Feasibility of Carbon Dioxide as Cushion Gas in Depleted Gas Reservoirs: An Experiment Study on CO₂–CH₄ Dispersion during Flow Alternation

Abstract

This study investigates the feasibility of utilizing carbon dioxide (CO₂) as a cushion gas in depleted reservoirs for enhanced gas storage efficiency and carbon sequestration against the backdrop of rising natural gas stable supply demand and climate change concerns. Simulations of gas storage reservoir scenarios require accurate dispersion parameters at flow alternation conditions to quantify the size of the miscible displacement front. Several experimental studies using core-flooding equipment aimed at measuring related parameters have been reported over the last decade but did not take flow alternation into consideration. We simulated directionally variable displacements to mimic the cyclic injection and extraction processes in gas storage, focusing on the dispersion characteristics of CO₂ and methane (CH₄) during flow alternation. Key findings were observed using Nuclear Magnetic Resonance (NMR) imaging, which provided real-time data on the spatial distribution and temporal changes of CH₄ signals in rock cores. The results revealed that dispersion, influenced predominantly by dispersion coefficients rather than molecular diffusion, was significantly higher during alternating flow compared to concurrent displacement. Additionally, CO₂ exhibited a greater dispersion effect when displacing CH₄ than the reverse. This enhanced mixing efficiency during flow alternation supports the potential of CO₂ as a cost-effective and efficient cushion gas, offering both improved storage performance and the added benefit of CO₂ sequestration. These findings contribute valuable insights for the numerical simulation and operational adaptation of CO₂ in gas storage reservoirs, emphasizing the importance of understanding fluid interactions under varying flow conditions to optimize storage efficiency and environmental benefits.

1. Introduction

The increasing global demand for energy coupled with the pressing need to address climate change has led to a surge of interest in innovative energy storage and carbon management solutions [1,2,3,4]. One promising strategy involves the utilization of carbon dioxide (CO₂) as a cushion gas in depleted reservoirs. Depleted reservoirs, which have exhausted their recoverable hydrocarbon resources, present a unique opportunity for gas storage due to their existing infrastructure and proven geologic containment capabilities. Compared to salt cavern gas storage, depleted reservoir gas storage offers larger storage capacity and lower maintenance costs. Traditionally, natural gas storage in these reservoirs has relied on using a portion of the stored gas itself as a cushion gas to maintain pressure and ensure deliverability, which results in significant sunk costs [5]. The concept of using CO₂ in this manner aligns with global efforts to mitigate climate change through carbon capture and storage (CCS) technologies. By storing CO₂ in depleted reservoirs, it is possible to reduce atmospheric CO₂ levels, thereby contributing to international carbon reduction goals.

This approach not only enhances the storage capacity and efficiency of natural gas but also offers a viable method for sequestering CO₂, thereby contributing to the reduction of greenhouse gas emissions. The economic incentives for petroleum operators to repurpose their depleted fields for gas storage with CO₂ cushion gas can provide a dual benefit of extending the life of these assets while participating in carbon mitigation strategies.

The use of CO₂ as an alternative cushion gas offers several advantages. The physical properties of carbon dioxide, such as higher density and lower compressibility compared to methane [6,7,8], can potentially improve the efficiency of gas storage operations.

The current studies primarily encompass research on fluid physical properties and flow mechanisms, experimental studies, and numerical simulation research on a field scale. The physical and chemical properties of CO₂ are crucial in determining its suitability as a cushion gas for natural gas storage [9]. Key factors include its phase behavior, density, and compressibility, which differ markedly from those of methane. CO₂’s higher density and unique phase behavior allow for greater storage efficiency and improved pressure maintenance [10]. Additionally, CO₂’s compressibility can enhance the deliverability of stored gas, potentially reducing overall storage costs and increasing operational flexibility [11]. These properties suggest that CO₂ could be a more efficient and cost-effective option for use as cushion gas compared to methane.

Experimental studies focus on understanding the behavior and interactions of CO₂ and methane (CH₄) within geological formations. These studies evaluated key parameters such as injectivity, storage capacity, and advection–diffusion effects associated with storage. There are few advanced imaging techniques, like Magnetic Resonance Imaging (MRI) and Computed Tomography (CT), provide detailed insights into the spatial distribution, saturation levels, and movement of fluids within the rock core, allowing for a more comprehensive understanding of the displacement mechanisms and efficiency [12,13,14]. MRI has been extensively used to visualize and quantify the distribution and flow of CO₂ and CH₄ within porous media. The non-invasive nature of MRI allows for real-time monitoring of fluid saturation and distribution changes during core flooding experiments. Key advantages of MRI include its ability to distinguish between different fluid phases and provide high-resolution images of fluid interfaces and saturation fronts.

MRI and CT methods are effective techniques for studying the flow mechanisms of methane and carbon dioxide at the core scale. In field-scale applications for oil and gas reservoirs, time-lapse seismic imaging [15] is particularly effective in monitoring the macroscopic migration patterns of carbon dioxide within formations. The fundamental principle behind this technique is that the injection of carbon dioxide into a reservoir alters the fluid saturation in the rock’s pores, which in turn affects the propagation velocity of seismic waves. Typically, the seismic wave velocity for gaseous or supercritical carbon dioxide is lower than that for water and oil. Therefore, through high-quality seismic data acquisition and meticulous data processing, time-lapse seismic imaging can detect even minute changes in amplitude, which generally correspond to changes in carbon dioxide saturation. On average, the detection accuracy of time-lapse seismic imaging can reach a range of several meters to tens of meters, making it an effective tool for monitoring carbon dioxide diffusion in field-scale reservoir applications [16]. However, for this study, which examines the feasibility of using carbon dioxide as cushion gas in natural gas storage, the signal-to-noise ratio of seismic response between methane and carbon dioxide is relatively low compared to that between gas and oil or water. Therefore, further advancements in data processing techniques are needed for field-scale research in this context [17].

Advanced reservoir simulation models have been extensively employed to predict the performance of CO₂ as a cushion gas in natural gas storage applications [18]. These sophisticated models [19,20] assess a range of critical parameters, including injection rates, pressure maintenance, gas recovery factors, and the interaction of CO₂ with reservoir rock and fluids. By simulating various scenarios [21], these models provide valuable insights into the dynamic behavior of CO₂ within the reservoir, helping to optimize injection and production strategies. Results from these simulations indicate that CO₂ can effectively maintain reservoir pressure, enhance gas recovery, and potentially improve the overall efficiency of gas storage operations in depleted fields.

Despite extensive theoretical and experimental research on the displacement process of carbon dioxide in geological formations, there is still a lack of studies on the mechanisms and patterns of the bidirectional flow of carbon dioxide and methane in cyclic flow systems, especially in gas storage reservoirs. In underground gas storage systems, frequent cyclical changes in pressure, high-velocity flows, and extensive alternations in flow direction exhibit more intricate migration patterns that warrant comprehensive investigation. The introduction of carbon dioxide as cushion gas allows for the realization of improved economic and environmental performance in these storage facilities; however, its fluid properties under geological conditions and interactions with methane and formation water increase the complexity of carbon dioxide migration within subsurface reservoirs. An in-depth examination of multiphase fluid migration laws in large-scale, high-frequency, and intense cyclically varying permeation systems will further illuminate the fundamental principles governing fluid flow in hydrocarbon reservoirs. This research would provide essential theoretical underpinnings for advancing carbon sequestration practices and optimizing injection-production strategies in underground gas storage facilities.

The primary objective of this study is to experimentally investigate the feasibility of using CO₂ as a cushion gas in depleted reservoirs. This includes examining the key factors that influence the performance and stability of CO₂ in this role, with a particular focus on the degree of mixing caused by diffusion and dispersion effects during flow. In this work, the advection-diffusion effects of carbon dioxide and methane in porous media were comprehensively investigated. A core-scale experimental scheme was developed to simulate the cyclic injection and displacement of methane and carbon dioxide, replicating the fluid flow processes in gas storage reservoirs. Real-time measurements of fluid distribution were conducted using MRI techniques, providing detailed insights into the flow dynamics. Subsequently, the advection-diffusion coefficients of carbon dioxide and methane in porous media were calculated for various scenarios, incorporating the operational characteristics of gas storage reservoirs. The feasibility of employing carbon dioxide as a cushion gas was validated. The findings of this study provide theoretical support for flow theory analysis, numerical simulations, and the practical operation of gas storage reservoirs, ultimately contributing to enhanced gas storage efficiency and carbon sequestration.

2. Theoretical Background

For underground gas storage, the key to enhancing the efficiency of carbon dioxide cushion gas utilization lies in controlling the mixing of carbon dioxide and the main component of natural gas, methane, in the formation. Diffusion, driven by concentration gradients, is a form of mass transfer characterized by isotropic behavior at the microscopic level, facilitated by Brownian motion, and can manifest independently of fluid flow [22]. On the other hand, dispersion arises from the interplay of convection and diffusion. Convection can result from gravity-driven segregation, causing vertical fluid movement due to density disparities. Horizontal fluid displacement can induce compositional heterogeneity, contributing to dispersion effects. Dispersion occurs when two fluids mix due to varying flow velocities and molecular diffusion.

In studies of high-pressure gas dispersion in porous media, several key factors influence the process. Temperature: Higher temperatures increase the diffusion coefficient due to enhanced molecular motion. Pressure: The dispersion coefficient rises with pressure up to a point, stabilizing under supercritical conditions. Flow velocity: The dispersion coefficient increases linearly with flow velocity. Displacement relationship: Methane displaces carbon dioxide more effectively than vice versa. Porosity: Increased porosity enhances diffusion by raising molecular collision rates. Vertical permeability: Higher vertical permeability promotes dispersion between cushion and working gases at the structure’s base. Radial permeability: Lower permeability limits dispersion, but an optimal level maintains stable flow and reduces interference. Reservoir deformation: Cyclical compression of reservoir rocks intensifies disturbances, affecting dispersion. Heterogeneity: Non-uniformity increases gas interface movement, elevating the diffusion coefficient. Gravity: The molar mass difference between methane and carbon dioxide causes gravitational differentiation, inhibiting mutual diffusion. Injection and withdrawal cycles: With repeated cycles, reservoir properties stabilize, and under gravity, cushion gas distribution stabilizes, decreasing the diffusion coefficient.

In core displacement experiments, the flow and dispersion predominantly occur along the axial direction of the core. Therefore, the study can be conducted based on a one-dimensional advection–diffusion equation. The general form of the equation can be described as follows [23,24]:

$$D{\displaystyle \frac{{\partial }^{2}C}{\partial x^2}}-v{\displaystyle \frac{\partial C}{\partial x}}={\displaystyle \frac{\partial C}{\partial t}}$$

(1)

where C is the carbon dioxide concentration at location x from the inlet of the sample core, t is time, v is the fluid velocity vector, and D is the molecular diffusion coefficient. The advection-diffusion equation was formulated under the assumption that both the interstitial velocity and dispersion coefficients remain independent of the carbon dioxide concentration. The equation describes how solute concentrations change over time and space due to the combined effects of advection and diffusion. To streamline and clarify the fundamental traits and behaviors of physic processes, the equation can be presented in dimensionless form:

$${\displaystyle \frac{1}{P_e}}{\displaystyle \frac{{\partial }^{2}C}{\partial x_D^2}}-{\displaystyle \frac{\partial C}{\partial x_D}}={\displaystyle \frac{\partial C}{\partial t_D}}$$

(2)

where

$x_D={\displaystyle \frac{x}{L}}$, dimensionless length, where L is the length of the sample core,

$t_D={\displaystyle \frac{tv}{L}}$, dimensionless time,

$P_e={\displaystyle \frac{vL}{D_L}}$, Péclet number is the dimensionless number to delineate the relative between convective and diffusive transport in fluid dynamics. Since the carbon dioxide injection inlet is at x = 0, then the carbon dioxide concentration C at initial condition is 0 at $t_D=0$, and the boundary conditions are $C=1$ at $x_D=0$ and $C\to 0$ as $x_D\to \infty$, the solution is as follows [25,26,27,28]:

$$C={\displaystyle \frac{1}{2}}\left\{erfc\left({\displaystyle \frac{x_D-t_D}{2\sqrt{t_D/P_e}}}\right)+e^{P_e{x}_D}erfc\left({\displaystyle \frac{x_D-t_D}{2\sqrt{t_D/P_e}}}\right)\right\}$$

(3)

The erfc in Equation (3) is the complementary error function, which represents the complementary cumulative distribution function for a Gaussian distribution with a mean of 0 and a variance of 1/2. It is useful for calculating tail probabilities in the normal distribution and can be used in applications involving diffusion processes and statistical physics.

Based on dimensionless equations, one can determine either the temporal evolution of concentration at a fixed location in a diffusive medium or its spatial distribution at a specific time. Experimental data yield the Péclet number, facilitating the computation of the diffusion coefficient.

Diffusion within porous media parallels phenomena observed in capillary tubes and is likewise characterized by the one-dimensional advection and diffusion equation [29], with a few distinct differences warranting consideration. It is essential to consider the diffusion disparities between the flow direction and the vertical direction, as well as the additional path length induced by the tortuosity of the flow paths during the gas permeation process.

Figure 1 shows the relation between the Péclet number and Longitudinal dispersion coefficients in underground gas storage. In the distal regions of injection and production wells, where subsurface flow velocities are low, indicating that diffusion predominantly governs the flow processes. At low values of the Péclet number, D_L/D towards $1/\tau$. The tortuosity $\tau$ of a sandstone core can be estimated by the following relationship [30]:

$$\tau =A\ln \left(1/\varphi \right)+1$$

(4)

where $\varphi$ is the porosity of the core, and A is an empirical constant that can be set equal to 0.41 in the sandstone core.

In these areas, the influence of tortuosity within the rock pore structure must be considered:

$${\displaystyle \frac{D_L}{D}}={\displaystyle \frac{1}{\tau }}+{\displaystyle \frac{\alpha v_m^n}{D}}$$

(5)

where n is an empirical exponent that allows for the non-linearity in the variation of D_L/D with v_m at very high velocities, but commonly, n is set equal to 1 [31] in sandstone, and α is dispersity.

Conversely, in the proximal zones with higher flow velocities, a larger Péclet number prevails, indicating that advective mixing predominantly controls the flow.

$${\displaystyle \frac{D_L}{D}}={\displaystyle \frac{v_m{d}_p}{D}}$$

(6)

where d_p is a characteristic length scale of the pore throat radius. The diffusion coefficient D between CH₄ and CO₂ at temperatures of 25, 50, and 75 °C and pressures ranging from 1.5 to 25 MPa has been correlated using a function derived from previous study data:

$$D_{{\mathrm{CO}}_2,{\mathrm{CH}}_4}={\displaystyle \frac{(-4.3884\times {10}^{-13}p+8.5440\times {10}^{-11})T^{1.75}}{p}}$$

(7)

Equation (7) was established by Hughes [32] to describe the correlation between the diffusion coefficients and temperature and pressure where D_CO2,_CH4 is the molecular diffusion coefficient of CO₂ in pure CH₄ calculated in m² s⁻¹ for p in MPa and T in K.

3. Experiments

3.1. Experimental Materials

In this study, simulated rock cores comprised 80.72 mm long and 24.95 mm diameter Berea sandstone cores, which were employed as experimental samples. The sample’s porosity, determined by the bulk NMR signal intensity, was measured to be 22.60%, with a corresponding tortuosity of 1.49 and permeability of 763 mD.

The experimental gas utilized is high-purity methane to simulate natural gas. Considering the purity of the carbon dioxide cylinder and the temperature-pressure losses within the experimental apparatus, based on experimental experience, the temperature should be set between 40–60 degrees Celsius, while the pressure needed to be maintained above 12 MPa to increase the density of methane to meet the signal strength requirements for magnetic resonance.

To simulate the underground fluid migration process in underground gas storage and achieve dynamic observation of carbon dioxide-methane fluid displacement processes, an integrated online nuclear magnetic resonance (NMR) scanning device was employed in this study. The system comprises a displacement system, a high-temperature and high-pressure circulation system, an NMR scanning system, and a back-pressure control system. The displacement system primarily facilitates the connection of methane and carbon dioxide gas cylinders for gas injection and pressure control. Key components include gas booster pumps, intermediate containers, buffers, and pressure-regulating valves. The high-temperature and high-pressure circulation system is chiefly responsible for regulating the temperature and confining pressure of the core samples, utilizing circulation pumps and heating devices. To mitigate interference from hydrogen atoms in water during online NMR scanning, fluorinated liquids serve as circulating media to control temperature and pressure. The NMR scanning system employs the MesoMR12-060H-I NMR scanner, featuring a core holder comprising gradient coils and permanent magnets. The back-pressure system simulates reservoir displacement conditions and governs the pressure at the outlet end of the core, thereby stabilizing gas flow within the core. The other auxiliary equipment includes check valves, tee joints, pressure gauges, flow meters, and online chromatographic analyzers.

An experimental system, depicted in Figure 2, was established to simulate cushion gas performance during injection and withdrawal processes in underground gas storage. Given that a single core unit may encounter both huff–puff and displacement injection-extraction scenarios in actual operations, line connections in the experimental setup were optimized. This allows both sides of the core to function as either inlet or outlet, accommodating diverse operational conditions in the experiment.

3.2. Experiment Procedure and Details

The experiments simulated two scenarios, each consisting of two processes: (a) Berea sandstone core sample saturated with methane undergoing carbon dioxide huff–puff; (b) Berea sandstone core sample saturated with carbon dioxide undergoing methane huff–puff; (c) methane displacement by carbon dioxide; (d) carbon dioxide displacement by methane.

In the displacement process, the inlet and outlet of the core remain constant. Carbon dioxide and methane are sequentially injected at the inlet to simulate the directional displacement of cushion gas by working gas in underground storage. Analogous to carbon dioxide displacement in gas reservoir development, the injection well is located at the bottom edge of the reservoir structure, while the production well is positioned at the middle or top. This method investigates the mixing of carbon dioxide and methane gases during displacement flow in porous media.

Huff–puff involves initially saturating with carbon dioxide or methane followed by the other gas injection from the inlet while maintaining the outlet closed to simulate the injection process. Subsequently, the inlet and outlet are switched, converting the original inlet into the outlet, and methane withdrawal or carbon dioxide exhaust is simulated by controlling the back-pressure regulator. This experiment simulates the flow process of cushion gas and working gas in single-well injection and withdrawal scenarios of underground storage. It also illustrates the mixing of cushion and working gases during the transitional flow direction changes in the reservoir.

The Berea core sample undergoes MRI scanning; a detailed experimental process is provided in Figure 3. To fill the system with methane, the back pressure regulator was set to the desired pressure, and valve V1 was opened. When the methane in the core reached the desired pressure, the pump was adjusted to deliver a specified flow rate and pressure, increasing the CO₂ pressure upstream of V2. Once the CO₂ pressure slightly exceeded the CH₄ pressure in the core, V1 was closed, and V2 was opened, switching the flow source from CH₄ to CO₂. The CH₄ pump was stopped immediately after the switch. The switchover time was recorded, and the spectrometer was set to automatically record spectra at fixed intervals. For CO₂, the filling process was the reverse, which will not be elaborated on.

The MRI measurements are more challenging in terms of signal-to-noise ratio due to the CH₄ gas density. The Spin Echo Single Point Image (SE-SPI) was employed as a pulse sequence for measurement. The advantages of SE-SPI as high spatial resolution, strong resistance to artifacts, and effective compensation for magnetic field inhomogeneity, can meet the demand of CH₄ axial concentration detection. The SE-SPI sequence sampling frequency was set to 100 kHz, with a main frequency of 12 MHz and a frequency offset of 565,397.34 Hz. The 90-degree pulse width was 21.00 µs, and the 180-degree pulse width was 37.04 µs. There were 304 echoes and 11 sampling layers, and the gradient stepping parameters were automatically matched.

4. Results and Discussion

4.1. Concentration Profiles

Figure 4 illustrates the 11 time-sample lines distribution of normalized signal intensity acquired by MRI over time and position for four cases mentioned in Section 3.2. The experiments were conducted at a flow rate of 0.648 mm/s, temperature of 40 °C, and pressure of 12 MPa. In the graph, the x-axis represents flooding time, the y-axis represents core position, and the z-axis represents normalized signal intensity. The behavior of CO₂ and CH₄ during alternative and constant flow processes can be observed by these data. The profiles exhibit a relatively low signal-to-noise ratio (SNR) due to the limited MRI signal and the necessity for rapid profile measurements. This speed was crucial to prevent significant blurring caused by signal displacement as core flooding progressed during the acquisition window. Despite the low SNR, certain trends are clearly discernible. A value of 1 represents the mean CH₄ signal for the sample core, serving as the normalization target in the presence of CH₄ saturation at the target pressure.

Figure 4a shows the concentration profile of CO₂ huff and puff on CH₄ in a sandstone sample. Over time, the process began with the injection of CO₂, causing a decrease in the signal intensity, detected through CH₄, near the 0–3 cm at the inlet of the core. When it turned to the CO₂ expel process, the signal near the inlet raised again, indicating the return or redistribution of CH₄. At the outlet end located at 6–8 cm, the signal intensity consistently decreases throughout the process due to the mixture of these two gases, leading to a lower overall CH₄ content in this region. Conversely, in Figure 4b, the CH₄ huff and puff on CO₂ process shows an increase in signal during CH₄ injection and a decrease during withdrawal.

Comparing processes a and b in Figure 4, the distinct patterns in signal changes highlight the superior diffusion properties of CO₂ compared to CH₄. CO₂ spreads more effectively through the core, facilitating a more uniform and effective displacement of CH₄. During the CO₂ huff and puff process, the mixing at the core’s outlet end is less pronounced compared to the CH₄ huff and puff process. This indicates that CO₂ injection results in a more stratified and less mixed gas distribution. The lower mixing degree of CO₂ near the core exit can be attributed to CO₂’s higher density and lower viscosity in its supercritical state, which allows it to maintain a more stable and less diffusive displacement front. This characteristic is advantageous for applications where minimal gas mixing is desired to maintain the high purity and calorific value of the recovered gas. In contrast, the CH₄ injection process, characterized by deeper front advancement but higher mixing, indicates that while CH₄ can penetrate further into the core, it also results in a broader mixing zone.

Figure 4c depicts the direct displacement of CH₄ by CO₂. The CH₄ concentration gradually decreased from the core plug inlet to the outlet as it was progressively displaced, and Figure 4d illustrates the opposite process, which is the displacement of CO₂ by CH₄. In the core plug, CO₂ breakthrough at the core exit located at 70 mm occurred at 41 min during flooding, while CH₄ breakthrough at 29 min. The direct comparison between Figures c and d reveals the superior displacement efficiency of CO₂ over CH₄. CO₂’s higher diffusivity and density enable it to penetrate the core more effectively, pushing out CH₄ in a more uniform and efficient manner. In contrast, CH₄’s displacement of CO₂ is slower and less uniform, which is consistent with the results of previous studies.

4.2. Breakthrough Profiles

To mitigate the influence of inlet and outlet port effects on the data, signal intensity data values reflecting temporal changes were acquired at a length of 10 mm for the huff and puff process and at a length of 10 mm and 70 mm for the displacement process, respectively, within the sandstone core.

Figure 5 shows the signal intensity changes with flooding time where we can obtain the breakthrough curves for each process respectively. The first phase in Figure 5a illustrates the CO₂ injection process, where the methane signal intensity decreases between 64 and 92 min with the injection of CO₂. Around 150 min, the process switches to withdrawal, and as CO₂ is expelled, the methane signal recovers and rises between 223 and 263 min. At the observation position of x = 10 mm, the methane signal intensity only recovers to about 55% of saturation by the end of the experiment.

Figure 5b presents the opposite process, where CO₂ is injected into a methane-saturated core. The signal intensity rises between 57 and 90 min and then declines between 185 and 218 min, stabilizing at around 18% by the end of the experiment.

Figure 5c depicts the CO₂ displacement of methane. For easier analysis of data patterns, the CO₂ concentration is calculated from the methane signal intensity. Red circles represent the CO₂ concentration measured at x = 10 mm, while blue stars indicate the concentration at x = 70 mm.

Figure 5d shows the methane displacement of CO₂. Comparing the two sets of experiments in Figure 5c,d, the CO₂ displacement of the methane process shows a longer time difference between the rise in concentration at the outlet and inlet ends and a more gradual increase. This indicates that CO₂ is more efficient than methane in displacement processes, resulting in a more uniform advancement front.

4.3. Dispersion Coefficient and Flow Alternation Effects

Based on the fundamental theory of gas diffusion, the dispersion coefficient was determined by fitting the displacement experimental data in Figure 5 using Equation (3) to solve for the Peclet number (Pe). Subsequently, the dispersion coefficient was calculated at the experimental temperature and pressure, and the diffusion coefficient was derived accordingly.

In this study, Python 3 programming language was used, employing functions from the NumPy and SciPy libraries to construct Equation (3) for the data fitting algorithm. Considering the form of the data samples for fitting, to highlight data patterns, data from 0–103 min and 221–300 min were selected for the CO₂ huff and puff process on CH₄, and data from 39–140 min and 153–240 min were selected for the CH₄ huff and puff process on CO₂, as grey square marked in Figure 5a,b. These data segments were used as fitting samples for the mutual displacement processes of the two gases, with concentrations normalized according to the fitting formula.

Fitting calculations were performed on eight datasets from the four experimental processes, with the results presented in

Table 1. Comparison of dispersion coefficients in different processes within a Berea sandstone core (porosity: 22.60%, permeability: 763 mD) at a flow rate of 0.648 mm/s, temperature: 40 °C, and pressure: 12 MPa.

Experiment Process		Diffusion Coefficient 10−8 m2/s	Dispersion Coefficient 10−8 m2/s
(a) CO2 huff and puff on CH4	CO2 injection	15.58	33.33
	CO2 withdraw		94.83
(b) CH4 huff and puff on CO2	CH4 injection		57.74
	CH4 withdraw		62.74
(c) CO2 displaces CH4	Position X = 10 mm		5.20
	Position X = 70 mm		4.28
(d) CH4 displaces CO2	Position X = 10 mm		14.82
	Position X = 70 mm		7.45

. The results indicate that under identical experimental conditions, the diffusion coefficient of CH₄ displacing CO₂ in the huff and puff process is up to 15 times higher than in the co-current displacement process, and the diffusion coefficient of CO₂ displacing CH₄ is up to 12 times higher than in the co-current displacement process.

During the flow direction switch in the huff and puff process, local counter-current flow is generated in the initial unified flow field. The significant shear forces and turbulence effects in the counter-current flow result in higher mixing efficiency and a larger dispersion coefficient. This flow pattern leads to complex flow paths in the porous medium, enhancing the dispersion effect and intensifying gas mixing. In contrast, the co-current displacement process, characterized by steady flow rates and uniform gas flow direction, exhibits less shear force and turbulence, resulting in a smaller dispersion coefficient.

In both huff and puff and flooding processes, the dispersion coefficient in the methane displacement of carbon dioxide is approximately 1–2 times greater than in the carbon dioxide displacement of methane. Methane, with its lower density and viscosity, more easily penetrates and mixes with the denser, more viscous carbon dioxide, enhancing the mixing effect and increasing the dispersion coefficient. The flow dynamics between the two gases differ significantly; methane’s lower density can result in buoyancy effects, causing more complex flow patterns and increased mixing. Additionally, methane has a higher molecular diffusion coefficient than carbon dioxide due to its smaller molecular size, contributing to a greater overall dispersion coefficient during displacement. The interfacial tension between methane and carbon dioxide is lower, facilitating easier mixing and higher dispersion. Furthermore, the higher flow rate and lower viscosity of methane generate more shear forces and turbulence at the interface compared to the more stable flow of carbon dioxide displacing methane, leading to enhanced mixing and dispersion. These combined factors result in a larger dispersion coefficient when methane displaces carbon dioxide.

In core displacement experiments involving methane displacing carbon dioxide or vice versa, the diffusion coefficient measured at the inlet end is typically slightly greater than that at the outlet end. Several factors can explain this phenomenon. Firstly, the concentration gradient at the inlet is higher, enhancing molecular diffusion and resulting in a higher apparent diffusion coefficient. The initial mixing dynamics at the inlet may produce more turbulence and shear forces, which can enhance diffusion and dispersion; these effects tend to diminish as the gases travel through the core, leading to a lower diffusion coefficient at the outlet. Variations in pressure and temperature along the core can also affect gas properties and flow dynamics; higher pressure at the inlet can increase the diffusion coefficient, while lower pressure at the outlet can decrease it. Heterogeneity in core porosity and permeability may influence local flow and diffusion rates, with potentially higher permeability at the inlet promoting greater diffusion. Additionally, saturation effects mean the core at the inlet may be more fully saturated with the displacing gas, enhancing diffusion efficiency, whereas the outlet may retain more of the displaced gas. Lastly, as gases move through the core, flow conditions may transition from turbulent to laminar; turbulent flow at the inlet enhances mixing and diffusion, whereas laminar flow at the outlet reduces these effects. These combined factors result in a higher diffusion coefficient at the inlet compared to the outlet in these core displacement experiments.

Figure 6 compares the dispersion coefficient computed in this study with results from prior research under similar temperature, pressure, and displacement velocity conditions. Previous studies primarily derived diffusion coefficients through co-current displacement. Our study’s displacement process aligns with past research, while dispersion coefficients from throughput during flow direction switches resemble results from high-flow-rate co-current displacement. Further analysis can explore the correspondence between flow direction switches and flow rates with more experimental data samples.

5. Conclusions

The utilization of carbon dioxide as cushion gas in gas storage facilities differs significantly from its application in enhanced oil recovery (EOR) projects aimed at improving oil recovery rates. Investigating the flow process in gas storage requires consideration of the alternating flow directions and their dispersal effects on methane and carbon dioxide.

Building upon core flooding experiments, a suitable experimental procedure was established to simulate directional displacement and mimic the throughput of rock cores. This enabled the simulation of the mutual flow interaction between carbon dioxide and methane under various conditions. Utilizing the SE-SPI sequence of nuclear magnetic resonance facilitated online observation of methane signals’ spatial distribution and temporal changes along the X-direction in the rock cores, establishing a method for experimental data acquisition.

Compared to molecular diffusion, dispersion between methane and carbon dioxide fluids is predominantly influenced by dispersion coefficients. During the throughput process where flow direction changes, dispersion is 12–15 times higher compared to co-current displacement, indicating a significant role of flow direction alteration in gas mixing. Additionally, dispersion coefficients during methane displacement by carbon dioxide are approximately 1–2 times higher than during carbon dioxide displacement by methane.

This core-scale study will greatly contribute to numerical simulations and the adaptability analysis of carbon dioxide as a cushion gas in depleted oil and gas reservoirs. Furthermore, these discussions on dispersion effects can positively impact the evaluation of the distribution range of mixed gas zones in reservoirs, purity control of injection and production gases, and calculations of maximum carbon dioxide storage capacity.

To acknowledge the limitations of this study, we note that the restricted number of experiments limits the ability to capture the full diversity of natural reservoir conditions. Expanding the range of experimental conditions and methodologies would provide a more comprehensive dataset, leading to stronger and more generalized conclusions for quantitative analysis into the transition from turbulent to laminar flow and its implications for diffusion and mixing.