Time-Varying Characteristics of CH₄ Displacement–Replacement Effect in Coal Seams During CO₂-Enhanced Coalbed Methane Recovery

Abstract

Carbon dioxide (CO₂)-enhanced coalbed methane recovery involves a complex process of mixed-gas adsorption, desorption, and diffusion–transport. The literature suggests that an appropriate range of CO₂ injection pressure and an optimal injection time window are critical for coal seams with varying reservoir conditions. That is, higher pressure and longer injection periods do not necessarily lead to better displacement performance. Therefore, in this study, experimental research was conducted on the time-varying characteristics of the displacement–replacement effect of CO₂-enhanced methane (CH₄) extraction from coal seams, and the following results were obtained. (1) The process of displacement–replacement of CH₄ by CO₂ in coal seams can be divided into five stages: a stage of spontaneous CH₄ desorption caused by partial-pressure effects, a replacement-dominated stage, a stage where replacement and displacement act jointly, a displacement-dominated stage, and a stabilization stage. (2) For all three coal samples (anthracite, coking coal, and long-flame coal), cumulative CH₄ desorption increases with increasing CO₂ injection pressure below 5 MPa and finally stabilizes. However, when CO₂ injection pressure exceeds 5 MPa, the effect weakens, possibly due to the dynamic changes in CO₂ partial pressure. (3) The displacement–replacement ratio decreases with increasing CH₄ equilibrium pressure. Additionally, the larger the difference between the CO₂ injection pressure and the CH₄ equilibrium pressure, the better the displacement–replacement effect.

1. Introduction

Coal serves as China’s fundamental and backup energy source, playing a deeply integrated role in the country’s economy. Coal bed methane (CH₄, CBM) is a valuable, high-quality, and clean resource associated with coal, and its efficient extraction is crucial for preventing and controlling disasters related to its catastrophic explosions, making it an important option and cleaner than conventional fossil fuels [1,2,3,4]. China’s coal seam structure is complex, with generally low permeability of coal. Shallow coal resources are notably depleting, leading to a shift in coal development to deeper levels, which has now become the norm. The increasingly evident low-permeability characteristics of coal seams, complex geology, and technical limitations have become the bottlenecks, making CH₄ extraction more difficult and increasing the pressure to prevent and control CH₄ disasters [5,6]. Thus, industrial innovation is required to manage hazards and maintain productivity at greater depths. Unfortunately, traditional negative pressure extraction technology cannot overcome the challenge of low permeability in coal seams. Pre-extraction is time consuming and yields slow results, failing to meet the needs of mining succession and underground safety production [7]. To address the challenge of low permeability in coal seams, China has implemented measures such as mining protective layers, hydraulic fracturing/slotting/punching, and loosening blasting to enhance CH₄ drainage and improve coal seam permeability [8]. Although most permeability enhancement measures have successfully improved the permeability of coal seams, the issue of a sharp decline in extraction efficiency due to the decrease in reservoir pressure during the later stages of mining remains unresolved. Therefore, development of a simple and effective new technology to improve coal seam permeability and enhance gas extraction efficiency is urgently demanded [9]. With the continuous advancement of science and technology, breakthroughs have been made in gas injection displacement–replacement technology [10]. The successful experiment of carbon dioxide (CO₂)-enhanced CBM (CO₂-ECBM) recovery via gas injection has provided a new innovative approach to improve underground gas extraction efficiency using gas injection displacement. The injection of CO₂ into the coal seam can not only compete with CH₄ stored in the coal seam for adsorption, reduce the effective partial pressure of the gas, and promote the desorption of adsorbed gas but can also increase the internal pressure of the coal body, enhance the mixed gas percolation velocity, effectively compensate for the reservoir pressure drop during the later stages of extraction, and provide sufficient power and reliable migration pathways for the reservoir flow field [11] (Figure 1). Simultaneously, CO₂ can be stored in the coal seam, which can significantly reduce its greenhouse effect. This technology has attracted tremendous research attention due to its safety, economic feasibility, environmental friendliness, and significant improvement in gas recovery rate, and offers promising application prospects in the near future.

Many researchers have conducted similar experimental research and concluded that displacement and replacement effects occur throughout the gas injection process, but the dominant role varies at different stages [12,13,14]. Furthermore, several experiments were performed on CO₂ displacement in large-sized coal rock specimens, and it was found that factors such as gas injection pressure, speed, gas content, reservoir structure, and permeability jointly determined the displacement effect [15,16]. For instance, Wang et al. conducted CO₂/N₂ replacement experiments on CBM under different gas injection pressure and stress conditions and analyzed the impact of experimental conditions on the replacement volume ratio and gas breakthrough time [17,18]. Wang et al. used Comsol to compare the stimulation effects of injecting N₂ and CO₂ on CBM displacement, concluding that injecting CO₂ was more effective at increasing CH₄ production than injecting N₂, and the gas content in the coal seam decreased at a faster rate with the increase in the gas injection pressure [19]. Sun et al. reported that injecting CO₂ not only reduced the partial pressure of CBM and accelerated its desorption but also made the coal body more prone to adsorbing CO₂ gas, which could compete with and adsorb CH₄ molecules in the coal, thereby increasing the production of CBM [20]. Several researchers focused on the technical characteristics of gas injection displacement to enhance the recovery of CBM [21,22,23,24]. Based on the percolation equation, diffusion equation, and multi-component gas adsorption equation, they established a coupled equation and introduced practical examples for its solution, deriving the pressure distribution of CBM, gas concentration distribution, and a quantitative relationship between permeability and gas concentration.

Focusing on underground gas control in coal mines, Wen et al. proposed a technique for fracturing coal and rock and displacing coal-seam CH₄ using liquid CO₂ (Figure 2). They designed field tests involving the displacement of coal-seam CH₄ by CO₂, which effectively shortened the pre-drainage time and reduced the drilling workload for drainage boreholes [25,26,27]. The phase-transition process of liquid CO₂ injected into the coal seam through boreholes is illustrated in Figure 3. In the figure, A–B is liquid-phase pressurization, B–C is fluid–solid heat transfer, C–D is liquid-phase seepage, D–E represents two-phase seepage and diffusion, and E-F is gas-phase adsorption and diffusion. The effectiveness of liquid CO₂ in enhancing coal-seam CH₄ drainage primarily depends on the gas-phase adsorption–diffusion–seepage stage (D–F in Figure 3). This stage involves complex physical processes including gas-phase CO₂ seepage, diffusion, and adsorption, and features multi-field coupling among the temperature field, pressure field, and gas concentration field.

After injecting CO₂ into a coal seam, high-pressure gas flow initially carries part of the CH₄ out of the coal, reducing the amount of free CH₄ and weakening the displacement effect. With the continuous diffusion of CO₂ into the coal matrix, the sorption replacement effect begins to act, promoting the desorption and diffusion of adsorbed CH₄. This increases the free CH₄ and simultaneously strengthens the displacement effect. Therefore, compared with the displacement effect, the replacement effect exhibits a clear lag, and the two effects promote and constrain each other through a mutual feedback relationship, which is a key factor influencing CH₄ production. However, currently employed CO₂ displacement–replacement experiments generally analyze only the enhancement of CH₄ recovery, and research on the time-varying characteristics of the displacement and replacement effects is still lacking.

Briefly, CO₂-enhanced CBM (ECBM) recovery is a complex process involving adsorption, desorption, and diffusion–transport of mixed fluids. Studies have shown that, for coal seams under different reservoir conditions, there exists an appropriate range of CO₂ injection pressure and an effective time window. That is, higher pressure and longer injection times do not necessarily yield better displacement performance. Therefore, this study focuses on the following three issues. The current theoretical research on CO₂-enhanced extraction of CH₄ from coal seams remains imperfect, the injection parameters lack scientific guidance, and full enforcement of the displacement effect is difficult. In this study, experimental research was conducted on the time-varying characteristics of the displacement–replacement effect of CO₂-enhanced extraction of CH₄ from coal seams. The results reveal the time-varying characteristics of the dominant position of displacement and replacement effects and aid in determining the key control parameters corresponding to displacement and replacement effects, providing theoretical guidance for optimizing on-site extraction and injection schemes.

2. Experimental Setup and Scheme

The experimental setup integrated a large-bore nuclear magnetic resonance (NMR) imaging analyzer (MacroMR12-150H-I) with a high-pressure gas-injection displacement platform. The main components include an NMR imaging analyzer, a coal sample vessel, pneumatic valves, a gas storage tank, a pressure control unit, temperature sensors, a vacuum pump, and gas cylinders (Figure 4).

2.1. Experimental Principle

During the experiment, the following relationship exists for CH₄ gas:

$${V_{\mathit{dei}\left(C{H}_4\right)}=V}_{\mathit{ad}0(C{H}_4)}-V_{\mathit{adi}\left(C{H}_4\right)}$$

(1)

$$V_{\mathit{freei}\left(C{H}_4\right)}=V_{\mathit{dei}\left(C{H}_4\right)}+V_{\mathit{free}0(C{H}_4)}$$

(2)

where $V_{\mathit{dei}\left(C{H}_4\right)}$ is the desorption amount of CH₄, $V_{\mathit{ad}0(C{H}_4)}$ denotes the initial adsorption capacity of CH₄, $V_{\mathit{adi}\left(C{H}_4\right)}$ is the amount of residual CH₄ adsorption at time i, $V_{\mathit{freei}\left(C{H}_4\right)}$ is the free CH₄ gas volume at time i, and $V_{\mathit{free}0(C{H}_4)}$ represents the free CH₄ gas volume at the beginning of the experiment.

The partial pressure of free CH₄ gas at the time i is expressed as follows:

$${\mathrm{P}}_{\mathrm{freei}(\mathrm{C}{\mathrm{H}}_4)}={\displaystyle \frac{\mathrm{Z}{\mathrm{n}}_{\mathrm{i}(\mathrm{C}{\mathrm{H}}_4)}\mathrm{RT}}{{\mathrm{V}}_{\mathrm{freei}(\mathrm{C}{\mathrm{H}}_4)}}}$$

(3)

where ${\mathrm{P}}_{\mathrm{freei}(\mathrm{C}{\mathrm{H}}_4)}$ is the partial pressure of CH₄ gas in free state at time i, $\mathrm{Z}$ denotes the compression factor of the mixture at the experimental temperature, R is the general gas constant, i.e., $8.314 \mathrm{J} (\mathrm{m}\mathrm{o}\mathrm{l} \mathrm{K})$, T is the temperature in K, and $V_0$ denotes the volume of free space.

According to Dalton’s partial pressure law, the partial pressure of CO₂ at time i can be obtained as follows:

$${\mathrm{P}}_{\mathrm{freei}(\mathrm{C}{\mathrm{O}}_2)}={\mathrm{P}}_{\mathrm{i}}-{\mathrm{P}}_{\mathrm{freei}(\mathrm{C}{\mathrm{H}}_4)}$$

(4)

Therefore, the amount of free state CO₂ at time i is

$$V_{\mathit{freei}\left(C{O}_2\right)}={\displaystyle \frac{\mathrm{Z}{\mathrm{n}}_{\mathrm{i}(\mathrm{C}{\mathrm{O}}_2)}\mathrm{RT}}{{\mathrm{P}}_{\mathrm{freei}(\mathrm{C}{\mathrm{O}}_2)}}}$$

(5)

Moreover, the amount of adsorbed CO₂ is expressed as follows:

$$V_{\mathit{ad}0(C{\mathrm{O}}_2)}=V_{0(C{\mathrm{O}}_2)}-V_{\mathit{freei}\left(C{\mathrm{O}}_2\right)}$$

(6)

2.2. Experimental Scheme

Coal samples of anthracite, coking coal, and long-flame coal were selected for the experiments, and they were dried in an oven at 80 °C. First, an NMR CH₄ gas calibration test was conducted at temperatures of 20–60 °C and test pressures of 1–6 MPa. Subsequently, a time-varying experiment was conducted on the displacement–replacement effects of CO₂-enhanced extraction of coal-seam CH₄. The prepared coal samples with dimensions of 100 mm × 50 mm were subjected to coal quality analysis and measurements of true density and apparent density. The mass of the loaded coal sample, free volume of the sample chamber, V₁ = 33.39 mL, and the free volume of the reference tank, V₂ = 44.87 mL, were recorded. The experimental temperature was 20–60 °C, the CH₄ equilibrium pressure was 1–3 MPa, and the CO₂ injection pressure was 2–6 MPa with a step of 1 MPa.

Table 1. Experimental parameters and corresponding results for the coal cores.

Experimental Parameters	Long Flame Coal	Coking Coal	Anthracite
Moisture/%	5.58	3.15	1.86
Ash/%	12.37	9.95	9.51
Volatile Matter/%	42.28	27.68	16.28
Porosity/%	6.38	6.07	5.76
Bound flow saturation/%	55.7079	50.98	56.093
Free fluid saturation/%	44.4018	49.02	43.906

presents the industrial analysis results of the coal sample.

3. NMR CH₄ Calibration Experiment

Prior to the experiment, the lines were evacuated for 6 h, and then CH₄ was injected into the sample chamber at a pressure of 1–6 MPa to acquire NMR signals under different pressure and temperature conditions. Considering the temperature of 30 °C as a representing example, the T₂ spectrum of free CH₄ was obtained, as shown in Figure 5.

The NMR test results of free gas reveal that the T₂ spectrum of free gas exhibits only one characteristic peak, and both the peak area (integral amplitude) and the transverse relaxation time T₂ are proportional to gas pressure. This means that as pressure increases, the peak shifts to longer T₂ (rightward). Therefore, in the NMR spectra of coal gas adsorption/desorption, the spectral ranges corresponding to adsorbed and free gas can be distinguished.

Based on the T₂ spectra of free CH₄, the signal amplitude integration corresponding to free CH₄ at 1–6 MPa was extracted to plot a fitted curve of pressure versus T₂ signal amplitude integrations of free CH₄, as shown in Figure 6. According to natural gas calculation of compression factor [28], the compression factor Z was calculated under different pressures, and the corresponding results are listed in

Table 2. Relationship between compressibility factor Z and methane mass.

Pressure/MPa	Z	CH4 Mass/g	Amplitude Integral
0.99	0.98	0.2254	656.6120
2.07	0.96	0.4811	1490.8610
2.96	0.94	0.7025	2121.6470
4	0.92	0.9700	2914.1360
4.95	0.9	1.2271	3442.1290
5.95	0.89	1.4915	4417.5120
6.94	0.87	1.7797	5047.4240
7.96	0.86	2.0650	5822.2680

. Then, the mass of CH₄ under different pressure and temperature conditions was calculated by using the real-gas equation of state PV = ZnRT. Therefore, by this method, the measured relationship between pressure and the T₂ signal amplitude integration of free CH₄ can be converted into a correspondence between CH₄ mass and the T2 signal amplitude integration of free CH₄, as shown in Figure 7.

The results reveal that, at different temperatures, the CH₄ mass is proportional to the integrated signal amplitude of the NMR T₂ spectrum. In other words, the greater the mass of free CH₄, the larger the integrated signal amplitude. The relationship is linear, with coefficients of determination R² all exceeding 0.9960. Therefore, by using the fitted curve between the integrated T₂ signal amplitude and CH₄ mass, the CH₄ mass under different pressure conditions can be calculated, thereby completing the calibration of free-state CH₄.

4. Experimental Study on the Time-Varying Characteristics of Displacement–Replacement Effects in CO₂-Enhanced Extraction of Coal-Seam CH₄

Injection of gaseous CO₂ into coal seams to displace and replace CH₄ is a dynamic and complex process. The driving mechanisms that enhance CH₄ drainage differ across injection stages, influenced by both displacement and replacement effects. Throughout the injection process, these two effects dominate at different times and gradually transition from one to the other. These displacement and replacement effects are influenced by CO₂ injection pressure, in situ CH₄ pressure, temperature, and injection duration. A quantitative study of these factors is necessary to establish rational production-enhancement schemes and to select target reservoirs. Therefore, understanding the time-dependent characteristics of displacement–replacement effects, establishing quantitative metrics for CH₄ production from each effect, and identifying the key controlling parameters for each can provide theoretical guidance for optimizing field injection–production strategies.

The coal samples used in the experiments included long-flame coal, coking coal, and anthracite. To calculate the amount of CH₄ desorbed during the CO₂ gas displacement–replacement of CH₄, NMR T₂ spectra were first acquired under each set of conditions. After obtaining the T₂ spectra, the relationship between the integrated T₂ signal amplitude and free-phase CH₄ was used to determine the time evolution of CH₄ desorption. Further, the residual adsorbed CH₄, the adsorbed amount of CO₂, and the amount of free-phase CO₂ were indirectly calculated.

4.1. Effect of CO₂ Injection Pressure

Gaseous CO₂ was injected at pressures of 2–6 MPa by a controlled-variable method, with the CH₄ equilibrium pressure set at 1 MPa and the temperature at 30 °C. The CH₄ desorption per unit time was calculated. By analyzing the time evolution of CH₄-stage desorption amount, the time-varying characteristics of the displacement and replacement effects were elucidated, and the optimal CO₂ injection pressure range was identified.

4.1.1. Time-Varying Characteristics of CH₄-Stage Desorption Amount

The relationships between the CH₄-stage desorption amount and displacement time and CO₂ injection pressure are shown in Figure 8.

Figure 8 demonstrates that in the P₁ stage (anthracite: 0–60 min; coking coal and long-flame coal: 0–30 min), the desorption amount of CH₄ gas increased rapidly with experimental time. In the P₂ stage (anthracite: 60–90 min; coking coal and long-flame coal: 30–60 min), the upward trend shows a clear stage-wise slowdown. Conversely, in the P₃ stage (anthracite: 90–150 min; coking coal: 60–120 min; long-flame coal: 60–150 min), the stage desorption amount of CH₄ gas again increased rapidly. By contrast, in the P4 stage (anthracite: 150–210 min; coking coal: 120–210 min; long-flame coal: 150–240 min), it decreased rapidly; and in the P₅ stage (anthracite and coking coal: 210–270 min; long-flame coal: 240–270 min), it tended to stabilize.

In the P₁ stage, when the connecting valve is opened and CO₂ gas enters the coal sample chamber, CO₂ first rapidly occupies the remaining adsorption sites because of the smaller size of CO₂ molecules compared to CH₄ molecules. Part of the CH₄ undergoes natural desorption and is expelled from the coal matrix due to the reduction in its partial pressure. Therefore, although the desorption amount of CH₄ gas increases rapidly with time in this stage, the cumulative desorption amount of CH₄ is still relatively small. Upon reaching the P₂ stage, pressure in the coal sample chamber tends to stabilize, the remaining adsorption sites within the coal are gradually occupied by CO₂ that has penetrated the coal matrix, CO₂ begins competitive adsorption with CH₄, and the replacement effect becomes dominant. Consequently, the stage desorption amount of CH₄ gas continues to rise, but more gradually. By the P₃ stage, the remaining adsorption sites in the coal have been completely occupied by CO₂ that has penetrated the coal. This stage includes not only the replacement effect of CO₂ on CH₄ but also the displacement effect, and both effects reach their peak, thus the stage desorption amount of CH₄ gas rises sharply. In the P₄ stage, with the decrease in the residual adsorbed CH₄ in the coal, the competitive adsorption between CO₂ and CH₄ gradually weakens, the replacement effect also diminishes, and the displacement effect becomes dominant. This leads to a continuous decline in the stage desorption amount of CH₄ gas. In the P5 stage, very little residual adsorbed CH₄ is left in the coal, the partial pressure of CH₄ is essentially stable, and the free CH₄ expelled from the coal under the displacement effect of CO₂ also stabilizes. Therefore, the stage desorption amount of CH₄ gas in this stage tends to stabilize.

The process of CO₂ gas displacement–replacement of CH₄ in coal seams can be divided into five stages, namely the following: (1) a stage of spontaneous CH₄ desorption caused by partial-pressure effects; (2) a replacement-dominated stage; (3) a stage where replacement and displacement act jointly; (4) a displacement-dominated stage; and (5) a stabilization stage.

4.1.2. Time-Varying Characteristics of Cumulative CH₄ Desorption Amount

A comparative analysis was performed on the cumulative CH₄ desorption at the end of the experiment under different CO₂ injection pressures, as shown in Figure 9.

Figure 9 and Figure 10 illustrate that at the end of the experiment, the cumulative desorption amount of CH₄ gas from the three coal samples increased with increasing CO₂ injection pressure and finally tended to be stable.

Table 3. The relationship between the increase rate of CH₄ desorption and CO₂ injection pressure.

CO2 Injection Pressure/Mpa	Increase Rate of CH4 Cumulative Desorption/%
	Long Flame Coal	Coking Coal	Anthracite
3	4.86	2.43	11.59
4	26.96	18.50	16.75
5	40.35	25.26	29.12
6	33.27	21.38	23.30

summarizes that when the injection pressure of CO₂ gas increases from 2 to 5 MPa, the increase in the CH₄ desorption of long flame coal, coke, and anthracite is 29.12%, 25.26%, and 40.35%, respectively. When the injection pressure of CO₂ gas increases from 2 to 6 MPa, the increase in the CH₄ desorption of long flame coal is 23.30%, that of coke is 21.38%, and anthracite shows a 33.27% increase. This may be attributed to the higher difference in pressure, which leads to a faster desorption rate of CH₄ during the P₁–P₃ stage (0–150 min), resulting in a higher cumulative desorption amount. However, simultaneously, the rate of decrease in CO₂ partial pressure in the coal sample tank is also faster. By the time, the experiment reaches the P₄–P₅ stage (150–270 min), the partial pressure of CO₂ at 5 MPa injection pressure during this stage may be higher than that at 6 MPa, resulting in higher displacement and replacement efficiency under the condition of 5 MPa CO₂ injection pressure during this stage.

4.1.3. Time-Varying Characteristics of the Displacement-to-Replacement Ratio

The effectiveness of CO₂ displacement and replacement is generally represented by the displacement/replacement ratio. That is, the higher the ratio, the higher the efficiency, and the better the effect. It is defined as the ratio of the amount of CO₂ adsorbed to the amount of CH₄ desorbed, and its calculation formula is represented as follows:

$$\mathrm{C}={\displaystyle \frac{{\mathrm{A}}_{{\mathrm{CO}}_2}}{{\mathrm{D}}_{{\mathrm{CH}}_4}}}$$

(7)

where C is the driving-out/displacement ratio; ${\mathrm{D}}_{{\mathrm{CH}}_4}$ is the amount of CH₄ desorbed from the coal, mol; and ${\mathrm{A}}_{{\mathrm{CO}}_2}$ denotes the amount of CO₂ adsorbed by the coal, mol.

Figure 11 illustrates that the displacement–replacement ratio increases with experimental time and then tends to stabilize. In the early stage of the experiment (stage T₁ in the figure), the displacement–replacement ratio rises rapidly with time. This is because after CO₂ invades coal, it reaches the pores via seepage and diffusion, quickly occupies the remaining adsorption sites, and competes with CH₄ for adsorption, thereby displacing adsorbed CH₄. During this stage, the diffusion coefficient of CO₂ is much higher than that of CH₄, thus the amount of CO₂ entering the coal far exceeds that of CH₄ exiting, leading to a rapid increase in the displacement–replacement ratio. In the mid-stage of the experiment (T₂), CO₂ completely occupies the remaining adsorption sites. The decrease in gas concentration gradients weakens diffusion while competitive adsorption becomes stronger. During this stage, not only replacement of adsorbed CH₄ by CO₂ occurs but also displacement of adsorbed CH₄ by CO₂ is observed. With the prolongation of time, the replacement effect gradually becomes dominant, causing the growth of the displacement–replacement ratio to slow down. In the late stage of the experiment (T₃), as adsorbed CH₄ continues to be displaced, the residual adsorbed CH₄ in the coal diminishes, and the replacement effect weakens accordingly. Therefore, the displacement–replacement ratio gradually levels off during this stage.

4.2. Effect of CH₄ Equilibrium Pressure

The experiment utilized a controlled-variables method. Gaseous CO₂ was injected at 5 MPa under CH₄ equilibrium pressures ranging from 0.5 to 2.5 MPa and at a temperature of 30 °C. The CH₄ desorption per unit time was calculated, and the temporal evolution of CH₄ desorption stage was analyzed to uncover the time-varying characteristics of the displacement and replacement effects at varying CH₄ equilibrium pressures. This analysis aided in determining the applicability window for efficient CO₂-enhanced drainage of coal seam CH₄.

4.2.1. Time-Varying Characteristics of CH₄-Stage Desorption Amount

The relationships of the CH₄-stage desorption amount with displacement time and CO₂ injection pressure are shown in Figure 12.

Figure 12 illustrates that under different CH₄ equilibrium pressures, the CH₄ desorption stage exhibits trends that are highly consistent with those observed under varying CO₂ injection pressures. Similarly, based on the dominant mechanism in each stage, the entire process can be divided into five stages: (1) natural desorption of CH₄ induced by partial-pressure effects; (2) onset of the replacement effect; (3) coaction of replacement and displacement effects; (4) weakening of the replacement effect; and (5) displacement-dominated stage.

4.2.2. Time-Varying Characteristics of Cumulative CH₄ Desorption Amount

The cumulative amount of CH₄ desorbed at the end of the experiments under different CH₄ equilibrium pressure conditions was selected for comparative analysis, as shown in Figure 13.

The curves shown in Figure 13 demonstrate that for all three coal samples, the cumulative CH₄ desorption first increases slowly and then rises rapidly with the progress of the experiment. Moreover, under different CH₄ equilibrium pressure conditions, the time-varying characteristics differ. That is, the higher the CH₄ equilibrium pressure, the shorter the initial slow-growth stage. The bar chart in Figure 13 further shows that the higher the CH₄ equilibrium pressure, the greater the cumulative CH₄ desorption. This is attributed to the fact that under the same CO₂ injection pressure, the CH₄ equilibrium pressure directly affects the initial CH₄ content within the coal and the extent of spontaneous desorption driven by partial pressure. With the increase in the CH₄ equilibrium pressure, the pressure difference relative to the CO₂ injection pressure decreases, thus weakening the partial-pressure effect after CO₂ injection. Therefore, the cumulative CH₄ desorption increases slowly at the beginning. Simultaneously, a higher initial CH₄ content enhances the replacement effect and displacement effect, leading to a subsequent rapid increase in cumulative CH₄ desorption.

When the CH₄ equilibrium pressure is 0.5–1.5 MPa, the cumulative CH₄ desorption shows a slow increase during the first 90 min and then rises rapidly beyond 90 min. When the CH₄ equilibrium pressure is in the range of 2.0–2.5 MPa, it increases slowly during the first 30 min and then rises rapidly thereafter. Thus, the higher the CH₄ equilibrium pressure, the shorter the period of spontaneous CH₄ desorption, and the longer the period dominated by replacement and displacement effects.

4.2.3. Time-Varying Characteristics of the Displacement-to-Replacement Ratio

Figure 14 exhibits that the displacement–replacement ratio rises rapidly with experimental time and then levels off, which is consistent with the conclusions mentioned above. Moreover, the displacement–replacement ratio decreases with increasing CH₄ equilibrium pressure. As shown in

Table 4. Relationship between CH₄ pressure difference and displacement–replacement decline.

Pressure Difference/Mpa	Decline of Displacement and Displacement Ratio/%
	Long Flame Coal	Coking Coal	Anthracite
0.5	26.44	26.34	11.52
1	42.01	47.59	24.10
1.5	60.29	60.36	52.28
2	72.83	80.14	70.48

, the increase in the CH₄ equilibrium pressure from 0.5 to 2.5 MPa leads to a decrease in the displacement–replacement ratios for the three coal samples at 270 min: 72.83% for long-flame coal, 80.14% for coking coal, and 70.48% for anthracite. This result indicates that the larger the pressure difference between the CO₂ injection pressure and the CH₄ equilibrium pressure, the more effective the displacement–replacement process.

5. Conclusions

The process by which CO₂ gas displaces and replaces CH₄ in coal seams can be divided into five stages: spontaneous CH₄ desorption induced by partial-pressure effects; a replacement-effect dominated stage; a stage where replacement and displacement effects act jointly; a displacement-effect dominated stage; and a steady stage.

Under the conditions of different CH₄ equilibrium pressures, the variation trend of CH₄ gas desorption at different stages is highly consistent with that under different CO₂ injection pressures. Moreover, both of them show a rapid increase and then decrease with time and finally stabilizes. The inflection point of the curve can be used as the basis for dividing each stage in the entire process of CO₂ displacement and replacement of coal seam CH₄.

For all three coal samples, the cumulative CH₄ desorption increased with increasing CO₂ injection pressure and eventually stabilized. However, the effect weakened when the CO₂ injection pressure exceeded 5 MPa. This weakening may have been caused by the dynamic changes in the partial pressure of CO₂.

The displacement–replacement ratio decreases with increasing CH₄ equilibrium pressure. When the CH₄ equilibrium pressure rises from 0.5 to 2.5 MPa, the displacement–replacement ratio at 270 min for the three coal samples decreases by 72.83% for long-flame coal, 80.14% for coking coal, and 70.48% for anthracite. This indicates that the larger the pressure difference between the CO₂ injection pressure and the CH₄ equilibrium pressure, the more effective the displacement–replacement process.