Molecule Simulation of CH₄/CO₂ Competitive Adsorption and CO₂ Storage in Shale Montmorillonite

Abstract

The main source of production in the middle and late stages of shale gas extraction is the adsorbed gas in shale, and the adsorbed gas in shale mainly comes from organic matter casein and clay minerals in shale; therefore, this paper uses sodium-based montmorillonite to characterize the clay minerals in shale and study the CH₄ adsorption law in clay minerals, and this study has certain guiding significance for shale gas extraction. In addition, this paper also conducts a study on the competitive adsorption law of CH₄ and CO₂, and at the same time, predicts the theoretical sequestration of CO₂ in shale clay minerals, which is a reference value for the study of CO₂ burial in shale and is beneficial to the early realization of carbon neutral. In this paper, the slit model of sodium-based montmorillonite and the fluid model of CH₄ and CO₂ were constructed using Materials Studio software, and the following two aspects were studied based on the Monte Carlo method: Firstly, the microscopic adsorption behavior of CH₄ in sodium-based montmorillonite was studied, and the simulations showed that the adsorption capacity of montmorillonite decreases with increasing temperature, increases and then decreases with increasing pressure, and decreases with increasing pore size. CH₄ has two states of adsorption and free state in the slit. The adsorption type of CH₄ in montmorillonite is physical adsorption. Secondly, the competitive adsorption of CH₄ and CO₂ in sodium-based montmorillonite was studied, and the simulations showed that the CO₂ repulsion efficiency increased with increasing CO₂ injection pressure, and the CO₂/CH₄ competitive adsorption ratio decreased with increasing pressure. The amount of CO₂ storage decreased with increasing temperature and increased with increasing CO₂ injection pressure.

1. Introduction

Shale oil and gas are kinds of unconventional oil and gas resources with considerable geological reserves. The adsorbed state is one of the main states of CH₄ occurrence in shales (the other state is the free state). The proportion of adsorbed gas in different shale gas reservoirs varies from 20% to 85% of the whole reservoir, with an average of about 50% [1]. The pore structure of shale gas reservoirs is complex, with the most developed micro- and nano-pores; therefore, the storage and transport of shale gas are very different compared to conventional gas. Conventional core experiments do not accurately describe the gas adsorption characteristics and mechanisms in shale, while molecular simulations can accurately study the adsorption patterns of molecules under micro- and nano-pores and make quantitative characterization for the adsorption studies of shale gas.

Liu, Y., Liu, B., Xiong, J., Srinivas, G., et al. conducted molecular simulations of CH₄ adsorption in graphite oxide slits using graphene oxide instead of kerogen and summarized the effects of temperature, pressure, pore size, and functional group type on CH₄ adsorption [2,3,4,5]. Jin Z.H., Xu C.X., Xiong, J., Liang, L.X., et al. constructed molecular models of clastic minerals such as quartz and studied the microscopic adsorption patterns of shale gas in the pores of clastic minerals [6,7,8,9]. Babatunde, K.A., Tian, S.C., Sui, H., Katti, D.R., Tang, X., Shi, Y., Collell, J., Ru, X., Ungerer, P. et al. developed molecular models of different types of kerogen by molecular simulation software, analyzed the influence of variables such as temperature and pressure on the adsorption capacity of caseinates, ranked the adsorption capacity of different types of caseinates, and revealed the influence of water content changes on the adsorption of multi-component gases in caseinates. The effect of water content on the adsorption of multicomponent gases in the roots was revealed [10,11,12,13,14,15,16,17,18]. Xiong, J., Feng, D., Lv, Z.L., Huang, T., Ren, J.H., Greathouse, J.A., Li, W., et al. developed molecular models of clay minerals such as montmorillonite, illite, and kaolinite by molecular simulation software, and the effects of pore size, temperature, water content, and different compositions on the adsorption behavior of CH₄ and CO₂ in the slit model of each mineral type were discussed, and the strength of the adsorption capacity of the three clay minerals was summarized [19,20,21,22,23,24,25]. In summary, initially, some scholars proposed to replace the dry casein with graphene-containing oxygen functional groups to make it closer to the organic matter structure of shale. In recent years, some scholars have established specific kerogen models and clay mineral models to study the adsorption pattern and mechanism of CH₄ in them and analyze the effects of pore size, temperature, and pressure on adsorption.

At the present stage, scholars in China and abroad have mainly conducted research on the adsorption of organic matter and clay minerals in shale, and these studies did not delve into the effects of factors such as temperature and pressure on the competitive adsorption of CH₄ and CO₂. Therefore, this paper focuses on the microscopic adsorption behavior of CH₄ in sodium-based montmorillonite and the competitive adsorption behavior of CH₄ and CO₂. The study of the microscopic adsorption behavior of CH₄ provides a theoretical basis for the understanding of shale gas seepage patterns and storage characteristics; the study of the competitive adsorption behavior of CH₄ and CO₂ not only provides a theoretical basis for the enhanced extraction of shale gas by CO₂ injection but also reveals the sequestration capacity of shale clay minerals for CO₂ and provides a research idea for the geological storage of CO₂, and geological carbon sequestration is a way of CO₂ emission reduction.

2. Simulation Model and Potential Energy Parameters

2.1. Model Building

Shale has the following three main components: organic matter, clay minerals, and non-clay minerals, while clay minerals are dominated by illite, montmorillonite, and illite/smectite formation [26,27,28,29,30]. In this paper, a montmorillonite cell model (shown in Figure 1a) was constructed by using the molecular simulation software, Material Studio, with sodium-based montmorillonite as the skeleton. The specific parameters of this cell model are a = 5.23 Å, b = 9.06 Å, c = 12.5 Å, α = 90°, β = 99°, and γ = 90°, and the atomic coordinate parameters are shown in

Table 1. Spatial coordinates of each atom and cation in the cell.

Atoms	c = 1.25 nm			c = 1.53 nm
	x	y	z	x	y	z
Al	0	3.02	12.5	0	3.02	15.5
Si	0.472	1.51	9.58	0.472	1.51	12.58
O	0.122	0	9.04	0.122	0	12.04
O	−0.686	2.615	9.24	−0.686	2.615	12.04
O	0.772	1.51	11.2	0.772	1.51	14.2
O(OH)	0.808	4.53	11.25	0.808	4.53	14.25
H(OH)	−0.103	4.53	10.812	−0.103	4.53	13.182
Na+	0	4.53	6.25	0	4.53	9.25

[31]. The montmorillonite slit model was then established by the steps of the tessellation of the cell, establishing the interface model, and performing supercell (shown in Figure 1c), where H denotes the pore size of the slit model, and the values of H taken in this paper are 1 nm, 2 nm, 3 nm, 4 nm, 5 nm, 6 nm, 8 nm, and 10 nm, respectively. The specific parameters of the final slit model are x = 52.30 Å, y = 45.30 Å, and z varies from 32 Å to 122 Å with different slit aperture sizes. To study the competitive adsorption pattern of CH₄ and CO₂ in sodium-based montmorillonite, this paper also established CH₄ and CO₂ models (shown in Figure 1d,e) based on the establishment of sodium-based montmorillonite. The bond length and bond angle parameters of the two fluid models are labeled in Figure 1d,e.

2.2. Potential Energy Selection and Parameters

In this paper, the L-J potential function is used for the simulation, and the various potential and charge parameters that appear in the simulation are shown in

Table 2. Potential energy parameters and charges of each atom [32] Reproduced with permission from Wang J, Acta Mineral. Sin.; published by the Chinese Academy of Sciences, 2011.

Types	Atom Types	(ε/KB)/K	σ/nm	q/c
CH4	CH4	148.1	0.373	0
CO2	C	28.129	0.2757	0.6512
	O	80.507	0.3033	−0.3256
Montmorillonite	Al	0	0	3
	Mg	0	0	2
	Si	3153	0.184	1.2
	O	156	0.317	−1
	Na+	100	0.259	1

[32]. Both the montmorillonite model and the two-fluid models are assumed to be rigid bodies during the simulation because both CH₄ molecules and CO₂ molecules are electrically neutral, but the sodium ions in the montmorillonite model are positively charged, so the interaction between the two fluids and the atoms in montmorillonite needs to consider long-range charge Coulomb forces in addition to short-range van der Waals forces, and the L-J potential function is described as [33]:

$$E={\epsilon }_{ij}\left[{\left(\frac{{\delta }_{ij}}{r_{ij}}\right)}^{12}-{\left(\frac{{\delta }_{ij}}{r_{ij}}\right)}^6\right]+\frac{q_i{q}_j}{4\pi {\epsilon }_0{r}_{ij}}$$

(1)

where: $\delta$ and $\epsilon$ denote the potential energy parameter, which is related to the type of interacting atoms; $r_{ij}$ denotes the distance between two atoms, nm; $q_i$ and $q_j$ denote the atomic charge in the system, C; ${\epsilon }_0$ denotes the dielectric constant, 8.854 × 10⁻¹² F/m.

2.3. Model Verification

A low-pressure isothermal nitrogen adsorption simulation was performed using the established montmorillonite model, and the results obtained from the simulation were compared with those obtained from sodium-rich montmorillonite nitrogen adsorption experiments in Wyoming, USA [33] to verify the authenticity of the model. The results of the comparison are shown in Figure 2 (both experimental and simulated conditions are T = 334 K and P = 0–30 MPa), and it can be concluded that although there is an error between the isothermal adsorption simulation results and the experimental results, the error between the two is small, within 10%, indicating that the established sodium-rich montmorillonite model is more realistic and can represent the actual situation in the subsurface. The reason for the error is that the real sodium-rich montmorillonite in the subsurface has a more complex pore structure compared with the model.

3. Study on Adsorption Law of CH₄

3.1. Simulation Methods and Conditions

In this paper, two molecular simulation methods are used: the first one is the giant regular Monte Carlo simulation, and the second one is the molecular dynamics simulation, based on which the Sorption module of the Material Studio software is used to realize the simulation of CH₄ adsorption by montmorillonite. The total number of simulation steps was 1 × 10⁶, of which the first 1.0 × 10⁵ steps were used for the equilibrium simulation of the system and the second 9.0 × 10⁵ steps were used for the process simulation. Six temperature points (278 K, 298 K, 318 K, 338 K, 358 K, and 378 K), six pressure points (5 MPa, 10 MPa, 15 MPa, 20 MPa, 25 MPa, and 30 MPa), and eight pore size points (1 nm, 2 nm, 3 nm, 4 nm, 5 nm, 6 nm, 8 nm, and 10 nm) were set for the simulation.

The critical temperature and pressure of CH₄ are 190.55 K and 4.59 MPa, and the temperature and pressure points simulated in this paper are higher than the critical temperature and pressure of CH₄. The CH₄ is in a supercritical state during the simulation, and there is a large gap between the total adsorbed gas and the excess adsorbed gas in this state. Therefore, the total adsorbed gas needs to be converted into excess adsorbed gas [34]. The conversion formula is as follows:

$$n_{ex}=N-{\rho }_g(V_a+V_g)\times {10}^3/MS$$

(2)

where $n_{ex}$ is the excess adsorption capacity, mmol/m²; N is the simulated total gas volume, mmol/m²; ${\rho }_g$ is the gas phase density, g/cm³; $V_a+V_g$ is the free space volume of the adsorption system, cm³; M is the molecular mass of the gas, g/mol; S is the specific surface area of the cell, m².

3.2. Analysis of Simulation Results

(1)

Effect of pressure on CH₄ adsorption under different pore sizes of montmorillonite slit

Figure 3 shows the total adsorption and excess adsorption of CH₄ at different pressures with different slit pore sizes, respectively. From Figure 3b, it can be found that the adsorption capacity gradually increases from 0.0 MPa to 10.0 MPa when the pressure increases and reaches the peak at 10 MPa, then shows a decreasing trend in the interval from 10.0 MPa to 30.0 MPa. Since the adsorption of CH₄ by montmorillonite slit is an interfacial phenomenon, the excess adsorption capacity will rise first and then fall. During the adsorption process, two kinds of forces exist at the interfacial interface between the montmorillonite slit wall and CH₄. One is the mutual gravitational force between CH₄ molecules, which is called gravitational force A. The other is the gravitational force of the montmorillonite slit wall on CH₄, which is called gravitational force B. When gravitational force A is smaller than gravitational force B, a potential trap occurs, and most of the CH₄ accumulates on both sides of the montmorillonite slit under the action of gravitational force B. This is due to the imbalance of gravitational forces. This phenomenon of the uneven density distribution of adsorbents due to the unbalanced gravitational force is the adsorption phenomenon. When the pressure is greater than 10.0 MPa, the bulk phase density of CH₄ becomes larger, so the gravitational force A gradually becomes larger, and the corresponding gravitational force B starts to decrease. This change in the gravitational force relationship directly affects the density distribution of CH₄ and the excess adsorption of montmorillonite slits. It is also shown in Figure 3b that the larger the pore size of the montmorillonite slit, the lower the capacity of the excess adsorption of CH₄. The three-dimensional configuration of the montmorillonite slit for some pore sizes is shown in Figure 4.

(2)

Effect of temperature on CH₄ adsorption under different pore sizes of montmorillonite slits

Figure 5 shows the values of CH₄ adsorption at different temperatures for different montmorillonite slit pore sizes, respectively. Figure 5b shows that the excess adsorption decreases with increasing temperature. This is because, when the temperature increases, the effect of molecular kinetic energy change on the adsorption capacity of montmorillonite takes the major part, and the adsorption capacity is inversely proportional to the change of temperature, with the higher the temperature, the lower the adsorption capacity instead. From Figure 5b, it is easy to find that the adsorption capacity peak at the temperature of 278.0 K. From the comparison of the excess adsorption capacity of different montmorillonite slit pore sizes, the best adsorption effect of montmorillonite on CH₄ was observed at the pore size of 1 nm and the worst at 10 nm.

(3)

Density variation under different pore sizes of montmorillonite slit

Figure 6 shows the density comparison of CH₄ under different pore sizes of the montmorillonite slit. It can be found in Figure 6 that the peak of CH₄ density distribution is located near the wall of the montmorillonite slit. Moreover, when the width of the oxidized montmorillonite slit pore size is 1 nm, most of the CH₄ is attached to both sides of the slit and exists in the adsorption state. When the slit width is 2~5 nm, most of the CH₄ is still attached to the slit wall, but some of it is also dispersed in the pores in the middle of the slit. When the slit width is 6~10 nm, the density of CH₄ dispersed in the pores increases some more compared with 2~5 nm. Therefore, there are two occurrences of CH₄ in the slit of montmorillonite with different pore sizes. In the small pore size, CH₄ is mainly in the adsorbed state, and as the slit width increases, the free state of CH₄ becomes more, and the two occurrences in the slit will coexist.

(4)

Heat of adsorption

The heat generated by the adsorption process is the heat of adsorption, and the value of the heat of adsorption can measure the degree of the strength of adsorption. Higher values of the heat of adsorption indicate stronger adsorption. Figure 7 represents the average equivalent heat of adsorption of CH₄ at different montmorillonite slit pore sizes. From Figure 7, it can be found that the larger the slit pore size is, the less the average equivalent heat of adsorption of CH₄ is, and the decreasing trend of the heat of adsorption tends to level off gradually. When the slit pore size was 1 nm, the average equivalent heat of adsorption of CH₄ was 23.458 KJ/mol, and when the slit pore size was 10 nm, the average equivalent heat of adsorption of CH₄ was 8.849 KJ/mol, both of which were lower than the standard for chemisorption (42.0 KJ/mol), indicating that the adsorption of CH₄ on different montmorillonite slit pore sizes was physical adsorption. In addition, the adsorption heat curve also shows that the adsorption capacity of the small pore size slit is stronger than that of the large pore size slit, and the adsorption capacity of the slit decreases with the increase in pore size.

4. Study of Competitive Adsorption Pattern of CH₄ and CO₂

4.1. Simulation Method and Conditions

The pore size distribution curve of montmorillonite samples (Figure 8) shows that the pore size of montmorillonite is relatively small, dominated by micropores and mesopores less than 10 nm, and peaks between 5 nm and 6 nm, which indicates that the size of montmorillonite pores in shale is mainly concentrated in 5~6 nm [26]. Therefore, in this paper, a montmorillonite slit of 5 nm was used to conduct a simulation study of the competitive adsorption of CH₄ and CO₂. The simulation method used is consistent with Section 2.1. Two sets of conditions were set for the simulation: one set with a constant temperature of 298 K, the constant initial pressure of 5 MPa for CH₄, and eight pressure points (0 MPa to 7 MPa) for CO₂ pressure, whose group purpose was to analyze the CO₂ adsorption capacity in the mixed phase of CH₄ and CO₂ and to predict the theoretical CO₂ sequestration in montmorillonite. In another group with a constant temperature of 298 K and the initial pressures of CH₄ and CO₂ set to the same value, with 6 pressure points (5~10 MPa), the purpose of this group is to calculate the CO₂/CH₄ competitive adsorption ratio.

4.2. Analysis of Simulation Results

(1)

CO₂ adsorption capacity in mixed-phase

Figure 9 shows the total adsorption and excess adsorption curves of the two fluids with a constant initial pressure of CH₄ and varying initial pressure of CO₂. From Figure 9, it can be found that the excess adsorption of CH₄ gradually decreases (from 0.019 mmol/m² to 0.006 mmol/m²) and the excess adsorption of CO₂ gradually increases (from 0.00 mmol/m² to 0.052 mmol/m²) as the initial pressure of CO₂ increases. In addition, the CO₂-repelling CH₄ efficiency curve (shown in Figure 10) was obtained by computational processing in this paper, and Figure 10 shows that the CO₂ repelling efficiency increases with the increase in the initial pressure of CO₂. Figure 11 shows the comparison curves of the CO₂ storage volume at different temperatures and different CO₂ injection pressures, from which it can be concluded that the CO₂ storage volume gradually decreases with the increase in temperature, and the higher the temperature, the smaller the decrease in storage volume. With the increase in CO₂ injection pressure, the storage volume gradually increases, and the higher the pressure, the smaller the increase in storage volume.

(2)

CO₂/CH₄ competitive adsorption ratio

The simulation was carried out under the condition that the initial pressures of CH₄ and CO₂ were equal and increased synchronously. The total and excess adsorption of CH₄ and CO₂ at each pressure point are shown in Figure 12. As the total pressure gradually increased from 10 MPa to 20 MPa, the excess sorption of CH₄ increased from 0.007 mmol/m² to 0.013 mmol/m², the excess sorption of CO₂ increased from 0.014 mmol/m² to 0.019 mmol/m², and the excess sorption of both CH₄ and CO₂ increased with the increase in pressure. Figure 13 shows the scatter plot of the pressure versus CO₂/CH₄ competitive adsorption ratio and its regression curve, from which it can be concluded that the CO₂/CH₄ competitive adsorption ratio gradually decreases with the increase in pressure.

5. Conclusions

(1)

At constant temperature, the excess adsorption of CH₄ in the montmorillonite slit increases first and then decreases with increasing pressure and reaches a peak between 10.0 MPa and 15.00 MPa. At constant pressure, the excess adsorption decreases gradually with increasing temperature and is at a peak at 278.0 K. The adsorption effect decreases as the pore size becomes larger, with the maximum adsorption of 1 nm pore size.

(2)

Comparing the changes in the CH₄ density at the 1 nm~10 nm pore size, it was found that the peak of the CH₄ density appeared at the slit wall after the simulation of the adsorption process was performed. The CH₄ in the slit of montmorillonite has two occurrences and is mainly in the adsorption state. With the increase in the slit width, the free state of CH₄ becomes more and the slit appears to have two occurrences coexisting.

(3)

The adsorption of CH₄ on the slit of montmorillonite is physical adsorption; the adsorption capacity of the slit decreases with increasing pore size.

(4)

When the adsorbent is the coexistence of CH₄ and CO₂, the initial pressure of CH₄ is constant, and the repulsion efficiency of CO₂ increases with the increase in the initial pressure of CO₂; it is also analyzed that the amount of CO₂ storage decreases with the increase in temperature and increases with the increase in injection pressure.

(5)

When the initial pressure of CH₄ and CO₂ are equal, it can be concluded from the curve of pressure and the CO₂/CH₄ competitive adsorption ratio that the competitive adsorption ratio is negatively correlated with the pressure, and the higher the pressure the lower the competitive adsorption ratio.