO
2
injection (Scenario (a)). This is caused by the injection of water
through the production period which results in a reduced amount of injected CO
2
and smaller reservoir pore-volume utilization for CO
2
storage.
179
Figure 5-25. Comparison of (a) Cumulative oil production and (b) Mass of the
stored CO
2
for the optimized cases with known geology and unknown geology and
the base case of immiscible flooding in scenario (b)
An improvement in the NPV of about 58% with respect to the base case is
obtained in this case study for both optimized cases. This is a significant
improvement compared to the results from the optimized scenario (a). The
increased profits due to larger oil production dominate the decrease of the credits
received because of stored CO
2
during the reservoir life. The NPV is mainly
affected by the improvements in oil recovery (Figure 5-26).
180
Figure 5-26. Comparison of Dimensionless Net Present Value for the optimized
cases with known geology and unknown geology and base case of immiscible flooding
in scenario (b)
Figure 5-27 and Figure 5-28 depict the water and CO
2
injection rates vs. the
control steps for optimized cases based on the reference field and the closed-loop
optimization. In all the injectors, the water is used to maintain the pressure and
drive the oil from the reservoir. After some water injection, closed-loop EnOpt
converts the project into gas injection in order to increase the NPV by
sequestrating the CO
2
and improving the displacement efficiency. This control
strategy results in delaying the CO
2
breakthrough at the producers. As can be
seen in Figure 5-27 and Figure 5-28, the EnOpt methodology results in pulse-
181
shaped injection profiles and keeps the oil production rates at relatively higher
values.
Table 5-5 shows the share of each injector from the total CO
2
and water
injected during the reservoir lifetime. Overall, all the shares of injectors in both
optimized cases are almost identical; however, each injector’s daily CO
2
and
water injection rates are changing in time. As shown in Figure 5-27 and Figure
5-28, the injection profiles of all the injectors are pulse-shaped. Because of the
disadvantages of the continuous CO
2
floods, the CO
2
-injection profile is
automatically chosen to be pulse-shaped by the EnOpt for all the injectors. To
obtain pulse-shaped injection profiles, the well is shut-in for some period of time
during which the diffusion processes dominate the fluid flow processes behind the
flood front and lead to more efficient displacement of the oil.
Clearly, the injectors 1 and 3 show larger shares of CO
2
and water injection
rates whereas the injection wells 2 and 4 show a smaller allocated CO
2
rate. This
suggests setting and lower than the rest of the injection rates (Table
5-5). This can be explained by the higher permeability regions around the
injection wells 2 and 4. In order to obtain a higher NPV, the injection rates near
the higher permeability regions need to be reduced to allow for uniform sweep
efficiency throughout the reservoir.
182
Figure 5-27. The share of CO
2
injection for different injectors for immiscible
flooding in scenario (b) for optimized cases with known and unknown geology
183
Figure 5-28. The share of water injection for different injectors for immiscible
flooding in scenario (b) for optimized cases with known and unknown geology
Table 5-5. Share of each injector from the total CO
2
and water in scenario (b)
Known geology Unknown geology
Share of CO
2
Share of water Share of CO
2
Share of water
Injector 1 48.27% 30.56% 37.65% 27.44%
Injector 2 13.97% 21.08% 20.91% 18.79%
Injector 3 30.72% 30.56% 28.39% 33.84%
Injector 4 7.04% 17.80% 13.06% 19.92%
184
Figure 5-29 and Figure 5-30 show the oil and water production rates in all the
four wells along with their reference values. These figures show the comparison
between the estimated properties and those of the reference model. It is observed
that the degree of uncertainty in oil production has been reduced, the models are
capable of reproducing the historical values of the production data, and the
future performance has been forecasted accurately. The following figures are
indicative of the above facts:
Figure 5-29. Data match from the initial and updated ensemble in scenario (b).
The solid red line is the reference oil production profile, the dark black represents
the responses from the updated ensemble and gray represents the responses from the
initial ensemble
185
Similar results are observed for the cumulative water production. The result
of water production is not good as a result of oil production. The results of
Figure 5-30 indicate that all realizations in producer 1, 2 and 3 predict a
cumulative water production smaller than the truth while the producer 4
prediction is larger than the reference case.
Figure 5-30. Data match from the initial and updated ensemble in scenario (b).
The solid red line is the reference water production profile, the dark black represents
the responses from the updated ensemble and gray represents the responses from the
initial ensemble
Figure 5-31 and Figure 5-32 show the producing GOR and bottom-hole
pressure in different producers generated by Eclipse for the true model and all 50
186
initial and updated ensemble members. It can be observed that the updated
values better estimate the reference properties. The ensemble members of GOR
converge almost instantly to the actual observation data once EnKf is switched
on after day 60. After day 720 when EnKf is switched off, the state vectors of the
ensemble still very closely follow the observed data until day 3600 that confirms
the predictive power of our estimates. Figure 5-32 shows similar trends for the
bottom-hole pressure profile.
Figure 5-31. Data match from the initial and updated ensemble in scenario (b).
The solid red line is the reference gas-oil ratio profile, the dark black represents the
responses from the updated ensemble and gray represents the responses from the
initial ensemble
187
During the prediction period, the average GOR and BHP for the ensembles is
very close to the truth.
Figure 5-32. Data match from the initial and updated ensemble in scenario (b).
The solid red line is the reference bottom-hole pressure, the dark black represents
the responses from the updated ensemble and gray represents the responses from the
initial ensemble
Figure 5-33 and Figure 5-34 depict the estimated CO
2
-mole fraction in liquid
and gas phases of the production in the initial ensemble, final ensemble, and the
reference model. It can be seen that after the application of EnKf, the updated
values of the estimated properties show a better match than those of the
reference model. It is fairly clear that, although the final ensemble members for
188
both parameters match production data better than the initial ensemble
members, the matches to liquid and gas phases of CO
2
production of the
reference case are not good with EnKf due to the sensitivity of gas saturation to
the vertical and horizontal permeability.
Figure 5-33. Data match from the initial and updated ensemble in scenario (b).
The solid red line is the reference CO
2
liquid mole fraction, the dark black represents
the responses from the updated ensemble and gray represents the responses from the
initial ensemble
189
Figure 5-34. Data match from the initial and updated ensemble in scenario (b).
The solid red line is the reference CO
2
gas mole fraction profile, the dark black
represents the responses from the updated ensemble and gray represents the
responses from the initial ensemble
It is observed that the degree of uncertainty has been reduced, the models are
capable of reproducing the historical values of the production data, and the
future performance has been forecasted accurately. The following two figures and
table are indicative of the above facts.
190
Figure 5-35. RMSE performance metrics for immiscible case in scenario (b)
Note that the metrics defined to measure the performance of the methodology
show poorer results compared to those in the first scenario. However the trend is
similar to the previous cases. To summarize, the updated models are able to
predict the reservoir performance.
Figure 5-37 shows the average of the updated ensemble of the field. The
estimate of the average field at 720 days bears geological resemblance to the
truth and results in good matches of production data as shown earlier but is far
from the true k field in many aspects (especially in Layer 1-3).
191
Figure 5-36. SPREAD performance metrics for immiscible case in scenario (b)
Table 5-6. Average data mismatch for immiscible case in scenario (b)
Initial Ensemble Final Ensemble
Oil production rate (STB/D) 25.39 5.91
Water production rate (STB/D) 29.34 9.75
GOR(MSCf/STB) 55.53 5.94
BHP(psia) 2.03 1.60
192
Layer 1 Layer 2
Layer 3 Layer 4
Layer 5
Figure 5-37. Mean of updated ensembles of horizontal permeability of the
reservoir for immiscible case in scenario (b)
193
5.5.3 Scenario (c)
As discussed in the previous sections, viscous fingering and poor volumetric
sweep in continuous CO
2
flooding can be improved by the simultaneous injection
of water and CO
2
. The water slugs provide more favorable mobility ratios in this
process than that of a pure CO
2
process. This case is similar to scenario (b). The
difference is in the constraints that are imposed on the total CO
2
-injection rate.
The total CO
2
-injection rate is constant and equal to 4000 Sm
3
/day (at a
temperature of 20
and pressure of 60 bars). The maximum water-injection rate
for each of the injectors is 1000 Sm
3
/day.
Figure 5-38 compares the total cumulative oil production and CO
2
storage
obtained in the optimized cases with known and unknown geology with those
obtained in the base case. The results are compared with the results of a base
case in which all injection rates are fixed at 1000 Sm
3
/day of pure CO
2
. One can
observe that the cumulative oil production in scenario (c) is significantly higher
than that of the base case and the optimized cases of scenario (a). The total
recovered oil in optimized cases is lower in this case study compared to the
cumulative oil production of the optimized cases in scenario (b) due to the
imposed constraints on the total CO
2
injection. It can be seen that the total
amount of the stored CO
2
in this case is almost the same as the base case. The
results clearly demonstrate a higher cumulative oil production and a lower CO
2
storage at the end of the optimization. The total oil production profiles of the
194
known geology optimized case and the unknown geology optimized case overlap
each other.
Figure 5-38. Comparison of (a) Cumulative oil production and (b) Mass of the
stored CO
2
for the optimized cases with known geology and unknown geology and
the base case of immiscible flooding in scenario (c)
The optimization results indicate that the NPV of the project doubles during
the optimization process (Figure 5-39). This is a significant improvement
compared to the results obtained in scenario (a). Although in this case study the
total amount of stored CO
2
is almost equal to that of the base case, the increase
in NPV is due to the large increase in the oil production. If the cost of the CO
2
195
injection is much higher than the one used in this case study, the optimized
control settings should lead to reduction of the CO
2
production and increase in
the NPV.
Figure 5-39. Comparison of Dimensionless Net Present Value for the optimized
cases with known geology and unknown geology and base case of immiscible flooding
in scenario (c)
Figure 5-40 and Figure 5-41 show the variation of the injection rates over
time obtained by the EnOpt procedure. Notice that the decreasing/increasing
trends in various injection wells are in general agreement with those of scenario
(b) as required to be reduced/increased for an even sweep of the reservoir and
higher NPV. These results indicate that the closed-loop optimization method
leads to keeping relatively higher CO
2
-injection rates for Injector 1 in the very
196
early stages of the injection. The NPV is maximized by switching the injection
phase from water into CO
2
and vice versa. Water as the displacing fluid improves
the horizontal sweep efficiency by controlling the mobility ratio, and CO
2
affects
the vertical sweep efficiency and thus their simultaneous injections maximize the
total sweep efficiency of the reservoir. Due to application of the level set function,
the EnOpt methodology is able to make rapid changes to the control parameters
as can be observed in Figure 5-40 and Figure 5-41.
Figure 5-40. The share of CO
2
injection for different injectors for immiscible
flooding in scenario (c) for optimized cases with known and unknown geology
197
Figure 5-41.The share of water injection for different injectors for immiscible
flooding in scenario (c) for optimized cases with known and unknown geology
Table 5-7. Share of each injector from the total CO
2
and water in scenario (c)
Known geology Unknown geology
Share of CO
2
Share of water Share of CO
2
Share of water
Injector 1 53.33% 14.53% 50.70% 15.73%
Injector 2 24.13% 26.35% 20.84% 27.03%
Injector 3 19.40% 36.23% 19.65% 29.43%
Injector 4 3.15% 22.89% 8.81% 27.82%
198
As can be seen in Table 5-7, in order to delay the gas breakthrough, the
injectors 2, 3 and 4 are injected with the largest amount of water in the
optimized case scenarios while injector 1 is allocated the greatest share of the
total injected CO
2
in both
optimized cases.
In this case study, the reservoir specifications are similar to the previous case
studies. The log-permeability fields for the reference model and the initial
ensemble are generated using the same geostatistical model parameters as the
reference model. The state vector includes static model parameters and log
permeability, along with dynamic state variables such as pressure, water
saturation, and gas saturation. The simulated production data, including oil and
water production rates, producing gas/oil ratio, bottom-hole pressure of injectors,
and liquid and gas phases of CO
2
production, are used in the data assimilation.
Figure 5-42 and Figure 5-43 show the oil and water production rates in all of
the four wells along with their reference values. These figures show the
comparison between the estimated properties and those of the reference model. It
is observed that the degree of uncertainty in oil production has been reduced, the
models are capable of reproducing the historical values of the production data,
and the future performance has been forecasted accurately. The following figures
are indicative of the above facts. Similar results are observed for the water
production; however the result of water production is not as good as a result of
the oil production.
199
Figure 5-42. Data match from the initial and updated ensemble in scenario (c).
The solid red line is the reference oil production profile, the dark black represents
the responses from the updated ensemble and gray represents the responses from the
initial ensemble
200
Figure 5-43. Data match from the initial and updated ensemble in scenario (c).
The solid red line is the reference water production profile, the dark black represents
the responses from the updated ensemble and gray represents the responses from the
initial ensemble
Figure 5-44 and Figure 5-45 compare the producing GOR and bottom-hole
pressure in different producers generated for the true model and all 50 initial and
updated ensemble members. It can be observed that the updated values better
estimate the reference properties. During the prediction period, the average GOR
and BHP for the ensembles is very close to the truth.
It is fairly clear that, although the final ensemble members for both
parameters match production data better than the initial ensemble members, the
201
matches to bottom-hole pressure are better with EnKf compared to the matches
with GOR.
Figure 5-44. Data match from the initial and updated ensemble in scenario (c).
The solid red line is the reference gas-oil ratio profile, the dark black represents the
responses from the updated ensemble and gray represents the responses from the
initial ensemble
202
Figure 5-45. Data match from the initial and updated ensemble in scenario (c).
The solid red line is the reference bottom-hole pressure, the dark black represents
the responses from the updated ensemble and gray represents the responses from the
initial ensemble
Figure 5-46 and Figure 5-47 depict the estimated CO
2
mole fraction in liquid
and gas phases of the production in the initial ensemble, final ensemble, and the
reference model. The ensemble obtained from the EnKf appears to have enough
variability in the prediction phase, which is important for assimilating additional
production data in the future.
203
Figure 5-46. Data match from the initial and updated ensemble in scenario (c).
The solid red line is the reference CO
2
liquid mole fraction, the dark black represents
the responses from the updated ensemble and gray represents the responses from the
initial ensemble
204
Figure 5-47. Data match from the initial and updated ensemble in scenario (c).
The solid red line is the reference CO
2
gas mole fraction profile, the dark black
represents the responses from the updated ensemble and gray represents the
responses from the initial ensemble
It is observed that the proposed methodology is capable of generating
predictive models. Figure 5-48 and Figure 5-49 and the following table are also
indicative of this fact.
205
Figure 5-48. RMSE performance metrics for immiscible case in scenario (c)
Figure 5-49. SPREAD performance metrics for immiscible case in scenario (c)
206
Table 5-8. Average data mismatch for immiscible case in scenario (c)
Initial Ensemble Final Ensemble
Oil production rate (STB/D) 51.32 7.22
Water production rate (STB/D) 28.68 6.05
GOR(MSCf/STB) 259.95 41.72
BHP(psia) 9.28 2.06
Figure 5-50 shows the mean of the ensembles updated by the EnKf at day
720. The permeabilities out of the physical bounds are truncated before
calculating the mean. The mean permeability field updated by the EnKf is
different from the reference, while this case shows a much better match compared
to scenario (b).
207
Layer 1 Layer 2
Layer 3 Layer 4
Layer 5
Figure 5-50. Mean of updated ensembles of horizontal permeability of the
reservoir for immiscible case in scenario (c)
208
5.6 Conclusion
An ensemble-based closed-loop optimization is introduced in this chapter. It
combines the ensemble Kalman filter (EnKf), with the ensemble-based
optimization (EnOpt). EnOpt shares the ensemble feature with EnKf, and the
sensitivities needed in the data assimilation and production optimization are both
approximated from an ensemble in a very straightforward manner without the
need for adjoint computations. The ensemble-based closed-loop optimization is
very flexible and can be easily combined with any reservoir simulator and
financial model with fairly limited amount of code development. The ensemble
feature of this closed-loop optimization method also makes it well suitable for
parallel computing. In the ensemble-based closed-loop optimization, an ensemble
of reservoir models is updated by EnKf to be consistent with production data.
This ensemble of reservoir models reflects the best estimate of the reservoir and
the associated uncertainty. To achieve robustness, the objective of the closed-loop
optimization is chosen to maximize the expectation of the net present value. The
objective function can be easily modified to reflect a different risk tolerance if
necessary.
The applicability of the ensemble-based closed-loop optimization is assessed
using several examples. The results of the ensemble-based closed-loop
optimization are compared with other alternative control scenarios, namely no-
control and optimization with known geology. A good estimate of the
209
permeability field was obtained through EnKf. The net present value of the field
is significantly increased by the closed-loop optimization, and the level is
comparable with the hypothetical case where the optimization is performed based
on known geology. In this example the model-based optimization (closed-loop
optimization or optimization based on known geology) clearly outperforms the
no-control case.
The reference field of this synthetic study is chosen to be similar to the
example that has been used in previous chapters. Because the reservoir has
relatively simple features, the estimation of the reservoir properties was
satisfactory after assimilating production data at the first data time. Subsequent
improvement with later data was not great. As a consequence, the optimization
at the later data times did not improve the net present value significantly from
the one obtained at the first data time.
210
Chapter 6: Summary, Conclusions and
Recommendations
6.1 Summary and conclusions
Injection of carbon dioxide into depleted reservoirs can substantially improve
the hydrocarbon recovery and reduce the amount of CO
2
in the atmosphere. The
incremental oil recovery by CO
2
injection can offset some of the expenses
associated with CO
2
storage such as capture, transportation and compression
costs. In the context of enhanced oil recovery, successful CO
2
-injection processes
have minimized the mass of CO
2
needed to recover a barrel of oil. The goal of
sequestering maximum carbon dioxide while maximizing oil recovery rate from an
oil reservoir is substantially different from the goal of recovery alone.
The first objective of this research project was to better understand and
evaluate the potential for both enhanced oil recovery and CO
2
storage in mature
oil reservoirs over a wide range of field conditions. The second objective was to
develop a methodology to co-optimize enhanced oil recovery and CO
2
storage in
the reservoir.
We have modified the objective function used by other investigators to better
analyze the EOR-sequestration process. Different flood designs should be applied
211
for coupled CO
2
sequestration and EOR projects compared to EOR projects.
Different injection schemes, including WAG, GAW and continuous pure CO
2
injection were considered. Of the various scenarios studied, the highest NPV was
observed for the WAG scheme, especially in immiscible cases. This may be
attributed to the improved mobility control provided by water slugs, which leads
to an improved macroscopic sweep efficiency.
The main economic concern in coupled CO
2
sequestration and EOR projects is
the very high cost associated with capture of CO
2
from power plants. In this
study, economic incentives were investigated to determine how much incentive
would be needed to promote storage of CO
2
in oil reservoirs and make such
projects profitable. Economic calculations based upon results from compositional
simulations were performed to quantify the need for CO
2
credits. We attempted
to maximize the Net Present Value (NPV) which takes into consideration the
costs associated with CO
2
production and injection as well as the revenues from
oil production and carbon credits. Although previous studies defined objective
function to aim at maximizing extra oil recovery and maximizing the CO
2
storage
capacity of the reservoir simultaneously, these functions did not take into account
the costs of CO
2
-injection factors such as capture and transportation costs. In
this study, we aimed to maximize the profitability of the project by considering
factors such as flood performance and CO
2
incentives. In order to carry out this
study, two comparative cases (miscible and immiscible) were developed.
212
Incentives in the form of tax credits are needed to support carbon capture and
storage (CCS) projects under immiscible conditions. However, under miscible
conditions, coupled EOR and sequestration projects may be profitable even
without carbon incentives, and they could become more profitable with such
incentives.
A new co-optimization framework has been presented on the basis of the
ensemble Kalman filter for continuous model updating, which was applied to
coupled CO
2
-EOR and sequestration projects in this research. The reservoir
geological model is always subject to high uncertainty due to the limited
knowledge of the reservoir. Optimizing based on a single best estimate of the
reservoir might fail severely if this best estimate is far from reality. In order to
obtain a robust control strategy, co-optimization techniques should be able to
take into account the uncertainty associated with the estimate of uncertain
reservoir properties.
This dissertation is devoted to the use of the ensemble-based method in both
data assimilation and CO
2
-EOR and sequestration co-optimization, and their
combined use in an ensemble-based closed-loop co-optimization framework. The
ensemble Kalman filter, a Monte Carlo-based method, has been shown to be
appropriate for data assimilation of large-scale nonlinear problems. The ensemble
Kalman filter represents the probability of the model parameters through an
ensemble of reservoir models, and this Monte Carlo feature reduces the
213
dimensionality of the inverse problem from the number of unknown parameters
to the number of realizations. The cross-correlation between predicted data and
the model parameters are easily obtained from the ensemble. This cross-
correlation provides the sensitivity needed for data assimilation and the expensive
calculation of the gradient is thus avoided.
The ensemble-based optimization (EnOpt) uses a similar idea to the
ensemble-based data-assimilation methods for approximation of the sensitivity
needed to compute the optimal control settings. EnOpt can be combined with the
ensemble-based data-assimilation methods to form an ensemble-based closed-loop
optimization. In the ensemble-based closed-loop optimization, an ensemble of
reservoir models is updated to honor the data, and EnOpt is coupled with this
ensemble of reservoir models in an effort to maximize the expectation of the net
present value. The ensemble feature of this closed-loop optimization method
makes it efficient for large-scale problems and also very flexible in terms of the
choice of the reservoir simulator and the economic model. For robust
optimization using reservoir models with uncertain parameters, expectation of the
net present value should be used as the objective function, in which case the
sensitivity of the expected net present value to the control variables is obtained
from a coupled ensemble of controls and ensemble of geological realizations.
We have employed a closed-loop EnOpt procedure to optimize the NPV of
the reservoir by controlling the injection patterns. Our proposed methodology has
214
been applied to a 3-D heterogeneous reservoir with known and unknown geology.
We have validated the EnOpt procedure using three different case studies each
with known and unknown geology and a unique set of optimization constraints.
The results of the ensemble-based closed-loop co-optimization have been
compared with those obtained from other possible reservoir operation scenarios,
such as wells with no controls and co-optimization with known geology. The
optimization process has shown remarkable improvements in the net present
value and the cumulative oil production. Our results indicate that for better
results, pulse-shaped injection profiles should be used in a CO
2
-only flood in order
to maximize the amount of oil swelling and mobilizing. Pulse-shaped gas-injection
profiles have been applied to provide a method of mobility control in the CO
2
-
EOR and sequestration processes where water injection is not feasible. The
advantage of this methodology over the adjoint-based methods is that it does not
require explicit knowledge of the simulator-flow equations and thus is
computationally less tedious. A commercial simulator can easily be applied to
this optimization technique without tampering with its source code.
6.2 Recommendations and future work
Since most of the coupled CO
2
sequestration and EOR projects will be
performed in mature oil fields, it is necessary to account for modifications on well
configurations of the target reservoirs. Therefore, it is important to examine the
215
effect of additional injectors and producers to be drilled during the life of the
project. This will give a dynamic nature to the problem compared to what was
performed in our study. Questions such as "What type of wells should be
added?" and "What time should they be added?" will change the economic
pattern of the process. Therefore, it is recommended that detailed studies be
performed considering both static and dynamic variables on coupled CO
2
sequestration and EOR projects.
Well placement is one of the crucial decisions made during the exploration
and development phase of projects. Most of the time, the large number of
possibilities, constraints on computational resources and the size of the simulation
models limit the number of possible scenarios that may be considered. Optimum
reservoir performance is highly dependent on well locations. Determination of
optimal well locations certainly cannot be based on intuitive judgment alone
owing to the fact that engineering and geologic variables affecting reservoir
performance are not only nonlinearly correlated, but also time and process
dependent. Hence, there is the need for an objective well-placement optimization
tool. Optimization may be defined as the process of adjusting the inputs to a
device or mathematical process or experiment in order to find the minimum or
maximum output or result.
Even though the standard implementation of the EnKF and EnOpt
algorithms are far more efficient for dynamic data assimilation than stochastic
216
methods and gradient-based methods, the sequential run of reservoir simulation
for each of the ensemble members is still computationally demanding and time
consuming, especially for large-scale numerical models. In addition, the memory
of a single processor dictates the size of a reservoir model (an ensemble member)
that can be used in practice. In the EnKF and EnOpt methods, a suite of
reservoir models (set of ensemble members) and control parameters runs
independently forward in time, and is continuously updated as new data becomes
available. For these reasons, it is advantageous to parallelize the closed-loop
EnOpt framework. In the future, the main focus could be on development and
implementation of a parallel closed-loop ensemble-based optimization framework
for optimization and assimilation of production data.
Another important factor that has not thoroughly been investigated in our
study, and can have great influence on the performance of a CO
2
-EOR project is
the phase behavior of the injected and in-situ fluids such as the effect of
impurities in the CO
2
stream on the flood performance and amount of stored CO
2
.
Since most of the produced CO
2
streams from power plants and other emission
sources are contaminated by other gases such as N
2
, H
2
S, etc., it is important to
perform this type of study. An optimization study can be performed to see what
level and what type of impurities can be allowed in injecting a stream for coupled
CO
2
sequestration and EOR projects to achieve relatively high profits as well as
high amounts of stored CO
2
.
217
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Abstract (if available)
Abstract
Sequestration of carbon dioxide (CO₂) in depleted or partially depleted oil reservoirs is a plausible option to reduce CO₂ emissions into the atmosphere. Carbon dioxide has been used as the injection fluid in Enhanced Oil Recovery (EOR) operations. The goal of such projects is to improve the profitability by maximizing the oil production (to increase the revenue) and minimizing the CO₂ injection (to decrease the costs). However, in sequestration projects, subsurface storage of the injected CO₂ needs to be maximized. ❧ The objective of this study is to develop a framework to co-optimize oil extraction and CO₂ sequestration. In the proposed framework, the net present value (NPV) of the project is selected as the optimization objective function. In my work, factors such as the cost of capturing the produced CO₂, CO₂ transportation and recycling are taken into account. A number of simulations are studied to achieve comprehensive understanding of the financial performance of the coupled CO₂ sequestration and EOR projects. The simulations show that the projects would be unprofitable for immiscible cases when using current typical costs of CO₂ capture from power plants unless there is some form of credit for storage. In contrast, in miscible cases, the projects may be profitable even without considering any CO₂ credits, and their profitability is further enhanced with possible carbon credits. ❧ With the advances in smart well technology, maximizing net present value of oil recovery and CO₂ storage can be achieved substantially by managing the operation intelligently in a closed-loop optimization framework. Closed-loop optimization consists of two parts: data assimilation and NPV optimization. Data assimilation adjusts the reservoir geological model to honor the production data and reduces the uncertainty of the estimate of reservoir geological properties. NPV optimization modifies the operational strategy based on the updated geological model. ❧ The Ensemble-based Optimization (EnOpt) algorithm has been selected as the optimization algorithm and the well-injection patterns and rates as the controlling variables. EnOpt can be easily combined with the ensemble-based data-assimilation methods to form an ensemble-based closed-loop optimization framework. The production rate data are assimilated in real-time by an ensemble Kalman filter for characterization of the reservoir. Simultaneously, EnOpt optimizes the expectation of net present value based on the up-to-date reservoir models. Several cases are used to demonstrate the applicability of the developed technique. Our results show that the oil recovery and the NPV can be increased significantly. The proposed methodology is fairly robust, does not require adjoint programming and can be readily used with any reservoir simulator. The workflow presented in this work can be used to design and co-optimize the coupled CO₂ sequestration and EOR projects.
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The study of CO₂ mass transfer in brine and in brine-saturated Mt. Simon sandstone and the CO₂/brine induced evolution of its transport and mechanical properties
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Performance prediction, state estimation and production optimization of a landfill
Asset Metadata
Creator
Jahangiri, Hamid Reza
(author)
Core Title
Optimization of coupled CO₂ sequestration and enhanced oil recovery
School
Viterbi School of Engineering
Degree
Doctor of Philosophy
Degree Program
Petroleum Engineering
Publication Date
04/26/2012
Defense Date
03/19/2012
Publisher
University of Southern California
(original),
University of Southern California. Libraries
(digital)
Tag
CO₂ sequestration,co-optimization,enhanced oil recovery,ensemble based optimization,net present value,OAI-PMH Harvest
Language
English
Contributor
Electronically uploaded by the author
(provenance)
Advisor
Zhang, Dongxiao (
committee chair
), Ershaghi, Iraj (
committee member
), Mendel, Jerry M. (
committee member
)
Creator Email
h.r.jahangiri@gmail.com,hjahangi@usc.edu
Permanent Link (DOI)
https://doi.org/10.25549/usctheses-c3-13500
Unique identifier
UC11288855
Identifier
usctheses-c3-13500 (legacy record id)
Legacy Identifier
etd-JahangiriH-645.pdf
Dmrecord
13500
Document Type
Dissertation
Rights
Jahangiri, Hamid Reza
Type
texts
Source
University of Southern California
(contributing entity),
University of Southern California Dissertations and Theses
(collection)
Access Conditions
The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the a...
Repository Name
University of Southern California Digital Library
Repository Location
USC Digital Library, University of Southern California, University Park Campus MC 2810, 3434 South Grand Avenue, 2nd Floor, Los Angeles, California 90089-2810, USA
Tags
CO₂ sequestration
co-optimization
enhanced oil recovery
ensemble based optimization
net present value