Experimental Evaluation of CO₂ Displacement for Enhanced Gas Recovery in a Carbonate Gas Reservoir

Abstract

Addressing the problem of limited methane (CH₄) recovery degree under different production conditions in a target low-permeability carbonate gas reservoir, this study intends to further investigate the effect of carbon dioxide (CO₂) injection on enhanced gas recovery (EGR). A group of long-core physical simulation experiments of CO₂ injection for EGR was adopted. Field injection–production parameters were converted to laboratory conditions through similarity criteria to simulate the actual production process of gas wells. Systematic experiments on CH₄ depletion and CO₂ displacement were carried out under different irreducible water saturation, gas injection timing pressure and injection rates. The influence laws of each key parameter on the CO₂ breakthrough time and CH₄ recovery degree were analyzed emphatically, and the optimal injection–production scheme was obtained. For the target low-permeability carbonate gas reservoir (permeability < 1 mD), the optimal CO₂ injection scheme is as follows: for layers with medium to high irreducible water saturation (≥40%), CO₂ injection at a rate of 36,000 m³/d per well after the end of stable production (formation pressure > 7.38 MPa) can increase the CH₄ recovery degree by 3–5%. This study provides experimental support for the optimization of CO₂ injection schemes for enhanced recovery in gas reservoirs and the adjustment of gas reservoir development strategies under different irreducible water saturation conditions.

1. Introduction

After depletion production of conventional gas reservoirs, the remaining natural gas is difficult to recover by conventional methods (well pattern infill, pressure-depletion production, dewatering and gas lifting) [1]. Injecting CO₂ (carbon dioxide) into developed reservoirs to enhance gas recovery (EGR) is one of the enhanced, aggressive techniques for improving recovery. The concept of CO₂ injection to enhance gas recovery (CO₂-EGR) was proposed in the 1990s, and the team led by Oldenburg at the Lawrence Berkeley National Laboratory first established a complete theoretical and numerical modeling framework in 2001 [2,3], thereby formally laying the academic foundation for CO₂-EGR technology [4,5,6]. Numerous subsequent researchers have further refined the theory, clarified reservoir CO₂-injection recovery mechanisms (such as miscible/immiscible displacement, gravity segregation, dissolution-driven relative permeability modification, and competitive adsorption) and conducted reservoir case simulations to advance the technology toward field application.

CO₂-EGR field implementations have produced few landmark projects, including the K12-B depleted sandstone gas reservoir (Netherlands), the Altmark sandstone gas field (Germany), and the Budafa fractured carbonate gas field (Hungary). China’s CO₂-EGR technology is overall at the pilot-test stage [7], with sites including the Wolonghe depleted carbonate gas reservoir in Sichuan, the Puguang high-sulfur carbonate gas field, the Sulige tight gas field in Changqing, and the Fushan condensate oil-and-gas reservoir in Hainan. Overall, field implementation projects remain limited, and the mechanisms and effectiveness of CO₂ injection for enhanced gas recovery (CO₂-EGR) require further research and evaluation.

The existing studies have verified the technical feasibility of CO₂-EGR [8,9]. Supercritical carbon dioxide exhibits characteristics such as a smaller diffusion coefficient, higher density, and greater viscosity, relative to methane under the same temperature and pressure conditions. The mechanisms of CO₂ injection for enhanced gas recovery in conventional gas reservoirs mainly include pressure support and displacement and water dissolution and permeability enhancement [10,11]. Pressure support and displacement means that injected CO₂ rapidly replenishes the formation energy and increases the reservoir pressure, driving the CH₄ retained in pores to migrate toward production wells and enhancing displacement power. CO₂ and CH₄ are completely miscible under reservoir conditions; however, supercritical CO₂ has lower diffusivity and higher viscosity than CH₄. A miscible zone is formed through molecular diffusion and convective dispersion, gradually displacing CH₄ from the pore space. Water dissolution and permeability enhancement refers to the fact that part of the injected CO₂ dissolves in irreducible water, reducing the CO₂ dispersion coefficient. The CO₂–water–rock interaction improves flow pathways and enhances the gas phase flow capacity, allowing for more CH₄ to be effectively displaced. For CO₂ enhanced gas recovery (CO₂-EGR) in conventional gas reservoirs, the key controlling parameters include the reservoir irreducible water saturation, CO₂ injection pressure, and injection rate, which govern the miscibility degree between CO₂ and CH₄, CO₂ breakthrough time, and CH₄ recovery. This paper systematically reviews the laboratory and simulation research progress of CO₂-EGR. Table 1 summarizes the existing studies on the effects of irreducible water saturation, gas injection timing pressure, and gas injection rate/injection–production ratio on CH₄ recovery and CO₂ breakthrough time.

1.1. Irreducible Water Saturation

The effect of irreducible water saturation on CH₄ recovery by CO₂ injection is controversial.

On one hand, some scholars argue that increasing the irreducible water saturation significantly reduces CH₄ recovery and accelerates CO₂ breakthrough. The reason is that high irreducible water saturation occupies micro- and small pores, increases the tortuosity of the pore structure, enlarges the CO₂ dispersion coefficient, intensifies gas mixing, and leads to early CO₂ breakthrough [6,12,13,14].

On the other hand, other scholars propose that increasing the irreducible water saturation improves CH₄ recovery and delays CO₂ breakthrough. The reason is that high irreducible water saturation occupies narrow pore throats, forcing gas to flow uniformly along large pore channels, reducing reservoir heterogeneity. In addition, CO₂ dissolution in residual water shortens the mixing zone, decreases the CO₂ dispersion coefficient, and delays CO₂ breakthrough [15,16,17,18,19,20,21,22].

1.2. CO₂ Injection Timing Pressure

“CO₂ Injection Timing Pressure” refers to the reservoir pressure at the time of CO₂ injection. Studies on CO₂ injection timing pressure can be divided into two categories.

Some scholars did not consider the reservoir depletion process and directly conducted displacement experiments at different pressures. They used CH₄ recovery and CO₂ breakthrough time obtained from simple displacement as the criteria for determining the optimal CO₂ injection timing pressure. Results from these studies show that a higher injection timing pressure leads to better recovery enhancement and longer breakthrough time. The reason is that as the pressure increases, the dispersion coefficient of CO₂ decreases, and the mixing zone between CO₂ and CH₄ becomes narrower, resulting in higher recovery [5,8,21,23,24,25,26,27].

Other scholars considered the reservoir depletion process and performed CO₂ injection after depleting the gas reservoir to different pressure levels. They used the sum of depletion recovery and incremental recovery by CO₂ injection as the ultimate CH₄ recovery and the criterion for the optimal reservoir pressure at injection. Results show that gas injection in the late stage of depletion, when reservoir pressure is relatively low, maximizes the ultimate gas recovery. Although CO₂ injection at an early stage improves incremental recovery by CO₂ to a high extent, it fails to fully utilize the natural elastic energy of the reservoir and causes early gas quality contamination by CO₂, resulting in lower ultimate recovery [2,4,28,29,30,31].

1.3. Gas Injection Rate or Injection–Production Ratio

Studies on the CO₂ injection rate can be divided into two categories.

Some scholars believe that a higher injection rate can improve CH₄ recovery. High-rate injection is beneficial because it rapidly replenishes the reservoir energy, maintains stable pressure, reduces the excessive mixing of CO₂ and CH₄, and thus lowers the degree of gas contamination. In contrast, at low injection rates, diffusion dominates and convective displacement is weak, allowing the CO₂ and CH₄ to mix thoroughly and form a wide miscible zone, which reduces CH₄ recovery [16,21,22,29,32,33,34].

Other scholars argue that low injection rates reduce gas dispersion coefficients, prolong contact time between gas and irreducible water, enhance CO₂ dissolution and gravitational differentiation, and improve displacement front stability, thereby delaying CO₂ breakthrough and increasing CH₄ recovery. However, high injection rates intensify mixing and cause an early CO₂ breakthrough, thus reducing CH₄ recovery [25,30,35,36,37].

Overall, the existing studies have investigated the mechanisms and influencing parameters of CO₂-EGR. However, most experiments have not been scaled according to actual field development conditions, and the parameters used are not representative of the field reality. Most of the enhanced recovery factors reported in previous experiments were either based on depletion experiments or did not involve the depletion process at all, without a direct comparison with concurrent depletion experiments (Table 1). This leads to deviations in the final evaluation of the CO₂-EGR performance. In addition, most studies focus on conventional sandstone and tight sandstone reservoirs, while research on carbonate reservoirs remains insufficient (Table 1). Therefore, this study intends to conduct long-core displacement experiments, converting the field scale to the laboratory scale using similarity criteria. Taking a typical carbonate gas reservoir as the target, the effects of different irreducible water saturations, CO₂ injection timing pressures, and injection rates on CH₄ recovery and CO₂ breakthrough time are investigated. The experimental results can better reflect the actual reservoir behavior, thereby providing a solid theoretical basis for the design of injection–production schemes in related field pilot tests.

Table 1. Literature review on CO₂ injection for enhancing CH₄ recovery in gas reservoirs.

Reference Number	Reservoir Lithology	Core Sample Properties	Investigated Factors (with Specific Parameters)	Whether the Experimental Process Includes the Depletion Process	Maximum CH4 Recovery	Maximum Increment in CH4 Recovery	Longest CO2 Breakthrough Time/Pore Volume
[5]	Sandstone	φ = 23%, L = 30.5 cm, D = 2.54 cm	P = 3.55–20.79 MPa	no	86		160 min
[14]	Sandstone	φ = 15–25%, K = 217 mD	Swi = 0/10%	no	97.98		22 min
[15]	Sandstone	φ = 25%, K = 500 Md, L = 30.48 cm, D = 3.81 cm	Swi = 0/20%, V = 9.03–33.80 ×10−3 mm/s	no	67		0.6
[16]	Sandstone	K = 2.2/9.7/103 mD, φ = 11.6%/15.6%/19.8%, L = 81 cm, D = 2.5 cm	V = 3.4–27.16 × 10−3 mm/s	no	98.63		0.8
[18]	Tight sandstone	K = 0.325 mD, φ = 9.36%, Swi = 41.5%, L = 100 cm, D = 2.5 cm	V = 6.8–27.16 × 10−3 mm/s	no	60		0.6
[19]	Tight sandstone	K = 0.41 mD	Swi = 0.2/0.3/0.4/0.5	yes	64	22
[21]	Carbonate	K= 1.564 mD, φ = 2.22%, L = 26.8 cm, D = 2.5 cm	Swi = 0/0.15/0.25/0.35, P = 2/4/6/8 MPa, V = 3.4–27.16 × 10−3 mm/s	yes	96.27	8.41	0.8
[25]	Tight sandstone	L = 1 m, D = 2.5 cm, φ = 9.9%, K = 0.652 mD	Vinject/Vproduce = 0.5/1/2, P = 20/30 MPa	yes	57	9.46	0.4
[26]	Sandstone	K = 30 mD, φ = 11%, Swi = 53%	P = 7–14 MPa	yes	99	49	1.5
[27]	Sandstone	φ = 0.16, K = 100–400 mD	V = 0.3/0.6 mL/min, P = 4.6/8/10 MPa	no	34.92		20 min
[29]	Tight sandstone	K = 0.1–3 mD, φ = 7–15%, Swi = 35%, L = 10 cm, D = 2.5 cm	P = 5/8/12/16 MPa, V = 1.70–13.58 × 10−3 mm/s	yes	95.42	15.95	0.7
[30]	Carbonate	K = 0.14–1.89 mD, φ = 8–11%, L = 68 cm, D = 2.5 cm	P = 12–18 MPa, V = 3.4–13.58 × 10−3 mm/s	yes	96	28	95 min
[31]	Tight sandstone	K = 0.652 mD, φ = 9.9%	P = 10/15/30 MPa	yes	99	40	0.6
[33]	Tight sandstone	K = 2.1 mD, φ = 11.2%, L = 1 m, D= 2.5 cm	V = 3.4–27.16 × 10−3 mm/s	no	99		1
[34]	Sandstone	K = 16 mD, φ = 33%	P = 5/7 MPa, V= 4–5 × 10−3 cm/s	no	92.8		0.8

(Note: Swi in the table refers to irreducible water saturation).

Table 1. Literature review on CO₂ injection for enhancing CH₄ recovery in gas reservoirs.

Reference Number	Reservoir Lithology	Core Sample Properties	Investigated Factors (with Specific Parameters)	Whether the Experimental Process Includes the Depletion Process	Maximum CH4 Recovery	Maximum Increment in CH4 Recovery	Longest CO2 Breakthrough Time/Pore Volume
[5]	Sandstone	φ = 23%, L = 30.5 cm, D = 2.54 cm	P = 3.55–20.79 MPa	no	86		160 min
[14]	Sandstone	φ = 15–25%, K = 217 mD	Swi = 0/10%	no	97.98		22 min
[15]	Sandstone	φ = 25%, K = 500 Md, L = 30.48 cm, D = 3.81 cm	Swi = 0/20%, V = 9.03–33.80 ×10−3 mm/s	no	67		0.6
[16]	Sandstone	K = 2.2/9.7/103 mD, φ = 11.6%/15.6%/19.8%, L = 81 cm, D = 2.5 cm	V = 3.4–27.16 × 10−3 mm/s	no	98.63		0.8
[18]	Tight sandstone	K = 0.325 mD, φ = 9.36%, Swi = 41.5%, L = 100 cm, D = 2.5 cm	V = 6.8–27.16 × 10−3 mm/s	no	60		0.6
[19]	Tight sandstone	K = 0.41 mD	Swi = 0.2/0.3/0.4/0.5	yes	64	22
[21]	Carbonate	K= 1.564 mD, φ = 2.22%, L = 26.8 cm, D = 2.5 cm	Swi = 0/0.15/0.25/0.35, P = 2/4/6/8 MPa, V = 3.4–27.16 × 10−3 mm/s	yes	96.27	8.41	0.8
[25]	Tight sandstone	L = 1 m, D = 2.5 cm, φ = 9.9%, K = 0.652 mD	Vinject/Vproduce = 0.5/1/2, P = 20/30 MPa	yes	57	9.46	0.4
[26]	Sandstone	K = 30 mD, φ = 11%, Swi = 53%	P = 7–14 MPa	yes	99	49	1.5
[27]	Sandstone	φ = 0.16, K = 100–400 mD	V = 0.3/0.6 mL/min, P = 4.6/8/10 MPa	no	34.92		20 min
[29]	Tight sandstone	K = 0.1–3 mD, φ = 7–15%, Swi = 35%, L = 10 cm, D = 2.5 cm	P = 5/8/12/16 MPa, V = 1.70–13.58 × 10−3 mm/s	yes	95.42	15.95	0.7
[30]	Carbonate	K = 0.14–1.89 mD, φ = 8–11%, L = 68 cm, D = 2.5 cm	P = 12–18 MPa, V = 3.4–13.58 × 10−3 mm/s	yes	96	28	95 min
[31]	Tight sandstone	K = 0.652 mD, φ = 9.9%	P = 10/15/30 MPa	yes	99	40	0.6
[33]	Tight sandstone	K = 2.1 mD, φ = 11.2%, L = 1 m, D= 2.5 cm	V = 3.4–27.16 × 10−3 mm/s	no	99		1
[34]	Sandstone	K = 16 mD, φ = 33%	P = 5/7 MPa, V= 4–5 × 10−3 cm/s	no	92.8		0.8

(Note: Swi in the table refers to irreducible water saturation).

2. Experimental Materials, Equipment and Methods

2.1. Experimental Materials and Equipment

The main lithologies of the carbonate reservoir are crystalline dolomite and siliceous dolomite: mostly gray, dark gray and grayish-black, as presented in Figure 1a. Based on core observation and casting thin sections, the reservoir storage spaces are dominated by intercrystalline pores and intercrystalline dissolved pores, with low average porosity, and the throats serve as the main percolation pathways, as presented in Figure 1b. Representative core samples were selected from the target carbonate gas reservoir for long core experiments, with the core properties presented in Table 2. The core samples show a good porosity–permeability correlation. These core samples were spliced to simulate the heterogeneity of the target reservoir. The average permeability (0.478 mD) and porosity (8.55%) of the core samples were consistent with the field reservoir properties. The formation water was prepared in accordance with the ion composition of the field formation water (as presented in Table 3); it is of the calcium chloride type with a salinity of 37,000 mg/L, falling into the low-salinity condition. Please refer to these three studies [38,39,40] for the geological characteristics, physical properties and pore structure of the target carbonate gas reservoir.

Figure 1. (a) Siliceous dolomite sample picture from target carbonate gas reservoir; and (b) casting thin section of medium-crystalline dolomite, showing developed intercrystalline pores and intercrystalline dissolved pores.

Table 2. Field core property data table.

Sample Number	Sample Length, cm	Sample Diameter, cm	Permeability, mD	Porosity, %
1	6.993	2.542	0.502	9.10
2	7.059	2.547	0.435	7.86
3	7.016	2.550	0.632	10.65
4	7.048	2.559	0.528	5.53
5	7.047	2.554	0.331	8.84
6	6.973	2.543	0.377	9.47
7	7.034	2.552	0.539	8.40
Average	/	/	0.478	8.55

Table 3. Composition of formation water.

Ion Content of Formation Water, mg/L								Total Salinity
Positive Ion				Negative Ion
K+ + Na+	Ca2+	Mg2+	Ba2+	Cl−	SO42−	HCO3−	CO32−
5620.4	8831.4	103.25	107.08	21,768	99.89	183.41	/	37,447

Figure 2 displays the experimental equipment (Nantong Huaxing Petroleum Instrument Co., Ltd., Nantong City, Jiangsu Province, China).

Figure 2. Flow chart of CO₂ injection and CH₄ displacement experiment for long core.

The main components of the long core experimental setup include a thermostatic chamber, a Quizix flow pressure pump (Chandler Engineering, Tulsa, OK, USA), a 3-pressure-measurement-point long core holder, pressure transducers, a backpressure pump, a high precision flowmeter, a gas collection bag, a gas chromatograph, and other auxiliary devices. The inlet end of the long core represents the well control boundary, while the outlet end corresponds to the bottom of the well. Pressure measurement points P1, P2 and P3 are used to represent the pressure at different positions from the bottom of the well to the well control boundary.

2.2. Experimental Similarity Criterion Design

The formation pressure and temperature adopted in the experiment were consistent with those in the gas field, as were the core porosity, permeability and irreducible water saturation. Acid fracturing stimulation has been conducted near the wellbore in actual field operations, resulting in relatively high permeability there. To simulate the actual reservoir characteristic of decreasing permeability from the near-wellbore to the far-wellbore zone, the long core samples were spliced in a way that their permeability decreases progressively from the inlet end to the outlet end in the displacement experiment to reflect the heterogeneity of the reservoir. In terms of production regime, the radial flow in the gas well was converted to the linear flow of the long core via Equations (1) and (2) [41,42]. The CH₄ (methane) production rate of a single well in the field was 90,000 m³/d, which was converted to 25 mL/min for the long core experiment under normal temperature and pressure conditions. Subsequently, the flow rate was converted to 0.48 mL/min under high-temperature and high-pressure conditions, in accordance with the real gas equation of state. It was then converted to a one-dimensional linear velocity of 16.33 × 10⁻³ mm/s, based on the cross-sectional area of the core sample. For gas wells, the injection timing pressure is defined as the ratio of the average reservoir pressure at injection to the initial formation pressure. In experiments, the injection timing pressure is defined as the ratio of the core pressure at injection to the initial core pressure. The average pressure retention level during the experiment is defined as the average pressure value of the core divided by the initial core pressure. In gas well operation, gas production is generally conducted at a constant rate of 90,000 m³/d until the abandonment pressure is reached, after which production is ceased; the abandonment pressure is close to the atmospheric pressure. The experimental production regime was consistent with the gas well production, where gas production was carried out at a constant rate of 25 mL/min until the abandonment pressure, and then the gas production was stopped. Differently from the experiments reported in the existing literature, in this study, the depletion process and gas production rate under the field production regime are taken into account, and the feasibility of CO₂ injection for enhanced gas recovery on the basis of depletion development is demonstrated.

$$q={\displaystyle \frac{69.12Q_R{r}_{w}h}{D^2}}$$

(1)

where $q$—daily gas production rate of a single well, 10⁴ m³; $Q_R$—gas flow rate under laboratory conditions, m³/s; $r_w$—wellbore radius, m; $h$—reservoir thickness, m; and $D$—core diameter, m.

$$PV=ZnRT$$

(2)

where $P$, $V$, and $T$ represent the pressure, volume, and temperature of the gas, respectively and $Z$, $n$ and $R$ represent the gas compressibility factor, amount of substance of gas and universal gas constant, respectively.

The field and experimental parameters are presented in Table 4.

Table 4. Conversion parameters of field and experimental conditions.

Category	Parameter Name	Field	Long Core Experiment
Reservoir characteristics	Formation pressure	55 MPa	55 MPa
	Formation temperature	85 °C	85 °C
	Porosity	Average 8.5%	Average 8.5%
	Permeability	Average 0.5 mD	Average 0.5 mD
	Saturation	20–60%	20–60%
Engineering parameters	Gas production rate	9 × 104 m3/d	16.33 × 10−3 mm/s
	CO2 injection rate	3.6 × 104 m3/d	6.53 × 10−3 mm/s
	Injection timing pressure	10%, 30%, 46%	10%, 30%, 46%

2.3. Experimental Procedures

1.

Select core samples, dry them in an oven for 24 h, and then weigh the dry mass $m_0$.

2.

Place the core in a saturation vessel and evacuate the core for 24 h, followed by pressurized saturation with formation water for another 24 h, and the weight of the water-saturated core sample $m_1$ is measured. Then, install the cores into the core holder and conduct CH₄-displacing-water to establish the initial irreducible water saturation required for the experiment. Measure the mass $m_w$ of produced water during methane flooding; by controlling the mass of displaced water, the initial irreducible water saturation $S_w$ required for the experiment is finally established. The formula for calculating irreducible water saturation is given as Equation (3).

$$S_w={\displaystyle \frac{m_1-m_0-m_w}{m_1-m_0}}\times 100$$

(3)

where $m_0$ represents the dry mass of the rock sample, $m_1$ represents the weight of the water-saturated core sample, $m_w$ represents the weight of produced water during methane flooding and $S_w$ represents the initial irreducible water saturation of the rock sample.

3.

Set the oven to the experimental temperature (85 °C). Inject CH₄ into the cores with a Quizix flow pressure pump for a certain period to achieve complete CH₄ saturation of the cores, until the inlet pressure is consistent with the backpressure valve pressure (55 MPa). Increase the confining pressure continuously during the CH₄ injection process, maintaining it at 5 MPa higher than the internal pressure at all times, with the final confining pressure reaching 60 MPa.

4.

First, perform a set of pure CH₄ depletion experiments as the baseline test. On the basis of CH₄-saturated cores (55 MPa), set a constant outlet flow rate of 25 mL/min until the outlet pressure depletes to atmospheric pressure; then, reduce the flow rate to 0 mL/min to terminate the experiment, and record the flow rate and pressure at each measurement point in real time.

5.

Subsequently, conduct the CO₂ injection and CH₄ displacement experiment. On the basis of CH₄ saturated cores (55 MPa), set a constant outlet flow rate of 25 mL/min and first conduct a CH₄ depletion development until the average core pressure reaches the CO₂ injection timing pressure. Set the injection flow rate with a Quizix flow pressure pump to drive CO₂ from the intermediate container into the long cores at a constant flow rate from the inlet. Measure the outlet flow rate and pressure at each measurement point during the experiment, and collect the produced gas at the outlet with gas collection bags simultaneously.

6.

Terminate the displacement experiment after injecting CO₂ at least one time at pore volume (PV).

7.

Measure the gas samples collected in the gas bags in chronological order with a gas chromatograph. Plot the CO₂ breakthrough curve by combining the experimental time data, and calculate the enhanced gas recovery based on the produced gas flow rate and gas composition.

8.

Repeat the above experimental procedures by altering the core irreducible water saturation, CO₂ injection timing pressure or CO₂ injection rate.

2.4. Experimental Error Analysis

(1)

Measurement uncertainties in the experiment mainly originate from two sources.

①

Accuracy of various sensors. Pressure sensor: uncertainty of ±0.25%. Flow sensor: uncertainty of ±0.5%. Gas chromatograph: uncertainty of ±0.01%.

②

Changes in pore structure and physical properties caused by repeated core tests: uncertainty of ±1.0%.

(2)

A low dead-volume experimental setup was adopted, and the dead-volume of the experiment system was subtracted when calculating the CH₄ recovery factor and CO₂ breakthrough time.

(3)

Gas chromatography (GC) calibration: The accuracy of GC analysis was regularly verified using standard gases to ensure accurate measurement of methane and injected gas concentrations.

Sampling frequency: Produced gas composition was analyzed every 5–7 min to avoid missing the CO₂ breakthrough point due to excessively long sampling intervals.

(4)

Core-scale experiments cannot fully represent reservoir heterogeneity. The recovery factor of the Hungarian field trial (35%) is significantly lower than that of laboratory results (70%) [10], indicating that scale effects and reservoir heterogeneity are key sources of error in data extrapolation.

3. Results and Discussion

The experimental results are divided into four parts, including the results of the depletion experiments and the results of the CO₂ injection for enhanced CH₄ recovery experiments corresponding to different irreducible water saturations, injection timing pressures and injection rates. Among them, the depletion experiments correspond to the core samples at different irreducible water saturations. The key data from the ten experiments are summarized in Table 5 in this paper. Among them, Experiments (1)–(3) are depletion contrast experiments under different irreducible water saturation conditions, Experiments (4)–(6) are irreducible water saturation contrast experiments, Experiments (5), (7) and (8) are gas injection timing pressure contrast experiments, and Experiments (5), (9) and (10) are gas injection rate contrast experiments. Representative experimental results are selected in Table 5, including the final recovery degree, the cumulative injected PV of CO₂ when the CO₂ content in the produced gas reaches 20%, the cumulative CH₄ recovery degree, the CH₄ recovery degree at 20% CO₂ content and the increment in CH₄ recovery degree compared with the depletion experiment at the same stage. Column 6 in Table 5 refers to the CH₄ recovery degree when CH₄ production no longer increases. Columns 7 and 8 represent the CO₂ injection pore volume (PV) multiple and the corresponding CH₄ recovery degree when the CO₂ content in the produced gas reaches 20%. Depletion experiments serve as the base control experiments for subsequent CO₂ injection tests. The depletion experiment on core samples with 20% irreducible water saturation acts as the base control for the CO₂ injection experiment on core samples with the same 20% irreducible water saturation, and the same applies to the other cases. The incremental CH₄ recovery degree of the CO₂ injection experiment is calculated relative to the CH₄ recovery degree of the depletion experiment at the same time point, as shown in the last column of Table 5. The laws governing recovery enhancement corresponding to different injection conditions are analyzed as follows.

Table 5. Summary table of experimental results for enhanced CH₄ recovery by CO₂ injection with different schemes.

Experimental Categories	Experiment No.	Irreducible Water Saturation	Injection Timing Pressure, MPa	Injection Rate, ×10−3 mm/s	Final Cumulative Methane Recovery Degree	Cumulative Injected PV at 20% CO2 Content	CH4 Recovery Degree at 20% CO2 Content	Increment in CH4 Recovery Degree at 20% CO2 Content
Depletion	(1)	Swi = 20%	/	/	95.4%		/	/
	(2)	Swi = 40%	/	/	85.8%		/	/
	(3)	Swi = 60%	/	/	48.3%		/	/
Irreducible water saturation	(4)	Swi = 20%	16.2	6.53	83.43	0.26	83.37%	−8.27%
	(5)	Swi = 40%	16.2	6.53	89.4%	0.65	86.4%	+4.7%
	(6)	Swi = 60%	38.5	6.53	57.9%	1.5	50.45%	+3.1%
Injection timing pressure	(7)	Swi = 40%	25.5	6.53	86.6%	0.78	77.9%	−2.1%
	(8)	Swi = 40%	5.5	6.53	83.3%	1.2	83.3%	−2.3%
Injection rate	(9)	Swi = 40%	16.2	3.26	81.5%	0.4	76.9%	−4%
	(10)	Swi = 40%	16.2	13.05	78.1%	1.0	68.9%	−9.2%

3.1. Comparison of Depletion Experiment Results for Different Irreducible Water Saturation Levels

Figure 3 illustrates that a comparison of the depletion experiment results for different irreducible water saturations reveals that a higher irreducible water saturation leads to a more severe gas–water Jamin effect during the depletion process, accompanied by poorer gas percolation capacity and a longer pressure transmission time from the well control boundary to the well bottom. This results in a lower ultimate gas recovery degree, a shorter stable production period, a slower pressure decline between wells and a higher abandonment pressure, all of which are less conducive to the primary gas recovery of gas reservoirs. The final CH₄ recovery degrees of different depletion experiments are 95.4%, 85.8% and 48.3% at irreducible water saturations of 20%, 40% and 60%, respectively. The results are comparable to depletion experimental results of similar-property core samples in previous studies (Table 1). For every 1% increase in irreducible water saturation, the depletion gas recovery degree decreases by approximately 1.2%.

Figure 3. Comparison chart of depletion experiment results for core samples with different irreducible water saturations.

3.2. Comparison of CO₂ Displacement Experiment Results for Different Irreducible Water Saturation Levels

All three sets of experiments were performed with CO₂ injection at the same injection timing pressure (16.2 MPa), and CO₂ was injected into the core at a constant flow rate of 6.53 × 10⁻³ mm/s. A CO₂ content of 20% at the core outlet indicates that the bottom-hole CO₂ concentration reaches 20% during field CO₂ injection. The produced gas from production wells must be purified after entering the manifold, which will increase the operational cost. Therefore, the time point at which the CO₂ content at the outlet reaches 20% is selected as the benchmark to evaluate the magnitude of CO₂-EGR. The gas injection volume is characterized by the multiple of core PV.

Figure 4a,b compares the variation curves of the average pressure retention level of the rock sample and the CH₄ recovery rate under different irreducible water saturation. Figure 4c,d compares the variations in the composition of the produced gas corresponding to different irreducible water saturations. For the core sample with 20% irreducible water saturation, the results show that CO₂ breakthrough occurs when approximately 0.1 PV of CO₂ is injected (CO₂ injection time 25 min), and the CO₂ component content rises rapidly after breakthrough. The CO₂ component content at the outlet reaches 20% with an injection of 0.26 PV (CO₂ injection time 55 min), at which point the CO₂ injection recovery degree decreases by 8.3% compared with the concurrent depletion recovery degree. For the core sample with 40% irreducible water saturation, CO₂ breakthrough occurs at an injection of about 0.46 PV of CO₂ (CO₂ injection time 60 min), and the CO₂ component content rises relatively rapidly after breakthrough. The CO₂ component content at the outlet reaches 20% with an injection of 0.65 PV (CO₂ injection time 100 min), at which point the CO₂ injection recovery degree increases by 4.7%, relative to the concurrent depletion recovery degree. For the core sample with 60% irreducible water saturation, CO₂ breakthrough occurs at an injection of approximately 1 PV of CO₂ (CO₂ injection time 140 min), and the CO₂ component content rises slowly after breakthrough. The CO₂ component content at the outlet reaches 20% with an injection of about 1.5 PV (CO₂ injection time 195 min), at which point the CO₂ injection recovery degree increases by 3.1% compared with the concurrent depletion recovery degree.

Figure 4. Curves of relationship between (a) average pressure retention level and experiment time, (b) methane recovery degree and experiment time, (c) component content and CO₂ injection time, and (d) component content and cumulative CO₂ injection PV multiple in CO₂ injection experiments for different irreducible water saturation.

This indicates that after the end of stable production, CO₂ injection in well blocks with low irreducible water saturation is more likely to cause gas channeling, thus reducing the gas reservoir recovery degree. In well blocks with moderate irreducible water saturation, more water in the pores dissolves the CO₂, leading to a decrease in the CO₂ diffusion coefficient, a delay in the CO₂ breakthrough time and an increase in the methane recovery degree. However, with a further increase in pore water, irreducible water in well blocks with high irreducible water saturation clogs more micro-pores, small pores, and even large pores, resulting in a decrease in residual gas after depletion. Consequently, the efficiency of CO₂ in displacing the remaining methane inside the core sample is also affected and reduced. Therefore, after the end of stable production, well blocks with a moderate irreducible water saturation are more suitable for energy supplement and the displacement of residual gas in pores by means of CO₂ injection for low-permeability core samples (<1 mD). Compared with the existing relevant studies, the results in this paper not only consider the effect of irreducible water saturation on dissolving CO₂ and reducing the CO₂ dispersion coefficient, but also account for the limited enhancement in recovery caused by irreducible water occupying pore space. Therefore, the results obtained in this paper can more comprehensively reflect the conditions of real gas reservoirs.

3.3. Comparison of CO₂ Displacement Experiment Results for Different Injection Timing Pressures

In this group of experiments, the irreducible water saturation of all core samples was 40%, and the CO₂ injection rate was uniformly 6.53 × 10⁻³ mm/s. The gas injection timing pressure is defined as a dimensionless quantity, i.e., the percentage of the average core pressure at the time of CO₂ injection, relative to the initial formation pressure of 55 MPa. All gas injection timing pressures in this study fall into the category of late-stage gas injection (i.e., implemented after more than 50% of the original reserves have been produced). For CO₂ at a temperature of 85 °C, when the pressure is lower than 7.38 MPa (the supercritical pressure of CO₂), CO₂ exists in a gaseous state with a low density and high kinematic viscosity, and the diffusion term dominates according to the advection–dispersion equation (ADE) (Equation (4)); when the pressure is higher than 7.38 MPa (the supercritical pressure of CO₂), CO₂ exists in a supercritical state with a low kinematic viscosity and high density, and the advection term becomes dominant based on the same equation.

$$K_L{\displaystyle \frac{{\partial }^{2}C}{\partial x^2}}={\displaystyle \frac{\partial C}{\partial t}}+u{\displaystyle \frac{\partial C}{\partial x}}$$

(4)

where $C$, $u$, and $K_L$ represent the displacing-fluid concentration, the interstitial velocity, and the longitudinal dispersion coefficient of the displacing fluid, respectively; $t$ and $x$ represent time and position.

Figure 5a,b compares the variation curves of the average pressure retention level of the rock sample and the CH₄ recovery rate under different injection timing pressures (i.e., under different pressure conditions). Injecting CO₂ when stable production ceases (i.e., when the formation pressure drops to approximately 16.2 MPa) enables full utilization of both the reservoir’s elastic energy and the supercritical state of CO₂, leading to a maximum increase in the recovery degree of 4.7%, relative to the depletion experiment. CO₂ exists in a supercritical state with low kinematic viscosity and favorable displacement efficiency. However, injecting CO₂ at a relatively high formation pressure (25.5 MPa) fails to fully utilize the reservoir’s elastic energy, causing CO₂ to mix with CH₄ and ultimately reducing the core recovery degree by 2.1% compared with the depletion experiment. Injecting CO₂ at a low formation pressure (5.5 MPa) results in CO₂ being in a gaseous state with high kinematic viscosity and a high diffusion coefficient, leading to poor displacement efficiency. Under this condition, CO₂ injection cannot restore the formation energy, and fully mixing CO₂ with CH₄ also causes a 2.3% reduction in the core recovery degree, relative to the depletion experiment. Therefore, for late-stage gas injection, to improve the ultimate recovery degree, the reservoir pressure at the time of CO₂ injection should not be excessively low and should be at least above the supercritical pressure of CO₂ (7.38 MPa) to maintain the CO₂ displacement efficiency.

Figure 5. Curves of relationship between (a) average pressure retention level and experiment time, (b) methane recovery degree and experiment time, (c) component content and CO₂ injection time, and (d) component content and cumulative CO₂ injection PV multiple in CO₂ injection experiments for different injection timing pressures.

Figure 5c,d compares the variations in the composition of the produced gas corresponding to different injection timing pressures (i.e., under different pressure conditions). When the pressure is higher than 7.38 MPa (the supercritical point of CO₂), a higher pressure results in a higher CO₂ kinematic viscosity and a lower diffusion coefficient, which is more conducive to retarding gas channeling. When the pressure is lower than 7.38 MPa, the movement of CO₂ is dominated by diffusion, which is much slower than advection; this thus helps to delay gas channeling and expand the mixing zone. However, considering the release of the reservoir’s own elastic energy, the reservoir pressure for CO₂ injection is neither excessively low nor excessively high to achieve the optimal effect, but instead has a critical value. Compared to the existing related studies, the results of CO₂ injection in this paper are benchmarked against the depletion outcomes at corresponding timings. This result accounts for both the depletion recovery degree of CH₄ and the dispersion coefficient of CO₂ under varying pressure conditions, thus yielding findings that more comprehensively reflect the actual behavior of gas reservoirs.

3.4. Comparison of CO₂ Displacement Experiment Results for Different Injection Rates

Based on the experimental results of injection timing pressure (with 40% irreducible water saturation), the optimal injection timing pressure is determined to be when the formation pressure drops to 30% of the original pressure, i.e., 16.2 MPa. Building on this optimal injection timing pressure, the enhanced recovery effects corresponding to different injection rates are simulated by this group of experiments. The injection rates were converted into one-dimensional flow velocities under the reservoir temperature and pressure conditions via Equations (1) and (2), so as to facilitate the comparison with the research results reported in the other literature. The experimental results of different injection rates after the average pressure drops to 16.2 MPa for reservoirs with a irreducible water saturation of 40% are presented in Figure 6. Figure 6a,b compares the variation curves of the average pressure retention level of the rock sample and the CH₄ recovery rate under different CO₂ injection rates. Figure 6c,d compares the variations in the composition of the produced gas corresponding to different CO₂ injection rates.

Figure 6. Curves of relationship between (a) average pressure retention level and experiment time, (b) methane recovery degree and experiment time, (c) component content and CO₂ injection time, and (d) component content and cumulative CO₂ injection PV multiple in CO₂ injection experiments for different CO₂ injection rates.

At an injection rate of 3.26 × 10⁻³ mm/s, the volume of injected CO₂ was insufficient to maintain the formation pressure, causing the formation pressure to decrease continuously to near 7.38 MPa. Owing to the low injection rate, the time required for the CO₂ content in the produced gas to reach 20% was the latest (120 min). At this stage, CO₂ was close to a gaseous state, with a high kinematic viscosity and high diffusion coefficient, resulting in a poor displacement effect; thus, the CH₄ recovery degree decreased by 4% relative to that of the depletion experiment.

At an injection rate of 6.53 × 10⁻³ mm/s, a relatively large volume of CO₂ was injected, which maintained the average formation pressure at approximately 16 MPa. With a moderate injection rate, the time for the CO₂ content in the produced gas to reach 20% was intermediate (100 min). Under this condition, CO₂ was in a supercritical state with a low kinematic viscosity and a low diffusion coefficient, leading to an excellent CH₄ displacement effect; consequently, the CH₄ recovery degree increased by 4.7% compared with that of the depletion experiment.

At an injection rate of 13.05 × 10⁻³ mm/s, the maximum volume of CO₂ was injected, which elevated the formation pressure. However, the relatively high injection rate also induced a premature CO₂ breakthrough, with the time for the CO₂ content in the produced gas to reach 20% being the shortest (82 min). Although CO₂ was in a supercritical state under this condition, the excessively high injection rate enhanced advective displacement and caused premature CO₂ breakthrough, resulting in a 9.2% decrease in the recovery degree, relative to that of the depletion experiment.

Therefore, for the low-permeability carbonate core samples (<1 mD) of the target reservoir, the optimal injection rate is approximately 6.53 × 10⁻³ mm/s at the experiment scale (3.6 × 10⁴ m³/d at reservoir scale), which is close to the optimal injection rate reported in the literature (Table 1).

A comprehensive analysis of the data from the ten experiments reveals that CO₂ injection can enhance the CH₄ recovery degree of carbonate rocks in the target gas reservoir (with permeability < 1 mD) by 3–5%. However, the conditions for such recovery enhancement are rather stringent: CO₂ injection can only exert a positive effect on improving the recovery degree of carbonate gas reservoirs under the combined conditions of medium to high irreducible water saturation reservoirs, the middle and late production stages after the end of stable production (with reservoir pressure above 7.38 MPa), and a moderate injection rate. Under other conditions, the CO₂ injection will reduce the recovery degree due to premature breakthrough or reservoir gas contamination, thus exerting a negative impact of CO₂ injection on CH₄ displacement. In addition, the core samples exhibit strong pore structure homogeneity; therefore, the experimental results are not applicable to gas reservoirs with strong heterogeneity and require further verification combined with other research methods.

4. Conclusions

(1) For the target low-permeability carbonate gas reservoir (permeability <1 mD), layers with medium to high irreducible water saturation are more suitable for CO₂ injection to enhance CH₄ recovery compared with those with low irreducible water saturation. There exists an optimal range of reservoir irreducible water saturation for CO₂ injection to enhance CH₄ recovery. Increasing the irreducible water saturation helps to delay the CO₂ breakthrough.

(2) For the target low-permeability carbonate gas reservoir, late-development-stage CO₂ injection is conducive to improving the CH₄ recovery degree, yet the reservoir pressure must not be lower than 7.38 MPa, which is the supercritical pressure of CO₂. The optimal timing is after the end of stable production and before the formation pressure drops to 7.38 MPa. This timing enables full utilization of both the reservoir elastic energy and the supercritical state of CO₂, thus enhancing the CH₄ recovery degree. Injecting CO₂ at either low or high reservoir pressure will result in a widened miscibility zone of CH₄ and CO₂.

(3) For the target low-permeability carbonate gas reservoir, either excessively high or low injection rates are unfavorable for CO₂ injection to enhance CH₄ recovery. A low injection rate results in an insufficient volume of injected CO₂ to maintain the formation pressure, leading to poor CO₂ displacement efficiency and a reduced recovery degree. A high injection rate can supplement the formation energy rapidly, but it also causes premature CO₂ breakthrough, which likewise lowers the recovery degree. Therefore, there exists an optimal range of CO₂ injection rates for enhancing CH₄ recovery.

(4) The experimental parameters were converted to field parameters via similarity criteria. For the target low-permeability carbonate gas reservoir, the suitable reservoir irreducible water saturation for CO₂ injection is approximately 40–60%, the optimal injection timing pressure is when the reservoir pressure drops to near 7.38 MPa, and the optimal injection rate is about 36,000 m³/d per well. Under the optimal injection conditions, CO₂ injection is expected to increase the recovery degree by 3–5% compared with the single depletion production method. The findings of this study are based on core samples with relatively good homogeneity; their applicability to reservoirs with strong heterogeneity remains to be verified.