A two-phase, multi-component model for efficient CO2 storage and enhanced gas recovery in low permeability reservoirs

Introduction: Carbon dioxide (CO₂) enhanced gas recovery represents a viable strategy for sequestering CO₂ while concurrently augmenting gas production from subsurface reservoirs. Gas reservoirs, as inherent geological formations, are optimal repositories for gaseous compounds, rendering them suitable for CO₂ storage. Nevertheless, the economic viability of pure CO₂ storage necessitates integration with oil and gas recovery mechanisms to facilitate widespread CO₂ utilization.

Method: This study addresses the complexities of CO₂ enhanced gas recovery through a comprehensive approach that combines theoretical model and numerical simulations. A numerical model is developed to simulate three-component diffusion involving CO₂, and methane (CH₄) in a two-phase system comprising gas and water.

Results: The investigation systematically explores the process of enhanced CH₄ extraction and CO₂ injection into the reservoir and examines the influencing factors on extraction. Simulation results reveal a power-law decrease in CH₄ production rate, stabilizing at a constant extraction rate. Enhanced CH₄ extraction benefits from increased porosity, with higher porosity levels leading to greater CH₄ extraction. Permeability augmentation positively influences CH₄ production, although with diminishing returns beyond a certain threshold. The CO₂ injection rate shows a direct proportionality to CH₄ production. However, elevated CO₂ injection rates may increase reservoir pressure, potentially causing cap rock damage and CO₂ gas flushing.

Discussion: This study contributes valuable theoretical insights to the field of CO₂ enhanced gas recovery engineering, shedding light on the intricate dynamics of multi-component fluid transport processes and their implications for sustainable CO₂ utilization.

1 Introduction

CO₂ is the main greenhouse gas. In order to mitigate and ameliorate the impact of the greenhouse effect on human life, countries around the world are actively taking measures and countermeasures to reduce CO₂ emissions. Among them, CO₂ geological storage has received great attention globally as an effective method to reduce carbon emissions (Bachu, 2000; Weiyang and Chen, 2005; LIU et al., 2005; U. S. Department of Energy and Office of Fossil Energy and National Energy Technology Laboratory, 2005; Pei et al., 2005; Liu et al., 2005). Common sites for geological storage of CO₂ include deep saline formations, depleted oil and gas reservoirs, unrecoverable reservoirs and oceans (Bonder, 1992; Li and Bai, 2005; XU et al., 2005; Yuchao, 2005; Wu et al., 2008). However, pure CO₂ storage is expensive, so it is necessary to combine the storage with the enhancement of oil and gas recovery to realize the large-scale utilization of CO₂. The gas storage of gas-bearing reservoirs and the closure of the trap have been fully confirmed in the long-term natural gas storage stage and the development stage of natural gas, so it is feasible to realize the buried storage in the gas reservoir.

The mechanism of CO₂ to improve gas recovery mainly has the following four aspects: 1. Increase the reservoir pressure gradient to improve the natural gas seepage rate; 2. The significant density difference between CO₂ and natural gas will lead to gravitational differentiation, so the CO₂ at the bottom of the reservoir has a lifting effect on the natural gas; 3. Under the conditions of temperature and pressure of the reservoir, CO₂ tends to be in a supercritical state, and its viscosity is much higher than that of the natural gas, which produces the ratio of the fluidity that is favorable for the replacement; 4. The CO₂ displaces CH₄ in the reservoir through the competition adsorption effect (Busch et al., 2006; Liang et al., 2010; Katayama, 2023). Enhanced gas recovery using CO₂ not only enables geological storage of CO₂, but also increases CH₄ production (Hamza et al., 2021; Zhang et al., 2023).

The mixing of injected CO₂ and natural gas in the reservoir affects the driving efficiency and leads to the rapid breakthrough of CO₂ in the production wells, resulting in the poor effect of driving the gas to improve recovery, and the CO₂ in the recovered gas further increases the difficulty and cost of the surface treatment process and reduces the comprehensive economic benefits of CO₂-EGR, so it is of great significance to control the CO₂-CH₄ mixing. K. Damen et al. (Damen et al., 2005) analyzed the economics of reservoir geological disposal of CO₂ collected from China using a multi-criteria analysis including technical and socio-economic criteria. Y. Kurniawan et al. (Kurniawan et al., 2006) used numerical simulations to investigate the competitive adsorption of two-component (CH₂-CO₄) gas in crack like pore structures; V. Goetz et al. (Goetz et al., 2006) conducted experimental studies on the adsorption of CO₂ and CH₄ mixed gases on activated carbon and obtained adsorption isotherms for different gases. K. Jessen et al. (Jessen et al., 2008) conducted experimental and simulation studies on CH₄ extraction by gas injection, but the coal samples used were powder synthesized specimens; T. Theodore et al. (Theodore et al., 2004) introduced experimental and simulation studies on CO₂ storage in reservoirs jointly conducted by the University of Southern California and the Australian National University, focusing on the impact of reservoir structure on CO₂ geological disposal.

Indoor experiments on CO₂ and reservoir fluids are often limited by time and space, and the experiments cannot effectively reflect the interaction between CO₂ and reservoir fluids across time and space scales in the CO₂-EGR process. Although numerical simulation can solve the problems of time and space scales, CO₂ and reservoir fluids involve multiphase and multi-component coupling processes. Therefore, numerical models that characterizes the migration of multiple components such as CO₂, CH₄, and reservoir water in reservoirs are needed for numerical simulation analysis of CO₂ enhanced CH₄ recovery.

In this article, we derive the control equation for two-phase, three component flow and establish a numerical model for CO₂ injection and production of CH₄ based on the proposed multiphase multi-component flow theory. We use Partial Differential Equation Module (PDE) of COMSOL for solving the governing equations, studying the migration of CO₂, CH₄ and water in the process of CO₂ injection and production in the isotropic reservoir. By changing the permeability, porosity and CO₂ injection rate of the reservoir, we studied the influence of reservoir parameters and injection schemes on the distribution of reservoir stress and the extraction of CH₄.

2 Mathmatical model

2.1 Governing equation of gas-water two-phase flow

Base on the mass conservation of the aquifer fluid, the continuity equation for gas-water two-phase flow is as follows (Martin et al., 2005a; Martin et al., 2005b; Ma et al., 2021; Ma et al., 2023):

$\frac{\partial {\mathrm{m}}_{\mathrm{\alpha }}}{\partial \mathrm{t}}+\nabla \cdot \left({\mathrm{\rho }}_{\mathrm{\alpha }}{v}_{\mathrm{\alpha }}\right)-{\mathrm{q}}_{\mathrm{\alpha }}=0,\mathrm{\alpha }=\mathrm{w},\mathrm{g}(1)$

where $m_{\alpha }$ is the fluid mass, $q_{\alpha }$ is the source ($\alpha =\mathrm{w},\mathrm{g}$ represents water and gas, respectively). The fluid velocity is described by Darcy’s law:

$v_{\alpha }=-\frac{k{k}_{\alpha }^r}{{\mu }_{\alpha }}\left(\nabla P_{\alpha }-{\rho }_{\alpha }\mathit{g}\right)(2)$

where $k$ represents permeability, and $k_{\alpha }^r$ is the relative permeability, ${\mu }_{\alpha }$ is fluid viscosity, $P_{\alpha }$ is pore pressure, ${\rho }_{\alpha }$ is the fluid density, and $\mathit{g}$ is the gravitational acceleration. The mass of each phase can be described as:

$m_{\alpha }=S_{\alpha }{\rho }_{\alpha }\varphi (3)$

where $S_{\alpha }$ is fluid saturation, ${\rho }_{\alpha }$ is fluid density, $\varphi$ is porosity.

2.2 Governing equations of gas diffusion

According to Fick’s law, the diffusion flux per unit cross-sectional area perpendicular to the diffusion direction per unit time is directly proportional to the concentration gradient at that cross-section (Nie et al., 2000; Qin et al., 2012; Qin et al., 2013; Li, 2015; Wang, 2015):

$\left[\frac{\partial }{\partial x}\left(D_{AB}{S}_g\varphi M_A\frac{d{C}_A}{dx}\right)+\frac{\partial }{\partial y}\left(D_{AB}{S}_g\varphi M_A\frac{d{C}_A}{dy}\right)+\frac{\partial }{\partial z}\left(D_{AB}{S}_g\varphi M_A\frac{d{C}_A}{dz}\right)\right]dxdydzdt(4)$

$J_A=-D_{AB}\frac{d{C}_A}{dz}(5)$

where $J_A$ is the diffusion flux per unit area of component $A$ in the z-direction per unit time; $D_{AB}$ is the diffusion coefficient between components $A$ and $B$; $C_A$ is the gas concentration of component $A,{dC}_A/dz$ is the concentration gradient of component $A$ in the z-direction. In the unit, the molecular diffusion flux $J_A$ of component $A$ gas in the gas phase on the left side. Within $dt$ time, the mass of component $A$ gas flowing into the unit through molecular diffusion in the x-direction is:

$-D_{AB}{S}_g\varphi M_A\frac{d{C}_A}{dx}dydzdt(6)$

The mass of component $A$ gas flowing out of the unit through molecular diffusion in the x-direction on the right side of the unit is:

$\left[\left(-D_{AB}{S}_g\varphi M_A\frac{d{C}_A}{dx}\right)+\frac{\partial }{\partial x}\left(-D_{AB}{S}_g\varphi M_A\frac{d{C}_A}{dx}\right)dx\right]dydzdt(7)$

Within $dt$ time, the mass difference of component $A$ in the unit due to gas diffusion is:

$-\left[\frac{\partial }{\partial x}\left(v_{gx}{M}_A{C}_A\right)+\frac{\partial }{\partial y}\left(v_{gy}{M}_A{C}_A\right)+\frac{\partial }{\partial z}\left(v_{gz}{M}_A{C}_A\right)\right]dxdydzdt(8)$

In summary, the gas convection diffusion equation is obtained as follows:

$\frac{\partial \left(\varphi M_A{C}_A{S}_g\right)}{\partial t}+\nabla ·\left({\mathit{v}}_{\mathit{g}}{M}_A{C}_A\right)-\nabla ·\left(\varphi D_{AB}{S}_g{M}_A\nabla C_A\right)=0(9)$

2.3 Equation assembly

Substituting Eq. 2 into Eqs 1, 9, the two-phase multi-component seepage model is obtained as follows:

$\frac{\partial \left(\varphi {\rho }_w{S}_w\right)}{\partial t}-\nabla ·\left({\rho }_w\frac{k{k}_{rw}}{{\mu }_w}\left(\nabla p_w\right)\right)=0(10)$

$\frac{\partial \left(\varphi M_A{C}_A{S}_g\right)}{\partial t}-\nabla ·\left(M_A{C}_A\frac{k{k}_{rg}}{{\mu }_g}\left(\nabla p_g\right)\right)-\nabla ·\left(\varphi D_{AB}{S}_g{M}_A\nabla C_A\right)=0(11)$

$\frac{\partial \left(\varphi M_B{C}_B{S}_g\right)}{\partial t}-\nabla ·\left(M_B{C}_B\frac{k{k}_{rg}}{{\mu }_g}\left(\nabla p_g\right)\right)-\nabla ·\left(\varphi D_{AB}{S}_g{M}_B\nabla C_B\right)=0(12)$

where $M_A$ and $M_B$ are fixed values for the relative molecular weight of the gas, and $\rho =MC$, therefore the equation can be transformed into:

$\frac{\partial \left(\varphi {\rho }_w{S}_w\right)}{\partial t}-\nabla ·\left({\rho }_w\frac{k{k}_{rw}}{{\mu }_w}\left(\nabla p_w\right)\right)=0(13)$

$\frac{\partial \left(\varphi {\rho }_A{S}_g\right)}{\partial t}-\nabla ·\left({\rho }_A\frac{k{k}_{rg}}{{\mu }_g}\left(\nabla p_g\right)\right)-\nabla ·\left(\varphi D_{AB}{S}_g\nabla {\rho }_A\right)=0(14)$

$\frac{\partial \left(\varphi {\rho }_A{S}_g\right)}{\partial t}-\nabla ·\left({\rho }_B\frac{k{k}_{rg}}{{\mu }_g}\left(\nabla p_g\right)\right)-\nabla ·\left(\varphi D_{AB}{S}_g\nabla {\rho }_B\right)=0(15)$

Due to the presence of two gases in the gas phase, the pressures of the two gases are defined as $p_A$、 $p_B$:

$p_g=p_A+p_B(16)$

Substitute the saturation equation and capillary pressure equation into:

$\left\{\begin{array}{c}{S}_w+S_g=1\\ p_w=p_g-p_c\end{array}\right.(17)$

There are five variables for solving the equation system: $S_w$、 $S_g$、 $p_w$、 $p_A$ and $p_B$. There are also five equations, which are closed and solvable. The remaining parameters are calculated using the method of calculating physical properties parameters: ${\rho }_i={\rho }_i\left(p_i\right);{\mu }_g={\mu }_g\left(p_g\right);{\mu }_w={\mu }_w\left(p_w\right);k_{rw}=k_{rw}\left(S_w\right);k_{rw}=k_{rw}\left(S_w\right);p_c=p_c\left(S_w\right)$. Substitute the equations into and eliminate $S_g$、 $p_w$ and $p_g$. We obtain a system of equations for variables $S_w$、 $p_A$ and $p_B$:

$\frac{\partial \left(\varphi {\rho }_w{S}_w\right)}{\partial t}-\nabla ·\left({\rho }_w\frac{k{k}_{rw}}{{\mu }_w}\left(\nabla \left(p_A+p_B-p_c\right)\right)\right)=0(18)$

$\frac{\partial \left(\varphi {\rho }_A\left(1-S_w\right)\right)}{\partial t}-\nabla ·\left({\rho }_A\frac{k{k}_{rg}}{{\mu }_g}\left(\nabla \left(p_A+p_B\right)\right)\right)-\nabla ·\left(\varphi D_{AB}\left(1-S_w\right)\nabla {\rho }_A\right)=0(19)$

$\frac{\partial \left(\varphi {\rho }_B\left(1-S_w\right)\right)}{\partial t}-\nabla ·\left({\rho }_B\frac{k{k}_{rg}}{{\mu }_g}\left(\nabla \left(p_A+p_B\right)\right)\right)-\nabla ·\left(\varphi D_{AB}\left(1-S_w\right)\nabla {\rho }_B\right)=0(20)$

According to the Brooks Corey model capillary pressure calculation formula, the capillary pressure is as follows:

$\nabla p_c=\frac{d{p}_c}{d{S}_w}\nabla S_w=\frac{P_t\left(-1/\omega \right)S_e^{-1/\omega -1}}{1-S_w^r-S_g^r}\nabla S_w(21)$

$\frac{\partial p_c}{\partial t}=\frac{d{p}_c}{d{S}_w}\frac{\partial S_w}{\partial t}=\frac{P_t\left(-1/\omega \right)S_e^{-1/\omega -1}}{1-S_w^r-S_g^r}\frac{\partial S_w}{\partial t}(22)$

The final control equation is as follows:

$\left(\varphi {\rho }_w-\varphi {\rho }_w{c}_w{S}_w\frac{d{p}_c}{d{S}_w}\right)\frac{\partial S_w}{\partial t}+\left(\varphi {\rho }_w{c}_w{S}_w\right)\frac{\partial p_A}{\partial t}+\left(\varphi {\rho }_w{c}_w{S}_w\right)\frac{\partial p_B}{\partial t}-\nabla \cdot \left({\rho }_w\frac{k{k}_w^r}{{\mu }_w}\left(\nabla p_A+\nabla p_B-p_c^{\prime }\nabla S_w\right)\right)=0(23)$

$\begin{array}{c}\left(-\varphi {\rho }_A\right)\frac{\partial S_w}{\partial t}+\left({\rho }_A\left(1-S_w\right)+\varphi {\rho }_A^{\prime }\left(1-S_w\right)\right)\frac{\partial p_A}{\partial t}+\left(\varphi {\rho }_A^{\prime }\left(1-S_w\right)\right)\hfill \\ \frac{\partial p_B}{\partial t}-\nabla \cdot \left.\left({\rho }_A\frac{k{k}_g^r}{{\mu }_g}\left.\left(\nabla p_A+\nabla p_B\right)\right)\nabla p_A+\nabla p_B\right)\right){\rho }_A\frac{k{k}_g^r}{{\mu }_g}-\nabla ·\left(\varphi D_{AB}\left(1-S_w\right){\rho }_A^{\prime }\nabla p_A\right)=0\hfill \end{array}(24)$

$\left(-\varphi {\rho }_B\right)\frac{\partial S_w}{\partial t}+\left(\varphi {\rho }_B^{\prime }\left(1-S_w\right)\right)\frac{\partial p_A}{\partial t}+\left(\varphi {\rho }_B^{\prime }\left(1-S_w\right)\right)\frac{\partial p_B}{\partial t}-\nabla \cdot \left.\left({\rho }_B\frac{k{k}_g^r}{{\mu }_g}\left.\left(\nabla p_A+\nabla p_B\right)\right)\right)\right){\rho }_B\frac{k{k}_g^r}{{\mu }_g}-\nabla ·\left(\varphi D_{AB}\left(1-S_w\right){\rho }_B^{\prime }\nabla p_B\right)=0(25)$

3 Verification

This section verifies the accuracy of the proposed two-phase multi-component model by comparing the results of Oldenburg’s simulation scheme (Oldenburg, 2003). The reservoir model has a vertical depth of 22 m and a horizontal length of 1000 m. The wellhead is located on the left boundary of the reservoir, 3 m away from the upper boundary. The remaining boundaries are no-flow. The reservoir model is shown in Figure 1. The reservoir has a constant temperature of 313.15 K, an initial reservoir pressure of 6 MPa, an initial water saturation of 0.2, a gas phase saturation of 0.8, and a gas phase entirely composed of CO₂. The simulation plan involves injecting CH₄ gas into the injection well at a rate of $1.8375\times {10}^{-2}\text{ kg}/\mathrm{s}$ for 180 days. The parameter properties of the simulation are listed in Table 1.

FIGURE 1

FIGURE 1. Geometric model and boundary conditions of the Oldenburg model.

TABLE 1

TABLE 1. Parameter properties of the simulation.

The simulation results are shown in Figure 2. As the CH₄ is injected, the CO₂ component is continuously pushed towards the right side of the reservoir, and the diffusion zone gradually increases. The distance between the center of the mixed zone and the wellhead gradually increases, the movement rate gradually decreases. This is consistent with the model results of Oldenburg, indicating the applicability and accuracy of this model in gas diffusion problems.

FIGURE 2

FIGURE 2. Simulation results at (A) 30 days, (B) 60 days, and (C) 180 day.

4 Model setup

We set up a reservoir model with a reservoir plane size of 6000 m × 4000 m. The reservoir is homogeneous and isotropic. The initial water saturation of the reservoir is 0.3, and the rest gas is CH₄. The initial reservoir pressure is 12 MPa, the absolute permeability is $K=2.0\times {10}^{-15}{m}^2$, and the porosity is 0.07. An injection well is located at the center of the reservoir to inject CO₂, and extraction wells are set at the four corners of the reservoir. The specific location and boundary conditions are shown in Figure 3. The simulation plan involves injecting CO₂ from the injection well at a rate of 0.25 kg/s for 500 days and analyzing the CH₄ rec overy situation. The specific parameters are listed in Table 2.

FIGURE 3

FIGURE 3. Geometry and boundary conditions of the simulation.

TABLE 2

TABLE 2. Case parameter settings.

5 Simulation results

In this section, we discussed CO₂ enhanced CH₄ recovery based on the two-phase multi-component seepage equation. Due to the geometric distribution of CO₂ injection wells and CH₄ extraction wells being symmetric in the simulation domain, in order to improve computational efficiency, we only analyzed a quarter of the CO₂ displacement CH₄ process.

As shown in Figure 4, after CO₂ is injected into the reservoir, CH₄ inside the reservoir is replaced. The gas pressure of CH₄ near the CO₂ injection well sharply decreases, and as the extraction progresses, CO₂ diffuses towards the vicinity of the extraction well. Near the extraction well, CH₄ pressure decreases uniformly, and CH₄ is extracted through the extraction well.

FIGURE 4

FIGURE 4. (A) 100 days, (B) 300 days, and (C) 500 days results of CH₄ pressure in reservoirs.

As shown in Figure 5, after CO₂ is injected into the reservoir, CH₄ and reservoir water are driven away together, forming a CO₂ enrichment zone near the injection well. Near the extraction well, due to the lower well pressure, water and CH₄ are extracted together, decreasing the water saturation.

FIGURE 5

FIGURE 5. (A) 100 days, (B) 300 days, and (C) 500 days reservoir water saturation results.

We study the CH₄ production and daily productivity, as shown in Figure 6, of the extraction wells. Among them, the daily productivity of CH₄ shows a power-law decreasing trend, with CH₄ productivity reaching its maximum in the early stages of extraction; As extraction proceeds, the daily CH₄ production rate decreases due to the decrease in reservoir pressure. In the later stage of extraction, CH₄ productivity reaches equilibrium and remains basically unchanged. The growth rate of production decreases as extraction progresses.

FIGURE 6

FIGURE 6. CH₄ production volume and daily productivity.

6 Sensitive analysis

6.1 Effect of porosity

In this section, we investigage the distribution of CH₄ pressure, water saturation, and evolution of CH₄ extraction under different reservoir porosities of 0.0175, 0.035, 0.14, and 0.21.

Porosity of reservoir has a significant impact on CH₄ pressure distribution. As shown in the Figure 7, the smaller the porosity of the reservoir, the greater the impact range of CO₂ injection of the same quality. This is because the reduction of pore space results in the same volume of CO₂ occupying a larger reservoir area. When the porosity of the reservoir is 0.0175, the CO₂ injection well and the CH₄ production well are connected, and all the CH₄ in the middle is driven out. When the porosity is greater than 0.14, the influence of porosity on pore pressure decreases.

FIGURE 7

FIGURE 7. CH₄ pressure with different porosities: (A): 0.0175 (B): 0.035 (C): 0.14 (D): 0.21.

As shown in Figure 8, the larger the porosity, the larger the pore volume of the same area reservoir, and more CO₂ needs to be injected to expand its influence area; The smaller the porosity, the larger the impact area of the same CO₂ injection amount, and more CH₄ and water from the reservoir pores are driven out by CO₂.

FIGURE 8

FIGURE 8. Water saturation at different porosities: (A): 0.0175 (B): 0.035 (C): 0.14 (D): 0.21.

As shown in Figure 9, with the increase of porosity, the CH₄ extraction rate increases; The larger the porosity, the more CH₄ stored near the extraction well. Under the same production well pressure and CO₂ injection rate, the greater the CH₄ production.

FIGURE 9

FIGURE 9. CH4 production.

6.2 Effect of permeability

In this section, we investigage the distribution of CH₄ pressure, water saturation, and evolution of CH₄ extraction with permeability being with $2\times {10}^{-13}{m}^2$, $2\times {10}^{-14}{m}^2$, $2\times {10}^{-16}{m}^2$ and $2\times {10}^{-17}{m}^2$.

The permeability of the reservoir determines the migration ability of fluids in the reservoir. As shown in Figure 10, the higher the permeability of the reservoir, the faster CO₂ diffuses from the injection well to the surrounding area at the same time. When the permeability is $2\times {10}^{-13}{m}^2$, the pressure of the CO₂ injection well and the CH₄ production well interact with each other, and CO₂ flows directly from the injection well to the production well. The lower the permeability, the less CH₄ displaced by CO₂ injection, which is not conducive to CH₄ extraction.

FIGURE 10

FIGURE 10. CH₄ pressure at different permeabilities (A): $2\times {10}^{-13}{m}^2$ (B): $2\times {10}^{-14}{m}^2$ (C): $2\times {10}^{-16}{m}^2$ (D): $2\times {10}^{-17}{m}^2$

As shown in Figure 11, the influence range of extraction and injection wells is highly correlated with the reservoir permeability. Within the same extraction time, reservoirs with higher permeability can produce more CH₄; Reservoirs with low permeability face greater difficulties in both CO₂ injection and CH₄ extraction, resulting in lower CO₂ recovery efficiency.

FIGURE 11

FIGURE 11. Water saturation at different permeabilities: (A): $2\times {10}^{-13}{m}^2$ (B): $2\times {10}^{-14}{m}^2$ (C): $2\times {10}^{-16}{m}^2$ (D): $2\times {10}^{-17}{m}^2$

Permeability has a great impact on CH₄ production. As shown in Figure 12, the greater the permeability, the more CH₄ extraction However, blindly increasing the permeability of the reservoir has a saturation value for the increase in CH₄ production. When the permeability of the reservoir increases from $2\times {10}^{-14}{m}^2$ to $2\times {10}^{-13}{m}^2$, CH₄ production changes slightly. This may be because the high permeability reservoir causes the injected CO₂ to diffuse to the production well and be extracted. When the permeability reaches a certain level, the reservoir pressure drops too quickly, and the CO₂ injection well and CH₄ production well are connected. After CO₂ breakthrough, The proportion of CH₄ in the production well decreases, making it difficult to extract CH₄.

FIGURE 12

FIGURE 12. CH₄ production under different permeabilities.

6.3 Effect of CO₂ injection rate

In this section, we investigage the distribution of CH₄ pressure and water saturation with injection rate being with $0.125\text{ kg}/\mathrm{s}$ and $0.5\text{ kg}/\mathrm{s}$.

As shown in Figure 13, the higher the CO₂ injection rate, the greater the reservoir pressure, and the larger the range of CO₂ diffusion. Due to CO₂ injecting water and CH₄ into the pores of the reservoir near the well, the CH₄ pressure near the CO₂ injection well decreases, forming a high-pressure zone at the front of the displacement.

FIGURE 13

FIGURE 13. CH₄ pressure at different injection rates (A): $0.125\text{\hspace{0.17em}kg}/$ (B): $0.5\text{\hspace{0.17em}kg}/\mathrm{s}$.

As shown in Figure 14, for water saturation at different injection rates. The higher the CO₂ injection rate, the more water and CH₄ are discharged at the same time, forming a low saturation zone near the injection well. For CH₄ extraction wells, the high pressure brought by high injection rates leads to more CH₄ being extracted, and the high CO₂ injection rate increases CH₄ extraction.

FIGURE 14

FIGURE 14. Water saturation at different injection rates (A): $0.125\text{\hspace{0.17em}kg}/$ (B): $0.5\text{\hspace{0.17em}kg}/\mathrm{s}$.

7 Conclusion

The process of CO₂-enhanced CH₄ extraction involves the intricate migration dynamics of gas and water phases, incorporating multiple components within the reservoir. Leveraging the derived two-phase flow and multi-component diffusion model, we present a comprehensive numerical model to elucidate the intricate phenomena associated with the multi-component seepage of CO₂-EGS. This model considers both the water phase and the gas phase, encompassing two distinct components: CO₂ and CH₄. The main conclusions are derived as follows.

1) With the injection of CO₂, both water and CH₄ within the reservoir pores are displaced. The CH₄ productivity exhibits a power-law decline, ultimately stabilizing at a constant extraction rate, with a progressively diminishing gradient of productivity increase. In the initial extraction stages, the CH₄ production rate attains its peak, declining subsequently due to the diminishing reservoir pressure. In the latter stage of extraction, CH₄ productivity reaches an equilibrium state, demonstrating sustained constancy.

2) Higher porosity levels result in augmented CH₄ reserves proximate to extraction wells. However, heightened porosity diminishes the influence of CO₂ on CH₄ recovery, as it reduces the area affected by the reservoir pressure of CO₂. Conversely, lower porosity levels extend the influence of a given CO₂ injection volume over a larger reservoir range, driving out CH₄ and water over an expansive area.

3) Elevated reservoir permeability accelerates CO₂ diffusion from injection wells to the surrounding region. While increased permeability enhances CH₄ production, an indiscriminate escalation of permeability reaches a saturation point for CH₄ production augmentation. Excessive permeability poses the risk of connecting CO₂ injection wells with CH₄ extraction wells, impeding CH₄ extraction upon CO₂ breakthrough.

4) The CO₂ injection rate directly influences the affected area within the reservoir. A higher injection rate results in increased reservoir pressure, leading to greater CH₄ extraction and improved production. Nonetheless, an excessively high CO₂ injection rate induces heightened reservoir pressure, potentially causing cap rock damage and consequent CO₂ release.

Data availability statement

The original contributions presented in the study are included in the article/Supplementary material, further inquiries can be directed to the corresponding author.

Author contributions

XW: Conceptualization, Methodology, Project administration, Visualization, Writing–original draft. QZ: Formal Analysis, Methodology, Visualization, Writing–original draft. YW: Investigation, Methodology, Writing–review and editing.

Funding

The author(s) declare that no financial support was received for the research, authorship, and/or publication of this article.

Acknowledgments

A special acknowledgment goes to the reviewers for their invaluable feedback.

Conflict of interest

Authors XW, QZ, and YW were employed by Shaanxi Yanchang Petroleum (Group) Co., Ltd.

Publisher’s note

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.

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