The developed model in the previous section is utilized to understand processes and driving forces active during leakage of CO2 into the shallower formations. This section is organized as follows. First, the effect of dimensionless numbers and interaction of forces on the displacement process and leakage is investigated. Next, the developed model is used to assess leakage in seven formations located in Alberta, Canada, which are considered potential options for geological storage of CO2.
3.1. Interaction of Gravity, Capillary, and Viscous Forces
To investigate the effect of forces acting on the fluid flow and rate of leakage, we define seven different datasets. Detailed comparison and properties of each set is presented in
Table 1. The following properties are assumed to be the same for all the seven datasets. Length of the domain (
) is considered to be 500 m. Density difference between CO
2 and brine (
) is assumed to be 300 kg/m
3 and porosity (
) is 0.2. Brine and CO
2 viscosity are assumed to be 0.86 and 0.06 mPa·s, respectively. Absolute permeability is taken to be 100 mD and residual water saturation (
) is assumed to be 0.3. Parameters used for these datasets are only for comparison and they are not related to a specific reservoir. The last three rows in
Table 1 show the calculated mobility ratio,
and
. Dataset 1 is considered as base case. In each dataset, the changing parameter is bolded in
Table 1. Two analysis groups have been established. First, the effect of changes in
and
is investigated, while
,
and
are kept constant (Datasets 2–4). Second, changes of relative permeability parameters of CO
2 and brine system are examined, which include the effect of mobility ratio and Corey exponents
nb and
nc (Datasets 5–7). Changes in gas saturation profile and gas dimensionless velocity are examined for each dataset. Breakthrough time is considered to be the time when migrating CO
2 appears at the outlet boundary.
Figure 3 shows the parameters map of
space. A reference equilibrium state between gravitational and viscous forces is indicated with dotted line at
and between capillary and viscous forces at
. In
Figure 3, the lower left sector represents domination of viscous forces over capillary and gravitational forces. As we move from this sector to the right or top, viscous forces lose their influence in favor of capillary (lower right sector) or gravitational (upper left sector) forces, respectively. Finally, in the upper right sector, capillary and gravitational forces dominate over viscous forces.
Capillary, gravity and viscous functions are plotted for all seven datasets in
Figure 4a–c. The shape and value of these functions are influenced by Corey exponents in relative permeability equation (
nc and
nb), and mobility ratio. Capillary function
(
Figure 4a) and gravity function
(
Figure 4b) have a bell shape, whereas shape of
is the same as the fractional flow equation in Buckley–Leveret problem.
In the first four datasets, dimensionless functions , and are same. In Datasets 5–7, relative permeability parameters are changed to evaluate their effect on flow process. Migration of CO2 plume depends on balance of these forces, which determines the security of storage.
Figure 5 shows the normalized gas saturation and contribution of different forces in CO
2 dimensionless velocity versus dimensionless length at time
for Datasets 1 to 4.
For Dataset 1 (
Table 1),
and
have the same magnitude and less than one, and position of this dataset in the parameter space map is in the lower left sector of
Figure 3. This is translated to dominance of viscous forces over capillary and gravity forces. As shown in
Figure 5, higher viscous forces lead to a CO
2 plume with sharp front. As a result, plume migration is slowest among other datasets (Datasets 2–4). In this case, gravitational forces are rather weak, leading to a low buoyancy-induced upward migration of CO
2.
In Dataset 2, the effect of capillary entry pressure,
, is investigated. By changing the capillary entry pressure (
) from 0.2 MPa to 1.5 MPa, capillary number (
) increases up to 1.161, while the gravity number (
) remains the same as the one used in Dataset 1. This leads to a shift to the lower right corner of the parameter map, as shown in
Figure 3. Increasing capillary number will increase the influence of capillary forces over viscous forces. Stronger capillary forces lead to a more diffusive-like front propagation. An earlier breakthrough is a result of higher capillary forces, as shown in the saturation distributions and velocity profiles for Datasets 1 and 2 in
Figure 5a,b (and later in
Figure 6a). As shown in
Figure 5c, as
increases in Dataset 2, contributions of capillary forces on CO
2 plume velocity (
) increases. As the effect of capillary forces increases, the inlet dimensionless velocity (
) of the migrating CO
2 takes values greater than one. This is because the dimensionless velocity of the migrating CO
2 is given by
. At high capillary forces, there is backward flow of brine as CO
2 migrates upward. This leads to
values to be less than zero that results in
values greater than one. In other words, a dimensionless velocity greater than one indicates backward flow of formation brine from the leakage pathway. This effect is particularly important in the early times and, as the plume evolves, the effect of capillary diminishes.
The effect of gravitational forces is examined using Dataset 3 while is kept similar to Dataset 1. As the density difference or the tilt angle () increase the effect of gravity on CO2 plume migration increases. The gravity number () varies up to 1.139 for a tilt angle of (or a vertical leakage pathway). By increasing , the effect of gravity forces on dimensionless velocity () increases and therefore a more buoyant flow regime is established leading to a faster plume evolution for Dataset 3, compared to Dataset 1. Such a flow regime may be preferred since it creates an extended contact between the injected CO2 and brine leading to higher dissolution of CO2 in brine. However, increasing enhances the effect of gravity segregation and leads to an earlier breakthrough of CO2 and possibly an enhanced risk of leakage, which is not desirable.
Next, we study the effect of total Darcy velocity by changing
= 3 × 10
−6 m/s to a lower value of
= 3 × 10
−7 m/s. Decreasing
causes an increase in both
and
. However, since velocity appears in both numbers, their ratio will stay the same. This will lead to a move to the upper right corner of the parameter map shown in
Figure 3. By moving to this sector, viscous forces lose their influence in favor of both capillary and gravity forces. The combined effect of increasing capillary and gravity forces will cause fastest evolution of CO
2 plume compared to other datasets. In
Figure 6a, the average gas saturation is plotted against dimensionless time for Datasets 1–4. In terms of leakage, Dataset 1 results in a more compact and less diffusive front with delayed breakthrough of the leaked CO
2 compared to the other cases. However, in such a case, a sudden release of CO
2 is expected.
On the other hand, when capillary forces are dominant (Dataset 2), the leaking CO
2 forms a diffusive front and consequently an earlier breakthrough of the gradually leaking CO
2 is expected. This may be practically important since it provides more time to take remedial actions. Similarly, increasing gravity effect in Dataset 3 results in an earlier breakthrough time. It is worth mentioning that the effect of increasing
by one order of magnitude on accelerating the breakthrough time, is much less than that of increasing
. Finally, for Dataset 4, the breakthrough time is the lowest among the other datasets due to domination of both capillary and gravity forces. In addition, as depicted in
Figure 5b, increasing dimensionless velocity (
) to values higher than one is more pronounced in this case due to the simultaneous effect of gravity and capillary. Early leakage of brine may be used as an indicator of subsequent leakage of CO
2. However, in cases such as Dataset 4, significant back flow of brine may occur, which can lead to less brine leakage prior to CO
2 leakage. This effect could be emphasized especially for higher values of
and
, where it could result in CO
2 leakage to shallower depths without significant leakage of brine.
We further study the effect of relative permeability parameters on the displacement process. Relative permeability depends on several factors such as pore size characteristics, wettability of fluids and phase saturation [
33]. Neglecting these dependencies will affect the interpretation of short and long-term fate of the injected CO
2 in deep saline aquifers. Therefore, detailed laboratory measurements are necessary to predict the dependency of the relative permeability to saturation of phases present in the medium. In our model, shape of the relative permeability curve is determined by the Corey exponents and endpoint relative permeability to each phase.
In this section, effects of mobility ratio (which could be due to changes on
or viscosity ratio),
nb and
nc on plume migration is investigated through Datasets 5–7. These parameters affect shapes of
,
and
functions. For simplicity, and to illustrate the effects, we considered
nc = nb = 2 for Datasets 1–5. The normalized gas saturation and contribution of different forces on CO
2 dimensionless velocity, versus dimensionless length is plotted in
Figure 7 at time
for Datasets 1 and 5–7.
In Dataset 5,
is taken to be 0.065 (one order less than
in Dataset 1). For a constant total velocity, reducing CO
2 endpoint relative permeability by one order of magnitude causes a decrease in
,
and
by the same order. As shown in
Figure 3, this will cause a shift to the lower left sector. Reducing
and
will make the displacement process highly viscous dominant. Additionally, unlike previous datasets, a change in mobility ratio will cause a change in capillary, gravity and viscous functions. As shown in
Figure 4a,b, a decrease in mobility ratio from
to
will dramatically increase the values of
and
functions. However, since the process is highly viscous dominant (due to small values of
and
), the contribution of these forces on plume velocity is negligible. Influence of reducing
on
is shown in
Figure 4c (comparing Dataset 5 with Dataset 1). From the frontal advance theory, a higher average saturation of CO
2 behind front is obtained for Dataset 5. As expected, the results shown in
Figure 7 reveal that a relative permeability curve with low
results in less CO
2 propagation velocity and a significant delay of the breakthrough time.
In Datasets 6 and 7, the effect of Corey exponents (as a measure of wettability) on behavior of CO
2 plume is investigated. Changes in Corey exponents will not change the dimensionless numbers of
and
and therefore position of various forces in the parameter space shown in
Figure 3 will be the same as Dataset 1. However, the Corey exponents affects shapes of functions
,
and
. In Dataset 6,
nc is kept the same as the one in Dataset 5 (
nc = 2), and
nb is increased to 4. As
nb increases, the relative permeability to brine,
and
decrease. As shown in
Figure 4c, by increasing
nb, the average saturation behind the front reduces. Therefore, increasing
nb will result in a faster plume evolution, and a decrease in time of breakthrough. This effect is better shown by comparing Datasets 6 and 1 in
Figure 7. Increasing
nc, from 2 to 4 in Dataset 7 results in a reduction in relative permeability of CO
2. Similar to Dataset 6, values of
and
will decrease, but the average saturation behind the front (
Figure 4c) increases and therefore a more efficient displacement and a delayed breakthrough time is achieved in this scenario as compared to Dataset 6.
Since the process is viscous dominant in Datasets 1 and 5–7, contribution of gravity and capillary forces on CO2 plume velocity is negligible, and no countercurrent displacement of brine is observed for these cases. Therefore, in these cases, brine will be displaced along with CO2 to the shallower formation.
Figure 6b shows the average normalized saturation versus dimensionless time for Datasets 1 and 5–7. The results showed that a lower endpoint relative permeability of CO
2 and therefore lower mobility ratio postpone the breakthrough time. Additionally, increasing
nc increases the breakthrough time.
It is important to note that the overall effect of the parameters that appear in both capillary and gravity numbers (
and
) as well as capillary, gravity and viscous functions (
,
, and
), determine the controlling mechanisms. These parameters (density, viscosity, capillary pressure, relative permeability, etc.) are dependent on the in-situ conditions of temperature, pressure, salinity and the interaction of fluids (CO
2 and brine) and rock. Therefore, for each case, dimensionless numbers and functions should be evaluated to determine the behavior of the system. To better show the effect of different forces, breakthrough time is calculated for different values of total Darcy velocity for Datasets 1 and 5 where mobility ratios are
and
, respectively. By increasing the total Darcy velocity,
and
will decrease, reflecting the effect of increasing viscous forces. For instance, for
, by increasing
from 1 × 10
−9 m/s to 1 × 10
−3 m/s, values of
and
will both change from as high as 46.5 to 0.00005. Therefore, for lower values of
, capillary and gravity forces dominate over viscous forces.
Figure 8a shows effects of gravity forces. Continuous lines display the calculated breakthrough time when all forces are included, and the dashed lines show breakthrough time when gravity effects are neglected. The results demonstrate that gravity effects lead to an earlier breakthrough time for small values of
due to increasing buoyancy effects. However, as
increases (viscous dominated regime), the effect of gravity becomes negligible. Next, we study the effect of capillary forces on breakthrough time. As shown in
Figure 8b, capillary forces have a significant effect on breakthrough time for small values of
. In other words, neglecting capillary effects results in overestimation of breakthrough time. However, the influence of capillary forces becomes negligible by increasing
.
3.2. Case Study on CO2 Storage Aquifers in Western Canada
In this section, the developed model is used to study potential CO
2 storage sites in central Alberta, Canada. Province of Alberta has the largest greenhouse gas emissions in Canada, with annual emissions close to 274.1 Mt CO
2 in 2015 [
34]. The province is underlain by the Alberta basin, which is suitable for CO
2 geological sequestration in all parts except for its shallow northeastern corner [
35]. The largest concentration of CO
2 sources in Alberta is in the Edmonton region where four coal-fired power plants are located near Wabamun Lake, west of Edmonton, which have combined annual CO
2 emissions of more than 30 Mt CO
2 [
36].
Figure 9 shows the location of major CO
2 emission sources in central Alberta, Canada. CO
2 sequestration in deep saline aquifers in proximity of these power plants is a promising option for reducing CO
2 atmospheric emissions since the deep coal seams and oil and gas reservoirs in local area do not have sufficient capacity for sequestration of CO
2. Because CO
2 sequestration in geological media and especially in deep saline aquifers is a recently growing field, no relevant measured data have been published regarding displacement characteristics of CO
2–brine systems at in situ conditions until early 2000. Relevant data were only available for CO
2–oil systems for enhanced oil recovery purposes and a handful of measurements for CO
2–oil–brine ternary systems.
To fill the knowledge gap, Bennion and Bachu conducted a series of experiments to measure relative permeability and capillary pressure characteristics at in-situ conditions for CO
2–brine systems [
33,
37,
38,
39,
40,
41,
42]. They studied sandstone, carbonate, shale and anhydrite rock formations in the Alberta basin in central Alberta. These formations are general representatives of the in-situ temperature, pressure, and salinity in entire Alberta basin, and likely for all on-shore North American sedimentary basins.
Table 2 presents a summary of in-situ conditions for the cored intervals from three sandstone and three carbonate formations in the Wabamun Lake area, southwest of Edmonton, Alberta [
33,
37]. The location of the wells from which core samples were taken is shown in
Figure 9. For the Wabamun Group, two samples with low and high permeability were evaluated which results in a total of seven different rock sets. Temperatures in
Table 2 are evaluated based on the depth of the samples by considering a geothermal gradient of 25 °C/km [
37].
The stratigraphic downhole model for strata in the Wabamun Lake area is available in the literature [
37]. Since site specific data for leakage pathways are not available, we used the same data reported for the storage formations to represent the characteristics of the leakage pathway. Nevertheless, the analysis provided is general and allows application of the developed scaling to a leakage pathway when site specific data are available.
Other parameters used in this study are presented in
Table 3. All the parameters in
Table 3, except the ones with asterisk, are taken from measurements of Bennion and Bachu [
37,
40]. Bennion and Bachu [
37] measured relative permeability parameters at reservoir conditions for rock samples of
Table 2 and reported absolute permeability, CO
2 and brine viscosity, end-point relative permeability of CO
2 (
), residual brine saturation (
), and generated drainage relative permeability curves for CO
2–brine systems. In another paper, Bennion and Bachu [
40] reported the fitted Corey exponents based on their measured relative permeability data for rock samples of
Table 2. Corey exponents are listed in
Table 3. In another work, Bennion and Bachu [
38] reported capillary pressure, interfacial tension and pore size distribution characteristics on a series of carbonate and sandstone formations from Wabamun Lake area in Alberta, together with those formations given in
Table 2. We used the reported CO
2–brine capillary pressure curves, from their study, and curve-fitted to Equation (15). The evaluated capillary entry pressures (
) are reported in
Table 3.
In
Table 3, density of brine is calculated based on Rowe and Chou [
43] correlation using temperature, pressure and salt mass fraction for different formations. CO
2 density is calculated using Soave–Redlich–Kwong (SRK) equations of state [
44]. Total Darcy velocity (
) in
Table 3 is estimated based on
, which reflects the maximum buoyancy velocity for CO
2 and is calculated using Darcy’s law based on the parameters for each formation. The calculated values in
Table 3 are in the range of reported Darcy velocities for CO
2 in the literature [
45,
46]. In addition, although different velocities could happen in the reservoir, this can be a good measure for comparison of different formations. Finally, we considered a length of 500 m and a tilt angle of
in this study. Generally, there are no data on the geometry and direction of the leakage pathways for the formations. We considered identical length and tilt angles for the study of all formations to provide a fair comparison between different storage formations.
The calculated values for
,
and
are presented in the last three rows of
Table 3. The estimated values of mobility ratio have a wide range, starting at 1.06 for Cooking Lake formation to 8.15 for Wabamun Low Perm formation. Estimated values of
and
are shown in a
space in
Figure 10. A reference equilibrium state between gravitational and viscous forces is indicated with dotted line at
, and between capillary and viscous forces at
. As shown in
Figure 10, all rock samples fall into the lower left sector where viscous forces dominate over capillary and gravity forces. It is seen that
varies three orders of magnitude, while variations of
are more gradual and fall within one order of magnitude for different formations.
As shown in
Figure 10, Cooking Lake carbonate has the lowest capillary and gravity numbers of
and
. The highest effect of gravity forces is in Basal Cambrian sandstone with
, and the highest effect of capillary forces is in Nisku carbonate with
.
It is worth mentioning that we used maximum buoyance velocity in the previous calculations. However, velocity of a migrating CO
2 plume may vary within orders of magnitude. To study the effect of total velocity used in our scaling analysis, we perform an analysis to investigate the effect of velocity on the position of various storage formations in the
parameter map. Using different values for the total Darcy velocity leads to different capillary and gravity numbers, but the ratio of these forces remains the same.
Figure 11 shows the estimated values for
and
when total Darcy velocity is varied from 10
−10 m/s to 10
−4 m/s for all the formations shown in
Table 3. This figure indicates that the ratio of capillary to gravity numbers stays the same as the velocity is changing while various formations have different ratios. In the case of Cooking Lake formation, for instance, while gravity forces are at equilibrium with viscous forces (i.e.,
), capillary forces are greatly dominated by viscous forces (
). On the other hand, for Nisku formation, when
, capillary number is
, which shows the effects of capillary forces are much higher for Nisku formation than that for Cooking Lake formation.
Other than
and
, relative permeability parameters are important in estimations of rate of leakage.
Figure 12a–c shows capillary, gravity and viscous functions for all formations shown in
Table 3. For all of the rock samples except Nisku and Ellerslie formations, the effect of capillary and gravity forces is reduced due to the small values of
and
, and therefore, viscous function,
, is the dominant term for estimating saturation and velocity profiles. Mobility ratio as well as Corey exponents of
nc and
nb determine the behavior of capillary, gravity and viscous functions. As indicated in previous section, a lower mobility ratio and a higher Corey exponent for CO
2 increase the time of breakthrough and the average normalized saturation behind the displacement front. Among the rock samples, Cooking Lake formation has the lowest mobility ratio of
and highest Corey exponent for CO
2 (
nc = 5.6), which results in the highest average saturation behind the displacement front (
Figure 12c). In addition, because of small mobility ratio, the values of
and
are relatively high for this case, though their effect on velocity profile is insignificant. Despite similar Corey exponents (
nc and
nb) of Wabamun Low Perm and Cooking Lake formation, mobility ratio is higher and equal to
for Wabamun Low Perm. Further, by comparing these formations (
Figure 12a,b), it can be inferred that Wabamun Low Perm has smaller
and
values in comparison to Cooking Lake formation, and the average saturation behind the displacement front is lower for Wabamun Low Perm as well (see
Figure 12c). For Basal Cambrian sandstone, mobility ratio is relatively high (
), however, the average saturation behind the displacement front is also high, since Corey exponent for CO
2 is
nc = 5 (
Figure 12c). Therefore, contribution of
and
are negligible due to the value of mobility ratio (
Figure 12a,b). Nisku formation has the lowest Corey exponent for CO
2,
nc = 1.1, and even though the mobility ratio for this formation is relatively small and equal to
M = 2.09, it has the lowest average saturation behind the displacement front (
Figure 12c). Additionally, as shown in
Figure 12a,b, contribution of
and
are relatively high for this dataset. Finally, the behavior of capillary, gravity and viscous functions for Wabamun High Perm and Ellerslie formations are very similar, since their mobility ratios and Corey exponents are almost equal.
Figure 13 shows the normalized gas saturation and contribution of different forces on CO
2 dimensionless velocity, for all rock samples at time
. It can be immediately observed that, due to the domination of viscous forces over capillary and gravity forces (small values of
and
), plume evolution and the dimensionless velocity greatly resemble the viscous function
, for all formations, except Nisku and Ellerslie, for which capillary forces are relatively high. Nisku formation has the fastest plume evolution and a countercurrent flow of brine is observed at the inlet due to the effect of capillary forces (
Figure 13b,c). Same as Nisku formation, Ellerslie formation does not develop a sharp font, and contribution of capillary forces on velocity causes a small countercurrent flow of brine at the inlet.
CO
2 front is relatively sharp for the rest of the formations. The front propagation for Cooking Lake formation is slow compared to other formations, which is due to the small mobility ratio and high
nc, as well as small
and
. Shapes of the CO
2 plume and velocity profiles are similar for Basal Cambrian and Wabamun Low Perm formations. This is because of their position on
map (
Figure 10) and similar values of mobility ratio and
nc (
Table 3). Again, in the above analysis, we used maximum buoyance velocity. However, velocity of a migrating CO
2 plume may vary within orders of magnitude, which can change the position of the formations in the
parameter map. Nevertheless, the scaling analysis provided is general and allows application to specific storage site when site specific data are available.
The average normalized gas saturation versus dimensionless time for all the formations are shown in
Figure 14, which are in good agreement with the saturation and velocity profiles discussed earlier. For instance, for the Cooking Lake formation, the breakthrough of CO
2 is delayed due to the less diffusive nature of the displacement front, whereas in the Nisku formation, the effect of capillary forces leads to a diffusive shape front and therefore an earlier breakthrough is expected with lower CO
2 saturation.
Since the discussed values are dimensionless, further discussion on the real time of breakthrough and the cumulative amount of leaked CO2 requires site specific data such as residual brine saturation and porosity of the formations. These parameters are not identical for all the formations and taking these parameters into account would influence the interpretation of results, as described in the following.
The real time of breakthrough and cumulative amount of leakage are calculated based on the dimensionless time of breakthrough and the average normalized saturation in
Figure 14 and
Table 4. The dimensionless time of breakthrough is converted to the real time of breakthrough using Equations (9) and (10), and the cumulative amount of leakage per m
2 of the cross-sectional area of the migration pathway is calculated using
, where
is the brine residual saturation and
is the average normalized saturation,
. The cumulative amount of leakage is plotted versus time for all formations in
Figure 15. As expected, the results are different from what has been expected based on
Figure 14. This is essentially due to the different values of residual brine saturation and porosity of different formations.
The maximum Darcy buoyancy velocity considered for each formation has a great impact on estimating the breakthrough time. Cooking Lake, Wabamun High Perm, and Nisku formations have the highest Darcy buoyancy velocities and thus lower estimated breakthrough times of 51, 56, and 40 days, respectively. Darcy buoyancy velocity decreases for Viking, Ellerslie, Basal Cambrian and Wabamun Low Perm formations, respectively, and as can be seen in
Figure 15, time of breakthrough is delayed for these formations, correspondingly. Porosity times maximum saturation,
, gives an estimate of the available pore volume for CO
2.
In addition, time of breakthrough is highest for Wabamun Low Perm formation, (~308 years), since the estimated Darcy velocity is lowest for this case compared to the other formations, (), and at the same time, the amount of leaked CO2 is lowest for this case, due to the small pore volume available for fluids flow (). A possible leakage from a storage aquifer through a leakage pathway can be remediated specially if detected early enough. On the other hand, chances of contribution of other trapping mechanisms and therefore reducing the amount of leakage is higher for cases with higher time of leakage, such as Wabamun Low Perm or Basal Cambrian formations.
Celia et al. [
47] assessed risk of brine and CO
2 leakage through abandoned wells in the same area that we discussed here (as depicted in
Figure 9). They simulated 50 years of CO
2 injection using a semi-analytical modeling approach over a study area of 2500 km
2. They concluded that the behavior of the system is dependent on the interplay of formation and fluid properties, maximum injectivity of the formation and the properties of the leaky wells. Generally, lower number of oil and gas wells penetrate the caprocks of deeper formations and this will clearly result in a tradeoff between depth of injection and risk of leakage. However, their simulations imply that the number and design of the injection wells and injectivity of the formations play a critical role on the assessment of leakage. Due to lack of data, they assigned the well permeabilities based on the probability distribution. With their assumption of a single vertical injection well and considering the limitation of injectivity, they concluded that Nisku and the Basal Cambrian formations are the two viable options for CO
2 injection.