Impact of Pore Structure and Hydrate Distribution on CO₂-CH₄ Replacement in CH₄ Hydrate: A Pore-Scale Numerical Analysis

Abstract

The mining of CH₄ hydrate through the CO₂-CH₄ replacement method mostly occurs within CH₄ hydrate-bearing sediments. Therefore, it is crucial to investigate the replacement process on the pore scale. This study aims to explore the impacts of pore microstructure and the CH₄ hydrate non-uniform distribution on the replacement of CO₂ for CH₄. A two-dimensional numerical model has been adopted to investigate this issue. A pore-scale numerical simulation is conducted in a physical model of real porous media. Then, the replacement process in a comparative model, in which the pore microstructure and the non-uniform distribution of the CH₄ hydrate are not considered, is simulated. The findings indicate that the CH₄ hydrate dissociation and the CO₂-CH₄ mixed hydrate generation are affected by the effective throat length of pores. When the pore microstructure and CH₄ hydrate heterogeneous distribution are ignored, the replacement rate and CO₂ storage rate are underestimated. However, the effective throat length does not exert a significant impact on the pure CO₂ hydrate generation, which is produced by the reaction of water with dissolved CO₂. In addition, in terms of gas migration, ignoring the heterogeneous distribution of CH₄ hydrate will underestimate the impact of initial water on the relative permeability of gas.

1. Introduction

Natural gas hydrates are efficient clean energy sources widely distributed in marine sediments and permafrost regions. As traditional fossil fuels are increasingly consumed, natural gas hydrates have attracted great attention owing to their substantial hydrocarbon reserves [1]. CH₄ is the main guest component constituting natural gas hydrate. Therefore, investigations into natural gas hydrate exploitation mainly concentrate on CH₄ hydrate. As a new CH₄ hydrate exploitation method, CO₂-CH₄ replacement can realize CO₂ sequestration [2,3,4] and CH₄ hydrate safe exploitation by exchanging CH₄ molecules in hydrate lattices with CO₂ molecules [5,6]. This characteristic makes the CO₂-CH₄ replacement a very promising method for CH₄ hydrate exploitation [7,8].

Complex energy and material transfer are involved in the process of replacing CH₄ with CO₂. First, depending on the reaction conditions, the replacement mechanism varies [9]. During the replacement process, molecular substitution within the crystal lattice is observed, possibly accompanied by partial decomposition of CH₄ hydrate and subsequent generation of CO₂ hydrate [10] and mixed hydrate [11,12]. Secondly, natural gas hydrates mostly occur in the pores of sediments and are distributed under the effect of the pore microstructure. Thus, the contact between the mobile phase, such as gas and water, and the hydrate phase is affected. During the replacement, as CH₄ hydrate decomposes, new hydrates are generated within the pore channels; thus, the changed hydrate distribution may cause blockage of the pore channels. Moreover, the existence of initial water can also lead to CO₂ hydrate generation within the pores [13,14]. In this way, the energy transfer and the migration of the fluid phase are also affected. In summary, investigations into the replacement of CH₄ with CO₂ should address the hydrate phase distribution, the fluid migration dynamics, role of water, and pore microstructure effects.

Huneker [15] studied the hydrates and liquid CO₂ distribution characteristics of CO₂-CH₄ replacement processes in reservoirs and proposed that low injection pressure can achieve high recovery in type 2 hydrate reservoirs. The simulation results of White et al. [16] on type 1 hydrate reservoirs showed that lower injection pressure can reduce secondary hydrate generation. Janicki et al. [17] investigated the impact of CO₂ injection into a partially consumed CH₄ hydrate reservoir, focusing on the resultant CH₄ production and the distribution characteristics of both CH₄ hydrate and CO₂ hydrate throughout the displacement process. They believed that CO₂ injection changed the temperature and pressure of the reservoir, leading to further decomposition of CH₄ hydrate. Core-scale dynamic displacement simulations by Phirani et al. [18] revealed that CH₄ hydrate decomposition is driven by either an elevated CO₂ mole fraction or reduced injection pressure during CO₂ flooding, attributed to the thermodynamic destabilization of CH₄ hydrate.

In CO₂-CH₄ replacement studies, the pore microstructure is typically simplified by characterizing bulk porosity and permeability to represent pore-scale effects, while the hydrate distribution is quantified through spatially averaged saturation. Oldenburg et al. [19] simulated the CH₄ recovery by continuously injecting CO₂ in a consumed natural gas reservoir. The distribution of gaseous CO₂ mass fraction and the gas flow rate in the reservoir, as well as the CH₄ production rate from the gas-producing well, were analyzed. Luo et al. [20] investigated the influences of vertical heterogeneity within reservoirs, as well as the strategic placement of perforations in injection and production wells, on the recovery of CH₄, storage of CO₂, and migration of CO₂ in the reservoir. Huneker [15] performed a parameter sensitivity analysis of the CH₄ production rate by changing parameters, such as CO₂ injection pressure, temperature, reservoir properties, and hydrate plugging model in the simulation. Zhao et al. [21] established a series of experiments aimed at examining the principles of replacement reactions when the hydrates and guest molecules were in different phase equilibrium regions.

Free water typically exists in hydrate reservoirs at the initial moment of CO₂-CH₄ replacement. The introduction of CO₂ results in the migration of free water within the porous medium, attributed to the displacement effects induced by the CO₂. Castellani et al. [22] experimented with CO₂-CH₄ replacement, and the result proved that water plays an indispensable role in CO₂ hydrate generation. Yuan et al. [23] proposed that the initial water facilitated the pure CO₂ hydrate formation, which was distinct from the CO₂ hydrate produced by CO₂-CH₄ substitution. And the presence of pure CO₂ hydrate reduced the replacement efficiency. Zhao et al. [24] concluded through a CO₂-CH₄ replacement experiment that the pressure associated with the replacement reaction was affected by the pure CO₂ hydrate formation. Another perspective suggests that the interfacial water layer on CH₄ hydrate particles enhance thermal conductivity, thereby accelerating the CO₂-CH₄ replacement, with the reaction rate exhibiting a linear dependence on the initial interfacial water content [25]. Therefore, the function of initial water in the replacement process is still unclear.

In the above works, hydrate distributions, fluid migration, and the parameters affecting CO₂-CH₄ replacement efficiency were studied in field-scale or core-scale numerical simulations or experiments. Although the results are meaningful for the application of CH₄ hydrate mining, they did not reveal the replacement mechanism in the pores because of the lack of pore microstructure details. Therefore, pore-scale investigations are required in the study of CO₂-CH₄ replacement.

However, compared with macroscale studies, the pore-scale investigations on CO₂-CH₄ replacement were few. Jadhawar et al. [26] conducted the first experimental investigation at the pore scale regarding the CO₂-CH₄ replacement. They injected CO₂ into a micro-glass pore model containing CH₄ hydrate and excess water and analyzed the composition of the produced gas. The results showed that excess water and CO₂ dissolved in water hindered the release of CH₄. Jang et al. [27] showed an image of CH₄ hydrate in a micro-model after immersion in liquid CO₂ for 30 min.

Despite the dependence of CO₂-CH₄ replacement efficiency on dynamic phase evolution and multiphase fluid migration within porous media, pore-scale phenomena eluded real-time observation because of the constraints of conventional experimental techniques. Therefore, numerical simulation is an important research method for CO₂-CH₄ replacement. Hsieh et al. [28] developed a numerical model for CO₂-CH₄ replacement, grounded in the theory of hydrate decomposition films. They also computed the flux of hydrate decomposition/generation occurring at the exterior of hydrate particles. However, their study did not consider the effects of porous media, fluid migration, initial water, and guest molecule diffusion. Fukumoto et al. [29] conducted a numerical study regarding the dissociation/generation of CH₄ hydrate at the pore scale. However, the current understanding remains limited regarding the effects of pore microstructure and the non-uniform distribution of CH₄ hydrate within hydrate-bearing sediments on CO₂-CH₄ replacement. The function of the initial water in the CO₂ hydrate generation and fluid migration remains ambiguous.

Consequently, in this paper, a pore-scale physical model is derived from the microscopic CT scanning image slices of porous media, aimed at reconstructing the microstructure of such materials. A two-dimensional numerical model of CO₂-CH₄ replacement in porous media is adopted [30]. Then an analysis is conducted on the impact of the effective length of the pore throat on the characteristics of the CO₂-CH₄ replacement reaction. The impact of initial water content on the formation of pure CO₂ hydrate, as well as the characteristics of fluid migration, is also discussed in the case of CH₄ hydrate heterogeneous distribution in pores. Finally, the results are compared with the CO₂-CH₄ replacement process without considering the pore microstructure and CH₄ hydrate distribution, and the deviation is analyzed. Herein, mixed hydrate refers to the CO₂-CH₄ mixed hydrate, which is produced by the CO₂-CH₄ replacement. Pure CO₂ hydrate is produced from water and CO₂ dissolved in water. CO₂ hydrate refers to the CO₂ hydrate in the CO₂-CH₄ mixed hydrate.

2. Methods

2.1. Physical Model

In the CO₂-CH₄ replacement within CH₄ hydrate, CO₂ is injected into the CH₄ hydrate reservoir between the bedrock and the low-permeability reservoir through the injection well; then, the produced gas can be collected from the production well. This process is called dynamic replacement, in which a mixture of CO₂ and CH₄ flows through the pores of the sediment.

The physical model of this study (Figure 1a) is constructed based on the microscopic CT scanning image slices of the real porous media [31]. The white parts in Figure 1 are the porous medium particles, the blue area is the pore channel, and the red areas around the particles are the CH₄ hydrate distribution areas. The two-dimensional model can show the basic structure of pores and the distribution of hydrates and the results can be used as a reference in engineering. Some experimental and numerical studies have used two-dimensional models to study the hydrate formation/decomposition behavior at the pore scale [26,32,33]. Consequently, this research employs a two-dimensional physical model to study the impact of pore microstructure and non-uniform distribution of CH₄ hydrate on the CO₂-CH₄ replacement.

The computational domain, partial grids, boundary conditions, and CH₄ hydrate distribution are also shown in Figure 1a. CO₂ is assumed to flow steadily into the computational domain, with a velocity inlet condition used at the left boundary and a pressure outlet condition imposed at the right boundary. All solid–fluid interfaces are treated as no-slip walls. A fixed point (Point a), positioned at the center of a pore channel, is monitored throughout the replacement process. An unstructured triangular mesh is employed for the simulation. Three throats with different effective lengths, as shown in Figure 1b, are studied. The effective throat length is determined by the total throat length, which is defined as the distance between the centers of the two pores connected by the throat [34].

CH₄ hydrate occurrence depth in the throat is defined in this paper as the length of half the shortest line segment passing through a throat contraction, with both ends on the CH₄ hydrate surface surrounding the porous medium particles. Each line segment representing CH₄ hydrate occurrence depth (Line Segments 1–3, Figure 1b) extends from the CH₄ hydrate surface to the center of the throat. The evolutions of relevant parameters at each point on the line segments are analyzed to study the impact of pore microstructure on the replacement of CH₄ with CO₂.

Table 1. Physical model parameters, coordinates of point a, the effective throat lengths, and the depths of CH₄ hydrate in throats.

Parameters	Units	Values
Length	$\mathrm{mm}$	3.00
Width	$\mathrm{mm}$	2.00
Porosity	%	43.83
Absolute permeability	D	64.20
X coordinate of point a	$\mathrm{mm}$	1.4169
Y coordinate of point b	$\mathrm{mm}$	0.9996
Effective length of Throat 1	$\mathsf{\mu }\mathrm{m}$	58.93
Effective length of Throat 2	$\mathsf{\mu }\mathrm{m}$	28.41
Effective length of Throat 3	$\mathsf{\mu }\mathrm{m}$	54.75
Depth of CH4 hydrate in Throat 1	$\mathsf{\mu }\mathrm{m}$	82.34
Depth of CH4 hydrate in Throat 2	$\mathsf{\mu }\mathrm{m}$	65.09
Depth of CH4 hydrate in Throat 3	$\mathsf{\mu }\mathrm{m}$	81.03

presents the parameters of the physical model, coordinates of point a, effective throat lengths, and the depth of CH₄ hydrate in each throat. The effective lengths of Throats 1 and 3 are comparable and greater than that of Throat 2, corresponding to greater CH₄ hydrate occurrence depths in these throats compared to Throat 2.

To explore the deviation of simulation results caused by ignoring the pore microstructure and CH₄ hydrate heterogeneous distribution in the pores, a homogeneous physical model is also established. Figure 2 illustrates the computational domain and boundary conditions of the homogeneous physical model. The configurations (dimensions, porosity, and absolute permeability) are maintained consistent with the pore-scale physical model established above, and the structured grids are used.

2.2. Numerical Model

A two-dimensional model of guest molecule exchange in CH₄ hydrate is adopted to simulate the pore-scale CO₂-CH₄ replacement dynamics [30] and based on the following reaction process.

CO₂ flows through the pore channels containing CH₄ hydrate, replacement and hydrate reformation occur at the CH₄ hydrate surface: CO₂ molecules preferentially occupy large cages while replaced CH₄ molecules occupy small ones. Thus, CO₂-CH₄ mixed hydrate is formed. Then, the CO₂ molecules in the gas phase must diffuse through the mixed hydrate layer before they can contact the CH₄ hydrate and continue the reaction. The released CH₄ molecules also need to diffuse through the mixed hydrate layer into the gas phase. Therefore, the replacement reaction becomes slow because of the influence of this diffusion-limited mass transfer. At the same time, the CO₂ dissolved in the water, when the conditions for CO₂ hydrate formation are met, CO₂ molecules would also react with the water in the pores, leading to the formation of pure CO₂ hydrate.

The current framework incorporates the following assumptions:

(1) Hydrate phases remain stationary within the pore channel;

(2) Aqueous-phase dissolution of CH₄ is negligible;

(3) CH₄ hydrate is distributed around the porous media particles;

(4) CH₄ hydrate coats the porous media particles with uniform saturation;

(5) Guest molecule diffusion through the mixed hydrate interfacial layer formed by the replacement of CH₄ with CO₂ at the CH₄ hydrate surface maintains dynamic equilibrium with the hydrate dissociation and generation kinetics.

The multiphase flow is governed by the Navier-Stokes equations, with phase-specific continuity expressed as follows:

$${\displaystyle \frac{\partial (\varphi S_q{\rho }_q)}{\partial t}}+\nabla \cdot (\varphi S_q{\rho }_q{\overrightarrow{v}}_q)={\displaystyle \sum _p({\dot{m}}_{pq}-{\dot{m}}_{qp})}$$

(1)

where $\varphi$, $S$, $\rho$, $\overrightarrow{v}$, t, and $\dot{m}$ represent sediment porosity, saturation, density, velocity vector, time, and the mass transfer rate, respectively; the subscripts $q$ and $p$ represent phases, which are gas phase ($\mathrm{g}$), aqueous phase ($\mathrm{l}$), CH₄ hydrate phase ($\mathrm{mh}$), CO₂ hydrate phase ($\mathrm{ch}$), and pure CO₂ hydrate phase ($\mathrm{pch}$), respectively.

The initial CH₄ hydrate decomposition rate is assumed to be ${\dot{n}}_{\mathrm{mh}}^{\mathrm{i}}$. Since a small amount of released CH₄ molecules are re-stored in the small cages of the mixed hydrate, ${\dot{n}}_{\mathrm{mh}}^{\mathrm{i}}$ needs to be corrected. The final absolute value of the CH₄ hydrate dissociation rate ${\dot{n}}_{\mathrm{mh}}$ is equal to the value of the CH₄ generation rate ${\dot{n}}_{\mathrm{m}}$, that is, as follows:

$${\dot{n}}_{\mathrm{mh}}=-{\dot{n}}_{\mathrm{m}}={\dot{n}}_{\mathrm{mh}}^{\mathrm{i}}+{\displaystyle \frac{v_1}{v_2}}{\dot{n}}_{\mathrm{ch}}$$

(2)

where $v_1$ and $v_2$ are the numbers of small and large cages per one water molecule, respectively. For sI hydrate, $v_1=1/23$ and $v_2=3/23$, respectively.

Given the kinetically limited nature of the CO₂-CH₄ replacement, a quasi-steady-state assumption is adopted: the guest molecule diffusion flux, $q$, through the mixed hydrate interface formed by CO₂-CH₄ maintains dynamic equilibrium with hydrate phase transitions (decomposition/formation), that is, as follows:

$${\dot{n}}_{\mathrm{mh}}^{\mathrm{i}}/\varphi S_{\mathrm{mh}}{A}_{\mathrm{Smh}}=-q_{\mathrm{m}}$$

(3)

$${\dot{n}}_{\mathrm{ch}}/\varphi S_{\mathrm{mh}}{A}_{\mathrm{Smh}}=-q_{\mathrm{c}}$$

(4)

where $A_{\mathrm{S}}$ is the particle-specific surface area.

Since the newly formed mixed hydrate layer is thin [35], the molar diffusion flux can be approximated as follows:

$$q_i=-D_i{\rho }_{\mathrm{ec}}{v}_2{(1-{\theta }_2)}^2\cdot {\displaystyle \frac{C_{i,2}(f_i^{\mathrm{g}}-f_i^{\mathrm{lc}})}{\delta }}$$

(5)

where D, ${\rho }_{\mathrm{ec}}$, $\theta$, $C$, $\delta$, and $f$ represent the guest molecule diffusion coefficient, amount of substance of water per unit volume of the hydrate, cage occupation, Langmuir constant, the thickness of the layer of mixed hydrate, and the component fugacity, respectively, the subscript $i$ represents component ($i=m$ for CH₄ and $i=c$ for CO₂), the subscript 2 represents large cages, the superscript $\mathrm{g}$ represents the gas phase, and local fugacity $f_i^{\mathrm{lc}}$ refers to the interfacial fugacity at the CH₄ hydrate/mixed hydrate interface. $(f_i^{\mathrm{g}}-f_i^{\mathrm{lc}})$ is the driving force for guest molecules to transport across the mixed hydrate layer. In this work, the value of ${\theta }_2$ is 0.98 [36]. The thickness of the layer of mixed hydrate can be calculated through the volume of hydrate obtained in the previous time step and the reaction area $\varphi S_{\mathrm{mh}}{A}_{\mathrm{Smh}}$. The fugacity of component $i$ in its gas phase is equal to the product of its fugacity coefficient and the partial pressure.

The kinetics model for hydrate phase transitions is employed to determine the molar reaction rates for CH₄ hydrate and CO₂ hydrate. In this model, the driving force for hydrate dissociation/formation is the disparity between the equilibrium fugacity of the guest molecules within the hydrate and the fugacity of those guest molecules in the gas phase [37]. Therefore, at the CH₄ hydrate/mixed hydrate boundary, the initial rate of decomposition for CH₄ hydrate, ${\dot{n}}_{\mathrm{mh}}^{\mathrm{i}}$, and the rate of CO₂ hydrate generation, ${\dot{n}}_{\mathrm{ch}}$, are as follows:

$${\dot{n}}_{\mathrm{mh}}^{\mathrm{i}}=-k_{\mathrm{d}0}\exp (-{\displaystyle \frac{\Delta E}{RT}})\varphi S_{\mathrm{mh}}{A}_{\mathrm{Smh}}(f_{\mathrm{m}}^{\mathrm{e}}-f_{\mathrm{m}}^{\mathrm{lc}})$$

(6)

$${\dot{n}}_{\mathrm{ch}}=k_{\mathrm{F}}\varphi S_{\mathrm{mh}}{A}_{\mathrm{Smh}}(f_{\mathrm{c}}^{\mathrm{lc}}-f_{\mathrm{c}}^{\mathrm{e}})$$

(7)

where $k_{\mathrm{d}0}$ and $k_{\mathrm{F}}$ are the intrinsic rate constant for CH₄ hydrate dissociation and the rate constant for CO₂ hydrate generation, respectively; $\Delta E$, R, and T are the CH₄ hydrate decomposition activation energy, universal gas constant, and temperature, respectively; $f^{\mathrm{e}}$ indicates the fugacity of the hydrate phase equilibrium.

Combining Formulas (2) to (7), the CH₄ hydrate/mixed hydrate interfacial guest molecule fugacity is finally obtained as follows:

$$f_i^{\mathrm{lc}}={\displaystyle \frac{f_i^{\mathrm{e}}k\delta +D_i{\rho }_{\mathrm{ec}}{v}_2{(1-{\theta }_2)}^2{C}_{i,2}{f}_i^{\mathrm{g}}}{k\delta +D_i{\rho }_{\mathrm{ec}}{v}_2{(1-{\theta }_2)}^2{C}_{i,2}}}$$

(8)

where $k=k_{\mathrm{d}0}\exp (-{\displaystyle \frac{\Delta E}{RT}})$ when $i$ represents CH₄, and $k=k_{\mathrm{F}}$ when $i$ represents CO₂, respectively.

Based on the aforementioned equation, the local fugacity corresponds to the component fugacity in the gas phase when no mixed hydrate is generated. In this scenario, Equations (6) and (7) represent the traditional kinetics models for hydrate decomposition and formation. When the mixed hydrate begins to form, the local fugacity is the guest molecule fugacity at the interface between the mixed hydrate layer and the CH₄ hydrate. Thus, the influence of diffusion-limited mass transfer of guest molecules on hydrate decomposition/formation can be considered. As the thickness of the mixed hydrate layer increases, the effect of diffusion-limited mass transfer increases. Finally, the reaction is dominated by the diffusion-limited mass transfer mechanism.

The pure CO₂ hydrate formation rate ${\dot{n}}_{\mathrm{pch}}$ can be calculated as [38] follows:

$${\dot{n}}_{\mathrm{pch}}=k_{\mathrm{F}}\varphi S_{\mathrm{pch}}{A}_{\mathrm{Spch}}(f_{\mathrm{c}}^{\mathrm{l}}-f_{\mathrm{c}}^{\mathrm{e}})$$

(9)

where $f_{\mathrm{c}}^{\mathrm{l}}$ is the fugacity of CO₂ in the aqueous phase.

The rate of CO₂ dissolution in water can be calculated as follows:

$${\dot{n}}_{\mathrm{c},\mathrm{gl}}={\beta }_{\mathrm{l}}\varphi S_{\mathrm{g}}{\displaystyle \frac{6}{d_{\mathrm{B}}}}(c_{\mathrm{c},\mathrm{l}}^{*}-c_{\mathrm{c},\mathrm{l}})$$

(10)

where ${\beta }_{\mathrm{l}}=2.0\times {10}^{-8}\mathrm{m}/\mathrm{s}$ and $d_{\mathrm{B}}={10}^{-4}\mathrm{m}$ are the coefficients for mass transfer and the bubble diameter, respectively, and $c_{\mathrm{c},\mathrm{l}}^{*}$ and $c_{\mathrm{c},\mathrm{l}}$ are the equilibrium concentration and actual CO₂ concentration in the aqueous phase, respectively.

All molar reaction rates used in this paper are summarized in

Table 2. Molar variation rates used in the numerical model in this paper.

Molar Variation Rate	Symbol	Expression
Initial decomposition rate of CH4 hydrate	${\dot{n}}_{\mathrm{mh}}^{\mathrm{i}}$	$-k_{\mathrm{D}}\varphi S_{\mathrm{mh}}{A}_{\mathrm{Smh}}(f_{\mathrm{m}}^{\mathrm{e}}-f_{\mathrm{m}}^{\mathrm{lc}})$
CH4 generation rate	${\dot{n}}_{\mathrm{m}}$	$-{\dot{n}}_{\mathrm{mh}}^{\mathrm{i}}-{\displaystyle \frac{v_1}{v_2}}{\dot{n}}_{\mathrm{ch}}$
CH4 hydrate decomposition rate	${\dot{n}}_{\mathrm{mh}}$	${\dot{n}}_{\mathrm{mh}}^{\mathrm{i}}+{\displaystyle \frac{v_1}{v_2}}{\dot{n}}_{\mathrm{ch}}$
CO2 hydrate formation rate	${\dot{n}}_{\mathrm{ch}}$	$k_{\mathrm{F}}\varphi S_{\mathrm{mh}}{A}_{\mathrm{Smh}}(f_{\mathrm{c}}^{\mathrm{lc}}-f_{\mathrm{c}}^{\mathrm{e}})$
CO2 dissolution rate	${\dot{n}}_{\mathrm{c},\mathrm{gl}}$	${\beta }_{\mathrm{l}}\varphi S_{\mathrm{g}}{\displaystyle \frac{6}{d_{\mathrm{B}}}}(c_{\mathrm{c},\mathrm{l}}^{*}-c_{\mathrm{c},\mathrm{l}})$
Pure CO2 hydrate formation rate	${\dot{n}}_{\mathrm{pch}}$	$k_{\mathrm{F}}\varphi S_{\mathrm{pch}}{A}_{\mathrm{Spch}}(f_{\mathrm{c}}^{\mathrm{l}}-f_{\mathrm{c}}^{\mathrm{e}})$

.

In this model, CH₄ and CO₂ are gas phase components, while water and the CO₂ dissolved in the water are the aqueous phase components. Thus, the species transport equation can be expressed as follows:

$$\begin{array}{l}{\displaystyle \frac{\partial (\varphi S_q{\rho }_q{Y}_q^i)}{\partial t}}+\nabla \cdot (\varphi S_q{\rho }_q{\overrightarrow{v}}_q{Y}_q^i)=\\ -\nabla \cdot \varphi S_q\cdot (-{\rho }_q{D}_{\mathrm{m},q}^i\nabla Y_q^i-D_{\mathrm{T},q}^i{\displaystyle \frac{\nabla T}{T}})+{\displaystyle \sum _p({\dot{m}}_{pq}^i-{\dot{m}}_{qp}^i)}\end{array}$$

(11)

where $Y$ is the mass fraction, the superscript $i$ is the component, and $D_{\mathrm{m}}$ and $D_{\mathrm{T}}$ are the diffusion coefficients for mass and thermal energy, respectively.

It is considered that the region of CH₄ hydrate accumulation can be characterized as a porous medium, with a porosity value of 0.719. Additionally, the potential presence of slip flow within this context is taken into account through the application of the Knudsen number $Kn$.

$$Kn=\lambda /L$$

(12)

where $L$ and $\lambda$ are the characteristic geometric length and the mean free path of molecules, respectively.

Based on the model assumptions in this paper, the velocities of hydrates are zero. Therefore, the momentum conservation equation reduces to the following:

$$\begin{array}{l}{\displaystyle \frac{\partial (\varphi S_q{\rho }_q{\overrightarrow{v}}_q)}{\partial t}}+\nabla \cdot (\varphi S_q{\rho }_q{\overrightarrow{v}}_q{\overrightarrow{v}}_q)=-\varphi S_q\nabla p+\varphi S_q{\rho }_q\overrightarrow{g}+\varphi {\displaystyle \sum _p{\overrightarrow{R}}_{pq}}\\ +{\displaystyle \sum _p({\dot{m}}_{pq}{\overrightarrow{v}}_{pq}-{\dot{m}}_{qp}{\overrightarrow{v}}_{qp})}-S_q{\displaystyle \frac{{\varphi }^2{\mu }_q}{K_q}}{\overrightarrow{v}}_q\end{array}$$

(13)

where $p$, $K$, and $\mu$ present pressure, permeability, and dynamic viscosity, respectively, ${\rho }_q\overrightarrow{g}$ is the gravitational volume force of the $q$ phase, ${\overrightarrow{R}}_{pq}$ and ${\overrightarrow{v}}_{pq}$ are the interface drag force and velocity between $p$ and $q$ phase, respectively.

The permeability of the $q$ phase $K_q$ can be expressed as [17]

$$K_q={({\displaystyle \frac{s_q-s_{q,\mathrm{r}}}{1-s_{q,\mathrm{r}}}})}^3{K}_0(S_{\mathrm{g}}+S_{\mathrm{l}}){({\displaystyle \frac{(1-\varphi )(S_{\mathrm{g}}+S_{\mathrm{l}})}{1-\varphi (S_{\mathrm{g}}+S_{\mathrm{l}})}})}^{2\kappa }$$

(14)

where $K_0$, $\kappa$, and $s_{q,\mathrm{r}}$ are the permeability of the porous medium, the Brooks–Corey parameter, and the residual saturation of the $q$ phase, respectively [16].

The energy generated by the decomposition/formation of each hydrate phase and the heat transfer between phases are considered in this model. The energy conservation equation can be given as follows:

$${\displaystyle \frac{\partial (\varphi S_q{\rho }_q{h}_q)}{\partial t}}+\nabla \cdot (\varphi S_q{\rho }_q{\overrightarrow{v}}_q{h}_q)=-\varphi S_q{\displaystyle \frac{\partial p_q}{\partial t}}+{\dot{n}}_q{H}_q+{\displaystyle \sum _p(\varphi Q_{pq}+{\dot{m}}_{pq}{h}_{pq}-{\dot{m}}_{qp}{h}_{qp})}$$

(15)

where $Q$ and $h$ are the interphase heat exchange intensity and the specific enthalpy, respectively, for hydrate phases, ${\dot{n}}_q{H}_q$ is the energy source generated by hydrate decomposition/formation, and $H$ represents the hydrate decomposition/formation latent heat.

The replacement rate, ${\eta }_{\mathrm{Re}}$, is used to evaluate the CO₂ replacement efficiency, while the CO₂ storage efficiency is determined through the CO₂ storage rate, ${\eta }_{\mathrm{Capture}}$. ${\eta }_{\mathrm{Re}}$, and ${\eta }_{\mathrm{Capture}}$ can be expressed as [39] follows:

$${\eta }_{\mathrm{Re}}=\left[(n_{\mathrm{mh}}^{\mathrm{i}}-n_{\mathrm{mh},\mathrm{resid}})/n_{\mathrm{mh}}^{\mathrm{i}}\right]\times 100\%$$

(16)

$${\eta }_{\mathrm{Capture}}=(n_{\mathrm{c},\mathrm{hydrate}}/n_{\mathrm{c},\mathrm{injected}})\times 100\%$$

(17)

where $n_{\mathrm{mh}}^{\mathrm{i}}$ and $n_{\mathrm{mh},\mathrm{resid}}$ are the initial and residual molar contents of the CH₄ hydrate in the replacement reaction, respectively; $n_{\mathrm{c},\mathrm{hydrate}}$ and $n_{\mathrm{c},\mathrm{injected}}$ are the molar contents of CO₂ sequestered in the hydrates and that are injected into the reservoir, respectively. In this paper, only the hydrate-trapped CO₂ is considered in the calculation of the CO₂ storage rate, the dissolved or free CO₂ in the pore network is excluded.

The Eulerian model for multiphase flow is adopted to establish the numerical model, and it is solved based on the pressure-based coupling algorithm. The second-order upwind is used to discrete the convection terms, and the control equations are nonlinearly coupled. The convergence criteria is that the residual is less than 1 × 10⁻⁶.

3. Model Validation

The established numerical model is validated against the experimental results of CO₂-CH₄ replacement carried out by Ryou et al. [40]. In Ryou’s experiment, gaseous CO₂ was continuously introduced into the porous medium that contained CH₄ hydrate, followed by the execution of the CO₂-CH₄ dynamic replacement in the CH₄ hydrate. After the dynamic replacement, the inlet and outlet were closed for two soaking replacement processes. The gas mixture produced at the outlet was collected and analyzed, and the replacement rates were calculated.

Ryou’s experiment was conducted in a CH₄ hydrate core sample. The core was a cylinder, and there was no external force in the normal direction of the symmetric surface. Therefore, the two-dimensional axisymmetric model can be adapted to approximately simulate this three-dimensional problem. Figure 3 illustrates the computational domain geometry and boundary conditions for model validation, featuring a no-slip isothermal wall with the temperature maintained at 275.15 K (consistent with initial domain conditions) at the upper boundary. The bottom boundary of the calculation domain is the axis of symmetry. A velocity inlet boundary condition is prescribed at the left-hand boundary, with a pressure outlet condition imposed at the right-hand boundary. The outlet pressure is the same as the initial pressure in the calculation domain, both of which are 3.89 MPa. Based on mesh analysis and other meshing methods used by scholars when studying related issues [41], a structured quadrilateral mesh with a total number of 8596 cells is adopted. Two sets of experiments are simulated to validate the modeling framework. The basic simulation parameters, such as initial conditions and model size, correspond to those documented by Ryou et al. and are listed in

Table 3. Initial conditions and parameters of porous media model for model validation.

Parameter	Unit	Value
Core radius	mm	27.50
Core length	mm	460.00
Initial/Wall temperature	K	275.15
Initial pressure	MPa	3.89
CO2 velocity at the inlet	m/s	2.51 × 10−5
Intrinsic permeability	D	16.34

. The divergent initial condition sets are listed in

Table 4. Initial conditions for the two experiments of Ryou et al. [40].

	Porosity (%)	${\mathit{S}}_{\mathbf{mh}}$ (%)	${\mathit{S}}_{\mathbf{w}}$ (%)
Exp. 1	41.74	28.87	7.61
Exp. 2	42.07	23.22	11.99

.

According to the experiment, the dynamic replacement process is simulated first. Following the dynamic replacement simulation, the conditions at the inlet and outlet boundary are reset to no-slip isothermal walls, with the outputs of the simulation for the dynamic replacement process serving as the initial conditions for the subsequent soaking replacement process. Real gas behavior is modeled using the SRK equation of state.

Finally, the replacement rate calculated by the simulation is compared with the experimental results, with the comparison results presented in Figure 4. After the dynamic replacement and the two soaking replacement processes of experimental case 1, the replacement rates were 25.70%, 30.84%, and 34.79%, respectively. The corresponding simulation results are 22.56%, 29.41%, and 33.56%, respectively. In comparison to the experimental findings, the relative errors observed are −12.22%, −4.62%, and −3.52%, respectively. Similarly, the replacement rates in processes of Experiment 2 were 19.31%, 30.18%, and 34.86%, respectively, and the corresponding simulation results are 21.95%, 28.95%, and 32.26%, respectively. In comparison to the experimental findings, the relative errors observed are 13.67%, −4.08%, and −7.49%, respectively. Some errors in the simulation results may be caused by model assumptions. Firstly, the fine hydrate crystals generated at the beginning of the reaction may be discharged with free water, resulting in overestimation of the reaction area. Therefore, the assumption of the stationarity of hydrate phases may lead to a higher replacement rate. Secondly, a small amount of CH₄ may be dissolved in the aqueous phase and flows away through the outlet, so ignoring the dissolution of CH₄ may cause a lower calculated replacement rate. Most of the relative errors observed between the simulation outcomes and the experimental findings fall within a range of ±10%. This indicates a strong concordance between the simulation and the experimental data, and the model established in this paper is suitable for simulating the CO₂-CH₄ replacement in the CH₄ hydrate.

4. Results

4.1. Simulation Setup

The numerical model validated above is employed to simulate Case 1~Case 3 based on the pore-scale physical model (see Figure 1) to explore the effects of pore microstructure on CO₂-CH₄ replacement within CH₄ hydrate. The impact of initial water on the replacement reaction concerning the heterogeneous distribution of CH₄ hydrate is also studied. The initial parameters for the two cases are presented in

Table 5. Initial parameters for the cases studied in this paper.

Parameter	Unit	Case 1	Comparative Case 1	Case 2	Comparative Case 2	Case 3
Initial pressure	MPa	3.00	3.00	3.00	3.00	3.00
Outlet pressure	MPa	3.00	3.00	3.00	3.00	3.00
Initial temperature	K	275.00	275.00	275.00	275.00	275.00
Inlet velocity	m/s	2.2 × 10−5	2.2 × 10−5	2.2 × 10−5	2.2 × 10−5	2.2 × 10−5
$S_{\mathrm{mh}}$ in CH4 hydrate distribution area	-	71.90%	-	71.90%	-	71.90%
Initial water saturation	-	10.00%	10.00%	0.00%	0.00%	30.00%

. In addition, two cases based on the homogeneous physical model (see Figure 2) are also simulated for comparison, namely, Comparative Case 1 and Comparative Case 2. The initial saturation of the CH₄ hydrate in the comparative case is equal to the average CH₄ hydrate saturation recorded within the computational domain of Case 1 (the same as in Case 2), which is 12.03%. The other initial conditions are the same as those in Cases 1 and 2 (see Table 5).

The impact of the effective throat length on the replacement reaction is explored through an analysis of the simulation results of Case 1. The deviation of the replacement rate and the CO₂ storage rate caused by ignoring the pore microstructure and the heterogeneous distribution of CH₄ hydrate is discussed by comparing the simulation results of Case 1 with those of Comparative Case 1. The comparison of Cases 1~3 examines the initial water impacts on the replacement, particularly in the context of CH₄ hydrate heterogeneous distribution. The deviation of the fluid migration caused by ignoring the pore microstructure and the CH₄ hydrate heterogeneous distribution is explored by comparing Case 1 and Comparative Case 1, as well as Case 2 and Comparative Case 2.

4.2. Mesh Independence Verification

For each physical model, three sets of meshes are used to verify mesh independence. The temporal evolution of replacement rates based on different grids is shown in Figure 5. The cells of the meshes for the pore-scale physical model are 125,986, 231,036, and 350,449, respectively. Finally, the replacement rates based on grid 1, grid 2, and grid 3 are 8.3658, 8.4390, and 8.4634, respectively. The relative error between the data based on grid 2 and grid 1 is 0.87%, while the relative error between the data based on grid 3 and grid 2 is 0.29%. The replacement rates based on Grid 2 and Grid 3 exhibit a notable similarity, thereby supporting the selection of Grid 2 for subsequent pore-scale analyses. Similarly, in the homogeneous physical model, the relative error between the replacement rate based on grid 2 and grid 1 is 0.71%, while the relative error between the replacement rate based on grid 3 and grid 2 is 0.22%. Therefore, the homogeneous physical model with 2400 cells is used to study the comparative cases.

4.3. Replacement Process and Influence of Effective Throat Length

In the CH₄ hydrate reservoirs, porous media particles accumulate to form pores and throats of varying sizes. The CH₄ hydrate coating on the particles of porous media contacts the injected CO₂ earlier than the CH₄ hydrate inside the throats. Thus, the replacement processes for the CH₄ hydrate inside the throats and the CH₄ hydrate distributed at the surface of the porous media particles are different. This difference would become more pronounced as the throat becomes longer and the CH₄ hydrate is stored deeper in the throat. Therefore, the influence of the effective throat length on the CO₂-CH₄ replacement within CH₄ hydrate is discussed in this section. The characteristics of the replacement reaction and the hydrate distribution under different effective throat lengths are analyzed. Finally, the pore-scale simulation results are compared with the comparative cases that do not consider the pore microstructure and the distribution of CH₄ hydrate. The deviation in the simulation results caused by ignoring the pore microstructure and CH₄ hydrate heterogeneous distribution in the pores is studied.

4.3.1. CO₂ Mass Fraction and Partial Pressure of CH₄

(1) CO₂ mass fraction in the gas phase

The distributions of CO₂ mass fraction in the gas phase at different times in Case 1 are shown in Figure 6, and the throats are marked by red ovals. The gaseous CO₂ mass fraction within the region characterized by the presence of CH₄ hydrate is observed to be lower than that in regions devoid of CH₄ hydrate. The phenomenon indicates that the CO₂ movement and diffusion into the CH₄ hydrate distribution area (especially the throats) are hindered. Thus, the permeability of the distribution area is reduced in comparison to the adjacent areas, attributable to the presence of CH₄ hydrate.

The influence of effective throat length is illustrated in Figure 6, which shows that the gaseous CO₂ mass fraction within the throat area containing CH₄ hydrate is significantly reduced. In the early stage of CO₂ injection (10 s), since Throat 1 is located closest to the inlet among the examined throats, the CO₂ mass fraction in it is the highest. Although Throat 3 has a similar effective length to Throat 1, it has the lowest CO₂ mass fraction in it because Throat 3 is located closer to the outlet. The influence of effective throat length on the distribution of gaseous CO₂ mass fraction is not obvious in this stage. With the continuous introduction of CO₂ (100 s and 250 s), the gaseous CO₂ mass fraction in the pores increases, and the values of the gaseous CO₂ mass fraction in Throat 1 and Throat 3 are similar. Concurrently, the mass fraction of the gaseous CO₂ in Throat 2, which has the shortest effective length, is the highest of all examined throats. This phenomenon shows that when CH₄ hydrate is stored in throats, a longer effective throat length is not conducive to CO₂ diffusion into the throat. Upon completion of the CO₂ injection period (400 s), the mass fraction of gaseous CO₂ within the pores exceeds 98%, and this value in the throats is slightly lower than that in other areas. The injection of CO₂ has lasted for a sufficient time for CO₂ to diffuse into the throats. Therefore, the variations in the gaseous CO₂ mass fraction within the throats and pores are not obvious.

The evolution of the gaseous CO₂ mass fraction within the regions of CH₄ hydrate distribution in the throats for Case 1 is shown in Figure 7. This figure illustrates the correlation between the gaseous CO₂ mass fraction at the surface of the CH₄ hydrate distribution region in the throats and the distance from the throat to the inlet. The closer the throat is to the inlet, the higher the CO₂ mass fraction at the surface of the distribution area. However, the gaseous CO₂ mass fraction at the surface of the CH₄ hydrate distribution region in Throat 2 located in the middle of the computational domain is similar to that of throat 3 located near the outlet. This result is caused by the diffusion of CO₂ toward the outlet. In the central region of the CH₄ hydrate distribution region in Throat 1, CO₂ diffuses slowly due to the long effective throat length. Therefore, at the beginning, the gaseous CO₂ mass fraction at the center of the distribution area in Throat 1 is the same as that in Throat 2. As CO₂ is continuously injected, the influence of the effective throat length on the gaseous CO₂ mass fraction begins to emerge. The gaseous CO₂ mass fraction at the center of the CH₄ hydrate distribution area in Throat 3 is similar to that in Throat 1, and lower than that in Throat 2, which has a shorter effective length. In summary, the gaseous CO₂ mass fraction at the surface of the CH₄ hydrate distribution area in the throats is mainly influenced by the mass fraction of gaseous CO₂ present in the pores adjacent to these throats. Conversely, the gaseous CO₂ mass fraction at the center of the CH₄ hydrate distribution area is mainly affected by the effective throat length.

(2) Partial pressure of CH₄

The distributions of CH₄ partial pressure in the gas phase at different times in Case 1 are shown in Figure 8. Under the displacement of the injected CO₂, the evolution of CH₄ distribution is almost exactly the opposite of the CO₂ mass fraction. The CH₄ partial pressure within the region characterized by the presence of CH₄ hydrate is observed to be higher than that in regions devoid of CH₄ hydrate. The phenomenon indicates that the movement and diffusion of CH₄ out of the CH₄ hydrate distribution area (especially the throats) are hindered. It also shows that the diffusion of CO₂ into the hydrate distribution area is limited.

The evolution of the CH₄ partial pressure within the regions of CH₄ hydrate distribution in the throats for Case 1 is shown in Figure 9. The CH₄ partial pressure still has an opposite trend to the evolution of CO₂ mass fraction. This figure illustrates that the closer the throat is to the inlet, the lower the CH₄ partial pressure at the surface of the distribution area. But as CO₂ diffuses toward the outlet, the CH₄ partial pressure at the surface of the CH₄ hydrate distribution region in Throat 2 located in the middle of the computational domain is similar to that of Throat 3 located near the outlet. In the central region of the CH₄ hydrate distribution region in Throat 1, CH₄ partial pressure decreases slowly due to the long effective throat length. As CO₂ is continuously injected, the influence of the effective throat length on the CH₄ partial pressure begins to emerge. The partial pressure of CH₄ at the center of the CH₄ hydrate distribution area in Throat 3 is similar to that in Throat 1, and higher than that in Throat 2, which has a shorter effective length. This indicates that the CH₄ partial pressure at the surface of the CH₄ hydrate distribution area in the throats is mainly influenced by the partial pressure of CH₄ present in the pores adjacent to these throats. The same conclusion as the gaseous CO₂ mass fraction can be drawn that at the center of the CH₄ hydrate distribution area, the decrease in CH₄ partial pressure is mainly affected by the effective throat length.

4.3.2. Hydrate Variation Rates

(1) CH₄ hydrate dissociation rate

The distributions of the CH₄ hydrate dissociation rate for Case 1 are illustrated in Figure 10. Initially, CO₂ is introduced at a steady flow rate. The partial pressure of gaseous CH₄ diminishes as a result of CO₂ injection, leading to the CH₄ hydrate dissociation under the reduced pressure (10–100 s). As the CO₂ partial pressure rises to reach the equilibrium pressure of CO₂ hydrate, mixed hydrate begins to form at the surface of the CH₄ hydrate. This process inhibits the further decomposition of CH₄ hydrate, resulting in a gradual decline in the CH₄ hydrate decomposition rate (250–400 s).

In the throats where CH₄ hydrate exists, at the initial stage of CO₂ displacement (10 s), the CH₄ partial pressure begins to decrease from the surface of the CH₄ hydrate distribution area as CO₂ diffuses into the throats. CH₄ hydrate begins to decompose from the surface of its distribution area due to this reduced pressure. The decomposition rate of CH₄ hydrate inside the distribution area will be higher than that at the surface of the distribution area (shown by the red ellipse) as the reaction proceeds (100–250 s). This phenomenon can be ascribed to two principal factors. Firstly, the decomposition of CH₄ hydrate at the surface of its distribution zone results in a slightly lower CH₄ hydrate saturation and a smaller reaction area. Secondly, the diffusion of CO₂ in the gas phase into the CH₄ hydrate distribution area requires a longer time compared to its diffusion to the immediate surface of the distribution area. The mixed hydrate in the distribution area is generated later, which makes the CH₄ hydrate inside the distribution area take a longer time to decompose.

The CH₄ hydrate decomposition rate at the surface of the CH₄ hydrate distribution region in each throat is initially related to the distance from the throat to the inlet (10 s). The proximity of the throat to the inlet is positively correlated with the CH₄ hydrate decomposition rate at the surface of the CH₄ distribution zone. However, at the center of the throats, there is an absence of CH₄ hydrate dissociation attributed to the limited cumulative time of CO₂ diffusion. As the reaction proceeds (100 s), the CH₄ hydrate at the center of each throat begins to decompose. The CH₄ hydrate decomposition rates at the center of Throat 1 and Throat 3 with longer effective lengths are slightly higher than that at the center of Throat 2 with a shorter effective length (250 s). This difference eventually disappears as the inhibitory impact of the mixed hydrate on the CH₄ hydrate dissociation increases (400 s).

The evolution of the CH₄ hydrate dissociation rate in Throats 1–3 for Case 1 is illustrated in Figure 11. As the reaction advances, the peak decomposition rate of CH₄ hydrate in each throat shifts from the periphery of the CH₄ hydrate distribution zone towards the center. Since Throat 1 is closer to the inlet and has a higher mass fraction of the gaseous CO₂ (see Figure 6), the driving force for CH₄ hydrate dissociation near the inlet is greater. Therefore, the CH₄ hydrate dissociation rate within the CH₄ hydrate distribution area of Throat 1 is higher than that of Throats 2 and 3. In Throat 2, the maximum CH₄ hydrate decomposition rate observed at the center of the CH₄ hydrate distribution area is lower than that recorded in Throat 1, and the time at which this maximum rate is achieved occurs earlier than in Throat 1. This shows that although the distance between Throat 2 and the inlet is longer, the effective length of Throat 2 is shorter than that of Throat 1, so the time required for CO₂ to diffuse into Throat 2 is shorter. Therefore, the gaseous CO₂ mass fraction at the center of the CH₄ hydrate distribution area in Throat 2 is higher. The cumulative time for CH₄ hydrate dissociation is reduced, and the generation of mixed hydrate, along with their inhibition for CH₄ hydrate decomposition, occurs at an earlier stage. The effective length of Throat 3 is similar to that of Throat 1, so the depth of CH₄ hydrate in the throat is not much different, resulting in similar evolution trends of CH₄ hydrate decomposition rates in Throat 3 and Throat 1. However, influenced by the distance from the throat to the inlet and the effective throat length, the maximum CH₄ hydrate decomposition rate at the center of Throat 3 is marginally greater than that of Throat 2. The duration required to reach the peak decomposition rate occurs subsequent to Throat 2 and precedes Throat 1.

(2) CO₂ hydrate formation rate

The distributions of the CO₂ hydrate formation rate at different times for Case 1 are illustrated in Figure 12. The generation of CO₂ hydrate signifies the appearance of mixed hydrate and the beginning of diffusion-limited mass transfer for guest molecules. An analysis of Figure 10 and Figure 12 indicates that the formation of CO₂ hydrate occurs after the dissociation of CH₄ hydrate. Initially (10 s), the gaseous CO₂ partial pressure is below the equilibrium pressure required for CO₂ hydrate formation due to insufficient CO₂ injection, resulting in the absence of CO₂ hydrate generation. Then (100 s), as the partial pressure of gaseous CO₂ rises, CO₂ hydrate begins to form at the surface of the CH₄ hydrate distribution area. It is important to note that the CO₂ has not yet attained the equilibrium pressure necessary for hydrate formation within the distribution zone; thus, no CO₂ hydrate is generated internally. Subsequently (250 s), the generation of mixed hydrate leads to a main occurrence of guest molecule replacement in the computational domain. Therefore, the rise in the amount of CO₂ hydrate corresponds directly to the decrease in the amount of CH₄ hydrate. Moreover, the increased amount of CO₂ hydrate at the center of the CH₄ hydrate distribution area in the throat is higher than that at the surface. This phenomenon can be attributed to the ability of CO₂ molecules to occupy the empty cages previously occupied by CH₄ molecules. The difference in the increase of CO₂ hydrate between the center and the surface of the throat gradually disappears with the further formation of the mixed hydrate (400 s).

Figure 13 illustrates the evolution of CO₂ hydrate formation rates in Throats 1–3 for Case 1. During the initial phase of CO₂ hydrate formation (90–130 s), no CO₂ hydrate is generated in the center of the CH₄ hydrate distribution area of each throat. Then, the CO₂ hydrate generation rate at the center of the CH₄ hydrate distribution area in Throat 2 was higher than that in Throats 1 and 3 (130–170 s). Subsequently, the distribution of CO₂ hydrate generation rate in each throat is consistent with the distribution of CH₄ hydrate dissociation rate under the impact of diffusion-limited mass transfer. Therefore, although the gaseous CO₂ mass fraction at the center of Throat 1 and Throat 3 is lower than that of Throat 2, the rates of CO₂ hydrate formation in Throat 1 and Throat 3 are higher than that in Throat 2 (190–250 s). Finally, with the accumulation of CO₂ hydrate at the center of the CH₄ hydrate distribution area within each throat, the reaction process is completely converted to the replacement of guest molecules within the hydrate. The CO₂ hydrate generation rate in each throat is constrained by the rate of variation of CH₄ hydrate (see 330 s and 900 s in Figure 11 and Figure 13).

(3) Pure CO₂ hydrate formation rate

The distributions of the formation rate of pure CO₂ hydrate at different times for Case 1 are shown in Figure 14. The pure CO₂ hydrate appears later than the CO₂ hydrate, as the dissolution of CO₂ in water is a prerequisite for achieving the equilibrium fugacity necessary for CO₂ hydrate formation. A substantial quantity of pure CO₂ hydrate is generated within the distribution area of CH₄ hydrate due to the retention of the initial water content. Conversely, in regions devoid of CH₄ hydrate distribution, the initial water is displaced and flows away through the outlet under the displacement of CO₂, and a small amount of pure CO₂ hydrate is generated within those pores. Furthermore, the effective throat length does not exert a significant impact on the pure CO₂ hydrate generation.

4.3.3. Hydrate Distributions

(1) CH₄ hydrate saturation

The evolution of CH₄ hydrate saturation at the CH₄ hydrate distribution area in Throats 1–3 for Case 1 is shown in Figure 15. CH₄ hydrate saturation decreases rapidly during the displacement of CO₂. Then, the decrease of CH₄ hydrate saturation slows down when CO₂ displacement is completed. Initially, CH₄ hydrate saturation at the surface of its distribution area in each throat is lower than that at the center due to the decomposition of CH₄ hydrate. However, as the rate of CH₄ hydrate decomposition at the center of the distribution area exceeds that at the surface, the saturation of CH₄ hydrate at the surface of each throat is higher than that at the center.

Since Throat 2 has the shortest effective length, the mass fraction of gaseous CO₂ at the center of the CH₄ hydrate distribution zone in Throat 2 is higher than that in Throats 1 and 3. Therefore, the CH₄ hydrate saturation at the center of the distribution area in Throat 2 is the highest in the end. Throat 1 has a longer effective length, and it takes longer for the CO₂ to diffuse into Throat 1 and reach CO₂ hydrate equilibrium pressure. In addition, Throat 1 is the closest to the inlet, so the CH₄ hydrate in Throat 1 decomposes first and has the longest time to decompose. Therefore, the CH₄ hydrate saturation at the center of the distribution area in Throat 1 is the lowest. The CH₄ hydrate saturation at the center of the CH₄ hydrate distribution area in Throat 3 is between that in Throat 1 and Throat 2 due to the influences of the longer effective throat length of Throat 3 and the longer distance from the inlet.

(2) CO₂ hydrate saturation

The evolution of CO₂ hydrate saturation at CH₄ hydrate distribution areas in Throats 1–3 for Case 1 is shown in Figure 16. The development of CO₂ hydrate lags behind the CH₄ hydrate dissociation. Initially, the saturation of CO₂ hydrate increases rapidly, then the increasing trend of CO₂ hydrate saturation slows down because of the diffusion-limited transfer of guest molecules. Moreover, the saturation of CO₂ hydrate at the surface of the CH₄ hydrate distribution area within each throat is always higher than that at the center of the distribution area.

As for the influence of the effective throat length, CH₄ hydrate is stored deeper in Throat 1 with a longer effective length, and it takes longer for CO₂ to diffuse into the center of the CH₄ hydrate distribution area in Throat 1. Therefore, the saturation of CO₂ hydrate at the center of the distribution area in Throat 1 consistently exhibits lower levels compared to Throat 2, which has a shorter effective length. Correspondingly, CO₂ hydrate formation occurs at an earlier stage at the center of the distribution area in Throat 2, resulting in a saturation level that is higher than those in Throats 1 and 3. However, due to the high CO₂ hydrate generation rate at the center of the distribution area in Throat 3 in the late stage of the reaction, the CO₂ hydrate saturation in Throat 3 is eventually slightly higher than that in Throat 2.

(3) Pure CO₂ hydrate saturation

The generation and distribution of pure CO₂ hydrate at the pore scale are mainly influenced by the non-uniform distribution of CH₄ hydrate within the pores and the initial water distribution. Therefore, in this paper, the distribution of pure CO₂ hydrate at the pore scale is studied through the average saturation of pure CO₂ hydrate within the regions designated for CH₄ hydrate, the areas devoid of CH₄ hydrate, and the whole computational domain. The results are compared with the average saturation of pure CO₂ hydrate in Comparative Case 1. Figure 17 illustrates the evolution of the average saturation of pure CO₂ hydrate for various cases. In Case 1, the injected CO₂ flows through the pore channels, resulting in the displacement of water within the regions devoid of CH₄ hydrate. However, in the regions where the CH₄ hydrate is present, the gas flow is obstructed. Therefore, part of the initial water remains trapped within these regions. Therefore, the average saturation of pure CO₂ hydrate within the CH₄ hydrate distribution zone is significantly higher than that in the areas devoid of CH₄ hydrate. In Comparative Case 1, where the pore microstructure and the non-uniform distribution of CH₄ hydrate are not considered, the injected CO₂ disperses uniformly in the entire calculation domain. As a result, a substantial volume of initial water is displaced from the outlet with the injected CO₂, leading to less pure CO₂ hydrate generation compared to Case 1. Finally, the average saturation of pure CO₂ hydrate in Comparative Case 1 is lower compared to Case 1.

4.3.4. Replacement Rate and CO₂ Storage Rate

Figure 18 illustrates the variations in replacement rate and CO₂ storage rate across various cases. The replacement rate in Case 1 considering the pore microstructure is higher than that in Comparative Case 1, attributable to the high CH₄ hydrate decomposition rate and the low CH₄ hydrate saturation at the throat center of Case 1. This difference mainly occurs during the CO₂ displacement. During the CO₂ displacement stage, CH₄ hydrate accumulates in the throat, so it requires more time for CH₄ in the throats to diffuse into the pores or for CO₂ in the pores to diffuse into the throats. This means that the CH₄ hydrate has more time to decompose, while the partial pressure of CO₂ is not large enough for CO₂ hydrate generation. That is to say, in the throats, more CH₄ hydrate decomposes, while the diffusion-limited transport mechanism caused by the mixed hydrate layer is weaker. It can be speculated that due to the non-uniform distribution of CH₄ hydrate, the CH₄ hydrate will have more time to decompose not only in the throats but also in the places where CH₄ hydrate gather accumulates. However, the throats and the accumulation of CH₄ hydrate that promote the decomposition of CH₄ hydrate are not considered in Comparative Case 1, so the replacement rate in Case 1 is higher than that in Comparative Case 1. Subsequently, because of the low saturation of pure CO₂ hydrate, the diffusion restriction on guest molecules caused by the newly formed hydrates is weak in Comparative Case 1. Therefore, the disparity in the replacement rate between Case 1 and its comparative case gradually decreases.

In terms of CO₂ storage rate, Case 1 demonstrates a higher CO₂ storage rate than Comparative Case 1. Despite the presence of a lower quantity of CO₂ hydrate in the central regions of the throats, a greater amount of pure CO₂ hydrate is produced within the distribution area of CH₄ hydrate, because free water is more likely to stay in areas where hydrates accumulate. Therefore, in the end, the CO₂ storage rate in Case 1 surpasses that of Comparative Case 1.

4.4. Influence of Initial Water

The impact of initial water presence on the replacement of CH₄ with CO₂ is primarily attributed to the pure CO₂ hydrate generation, which is produced through the interaction of water and the CO₂ that is dissolved in it. In the core-scale study, CH₄ hydrate and the generated hydrates are not evenly distributed in porous media, which in turn affects gas migration in the pores. This study examines the impact of initial water on the gas migration dynamics of the replacement process, particularly in scenarios where CH₄ hydrate is not evenly distributed. This analysis is conducted by comparing the simulation results from Cases 1 ~ 3. Through the examination of Case 1 and its comparative case, Case 2 and its comparative case, the calculation deviation of gas migration caused by ignoring the pore microstructure and uneven distribution of CH₄ hydrate is explored.

The gas migration in porous media can be characterized by the gas-phase relative permeability. Figure 19 illustrates the temporal variations in gas-phase relative permeability. In Case 2, where initial water is absent, the gas-phase relative permeability is observed to be greater than that in Case 1. Therefore, at the same inlet velocity, Case 1 should have a higher inlet pressure than Case 2. As the initial water saturation increases to 30% (Case 3), the gas-phase relative permeability becomes smaller, which means that gas injection will receive greater obstacles. In Case 1, as CO₂ displaces the initial water in the pores, the gas-phase relative permeability increases during the CO₂ displacement process. Then, as the pure CO₂ hydrate is generated from the initial water retained in the CH₄ hydrate distribution area, the gas-phase relative permeability slowly decreases. In Comparative Case 1, since the pore microstructure is not considered and the CH₄ hydrate is uniformly distributed, the gaseous CO₂ flows evenly in the entire calculation domain to displace the initial water. Thus, less water is retained in the calculation domain, and less pure CO₂ hydrate is generated. As a result, the gas-phase relative permeability is greater than that observed in Case 1. In Comparative Case 2 and Case 2 without initial water, the amount of pure CO₂ hydrate generated is small. Consequently, the neglect of CH₄ hydrate non-uniform distribution within the pores has a minimal impact on the gas-phase relative permeability.

The variations of replacement rate with time for cases with different initial water saturations are shown in Figure 20. In the early stage of the CO₂ displacement process, the increase of displacement rate is mainly contributed by the depressurization of CH₄ hydrate, and the initial water saturation has little effect on the replacement rate. With the further injection of CO₂, the partial pressure of CO₂ increases, and CO₂ hydrate and pure CO₂ hydrate begin to form. Therefore, the transfer of guest molecules between the gas phase and the hydrate phase is limited. This restriction effect increases with the increase of initial water saturation due to the generation of more pure CO₂ hydrate.

5. Conclusions

This study investigates the CO₂-CH₄ replacement within CH₄ hydrate at the pore scale by a two-dimensional numerical model and a physical model constructed from a microscopic CT scanning image slice of porous media. The influence of the pore microstructure on the CO₂-CH₄ replacement process and the influence of the initial water on gas migration when CH₄ hydrate is non-uniformly distributed are also explored. Ultimately, an analysis is conducted to assess the deviations that could be caused by ignoring the pore microstructure and CH₄ hydrate non-uniform distribution in the numerical simulation of CO₂-CH₄ replacement. The following principal conclusions are derived from this analysis:

(1) The formation, decomposition, and distribution of hydrates exhibit significant variability upon the positioning of CH₄ hydrate within the pore structure. Generally, the longer the effective length of the throat, the deeper the CH₄ hydrate is stored in the throat. This phenomenon is associated with a reduction in the saturation of both CH₄ hydrate and CO₂ hydrate at the center of the distribution area in the throat. The influence of the effective throat length on pure CO₂ hydrate generation is not obvious.

(2) Under the displacement of CO₂, the initial water is likely to be retained in pore channel termini and angular regions, where the flow velocity is comparatively low. This results in the pure CO₂ hydrate generation not only within the regions where CH₄ hydrate is present but also in the regions devoid of CH₄ hydrate. Such occurrences could increase the pressure loss and greatly hinder gas migration.

(3) When the pore microstructure and the CH₄ hydrate non-uniform distribution are ignored, the replacement rate and CO₂ storage rate are underestimated. Ignoring the heterogeneous distribution of CH₄ hydrate will underestimate the impact of initial water on gas migration, while the effect is not significant in scenarios where initial water is absent.

The findings presented in this study indicate that, in the practical implementation of CO₂-CH₄ dynamic replacement for CH₄ hydrate exploitation in reservoirs, if the homogeneous model was used to evaluate the reaction, the actual amount of CH₄ obtained and CO₂ stored would be slightly higher than the simulation results. That is, the simulation results are credible. However, if free water is present in the reservoir, the actual mining process would require higher inlet pressure than the simulation results to maintain fluid migration. How to correct the simulation results to determine the actual inlet pressure requires further research in the future.

This study focuses exclusively on the morphology of CH₄ hydrate coating porous medium particles. In further work, the influence of CH₄ hydrate morphology within porous media on CO₂-CH₄ replacement can be studied in more detail.