Density-Driven CO₂ Dissolution in Depleted Gas Reservoirs with Bottom Aquifers

Abstract

Depleted gas reservoirs with bottom water show significant potential for long-term CO₂ storage. The residual gas influences mass-transfer dynamics, further affecting CO₂ dissolution and convection in porous media. In this study, we conducted a series of numerical simulations to explore how residual-gas mixtures impact CO₂ dissolution trapping. Moreover, we analyzed the CO₂ dissolution rate at various stages and delineated the initiation and decline of convection in relation to gas composition, thereby quantifying the influence of residual-gas mixtures. The findings elucidate that the temporal evolution of the Sherwood number observed in the synthetic model incorporating CTZ closely parallels that of the single-phase model, but the order of magnitude is markedly higher. The introduction of CTZ serves to augment gravity-induced convection and expedites the dissolution of CO₂, whereas the presence of residual-gas mixtures exerts a deleterious impact on mass transfer. The escalation of residual gas content concomitantly diminishes the partial pressure and solubility of CO₂. Consequently, there is an alleviation of the concentration and density differentials between saturated water and fresh water, resulting in the attenuation of the driving force governing CO₂ diffusion and convection. This leads to a substantial reduction in the rate of CO₂ dissolution, primarily governed by gravity-induced fingering, thereby manifesting as a delay in the onset and decay time of convection, accompanied by a pronounced decrement in the maximum Sherwood number. In the field-scale simulation, the injected CO₂ improves the reservoir pressure, further pushing more gas to the producers. However, due to the presence of CH₄ in the post-injection process, the capacity for CO₂ dissolution is reduced.

1. Introduction

Human-made greenhouse gas emissions are the main driver of global warming and climate change [1]. Carbon geo-sequestration emerges as the most effective strategy to mitigate CO₂ emissions and advance towards carbon neutrality [2,3]. Suitable locations for CO₂ geological storage are identified as deep saline aquifers, depleted hydrocarbon reservoirs, and unmineable coal seams [4,5,6,7]. Among these, depleted gas reservoirs are notably cost-effective for CO₂ sequestration, benefiting from existing transportation and injection infrastructure and the use of abandoned wells [8]. Additionally, extensive research over the years has thoroughly assessed the integrity of caprock, sealing capacity, and storage potential of these gas reservoirs, ensuring long-term isolation of CO₂ from the atmosphere and reducing leakage risks [9].

The presence of formation water in depleted gas reservoirs provides the potential to enhance storage capacity and mitigate gas leakage risks for injecting CO₂ [10,11]. This injection process, influenced by various forces and reactions, enables CO₂ to be trapped in different forms: mobile and immobile, through structural, residual, solubility, and mineral trapping mechanisms [12]. Each mechanism is predominant at different stages of the injection and post-injection processes [13,14]. Enhancing solubility trapping, in particular, is essential to ensure the long-term storage of CO₂ and guarantee the security of carbon sequestration. The dissolved CO₂ ceases to exist as a distinct phase, thereby eliminating buoyancy-driven migration and minimizing the risk of leakage [15]. In addition, propelled by density variance, CO₂-rich brine descends, inducing convection with ambient brine, thereby enhancing dissolution rates and expanding storage capacity [16]. Moreover, the dissolved CO₂ may undergo geochemical reactions with cations in brine, such as calcium and magnesium, resulting in carbonate precipitates [17]. However, this reaction is typically a slow process spanning thousands of years [18], which falls beyond the scope of this work.

Due to the pivotal role of density-driven convection in solubility trapping and long-term carbon sequestration, a multitude of researchers have meticulously explored the intricacies of this mass transfer phenomenon [19,20,21]. By introducing dimensionless parameters like the Rayleigh number, onset time of convection, Sherwood number, and dissolution rate, it becomes possible to quantify the convective mixing process and assess the impact of associated influencing factors [22,23,24]. Previous studies have simplified theoretical models to single-phase and single-component, aiming to mitigate nonlinearity and enhance solution efficiency [25,26]. In contrast to the aforementioned models, the depleted gas reservoir stands out as multi-phase and multi-component due to the substantial presence of natural gas within the formation [27,28]. Furthermore, the considerable variation in gas saturation and composition, stemming from reservoir heterogeneity, significantly impacts both the height of the gas-water transition zone and the dynamics of CO₂ dissolution [29]. Consequently, conventional models fail to precisely depict the intricate dynamics of solubility trapping at a small scale within the depleted gas reservoir. While certain researchers delve into investigating the impact of gas impurities [30,31,32], additional investigation into density-driven convection regarding residual gas and the capillary transition zone remains imperative.

Though some researchers focus on the effect of gas impurities on CO₂ dissolution, a fixed boundary condition with single-phase flow is assumed. In addition, the complexity of accurately modeling the multiphase flow and mass transfer processes due to heterogeneous reservoir properties is still challenging. In this work, a sequence of numerical simulations was conducted to investigate the influence of gas mixtures and the capillary transition zone on solubility trapping dynamics within a depleted gas reservoir. Initially, a newly developed thermodynamic model, integrating modified cubic equations of state with an activity model, was introduced to accurately depict phase behavior. Subsequently, the Delft Advanced Research Terra Simulator (DARTS) was employed to efficiently and precisely model density-driven convection within the depleted gas reservoir by synthetic models and a realistic model. We focused on understanding the mass transport dynamics in the capillary transition zone, particularly under varying gas impurity conditions, using dimensionless parameters for analysis. Finally, our work was concluded by summarizing key findings derived from the numerical simulation results.

2. Materials and Methods

2.1. Conservation Equations

In this study, we consider the presence of both gas and liquid phases within a depleted gas reservoir. Specifically, these phases consist of three components: carbon dioxide (CO₂), methane (CH₄), and formation water. The main governing equations, along with the auxiliary equations, succinctly describe the dynamics of this two-phase, three-component isothermal flow system:

$$\frac{\partial }{\partial t}\left({\varphi }_s{\displaystyle \sum _{j=1}^{n_p}{x}_{cj}{\rho }_j{S}_j}\right)+div{\displaystyle \sum _{j=1}^{n_p}\left(x_{cj}{\rho }_j{\mu }_j+S_j{\rho }_j{J}_{cj}\right)+}{\displaystyle \sum _{j=1}^{n_p}{x}_{cj}{\rho }_j{\tilde{q}}_j}=0,c=1,2\cdots ,n_c,$$

(1)

where, ϕ is porosity; x_cj is the molar fraction of component c in phase j; ρ_j and s_j are phase density and saturation, respectively; μ_j is the phase Darcy velocity; D_cj is the diffusion coefficient of component c. J_cj is the Fick’s diffusion flux of component c.

Darcy’s law, expressed by Equations (2)–(4), is implemented to describe two-phase flow in porous media:

$$v_j=-K_s\frac{k_{rj}}{{\mu }_j}\left(\nabla p_j-{\rho }_{j}g\nabla D\right),$$

(2)

$$p_w=p_n-p_c,$$

(3)

$${\displaystyle {\sum }_{j=1}^{n_p}{S}_j=1,}$$

(4)

$$J_{cj}=-\varphi D_{cj}\nabla x_{cj},$$

(5)

where K is the permeability tensor of the matrix, v_j is the phase viscosity [mPa·s], and $K_{rj}$ is the phase relative permeability, $p_j$, g and Dare phase pressure [bar], gravitational acceleration constant [m/s²] and the depth of the domain [m]. Capillary pressure pe, often expressed as a function of saturation, is the pressure difference between the non-wetting $p_v$, and wetting phase $p_w$, x is a mass fraction, D is diffusion coefficient.

Furthermore, the rock is compressible, reflecting the change of porosity with pressure through:

$$\varphi ={\varphi }_0\left(1+c_r\left(p-p_{ref}\right)\right),$$

(6)

where ${\varphi }_0$, $p_{ref}$ is the reference pressure and $c_r$ is the rock compressibility.

2.2. Thermodynamic Model

The presence of residual natural gas and high salinity brine can alter the dynamic and thermal properties of fluids, thereby influencing mass-transfer behavior and the capacity for CO₂ sequestration. Central to understanding these effects is a thermodynamic model that delineates the equilibrium state between aqueous and non-aqueous phases. This model is fundamental for the accurate calculation of fluid properties and for performing reliable numerical simulations. It operates under the assumption that the thermodynamic properties of the phases are in a state of instantaneous local equilibrium. Specifically, for gas-liquid systems, the relevant aspects of the model are encapsulated in Equations (5)–(8):

$$z_c-V{y}_c-L{x}_c=0,c=1,2\cdots ,n_c,$$

(7)

$$f_{cV}\left(p,T,y_c\right)-f_{cL}\left(p,T,x_c\right)=0,c=1,2\cdots ,n_c,$$

(8)

$${\displaystyle \sum _{i=1}^{n_c}\left(x_c-y_c\right)=0,}$$

(9)

$$V+L=1,$$

(10)

where L and V are the mole fraction of the liquid and gas phases, respectively. $z_c$ is the overall composition. $x_c$ and $y_c$ are the mole fraction of component c in liquid and gas phases, respectively. $f_{iv}$ and $f_{il}$ denote the fugacity of component c in gas and liquid phases, respectively.

Given the substantial influence of gas mixtures and salinity on the phase behavior of gas-liquid systems, we adopt the fugacity-activity model for solving thermodynamic equilibrium. This method enables the calculation of the phase-equilibrium constant for each component:

$$K_c=\frac{y_c}{x_c}=\frac{a_c{h}_c}{p\varphi },$$

(11)

where $h_c$ and $a_c$ are Henry’s constant and activity coefficient of component $\mathrm{c}$, respectively; ${\varphi }_c$ is the fugacity coefficient of component c in the gas phase.

The calculation of the phase-equilibrium constant for the water component can be effectively conducted using the model proposed by Spycher [33]:

$$K_{H_{2}O}=\frac{K_{H_{2}O}^0}{{\varphi }_{H_{2}O}p}\exp \left[\frac{(p-1)V_{H_{2}O}}{RT}\right],$$

(12)

where $K_{H_{2}O}^0$ and $V_{H_{2}O}$ represent the equilibrium constant of the water component at reference pressure (0.1 MPa) and the average partial molar volume of water. ${\varnothing }_{H_{2}O}$ denotes the fugacity coefficient; R and T are the ideal gas constant and temperature, respectively.

The thermodynamic model is iteratively solved using the Rachford-Rice equation, as delineated in Equations (11)–(13):

$$g\left(V\right)={\displaystyle \sum _{i=1}^{n_c}\frac{z_i\left(K_i-1\right)}{V\left(K_i-1\right)+1}}=0,$$

(13)

$$x_j=\frac{z_j}{1+V\left(K_i-1\right)},$$

(14)

$$y_i=K_i{x}_i.$$

(15)

The iterative calculation of phase molar fractions and component partitioning is achievable through multistage negative flash analysis. Utilizing the outcomes of these negative flash calculations, the corresponding thermophysical properties (e.g., viscosity, density) can be determined by applying relevant relationships [34,35,36,37].

2.3. Numerical Model and Characteristic Parameters

The simulation considers a porous medium with impermeable closed boundaries (rastered) and open boundaries (non-rastered), as depicted in Figure 1a. Above the formation water lies a stagnant capillary transition zone (CTZ), where the formation water is saturated with CO₂ and methane, constituents of residual natural gas. Furthermore, to better understand the impact of the CTZ on density-driven convection, a single-phase model, maintaining a constant concentration of the dissolved gas at the top blocks, is used to serve as a basis for comparison (Figure 1b). To trigger CO₂ fingers, the concentration is initially perturbed just below the CO₂ emplacement with random values from a uniform distribution between 0 and a very small value (in this work, it’s 10⁻⁶ mol/mol).

The realistic model used in this work is a tight gas reservoir with 5100 m in length and 4400 m in width, located in the east of China (see Figure 1c,d). We use it to examine the impact of mixtures on CO₂ dissolution. This reservoir has an average vertical thickness of 250 m, spanning depths from 1191 to 1432 m. The gas-water contact occurs at a depth of 1345 m. Permeability varies from 0.07 to 2.15 mD, while porosity ranges from 0.005 to 0.054. The field contains 22 production wells and 6 injection wells, including two horizontal wells situated at the center of the gas layer. We maintain a production-to-injection ratio of 1.0. A CO₂ displacement process is conducted over 8 years, followed by 50 years of shut-in to monitor CO₂ migration. The average daily gas injection rate is 6000 m³ for vertical wells and 15,000 m³ for horizontal wells. The reservoir is currently at an average pressure of 10.5 MPa, with the daily gas production rate per well decreasing swiftly. The numerical model grid comprises 128 × 109 × 40 = 558,080 total cells, with 299,240 active cells.

Here a Corey-type relative-permeability model [38] is applied for calculation of phase relative permeability and capillary pressure. Capillary pressure and relative permeability can be determined through effective water saturation, as defined:

$$S_e=\frac{S_w-S_{wr}}{1-S_{wr}},$$

(16)

$$k_{rw}=S_e^{n_w},$$

(17)

$$k_{rg}=k_{rge}\left(S_{wr}\right){\left(1-S_e\right)}^2\left(1-S_e^{n_g}\right),$$

(18)

$$p_c=p_e{S}_e^{-1/\lambda },$$

(19)

where $P_e$, $\mathsf{\lambda }$ and $S_e$ are entry pressure, pore-size distribution coefficient, and effective water saturation, respectively. $S_{wr}$ is connate water saturation. $k_{rw}$ and $k_{rg}$ denote water and gas relative permeability, respectively.

Detailed parameters for numerical models are summarized in

Table 1. Parameters of the numerical model used in this work.

	Parameters	Case 1	Case 2	Case 3
Domain geometry	Top depth, m	1500		1191~1432
	Thickness, m	50		181.8~291.7
	Dimensions of model, -	100 × 50		128 × 109 × 40
	Gridblock size, m	0.5 × 0.5		-
Fluid properties	Phases	Single-phase	Two phases	Two phases
	CO2 density, kg/m3	f (state)
	Brine density, kg/m3	f (state)
	CO2 viscosity, mPa·s	f (state)
	Brine viscosity, mPa·s	f (state)
	Diffusion coefficient, m2/s	2 × 10−9
Porous media properties	Permeability, mD	300		0.07~2.15
	Porosity, -	0.25		0.005~0.054
	Residual brine saturation, Swc	0.2
	Residual CO2 saturation, Sgr	0
	Salinity, ppm	30,000
	Gas end point relative permeability, krge	1.0
	Exponent of gas relative permeability, ng	2
	Exponent of water relative permeability, nw	4
	Capillary entry pressure, bar	0.2

. The corresponding relative-permeability and capillary-pressure curves are shown in Figure 2.

In this work, we present an analysis of the mass-transfer behavior during density-driven convection, focusing on two key metrics: the CO₂ dissolution rate and the Sherwood number (Sh). The CO₂ dissolution rate, F, is utilized to measure the mass flux of CO₂ per unit area across the top boundary into the formation water.

$$F=H\varphi \frac{\partial \overline{c}}{\partial t}$$

(20)

where H is the thickness of pure-water zone, $\overline{c}$ is the average CO₂ concentration in formation water.

The Sherwood number is characterized as the ratio of the dissolution rate to the rate of diffusive mass transport.

$$Sh=\frac{R_c+R_{diff}}{R_{diff}},$$

(21)

where, R_c and R_diff denote the mass transfer rate by convection and diffusion, respectively.

In addition, we incorporate two additional key parameters, onset and decay time, to delve into the nuances of density-driven convection across various phases. Owing to the lack of a universally accepted definition for these terms, we adopt the methodology proposed by Pau and Li [39]. We define onset time as the moment when the CO₂ dissolution rate exceeds the diffusion-induced rate by 2%, and decay time as the point at which mass transport in formation water begins to diminish [39]. Utilizing these parameters in our numerical model, we simulate the density-driven convection process over 400 years. This simulation aims to explore the influence of CTZ and residual natural gas concentration on the efficiency of solubility trapping. To improve computational efficiency, the Delft Advanced Research Terra Simulator (DARTS) is used to perform all simulations. DARTS has been proven to be an efficient and accurate simulator through a series of benchmark studies related to various energy applications due to the application of the Operator-Based Linearization approach [26,40,41]. The OBL approach starts by grouping all physical properties fully defined by the thermodynamic state into state-dependent terms. The state-dependent terms are parameterized in physical space at the preprocessing stage or adaptively with a limited number of supporting points [42]. Then, in the course of a simulation, the physical terms in the current timestep are evaluated based on a multi-linear interpolation strategy [41,42].

3. Results

3.1. Effect of the Capillary Transition Zone

3.1.1. CO₂ Dissolution Rate

We first compare the dissolution rate and distribution of dissolved CO₂ in formation water to understand how CTZ affects density-driven convection. Figure 3 illustrates that CO₂ dissolution with CTZ occurs in four stages: Diffusion (Stage 1), Convection-Strengthened (Stage 2, a2, b2), Convection-Dominated (Stage 3, a3, b3), and Convection-Decay (Stage 4, a6, b6). This result is similar to the one observed in single-phase simulations. In Stage 1, the CO₂ dissolution rate is the same for both simulations because molecular diffusion predominantly drives mass transfer, showing minimal impact of stagnant CTZ on CO₂ dissolution. The CTZ introduces a more pronounced disturbance to the concentration boundary compared to a single-phase, constant-concentration boundary. This is primarily due to the enhanced fluid mobilities associated with the CTZ, which leads to an earlier initiation of density-driven convection (bl). Additionally, there is a faster increase in the dissolution rate during Stage 2 and an elevated mass flux into the formation water during Stage 3. The ongoing dissolution process, driven by the stagnant CTZ, progressively impedes mass transport within the formation water. Consequently, the dissolution rate diminishes, transitioning to a convection-decay phase (Stage 4, b5) approximately 78 years earlier than predicted by the single-phase simulation. In summary, the CTZ significantly accelerates the dissolution of a substantial portion of the injected CO₂ into the formation water over a relatively short period. Relying solely on the single-phase simulation could result in inaccurate assessments of convective mixing evolution and the extent of dissolution trapping in depleted gas reservoirs containing bottom water.

3.1.2. Sherwood Number

Figure 4 illustrates the progression of the Sherwood number in both single-phase and two-phase simulations. This progression, for both simulations, encompasses four stages, each aligning with changes in the dissolution rate. Notably, during Stages 2 and 3, the Sherwood number in the two-phase model is markedly higher than in the single-phase model, attributed to the vigorous perturbation and density-driven convection caused by the stagnant CTZ. The peak Sherwood number timing in both simulation types coincides well with the decay time depicted in Figure 3. However, it is important to note a discrepancy: the time at which convective fingers reach the bottom boundary (a4, b4) does not align with the decay time (a5, b5), diverging from findings in small-scale numerical simulations. The field-scale model, in contrast to its small-scale counterpart, exhibits lower permeability, significantly restricting the lateral expansion of CO₂-rich brine. Furthermore, the larger dimensions of the field-scale model diminish the influence of leading fingers. Consequently, both the dissolution rate and the Sherwood number continue to rise until the concentration of dissolved CO₂ reaches a certain threshold.

3.2. Effect of Residual Natural Gas Concentration

3.2.1. CO₂ Dissolution Rate

Figure 5a illustrates the progression of the CO₂ dissolution rate across varying concentrations of residual natural gas, spanning from 0% to 30%. The presence of gas mixtures adversely affects the initial three stages of solubility trapping. As the concentration of residual natural gas rises, it increasingly hinders the dissolution and mass transport of CO₂ in brine. Consequently, the onset time of the process is prolonged, escalating from 5.78 years to 10.50 years, and the decay time also increases, from 76.17 years to 122.75 years. Despite the extension of the second and third stages due to increased gas mixtures, there is a marked reduction in the CO₂ inventory, as shown in Figure 5b. This reduction significantly compromises the safety of carbon storage.

3.2.2. Sherwood Number

Figure 6 depicts how the Sherwood number changes with varying compositions of the gaseous phase. Initially, the Sherwood number remains constant at one, indicating the diffusion-dominated stage 1. The duration of Stage 1 extends as gas impurity increases, reflecting a reduction in CO₂ diffusion efficiency and convective stability. As mass transfer progresses, the Sherwood number rises gradually. However, increased gas impurity leads to a decline in the maximum Sherwood number, falling from 20.18 to 12.75, due to hindered diffusion and impeded density-driven convection. This reduction in the maximum Sherwood number signifies a substantial decrease in convection intensity. During the convection-decay stage (Stage 4), there is a sharp decrease in the Sherwood number. Despite this, convection remains relatively intense in formation water with lower dissolved CO₂ concentrations, especially in gas with higher impurity levels. Consequently, the Sherwood number for gases with higher residual natural gas concentration progressively exceeds that of gases with less impurity.

3.2.3. Density Difference and Saturation Profile

The variations in density between ambient brine and CO₂-enriched brine, along with changes in the saturation profile within the stagnant CTZ, are illustrated in Figure 7. As gas mixtures increase, the density difference in the formation water gradually diminishes. This is attributed to the reduced partial pressure of CO₂ and its subsequent solubility. Consequently, the diminishing density difference lessens the driving force of gravity-induced convection, thereby extending the duration of solubility trapping. Additionally, alterations in the residual natural gas concentration modify the saturation profile within the stagnant CTZ. An increase in gas mixtures leads to a decrease in water saturation in the CTZ, which in turn diminishes the flow capacity and the intensity of perturbations in the aqueous phase. The synergistic effect of these phenomena significantly hampers the mass transport of dissolved CO₂.

3.2.4. Onset Time and Decay Time

Figure 8 illustrates an exponential relationship between onset time, decay time, and gas impurity levels. The onset time is determined using the formula 5.958e0.02042c, where c represents the residual natural gas concentration. Similarly, the decay time follows the equation 75.714e0.01669c. This exponential correlation highlights the escalating influence of gas mixtures on mass transfer behavior as the concentration of residual natural gas increases.

3.3. Field-Scale Simulation for CO₂ Injection and Storage

3.3.1. CO₂ Injection Period

Figure 9, Figure 10 and Figure 11 illustrate the changes in reservoir pressure, CH₄ mole fraction, and CO₂ mole fraction following the cessation of CO₂ injection. Figure 9 shows that as CO₂ injection progresses, there is a steady increase in reservoir pressure, rising from an average of 10.5 MPa to 19.2 MPa. This increase enhances the extraction of the remaining gas due to the recovery of reservoir pressure. Figure 10 and Figure 11 depict the mole fraction distribution of CH₄ and CO₂ within the reservoir. During the post-injection process, the differing densities of CO₂ and CH₄ drive CO₂ to migrate towards the lower sections, thereby pushing CH₄ upwards. A comparison of the CH₄/CO₂ mole fraction distribution throughout the reservoir and near the horizontal wells indicates a notably higher concentration of CO₂ near the injection wells, with CH₄ primarily moving toward the production wells. The displacement of CO₂ in horizontal wells is significantly more pronounced than in vertical wells. Additionally, the CH₄ mole fraction at the bottom of the reservoir is slightly lower than at the top, suggesting a degree of gravitational segregation between the gases due to their density differences.

Figure 12 illustrates the temporal progression of CO₂ production volumes, specifically the CO₂ breakthrough times, across various wells. Well P16, strategically positioned between the vertical injection well I4 and the horizontal injection well IH5, witnessed an influx of CO₂ into the production stream nine months subsequent to the commencement of CO₂ injection. This event precipitated the simultaneous extraction of methane (CH₄) and CO₂. In contrast, Well P12, located amidst two horizontal injection wells and characterized by relatively superior reservoir properties, experienced CO₂ breakthrough approximately thirty months following the injection. Additionally, Wells P2 and P18, situated at greater distances from the injection wells, demonstrated extended durations prior to CO₂ breakthrough and notably lower CO₂ production volumes in comparison.

Figure 13 illustrates the temporal alterations in cumulative gas production within the target area. In the absence of sufficient energy supply, a decline in single-well productivity is observed after five years of depletion development, resulting in a slow increase in cumulative gas production. After ten years of development, the cumulative gas production reaches approximately 88.0 × 10⁶ m³. Following CO₂ injection, reservoir pressure gradually recovers, leading to a slow increase in cumulative gas production, predominantly governed by pressure at this stage. As the CO₂ displacement process progresses, a significant amount of CH₄ gas is driven into the production wells, causing an acceleration in the rate of increase in cumulative gas production (notably around three years post-CO₂ injection). Once CO₂ breakthrough occurs at the production wells, although the gas production capacity of individual wells remains relatively unchanged, the effective gas production volume decreases, adversely affecting economic benefits. By the end of the simulation period, the effective cumulative gas production increased by 16.71 × 10⁶ m³, marking an 18.9% increase compared to depletion development.

3.3.2. CO₂ Post-Injection Period

Following the injection of CO₂ into a reservoir, a portion of the injected CO₂ is extracted along with CH₄, while the rest remains within the reservoir, enabling the permanent sequestration of CO₂ after the closure of wells. Figure 14, Figure 15 and Figure 16 illustrate the distribution of pressure, CH₄ concentration, and CO₂ concentration in the gas reservoir at the end of the simulation period. Figure 14 indicates that once the wells are closed, the reservoir pressure gradually stabilizes, with a slight reduction in average reservoir pressure (approximately 17.5 MPa). This decrease is primarily attributed to CO₂ dissolution in water, leading to a reduced CO₂ concentration in the gas phase and consequently lower pressure. Figure 15 and Figure 16 reveal that due to density differences, CO₂ and CH₄ undergo redistribution within the reservoir. CO₂ tends to migrate towards the bottom, while CH₄ moves upwards. However, the two fluids do not completely separate from each other.

Figure 17 illustrates the temporal variation of CO₂ mass following the cessation of injection, with different forms. As the CO₂ plume migrates, the gas sweep area gradually expands, resulting in an increased volume of residual gas. Concurrently, the increased contact area between CO₂ and the formation water enhances the dissolution trapping. However, once the free gas is unable to diffuse further in the reservoir, meaning the contact area is constrained, the quantity of residual gas begins to decrease due to its dissolution in the formation water. This process leads to dissolution increasingly dominating the sequestration process over time. Consistent with the correlation delineated in the literature [43], the temporal evolution of the total contact area subsequent to the initiation of CO₂ injection can be mathematically expressed as A(t) = 2t/3 × 10⁶ m², where t represents the elapsed time in years. The dissolution flux, as estimated in this model, amounts to 8.42 kg/(m²·year). However, this figure contrasts markedly with the field-scale simulation results, wherein the average dissolution flux is quantified at merely 3.36 kg/(m²·year). This notable underestimation is attributed primarily to the coarse resolution of the simulation grid. In addition, due to the presence of CH₄, the capacity for CO₂ dissolution is reduced. Typically, the attainment of a converged dissolution flux necessitates a finer grid resolution, albeit at the cost of increased computational time. While multi-scale modeling presents a viable solution to this challenge, it falls outside the purview of the current study. The details for this technique can be found in the related literature [44].

4. Conclusions

We conducted numerical simulations to examine how the stagnant CTZ and residual natural gas concentration affect the solubility trapping of CO₂. The study involves a detailed analysis of CO₂ dissolution in formation water, considering the influence of gas mixtures. The key findings are:

[1]

The stagnant capillary zone significantly disrupts the concentration boundary layer, enhancing solubility trapping. This is evidenced by higher Sherwood numbers and maximum values in two-phase simulations compared to single-phase ones, indicating stronger convection due to the capillary zone;

[2]

The increased residual natural gas concentration lowers the CO₂ partial pressure and solubility, reducing the density contrast between ambient and CO₂-enriched brine and weakening convective mass transport. In addition, changes in gas composition alter the saturation profile in the capillary zone, further reducing the intensity of perturbations. These combined effects significantly hinder mass transport, leading to lower dissolution rates and Sherwood numbers;

[3]

The onset and decay times of mass transfer processes have an exponential relationship with residual natural gas concentration, highlighting the increasing impact of gas mixtures with higher residual gas levels;

[4]

The effective cumulative gas production increased by 16.71 × 10⁶ m³, marking an 18.9% increase compared to depletion development. However, the presence of CH₄ significantly reduces the amount of CO₂ dissolution.