Numerical simulation and optimization of CO2 sequestration in saline aquifers for enhanced storage capacity and secured sequestration

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I
NTERNATIONAL
J
OURNAL OF

E
NERGY AND
E
NVIRONMENT



Volume 4, Issue 3, 2013 pp.387-398

Journal homepage: www.IJEE.IEEFoundation.org


ISSN 2076-2895 (Print), ISSN 2076-2909 (Online) ©2013 International Energy & Environment Foundation. All rights reserved.
Numerical simulation and optimization of CO
2

sequestration in saline aquifers for enhanced storage
capacity and secured sequestration



Zheming Zhang, Ramesh K. Agarwal

Department of Mechanical Engineering & Materials Science, Washington University in St. Louis, MO
63130, USA.


Abstract
Saline aquifer geological carbon sequestration (SAGCS) is considered most attractive among other
options for geological carbon sequestration (GCS) due to its huge sequestration capacity. However, in
order to fully exploit its potential, efficient injection strategies need to be investigated for enhancing the
storage efficiency and safety along with economic feasibility. In our previous work, we have developed a
new hybrid code by integration of the multi-phase CFD simulator TOUGH2 with a genetic algorithm
(GA) optimizer, designated as GA-TOUGH2. This paper presents the application of GA-TOUGH2 on
two optimization problems: (a) design of an optimal water-alternating-gas (WAG) injection scheme for a
vertical injector in a generic aquifer and (b) the design of an optimal injection pressure management
scheme for a horizontal injector in a generic aquifer to optimize its storage efficiency. The optimization
results for both applications are promising in achieving the desired objectives of enhancing the storage
efficiency significantly while reducing the plume migration, brine movement and pressure impact. The
results also demonstrate that the GA-TOUGH2 code holds a great promise in studying a host of other
problems in CO
2
sequestration such as how to optimally accelerate the capillary trapping, accelerate the
dissolution of CO
2
in water or brine, and immobilize the CO
2
plume.
Copyright © 2013 International Energy and Environment Foundation - All rights reserved

Keywords: CO
2
sequestration; Computational fluid dynamics; Genetic algorithm; Injection pressure
management; Water-alternating-gas (WAG) injection.



1. Introduction
In recent years, there has been significant emphasis on the development and implementation of safe and
economical geological carbon sequestration (GCS) technologies due to heightened concerns on CO
2

emissions from pulverized-coal (PC) power plants. However, uncertainties about storage capacity as well
as long-term storage permanence remain major areas of concern before proceeding with the actual
deployment of CO
2
sequestration in large-scale aquifers with enormous investment. In addition,
challenges remain in enhancing the storage efficiency and safety (by reducing the extent of plume
migration, brine movement and pressure impact) as well as the energy efficiency and economic
feasibility of GCS by improving the injection operations. Numerical simulations prior to actual
sequestration can be employed to address some of these uncertainties. CFD solver Transportation of
Unsaturated Groundwater and Heat (TOUGH2) has been widely used for this purpose [1, 2]. Due to the
complexity of the mass/energy transport in GCS, injection strategies that may be beneficial in addressing
International Journal of Energy and Environment (IJEE), Volume 4, Issue 3, 2013, pp.387-398
ISSN 2076-2895 (Print), ISSN 2076-2909 (Online) ©2013 International Energy & Environment Foundation. All rights reserved.

388
one aspect of the sequestration (e.g. reduction in plume migration) may not be as effective in addressing
another important aspect of sequestration (e.g. reservoir pressure response and its management). In
addition, the storage efficiency of an aquifer is also dependent on various injection strategies and
parameters associated with them; the optimization of the storage efficiency of an aquifer is of great
interest in GCS. Therefore, a simulation tool that has the capability of determining the optimal solutions
by balancing various trade-offs among desired objectives in GCS is needed. As an effort to examine and
address these issues, we have developed a genetic algorithm (GA) based optimization module for
TOUGH2 which can optimally examine various injection strategies for increasing the storage efficiency
as well as reducing the plume migration (Zhang and Agarwal, 2012). It is designated as GA-TOUGH2,
and has been validated by conducting several benchmark studies [3, 4].
In this paper, we consider the optimization of two engineering techniques to increase the sequestration
efficiency and safety of GCS in saline aquifers. In the first study, we employ a water-alternating-gas
(WAG) injection technique to a generic saline aquifer to retard the vertical migration of in situ CO
2
, i.e.,
to reduce the CO
2
plume size. In the second study, our goal is to seek a particular CO
2
injection scenario
that will result in the management of injection pressure (with the constraint that it remains less than the
aquifer’s fracture pressure) so as to maximize the injection rate to increase the storage efficiency. In both
the studies, we would like to determine the optimum strategy to achieve the desired objective. In the
WAG injection scheme, the additional water injection results in greater pressure response and energy
consumption which needs to be traded off with the goal of reduced CO
2
migration in an optimal manner.
Optimization can help in determining the most efficient as well as effective WAG operation. For the
injection pressure management study, the goal is to manage the injection pressure such that it optimizes
the storage efficiency of the aquifer. The optimization results for both applications show great promise,
by significantly reducing the CO
2
migration (up to 50% reduction in plume size compared to
conventional CO
2
injection) and well regulated injection pressure (less than the formation's fracture
pressure) to increase the storage efficiency.

2. Methodology
In previous research, we successfully developed an optimization module for TOUGH2 using a genetic
algorithm (GA). GA belongs to a class of optimization techniques that are inspired by the biological
evolution [5]. It can iteratively converge to the global optima without having detailed information about
the design space. Implementation of GA-TOUGH2 is summarized in Figure 1. Details of this work can
be found in our previous papers [4, 6].



Figure 1. Dataflow schematic of GA-TOUGH2 numerical simulator

3. Optimization of WAG technique for reducing the plume migration
The storage efficiency of saline aquifer geological carbon sequestration (SAGCS), based on the aquifer's
pore space, is usually very low. This is due to the inherent nature that injected CO
2
is less dense than
brine, with which the aquifer is filled. Consequently, CO
2
tends to rise up to the ceiling (caprock) of the
aquifer and forms a large spreading plume, decreasing both the storage capacity, safety and economic
feasibility of SAGCS considerably. To address this problem, we examined the potential benefits of a
International Journal of Energy and Environment (IJEE), Volume 4, Issue 3, 2013, pp.387-398
ISSN 2076-2895 (Print), ISSN 2076-2909 (Online) ©2013 International Energy & Environment Foundation. All rights reserved.

389
reservoir engineering technique called water-alternating-gas (WAG) injection for carbon sequestration
compared to the constant-gas-injection (CGI) technique for its effect on both the storage capacity and the
plume migration. We employed GA-TOUGH2 to determine the most efficient injection pattern. As
shown later in this section, our calculations indicate that the adoption of WAG operation to SAGCS can
lead to significant gain in sequestration efficiency. One of the key parameters that determine the
migration of the in situ CO
2
is the mobility ratio M, defined as:

nwrn
wnrw
mk
M
mk
µ
µ
⋅
==
⋅
(1)

where
m
n
,
µ
n
, and
k
rn
are the mobility, viscosity, and relative permeability of the non-wetting phase (CO
2
)
respectively and
m
w
,
µ
w
, and
k
rw
are the mobility, viscosity, and relative permeability of the wetting phase
(brine) respectively. Typically a mobility ratio of 10~20 is expected for SAGCS with CGI operation.
Under the scenario of WAG operation, the alternating CO
2
-water slugs can be treated as quasi-mixture
entering the aquifer, leading to mobility ratio lower than that for pure CO
2
injection. The success of
WAG technique for SAGCS operations is supported by the following reasons: (1) lower
M
results in
more stable displacement of the reservoir fluid, (2) lower
M
reduces the upward migration of CO
2
[7],
and (3) injection of brine into the aquifer with or after CO
2
injection can accelerate the dissolution of
CO
2
and enhance its residual trapping by the enhanced convective mixing [8-11]. More details of the
benefits of WAG operation can found in the Appendix.
In the study of WAG operation, target CO
2
sequestration amount is set to be 0.5 million metric tons per
year, which is roughly half of the emission from a typical medium-sized PC power plant. For
demonstration purpose a WAG enabled SAGCS operation is assumed to last for 600 days before it is
shut down, although a typical lifespan of a PC power plant is around 30 years. Thus, a total of 0.822
million metric tons of CO
2
will be sequestered. During the 600 days of injection, 20 cycles of alternating
CO
2
-water slugs (each known as a single WAG cycle) will take place, as schematically shown in Figure
2. Four independent variables determine a unique WAG injection pattern: CO
2
injection rate, water
injection rate, WAG ratio (the injected CO
2
mass to injected water mass per cycle), and cycle duration.
Fitness function for optimization is defined as the CO
2
plume migration reduction (compared to the
migration under constant gas injection (CGI) operation) normalized by the total amount of water
injection, as given by Equation (2). The fitness function serves as the criteria for evaluating how efficient
a certain WAG operation would be. This choice of the optimization fitness function takes into
consideration both the performance and economic aspects of adapting the WAG operation, since the
water injection consumes extra energy for transportation and pumping. WAG injection pattern with the
largest fitness function value is most desirable. We define

CGI WAG
water
RR
fitness
m
−
=
(2)

where
R
CGI
and
R
WAG
are the CO
2
plume radius under CGI operation and WAG operation respectively.
m
water
is the total mass of injected water during WAG operation.
R
CGI
and
R
WAG
are measured at the top of
the reservoir due to the buoyancy of CO
2
. For simplicity, the following two assumptions are made: (a)
each WAG cycle has duration of 30 days and (b) all WAG cycles are identical to each other. The 30-day
cycle duration is chosen based on the authors’ judgment, following Nasir and Chong's conclusion that for
oil recovery purpose, different WAG cycle durations do not lead to significant difference in recovery
efficiency [12]. With these assumptions, the number of independent variables reduces to two. The
injection rates of CO
2
and the injection rates of water are chosen as the final optimization design
variables.
Optimization of WAG operation for a generic cylindrical aquifer with a vertical injector was
investigated. The principle of determining the size of the computational domain is that it should be able
to capture the CO
2
footprint until the end of simulation, and it should be sufficiently large so that the
boundary conditions have no significant effect on CO
2
migration. Following this principle, a hypothetical
cylindrical saline formation with radius of 3,000 m was modeled, while the radius-thickness ratio was set
to be 300. The injection well was located at the center of the domain above the bottom 20 m. Due to
International Journal of Energy and Environment (IJEE), Volume 4, Issue 3, 2013, pp.387-398
ISSN 2076-2895 (Print), ISSN 2076-2909 (Online) ©2013 International Energy & Environment Foundation. All rights reserved.

390
symmetry, only a radial slice of the domain was considered in the modeling. The computational domain
is shown in Figure 3 (a) in blue color (not to scale).




Figure 2. Schematic of the considered WAG operation




Figure 3. Computational domains for optimization of (a) WAG operation and (b) pressure management

Typical hydrogeological properties of a semi-heterogeneous saline aquifer with depth of 1,300m were
assigned to the simulation domain. No mass flow boundary condition was maintained at the ceiling and
the floor of the domain to simulate non-permeable cap-rock. Fixed-state boundary condition was applied
at the outer lateral boundaries of the domain, allowing the mass and energy to flow freely in and out of
the domain through the outer lateral boundaries as necessary. The fixed-state boundary condition
essentially represents an open system. Brine pumping was not modeled in the simulation domain by
assuming that the saline aquifer is sufficiently large and that the brine production is sufficiently far away
from the storage site; therefore, the induced CO
2
directional flow due to the presence of brine production
well is negligible. Steady-state simulations were conducted prior to the simulations of interest to
establish equilibrium condition throughout the domain. The equilibrium conditions were then used as the
initial conditions for the simulations of interest. Table A1 in the Appendix summarizes the details of the
domain properties.
Since it is inevitable that CO
2
will eventually rise and concentrate near the ceiling (caprock) of the
aquifer, the saturation of gaseous phase (SG) near the top-most layer of the simulation domain is
examined to estimate the CO
2
migration. In the plan-view of the top most layers, the final shape of the
CO
2
plume is expected to be circular due to the assumption that the formation properties of the aquifer
are homogenous. Table 1 gives details of the optimal WAG operation for each WAG cycle.


Table 1. Optimal WAG operation (per cycle)

I
CO2
(kg/s) Injection
duration (day)
I
water
(kg/s) Injection
duration (day)
WAG
ratio
Optimization fitness
(m/1000 tons of water)
36.13 13 33.35 17 0.847 0.1438


International Journal of Energy and Environment (IJEE), Volume 4, Issue 3, 2013, pp.387-398
ISSN 2076-2895 (Print), ISSN 2076-2909 (Online) ©2013 International Energy & Environment Foundation. All rights reserved.

391
The lateral extent of the CO
2
plume is determined by examining the gaseous phase distribution at the
ceiling of the aquifer. The intersection of the SG curve with the
x
-axis indicates the tip of the CO
2
plume,
i.e., the extent of CO
2
migration. Beyond this point, the aquifer is free from CO
2
contamination, so the
area up to this point is the CO
2
impact area. Any CO
2
leakage/contamination will occur only in the
impact area. Figure 4 shows the SG curve in the top-most layer of the simulation domain for optimized
WAG scheme and its comparison with SG curves obtained by three other non-optimized injection
schemes. The three other schemes are constant-gas-injection with low injection rate (low-CGI), constant-
gas-injection with high injection rate (high-CGI), and cyclic CO
2
injection. For the low-CGI case, CO
2
is
injected with a constant mass flow rate of 15.85 kg/s for 600 days; for the high-CGI case, CO
2
is injected
with a constant mass flow rate of 31.71 kg/s for 300 days; the cyclic CO
2
injection is the same as the
optimized WAG operation but without water injection. All cases have identical amount of sequestered
CO
2
as 0.822 million metric ton during the 600 days of operation.
Figure 5 shows the SG contours for the optimized WAG and non-optimized injection operations after
600 days of injection at the radial cross-section of the modeled formation.
Table 2 provides a detailed comparison among the optimized WAG and other three non-optimized
injection operations. The improvement (i.e., reduction) in plume migration is prominent.
The results presented above clearly show the benefits of the WAG operation for CO
2
sequestration.
However, we need to address the tradeoff of these benefits – i.e., the effect on other sequestration
variables, particularly the pressure, for ensuring the safety of sequestration. Pressure plays a crucial role
in ensuring the efficiency and safety of sequestration. According to the present investigation, adopting
the optimized WAG injection will cause the injection pressure to oscillate as the CO
2
injection and water
injection alternates. Considering the peak pressure under the optimized WAG injection, an 8% increase
of reservoir pressure from its pre-injection hydrostatic condition is found near the injection well.
Compared to this increase, a maximum of 2% increase in reservoir pressure is likely to be induced by the
three non-optimized injection scenarios. Although injection condition under WAG injection is harsher
due to increased injection pressure, it is not a cause of concern since the increase in injection pressure
due to WAG is small. However, it should be noted that the reservoir pressure response to the injection of
CO
2
and water is very sensitive to the hydrogeological properties of the saline formation, such as
porosity and permeability. Thus pressure analysis of WAG injection for different saline formations
should be made on a case-to-case basis. Figure 6 illustrates the injection pressure response for the four
injection scenarios studied.


0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0 50 100 150 200 250 300 350 400 450 500
Saturation of gaseous phase
Distance from domain center (m)
Cyclic CO2
Low rate CGI
High Rate CGI
Optimized WAG


Figure 4. SG underneath the caprock, optimal WAG and non-optimized injection operations
International Journal of Energy and Environment (IJEE), Volume 4, Issue 3, 2013, pp.387-398
ISSN 2076-2895 (Print), ISSN 2076-2909 (Online) ©2013 International Energy & Environment Foundation. All rights reserved.

392


Figure 5. Radial gas saturation for optimized WAG and other non-optimized injection techniques


Table 2. CO
2
migration comparison of optimized WAG and other non-optimized injection schemes

Relative to WAG Optimized
WAG
Cyclic CO
2

injection
High injection rate
CGI (15.7 kg/s)
Low injection rate CGI
(31.4 kg/s)
CO
2
plume migration 290 m 420 m 420 m 430 m
Additional migration - 130 m 130 m 140 m
Increased plume radius - 44.83 % 44.83 % 48.28 %
Increased footprint area - 109.75 % 109.75 % 119.86 %


10.2
10.4
10.6
10.8
11
11.2
11.4
00.511.522.5
Pressure (MPa)
Time since injection begines (year)
Optimized WAG
Cyclic CO2
Hight rate CGI
Low rate CGI
Pre-injection reservior condition


Figure 6. Injection pressure of optimized WAG and other non-optimized injection scenarios


4. Optimal management of injection pressure to increase the storage efficiency
Another key issue associated with GCS is the pressure response of the target storage site due to the
presence of the sequestered CO
2
. Because of the very limited compressibility of water, supercritical CO
2
,
and formation matrix, the pressure disturbance due to the injection may travel orders of magnitude faster
than the mass transportation. However, such pressure disturbance is not desirable. It compromises the
International Journal of Energy and Environment (IJEE), Volume 4, Issue 3, 2013, pp.387-398
ISSN 2076-2895 (Print), ISSN 2076-2909 (Online) ©2013 International Energy & Environment Foundation. All rights reserved.

393
energy efficiency of GCS by increasing the required injection pressure to maintain well injectivity, and
most importantly, it can potentially jeopardize the integrity of the formation matrix. Therefore, it
becomes crucial to manage the pressure response optimally to ensure the efficiency as well as the safety
of GCS operation. Two issues make the injection pressure one of the most important operation parameter
for SAGCS. One is the well injectivity and the other is the fracture pressure of the formation matrix. The
well injectivity is defined in Eq. (3); it serves as an indicator of the ability of an injection well to deliver
supercritical CO
2
to the reservoir.

2CO
injection reservior
Q
injectivity
pp
=
−
(3)

where
Q
CO2
is the injection mass rate (kg/s),
p
injection
is the injection pressure (Pa), and
p
injection
is the mean
reservoir pressure (Pa).
Following Darcy's law, the achievable CO
2
injection mass rate (
Q
CO2
) is proportional to the product of
relative permeability of CO
2
(
k
r,g
) and pressure gradient near the injection well (
∆p
). Recall that for two-
phase flow of supercritical CO
2
and brine,
k
r,g
is a function inversely proportional to the saturation of
brine (
S
b
). At the early stage of the CO
2
injection, the pore space near the injection well is primarily
occupied by brine, i.e., by high
S
b
at the adjacent area of the injection well. Consequently,
k
r,g
is
relatively low and this results in considerable difficulty to inject a given amount of CO
2
. A direct
indicator of such difficulty is the significant elevation in injection pressure, or in other words, extremely
low injectivity. The injectivity of CO
2
will not stay constant. As CO
2
injection continues, more brine will
be pushed out of the pore space adjacent to the injection well, thus lowering the
S
b
. Simultaneously,
k
r,g

will increase in a semi-exponential fashion. Therefore, during intermediate and late stage of CO
2

injection, it is expected that CO
2
injectivity should greatly improve, resulting in low injection pressure if
the injection mass rate remains unchanged. Therefore, one can obtain the schematic of the above
discussion as shown in Figure 7. It is intuitive to inject CO
2
at high injection rate, as higher injection rate
leads to greater amount of CO
2
to be sequestered for a given period, resulting in a time-efficient
injection. However, it is also true that higher injection rate requires greater injection pressure. Like any
other solid structure, geologic formation can only bear limited stress to maintain its integrity. Exerted
with excessive stress, it may fracture or collapse.



Figure 7. Schematic of injection pressure response under constant rate injection

The injection induced fracture will serve as passages for the mobile CO
2
to migrate to shallower aquifers
or even to the ground surface, endangering the ecosystem at the storage site. Therefore, every effort
should be made to ensure that under no circumstance the injection pressure shall exceed the fracture
pressure of the formation. Since the fracture pressure is an intrinsic property of the formation, it is likely
International Journal of Energy and Environment (IJEE), Volume 4, Issue 3, 2013, pp.387-398
ISSN 2076-2895 (Print), ISSN 2076-2909 (Online) ©2013 International Energy & Environment Foundation. All rights reserved.

394
to remain constant during the injection, shown as horizontal line in Figure 7. Figure 7 illustrates a crucial
issue that must be addressed. If CO
2
is pumped into the aquifer with a relatively high injection rate
(following the “High Injection Rate” curve in Figure 7), the excessive pressure response at the early
stage of injection can easily jeopardize the integrity of the formation; in contrast, if CO
2
is pumped with
a relatively low injection rate to ensure formation's integrity, the injection will be time-inefficient at the
intermediate and late stage (following the “Low Injection Rate” curve in Figure 7). If the injection rate
can be adjusted such that the injection pressure levels off, as it approaches the fracture pressure, the
overall time-efficiency of the sequestration will be greatly improved without compromising the
sequestration safety. Because the injection pressure is almost constant in such a scenario, we call it the
constant-pressure-injection (CPI). To achieve CPI, the injection rate must be adjusted with time than
being uniformly maintained. With injection rate as the design variable and threshold pressure (the
pressure limit chosen based on the formation's fracture pressure) as the constraint, optimization can be
carried out by maximizing the fitness function defined as:

2CO
threshold injection
Q
fitness function modified injectivity
pp
==
−
(4)

With fitness function approaching infinite (large value), CPI is obtained and the corresponding injection
scenario can be determined. The optimization designs with CPI were carried out using GA-TOUGH2.
Unlike the optimization design of WAG, it raised a challenge of how to describe the CO
2
injection rate as
a time-dependent continuous function, with limited discrete data points contained by the GA individuals.
The concept of Bézier curve was introduced to address this challenge. A Bézier curve is a parametric
curve frequently used in computer graphics and related fields [13]. It is defined by a set of control points,
and uses them as coefficients of a certain polynomial to describe continuous curves (refer to Appendix
for details). In this work, each CO
2
injection scenario is described by a cubic Bezier curve. An example
of cubic Bezier curve, using four control points defined as
P
1
,
P
2
,
P
3
, and
P
4
, is illustrated in Figure 8.



Figure 8. Schematic of a cubic (3rd order) Bezier curve


The CO
2
injection scenario is essentially a time dependent function of mass flow rate. Although being
smooth and continuous, discretization of the injection scenario with respect to time is needed to make the
problem tractable to numerical simulation. With such discretization, CO
2
injection rates become step
functions for each time interval, and ultimately approximate to the smooth injection scenario as time
interval becomes small enough. Injection rate for each discrete time interval is described at the midpoint
of the interval, called the sample point. Since both the information of time (
x
-axis) and flow rate (
y
-axis)
is needed to describe a certain injection scenario in GA-TOUGH2, an alternative expression of Bezier
curve in Cartesian coordinate system was derived. Assuming that the four control points are
P
0
(
x
0
, y
0
),
P
1
(
x
1
, y
1
),
P
2
(
x
2
, y
2
), and
P
3
(
x
3
, y
3
), then any point
P
(
x
(
t
)
, y
(
t
)) on the Bezier curve can be expressed as:

International Journal of Energy and Environment (IJEE), Volume 4, Issue 3, 2013, pp.387-398
ISSN 2076-2895 (Print), ISSN 2076-2909 (Online) ©2013 International Energy & Environment Foundation. All rights reserved.

395
Time:-
321
0
()
xx x
x tAtBtCtx=+++ Injection-rate:-
321
0
()
yyy
yt At Bt Ct y= +++
(5)

where the coefficients are defined as:

10 10
21 21
30 30
3( ) 3( )
3( ) 3( )

xy
xxy y
xxxy yy
Cxx Cyy
BxxC ByyC
AxxCB AyyCB
=− =−
=−− =−−
=−− − =−− −
(6)

Because the injection time must start from zero, the first control point is anchored to the y-axis by setting
x
0
= 0, i.e., P
0
(x
0
, y
0
) = P
0
(0, y
0
). Other than that, the control points' coordinates are arbitrarily generated
for each GA individual. With this formulation, an arbitrary CO
2
injection scenario beginning at t = 0 is
obtained by letting the parameter t increase from 0 to 1.
The simulation domain for the CPI study was a generic aquifer with a horizontal injection well. A thin
aquifer with the dimension of 8,000 m×8,000 m×100 m was modeled for the optimization study of CPI
operation. In the middle of the thickness direction sits an 800 m horizontal well. It is claimed by Jikich
and Sams [14] that significantly increased well injectivity could be achieved by using a horizontal well.
Due to symmetry, only a quarter of the domain is modeled, schematic of which is shown in Figure 3 (b)
in blue. Hydrogeological properties, initial conditions and boundary conditions applied to this
computational domain of Figure 3 (b) were identical to those for the WAG optimization. A threshold
pressure of 180 bar (50% increase from the initial pressure) was chosen to be the maximum allowable
injection pressure. The choice of the threshold pressure should result from a collaborative consideration
of various aspects, such as the fracture pressure and the safety factor. In the design, injection rate could
vary freely between 0 kg/s and 150 kg/s. Injection duration was 5 years.
Injection scenario obtained by the CPI design and the corresponding injection pressure is given in Figure
9. Two CGI cases, one with high injection rate (44 kg/s) and one with low injection rate (24 kg/s), are
also included in this figure for comparison. It can be clearly seen that GA-TOUGH2 successfully found
the optimized injection scenario, which keeps the injection pressure less than 1bar close to the designated
threshold pressure.
The advantage of CPI operation can be clearly seen comparing it to two CGI operations. It can be seen
that for the high rate CGI the injection pressure reaches 220 bar, a 40 bar overshoot from the threshold
pressure, and such an overshoot lasts for over 3.5 years before the injection pressure falls below 180 bar.
Such an intense and prolonged pressure overshoot can lead to catastrophic consequence to formation's
integrity. On the other hand, it can also be seen that for the low rate CGI the injection pressure diverted
from the threshold pressure at early stage after it peaked. Although the integrity of the formation is not
threatened, storage capacity is severely compromised. Only the CPI operation with five-year-averaged
injection rate of 38 kg/s ensures both storage efficiency and security.

5. Conclusions
The feasibility of adopting the water-alternating-gas (WAG) technique for CO
2
sequestration in saline
aquifers has been investigated with the objective of determining its sequestration efficiency compared to
the standard constant-gas injection (CGI) operation and its relative environmental risk (namely the extent
of plume migration). Using the GA-TOUGH2, optimization studies were conducted to determine the
most efficient WAG operations. For the generic aquifers considered, it was shown that CO
2
footprint
under the optimized WAG operation could be as small as half of the size compared to other non-
optimized injection operations. In addition, the additional water injection in WAG also brings down the
average gas saturation. The accelerated CO
2
dissolution is always desirable; since once dissolved, CO
2

becomes immobilized and is no longer considered as potential leakage risk.
GA-TOUGH2 was also successfully employed for optimizing the constant-pressure-injection (CPI)
design. In the optimized injection design it was ensured that the injection pressure never exceeded the
designated threshold pressure (the fracture pressure of the aquifer). The optimized injection pressure
design resulted in improved injectivity and thus in higher storage capacity. Both the reservoir
engineering techniques presented in this paper hold great promise towards increasing the carbon
sequestration efficiency and safety. These studies also demonstrate that GA-TOUGH2 is a
computationally accurate and efficient code to address various optimization problems in GCS.

International Journal of Energy and Environment (IJEE), Volume 4, Issue 3, 2013, pp.387-398
ISSN 2076-2895 (Print), ISSN 2076-2909 (Online) ©2013 International Energy & Environment Foundation. All rights reserved.

396

(a)


(b)

Figure 9. Injection scenarios and corresponding pressure response, CPI and two CGI injection cases


Appendix
A.1 Numerical Simulation domain and GA Setup
Typical hydrogeological properties of a semi-heterogeneous saline aquifer with depth of 1,300 m were
assigned to the simulation domain. No mass flow boundary condition was maintained at the ceiling and
floor of the domain to simulate non-permeable cap-rock. Fixed-state boundary condition was applied at
the outer lateral boundaries of the domain, allowing the mass and energy to flow freely in and out of the
domain through the outer lateral boundaries as necessary. The fixed-state boundary condition essentially
represents an open system. It should be noted that brine pumping well was not modeled in the simulation
domain. This is valid by assuming that the saline aquifer is sufficiently large and that the brine
production is sufficiently far away from the storage site; therefore, the induced CO
2
directional flow due
to the presence of brine production well is negligible. Steady-state simulations were carried out prior to
International Journal of Energy and Environment (IJEE), Volume 4, Issue 3, 2013, pp.387-398
ISSN 2076-2895 (Print), ISSN 2076-2909 (Online) ©2013 International Energy & Environment Foundation. All rights reserved.

397
the simulations of interest to establish gravity-capillary equilibrium condition throughout the domain.
The equilibrium conditions were then put back into the domain as the final initial conditions for the
simulations of interest. Table A1 summarizes details of the domain properties. It should be noticed that
there is a factor of 10 between the horizontal permeability and vertical permeability, making it easier for
CO
2
to travel in the lateral direction than upward. Geological characterizations of various saline aquifers
have shown that in the actual aquifers the horizontal permeability to vertical permeability ratio (or
equivalent directional permeability ratio) could be up to the order of hundred to thousand. For example,
the ratio is approximately 18 for the Utsira formation based on the layered model obtained from the core
sample.

Table A1. Geological properties, initial conditions and boundary conditions of the domain

Permeability (anisotropic) k
H
= 1.0 × 10
-12
m
2
, k
V
= 1.0 × 10
-13
m
2

Porosity 0.12
Residual brine saturation 0.2
Residual CO
2
saturation 0.05
Relative permeability Van Genuchten - Mualem
Capillary pressure Van Genuchten - Mualem
Thermal condition Isothermal
Boundary conditions Fixed-state on circumference of lateral boundary; no mass
flux on ceiling and floor
Initial condition P = 120 MPa, T = 45
o
C for equilibrium simulation
Initial CO
2
mass fraction X
CO2
= 0
Initial salt mass fraction X
sm
= 0.15


A.2 Bézier curve
A Bézier curve is a parametric curve frequently used in computer graphics and related fields. It is defined
by a set of control points, and uses them as coefficients of a certain polynomial to describe continuous
curves [13]. The control points of a Bézier curve can be denoted as P
0
through P
n
, with (n -1) being the
order of the Bézier curve. The order determines the complexity of the Bézier curve. A generalized
mathematical expression of an nth order Bézier curve can be formulated explicitly as follows.

()
0
() 1
n
ni
i
i
i
n
B tttP
i
−
=
⎛⎞
=−
⎜⎟
⎝⎠
∑
A1

where (n, i) is the binomial coefficient, P
i
is the i
th
control point defined prior to the generation of Bezier
curve, and t is a variable defined on [0,1]. An example of cubic Bezier curves, using four control points
defined as P
1
, P
2
, P
3
, and P
4
, is illustrated in Figure 8.

Acknowledgement
The financial support for this work was provided by the Consortium for Clean Coal Utilization (CCCU)
at Washington University in St. Louis.

References
[1]

Pruess K. TOUGH2: A General Numerical Simulator for Multiphase Fluid and Heat Flow.
Lawrence Berkeley Laboratory Report LBL-29400, Berkeley, California, 1991.
[2]

Pruess K., Oldenburg C., Moridis G. TOUGH2 User's Guide, Version 2.1. Lawrence Berkeley
Laboratory Report LBL-43134, Berkeley, California, 2011.
[3]

Class H., Ebigbo A., Helmig R., Dahle H.K., Nordbotten J.M., Celia M.A., et al. A Benchmark
Study on Problems Related to CO2 Storage In Geologic Formations. Computational Geosciences,
2009, 13(4): 409-434.
[4]

Zhang Z., Agarwal R.K. Numerical Simulation and Optimization of CO2 Sequestration in Saline
Aquifers. in: Proceedings of 10th Annual Conference on Carbon Capture and Sequestration,
Pittsburgh, PA, 2-5 May, 2011.