# Dynamic Behavior of CO2 in a Wellbore and Storage Formation: Wellbore-Coupled and Salt-Precipitation Processes during Geologic CO2 Sequestration

Authors: Jize Piao; Weon Shik Han; Sungwook Choung; Kue-Young Kim
Journal: Geofluids
 (2018)

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## Abstract

For investigating the wellbore flow process in CO2 injection scenarios, coupled wellbore-reservoir (WR) and conventional equivalent porous media (EPM) models were compared with each other. In WR model, during the injection, conditions for the wellbore including pressure and temperature were dynamically changed from the initial pressure (7.45–8.33 MPa) and temperature (52.0–55.9°C) of the storage formation. After 3.35 days, the wellbore flow reached the steady state with adiabatic condition; temperature linearly increased from the well-head (35°C) to the well-bottom (52°C). In contrast, the EPM model neglecting the wellbore process revealed that CO2 temperature was consistently 35°C at the screen interval. Differences in temperature from WR and EPM models resulted in density contrast of CO2 that entered the storage formation (~200 and ~600 kg/m3, resp.). Subsequently, the WR model causing greater density difference between CO2 and brine revealed more vertical CO2 migration and counterflow of brine and also developed the localized salt-precipitation. Finally, a series of sensitivity analyses for the WR model was conducted to assess how the injection conditions influenced interplay between flow system and the localized salt-precipitation in the storage formation.


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## Body

## 1. Introduction

As an approach for decreasing CO2 emissions into the atmosphere, geologic carbon storage (GCS) is one of considerable solutions for relieving global climate change [1]. While operating GCS projects, CO2, directly captured during industrial processes at fossil-fuel power plants, was injected through the wellbore and stored within the specific geologic formation covered by low-permeability caprock [2–4]. Until now, numerous GCS projects have been or are being conducted at various scales around the world to validate the safety of GCS technology [5]. For example, several pilot-scale projects were successfully completed CO2 injection at a rate of 10,000 metric tons per year; these projects included Frio, Texas [6], Nagaoka, Japan [7], Ketzin, and Germany [8] as well as Regional Carbon Sequestration Partnership’s (RCSP) Phase II program implemented by the US Department of Energy [9, 10]. In addition to pilot-scale projects, commercial-scale projects where CO2 was injected at an approximate rate of 1 million metric tons per year were completed or also in operation: Sleipner project in North Sea [11], Weyburn CO2-EOR Project in Canada [12], In Salah Project in Algeria [13], and Illinois Basin-Decatur Project which is one of the Phase III projects of US Department of Energy’s RCSP [14].During the demonstration of such pilot- or commercial-scale GCS projects, transported CO2 from the sources (e.g., coal-based power plants) must be injected through the wellbore, which is the pathway connecting the ground surface to the targeted subsurface formation [15]. Here, the wellbore is the connected open pipe while the subsurface formation is regarded as porous media. Due to the difference in their inherent configurations, within the wellbore, the inertial force is much greater than the viscous force, implying that Reynold’s number can be significantly large [16]. Solution approaches to solving CO2 transport are also different in each other. Within the wellbore, CO2 transport belongs to the pipe flow, which requires a solution of the Navier-Stocks equation [17]. On the other hand, once CO2 enters porous storage formations, CO2 transport must be explained by Darcy’s law [18]. Furthermore, CO2 injection wells were typically drilled over 1 km while penetrating multiple geologic formations. Therefore, while CO2 migrated through the wellbore, large variations in pressure and temperature could cause to change in CO2 phase and its thermophysical properties [19, 20].As described, due to complexities involved during the wellbore processes, a number of studies previously drew attention and suggested that, during the CO2 injection activity, profiles of both pressure and temperature in the wellbore could change dynamically [21–27]. For example, Lu and Connell [21] suggested that the wellbore fluids could exhibit multiphase (supercritical, liquid, gaseous CO2, and brine) concurrently experiencing their phase changes. Furthermore, both CO2 and brine could experience thermal alteration caused by frictional loss, thermal conduction, convection, and Joul-Thomson heating/cooling [22, 27–29]. Due to such complex alteration processes, both bottom-hole pressure and temperature would be significantly different from ones at the well-head. Subsequently, altered pressure and temperature profiles would significantly affect thermophysical properties of CO2 such as density, viscosity, enthalpy, internal energy, and solubility [19, 26, 30–32].When thermophysically altered CO2 entered the storage formation, the brine within porous media would be displaced. Subsequently, the dry-out zone would be developed in the vicinity of the injection well where residual brine evaporated to dry-CO2 while precipitating the solid salt [33, 34]. Previously, numerous studies including both experimental [35–37] and numerical studies [34, 38–41] evaluated development of dry-out zone and associated salt-precipitation. Among them, Oh et al. [36] conducted core-flooding experiments and captured the salt-precipitation at the core-inlet by using SEM images. In addition, Kim et al. [39] and Guyant et al. [40] used numerical approach to elaborate the salt-precipitation processes according to conditions for both the injection well and storage formation. In particular, within low injection rate and high permeability of the storage formation, buoyancy effect on CO2 became dominant, and consequently, the localized salt-precipitation was developed [41] concurrently elevating pressure around the injection well [42]. Most importantly, development of the localized salt was dependent on the degree of buoyancy force on CO2 plume, which was governed by the injection rate and thermophysical properties of CO2. Even though thermophysical CO2 properties could be changed significantly after CO2 experiencing the wellbore processes, only a few studies were considered the wellbore processes impacting on CO2 behavior in the storage formation [22, 24, 43–45].For example, a number of previous studies neglected the wellbore flow process or interpreted the wellbore flow by adopting Darcy’s law after assigning adequate rock properties [46–48]. This approach is called equivalent porous media (EPM) model. The primary reason for such simplification arises from technical difficulties solving both the wellbore and porous media flow at the same time. Nevertheless, it is recognized that fully coupled wellbore-reservoir models, capable of accounting for nonisothermal two-phase (CO2 and brine or water) flow, are necessary to evaluate the influence of wellbore flow on injected CO2 within the storage formation [44, 49]. Due to this reason, the purpose of this study was to advance current understanding related to the wellbore flow process by investigating the change of both pressure and temperature profiles within the wellbore, and subsequently, CO2 migration, and resulting accumulation of solid salt in the storage formation.


## 2. Method

### 2.1. Conceptual Model

In order to evaluate differences between equivalent porous media (EPM) and coupled wellbore-reservoir (WR) models, two base-cases which were two-dimensional radially symmetric and nonisothermal models (Case1 and Case 2) were employed (Figures 1(a) and 1(b)). Case 1 adopted the conventional EPM approach for simulating both an injection well and a storage formation while Case 2 utilized the WR model for simulating the injection well which coupled to the storage formation. In both cases, CO2 was injected into the storage formation which was the 40 m thick high-permeability (k) formation (k=3×10-13 m2 and ϕ=0.25) overlaid by the 50 m thick low-k sealing caprock (k=1×10-17 m2 and ϕ=0.2). These formations were positioned at a depth of 690 m below the ground surface, and their radial extent was 10,000 m. The storage formation was divided vertically into 10 layers (each layer with 4 m thickness) while the overlying sealing formation was divided into 5 layers having individually 10 m thickness. Then, they were horizontally discretized to 200 columns with the logarithmic increment from the injection well; the specific number and size of grid-blocks to the radial direction are shown in Figure 1.Figure 1
Schematic diagrams delineating the 2-dimensional radial models. (a) Case1 targeted to evaluate the EPM model and (b) Case 2 is for the WR model.For the initial condition, the hydrostatic pressure was assigned with the gradient of 10.58 kPa/m (top: 7.45 MPa to bottom: 8.33 MPa), and the geothermal gradient of 0.046°C/m was assigned with assuming the surface temperature of 20°C (model top: 52.0°C to bottom: 55.9°C). In addition, the dissolved NaCl mass fraction in the ambient brine was uniformly 15% with zero CO2 saturation. For the boundary conditions, both top and bottom boundaries were assigned to be no-flow condition without assigning the conductive heat flow at the bottom boundary; temperature field in the model was dominantly governed by the geothermal gradient assigned to lateral boundaries. The conductive heat flows were neglected because buoyant CO2 plume holding different temperature typically governed the temperature field adjacent to CO2 plume and the injection well. Furthermore, the right-most side of the targeted formation at 10,000 m was set to be the Dirichlet boundary. By assuming the Dirichlet boundary, it was expected that the pressure pulse after reaching this boundary would be affected.The primary difference between Case1 and Case 2 was the condition for the left boundary assigned to the storage formation where CO2 was injected. In Case 1 (EPM model), without the wellbore, CO2 was injected into 10 grid-blocks located at the left-most boundary with 1 kg/s injection rate (a total injection rate was 10 kg/s) during 1,095 days (3 years) (Figure 1(a)). The temperature of the injected CO2 was maintained at 35.0°C, assuming that CO2 velocity within the wellbore was fast enough to ignore conductive heat transfer from surroundings. Additionally, since there was no wellbore, it was assumed that the Joule Thompson effect was negligible. The ambient temperature based on assigned geothermal gradient was 54.2°C to 55.9°C in the storage formation. In Case 2 (WR model), for simulating CO2 transport through the wellbore, the wellbore consisting of 84 grid-blocks was added to the left-most boundary from the ground surface to the bottom of target formation (Figure 1(b)). The diameter of the wellbore was set to 0.2 m. From the ground surface to the depth of 690 m (the top of the sealing formation), the 69 grid-blocks with the individual vertical size of 10 m were assigned without coupling to the surrounding formation. However, conductive heat exchange between the wellbore and the surrounding formation was considered by calculating semianalytically [24, 49]. From the depth of 690 m to 780 m, the wellbore consisting of 15 grid-blocks was connected to the storage formation with the same dimension (sealing formation: 5 layers and storage formation: 10 layers). Among 15 grid-blocks, only 10 grid-blocks connected to the storage formation were considered to be the screen interval where CO2 mass was injected into the storage formation. Dry CO2 was injected from the well-head where the temperature of injected CO2 and the injection rate was maintained at 35.0°C and 10 kg/s, respectively. In both models, the relative permeability and capillary pressure were modeled with Corey’s curves [50] and van Genuchten function [51], respectively. The mathematical expressions and input parameters for Corey and van Genuchten functions were presented in Table 1.Table 1
Parameters and properties used in the basecase model. The definitions of symbols are explained in nomenclature.
Parameters for formation
Values
Permeability
Storage formation
3 × 10−13 m2
Sealing formation
1 × 10−17 m2
Porosity
Storage formation
0.25
Sealing formation
0.2
Salinity
15%
Surface pressure
1.01 × 105 Pa
Pressure gradient
10,577.8 Pa/m
Surface temperature
20°C
Temperature gradient
0.0461°C/m
Thermal conductivity
2.51 W/m·°C
Parameters for injection
Values
Injection rate
10 kg/s
Injection temperature
35°C
Wellbore diameter
0.2 m
Parameters for transport
Values
Relative permeability
Corey’s model
k
r
G
=
1
-
S
-
2
1
-
S
-
2;  krL=S-4
S-=SL-Slr/1-Slr-Sgr
S
l
r
=
0.3,  Sgr=0.05
Capillary pressure
van Genuchten model
P
c
=
-
P
0
S
∗
-
1
/
λ
′
-
1
1
-
λ
′
S
∗
=
S
L
-
S
l
r
/
S
l
s
-
S
l
r
Storage formation
λ
′
=
0.46,  Slr=0.2,  1/P0=1×10-4Pa-1
Sealing formation
λ
′
=
0.25,  Slr=0.2,  1/P0=1×10-5Pa-1Finally, in addition to Cases1 and 2, 6 subcases of Case 2 were developed to evaluate different injection conditions for the WR model (Table 2). Three parameters including the injected CO2 temperature, the injection rate, and the wellbore diameter were determined to analyze the role of the wellbore process on injected CO2. Particularly, the injected CO2 temperatures were selected from relatively high values (35°C–60°C) even though the high injected CO2 temperature will cause a high energetic cost because of heating up CO2 [52].Table 2
Description of sensitivity scenarios.
Case
Injection temperature(°C)
Injection rate(kg/s)
Wellbore diameter(m)
Case2
35
10
0.2
Case2-1
45
10
0.2
Case2-2
60
10
0.2
Case2-3
35
5
0.2
Case2-4
35
50
0.2
Case2-5
35
10
0.13
Case2-6
35
10
0.05


### 2.2. Numerical Simulator

In this study, two simulators were compared; one for the EPM model applying to Case1 was TOUGH2/ECO2N [53, 54] and the other for the WR model in Case 2 was T2Well/ECO2N [24, 55]. TOUGH2 is the numerical simulator capable of simulating nonisothermal multiphase and multicomponent fluids in multidimensional porous and fractured media [53]. The ECO2N is a fluid property module that describes the thermophysical properties of H2O-NaCl-CO2 system [54, 56]. T2Well/ECO2N, which is the suite of the TOUGH2/ECO2N, is the integrated simulator capable of accounting for both wellbore and storage subdomain where they are controlled by different governing equations [24]. Specifically, the viscous flow within the wellbore was predicted from one-dimensional momentum equation while porous media representing the storage formation were simulated with two-dimensional multiphase version of Darcy’s law.For the specific details regarded to TOUGH2, Pruess et al. [53] can be referred. Here, the governing equations related to T2Well/ECO2N are only explained; the primary governing equations representing mass, energy, and momentum within the wellbore and the storage formation are listed in Table 3. As shown in Table 3, the primary difference between porous medium and the wellbore is consideration of both kinetic (uβ2/2) and potential (gzcos⁡θ) energy terms in the energy flux and accumulation equations of the wellbore model. Therefore, while CO2 migrates through the wellbore, variations in both potential and kinetic energies interactively change the energy state of CO2 within the wellbore. Additionally, fluid velocities within the wellbore are determined by the mixture velocity (um) and the drift velocity (ud), which is calculated from the Drift-Flux-Model (DFM) [57]. Specifically, um is calculated by solving following momentum equation [55]:(1)∂∂tρmum+1A∂∂zAρmum2+γ=-∂P∂z-Γwfρmumum2A-ρmgcos⁡θ,where γ is expressed with the following equation: γ=SG/1-SGρGρLρm/ρm∗2C0-1um+ud2, which explains the slip between gas and liquid phases. Subsequently, ud is calculated with a function of gas saturation (SG) and other fluid properties: (2)ud=1-C0SGucKSG,Ku,C0mθC0SGρG/ρL+1-C0SG.In (2), the characteristic velocity (uc) indicates the rising velocity of gaseous bubble in a liquid column and mθ denotes the inclination effect of the wellbore. The function for K(·) is used for smooth transition of drift velocity between the bubble rising stage and the film flooding stage. Other terms in (2) can be found in the nomenclature. Further details about the T2Well/ECO2N simulator can be found in Pan et al. [55].Table 3
Governing equations utilized in T2Well/ECO2N, which represents fluids through the wellbore and storage formation. The definitions of symbols are explained in nomenclature.
Description
Equation
Conservation of mass and energy
d
d
t
∫
V
n
M
κ
d
V
n
=
∫
Γ
n
F
κ
·
n
d
Γ
n
+
∫
V
n
q
κ
d
V
n
Mass accumulation
M
κ
=
ϕ
∑
β
S
β
ρ
β
X
β
κ,  for each mass component κ
Mass flux
F
κ
=
∑
β
u
β
ρ
β
X
β
κ,  for each mass component κ
Porous medium
Energy flux
F
N
K
1
=
-
λ
∇
T
+
∑
β
h
β
ρ
β
u
β
Energy accumulation
M
N
K
1
=
(
1
-
ϕ
)
ρ
R
C
R
T
+
ϕ
∑
β
ρ
β
S
β
u
β
Darcy velocity
u
β
=
-
k
k
r
β
μ
β
∇
P
β
-
ρ
β
g  Darcy’s Law for each phase β, with Pβ=PG+Pc
Wellbore
Energy flux
F
N
K
1
=
-
λ
∇
T
+
∑
β
ρ
β
S
β
u
β
h
β
+
u
β
2
2
+
g
z
cos
⁡
θ
Energy accumulation
M
N
K
1
=
∑
β
ρ
β
S
β
U
β
+
u
β
2
2
+
g
z
cos
⁡
θ
Phase velocity
u
G
=
C
0
ρ
m
ρ
m
∗
u
m
+
ρ
L
ρ
m
∗
u
d  Drift-flux model
u
L
=
1
-
S
G
C
0
ρ
m
1
-
S
G
ρ
m
∗
u
m
-
S
G
ρ
G
1
-
S
G
ρ
m
∗
u
d  Drift-flux model
Source: modified after Pan et al. [49].In regard to the salt-precipitation process occurring adjacent to the injection well, a number of previous studies have been conducted with TOUGH2/ECO2N [34, 38–42]. However, only a few studies considered the influence of salinity on both wellbore and reservoir flow [25, 58]. In TOUGH2/ECO2N, the salt-precipitation occurred when water vaporized into dry supercritical CO2, which was accounted for the equations of states developed by Spycher and Pruess [32]. The precipitation of salt is able to cause to reduction in both porosity and permeability adjacent to the injection well. In this work, reduction of porosity and permeability due to the salt-precipitation was calculated using a “tubes-in-series” model [53, 59].(3)kk0=θs21-Γ+Γ/ω21-Γ+Γθs/θs+ω-12(4)θs2=1-SS-ϕr1-ϕr(5)ω=1-1/Γ1/ϕr-1,where k/k0 denotes the permeability reduction factor. ω is calculated by two independent geometric parameters such as fraction of original porosity (ϕr=ϕ/ϕ0) and fractional length of pore body (Γ). According to few previous studies, both ϕr and Γ were set to be 0.8 [38, 39].


### 2.3. Gravity Number

The buoyancy effect is one of the significant factors for determining distribution of both CO2 plume and associated salt-precipitation [41, 42]. In order to quantitatively assess distribution of salt-precipitation in two cases, the gravity number (Ngv) was chosen for evaluating the buoyancy effect on the CO2 plume in the storage formation. Ngv defined below measures the degree of strength of gravity to viscous forces [60]:(6)Ngv=kvLsΔρgHuiμ.where kv is the vertical permeability, H is the thickness of the storage formation, and Ls, as a characteristic length, is chosen to be equal to the horizontal length of the storage formation. Δρ is the density difference between CO2 and brine, ui is the total averaged velocity to the horizontal direction predicted from grid-blocks between wellbore and storage formations, and μ is CO2 viscosity. In (6), greater Ngv indicates dominance of the gravity force on CO2 plume [61].


## 2.1. Conceptual Model

In order to evaluate differences between equivalent porous media (EPM) and coupled wellbore-reservoir (WR) models, two base-cases which were two-dimensional radially symmetric and nonisothermal models (Case1 and Case 2) were employed (Figures 1(a) and 1(b)). Case 1 adopted the conventional EPM approach for simulating both an injection well and a storage formation while Case 2 utilized the WR model for simulating the injection well which coupled to the storage formation. In both cases, CO2 was injected into the storage formation which was the 40 m thick high-permeability (k) formation (k=3×10-13 m2 and ϕ=0.25) overlaid by the 50 m thick low-k sealing caprock (k=1×10-17 m2 and ϕ=0.2). These formations were positioned at a depth of 690 m below the ground surface, and their radial extent was 10,000 m. The storage formation was divided vertically into 10 layers (each layer with 4 m thickness) while the overlying sealing formation was divided into 5 layers having individually 10 m thickness. Then, they were horizontally discretized to 200 columns with the logarithmic increment from the injection well; the specific number and size of grid-blocks to the radial direction are shown in Figure 1.Figure 1
Schematic diagrams delineating the 2-dimensional radial models. (a) Case1 targeted to evaluate the EPM model and (b) Case 2 is for the WR model.For the initial condition, the hydrostatic pressure was assigned with the gradient of 10.58 kPa/m (top: 7.45 MPa to bottom: 8.33 MPa), and the geothermal gradient of 0.046°C/m was assigned with assuming the surface temperature of 20°C (model top: 52.0°C to bottom: 55.9°C). In addition, the dissolved NaCl mass fraction in the ambient brine was uniformly 15% with zero CO2 saturation. For the boundary conditions, both top and bottom boundaries were assigned to be no-flow condition without assigning the conductive heat flow at the bottom boundary; temperature field in the model was dominantly governed by the geothermal gradient assigned to lateral boundaries. The conductive heat flows were neglected because buoyant CO2 plume holding different temperature typically governed the temperature field adjacent to CO2 plume and the injection well. Furthermore, the right-most side of the targeted formation at 10,000 m was set to be the Dirichlet boundary. By assuming the Dirichlet boundary, it was expected that the pressure pulse after reaching this boundary would be affected.The primary difference between Case1 and Case 2 was the condition for the left boundary assigned to the storage formation where CO2 was injected. In Case 1 (EPM model), without the wellbore, CO2 was injected into 10 grid-blocks located at the left-most boundary with 1 kg/s injection rate (a total injection rate was 10 kg/s) during 1,095 days (3 years) (Figure 1(a)). The temperature of the injected CO2 was maintained at 35.0°C, assuming that CO2 velocity within the wellbore was fast enough to ignore conductive heat transfer from surroundings. Additionally, since there was no wellbore, it was assumed that the Joule Thompson effect was negligible. The ambient temperature based on assigned geothermal gradient was 54.2°C to 55.9°C in the storage formation. In Case 2 (WR model), for simulating CO2 transport through the wellbore, the wellbore consisting of 84 grid-blocks was added to the left-most boundary from the ground surface to the bottom of target formation (Figure 1(b)). The diameter of the wellbore was set to 0.2 m. From the ground surface to the depth of 690 m (the top of the sealing formation), the 69 grid-blocks with the individual vertical size of 10 m were assigned without coupling to the surrounding formation. However, conductive heat exchange between the wellbore and the surrounding formation was considered by calculating semianalytically [24, 49]. From the depth of 690 m to 780 m, the wellbore consisting of 15 grid-blocks was connected to the storage formation with the same dimension (sealing formation: 5 layers and storage formation: 10 layers). Among 15 grid-blocks, only 10 grid-blocks connected to the storage formation were considered to be the screen interval where CO2 mass was injected into the storage formation. Dry CO2 was injected from the well-head where the temperature of injected CO2 and the injection rate was maintained at 35.0°C and 10 kg/s, respectively. In both models, the relative permeability and capillary pressure were modeled with Corey’s curves [50] and van Genuchten function [51], respectively. The mathematical expressions and input parameters for Corey and van Genuchten functions were presented in Table 1.Table 1
Parameters and properties used in the basecase model. The definitions of symbols are explained in nomenclature.
Parameters for formation
Values
Permeability
Storage formation
3 × 10−13 m2
Sealing formation
1 × 10−17 m2
Porosity
Storage formation
0.25
Sealing formation
0.2
Salinity
15%
Surface pressure
1.01 × 105 Pa
Pressure gradient
10,577.8 Pa/m
Surface temperature
20°C
Temperature gradient
0.0461°C/m
Thermal conductivity
2.51 W/m·°C
Parameters for injection
Values
Injection rate
10 kg/s
Injection temperature
35°C
Wellbore diameter
0.2 m
Parameters for transport
Values
Relative permeability
Corey’s model
k
r
G
=
1
-
S
-
2
1
-
S
-
2;  krL=S-4
S-=SL-Slr/1-Slr-Sgr
S
l
r
=
0.3,  Sgr=0.05
Capillary pressure
van Genuchten model
P
c
=
-
P
0
S
∗
-
1
/
λ
′
-
1
1
-
λ
′
S
∗
=
S
L
-
S
l
r
/
S
l
s
-
S
l
r
Storage formation
λ
′
=
0.46,  Slr=0.2,  1/P0=1×10-4Pa-1
Sealing formation
λ
′
=
0.25,  Slr=0.2,  1/P0=1×10-5Pa-1Finally, in addition to Cases1 and 2, 6 subcases of Case 2 were developed to evaluate different injection conditions for the WR model (Table 2). Three parameters including the injected CO2 temperature, the injection rate, and the wellbore diameter were determined to analyze the role of the wellbore process on injected CO2. Particularly, the injected CO2 temperatures were selected from relatively high values (35°C–60°C) even though the high injected CO2 temperature will cause a high energetic cost because of heating up CO2 [52].Table 2
Description of sensitivity scenarios.
Case
Injection temperature(°C)
Injection rate(kg/s)
Wellbore diameter(m)
Case2
35
10
0.2
Case2-1
45
10
0.2
Case2-2
60
10
0.2
Case2-3
35
5
0.2
Case2-4
35
50
0.2
Case2-5
35
10
0.13
Case2-6
35
10
0.05


## 2.2. Numerical Simulator

In this study, two simulators were compared; one for the EPM model applying to Case1 was TOUGH2/ECO2N [53, 54] and the other for the WR model in Case 2 was T2Well/ECO2N [24, 55]. TOUGH2 is the numerical simulator capable of simulating nonisothermal multiphase and multicomponent fluids in multidimensional porous and fractured media [53]. The ECO2N is a fluid property module that describes the thermophysical properties of H2O-NaCl-CO2 system [54, 56]. T2Well/ECO2N, which is the suite of the TOUGH2/ECO2N, is the integrated simulator capable of accounting for both wellbore and storage subdomain where they are controlled by different governing equations [24]. Specifically, the viscous flow within the wellbore was predicted from one-dimensional momentum equation while porous media representing the storage formation were simulated with two-dimensional multiphase version of Darcy’s law.For the specific details regarded to TOUGH2, Pruess et al. [53] can be referred. Here, the governing equations related to T2Well/ECO2N are only explained; the primary governing equations representing mass, energy, and momentum within the wellbore and the storage formation are listed in Table 3. As shown in Table 3, the primary difference between porous medium and the wellbore is consideration of both kinetic (uβ2/2) and potential (gzcos⁡θ) energy terms in the energy flux and accumulation equations of the wellbore model. Therefore, while CO2 migrates through the wellbore, variations in both potential and kinetic energies interactively change the energy state of CO2 within the wellbore. Additionally, fluid velocities within the wellbore are determined by the mixture velocity (um) and the drift velocity (ud), which is calculated from the Drift-Flux-Model (DFM) [57]. Specifically, um is calculated by solving following momentum equation [55]:(1)∂∂tρmum+1A∂∂zAρmum2+γ=-∂P∂z-Γwfρmumum2A-ρmgcos⁡θ,where γ is expressed with the following equation: γ=SG/1-SGρGρLρm/ρm∗2C0-1um+ud2, which explains the slip between gas and liquid phases. Subsequently, ud is calculated with a function of gas saturation (SG) and other fluid properties: (2)ud=1-C0SGucKSG,Ku,C0mθC0SGρG/ρL+1-C0SG.In (2), the characteristic velocity (uc) indicates the rising velocity of gaseous bubble in a liquid column and mθ denotes the inclination effect of the wellbore. The function for K(·) is used for smooth transition of drift velocity between the bubble rising stage and the film flooding stage. Other terms in (2) can be found in the nomenclature. Further details about the T2Well/ECO2N simulator can be found in Pan et al. [55].Table 3
Governing equations utilized in T2Well/ECO2N, which represents fluids through the wellbore and storage formation. The definitions of symbols are explained in nomenclature.
Description
Equation
Conservation of mass and energy
d
d
t
∫
V
n
M
κ
d
V
n
=
∫
Γ
n
F
κ
·
n
d
Γ
n
+
∫
V
n
q
κ
d
V
n
Mass accumulation
M
κ
=
ϕ
∑
β
S
β
ρ
β
X
β
κ,  for each mass component κ
Mass flux
F
κ
=
∑
β
u
β
ρ
β
X
β
κ,  for each mass component κ
Porous medium
Energy flux
F
N
K
1
=
-
λ
∇
T
+
∑
β
h
β
ρ
β
u
β
Energy accumulation
M
N
K
1
=
(
1
-
ϕ
)
ρ
R
C
R
T
+
ϕ
∑
β
ρ
β
S
β
u
β
Darcy velocity
u
β
=
-
k
k
r
β
μ
β
∇
P
β
-
ρ
β
g  Darcy’s Law for each phase β, with Pβ=PG+Pc
Wellbore
Energy flux
F
N
K
1
=
-
λ
∇
T
+
∑
β
ρ
β
S
β
u
β
h
β
+
u
β
2
2
+
g
z
cos
⁡
θ
Energy accumulation
M
N
K
1
=
∑
β
ρ
β
S
β
U
β
+
u
β
2
2
+
g
z
cos
⁡
θ
Phase velocity
u
G
=
C
0
ρ
m
ρ
m
∗
u
m
+
ρ
L
ρ
m
∗
u
d  Drift-flux model
u
L
=
1
-
S
G
C
0
ρ
m
1
-
S
G
ρ
m
∗
u
m
-
S
G
ρ
G
1
-
S
G
ρ
m
∗
u
d  Drift-flux model
Source: modified after Pan et al. [49].In regard to the salt-precipitation process occurring adjacent to the injection well, a number of previous studies have been conducted with TOUGH2/ECO2N [34, 38–42]. However, only a few studies considered the influence of salinity on both wellbore and reservoir flow [25, 58]. In TOUGH2/ECO2N, the salt-precipitation occurred when water vaporized into dry supercritical CO2, which was accounted for the equations of states developed by Spycher and Pruess [32]. The precipitation of salt is able to cause to reduction in both porosity and permeability adjacent to the injection well. In this work, reduction of porosity and permeability due to the salt-precipitation was calculated using a “tubes-in-series” model [53, 59].(3)kk0=θs21-Γ+Γ/ω21-Γ+Γθs/θs+ω-12(4)θs2=1-SS-ϕr1-ϕr(5)ω=1-1/Γ1/ϕr-1,where k/k0 denotes the permeability reduction factor. ω is calculated by two independent geometric parameters such as fraction of original porosity (ϕr=ϕ/ϕ0) and fractional length of pore body (Γ). According to few previous studies, both ϕr and Γ were set to be 0.8 [38, 39].


## 2.3. Gravity Number

The buoyancy effect is one of the significant factors for determining distribution of both CO2 plume and associated salt-precipitation [41, 42]. In order to quantitatively assess distribution of salt-precipitation in two cases, the gravity number (Ngv) was chosen for evaluating the buoyancy effect on the CO2 plume in the storage formation. Ngv defined below measures the degree of strength of gravity to viscous forces [60]:(6)Ngv=kvLsΔρgHuiμ.where kv is the vertical permeability, H is the thickness of the storage formation, and Ls, as a characteristic length, is chosen to be equal to the horizontal length of the storage formation. Δρ is the density difference between CO2 and brine, ui is the total averaged velocity to the horizontal direction predicted from grid-blocks between wellbore and storage formations, and μ is CO2 viscosity. In (6), greater Ngv indicates dominance of the gravity force on CO2 plume [61].


## 3. Comparison of EPM and WR Models (Case 1 versus Case 2)

### 3.1. Analyses of Wellbore Flow Conditions

#### 3.1.1. Characterization of Multiple Stages in the Wellbore

In Case1 (EPM model), CO2 holding constant temperature of 35.0°C was injected into the storage formation (formation pressure from 7.95 MPa to 8.33 MPa) at a constant rate of 10 kg/s throughout the simulation time (Figure 1(a)). Following the injection conditions, CO2 injected into the storage formation was in supercritical phase consistently preserving its density and viscosity approximately larger than 600 kg/m3 and 5.0 × 10−5 Pa·s, respectively.In Case2 (WR model), CO2 holding 35.0°C was injected from the well-head at a rate of 10 kg/s (Figure 1(b)). Once CO2 was entered from the well-head, it transported through the 780 m depth wellbore (Figure 2(a)) while experiencing thermal disequilibrium processes such as heat convection, conduction, frictional effect, and Joule-Thomson effect [21, 27]. Consequently, the temperature of CO2 reaching the well-bottom was changed from 35.0°C (at the well-head) to approximately 52.0°C. Due to such dynamic disturbance in both temperature and pressure within the wellbore, the thermodynamic properties of CO2 entering from the well-head were also different with ones reaching the well-bottom.Figure 2
Changes in thermophysical properties of CO2 within the wellbore during 100 days; (a) a schematic diagram delineating CO2 transport within the wellbore and associated thermal effects; profiles for (b) CO2 saturation [-], (c) pressure [Pa], and (d) temperature [°C]. The two white dotted lines define the initiation of each different stage while injected CO2 is displacing the brine in the wellbore (1.2 × 10−5 (=1 sec) and 1.2 × 10−2 (=17.3 min)). The yellow dashed line in (b) represents the interface between gaseous and supercritical CO2 phase. The purple dashed lines shown in (c) and (d) indicate the dynamic interface between CO2 and brine.
(a)
(b)
(c)
(d)Figures2(b)–2(d) showed changes in CO2 saturation, pressure, and temperature throughout the wellbore during 100 days after CO2 injection began. According to CO2 saturation profile in Figure 2(b), three stages were characterized. Stage I (0 to 1.2 × 10−5 day (=1 sec)) defined the status of the wellbore where brine was fully saturated in the well; both pressure and temperature remained hydrostatic and geothermal gradient conditions, initially assigned to the model (Stage I in Figures 2(c) and 2(d)). During Stage II (1.2 × 10−5 day (=1 sec) to 1.2 × 10−2 day (=17.3 min)), the wellbore transited from single (or brine) to multiphase conditions where both brine and CO2 coexisted; the dynamic interface (dashed purple-line in Figures 2(c) and 2(d)) between injected CO2 and brine was developed. In addition, the phase transition of CO2 from gaseous to supercritical phase was observed at a depth of 468 m for the first time (3.2 × 10−3 day), which dynamically evolved with time (Figure 2(b)). Approximately after 3.35 day, gaseous CO2 in the wellbore completely transited to supercritical phase.Immediately after CO2 injection began at Stage II, CO2 suddenly pushed brine from the well-head, and therefore, increase in CO2 saturation was observed at the well-head (Figure 2(b)). Due to the encroachment of CO2 from the well-head, brine positioned at the well-bottom needed to enter the storage formation in which permeability (3 × 10−13 m2) and capillary pressure were significantly smaller and larger than the wellbore ones, respectively. Because of contrasts in both permeability and capillary pressure between the wellbore and storage formation, the pressure at the wellbore was built up and reached its peak at 2.3 × 10−4 day (Figure 2(c)). Then, subsequent pressure reduction implies that brine at the well-bottom was getting entered the storage formation with continuous CO2 injection from the well-head. Gradual decrease in the wellbore pressure was observed until the wellbore was completely replaced by CO2 at 1.2 × 10−2 day (Figure 2(c)).The temperature profile was somewhat similar to pressure one. At Stage I, temperature ranged from the well-head to well-bottom was 20.0°C to 56.0°C (Figure2(d)). Then, CO2 with temperature of 35.0°C was injected from the well-head. While 35.0°C CO2 displaced the brine from the well-head, relatively warm brine (approximately 50.0–56.0°C) positioned at the bottom of the wellbore entered the storage formation (Stage II). Concurrently, low-temperature brine (20.0°C) was pushed from the well-head to the deeper part of the wellbore by injected CO2. While the injected CO2 pushed low-temperature brine downward, diverse thermal processes including thermal convection, conduction, frictional effect, and Joule-Thomson effect occurred concurrently. However, because thermal convection representing the movement of shallow cold-brine toward the well-bottom was more dominant than other thermal effects, overall decrease in temperature was observed in the wellbore.Immediately after Stage III at 1.2 × 10−2 day, the wellbore was completed replaced by the injected CO2. Soon, both pressure and temperature increased together (6.9 × 10−2 day). This positive relationship can be attributed to Joule-Thomson effect ((∂T/∂P)H), which defines change in temperature during (de)compression of CO2 based on its counterpart of pressure change under the isenthalpic condition [62]. After 3.35 day, profiles for both pressure and temperature reached the steady-state condition while CO2 in the wellbore completely became supercritical phase (Figure 2(b)). In summary, due to thermal processes such as frictional effect, heat conduction, and Joule-Thomson effect, temperature of CO2 which entered the storage formation reached approximately 51-52°C, which was greater than injected CO2 (35°C) but lower than temperature (54-55°C) of the storage formation.


#### 3.1.2. Variations in Thermophysical Properties of Injected CO2

Figure3 showed contours for density, viscosity, specific enthalpy, and Joule-Thomson coefficient of CO2 dependent on temperature and pressure, which were predicted from Span and Wagner [63]. Figures 3(a) and 3(b) delineated relatively wide ranges covering pressure from 0 to 30 MPa and temperature from 0 to 200°C. Therefore, appropriate ranges for pressure (6 to 10 MPa) and temperature (20 to 80°C) were selected, and CO2 injection condition was examined for both cases (Figures 3(c) and 3(d)).Figure 3
Contours of (a) density [kg/m3] and viscosity [10−5 Pa·s] and (b) enthalpy [kJ/kg] and Joule-Thomson coefficient [°C/MPa] in P-T space. Gray box represents a suitable condition for the wellbore during geologic CO2 sequestration (P: 6 to 10 MPa and T: 20 to 80°C). (c) and (d) represent contours for density, viscosity, enthalpy, and Joule-Thomson coefficient in P-T regime suitable for the wellbore. Purple symbols represent the conditions for CO2 injection in Case 1. Green symbols and lines represent the conditions for the wellbore in Case 2.
(a)
(b)
(c)
(d)The CO2 injection condition for Case 1 (EPM model; purple symbols) was plotted at 1,095 days (Figure 3(c)). After 1,095 days, pressure from the top to the bottom of the storage formation was changed from 9.16 to 9.26 MPa while maintaining 35°C. At this condition, the injected CO2 was completely supercritical phase with relatively large density (approximate 650 kg/m3) and viscosity (approximate 5.2 × 10−5 Pa·s) (Figure 3(c)).For Case2 (WR model), 4 profiles were selected; one was at the end of Stage II (1.2 × 10−2 day in Figure 2(b)) immediately after the wellbore was completely filled with CO2; at this time, the injected CO2 experienced phase transition from gaseous to supercritical phase at 155 m depth (Point A in Figures 2(b) and 3(c)). Presence of both gaseous and supercritical CO2 within the wellbore resulted in dynamic (or nonlinear) profile of CO2. At the well-head, temperature and pressure were 35°C and 6.96 MPa, which was plotted below the critical point (31.1°C and 7.38 MPa) of CO2. Then, at 155 m (Point A) temperature dropped to 32.6°C (ΔT=-2.4°C) while pressure increased to 7.37 MPa (ΔP=+0.4 MPa). Similar to Han et al. [27] and Lu and Connell [21], decrease in CO2 temperature occurred in the wellbore due to heat conduction with the surrounding formation; the temperature of the surrounding formation was 27.1°C in this depth. From the ground surface to 155 m, gaseous CO2 in the wellbore holds its density from 219 to 326 kg/m3, viscosity from 2.0 × 10−5 to 2.3 × 10−5 Pa·s, and Joule-Thomson coefficient decreasing from 9.1 to 8.2°C/MPa. Deeper than 155 m, gaseous CO2 transited to supercritical phase. Both temperature and pressure increased nonlinearly while deviating from isenthalpic lines (300–350 kJ/kg in Figure 3(d)), implying that supercritical CO2 in the wellbore did not reach the adiabatic condition yet; thus, various thermal processes including thermal conduction and friction actively affected CO2 temperature. When CO2 arrived at the well-bottom, its temperature reached 52.2°C with elevated pressure of 9.5 MPa. Compared to Case 1 (35°C), CO2 temperature at the well-bottom increased (ΔT=) +17.2°C. Due to significant discrepancy in CO2 temperature from these two cases, thermodynamic properties of CO2 were also different which affected the behavior of CO2 transport in the storage formation.The other three profiles (91, 365, and 1,095 days) were selected during Stage III. These profiles were paralleled to isenthalpic lines, implying that CO2 within the wellbore reached the adiabatic condition (Figures 3(c) and 3(d)). In this condition, Joule-Thomson effect on CO2 temperature would be more significant than any other thermal processes [21]. As seen in Figure 3(d), Joule-Thomson coefficient having positive values decreased from 8.8 to 6.4°C/MPa as approaching to the well-bottom; positive values of Joule-Thomson coefficient imply the adiabatic heating with CO2 compression, and its effect was relatively large at the shallow depth. All these three profiles revealed that gaseous CO2 filled the small portion of the well-head even after the arrival of the adiabatic condition. In addition, it is observed that the wellbore pressure slightly decreased with time; the small drop of the well-bottom pressure between 91 and 1,095 days was (ΔP=) −0.2 MPa (9.5 to 9.3 MPa). Correspondingly, CO2 density and viscosity at the well-bottom were decreased, (Δρ=) −19.9 kg/m3 (311.7 to 291.8 kg/m3) and (Δμ=) −0.1×10-5 Pa·s (2.5 to 2.4 × 10−5 Pa·s), respectively (Figure 3(c)).Overall, when comparing to CO2 density and viscosity from Case 2 (WR model), Case 1 (EPM model) was 680.0 kg/m3 and 5.4 × 10−5 Pa·s, respectively, at 1,095 days. As seen, discrepancies in thermophysical properties of CO2 were significant when two different injection schemes were used even with the same injection rate. This discrepancy became primary reasons for different distribution of CO2 plume within the storage formation and subsequently the patterns for the salt-precipitation, which will be discussed in following section.


### 3.2. Analyses of Storage Formation Conditions

#### 3.2.1. Patterns for CO2 Migration in the Storage Formations

Figure4 showed the distribution of CO2 saturation after 91, 365, and 1,095 days of CO2 injection; Figures 4(a)–4(c) and Figures 4(d)–4(f) were simulated with the EPM model (Case 1) and WR model (Case 2), respectively. Comparing two cases, the same mass of CO2 was injected into the storage formation (9.46 × 108 kg during 1,095 days), and consequently, CO2 plume migrated the equal distance of 1,048 m at the interface between the caprock and storage formation (Figures 4(c) and 4(f)). Nevertheless, at the bottom of the storage formation, the frontal location of CO2 plume was different (82.7 m and 66.9 m for Case 1 and Case 2, resp.), implying that more CO2 migrated vertically in Case 2, and therefore, more counterflowing brine was developed. According to (6), Ngv for each case was calculated and listed in Table 4. As expected, Ngv in Case 2 (2.76) was greater than Case 1 (2.20), implying that the buoyancy force acting on the CO2 plume was greater in Case 2.Table 4
Predicted gravity number for multiple cases as well as associated parameters used in (6).
Case
Time  (d)
u
i    (m/s)
ρ
b
r
i
n
e    (kg/m3)
ρ
C
O
2    (kg/m3)
μ   (Pa·s)
N
g
v
Case1
91
3.80 × 10−3
1097.7
557.4
4.5 × 10−5
2.33
365
3.84 × 10−3
1098.1
575.8
4.6 × 10−5
2.17
1,095
3.89 × 10−3
1098.5
571.0
4.5 × 10−5
2.20
Case2
91
8.73 × 10−3
1088.3
294.7
2.4 × 10−5
2.78
365
9.03 × 10−3
1084.7
287.2
2.4 × 10−5
2.74
1,095
9.41 × 10−3
1097.1
277.0
2.3 × 10−5
2.76
Sensitivity Scenarios
Case2-1
1,095
1.09 × 10−2
1096.5
248.0
2.2 × 10−5
2.56
Case2-2
1,095
1.26 × 10−2
1095.0
223.6
2.2 × 10−5
2.32
Case2-3
1,095
5.23 × 10−3
1097.5
251.4
2.2 × 10−5
5.36
Case2-4
1,095
2.49 × 10−2
1098.1
486.5
3.6 × 10−5
0.51
Case2-5
1,095
9.27 × 10−3
1097.2
280.4
2.3 × 10−5
2.77
Case2-6
1,095
4.07 × 10−3
1098.5
570.7
4.5 × 10−5
2.12
ρ
b
r
i
n
e, ρCO2, and μ are the average value of brine density, CO2 density, and CO2 viscosity in the storage formation, respectively.Figure 4
Distribution of CO2 saturation [-] shown as color contours and CO2 density [kg/m3] as dashed lines at a series of times (91, 365, 1,095 days). (a), (b), and (c) were simulated from the EPM model (Case 1) while (d), (e), and (f) were from the WR model (Case 2). The isodense lines represent the magnitude of density which follows the legend shown in (b) and (e).
(a)
(b)
(c)
(d)
(e)
(f)In Case1, density and viscosity of CO2 in the storage formation were greater than ~600 kg/m3 (Figures 4(a)–4(c)) and ~5.0 × 10−5 Pa·s, respectively (contour lines of CO2 viscosity were not plotted because they were similar to the isodense lines). However, density and viscosity decreased to ~200 kg/m3 and ~2.0 × 10−5 Pa·s, respectively, while approaching to the margin of the CO2 plume. In Case 2, CO2 density was relatively small, showing the range of 200 to 300 kg/m3 (Figures 4(d)–4(f)); CO2 density greater than 300 kg/m3 appeared only next to the injection well until 91 days (Figure 4(d)). In addition, CO2 viscosity ranged from 2.4 × 10−5 Pa·s adjacent to the wellbore to 2.0 × 10−5 Pa·s at the margin of the CO2 plume. Differences in CO2 properties such as density and viscosity in these two cases were amplified even after more CO2 was injected into the storage formation.


#### 3.2.2. Patterns for Salt-Precipitation and CO2/Brine Flow

At the dry-out zone, different patterns for the salt-precipitation also appeared in these two cases (Figure5). Here, the “dry-out zone” was defined as a zone where brine had been replaced by injected CO2, and consequently, its CO2 saturation approximately reached unity [34]. At the front of the dry-out zone (the interface of dry-CO2 and brine), pure H2O is continuously vaporized while remaining the solid salt in the pore. Degree and configuration of precipitated salt were governed by two factors; one was the migration speed of the dry-out front, which was governed by viscous force (e.g., injection rate and horizontal permeability of the storage formation). The others were factors governing buoyancy force (e.g., CO2 density, the rate for counterflowing brine, and vertical permeability of the storage formation). Additionally, the amount of salt (or salinity) supplied by the counterflowing brine also governed the amount of precipitated salt [37].Figure 5
Flux patterns for CO2 and brine near the injection well after the injection of 1,095 days. (a) and (d) predicted CO2 mass flow rate [kg/s] within grid-blocks representing the wellbore; blue circles are horizontal CO2 mass flow rate from the wellbore to the storage formation and red symbols are vertical CO2 mass flow rate within the wellbore. (b) and (e) indicate CO2 flux [kg/(s·m2) ] with CO2 saturation. (c) and (f) indicate brine flux [kg/(s·m2) ] with salt saturation. The arrows indicate directions for both CO2 and brine flux, and the colors represent their magnitude.
(a)
(b)
(c)
(d)
(e)
(f)In Case1 (EPM model) following the conventional modeling approach (1 kg/s of CO2), distribution of horizontal CO2 flux along the radial distance was almost uniform (e.g., 4.4 × 10−3 kg/(s·m2) at 9.04 m at 1,095 days) (Figures 5(a) and 5(b)). In contrast, the counterflowing brine with its magnitude of 1.5 × 10−7 kg/(s·m2) flew opposite to CO2 flux at 9.04 m (Figure 5(c)). The detailed snap-shots of the growing salt-precipitation were plotted at 91, 365, and 1,095 days in Figures 6(a)–6(c). As seen, the salt was uniformly accumulated throughout the entire thickness of the storage formation with its saturation of approximately 0.04. Correspondingly, the average permeability reduction (k/k0) calculated from (3) was 65.1% in 1,095 days. Slightly elevated salt saturation appeared at both nearby the wellbore and the interface between sealing and storage formations. Adjacent to the wellbore, the salt saturation increased to be 0.06 due to the complete vaporization of residual brine. At the interface of the sealing formation, the salt saturation was increased due to H2O vaporization from the inflowing brine. According to Kim et al. [39], residual brine flew from the sealing formation to the dry-out zone where brine was completely displaced by injected dry-CO2 (Figure 5(c)). Consequently, the maximum salt saturation and the k/k0 reached 0.078 and 39.2%, respectively.Figure 6
Distribution of salt saturation [-] shown as color contours and the dry-out front as dashed lines at a series of times (91, 365, and 1,095 days). (a), (b), and (c) were simulated from the EPM model (Case1), but (d), (e), and (f) were from the WR model (Case 2).
(a)
(b)
(c)
(d)
(e)
(f)The WR model (Case2) was able to predict the profiles for both horizontal and vertical CO2 mass flow rates within the wellbore (Figure 5(d)). Above the interface (740 m) between the storage and sealing formations, the vertical CO2 mass flow rate was consistently 10 kg/s because the wellbore was fully cased (red circle in Figure 5(d)). However, once CO2 entered the screened interval (740 to 780 m), the vertical CO2 mass flow rate decreased with the depth almost linearly and finally reached zero at the well-bottom. In this interval, the horizontal CO2 mass flow rate reflected the actual CO2 injection rate (blue circles in Figure 5(d)). As seen in Figures 5(a) and 5(d), the actual CO2 injection rates from both cases were different; in Case 2, the actual CO2 injection rates were larger at the upper storage formation except the interface similar to Vilarrasa et al. [64] and decreased toward the well-bottom. However, throughout the entire thickness, the average actual CO2 injection rate was the same as the injection rate assigned to Case 1 (i.e., 10 kg/s).Due to magnitude difference of actual CO2 injection rates throughout the screen interval, both viscous and buoyancy forces differently acted on CO2 plume between Case 1 and Case 2 [44]. Furthermore, relatively warm CO2 (e.g., 52°C) entered from the wellbore to the storage formation also amplified the buoyancy effect on CO2 plume (Figure 3(c)). Due to these reasons, in Case 2, the injected CO2 plume rose rapidly, inducing more counterflowing brine flux (5.0 × 10−6 kg/(s·m2) at 8 m at 1,095 days) along the bottom of the storage formation (Figure 5(f)). Because of strong buoyancy effect on the CO2 plume, the configuration of the dry-out zone where the salt was precipitated was nonuniform. In particular, the localized salt-peak was developed due to additional supply of salinity by counterflowing brine.At the zone where the localized salt was precipitated, the maximum salt saturation reached almost equal to porosity (0.25) implying significant deterioration of permeability; the cumulated salt-barrier restricted horizontal propagations of both CO2 and pressure, consequently reducing effectiveness of the injection well. Figures 6(d)–6(f) showed the development of salt-precipitation at 91, 365, and 1,095 days. According to Figure 6(f), it is distinct that the lower part of the dry-out front stopped expanding after 365 days when the localized salt-peak was developed.


## 3.1. Analyses of Wellbore Flow Conditions

### 3.1.1. Characterization of Multiple Stages in the Wellbore

In Case1 (EPM model), CO2 holding constant temperature of 35.0°C was injected into the storage formation (formation pressure from 7.95 MPa to 8.33 MPa) at a constant rate of 10 kg/s throughout the simulation time (Figure 1(a)). Following the injection conditions, CO2 injected into the storage formation was in supercritical phase consistently preserving its density and viscosity approximately larger than 600 kg/m3 and 5.0 × 10−5 Pa·s, respectively.In Case2 (WR model), CO2 holding 35.0°C was injected from the well-head at a rate of 10 kg/s (Figure 1(b)). Once CO2 was entered from the well-head, it transported through the 780 m depth wellbore (Figure 2(a)) while experiencing thermal disequilibrium processes such as heat convection, conduction, frictional effect, and Joule-Thomson effect [21, 27]. Consequently, the temperature of CO2 reaching the well-bottom was changed from 35.0°C (at the well-head) to approximately 52.0°C. Due to such dynamic disturbance in both temperature and pressure within the wellbore, the thermodynamic properties of CO2 entering from the well-head were also different with ones reaching the well-bottom.Figure 2
Changes in thermophysical properties of CO2 within the wellbore during 100 days; (a) a schematic diagram delineating CO2 transport within the wellbore and associated thermal effects; profiles for (b) CO2 saturation [-], (c) pressure [Pa], and (d) temperature [°C]. The two white dotted lines define the initiation of each different stage while injected CO2 is displacing the brine in the wellbore (1.2 × 10−5 (=1 sec) and 1.2 × 10−2 (=17.3 min)). The yellow dashed line in (b) represents the interface between gaseous and supercritical CO2 phase. The purple dashed lines shown in (c) and (d) indicate the dynamic interface between CO2 and brine.
(a)
(b)
(c)
(d)Figures2(b)–2(d) showed changes in CO2 saturation, pressure, and temperature throughout the wellbore during 100 days after CO2 injection began. According to CO2 saturation profile in Figure 2(b), three stages were characterized. Stage I (0 to 1.2 × 10−5 day (=1 sec)) defined the status of the wellbore where brine was fully saturated in the well; both pressure and temperature remained hydrostatic and geothermal gradient conditions, initially assigned to the model (Stage I in Figures 2(c) and 2(d)). During Stage II (1.2 × 10−5 day (=1 sec) to 1.2 × 10−2 day (=17.3 min)), the wellbore transited from single (or brine) to multiphase conditions where both brine and CO2 coexisted; the dynamic interface (dashed purple-line in Figures 2(c) and 2(d)) between injected CO2 and brine was developed. In addition, the phase transition of CO2 from gaseous to supercritical phase was observed at a depth of 468 m for the first time (3.2 × 10−3 day), which dynamically evolved with time (Figure 2(b)). Approximately after 3.35 day, gaseous CO2 in the wellbore completely transited to supercritical phase.Immediately after CO2 injection began at Stage II, CO2 suddenly pushed brine from the well-head, and therefore, increase in CO2 saturation was observed at the well-head (Figure 2(b)). Due to the encroachment of CO2 from the well-head, brine positioned at the well-bottom needed to enter the storage formation in which permeability (3 × 10−13 m2) and capillary pressure were significantly smaller and larger than the wellbore ones, respectively. Because of contrasts in both permeability and capillary pressure between the wellbore and storage formation, the pressure at the wellbore was built up and reached its peak at 2.3 × 10−4 day (Figure 2(c)). Then, subsequent pressure reduction implies that brine at the well-bottom was getting entered the storage formation with continuous CO2 injection from the well-head. Gradual decrease in the wellbore pressure was observed until the wellbore was completely replaced by CO2 at 1.2 × 10−2 day (Figure 2(c)).The temperature profile was somewhat similar to pressure one. At Stage I, temperature ranged from the well-head to well-bottom was 20.0°C to 56.0°C (Figure2(d)). Then, CO2 with temperature of 35.0°C was injected from the well-head. While 35.0°C CO2 displaced the brine from the well-head, relatively warm brine (approximately 50.0–56.0°C) positioned at the bottom of the wellbore entered the storage formation (Stage II). Concurrently, low-temperature brine (20.0°C) was pushed from the well-head to the deeper part of the wellbore by injected CO2. While the injected CO2 pushed low-temperature brine downward, diverse thermal processes including thermal convection, conduction, frictional effect, and Joule-Thomson effect occurred concurrently. However, because thermal convection representing the movement of shallow cold-brine toward the well-bottom was more dominant than other thermal effects, overall decrease in temperature was observed in the wellbore.Immediately after Stage III at 1.2 × 10−2 day, the wellbore was completed replaced by the injected CO2. Soon, both pressure and temperature increased together (6.9 × 10−2 day). This positive relationship can be attributed to Joule-Thomson effect ((∂T/∂P)H), which defines change in temperature during (de)compression of CO2 based on its counterpart of pressure change under the isenthalpic condition [62]. After 3.35 day, profiles for both pressure and temperature reached the steady-state condition while CO2 in the wellbore completely became supercritical phase (Figure 2(b)). In summary, due to thermal processes such as frictional effect, heat conduction, and Joule-Thomson effect, temperature of CO2 which entered the storage formation reached approximately 51-52°C, which was greater than injected CO2 (35°C) but lower than temperature (54-55°C) of the storage formation.


### 3.1.2. Variations in Thermophysical Properties of Injected CO2

Figure3 showed contours for density, viscosity, specific enthalpy, and Joule-Thomson coefficient of CO2 dependent on temperature and pressure, which were predicted from Span and Wagner [63]. Figures 3(a) and 3(b) delineated relatively wide ranges covering pressure from 0 to 30 MPa and temperature from 0 to 200°C. Therefore, appropriate ranges for pressure (6 to 10 MPa) and temperature (20 to 80°C) were selected, and CO2 injection condition was examined for both cases (Figures 3(c) and 3(d)).Figure 3
Contours of (a) density [kg/m3] and viscosity [10−5 Pa·s] and (b) enthalpy [kJ/kg] and Joule-Thomson coefficient [°C/MPa] in P-T space. Gray box represents a suitable condition for the wellbore during geologic CO2 sequestration (P: 6 to 10 MPa and T: 20 to 80°C). (c) and (d) represent contours for density, viscosity, enthalpy, and Joule-Thomson coefficient in P-T regime suitable for the wellbore. Purple symbols represent the conditions for CO2 injection in Case 1. Green symbols and lines represent the conditions for the wellbore in Case 2.
(a)
(b)
(c)
(d)The CO2 injection condition for Case 1 (EPM model; purple symbols) was plotted at 1,095 days (Figure 3(c)). After 1,095 days, pressure from the top to the bottom of the storage formation was changed from 9.16 to 9.26 MPa while maintaining 35°C. At this condition, the injected CO2 was completely supercritical phase with relatively large density (approximate 650 kg/m3) and viscosity (approximate 5.2 × 10−5 Pa·s) (Figure 3(c)).For Case2 (WR model), 4 profiles were selected; one was at the end of Stage II (1.2 × 10−2 day in Figure 2(b)) immediately after the wellbore was completely filled with CO2; at this time, the injected CO2 experienced phase transition from gaseous to supercritical phase at 155 m depth (Point A in Figures 2(b) and 3(c)). Presence of both gaseous and supercritical CO2 within the wellbore resulted in dynamic (or nonlinear) profile of CO2. At the well-head, temperature and pressure were 35°C and 6.96 MPa, which was plotted below the critical point (31.1°C and 7.38 MPa) of CO2. Then, at 155 m (Point A) temperature dropped to 32.6°C (ΔT=-2.4°C) while pressure increased to 7.37 MPa (ΔP=+0.4 MPa). Similar to Han et al. [27] and Lu and Connell [21], decrease in CO2 temperature occurred in the wellbore due to heat conduction with the surrounding formation; the temperature of the surrounding formation was 27.1°C in this depth. From the ground surface to 155 m, gaseous CO2 in the wellbore holds its density from 219 to 326 kg/m3, viscosity from 2.0 × 10−5 to 2.3 × 10−5 Pa·s, and Joule-Thomson coefficient decreasing from 9.1 to 8.2°C/MPa. Deeper than 155 m, gaseous CO2 transited to supercritical phase. Both temperature and pressure increased nonlinearly while deviating from isenthalpic lines (300–350 kJ/kg in Figure 3(d)), implying that supercritical CO2 in the wellbore did not reach the adiabatic condition yet; thus, various thermal processes including thermal conduction and friction actively affected CO2 temperature. When CO2 arrived at the well-bottom, its temperature reached 52.2°C with elevated pressure of 9.5 MPa. Compared to Case 1 (35°C), CO2 temperature at the well-bottom increased (ΔT=) +17.2°C. Due to significant discrepancy in CO2 temperature from these two cases, thermodynamic properties of CO2 were also different which affected the behavior of CO2 transport in the storage formation.The other three profiles (91, 365, and 1,095 days) were selected during Stage III. These profiles were paralleled to isenthalpic lines, implying that CO2 within the wellbore reached the adiabatic condition (Figures 3(c) and 3(d)). In this condition, Joule-Thomson effect on CO2 temperature would be more significant than any other thermal processes [21]. As seen in Figure 3(d), Joule-Thomson coefficient having positive values decreased from 8.8 to 6.4°C/MPa as approaching to the well-bottom; positive values of Joule-Thomson coefficient imply the adiabatic heating with CO2 compression, and its effect was relatively large at the shallow depth. All these three profiles revealed that gaseous CO2 filled the small portion of the well-head even after the arrival of the adiabatic condition. In addition, it is observed that the wellbore pressure slightly decreased with time; the small drop of the well-bottom pressure between 91 and 1,095 days was (ΔP=) −0.2 MPa (9.5 to 9.3 MPa). Correspondingly, CO2 density and viscosity at the well-bottom were decreased, (Δρ=) −19.9 kg/m3 (311.7 to 291.8 kg/m3) and (Δμ=) −0.1×10-5 Pa·s (2.5 to 2.4 × 10−5 Pa·s), respectively (Figure 3(c)).Overall, when comparing to CO2 density and viscosity from Case 2 (WR model), Case 1 (EPM model) was 680.0 kg/m3 and 5.4 × 10−5 Pa·s, respectively, at 1,095 days. As seen, discrepancies in thermophysical properties of CO2 were significant when two different injection schemes were used even with the same injection rate. This discrepancy became primary reasons for different distribution of CO2 plume within the storage formation and subsequently the patterns for the salt-precipitation, which will be discussed in following section.


## 3.1.1. Characterization of Multiple Stages in the Wellbore

In Case1 (EPM model), CO2 holding constant temperature of 35.0°C was injected into the storage formation (formation pressure from 7.95 MPa to 8.33 MPa) at a constant rate of 10 kg/s throughout the simulation time (Figure 1(a)). Following the injection conditions, CO2 injected into the storage formation was in supercritical phase consistently preserving its density and viscosity approximately larger than 600 kg/m3 and 5.0 × 10−5 Pa·s, respectively.In Case2 (WR model), CO2 holding 35.0°C was injected from the well-head at a rate of 10 kg/s (Figure 1(b)). Once CO2 was entered from the well-head, it transported through the 780 m depth wellbore (Figure 2(a)) while experiencing thermal disequilibrium processes such as heat convection, conduction, frictional effect, and Joule-Thomson effect [21, 27]. Consequently, the temperature of CO2 reaching the well-bottom was changed from 35.0°C (at the well-head) to approximately 52.0°C. Due to such dynamic disturbance in both temperature and pressure within the wellbore, the thermodynamic properties of CO2 entering from the well-head were also different with ones reaching the well-bottom.Figure 2
Changes in thermophysical properties of CO2 within the wellbore during 100 days; (a) a schematic diagram delineating CO2 transport within the wellbore and associated thermal effects; profiles for (b) CO2 saturation [-], (c) pressure [Pa], and (d) temperature [°C]. The two white dotted lines define the initiation of each different stage while injected CO2 is displacing the brine in the wellbore (1.2 × 10−5 (=1 sec) and 1.2 × 10−2 (=17.3 min)). The yellow dashed line in (b) represents the interface between gaseous and supercritical CO2 phase. The purple dashed lines shown in (c) and (d) indicate the dynamic interface between CO2 and brine.
(a)
(b)
(c)
(d)Figures2(b)–2(d) showed changes in CO2 saturation, pressure, and temperature throughout the wellbore during 100 days after CO2 injection began. According to CO2 saturation profile in Figure 2(b), three stages were characterized. Stage I (0 to 1.2 × 10−5 day (=1 sec)) defined the status of the wellbore where brine was fully saturated in the well; both pressure and temperature remained hydrostatic and geothermal gradient conditions, initially assigned to the model (Stage I in Figures 2(c) and 2(d)). During Stage II (1.2 × 10−5 day (=1 sec) to 1.2 × 10−2 day (=17.3 min)), the wellbore transited from single (or brine) to multiphase conditions where both brine and CO2 coexisted; the dynamic interface (dashed purple-line in Figures 2(c) and 2(d)) between injected CO2 and brine was developed. In addition, the phase transition of CO2 from gaseous to supercritical phase was observed at a depth of 468 m for the first time (3.2 × 10−3 day), which dynamically evolved with time (Figure 2(b)). Approximately after 3.35 day, gaseous CO2 in the wellbore completely transited to supercritical phase.Immediately after CO2 injection began at Stage II, CO2 suddenly pushed brine from the well-head, and therefore, increase in CO2 saturation was observed at the well-head (Figure 2(b)). Due to the encroachment of CO2 from the well-head, brine positioned at the well-bottom needed to enter the storage formation in which permeability (3 × 10−13 m2) and capillary pressure were significantly smaller and larger than the wellbore ones, respectively. Because of contrasts in both permeability and capillary pressure between the wellbore and storage formation, the pressure at the wellbore was built up and reached its peak at 2.3 × 10−4 day (Figure 2(c)). Then, subsequent pressure reduction implies that brine at the well-bottom was getting entered the storage formation with continuous CO2 injection from the well-head. Gradual decrease in the wellbore pressure was observed until the wellbore was completely replaced by CO2 at 1.2 × 10−2 day (Figure 2(c)).The temperature profile was somewhat similar to pressure one. At Stage I, temperature ranged from the well-head to well-bottom was 20.0°C to 56.0°C (Figure2(d)). Then, CO2 with temperature of 35.0°C was injected from the well-head. While 35.0°C CO2 displaced the brine from the well-head, relatively warm brine (approximately 50.0–56.0°C) positioned at the bottom of the wellbore entered the storage formation (Stage II). Concurrently, low-temperature brine (20.0°C) was pushed from the well-head to the deeper part of the wellbore by injected CO2. While the injected CO2 pushed low-temperature brine downward, diverse thermal processes including thermal convection, conduction, frictional effect, and Joule-Thomson effect occurred concurrently. However, because thermal convection representing the movement of shallow cold-brine toward the well-bottom was more dominant than other thermal effects, overall decrease in temperature was observed in the wellbore.Immediately after Stage III at 1.2 × 10−2 day, the wellbore was completed replaced by the injected CO2. Soon, both pressure and temperature increased together (6.9 × 10−2 day). This positive relationship can be attributed to Joule-Thomson effect ((∂T/∂P)H), which defines change in temperature during (de)compression of CO2 based on its counterpart of pressure change under the isenthalpic condition [62]. After 3.35 day, profiles for both pressure and temperature reached the steady-state condition while CO2 in the wellbore completely became supercritical phase (Figure 2(b)). In summary, due to thermal processes such as frictional effect, heat conduction, and Joule-Thomson effect, temperature of CO2 which entered the storage formation reached approximately 51-52°C, which was greater than injected CO2 (35°C) but lower than temperature (54-55°C) of the storage formation.


## 3.1.2. Variations in Thermophysical Properties of Injected CO2

Figure3 showed contours for density, viscosity, specific enthalpy, and Joule-Thomson coefficient of CO2 dependent on temperature and pressure, which were predicted from Span and Wagner [63]. Figures 3(a) and 3(b) delineated relatively wide ranges covering pressure from 0 to 30 MPa and temperature from 0 to 200°C. Therefore, appropriate ranges for pressure (6 to 10 MPa) and temperature (20 to 80°C) were selected, and CO2 injection condition was examined for both cases (Figures 3(c) and 3(d)).Figure 3
Contours of (a) density [kg/m3] and viscosity [10−5 Pa·s] and (b) enthalpy [kJ/kg] and Joule-Thomson coefficient [°C/MPa] in P-T space. Gray box represents a suitable condition for the wellbore during geologic CO2 sequestration (P: 6 to 10 MPa and T: 20 to 80°C). (c) and (d) represent contours for density, viscosity, enthalpy, and Joule-Thomson coefficient in P-T regime suitable for the wellbore. Purple symbols represent the conditions for CO2 injection in Case 1. Green symbols and lines represent the conditions for the wellbore in Case 2.
(a)
(b)
(c)
(d)The CO2 injection condition for Case 1 (EPM model; purple symbols) was plotted at 1,095 days (Figure 3(c)). After 1,095 days, pressure from the top to the bottom of the storage formation was changed from 9.16 to 9.26 MPa while maintaining 35°C. At this condition, the injected CO2 was completely supercritical phase with relatively large density (approximate 650 kg/m3) and viscosity (approximate 5.2 × 10−5 Pa·s) (Figure 3(c)).For Case2 (WR model), 4 profiles were selected; one was at the end of Stage II (1.2 × 10−2 day in Figure 2(b)) immediately after the wellbore was completely filled with CO2; at this time, the injected CO2 experienced phase transition from gaseous to supercritical phase at 155 m depth (Point A in Figures 2(b) and 3(c)). Presence of both gaseous and supercritical CO2 within the wellbore resulted in dynamic (or nonlinear) profile of CO2. At the well-head, temperature and pressure were 35°C and 6.96 MPa, which was plotted below the critical point (31.1°C and 7.38 MPa) of CO2. Then, at 155 m (Point A) temperature dropped to 32.6°C (ΔT=-2.4°C) while pressure increased to 7.37 MPa (ΔP=+0.4 MPa). Similar to Han et al. [27] and Lu and Connell [21], decrease in CO2 temperature occurred in the wellbore due to heat conduction with the surrounding formation; the temperature of the surrounding formation was 27.1°C in this depth. From the ground surface to 155 m, gaseous CO2 in the wellbore holds its density from 219 to 326 kg/m3, viscosity from 2.0 × 10−5 to 2.3 × 10−5 Pa·s, and Joule-Thomson coefficient decreasing from 9.1 to 8.2°C/MPa. Deeper than 155 m, gaseous CO2 transited to supercritical phase. Both temperature and pressure increased nonlinearly while deviating from isenthalpic lines (300–350 kJ/kg in Figure 3(d)), implying that supercritical CO2 in the wellbore did not reach the adiabatic condition yet; thus, various thermal processes including thermal conduction and friction actively affected CO2 temperature. When CO2 arrived at the well-bottom, its temperature reached 52.2°C with elevated pressure of 9.5 MPa. Compared to Case 1 (35°C), CO2 temperature at the well-bottom increased (ΔT=) +17.2°C. Due to significant discrepancy in CO2 temperature from these two cases, thermodynamic properties of CO2 were also different which affected the behavior of CO2 transport in the storage formation.The other three profiles (91, 365, and 1,095 days) were selected during Stage III. These profiles were paralleled to isenthalpic lines, implying that CO2 within the wellbore reached the adiabatic condition (Figures 3(c) and 3(d)). In this condition, Joule-Thomson effect on CO2 temperature would be more significant than any other thermal processes [21]. As seen in Figure 3(d), Joule-Thomson coefficient having positive values decreased from 8.8 to 6.4°C/MPa as approaching to the well-bottom; positive values of Joule-Thomson coefficient imply the adiabatic heating with CO2 compression, and its effect was relatively large at the shallow depth. All these three profiles revealed that gaseous CO2 filled the small portion of the well-head even after the arrival of the adiabatic condition. In addition, it is observed that the wellbore pressure slightly decreased with time; the small drop of the well-bottom pressure between 91 and 1,095 days was (ΔP=) −0.2 MPa (9.5 to 9.3 MPa). Correspondingly, CO2 density and viscosity at the well-bottom were decreased, (Δρ=) −19.9 kg/m3 (311.7 to 291.8 kg/m3) and (Δμ=) −0.1×10-5 Pa·s (2.5 to 2.4 × 10−5 Pa·s), respectively (Figure 3(c)).Overall, when comparing to CO2 density and viscosity from Case 2 (WR model), Case 1 (EPM model) was 680.0 kg/m3 and 5.4 × 10−5 Pa·s, respectively, at 1,095 days. As seen, discrepancies in thermophysical properties of CO2 were significant when two different injection schemes were used even with the same injection rate. This discrepancy became primary reasons for different distribution of CO2 plume within the storage formation and subsequently the patterns for the salt-precipitation, which will be discussed in following section.


## 3.2. Analyses of Storage Formation Conditions

### 3.2.1. Patterns for CO2 Migration in the Storage Formations

Figure4 showed the distribution of CO2 saturation after 91, 365, and 1,095 days of CO2 injection; Figures 4(a)–4(c) and Figures 4(d)–4(f) were simulated with the EPM model (Case 1) and WR model (Case 2), respectively. Comparing two cases, the same mass of CO2 was injected into the storage formation (9.46 × 108 kg during 1,095 days), and consequently, CO2 plume migrated the equal distance of 1,048 m at the interface between the caprock and storage formation (Figures 4(c) and 4(f)). Nevertheless, at the bottom of the storage formation, the frontal location of CO2 plume was different (82.7 m and 66.9 m for Case 1 and Case 2, resp.), implying that more CO2 migrated vertically in Case 2, and therefore, more counterflowing brine was developed. According to (6), Ngv for each case was calculated and listed in Table 4. As expected, Ngv in Case 2 (2.76) was greater than Case 1 (2.20), implying that the buoyancy force acting on the CO2 plume was greater in Case 2.Table 4
Predicted gravity number for multiple cases as well as associated parameters used in (6).
Case
Time  (d)
u
i    (m/s)
ρ
b
r
i
n
e    (kg/m3)
ρ
C
O
2    (kg/m3)
μ   (Pa·s)
N
g
v
Case1
91
3.80 × 10−3
1097.7
557.4
4.5 × 10−5
2.33
365
3.84 × 10−3
1098.1
575.8
4.6 × 10−5
2.17
1,095
3.89 × 10−3
1098.5
571.0
4.5 × 10−5
2.20
Case2
91
8.73 × 10−3
1088.3
294.7
2.4 × 10−5
2.78
365
9.03 × 10−3
1084.7
287.2
2.4 × 10−5
2.74
1,095
9.41 × 10−3
1097.1
277.0
2.3 × 10−5
2.76
Sensitivity Scenarios
Case2-1
1,095
1.09 × 10−2
1096.5
248.0
2.2 × 10−5
2.56
Case2-2
1,095
1.26 × 10−2
1095.0
223.6
2.2 × 10−5
2.32
Case2-3
1,095
5.23 × 10−3
1097.5
251.4
2.2 × 10−5
5.36
Case2-4
1,095
2.49 × 10−2
1098.1
486.5
3.6 × 10−5
0.51
Case2-5
1,095
9.27 × 10−3
1097.2
280.4
2.3 × 10−5
2.77
Case2-6
1,095
4.07 × 10−3
1098.5
570.7
4.5 × 10−5
2.12
ρ
b
r
i
n
e, ρCO2, and μ are the average value of brine density, CO2 density, and CO2 viscosity in the storage formation, respectively.Figure 4
Distribution of CO2 saturation [-] shown as color contours and CO2 density [kg/m3] as dashed lines at a series of times (91, 365, 1,095 days). (a), (b), and (c) were simulated from the EPM model (Case 1) while (d), (e), and (f) were from the WR model (Case 2). The isodense lines represent the magnitude of density which follows the legend shown in (b) and (e).
(a)
(b)
(c)
(d)
(e)
(f)In Case1, density and viscosity of CO2 in the storage formation were greater than ~600 kg/m3 (Figures 4(a)–4(c)) and ~5.0 × 10−5 Pa·s, respectively (contour lines of CO2 viscosity were not plotted because they were similar to the isodense lines). However, density and viscosity decreased to ~200 kg/m3 and ~2.0 × 10−5 Pa·s, respectively, while approaching to the margin of the CO2 plume. In Case 2, CO2 density was relatively small, showing the range of 200 to 300 kg/m3 (Figures 4(d)–4(f)); CO2 density greater than 300 kg/m3 appeared only next to the injection well until 91 days (Figure 4(d)). In addition, CO2 viscosity ranged from 2.4 × 10−5 Pa·s adjacent to the wellbore to 2.0 × 10−5 Pa·s at the margin of the CO2 plume. Differences in CO2 properties such as density and viscosity in these two cases were amplified even after more CO2 was injected into the storage formation.


### 3.2.2. Patterns for Salt-Precipitation and CO2/Brine Flow

At the dry-out zone, different patterns for the salt-precipitation also appeared in these two cases (Figure5). Here, the “dry-out zone” was defined as a zone where brine had been replaced by injected CO2, and consequently, its CO2 saturation approximately reached unity [34]. At the front of the dry-out zone (the interface of dry-CO2 and brine), pure H2O is continuously vaporized while remaining the solid salt in the pore. Degree and configuration of precipitated salt were governed by two factors; one was the migration speed of the dry-out front, which was governed by viscous force (e.g., injection rate and horizontal permeability of the storage formation). The others were factors governing buoyancy force (e.g., CO2 density, the rate for counterflowing brine, and vertical permeability of the storage formation). Additionally, the amount of salt (or salinity) supplied by the counterflowing brine also governed the amount of precipitated salt [37].Figure 5
Flux patterns for CO2 and brine near the injection well after the injection of 1,095 days. (a) and (d) predicted CO2 mass flow rate [kg/s] within grid-blocks representing the wellbore; blue circles are horizontal CO2 mass flow rate from the wellbore to the storage formation and red symbols are vertical CO2 mass flow rate within the wellbore. (b) and (e) indicate CO2 flux [kg/(s·m2) ] with CO2 saturation. (c) and (f) indicate brine flux [kg/(s·m2) ] with salt saturation. The arrows indicate directions for both CO2 and brine flux, and the colors represent their magnitude.
(a)
(b)
(c)
(d)
(e)
(f)In Case1 (EPM model) following the conventional modeling approach (1 kg/s of CO2), distribution of horizontal CO2 flux along the radial distance was almost uniform (e.g., 4.4 × 10−3 kg/(s·m2) at 9.04 m at 1,095 days) (Figures 5(a) and 5(b)). In contrast, the counterflowing brine with its magnitude of 1.5 × 10−7 kg/(s·m2) flew opposite to CO2 flux at 9.04 m (Figure 5(c)). The detailed snap-shots of the growing salt-precipitation were plotted at 91, 365, and 1,095 days in Figures 6(a)–6(c). As seen, the salt was uniformly accumulated throughout the entire thickness of the storage formation with its saturation of approximately 0.04. Correspondingly, the average permeability reduction (k/k0) calculated from (3) was 65.1% in 1,095 days. Slightly elevated salt saturation appeared at both nearby the wellbore and the interface between sealing and storage formations. Adjacent to the wellbore, the salt saturation increased to be 0.06 due to the complete vaporization of residual brine. At the interface of the sealing formation, the salt saturation was increased due to H2O vaporization from the inflowing brine. According to Kim et al. [39], residual brine flew from the sealing formation to the dry-out zone where brine was completely displaced by injected dry-CO2 (Figure 5(c)). Consequently, the maximum salt saturation and the k/k0 reached 0.078 and 39.2%, respectively.Figure 6
Distribution of salt saturation [-] shown as color contours and the dry-out front as dashed lines at a series of times (91, 365, and 1,095 days). (a), (b), and (c) were simulated from the EPM model (Case1), but (d), (e), and (f) were from the WR model (Case 2).
(a)
(b)
(c)
(d)
(e)
(f)The WR model (Case2) was able to predict the profiles for both horizontal and vertical CO2 mass flow rates within the wellbore (Figure 5(d)). Above the interface (740 m) between the storage and sealing formations, the vertical CO2 mass flow rate was consistently 10 kg/s because the wellbore was fully cased (red circle in Figure 5(d)). However, once CO2 entered the screened interval (740 to 780 m), the vertical CO2 mass flow rate decreased with the depth almost linearly and finally reached zero at the well-bottom. In this interval, the horizontal CO2 mass flow rate reflected the actual CO2 injection rate (blue circles in Figure 5(d)). As seen in Figures 5(a) and 5(d), the actual CO2 injection rates from both cases were different; in Case 2, the actual CO2 injection rates were larger at the upper storage formation except the interface similar to Vilarrasa et al. [64] and decreased toward the well-bottom. However, throughout the entire thickness, the average actual CO2 injection rate was the same as the injection rate assigned to Case 1 (i.e., 10 kg/s).Due to magnitude difference of actual CO2 injection rates throughout the screen interval, both viscous and buoyancy forces differently acted on CO2 plume between Case 1 and Case 2 [44]. Furthermore, relatively warm CO2 (e.g., 52°C) entered from the wellbore to the storage formation also amplified the buoyancy effect on CO2 plume (Figure 3(c)). Due to these reasons, in Case 2, the injected CO2 plume rose rapidly, inducing more counterflowing brine flux (5.0 × 10−6 kg/(s·m2) at 8 m at 1,095 days) along the bottom of the storage formation (Figure 5(f)). Because of strong buoyancy effect on the CO2 plume, the configuration of the dry-out zone where the salt was precipitated was nonuniform. In particular, the localized salt-peak was developed due to additional supply of salinity by counterflowing brine.At the zone where the localized salt was precipitated, the maximum salt saturation reached almost equal to porosity (0.25) implying significant deterioration of permeability; the cumulated salt-barrier restricted horizontal propagations of both CO2 and pressure, consequently reducing effectiveness of the injection well. Figures 6(d)–6(f) showed the development of salt-precipitation at 91, 365, and 1,095 days. According to Figure 6(f), it is distinct that the lower part of the dry-out front stopped expanding after 365 days when the localized salt-peak was developed.


## 3.2.1. Patterns for CO2 Migration in the Storage Formations

Figure4 showed the distribution of CO2 saturation after 91, 365, and 1,095 days of CO2 injection; Figures 4(a)–4(c) and Figures 4(d)–4(f) were simulated with the EPM model (Case 1) and WR model (Case 2), respectively. Comparing two cases, the same mass of CO2 was injected into the storage formation (9.46 × 108 kg during 1,095 days), and consequently, CO2 plume migrated the equal distance of 1,048 m at the interface between the caprock and storage formation (Figures 4(c) and 4(f)). Nevertheless, at the bottom of the storage formation, the frontal location of CO2 plume was different (82.7 m and 66.9 m for Case 1 and Case 2, resp.), implying that more CO2 migrated vertically in Case 2, and therefore, more counterflowing brine was developed. According to (6), Ngv for each case was calculated and listed in Table 4. As expected, Ngv in Case 2 (2.76) was greater than Case 1 (2.20), implying that the buoyancy force acting on the CO2 plume was greater in Case 2.Table 4
Predicted gravity number for multiple cases as well as associated parameters used in (6).
Case
Time  (d)
u
i    (m/s)
ρ
b
r
i
n
e    (kg/m3)
ρ
C
O
2    (kg/m3)
μ   (Pa·s)
N
g
v
Case1
91
3.80 × 10−3
1097.7
557.4
4.5 × 10−5
2.33
365
3.84 × 10−3
1098.1
575.8
4.6 × 10−5
2.17
1,095
3.89 × 10−3
1098.5
571.0
4.5 × 10−5
2.20
Case2
91
8.73 × 10−3
1088.3
294.7
2.4 × 10−5
2.78
365
9.03 × 10−3
1084.7
287.2
2.4 × 10−5
2.74
1,095
9.41 × 10−3
1097.1
277.0
2.3 × 10−5
2.76
Sensitivity Scenarios
Case2-1
1,095
1.09 × 10−2
1096.5
248.0
2.2 × 10−5
2.56
Case2-2
1,095
1.26 × 10−2
1095.0
223.6
2.2 × 10−5
2.32
Case2-3
1,095
5.23 × 10−3
1097.5
251.4
2.2 × 10−5
5.36
Case2-4
1,095
2.49 × 10−2
1098.1
486.5
3.6 × 10−5
0.51
Case2-5
1,095
9.27 × 10−3
1097.2
280.4
2.3 × 10−5
2.77
Case2-6
1,095
4.07 × 10−3
1098.5
570.7
4.5 × 10−5
2.12
ρ
b
r
i
n
e, ρCO2, and μ are the average value of brine density, CO2 density, and CO2 viscosity in the storage formation, respectively.Figure 4
Distribution of CO2 saturation [-] shown as color contours and CO2 density [kg/m3] as dashed lines at a series of times (91, 365, 1,095 days). (a), (b), and (c) were simulated from the EPM model (Case 1) while (d), (e), and (f) were from the WR model (Case 2). The isodense lines represent the magnitude of density which follows the legend shown in (b) and (e).
(a)
(b)
(c)
(d)
(e)
(f)In Case1, density and viscosity of CO2 in the storage formation were greater than ~600 kg/m3 (Figures 4(a)–4(c)) and ~5.0 × 10−5 Pa·s, respectively (contour lines of CO2 viscosity were not plotted because they were similar to the isodense lines). However, density and viscosity decreased to ~200 kg/m3 and ~2.0 × 10−5 Pa·s, respectively, while approaching to the margin of the CO2 plume. In Case 2, CO2 density was relatively small, showing the range of 200 to 300 kg/m3 (Figures 4(d)–4(f)); CO2 density greater than 300 kg/m3 appeared only next to the injection well until 91 days (Figure 4(d)). In addition, CO2 viscosity ranged from 2.4 × 10−5 Pa·s adjacent to the wellbore to 2.0 × 10−5 Pa·s at the margin of the CO2 plume. Differences in CO2 properties such as density and viscosity in these two cases were amplified even after more CO2 was injected into the storage formation.


## 3.2.2. Patterns for Salt-Precipitation and CO2/Brine Flow

At the dry-out zone, different patterns for the salt-precipitation also appeared in these two cases (Figure5). Here, the “dry-out zone” was defined as a zone where brine had been replaced by injected CO2, and consequently, its CO2 saturation approximately reached unity [34]. At the front of the dry-out zone (the interface of dry-CO2 and brine), pure H2O is continuously vaporized while remaining the solid salt in the pore. Degree and configuration of precipitated salt were governed by two factors; one was the migration speed of the dry-out front, which was governed by viscous force (e.g., injection rate and horizontal permeability of the storage formation). The others were factors governing buoyancy force (e.g., CO2 density, the rate for counterflowing brine, and vertical permeability of the storage formation). Additionally, the amount of salt (or salinity) supplied by the counterflowing brine also governed the amount of precipitated salt [37].Figure 5
Flux patterns for CO2 and brine near the injection well after the injection of 1,095 days. (a) and (d) predicted CO2 mass flow rate [kg/s] within grid-blocks representing the wellbore; blue circles are horizontal CO2 mass flow rate from the wellbore to the storage formation and red symbols are vertical CO2 mass flow rate within the wellbore. (b) and (e) indicate CO2 flux [kg/(s·m2) ] with CO2 saturation. (c) and (f) indicate brine flux [kg/(s·m2) ] with salt saturation. The arrows indicate directions for both CO2 and brine flux, and the colors represent their magnitude.
(a)
(b)
(c)
(d)
(e)
(f)In Case1 (EPM model) following the conventional modeling approach (1 kg/s of CO2), distribution of horizontal CO2 flux along the radial distance was almost uniform (e.g., 4.4 × 10−3 kg/(s·m2) at 9.04 m at 1,095 days) (Figures 5(a) and 5(b)). In contrast, the counterflowing brine with its magnitude of 1.5 × 10−7 kg/(s·m2) flew opposite to CO2 flux at 9.04 m (Figure 5(c)). The detailed snap-shots of the growing salt-precipitation were plotted at 91, 365, and 1,095 days in Figures 6(a)–6(c). As seen, the salt was uniformly accumulated throughout the entire thickness of the storage formation with its saturation of approximately 0.04. Correspondingly, the average permeability reduction (k/k0) calculated from (3) was 65.1% in 1,095 days. Slightly elevated salt saturation appeared at both nearby the wellbore and the interface between sealing and storage formations. Adjacent to the wellbore, the salt saturation increased to be 0.06 due to the complete vaporization of residual brine. At the interface of the sealing formation, the salt saturation was increased due to H2O vaporization from the inflowing brine. According to Kim et al. [39], residual brine flew from the sealing formation to the dry-out zone where brine was completely displaced by injected dry-CO2 (Figure 5(c)). Consequently, the maximum salt saturation and the k/k0 reached 0.078 and 39.2%, respectively.Figure 6
Distribution of salt saturation [-] shown as color contours and the dry-out front as dashed lines at a series of times (91, 365, and 1,095 days). (a), (b), and (c) were simulated from the EPM model (Case1), but (d), (e), and (f) were from the WR model (Case 2).
(a)
(b)
(c)
(d)
(e)
(f)The WR model (Case2) was able to predict the profiles for both horizontal and vertical CO2 mass flow rates within the wellbore (Figure 5(d)). Above the interface (740 m) between the storage and sealing formations, the vertical CO2 mass flow rate was consistently 10 kg/s because the wellbore was fully cased (red circle in Figure 5(d)). However, once CO2 entered the screened interval (740 to 780 m), the vertical CO2 mass flow rate decreased with the depth almost linearly and finally reached zero at the well-bottom. In this interval, the horizontal CO2 mass flow rate reflected the actual CO2 injection rate (blue circles in Figure 5(d)). As seen in Figures 5(a) and 5(d), the actual CO2 injection rates from both cases were different; in Case 2, the actual CO2 injection rates were larger at the upper storage formation except the interface similar to Vilarrasa et al. [64] and decreased toward the well-bottom. However, throughout the entire thickness, the average actual CO2 injection rate was the same as the injection rate assigned to Case 1 (i.e., 10 kg/s).Due to magnitude difference of actual CO2 injection rates throughout the screen interval, both viscous and buoyancy forces differently acted on CO2 plume between Case 1 and Case 2 [44]. Furthermore, relatively warm CO2 (e.g., 52°C) entered from the wellbore to the storage formation also amplified the buoyancy effect on CO2 plume (Figure 3(c)). Due to these reasons, in Case 2, the injected CO2 plume rose rapidly, inducing more counterflowing brine flux (5.0 × 10−6 kg/(s·m2) at 8 m at 1,095 days) along the bottom of the storage formation (Figure 5(f)). Because of strong buoyancy effect on the CO2 plume, the configuration of the dry-out zone where the salt was precipitated was nonuniform. In particular, the localized salt-peak was developed due to additional supply of salinity by counterflowing brine.At the zone where the localized salt was precipitated, the maximum salt saturation reached almost equal to porosity (0.25) implying significant deterioration of permeability; the cumulated salt-barrier restricted horizontal propagations of both CO2 and pressure, consequently reducing effectiveness of the injection well. Figures 6(d)–6(f) showed the development of salt-precipitation at 91, 365, and 1,095 days. According to Figure 6(f), it is distinct that the lower part of the dry-out front stopped expanding after 365 days when the localized salt-peak was developed.


## 4. Sensitivity Analyses for WR Model

In order to further evaluate the influence of wellbore processes on complete CO2 injection scenarios and associated salt-precipitation, sensitivity analyses were conducted by varying the injection conditions such as injected CO2 temperature, injection rate, and wellbore diameter. Then, outputs from developed sensitivity scenarios were compared relative to the base-case representing Case 2 (Table 2).


### 4.1. Effect of Injected CO2 Temperature at the Well-Head

Case2 (35°C), Case 2-1 (45°C), and Case 2-2 (60°C) were designed to evaluate the influence of injected CO2 temperature while fixing the injection rate of 10 kg/s and the wellbore diameter of 0.2 m. After 1,095 days, CO2 profiles predicted from three cases became parallel to isenthalpic lines, implying that CO2, after completely displacing brine within the wellbore, reached the adiabatic condition (Figure 7(a)). While constraining the injection rate, different injected CO2 temperature resulted in prediction of different well-head pressures (PCase2=7.24 MPa, PCase2-1=7.54 MPa and PCase2-2=7.79 MPa). Nevertheless, the well-bottom pressures were relatively consistent (PCase2=9.26 MPa, PCase2-1=9.29 MPa, PCase2-2=9.30 MPa). Within the wellbore, the hydrostatic pressure (Pbottom) at the well-bottom can be expressed to be Pbottom=Phead+ρCO2gH. The same injection rate (10 kg/s) indicates that Pbottom should be consistent at all cases. However, the magnitude of the second term (ρCO2gH) at the right-side varied because ρCO2 decreased with the increase in injected CO2 temperature; for example, ρCO2 at the well-bottom was 291.8 kg/m3, 251.6 kg/m3, and 216.8 kg/m3 in Cases 2, 2-1, and 2-2, respectively. While maintaining the same Pbottom, decrease in ρCO2gH resulted in elevated Phead as appeared in Figure 7(a). Due to this reason, CO2 existed as gaseous phase adjacent to the well-head in Case 2, but no more gaseous CO2 was present as the injected CO2 temperature was increased.Figure 7
(a) Changes of CO2 properties (density [kg/m3] and enthalpy [kJ/kg]) within the wellbore and (b) development of salt saturation [-] and built-up pressure [MPa] at the bottom layer. The small figure represents both horizontal and vertical CO2 mass flow rate [kg/s] within the wellbore at three different injection temperatures (35, 45, and 60°C) after 1,095 days.
(a)
(b)Within the storage formation, all cases showed the accumulation of localized salt, but the peak was closer to the well as the injected CO2 temperature decreased (Figure 7(b)); the localized salt-peak was positioned at 4.89 m, 5.16 m, and 6.37 m in Case 2 (35°C), Case 2-1 (45°C), and Case 2-2 (60°C), respectively. Previously, Kim et al. [41] noted that the localized salt-peak was developed closer to the injection well as the buoyancy effect was stronger (or greater Ngv, greater temperature). As seen, in our study, calculated Ngv of Case 2, Case 2-1, and Case 2-2 was 2.76, 2.56 and 2.32, respectively (Table 4). The relationship between injected CO2 temperature and Ngv was inconsistent with the previous premise defining that less dense (or warm) CO2 promoted vertical migration more. According to the Mass Flux equation (FK=∑βuβρβXβK) shown in Table 3, if CO2 completely displaced brine adjacent to the wellbore (assuming a single-phase and single-component), the Mass Flux equation can be simplified to be the FCO2=uCO2ρCO2. Here, average horizontal CO2 mass flow rate (Ir) is expressed to be Ir=FCO2·Ai. In this study, Ir was 1 kg/s at 10 grid-blocks of the screen interval and the interface area (Ai) of the grid-blocks was fixed to be 2.51 m2. Correspondingly, FCO2 was constant, resulting in the fact that any change in ρCO2 should accompany variation in uCO2. For example, in Case 2, Case 2-1, and Case 2-2 increase in the injected CO2 temperature accompanied the decrease in ρCO2, which resulted in elevated uCO2 within the storage formation.Subsequently, in (6), increase in uCO2, which was included in the denominator, decreased Ngv even if Δρ increased due to increasing the injected CO2 temperature. Due to this complicated relation, increase in injected CO2 temperature ultimately decreased the buoyancy effect on CO2 plume while enhancing viscous force (or enhancing uCO2). Additionally, the magnitude of the salt-peak (solid-line) was similar in all cases (approximately 0.19), implying that different CO2 temperature did not cause to variation in the size of the salt-peak. Nevertheless, the location of the salt-peak was different and also coincident to the realm where the pressure (dot-dashed) was built up, implying that the salt-peak served as a local barrier which prevented the propagation of pressure pulse to the far-region.


### 4.2. Effect of Injection Rate

The effect of injection rate on the wellbore process and associated salt-precipitation was investigated throughout Case2-3 (5 kg/s), Case 2 (10 kg/s), and Case 2-4 (50 kg/s) (Table 2). After 1,095 days, CO2 profiles in all cases reached the adiabatic condition (Figure 8(a)). At the well-head, greater injection rate pushing more CO2 to the well-bottom induced larger well-head pressure (PCase2-3 = 7.10 MPa, PCase2 = 7.24 MPa, and PCase2-4 = 8.06 MPa). Likewise, the well-bottom pressure was elevated (PCase2-3 = 9.03 MPa, PCase2 = 9.26 MPa, and PCase2-4 = 11.63 MPa).Figure 8
(a) Changes of CO2 properties (density [kg/m3] and enthalpy [kJ/kg]) within the wellbore and (b) development of salt saturation [-] and built-up pressure [MPa] at the bottom layer. The small panel represents both horizontal and vertical CO2 mass flow rate [kg/s] within the wellbore at three different injection rates (5, 10, and 50 kg/s) after 1,095 days.
(a)
(b)Under the adiabatic condition, change in pressure accompanied variation of temperature. For example, CO2 profile in Case 2-4 (50 kg/s) approximately lied along ~5°C/MPa contour line for Joule-Thomson coefficient shown in Figure 3(d). Considering that such a high injection rate minimized thermal exchange between CO2 within the wellbore and the surrounding formation, pressure difference (ΔPCase2-4 = 11.63 − 8.06 = 3.57 MPa) between the well-bottom and well-head resulted in change of temperature ΔTCase2-4 = ~5°C/MPa × 3.57 MPa = ~17.85°C), which was similar to the model-predicted temperature difference (ΔTCase2-4 = 17°C) between the well-bottom (52°C) and well-head (35°C) (Figure 8(a)). For Cases 2-3 (5 kg/s) and 2 (10 kg/s), CO2 profiles for relatively small injection rates fell on large Joule-Thomson coefficient (8.7~7.3°C/MPa) shown in Figure 3(d). By applying the same principle, it can be concluded that the wellbore dynamic model reasonably proved temperature disturbance on CO2 under the adiabatic condition.Within the storage formation, the salt-peak only occurred when the injection rate was small (Cases2-3 and 2 in Figure 8(b)). In particular, the smaller injection rate caused to the development of the salt-peak closer from the wellbore. For example, in Case 2-3, the localized salt-precipitation was developed at 0.65 m from the injection well by surrounding the half of the screen interval (from the well-bottom to 760 m). Similarly, in the magnified figure of Figure 8(a), CO2 profile in Case 2-3 was not linear at the well-bottom; the slope of CO2 profile was different from 760 to 780 m due to the development of salt-barrier. Because the salt-barrier was developed immediately next to the wellbore, the horizontal CO2 mass flow rate became almost zero (blue circles in the small figure of Figure 8(b)). Without CO2 entering the storage formation, the built-up pressure was small (ΔP=0.5 MPa; from 8.3 MPa to 8.8 MPa) (blue dot-dashed line in Figure 8(b)). This negligible change in pressure within the storage formation implies that the developed salt-barrier effectively segregated the pressure propagation from the wellbore to the storage formation.In high injection rate (Case2-4, 50 kg), the elevated viscous force minimized the development of the salt-peak. Therefore, the salt-accumulation horizontally extended to 27.1 m while developing the uniform salt saturation of 0.03 (Figure 8(b)). The pressure in the storage formation increased due to high injection rate but decreased logarithmically from the wellbore. In the wellbore, vertical CO2 mass flow rate decreased linearly from 740 m to the well-bottom (orange dashed line in the small figure of Figure 8(b)). Meanwhile, the horizontal CO2 mass flow rate was 5 kg/s in each grid-block except at the interface of the seal and the well-bottom. Finally, the calculated Ngv of Case 2-3 where the dry-out front was only extended to 0.65 m was the largest (5.36), but the Ngv of Case 2-4 was only 0.51 with the extended dry-out front to be 27.10 m (Table 4).


### 4.3. Effect of Wellbore Diameter

In this study, after fixing the injected CO2 temperature (35°C) and rate (10 kg/s), the wellbore diameter was varied at Case 2-6 (0.05 m), Case 2-5 (0.13 m), and Case 2 (0.2 m) (Table 2). As shown in Figure 9(a), CO2 profiles of both Case 2 and Case 2-5 were almost parallel to isenthalpic lines, indicating the arrival of the adiabatic condition. CO2 profile of Case 2-5 was slightly shifted from Case 2; discrepancies were ΔPwell-head = 0.06 MPa, ΔPwell-bottom = 0.01 MPa, and ΔTwell-bottom = 0.52°C, respectively. Similarly, magnitudes of vertical and horizontal CO2 mass flow rates were nearly the same, and thus, both configuration of the precipitated salt-barrier and built-up pressure were almost equivalent (Figure 9(b)). Ngv for Case 2 and Case 2-5 also showed similar values, 2.76 and 2.77, respectively (Table 4).Figure 9
(a) Changes of CO2 properties (density [kg/m3] and enthalpy [kJ/kg]) within the wellbore and (b) development of salt saturation [-] and built-up pressure [MPa] at the bottom layer. The small figure represents both horizontal and vertical CO2 mass flow rate [kg/s] within the wellbore with three different wellbore diameters (0.05, 0.13, and 0.2 m) after 1,095 days.
(a)
(b)When the wellbore diameter decreased furthermore to 0.05 m (Case2-6), CO2 profile was changed significantly (Figure 9(a)). First of all, the pressure profile was overturned. Previously, both Case 2 and Case 2-5 revealed that the wellbore pressure was elevated with increase in depth, and thus, the well-bottom pressure was the highest. However, in Case 2-6, the well-head pressure was the highest one (9.9 MPa after 1,095 days), and the pressure decreased along the depth, reaching to 9.1 MPa adjacent to the interface (746 m depth) (the magnified figure in Figure 9(a)). Below 746 m, the pressure overturned with increasing both (ΔP=) 0.2 MPa and (ΔT=) 0.4°C to the well-bottom. In order to understand pressure overturn within the wellbore, it is important to understand the relationship between gravitation and frictional forces.While CO2 migrates through the wellbore, both gravity and frictional forces must leverage each other. Here, the gravitational force can be calculated from Fg=ρCO2VCO2g; VCO2 is CO2 volume. The frictional force (Ff=τwΓwlw) can be obtained by multiplying the shear stress (τw) to the perimeter of wellbore (Γw=πd,  d is the wellbore diameter) and the wellbore length (lw). Considering that the wellbore is completely filled with CO2 after 1,095 days, the shear stress (τw) can be calculated with the following equation [55]:(7)τw=12fρCO2uCO2uCO2.Here, the friction coefficient (f) is dependent on the Reynolds number (Re=ρCO2uCO2d/μCO2) within the wellbore. Then, Ff can be expressed as(8)Ff=τwΓwlw=12fρCO2uCO2uCO2Γwlw.As described before, the vertical mass flow rate is Ir=FCO2·A=ρCO2uCO2πd/22. Subsequently, Ir can be rearranged by replacing uCO2 in Ff shown in (9)Ff=8fIr2ρCO2πd3lw.When the CO2 injection rate was constant at the well-head, the vertical CO2 mass flow rate (Ir) was also invariable from the well-head to the interface (the orange dashed line in the small figure of Figure 9(b)). At constant Ir, (9) represents the fact that Ff is dependent on friction coefficient (f), CO2 density (ρCO2), and wellbore diameter (d) and length (lw). In particular, the third power of wellbore diameter (d3) in (9) indicates that the wellbore diameter can influence Ff more than any other parameters. For example, when the wellbore diameter was decreased 4 times from 0.2 m (Case 2) to 0.05 m (Case 2-6), the average Ff per unit depth between the well-head and 746 m increased from 0.5 N/m to 16.0 N/m (32 times). However, the average Fg per unit depth decreased from 82.2 N/m to 13.8 N/m (approximately 6 times). As seen, when the wellbore diameter was sufficiently small (e.g., 0.05 m), Ff was large enough to exceed Fg, which induced the overturn of the pressure profile.Within the wellbore, the pressure relationship between two grid-blocks next to each other can be written asP2A=P1A+Fg-Ff. Here, P1 is the pressure of the grid-block 1 positioning above the grid-block 2, and A is the cross-section area between two grid-blocks. When Ff was greater than Fg (Ff>Fg), P1 should be greater than P2   (P1>P2), indicating that the well-head pressure was the largest along the wellbore and decreased with the depth, as seen in Case 2-6. The similar pressure profile along the wellbore was also observed by Pan et al. [24] who simulated the wellbore processes at a 100 kg/s injection rate.Interestingly, at Case2-6 (0.05 m), pressure was increased again with the depth below 746 m (the magnified figure in Figure 9(a)). It can be attributed to decrease in vertical CO2 mass flow rate (Ir) at the screen interval where horizontal CO2 mass flow rate increased (the orange circle in the small figure of Figure 9(b)). Decrease in Ir induced a decrease in Ff as seen in (9). Therefore, at the screen interval, Fg overcame Ff in turn; for example, from 746 m to the well-bottom average Fg and Ff per unit depth were 13.3 N/m and 3.9 N/m, respectively.In additional to the pressure profile, the temperature profile along the wellbore was also perturbed due to the variation in the wellbore diameter. Different from Cases2 and 2-5, CO2 profile in Case 2-6 was not situated at the isenthalpic condition; from the well-head to 746 m, temperature change was negligible (ΔT= 0°C), and from 746 m to the well-bottom CO2 temperature was slightly increased (ΔT=0.4°C) (the magnified figure in Figure 9(a)). From the well-head to 746 m, no change in CO2 temperature indicates that CO2 in the wellbore did not experience major thermal disturbances due large vertical CO2 velocity. However, below 746 m, decrease in Ir accompanied the reduction of uCO2, resulting to slight enhancement of thermal conduction between storage formation and the wellbore. Nevertheless, due to lack of thermal perturbation in Case 2-6, temperature of CO2 entering the storage formation was almost the same to one for Case 1 (EPM model) (Figures 3(c) and 9(a)). Thermophysical properties of CO2 entering the storage formation were similar to each other. As shown in Figure 9(b), the dry-out front expanded to similar distance (8.61 m) to Case 1 where the dry-out front expanded to 9.04 m without developing the localized salt-precipitation (Figure 5(c)). The calculate Ngv was also similar to each other (Case 2-6: 2.12 and Case 1: 2.20), which implies that the injection condition from the small diameter wellbore could mimic one for Case 1 (EPM model) under the specific conditions.


### 4.4. Gravity Number versus Dry-Out Front

Development of salt-barrier and its extent from the wellbore were governed by dominance between buoyancy and viscous forces, which was estimated from gravity number (Ngv) (Table 4). Interestingly, Ngv revealed the negative relationship with the extension of the dry-out front (Figure 10); the threshold of the Ngv developing the localized salt-barrier was approximately 2.3. At that time, the extent of localized salt-barrier was less than 8 m from the injection well. In Case 1 (the EPM model), the 10 grid-blocks imitated the wellbore where CO2 flow was solved with Darcy’s law (Figure 1(a)). Here, the salt saturation uniformly extended to 9.04 m from the wellbore without developing the localized salt-precipitation (the star symbol in Figure 10). Whereas in Case 2 (diamond symbol) adopting the WR model, Ngv increased while developing the localized salt-barrier, and the dry-out front became smaller than 4.89 m.Figure 10
Relationship delineating between gravity number and the location of dry-out front after 1,095 days. The red box indicates the area developing the localized salt-precipitation.For the sensitivity study of the wellbore diameter, both predictedNgv and dry-out extent were almost the same in both Case 2 (0.2 m) and Case 2-5 (0.13 m). However, when the wellbore diameter decreased further to 0.05 m (Case 2-6), the viscous force became dominant in the storage formation. Consequently, the salt was precipitated uniformly to 8.61 m. Indeed, the 0.05 m diameter wellbore behaved similarly to Case 1 (EPM model). Effect of the injected CO2 temperature was minimal (Case 2, Case 2-1, and Case 2-2) (Figure 10). While the temperature of injected CO2 increased, CO2 density was decreased, which resulted in elevated CO2 velocity (uCO2) within the storage formation (see discussion in Section 4.1). Due to the elevated uCO2, viscous force became dominant, and thus, the dry-out front was extended further (Case 2-1: 5.16 m and Case 2-2: 6.37 m).Finally, sensitivity analysis with the injection rate (Case2-3, Case 2, and Case 2-4) revealed that the injection rate plays a significant role in the dry-out zone extent and development of the localized salt-precipitation (Figure 10). When the injection rate decreased to the 5 kg/s, the localized salt-barrier was developed immediately adjacent to wellbore (0.65 m). Consequently, the salt-barrier prevented the CO2 entering the storage formation. On the contrary, the large injection rate (50 kg/s) significantly enhanced viscous force of CO2 plume in the storage and extended the dry-out front to the furthest distance (27.10 m) in all cases without the development of localized salt-precipitation.


## 4.1. Effect of Injected CO2 Temperature at the Well-Head

Case2 (35°C), Case 2-1 (45°C), and Case 2-2 (60°C) were designed to evaluate the influence of injected CO2 temperature while fixing the injection rate of 10 kg/s and the wellbore diameter of 0.2 m. After 1,095 days, CO2 profiles predicted from three cases became parallel to isenthalpic lines, implying that CO2, after completely displacing brine within the wellbore, reached the adiabatic condition (Figure 7(a)). While constraining the injection rate, different injected CO2 temperature resulted in prediction of different well-head pressures (PCase2=7.24 MPa, PCase2-1=7.54 MPa and PCase2-2=7.79 MPa). Nevertheless, the well-bottom pressures were relatively consistent (PCase2=9.26 MPa, PCase2-1=9.29 MPa, PCase2-2=9.30 MPa). Within the wellbore, the hydrostatic pressure (Pbottom) at the well-bottom can be expressed to be Pbottom=Phead+ρCO2gH. The same injection rate (10 kg/s) indicates that Pbottom should be consistent at all cases. However, the magnitude of the second term (ρCO2gH) at the right-side varied because ρCO2 decreased with the increase in injected CO2 temperature; for example, ρCO2 at the well-bottom was 291.8 kg/m3, 251.6 kg/m3, and 216.8 kg/m3 in Cases 2, 2-1, and 2-2, respectively. While maintaining the same Pbottom, decrease in ρCO2gH resulted in elevated Phead as appeared in Figure 7(a). Due to this reason, CO2 existed as gaseous phase adjacent to the well-head in Case 2, but no more gaseous CO2 was present as the injected CO2 temperature was increased.Figure 7
(a) Changes of CO2 properties (density [kg/m3] and enthalpy [kJ/kg]) within the wellbore and (b) development of salt saturation [-] and built-up pressure [MPa] at the bottom layer. The small figure represents both horizontal and vertical CO2 mass flow rate [kg/s] within the wellbore at three different injection temperatures (35, 45, and 60°C) after 1,095 days.
(a)
(b)Within the storage formation, all cases showed the accumulation of localized salt, but the peak was closer to the well as the injected CO2 temperature decreased (Figure 7(b)); the localized salt-peak was positioned at 4.89 m, 5.16 m, and 6.37 m in Case 2 (35°C), Case 2-1 (45°C), and Case 2-2 (60°C), respectively. Previously, Kim et al. [41] noted that the localized salt-peak was developed closer to the injection well as the buoyancy effect was stronger (or greater Ngv, greater temperature). As seen, in our study, calculated Ngv of Case 2, Case 2-1, and Case 2-2 was 2.76, 2.56 and 2.32, respectively (Table 4). The relationship between injected CO2 temperature and Ngv was inconsistent with the previous premise defining that less dense (or warm) CO2 promoted vertical migration more. According to the Mass Flux equation (FK=∑βuβρβXβK) shown in Table 3, if CO2 completely displaced brine adjacent to the wellbore (assuming a single-phase and single-component), the Mass Flux equation can be simplified to be the FCO2=uCO2ρCO2. Here, average horizontal CO2 mass flow rate (Ir) is expressed to be Ir=FCO2·Ai. In this study, Ir was 1 kg/s at 10 grid-blocks of the screen interval and the interface area (Ai) of the grid-blocks was fixed to be 2.51 m2. Correspondingly, FCO2 was constant, resulting in the fact that any change in ρCO2 should accompany variation in uCO2. For example, in Case 2, Case 2-1, and Case 2-2 increase in the injected CO2 temperature accompanied the decrease in ρCO2, which resulted in elevated uCO2 within the storage formation.Subsequently, in (6), increase in uCO2, which was included in the denominator, decreased Ngv even if Δρ increased due to increasing the injected CO2 temperature. Due to this complicated relation, increase in injected CO2 temperature ultimately decreased the buoyancy effect on CO2 plume while enhancing viscous force (or enhancing uCO2). Additionally, the magnitude of the salt-peak (solid-line) was similar in all cases (approximately 0.19), implying that different CO2 temperature did not cause to variation in the size of the salt-peak. Nevertheless, the location of the salt-peak was different and also coincident to the realm where the pressure (dot-dashed) was built up, implying that the salt-peak served as a local barrier which prevented the propagation of pressure pulse to the far-region.


## 4.2. Effect of Injection Rate

The effect of injection rate on the wellbore process and associated salt-precipitation was investigated throughout Case2-3 (5 kg/s), Case 2 (10 kg/s), and Case 2-4 (50 kg/s) (Table 2). After 1,095 days, CO2 profiles in all cases reached the adiabatic condition (Figure 8(a)). At the well-head, greater injection rate pushing more CO2 to the well-bottom induced larger well-head pressure (PCase2-3 = 7.10 MPa, PCase2 = 7.24 MPa, and PCase2-4 = 8.06 MPa). Likewise, the well-bottom pressure was elevated (PCase2-3 = 9.03 MPa, PCase2 = 9.26 MPa, and PCase2-4 = 11.63 MPa).Figure 8
(a) Changes of CO2 properties (density [kg/m3] and enthalpy [kJ/kg]) within the wellbore and (b) development of salt saturation [-] and built-up pressure [MPa] at the bottom layer. The small panel represents both horizontal and vertical CO2 mass flow rate [kg/s] within the wellbore at three different injection rates (5, 10, and 50 kg/s) after 1,095 days.
(a)
(b)Under the adiabatic condition, change in pressure accompanied variation of temperature. For example, CO2 profile in Case 2-4 (50 kg/s) approximately lied along ~5°C/MPa contour line for Joule-Thomson coefficient shown in Figure 3(d). Considering that such a high injection rate minimized thermal exchange between CO2 within the wellbore and the surrounding formation, pressure difference (ΔPCase2-4 = 11.63 − 8.06 = 3.57 MPa) between the well-bottom and well-head resulted in change of temperature ΔTCase2-4 = ~5°C/MPa × 3.57 MPa = ~17.85°C), which was similar to the model-predicted temperature difference (ΔTCase2-4 = 17°C) between the well-bottom (52°C) and well-head (35°C) (Figure 8(a)). For Cases 2-3 (5 kg/s) and 2 (10 kg/s), CO2 profiles for relatively small injection rates fell on large Joule-Thomson coefficient (8.7~7.3°C/MPa) shown in Figure 3(d). By applying the same principle, it can be concluded that the wellbore dynamic model reasonably proved temperature disturbance on CO2 under the adiabatic condition.Within the storage formation, the salt-peak only occurred when the injection rate was small (Cases2-3 and 2 in Figure 8(b)). In particular, the smaller injection rate caused to the development of the salt-peak closer from the wellbore. For example, in Case 2-3, the localized salt-precipitation was developed at 0.65 m from the injection well by surrounding the half of the screen interval (from the well-bottom to 760 m). Similarly, in the magnified figure of Figure 8(a), CO2 profile in Case 2-3 was not linear at the well-bottom; the slope of CO2 profile was different from 760 to 780 m due to the development of salt-barrier. Because the salt-barrier was developed immediately next to the wellbore, the horizontal CO2 mass flow rate became almost zero (blue circles in the small figure of Figure 8(b)). Without CO2 entering the storage formation, the built-up pressure was small (ΔP=0.5 MPa; from 8.3 MPa to 8.8 MPa) (blue dot-dashed line in Figure 8(b)). This negligible change in pressure within the storage formation implies that the developed salt-barrier effectively segregated the pressure propagation from the wellbore to the storage formation.In high injection rate (Case2-4, 50 kg), the elevated viscous force minimized the development of the salt-peak. Therefore, the salt-accumulation horizontally extended to 27.1 m while developing the uniform salt saturation of 0.03 (Figure 8(b)). The pressure in the storage formation increased due to high injection rate but decreased logarithmically from the wellbore. In the wellbore, vertical CO2 mass flow rate decreased linearly from 740 m to the well-bottom (orange dashed line in the small figure of Figure 8(b)). Meanwhile, the horizontal CO2 mass flow rate was 5 kg/s in each grid-block except at the interface of the seal and the well-bottom. Finally, the calculated Ngv of Case 2-3 where the dry-out front was only extended to 0.65 m was the largest (5.36), but the Ngv of Case 2-4 was only 0.51 with the extended dry-out front to be 27.10 m (Table 4).


## 4.3. Effect of Wellbore Diameter

In this study, after fixing the injected CO2 temperature (35°C) and rate (10 kg/s), the wellbore diameter was varied at Case 2-6 (0.05 m), Case 2-5 (0.13 m), and Case 2 (0.2 m) (Table 2). As shown in Figure 9(a), CO2 profiles of both Case 2 and Case 2-5 were almost parallel to isenthalpic lines, indicating the arrival of the adiabatic condition. CO2 profile of Case 2-5 was slightly shifted from Case 2; discrepancies were ΔPwell-head = 0.06 MPa, ΔPwell-bottom = 0.01 MPa, and ΔTwell-bottom = 0.52°C, respectively. Similarly, magnitudes of vertical and horizontal CO2 mass flow rates were nearly the same, and thus, both configuration of the precipitated salt-barrier and built-up pressure were almost equivalent (Figure 9(b)). Ngv for Case 2 and Case 2-5 also showed similar values, 2.76 and 2.77, respectively (Table 4).Figure 9
(a) Changes of CO2 properties (density [kg/m3] and enthalpy [kJ/kg]) within the wellbore and (b) development of salt saturation [-] and built-up pressure [MPa] at the bottom layer. The small figure represents both horizontal and vertical CO2 mass flow rate [kg/s] within the wellbore with three different wellbore diameters (0.05, 0.13, and 0.2 m) after 1,095 days.
(a)
(b)When the wellbore diameter decreased furthermore to 0.05 m (Case2-6), CO2 profile was changed significantly (Figure 9(a)). First of all, the pressure profile was overturned. Previously, both Case 2 and Case 2-5 revealed that the wellbore pressure was elevated with increase in depth, and thus, the well-bottom pressure was the highest. However, in Case 2-6, the well-head pressure was the highest one (9.9 MPa after 1,095 days), and the pressure decreased along the depth, reaching to 9.1 MPa adjacent to the interface (746 m depth) (the magnified figure in Figure 9(a)). Below 746 m, the pressure overturned with increasing both (ΔP=) 0.2 MPa and (ΔT=) 0.4°C to the well-bottom. In order to understand pressure overturn within the wellbore, it is important to understand the relationship between gravitation and frictional forces.While CO2 migrates through the wellbore, both gravity and frictional forces must leverage each other. Here, the gravitational force can be calculated from Fg=ρCO2VCO2g; VCO2 is CO2 volume. The frictional force (Ff=τwΓwlw) can be obtained by multiplying the shear stress (τw) to the perimeter of wellbore (Γw=πd,  d is the wellbore diameter) and the wellbore length (lw). Considering that the wellbore is completely filled with CO2 after 1,095 days, the shear stress (τw) can be calculated with the following equation [55]:(7)τw=12fρCO2uCO2uCO2.Here, the friction coefficient (f) is dependent on the Reynolds number (Re=ρCO2uCO2d/μCO2) within the wellbore. Then, Ff can be expressed as(8)Ff=τwΓwlw=12fρCO2uCO2uCO2Γwlw.As described before, the vertical mass flow rate is Ir=FCO2·A=ρCO2uCO2πd/22. Subsequently, Ir can be rearranged by replacing uCO2 in Ff shown in (9)Ff=8fIr2ρCO2πd3lw.When the CO2 injection rate was constant at the well-head, the vertical CO2 mass flow rate (Ir) was also invariable from the well-head to the interface (the orange dashed line in the small figure of Figure 9(b)). At constant Ir, (9) represents the fact that Ff is dependent on friction coefficient (f), CO2 density (ρCO2), and wellbore diameter (d) and length (lw). In particular, the third power of wellbore diameter (d3) in (9) indicates that the wellbore diameter can influence Ff more than any other parameters. For example, when the wellbore diameter was decreased 4 times from 0.2 m (Case 2) to 0.05 m (Case 2-6), the average Ff per unit depth between the well-head and 746 m increased from 0.5 N/m to 16.0 N/m (32 times). However, the average Fg per unit depth decreased from 82.2 N/m to 13.8 N/m (approximately 6 times). As seen, when the wellbore diameter was sufficiently small (e.g., 0.05 m), Ff was large enough to exceed Fg, which induced the overturn of the pressure profile.Within the wellbore, the pressure relationship between two grid-blocks next to each other can be written asP2A=P1A+Fg-Ff. Here, P1 is the pressure of the grid-block 1 positioning above the grid-block 2, and A is the cross-section area between two grid-blocks. When Ff was greater than Fg (Ff>Fg), P1 should be greater than P2   (P1>P2), indicating that the well-head pressure was the largest along the wellbore and decreased with the depth, as seen in Case 2-6. The similar pressure profile along the wellbore was also observed by Pan et al. [24] who simulated the wellbore processes at a 100 kg/s injection rate.Interestingly, at Case2-6 (0.05 m), pressure was increased again with the depth below 746 m (the magnified figure in Figure 9(a)). It can be attributed to decrease in vertical CO2 mass flow rate (Ir) at the screen interval where horizontal CO2 mass flow rate increased (the orange circle in the small figure of Figure 9(b)). Decrease in Ir induced a decrease in Ff as seen in (9). Therefore, at the screen interval, Fg overcame Ff in turn; for example, from 746 m to the well-bottom average Fg and Ff per unit depth were 13.3 N/m and 3.9 N/m, respectively.In additional to the pressure profile, the temperature profile along the wellbore was also perturbed due to the variation in the wellbore diameter. Different from Cases2 and 2-5, CO2 profile in Case 2-6 was not situated at the isenthalpic condition; from the well-head to 746 m, temperature change was negligible (ΔT= 0°C), and from 746 m to the well-bottom CO2 temperature was slightly increased (ΔT=0.4°C) (the magnified figure in Figure 9(a)). From the well-head to 746 m, no change in CO2 temperature indicates that CO2 in the wellbore did not experience major thermal disturbances due large vertical CO2 velocity. However, below 746 m, decrease in Ir accompanied the reduction of uCO2, resulting to slight enhancement of thermal conduction between storage formation and the wellbore. Nevertheless, due to lack of thermal perturbation in Case 2-6, temperature of CO2 entering the storage formation was almost the same to one for Case 1 (EPM model) (Figures 3(c) and 9(a)). Thermophysical properties of CO2 entering the storage formation were similar to each other. As shown in Figure 9(b), the dry-out front expanded to similar distance (8.61 m) to Case 1 where the dry-out front expanded to 9.04 m without developing the localized salt-precipitation (Figure 5(c)). The calculate Ngv was also similar to each other (Case 2-6: 2.12 and Case 1: 2.20), which implies that the injection condition from the small diameter wellbore could mimic one for Case 1 (EPM model) under the specific conditions.


## 4.4. Gravity Number versus Dry-Out Front

Development of salt-barrier and its extent from the wellbore were governed by dominance between buoyancy and viscous forces, which was estimated from gravity number (Ngv) (Table 4). Interestingly, Ngv revealed the negative relationship with the extension of the dry-out front (Figure 10); the threshold of the Ngv developing the localized salt-barrier was approximately 2.3. At that time, the extent of localized salt-barrier was less than 8 m from the injection well. In Case 1 (the EPM model), the 10 grid-blocks imitated the wellbore where CO2 flow was solved with Darcy’s law (Figure 1(a)). Here, the salt saturation uniformly extended to 9.04 m from the wellbore without developing the localized salt-precipitation (the star symbol in Figure 10). Whereas in Case 2 (diamond symbol) adopting the WR model, Ngv increased while developing the localized salt-barrier, and the dry-out front became smaller than 4.89 m.Figure 10
Relationship delineating between gravity number and the location of dry-out front after 1,095 days. The red box indicates the area developing the localized salt-precipitation.For the sensitivity study of the wellbore diameter, both predictedNgv and dry-out extent were almost the same in both Case 2 (0.2 m) and Case 2-5 (0.13 m). However, when the wellbore diameter decreased further to 0.05 m (Case 2-6), the viscous force became dominant in the storage formation. Consequently, the salt was precipitated uniformly to 8.61 m. Indeed, the 0.05 m diameter wellbore behaved similarly to Case 1 (EPM model). Effect of the injected CO2 temperature was minimal (Case 2, Case 2-1, and Case 2-2) (Figure 10). While the temperature of injected CO2 increased, CO2 density was decreased, which resulted in elevated CO2 velocity (uCO2) within the storage formation (see discussion in Section 4.1). Due to the elevated uCO2, viscous force became dominant, and thus, the dry-out front was extended further (Case 2-1: 5.16 m and Case 2-2: 6.37 m).Finally, sensitivity analysis with the injection rate (Case2-3, Case 2, and Case 2-4) revealed that the injection rate plays a significant role in the dry-out zone extent and development of the localized salt-precipitation (Figure 10). When the injection rate decreased to the 5 kg/s, the localized salt-barrier was developed immediately adjacent to wellbore (0.65 m). Consequently, the salt-barrier prevented the CO2 entering the storage formation. On the contrary, the large injection rate (50 kg/s) significantly enhanced viscous force of CO2 plume in the storage and extended the dry-out front to the furthest distance (27.10 m) in all cases without the development of localized salt-precipitation.


## 5. Discussion

The numerical studies varying multiple CO2 injection scenarios were conducted to elaborate the relationship between the wellbore process and associated changes occurred within the storage formation. Due to the complex involving wellbore flow and the salt-precipitation, the dynamic changes of CO2 properties and wellbore conditions were necessary to be evaluated. Here, the transient, coupled wellbore-reservoir model aided to simulate the CO2 flow more precisely than conventional EPM model for various injection scenarios in geologic CO2 sequestration. For example, migration patterns of CO2 plume, which was governed by thermodynamic properties of CO2, could affect the storage capacity and possibly leakage potentials [65]. The resulting development of the localized salt-barrier was able to significantly influence the injectivity [40, 41].In the simulation studies, a few limitations were included. The injected CO2 temperature at the well-head was chosen to be higher than the critical temperature. Therefore, the injected CO2 from the well-head was always to be supercritical state. However, in the field implementation, the high CO2 temperature implies high energetic cost requiring for heating up CO2 [52]. Therefore, for the consideration of economically optimum CCS operations, the injection of gaseous CO2 should be evaluated using the wellbore dynamic model too. In addition, dependent on conditions of the storage formation, the rate of conductive heat transfer between CO2 plume and formation fluid would be different as well as the magnitude of salt-precipitation [66]. In this work, assigned temperature and pressure gradients in the model were greater than ones for typical sedimentary basins. In particular, conditions for the storage formation such as temperature, pressure gradients, and the injection depth were referred from the first pilot-scale CO2 injection project at Yeong-il embayment in Korea, which is located close to the tectonically active region in Japan [67]. Due to consideration of relatively warm and pressurized storage formation, CO2 plume behavior within both the wellbore and the storage formation could be different from CO2 injected in conventional sedimentary basins. Finally, even if this study did not consider, properties of the storage formation involving permeability, porosity, heterogeneity, burial depth, and lithology of the storage formation could influence CO2 flux entering from the wellbore to the storage formation and resulting salt-precipitation. Nevertheless, such effects were not considered here, but they are equally important to be evaluated.


## 6. Conclusions

The WR model (Case2) was selected to simulate fluid flows in both the wellbore and the storage formation. Additionally, the EPM model (Case 1) was compared to the WR model (Case 2) for evaluating any discrepancies (Figure 1). After considering the wellbore flow process, entering CO2 mass flow rate, CO2 phase, and thermodynamic properties at the screen interval can be predicted more accurately. Consequently, the patterns of CO2 plume and salt-precipitation at the storage formation showed different distribution between two cases. The precipitated salt in Case 2 served as a barrier to prevent horizontal propagation of CO2 plume from the injection well and also deteriorate the injectivity. Then, the transient, coupled wellbore-reservoir model can simulate the CO2 flow more precisely than conventional EPM model for various injection scenarios in GCS. Additionally, under the different injection conditions (injected CO2 temperature, injection rate, and wellbore diameter) the simulation results, such as pressure build-up, CO2 migration, and patterns of salt-precipitation, showed various values. Therefore, through a series of multiple simulations, it can be concluded that the wellbore flow processes can play an important role in the CO2 injection scenarios and significantly influence the changes which occurred by CO2 injection in the storage formation. The dynamic changes of CO2 properties and wellbore conditions are necessary for modeling the CO2 migration and development of salt-precipitation at the storage formation. For example, patterns of CO2 plume, which was determined by thermodynamic properties of CO2, can particularly affect the storage capacity and possibly leakage potentials. In addition, development of the localized salt-barrier can significantly influence the injectivity. Therefore, this study not only deepens understanding of wellbore flow process but also can provide theoretical support for the commercial-scale of CO2 injection projects.



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*Source: 1789278-2018-01-29.xml*