Mechanistic insight into the displacement of CH₄ by CO₂ in calcite slit nanopores: the effect of competitive adsorption

Abstract

Grand Canonical Monte Carlo (GCMC) and molecular dynamics (MD) simulation methods were used to investigate the adsorption and diffusion properties of CH₄ and CO₂ in calcite slit nanopores with a pore width of ∼22 Å. It was found that, in contrast to CH₄, CO₂ molecules have a much higher capacity to be adsorbed onto calcite pore surfaces. The diffusion capacity of CO₂ molecules is much less in comparison with that of CH₄ molecules, which could be attributed to diverse interactions between CO₂ gas molecules and calcite nanopore surfaces. An effective displacement process of residual adsorbed CH₄ in calcite slit nanopores by CO₂ was performed, and it was found that the displacement efficiency was enhanced with an increase in the bulk pressure. This work provides microscopic information about the adsorption and diffusion properties of CH₄ and CO₂ in calcite nanopores, and confirmed the feasibility of the displacement of adsorbed CH₄ in calcite nanopores by CO₂, with the purpose of providing useful guidance for enhancing the extraction of shale gas by injecting CO₂.

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1. Introduction

Along with the global energy shortage, unconventional gas extraction, in particular the extraction of shale gas, has received more attention.^1,2 Recently, the enhanced recovery of shale gas by injecting CO₂ (CO₂-EGR) has been regarded as a promising technique, which not only achieves CO₂ capture and storage (CCS), but also improves the recovery of shale gas; thereby, the CO₂-EGR technique could combine environmental and industrial benefits perfectly.^3–6

A number of studies of the adsorption and diffusion properties of CH₄ and CO₂ in nanoporous materials such as zeolites and metal–organic frameworks (MOFs) have been conducted both experimentally and theoretically.^7–11 Abundant research into the microbehavior of CH₄ and CO₂ in simulated nanoporous layers has also been performed by computer simulations.^12–16 For example, Lee et al.¹⁷ investigated the microscopic desorption and transport properties of CH₄ at heterogeneous interfaces of kerogen, and Yuan et al.¹⁸ examined the microbehavior of the enhanced recovery of confined CH₄ by CO₂ in carbon nanotubes (CNTs). Moreover, a model of gas flow for the injection of CO₂ into shale reservoirs was proposed by Edwards et al.,¹⁹ which indicated high performance of CO₂-EGR for individual wells. In addition, in our previous work,²⁰ competitive adsorption between CH₄ and CO₂ in quartz nanopores was determined and a detailed microscopic view was also provided of these C1 substances in quartz component shale formations.

According to the literature, shale is composed of organic matter and inorganic minerals, and nanoscale pores account for a large portion of the effective porosity in shale layers. Nanopores are classified into three types by the pore diameter: micropores (d < 2 nm), mesopores (d = 2–50 nm) and macropores (d > 50 nm), and the vast majority of CH₄ trapped in shale layers is in a state of adsorption in nanopores with primary porosity (micropores and mesopores).^21–24 Recent studies indicate that although the organic matter, which consists of polyaromatics and alkyl-substituted aromatic units, is considered to be the primary substance that traps CH₄,^25,26 the inorganic minerals account for a large proportion of shale formations. Quartz, calcite, clay and feldspar are considered to constitute the major components of shale layers.²⁷ A recent study shows that in the shale play of the Qaidam Basin, China, the calcite mineral content could reach as high as 71%.²¹ Calcite is mainly composed of calcium carbonate, which constitutes a large proportion of shale formations in some shale plays. In comparison with the extensive investigations about the behaviors of gases in nanopores of kerogen and silica minerals, studies of CH₄ and CO₂ in nanoporous calcite matter are rare. The microbehavior of CH₄ and CO₂ in calcite nanopores and definite detailed information about the displacement process of adsorbed CH₄ by CO₂, which are exactly what we desire to discover, are still unclear.

In this study, models of calcite slit nanopores were constructed to represent shale formations. A GCMC method was used to study the gas adsorption process, and an MD simulation method was used to examine the diffusion properties of gases and the displacement process of adsorbed CH₄ by CO₂, with the purpose of determining the microbehavior of CH₄ and CO₂ molecules in calcite nanopores and predicting the possibility and efficiency of the displacement of adsorbed CH₄ by CO₂, which could enrich theoretical knowledge about the molecular behavior of CH₄ and CO₂ in nanosized porous media and should be very helpful for a better understanding of the CO₂-EGR technique.

2. Models and methods

2.1 Atomistic models

The simulation system was defined as a periodic nanosized slit with a pore width of ∼22 Å. A simulation box with dimensions of 34.4 Å × 26 Å × 38 Å was constituted by two calcite blocks, and each block had a thickness of three calcite layers (Fig. 1). Exposed calcite surfaces in the slit nanopores were obtained by cutting calcite crystals along the (104) crystallographic face, as described in the previous literature.^28–30 Parameters of calcite were used as described in the work of Lopez-Ramirez et al.,²⁹ which gave a good prediction of the adsorption of water and metal ions on the calcite surface. The entire sorbent was regarded as rigid during the whole simulation. For gases, five-site and three-site rigid models were used to represent CH₄ and CO₂ molecules, respectively, according to the literature.^31,32

Fig. 1 Model of calcite slit nanopore with a pore width of ∼22 Å. Atoms: O in red, C in grey and Ca in green.

2.2 Simulation details

The temperature and pressure used in this study were selected taking into consideration those in actual shale gas reservoirs^21,22 and as an approximation of the fact that the temperature and pressure in deep shale formations are equal to the geothermal temperature and hydrostatic pressure, respectively. According to research work by Brochard et al.,¹⁶ an average geothermal gradient of 25 °C km⁻¹ and a surface temperature of 15 °C were employed to represent the temperature and pressure conditions with variations in the layer depth. Therefore, in consideration of the differences and indeterminacy of the geothermal gradient and surface temperature for various shale plays, four sets of temperatures, namely, 273, 323, 343, and 373 K (in a range of layer depths of about 300–3000 m), along with a pressure range from 0.01 MPa to 20 MPa, were selected in this study.

The COMPASS³³ force field was used to perform the whole simulations using the Materials Studio (MS) software package, with the total potential expressed as follows:

GCMC and MD methods were employed to investigate the microbehavior of gases in nanopores, as described in our previous work.²⁰ The adsorption properties of CH₄ and CO₂ in calcite slit nanopores were modeled by a GCMC method. The Lennard-Jones 9-6 potential was used to represent the van der Waals (vdW) term, whereas the electrostatic interaction was modeled by the coulombic function. Each equilibration and calculation process of adsorption comprised 5 × 10⁶ steps, respectively. An MD simulation method was used to model the diffusion properties of CH₄ and CO₂, along with the displacement process of residual adsorbed CH₄ by CO₂ in calcite slit nanopores. The NPT ensemble was used to investigate the self-diffusion properties of gases using the pressure barostat of the Berendsen algorithm, whereas the gas desorption and displacement processes were examined using the NVT ensemble with the temperature thermostat of the Nose algorithm. Each MD simulation process took place over a run time of 5.0 ns with a time step of 1 fs, and the last 1.0 ns of the MD process was used for analysis.

3. Results and discussion

3.1 Adsorption properties of CH₄ and CO₂ in calcite slit nanopores as a single component

The adsorption isotherms of CH₄ and CO₂ in calcite nanopores as a single component are shown in Fig. 2 and could be well described by the Langmuir isotherm model using the following equation:where V_L and b correspond to the Langmuir constants of a pure gas and P is the equilibrium pressure of the pure component. Recent studies have indicated that in some nanoporous layers of coal seams and shale the adsorption of CH₄ and CO₂ could be described by the Langmuir model.^34–36 In our previous work, it was determined that the adsorption of both CH₄ and CO₂ is in good agreement with the Langmuir model in quartz nanopores with a diameter of ∼2 nm.²⁰ From Fig. 2 it could be found that in comparison with CH₄ the adsorption loading of CO₂ increases rapidly at low pressures from the initial level, which could be attributed to strong interactions between the CO₂ molecules and the calcite pore surfaces, and then increases gradually with a continued increase in pressure.

Fig. 2 Adsorption isotherms (symbols) and isotherms fitted by the Langmuir model (lines) of CH₄ (a) and CO₂ (b) in calcite slit nanopores as a single component at various temperatures.

Fig. 3 shows that both CH₄ and CO₂ molecules have a tendency to be adsorbed onto the nanopore surfaces. The vast majority of CO₂ molecules are adsorbed onto the pore surfaces, and an adsorption layer with a thickness of almost one molecular layer is formed, which nearly becomes saturated even at an initial pressure of 3 MPa (Fig. 3b and 4II); the adsorption density does not change much as the pressure increases. The adsorption density of CH₄ is clearly lower than that of CO₂ at 3 MPa, and increases gradually with an increase in pressure. When the pressure reaches 20 MPa, the adsorption layers of CH₄ and CO₂ beside the pore surface both reach saturation and the adsorption densities are similar. The results indicate that the interactions between CO₂ molecules and the pore surface are much stronger than those of CH₄ molecules.

Fig. 3 Molecular density profiles of CH₄ (a) (solid lines) and CO₂ (b) (dashed lines) in calcite slit nanopores as a single component at different pressures and 323 K. Z represents the direction perpendicular to the pore surface, and Z = 0 refers to the center of the pore.

Fig. 4 Snapshots of equilibration state of CH₄ (I) and CO₂ (II) adsorbed in calcite slit nanopores at pressures of 3 (a), 6 (b), 10 (c), 15 (d) and 20 (e) MPa, T = 323 K.

3.2 Competitive adsorption of CH₄ and CO₂ in calcite slit nanopores

The adsorption isotherms of binary mixtures of CH₄ and CO₂ in calcite nanopores are shown in Fig. 5. It can be found that the adsorption tendencies of mixtures of CH₄ and CO₂ are similar to those of the single components, respectively, but that the adsorption loading decreases.

Fig. 5 Adsorption isotherms of binary mixtures of CH₄ (a) and CO₂ (b) in calcite slit nanopores at various temperatures.

The competitive adsorption capacities of CH₄ and CO₂ in a mixture are represented by the selectivity parameter S, which is defined by the following equation:

where x is the fraction of the gas component in the adsorbed phase and y is the fraction of the gas component in the bulk phase. As shown in Fig. 6a, the value of S_CO2/CH4 is very high at the initial low pressures at various temperatures but decreases sharply with an increase in pressure, which indicates that CO₂ molecules have a higher ability to be adsorbed onto calcite surfaces preferentially. The distribution of the adsorption densities of mixed CH₄ and CO₂ in calcite also shows that, in contrast to CH₄, CO₂ molecules have a higher ability to be adsorbed onto the pore surfaces (Fig. 6b).

Fig. 6 (a) Variation in selectivity parameter S of CO₂ over CH₄ as a function of pressure at various temperatures; (b) distribution of adsorption densities of CH₄ and CO₂ in a mixture in calcite slit nanopores at 20 MPa and 323 K. Color of densities: green, CH₄; red, CO₂.

In order to understand the theoretical basis of the different adsorption properties of CH₄ and CO₂ molecules in calcite nanopores, the interaction energies for the adsorption process of each gas molecule with the sorbent were calculated and the results are listed in Table 1. It can be found that the interactions between CO₂ molecules and the pore surfaces are much stronger than those of CH₄, which is why CO₂ molecules are preferentially adsorbed onto the pore surfaces and are adsorbed much more tightly in comparison with CH₄. Electrostatic interactions act as the main factor in the adsorption of CO₂ in calcite nanopores in comparison with CH₄. According to the adsorption characteristics of CO₂, which are shown in Fig. 4II, CO₂ molecules are preferentially adsorbed perpendicularly onto calcite pore surfaces with one of the O atoms of the CO₂ molecule attracted to Ca atoms at the pore surface. According to research work by Lu et al.,³⁷ positively charged Ca²⁺ ions at the calcite surface provide a greater contribution to the adsorption of gases via electrostatic interaction. Thus, vdW interactions and electrostatic interactions both contribute to the adsorption of CO₂ molecules. However, in the case of CH₄, which is a tetrahedral molecule, the C atom is partly attracted to the positive part of the pore surface but is surrounded by four H atoms, which are repelled, so the electrostatic interactions between CH₄ molecules and the calcite surface are much weaker than those of CO₂.

Table 1 Interactions between the gas molecules and the sorbent at different pressures and 323 K

Adsorption pressure (MPa)	CH4 (kcal mol^−1)		CO2 (kcal mol^−1)
	vdW interaction	Electrostatic interaction	vdW interaction	Electrostatic interaction
3	−1.40	−1.72	−0.58	−9.51
6	−1.39	−1.69	−0.55	−8.15
10	−1.58	−1.61	−0.72	−6.74
15	−1.53	−1.59	−1.06	−5.95
20	−1.60	−1.45	−1.04	−5.81

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3.3 Diffusion properties of CH₄ and CO₂ in calcite slit nanopores as a single component

The self-diffusion properties of the molecules were used to study the microscopic diffusion capacities of the gases in calcite slit nanopores using the mean squared displacement (MSD), which is defined by the following equation:where N is the number of particles of the same type and r_i(t) is the particle position when the time is t. Molecules of CH₄ and CO₂ adsorbed close to the pore surface were selected to calculate the MSDs. As shown in Fig. 7, the MSDs of CH₄ molecules are much larger than those of CO₂, which indicates that CO₂ molecules are adsorbed more tightly onto the pore surface in comparison with CH₄. The MSDs of both CH₄ and CO₂ decrease gradually with an increase in pressure at a constant temperature, which is attributed to the increased steric hindrance caused by the increase in the number of adsorbed molecules inside the nanopores. In contrast to CH₄, the range of the MSDs of CO₂ decreases slightly with an increase in pressure, which also explains well that CO₂ molecules remain tightly adsorbed onto the pore surface from the beginning to the end, and a tight adsorption layer of CO₂ exists continuously during the entire adsorption process.

Fig. 7 MSDs of CH₄ (a) (solid lines) and CO₂ (b) (dashed lines) adsorbed close to the surface of calcite slit nanopores versus simulation time at various pressures and 323 K.

The desorption capacities of the gases were determined from the ratio of the gas molecules diffusing out from the calcite slit nanopores by the following equation:

where E_de is the desorption capacity, N_ad is the amount of gas in the initial adsorption equilibrium conformation (P = 20 MPa, T = 323 K), and N_re is the amount of residual gas left in the nanopores after the desorption process. Five systems with different equilibrium pressures of ∼1, 3, 6, 10 and 15 MPa were investigated, respectively, as shown in Fig. 8. It was found that the desorption capacity of CH₄ increased with a decrease in the equilibrium pressure. About 82% of CH₄ could diffuse out from the nanopores freely when the pressure decreased to 1 MPa, whereas the desorption capacity of CO₂ was lower in comparison with that of CH₄, and only about 61% of CO₂ molecules could diffuse out at an equilibrium pressure of 1 MPa. Snapshots of the equilibrium state also show that a tight adsorption layer of CO₂ always exists during the desorption process, which is consistent with the conclusion mentioned above.

Fig. 8 Desorption capacities of CH₄ (black line) and CO₂ (red line) in calcite slit nanopores at different equilibrium pressures and 323 K, with the corresponding simulation snapshots of residual gases in nanopores at 3 and 15 MPa.

3.4 Displacement of adsorbed CH₄ in calcite slit nanopores by CO₂

The microscopic displacement properties of CH₄ in calcite slit nanopores were studied using CO₂ as the “bulk” phase. The initial state of residual CH₄ in nanopores was derived from the equilibrium state of the desorption process at P = 3.0 MPa and T = 323 K. A model of the displacement system with a bulk pressure of CO₂ of 20 MPa is shown in Fig. 9. The Peng–Robinson equation of state was used to calculate the bulk pressure by adjusting the number of CO₂ molecules (Table S1†).³⁸

Fig. 9 Model of the state of the displacement of residual CH₄ in calcite slit nanopores (the residual equilibrium state is P = 3.0 MPa and T = 323 K) by CO₂ at a bulk pressure of 20 MPa and 323 K.

The displacement efficiency was determined by calculating the ratio of the number of displaced CH₄ molecules to the initial number of residual CH₄ molecules in calcite slit nanopores by the following equation:

in which E_dis is the displacement efficiency, N_dis is the number of CH₄ molecules displaced by CO₂ from the nanopores, and N′_re is the number of residual CH₄ molecules in nanopores after the desorption process at P = 3.0 MPa and T = 323 K. As shown in Fig. 10, the displacement efficiency could be as high as 94% when the bulk pressure is 20 MPa, and decreases with a decrease in the bulk pressure. When the bulk pressure is 6 MPa, as CO₂ is in the gas state, the displacement efficiency is 72%. Therefore, it was determined that adsorbed CH₄ in calcite slit nanopores could be easily displaced by CO₂, in particular in the supercritical fluid state.

Fig. 10 Displacement efficiency of residual CH₄ (the residual gas state is P = 3.0 MPa and T = 323 K) by CO₂ in calcite slit nanopores at various displacement bulk pressures and 323 K.

The equilibrium states of gases in calcite slit nanopores after the displacement process at different bulk pressures are shown in Fig. 11, which also clearly indicates that CO₂ molecules could be adsorbed tightly onto the pore surfaces and displace residual CH₄ molecules perfectly. With an increase in the bulk pressure, along with the increased density of supercritical CO₂, the displacement efficiency was enhanced.

Fig. 11 Snapshots of the displacement equilibrium states of gases in calcite slit nanopores at different bulk pressures of 6 MPa (a), 10 MPa (b), 15 MPa (c) and 20 MPa (d), T = 323 K.

4. Conclusion

In this study, the adsorption and diffusion properties of CH₄ and CO₂ in calcite slit nanopores were investigated using GCMC and MD simulation methods. It was found that, in contrast to CH₄, CO₂ molecules have a much higher ability to be adsorbed onto pore surfaces preferentially. Even at low initial pressures, a saturated adsorption layer of CO₂ beside the pore surface was obtained rapidly. The diffusion capacity of CO₂ is much lower in comparison with that of CH₄, and a tight adsorption layer always exists during the entire desorption process. All these differences could be attributed to interactions between the gas molecules and the calcite pore surfaces. The microbehavior of adsorbed CH₄ in calcite slit nanopores during the process of displacement by CO₂ was studied. Residual CH₄ could be effectively displaced by CO₂, and the displacement efficiency could be enhanced with an increase in the displacement bulk pressure.

This study revealed the adsorption and diffusion properties of CH₄ and CO₂ in calcite slit nanopores on a microscopic scale, along with the microscopic displacement properties of residual CH₄ by CO₂, which should be helpful for a better understanding of the microscopic states of gas molecules in shale and might provide guidance for the extraction of shale gas by CO₂-EGR.

Conflict of interest

The authors declare no competing financial interests.

Acknowledgements

The funding by the National Science Fund of China (No. 21473103 and 61575109) is gratefully acknowledged.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c6ra23456a

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