Numerical research on CO2 storage efficiency in saline aquifer with

Journal of Natural Gas Science and Engineering 23 (2015) 338e345
Contents lists available at ScienceDirect
Journal of Natural Gas Science and Engineering
journal homepage: www.elsevier.com/locate/jngse
Numerical research on CO2 storage efficiency in saline aquifer with
low-velocity non-Darcy flow
ZhiYong Song a, Hongqing Song a, b, *, Yang Cao b, John Killough b, Juliana Leung c,
Gang Huang a, d, Sunhua Gao b
a
School of Civil and Environmental Engineering, University of Science and Technology Beijing, China
Department of Petroleum, Texas A&M University, TX, USA
Department of Civil and Environmental Engineering, University of Alberta, Canada
d
Key Laboratory of Educational Ministry for High Efficient Mining and Safety in Metal Mine, University of Science and Technology Beijing, China
b
c
a r t i c l e i n f o
a b s t r a c t
Article history:
Received 22 December 2014
Received in revised form
12 February 2015
Accepted 13 February 2015
Available online
Low permeability saline aquifers, which are widely distributed around this world, have great potential
for injected CO2 storage. Fluid flow in low permeability layers shows characteristics of low-velocity nonDarcy flow. A mathematical model considering the effect of threshold pressure gradient (TPG) for CO2
flow and storage in low permeability saline aquifer has been developed, and the corresponding numerical model has been formulated and solved. From the numerical results, we can conclude that the
injection rate, cumulative CO2 injected, and the storage efficiency for the case with TPG are always less
than those of the case without TPG because of the sharp pressure decline and increased energy consumption. Under this paper's calculation condition, the storage efficiency when considering TPG is about
10% less than the case without considering TPG. If the TPG effect was to be ignored in the design of CO2
storage in low permeability saline aquifers, the CO2 storage efficiency will be overestimated. The research
enlarges the theoretical basis of carbon capture and storage (CCS) and provides a more accurate method
to evaluate CO2 storage efficiency.
© 2015 Published by Elsevier B.V.
Keywords:
Carbon capture and storage (CCS)
Low permeability
Saline aquifer
Storage efficiency
Low-velocity non-Darcy flow
Threshold pressure gradient (TPG)
1. Introduction
Since the 20th century, fossil fuels have been heavily exploited
with large amount of CO2 being emitted into the atmosphere,
which is believed to be one of the main reasons for global warming
and climate change (Salimi et al., 2012). The current situation of
greenhouse effect is grim; therefore, reducing the emission of CO2
to slow down or reverse the global warming trend becomes paramount (Bachu and Bennion, 2009; Court et al., 2012). Recently,
more and more countries have realized the significance of carbon
emission reduction technologies, among which carbon capture and
storage (CCS) has been considered as the most effective way in
reducing carbon emission (Zhou et al., 2008). Among many CO2
storage ways, geological storage is considered as a very attractive
method. Comparing to other types of storage reservoirs, such as
depleted oil and gas reservoirs and unmineable coalbeds, saline
* Corresponding author. School of Civil and Environmental Engineering, University of Science and Technology Beijing, Beijing 100083, China.
E-mail address: [email protected] (H. Song).
http://dx.doi.org/10.1016/j.jngse.2015.02.013
1875-5100/© 2015 Published by Elsevier B.V.
aquifer is believed to be the best geological storage site due to its
large storage capacity (Bachu, 2008; Morris et al., 2011). Studies
show that most saline aquifers have low permeability. The research
on the CO2 flow and storage in low permeability saline aquifers has
important significance for mitigating greenhouse effect and
improving CO2 storage efficiency (Okwen et al., 2010; Castelletto
et al., 2013).
When the injected CO2 is in supercritical state (CO2 critical
pressure: 7.382 MPa and critical temperature: 31.408 C), the
storage efficiency will be largely improved (Walter et al., 2012).
Under supercritical condition, the process of injection and storage
of CO2 in saline aquifer is actually a two-phase flow problem
involving supercritical CO2 and saline water. Darcy's Law describes
the condition when pressure loss is completely determined by the
viscous force, and the larger the contact area between the fluid and
solid, the larger the viscous loss (Mitrovi
c and Malone, 2011). For
most cases, Darcy's Law is valid. While fluid flow in low permeability formations, additional pressure loss will be induced by a
number of factors, such as molecular force on solideliquid interface, the swelling effect of clay minerals and the migration of rock
Z. Song et al. / Journal of Natural Gas Science and Engineering 23 (2015) 338e345
€ ller and Viebahn, 2011), rendering Darcy's Law to be
particles (Ho
invalid for describing fluid flow in low permeability reservoirs (Wu,
2002; Sukop et al., 2013; Fumagalli and Scotti, 2013). This contributes to non-Darcy flow in low permeability formations. Many
experiments show that in some cases, the fluid can start flowing
only after the applied pressure gradient overcomes certain initial
pressure gradient (Zeng et al., 2011), and this certain initial pressure
gradient is called threshold pressure gradient or TPG (no flow occurs when pressure gradient is less than TPG).
The existence of TPG has been widely reported. As early as 1885,
through tests on fluid flow in tight rock, Newell concluded that for
flow in tight rock, there is no simple linear relationship between
velocity and pressure gradient (King and Slichter, 1899). In 1919,
Brownlie studied flow in aquifer and found that flow occurs only
after pressure gradient exceeds a certain value (Miller-Bownlie,
1919). In 1970s, both Mitehell and Russell performed experiments
studying low-velocity water flowing through unconsolidated soils
and loose mixtures, and they found that the relationship of flow
rate and pressure gradient does not follow Darcy's Law (Mitchell
and Younger, 1967; Russell and Swartzendruber, 1971). Later,
Prada and Civan tested saline water flow through tight rock samples, and concluded that TPG exists when the velocity is less than
1.219 m/d (Prada and Civan, 1999). Through analyzing core data,
Ren et al. systemically investigated the influence of permeability,
viscosity, and water saturation on TPG and proposed an empirical
equation for calculating TPG, which facilitated the reservoir
parameter determination for low permeability reservoirs (Ren
et al., 2007). However, much of the research on low velocity nonDarcy flow has focused on oil and gas reservoirs.
Over last decade, the CO2 storage has become a popular topic.
Many scholars have devoted themselves to studying the process of
CO2 injection into saline aquifer and the improvement of storage
efficiency. Bachu et al. and Vanessa et al. studied the influence of
the content of other gases (CH4, N2, SO2, and H2S), the geological
condition of storage, and the fluid state on the CO2 injection process, which can be used to monitor the injection process and prevent leakage (Bachu and Bennion, 2009; Vanessa et al., 2014). Xi
Jiang numerically simulated and analyzed the CO2 leakage during
the long-term storage of CO2 in saline aquifers (Jiang, 2011). Kopp
studied the CO2 storage capacity in saline aquifers using dimensionless analysis (Kopp et al., 2009). Okwen et al. established the
CO2 storage efficiency evaluation model (Okwen et al., 2010; Huang
et al., 2014). However, the aforementioned researches are all based
on Darcy's Law. As pointed out previously, in low permeability saline aquifers, low-velocity fluid flow leads to non-Darcy flow, and
considering only Darcy flow in evaluating the CO2 flow and storage
in saline aquifers cannot achieve enough accuracy (Pruess and
Muller, 2009; Mijic et al., 2014). In order to more accurately access the storage capacity of saline aquifers and the injection efficiency of CO2, the TPG of fluid flow in low permeability saline
aquifers needs to be considered, and the corresponding appropriate
mathematical model needs to be established.
Few studies have been conducted to investigate the effects of
TPG on CO2 flow and storage in saline aquifers, on accounting of
this, a novel supercritical CO2/saline water two-phase flow model
incorporating the effect of TPG is proposed in this paper to simulate
the process of CO2 flow and storage in saline aquifers and, thereby,
to evaluate the CO2 storage capacity and efficiency in saline aquifers. Through numerical simulation and analysis, the influence of
various parameters (especially TPG) on CO2 storage efficiency is
investigated. This study provides the computational and theoretical
basis for the storage site selection and risk appraisal in the process
of supercritical CO2 injection and storage in saline aquifers.
The following contents are included in this paper: (1) establish
the supercritical CO2/saline water two phase flow model to
339
describe CO2 flow in low permeability saline aquifer and summarize the appropriate solving conditions based on the geological
characteristics of saline aquifers; (2) build the corresponding numerical model and set the related initial and boundary conditions;
(3) simulate two injection schemes (constant rate injection and
constant bottom hole pressure (BHP) injection) to investigate the
influence of TPG on CO2 flow and storage efficiency; (4) discuss the
characteristics of CO2 storage in low permeability saline aquifers
based on the above investigation, which will provide guidance for
future CO2 geological storage in saline aquifers.
2. Mathematical model for low-velocity non-Darcy flow
2.1. Physical model description
As mentioned before, the supercritical CO2 flow and storage in
saline aquifers is a very complex process and involves two-phase
flow in porous media. In this paper, a cylindrical vertical saline
aquifer with the radius of re is considered. In order to focus on the
influence of TPG to CO2 injection and storage, the saline aquifer is as
assumed to be homogeneous. A vertical injection well is drilled in
the center of the reservoir with the well radius of 0.1 m. The
thickness of the saline aquifer is designated as h. Fig. 1 shows the
schematic of the physical model. Two different injection schemes
are simulated in this paper. One is constant rate injection; the other
is constant bottom-hole pressure (BHP) injection. The corresponding acquired simulation results of these two cases with and
without TPG consideration are compared to show the influence of
non-Darcy flow on these two production schemes.
The following constraints and assumptions are invoked in the
modeling process and theoretical analysis:
(1) The porous medium is initially saturated with brine. After the
injection of CO2, the residual saturation of brine is Srw.
(2) The temperature of the saline aquifer is constant during the
simulation.
(3) Temperature and pressure in geological formation is high
enough to keep CO2 in supercritical state.
(4) The mixing of CO2 and brine is completed instantly during
continuous injection, and the brine and the supercritical CO2
are immiscible.
(5) The injection pressure P is constrained to within 75% of the
stress of the upper layer.
With the above model, it can be shown that the injected supercritical CO2 will flow radially and uniformly away from the injection point into the saline aquifer.
2.2. Governing equations of low-velocity non-Darcy flow
As CO2 is injected into the saline aquifer, supercritical CO2 will
Fig. 1. Schematic of the physical model after injection of CO2.
340
Z. Song et al. / Journal of Natural Gas Science and Engineering 23 (2015) 338e345
Fig. 2. Flow chart of IMPEM method.
As for the momentum equations, the supercritical CO2 flow in
low permeability saline aquifer bears characteristics of non-Darcy
flow, and the threshold pressure needs to be included into
consideration. Therefore, the general momentum equations for
two-phase supercritical CO2 and brine flow can be expressed as:
k$krc
vc ¼ ðVPc rc gsinq VPthc Þ
mc
(2a)
k$krw
ðVPw rw gsinq VPthw Þ
vw ¼ mw
(2b)
For single aqueous phase flow, the momentum equation is
expressed as:
k
vw ¼ ðVPw rw gsinq VPthw Þ
mw
Fig. 3. Injection rate vs time for constant rate scheme.
gradually expand with time. The continuity equations for the supercritical CO2 and brine are (Song et al., 2014; Zhu et al., 2011):
i
h
v
V$ rc $Vc ¼ ð∅rc Sc Þ
vt
(1a)
i
h
v
V$ rw $Vw ¼ ð∅rw Sw Þ
vt
(1b)
where rc, rw are the density of CO2 and brine, respectively, kg/m3;
Vc , Vw are the percolation velocity vector of CO2 and brine,
respectively, m/s; Sc, Sw are the saturation of CO2 and brine.
(3)
where krc krw are the relative permeability of CO2 and brine,
respectively; k is the permeability of saline aquifer; mc, mw are the
viscosity of CO2 and brine, respectively; Pc, Pw are the pressure of
CO2 and brine, respectively; g is the gravitational constant; q is the
angle between flow and horizontal direction; Pthc, Pthw is the
threshold pressure for CO2 and brine, respectively.
2.3. State equations
As stated in Section 2.1, the mixture of CO2 and brine completely
fills the porous medium instantaneously during the process of
continual injection of CO2, thus the sum of saturations should be
equal to one, that is:
Sc þ Sw ¼ 1
(4)
A suitable permeability saturation relationship curve is
Z. Song et al. / Journal of Natural Gas Science and Engineering 23 (2015) 338e345
important in predicting CO2 storage efficiency. Measured permeability saturation curves usually vary among different layers of the
saline aquifers (Pini and Benson, 2013). Court has summarized
some empirical equations to attain the permeability saturation
curve and the corresponding data. In this paper, we choose the
following relationships (Court et al., 2012):
krc ¼ krcmax
Sc Scr
1 Scr Swr
krw ¼ krwmax
ð∅rc Sc Þ
a
Sc Scr
1 Scr Swr
(5a)
b
341
injection well located in a cylindrical reservoir, for production well
case, the “þ” sign in front of Tpgc(i±1),Tpgc(i) will become “-”. This is
because the threshold pressure will always be acting as a resistance
to fluid flow. In our actual formulation, an “if” statement is implemented first to check if the pressure difference between the
neighboring two cells is less than the threshold pressure between
them; if the output is “yes”, then no flow condition is incurred, and
the calculation of Eq. (7a) is skipped. It should be mentioned that
for simplicity, we have ignored the source/sink/gravity terms in this
discretizing demonstration, and the azimuthal symmetry and independence of z for the cylindrical coordinate.
(5b)
2
ð∅rc Sc Þ
1 6Tcðiþ12Þ Pcðiþ1Þ Pci þ TpgcðiÞ riþ12 ri þ Tpgcðiþ1Þ riþ1 riþ12
¼
4
Dri
riþ1 ri
Dt
nþ1
n
3
Tcði1Þ PcðiÞ Pcði1Þ þ Tpgcði1Þ ri1 ri1 þ TpgcðiÞ ri ri1
7
2
2
2
5
ri ri1
where Scr, Swr are the residual saturations of CO2 and brine,
respectively; krcmax, krwmax are the maximum relative permeability
of CO2 and brine, respectively; a, b are constants depending on the
pore structure of saline aquifer rock. And the specific values of the
above coefficients (krcmax, krwmax, a, and b) can be obtained by linear
regression from sample test data.
3. Numerical solutions
Based on the finite-difference discretization technique, a new
numerical program considering the effect of TPG was developed in
our paper to simulate the CO2-brine two-phase displacement
process. The material balance equations considering TPG effect of
CO2 phase and brine phase are used as the governing equations,
which are shown in Eq. (6a) and Eq. (6b).
CO2 phase mass balance equation:
vð∅rc Sc Þ
¼ V$
vt
kkrc
rc V Pc rc gD Tpgc Ds þ qc
mc
(6a)
ri±1 ¼
ri±1 þ ri
2
(7b)
ri±1 ¼
ri±1 ri
ln ri±1 ri
(7c)
2
2
The transmissibility coefficient T is defined as in Eq. (7d):
Tcði±1Þ ¼
vð∅rw Sw Þ
kkrw
¼ V$
rw V Pw rw gD Tpgw Ds
þ qw
vt
mw
2
(6b)
where ∅ is porosity; k is absolute permeability; D is vertical depth;
Ds is flow length; Tpgc, Tpgw is the threshold pressure gradient for
CO2 and brine, respectively; and qc, qw is source/sink term of CO2
and brine, respectively. The capillary pressure equation is:
Pc ¼ Pw Pccw ðSw Þ
where ri is the radial coordinate of the grid block center of cell i. The
“center” is defined here as the node location at which properties
are representative of the grid block and may not necessarily coincide with the geometric center. Dri is the length of the cell i, which
equals to riþ1 ri1 , the radial locations of the grid block bound2
2
aries for cell i. Different options can be selected to generate the grid
block centers and boundaries; for example, the grid block centers
can be either uniformly or logarithmically distributed along the
radial direction, and the grid block boundary riþ1 ; ri1 can be
2
2
calculated using either (7b) or (7c).
Water phase mass balance equation:
(6c)
Where Pccw is the CO2-water capillary pressure, which is a function
of saturation.
To demonstrate the discretization scheme used in this paper, Eq.
(6a) is chosen as an example and discretized using the finite difference method. Eq. (7a) is the acquired discretization form in a
cylindrical coordinate. Note that Eq. (7a) is derived for a single
(7a)
kkrc
r
mc c
(7d)
i±12
Note that in Eq. (7a)-Eq. (7d), the subscript of i represents the
grid number, the superscript of n represents the time step.
The IMPEM (implicit pressure explicit component mass) option
is chosen as the computational method. In each iteration, the
pressure equation considering the influence of TPG is solved first,
and then the component masses will be calculated explicitly using
the governing equations; after the phase stability analysis and flash
calculation, the other parameters/coefficients (such as relative
permeability, viscosity, and density) can be updated correspondingly. During the calculation step, Peng-Robinson EOS and LohrenzeBrayeClark correlation (Lohrenz et al., 1964) are modified
and used to calculate the fluid density and viscosity, respectively.
The relative permeability curve of supercritical CO2 and brine is
adopted from Fig. 4 of Song et al. (2014). Special care has already
been taken to guarantee the stability of this computation method. A
schematic showing the main calculation steps is shown in Fig. 2.
342
Z. Song et al. / Journal of Natural Gas Science and Engineering 23 (2015) 338e345
Fig. 5. Injection rate vs time for constant pressure scheme.
Fig. 4. Cumulative CO2 injected vs time for constant rate scheme.
4. Results and discussions
Two injection schemes (constant rate injection and constant
BHP injection) were applied in a horizontal saline aquifer for the
simulation. For constant injection rate scheme, the injection rate is
set as the initial constraint; and as the injection continues, the BHP
will increase gradually to some extent, and the model will switch to
constant BHP injection constraint (i.e., constant injection pressure)
to prevent the formation from being fractured. For both schemes,
the injection rate, cumulative CO2 injected, pressure profile and the
CO2 storage efficiency (refer the definition in Part 4.3) will be
investigated and shown in the corresponding figures. We will
compare the results for both schemes with and without TPG to
illustrate the significance of TPG influence in CO2 injection and
storage in saline aquifer. A typical data set for our numerical
simulation is shown in Table 1.
4.1. Injection characteristics with TPG and without TPG
Fig. 3 and Fig. 4 compare the injection rate and cumulative CO2
injected for the constant rate injection scheme with and without
TPG respectively. The constant rate is 342.5 ton/day (about
0.125 Mton/year), and the subsequent constant BHP constraint is
22 MPa. It is observed from Fig. 3 that the stable injection time with
TPG will be shortened compared to the case without TPG, specifically, a comparison of about 3200 days with TPG as opposed to
4260 days without TPG. We can also estimate from Fig. 4 that after
about 20 years, the cumulative injection of the case with TPG will
Table 1
Data used for numerical simulation.
Parameters
Symbol
Unit
Values
Wellbore radius
Reservoir radius
Saline aquifer thickness
Saline aquifer porosity
Temperature
Initial pressure
Injection rate for constant rate scheme
BHP for constant BHP scheme
TPG
Permeability
Flow angle
rw
re
h
∅
T
Pi
q
Pwf
TPG
K
m
m
m
%
C
MPa
ton/day
MPa
MPa/m
mD
q
0.1
5000
30
10
35
10
1389.8
22
0.001
5
0
Fig. 6. Cumulative CO2 injected vs time for constant pressure scheme.
be 11% less than the case without TPG (1.89 Mton vs 2.13 Mton).
Fig. 5 and Fig. 6 show the comparison of the injection rate and
cumulative CO2 injected for the constant BHP injection scheme
with and without TPG, respectively. We set the constant BHP as
22 MPa. From Fig. 5, it is noted that the injection rate for the case
with TPG is apparently smaller than the one without TPG, and towards the end of the injection period, their rates are getting closer
to each other. The similar conclusion can be achieved from Fig. 6:
after 20 years, the cumulative injection of the case with TPG will be
about 14% less than the case without TPG (1.97 Mton vs 2.29 Mton).
For both injection schemes, when we consider TPG effects, the
injection of CO2 becomes more difficult, and the cumulative CO2
injected is significantly less. The reason behind this observation
should be that the existence of TPG introduces additional resistance
to the fluid flow and CO2 injection, and much of the energy provided is dissipated in overcoming TPG instead of facilitating CO2
injection and driving fluid moving. Moreover, we speculate that a
sharper pressure decline would occur for the schemes with TPG,
which will be tested and verified in the next part.
Z. Song et al. / Journal of Natural Gas Science and Engineering 23 (2015) 338e345
343
Fig. 9. Reservoir pressure profile at 1000 day for constant BHP injection scheme.
Fig. 7. Reservoir pressure profile at 1000 day for constant rate injection scheme.
4.3. Storage efficiency with TPG and without TPG
4.2. Pressure characteristics with TPG and without TPG
Fig. 7 and Fig. 8 show the saline aquifer pressure profile at 1000
days for the constant rate injection scheme with and without TPG,
respectively. From this figures, we notice that the pressure in the
region around the wellbore is considerably higher for the case with
TPG than the one without TPG. This means that to keep the same
injection rate, larger pressure needs to be provided in the wellbore
when considering TPG. Indeed, we can observe that the pressure of
the case with TPG declines much faster than the one without TPG,
which is quite reasonable considering that a lot of the energy is
consumed by counteracting the threshold pressure influence.
Figs. 9 and 10 show the saline aquifer pressure profile at 1000
days for the constant BHP injection scheme with and without TPG.
From this figure, we can also infer that the pressure for the case
with TPG decreases much faster than that of the case without TPG.
This verifies our speculation and reflects the significant influence of
TPG in pressure distribution of CO2 injection and storage in saline
aquifer.
We have defined the CO2 storage efficiency as the volume of CO2
injected to the pore volume of the saline aquifer both at underground condition. Fig. 11 and Fig. 12 show the corresponding results
for the two injection schemes. As illustrated by the two figures, the
storage efficiency for the case with TPG is always less than the one
without TPG. After 20 years' operation, for both injection schemes
the discrepancy is approximately 10% comparing to the cases
without TPG.
5. Conclusion
(1) A novel mathematical model considering the effect of
threshold pressure gradient for CO2 flow and storage in low
permeability saline aquifer has been developed, and the
corresponding numerical model has been completed and
solved. Two injection schemes, constant rate injection
scheme and constant BHP injection scheme, have been
investigated and analyzed in the numerical simulation.
(2) From the numerical results, we can observe that for both
operation schemes, the injection rate, cumulative CO2
injected, and the storage efficiency for the case with TPG are
Fig. 8. Pressure distribution at 1000 day for constant rate injection scheme (a) with TPG; (b) without TPG.
344
Z. Song et al. / Journal of Natural Gas Science and Engineering 23 (2015) 338e345
Fig. 10. Pressure distribution at 1000 day for constant BHP injection scheme (a) with TPG; (b) without TPG.
always less than those of the case without TPG. For example,
under our calculation condition, the storage efficiency when
considering TPG is about 10% less than the case without
considering TPG in our studied case. This can be explained
from the pressure profile, which shows that when TPG is
included, the pressure declines sharply, and more energy is
needed.
(3) CO2 injection and storage in low permeability saline aquifer
involves non-Darcy flow, and the threshold pressure
gradient effect cannot be ignored in the design of CO2 storage
in saline aquifer project. Otherwise, the CO2 storage efficiency will be overestimated in low permeability saline
aquifers.
(4) The research on the CO2 flow and storage in low permeability
saline aquifers enlarges the theoretical basis of CCS and
provides a more accurate method to evaluate CO2 storage
efficiency. It has important significance for greenhouse gas
control.
Fig. 11. CO2 storage efficiency for constant rate scheme.
Acknowledgment
This work is supported by the Fundamental Research Funds for
the Central Universities under Grant No. FRF-TP-14-076A2.
References
Fig. 12. CO2 storage efficiency for constant BHP scheme.
Bachu, S., Bennion, D.B., 2009. Chromatographic partitioning of impurities contained in a CO2 stream injected into a deep saline aquifer: Part 1. Effects of gas
composition and in situ conditions. Int. J. Greenh. Gas Control 3 (4), 458e467.
Bachu, S., 2008. CO2 storage in geological media: role, means, status and barriers to
deployment. Prog. Energy Combust. Sci. 34 (2), 254e273.
, O., Daniel, J.M.,
Castelletto, N., Teatini, P., Gambolati, G., Bossie-Codreanu, D., Vincke
Battistelli, A., Marcolini, M., Donda, F., Volpi, V., 2013. Multiphysics modeling of
CO2 sequestration in a faulted saline formation in Italy. Adv. Water Resour. 62,
570e587.
Court, B., Bandilla, K.W., Celia, M.A., Janzen, A., Dobossy, M., Nordbotten, J.M., 2012.
Applicability of vertical-equilibrium and sharp-interface assumptions in CO2
sequestration modeling. Int. J. Greenh. Gas Control 10, 134e147.
Fumagalli, A., Scotti, A., 2013. A numerical method for two-phase flow in fractured
porous media with non-matching grids. Adv. Water Resour. 62, 454e464.
Huang, X., Bandilla, K.W., Celia, M.A., Bachu, S., 2014. Basin-scale modeling of CO2
storage using models of varying complexity. Int. J. Greenh. Gas Control 20,
73e86.
€ller, S., Viebahn, P., 2011. Assessment of CO2 storage capacity in geological forHo
mations of Germany and Northern Europe. Energy Procedia 4, 4897e4904.
Jiang, X., 2011. A review of physical modelling and numerical simulation of longterm geological storage of CO2. Appl. Energy 88 (11), 3557e3566.
Kopp, A., Class, H., Helmig, R., 2009. Investigations on CO2 storage capacity in saline
aquifers. Int. J. Greenh. Gas Control 3 (3), 263e276.
King, H.F., Slichter, C.S., 1899. Principles and Conditions of the Movement of Ground
Z. Song et al. / Journal of Natural Gas Science and Engineering 23 (2015) 338e345
Water. Government Printing Office, pp. 59e294.
Lohrenz, J., Bray, B.G., Clark, C.R., 1964. Calculating viscosity of reservoir fluids from
their composition (Oct. 1964). J. Petrol. Tech. 1171e1176. Trans., AIME, 231.
Mijic, A., LaForce, T.C., Muggeridge, A.H., 2014. CO2 injectivity in saline aquifers: the
impact of non-Darcy flow, phase miscibility, and gas compressibility. Water
Resour. Res. 50, 4163e4185.
Mitchell, J.K., Younger, J.S., 1967. Abnormalities in Hydraulic Flow through Fine
Grained Soils. Am. Soc. for Test. and Mater., p. 106
Miller-Bownlie, T.A., 1919. Subsoil water in relation to tube wells. India East. Eng. 42
(2), 116e131.
Mitrovi
c, M., Malone, A., 2011. Carbon capture and storage (CCS) demonstration
projects in Canada. Energy Procedia 4, 5685e5691.
Morris, J.P., Detwiler, R.L., Friedmann, S.J., Vorobiev, O.Y., Hao, Y., 2011. The largescale geomechanical and hydrogeological effects of multiple CO2 injection
sites on formation stability. Int. J. Greenh. Gas Control 5 (1), 69e74.
Okwen, R.T., Stewart, M.T., Cunningham, J.A., 2010. Analytical solution for estimating storage efficiency of geologic sequestration of CO2. Int. J. Greenh. Gas
Control 4 (1), 102e107.
Pini, R., Benson, S.M., 2013. Simultaneous determination of capillary pressure and
relative permeability curves from core-flooding experiments with various fluid
pairs. Water Resour. Res. 49, 3516e3530.
Prada, A., Civan, F., 1999. Modification of Darcy's law for the threshold pressure
gradient. J. Petrol. Sci. Eng. 2 (22), 237.
Pruess, K., Muller, N., 2009. Formation dry-out from CO2 injection into saline
aquifers: 1. Effects of solids precipitation and their mitigation. Water Resour.
Res. 45 (W03), 402.
Russell, D.A., Swartzendruber, D., 1971. Flux Gradient Relationships for Saturated
Flow of Water through Mixtures of Sand, Silt, & Clay. Soli Sci. Soc. of Am. Proc.,
p. 21
345
Ren, X.J., Qi, Y., Zhang, Y.S., 2007. Research development of low-velocity non-Darcy
flow in porous media. J. Xi'an Shiyou Univ. (Nat. Sci. Ed.) 22 (S1), 32e36.
Salimi, H., Wolf, K., Bruining, J., 2012. The influence of capillary pressure on the
phase equilibrium of the CO2-water system: application to carbon sequestration
combined with geothermal energy. Int. J. Greenh. Gas Control 11, S47eS66.
Song, H.Q., Huang, G., Li, T.X., Zhang, Y., Lou, Y., 2014. Analytical model of CO2
storage efficiency in saline aquifer with vertical heterogeneity. J. Nat. Gas Sci.
Eng. 18, 77e89.
Sukop, M.C., Huang, H., Alvarez, P.F., Variano, E.A., Cunningham, K.J., 2013. Evaluation of permeability and non-Darcy flow in vuggy macroporous limestone
aquifer samples with lattice Boltzmann methods. Water Resour. Res. 49,
216e230.
Vanessa, F.Y., Hamid, R., Masoud, A., 2014. Impact of light component stripping
during CO2 injection in Bakken formation. In: Unconventional Resources
Technology Conference, pp. 25e27.
Walter, L., Binning, P.J., Oladyshkin, S., Flemisch, B., Class, H., 2012. Brine migration
resulting from CO2 injection into saline aquifers e an approach to risk estimation including various levels of uncertainty. Int. J. Greenh. Gas Control 9,
495e506.
Wu, Y., 2002. An approximate analytical solution for non-Darcy flow toward a well
in fractured media. Water Resour. Res. 38, 5-1e5-7.
Zeng, B., Cheng, L., Li, C., 2011. Low velocity non-linear flow in ultra-low permeability reservoir. J. Petrol. Sci. Eng. 80 (1), 1e6.
Zhu, W.Y., Song, H.Q., Huang, X.H., Liu, X., He, D.B., Ran, Q.Q., 2011. Pressure characteristics and effective deployment in a water-bearing tight gas reservoir with
low-velocity non-Darcy flow. Energy Fuels 25 (4), 1111e1117.
Zhou, Q., Birkholzer, J.T., Tsang, C., Rutqvist, J., 2008. A method for quick assessment
of CO2 storage capacity in closed and semi-closed saline formations. Int. J.
Greenh. Gas Control 2 (4), 626e639.