# Molecular Simulation of Coal Molecular Diffusion Properties in Chicheng Coal Mine

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## Abstract

**:**

_{4}and CO

_{2}in coal for the development of coalbed methane, the aim of this paper is to reveal the influence mechanism of pressure, temperature, water content and other factors on the molecular diffusion behavior of gas at the molecular level. In this paper, non-sticky coal in Chicheng Coal Mine is taken as the research object. Based on the molecular dynamics method (MD) and Monte Carlo (GCMC) method, the diffusion characteristics and microscopic mechanism of CH

_{4}and CO

_{2}in coal under different pressures (100 kPa–10 MPa), temperatures (293.15–313.15 K) and water contents (1–5%) were analyzed in order to lay a theoretical foundation for revealing the diffusion characteristics of CBM in coal, and provide technical support for further improving CBM extraction. The results show that high temperature is conducive to gas diffusion, while high pressure and water are not conducive to gas diffusion in the coal macromolecular model.

## 1. Introduction

_{4}and CO

_{2}gases in coal. Diffusion is an important part of gas migration in coal, which is usually related to gas type, moisture, gas pressure and temperature [3].

_{2}, CH

_{4}and CH

_{4}in coal of different rank under stress, and studied molecular simulation of adsorption and diffusion behavior of CO

_{2}, CH

_{4}and CH

_{4}in different coal macromolecular models. Miao Zhang et al. [5] carried out an adsorption–desorption diffusion test of CO

_{2}in coal particles under different temperature and pressure conditions, and used different adsorption and diffusion models to fit and analyze the test results. Dai Xuanyan [6] studied the adsorption and diffusion states of single and mixed components of (1:1) CH

_{4}and CO

_{2}of three minerals (illite, montmorillonite and calcite), and found that the self-diffusion coefficients of CH

_{4}and CO

_{2}first decreased and then increased with an increase in buried depth. Junlin Liu et al. [7] studied the diffusion behavior of CO

_{2}and CH

_{4}gases in the CO

_{2}-ECBM process by taking the pore characteristics of coal reservoirs of 13 coals in Liuzhuang Mine and 7 coals in Qidong Mine in the low-permeability coal-bearing area of Lianghuai, China, as the research object. Kaiyuan Li [8], based on coal gangue samples of different particle-size groups as research objects, simulated the characteristics of CO

_{2}diffusion over time in porous media samples by using laboratory isothermal adsorption experiments, equation fitting, software simulation and other methods. You et al. [9] used molecular simulation to replace a lignite model with graphite surface containing OH, -COOH and carbonyl groups. By analyzing the radial distribution function and diffusion coefficient of H

_{2}O molecules, it was concluded that -COOH was the preferred adsorption site. Hu et al. [10] compared the diffusion characteristics of CO

_{2}and CH

_{4}in coal, and found that the CO

_{2}diffusion coefficient was about 10

^{−9}m

^{2}/s. An Fenghua [11] studied the diffusion coefficient under different stress, concentration gradient, temperature and gas type conditions with the direct steady-state method based on Fick’s law, and the results show that the diffusion coefficient of gas has a negative linear relationship with stress. Xu et al. [12] proposed a new laboratory measurement method for methane diffusion coefficient in coal matrix, using coal matrix flakes instead of coal particles as measurement samples. By means of molecular simulation, Yu Song [13] et al. studied the diffusion characteristics of CO

_{2}and CH

_{4}molecules using a Wise bituminous coal macromolecular structure model, indicating that CO

_{2}and CH

_{4}are mainly diffused via micropores in the coal model. Liu et al. [14] studied the effect of coal type size on gas diffusion of pulverized coal and lump coal under unconstrained conditions, and the results showed that there was a scale effect on gas diffusion in coal. Keshavarz et al. [15] studied the effects of maceral composition and coal rank on the diffusion rate of CO

_{2}and CH

_{4}in 18 Australian bituminous and subbituminous coals. Hu et al. [16] further established a simplified numerical method for a dual-dispersion diffusion model and compared it with the experimental results. Hu et al. [17] studied the self-diffusion and mutual diffusion of CO

_{2}-CH

_{4}mixture via molecular simulation, and the results showed that the self-diffusion coefficient decreased with an increase in gas concentration and increased with an increase in temperature.

_{2}were all greater than that of CH

_{4}, and CO

_{2}was more sensitive to temperature changes. The equivalent adsorption heat of CO

_{2}and CH

_{4}adsorbed in wet coal with different water content decreased with an increase in pressure and increased with an increase in water content [18]. The diffusion mechanism of CH

_{4}and CO

_{2}in coal is analyzed in this paper. The effects of temperature, pressure and water content on the diffusion of CO

_{2}and CH

_{4}on the macromolecular structure of non-stick coal are mainly studied, which is very important for the development of coalbed methane.

## 2. Results and Discussion

#### 2.1. Structural Characterization and Construction of Macromolecular Structure of Coal

^{3}, R°

_{max}0.665%) from the 1502−2 working face of Chicheng Coal Mine were selected. The coal samples were crushed, screened and divided using a crusher and a vibrating screen machine to produce analytical samples with a particle size below 200 mesh. Based on the results of the elemental analysis, Fourier-transform infrared spectroscopy (FT−IR), X-ray photoelectron spectroscopy (XPS) and carbon-13 nuclear magnetic resonance (

^{13}C NMR) experimental characterization, the molecular formula of non-sticky coal in Chicheng Coal Mine was determined to be C

_{207}H

_{181}O

_{32}N

_{3}S (C: 76.39%, N: 1.29%, O: 15.73%, H: 5.61%, S: 0.99). The coal macromolecular model is shown in Figure 1 [18].

^{3}, which closely approximates that of real coal, as shown in Figure 3 [18].

#### 2.2. Theoretical Formula of Gas Diffusion Characteristics of Coal

_{2}and CH

_{4}gases in the non-stick coal large molecular structure was obtained. The root mean square shift (MSD) formula is as follows [21]:

_{i}(t) and r

_{i}(0) are the position vectors at t time and initial time of the i-th gas molecule, respectively, in ps; N

_{t}is the number of molecular dynamics steps; and t

_{0}is the initial time.

^{2}/s.

## 3. Materials and Methods

#### 3.1. Influence of Temperature on Diffusion Performance

_{2}and CH

_{4}at an adsorption pressure of 5 MPa and temperatures of 293.15 K, 298.15 K, 303.15 K, 308.15 K and 313.15 K. Through linear fitting of the mean azimuth shift curve, the diffusion coefficients of CO

_{2}and CH

_{4}at different temperatures can be obtained, as shown in Table 1. The simulation results show that the diffusion coefficients of CO

_{2}and CH

_{4}in the coal samples gradually increase with an increase in temperature. Under the same conditions, the diffusion coefficient of CH

_{4}is smaller than that of CO

_{2}. The reason is that the kinetic energy of gas molecules increases with an increase in temperature, so the movement rate in the pores of coal body increases, which is conducive to the diffusion of gas molecules. The resistance to diffusion is smaller, so a high temperature can promote the diffusion rate of gas in coal.

_{0}refers to the pre-factor, in m

^{2}/s, and E

_{D}is the diffusion activation energy, in kJ/mol.

_{2}is 4.57 kJ·mol

^{−1}and that of CH

_{4}is 3.56 kJ·mol

^{−1}, and the activation energy of CO

_{2}is greater than that of CH

_{4}because the molecular diameter of CO

_{2}is smaller than that of CH

_{4}, which is more favorable for diffusion in micropores. It also shows that the system of CO

_{2}and coal molecules is more dependent on temperature.

_{2}and CH

_{4}in coal, the equipotential surface diagram of CO

_{2}and CH

_{4}at different temperatures with pressure of 5 MPa was obtained according to the trajectory file obtained via simulation calculation, as shown in Figure 7. The absolute value of equipotential value reflects the density of molecular distribution, and a lower equipotential value indicates a wider probability distribution, that is, the diffusion effect is better [22,23].

_{2}gas is 2.079, 1.602 and 1.040, and that of CH

_{4}is 2.294, 1.914 and 1.398, respectively. The equipotential value of CH

_{4}is greater than that of CO

_{2}. The maximum equipotential values of CO

_{2}and CH

_{4}gases in coal gradually decrease with an increase in temperature, which indicates that the two gases can be more widely and evenly distributed in the pores on the surface of coal molecules. The increase in temperature increases the movement frequency of nuclei and electrons inside gas molecules, which leads to the acceleration of gas diffusion rate in coal.

#### 3.2. Influence of Pressure on Diffusion Performance

_{2}and CH

_{4}when the adsorption temperature is 298.15 K and the adsorption pressure is 1 MPa, 3 MPa, 5 MPa, 7 MPa and 9 MPa. Through linear fitting of the mean azimuth shift curve, the diffusion coefficients of CO

_{2}and CH

_{4}under different pressures are shown in Table 2. The simulation results show that the diffusion coefficients of CO

_{2}and CH

_{4}gradually decrease with an increase in pressure, indicating that a high pressure is not conducive to the diffusion of gas in coal, because with an increase in pressure, the average free path of the two gas molecules decreases [22], and they are more likely to collide with the surface of coal, thus inhibiting the diffusion of gas in coal. The diffusion coefficient of CO

_{2}is always greater than that of CH

_{4}under the same pressure.

_{2}and CH

_{4}changing with adsorption pressure at a temperature of 298.15 K and pressures of 3 MPa, 6 MPa and 9 MPa. It can be found from the simulation results that the equipotential values of CO

_{2}and CH

_{4}gradually increase with an increase in pressure. The maximum equipotential values of CO

_{2}at 3 MPa, 6 MPa and 9 MPa are 1.074, 1.766 and 2.196, respectively, and the maximum equipotential values of CH

_{4}are 1.574, 2.374 and 3.089, respectively, indicating that the higher the pressure, the higher the maximum equipotential value. The greater the adsorption capacity of two gases, the stronger the interaction energy between molecules, and the greater the binding degree of gas molecular diffusion. Under the same pressure condition, the equipotential value of CH

_{4}is higher than that of CO

_{2}, indicating that with an increase in pressure, the filling ability of CH

_{4}in the micropores on the coal surface is stronger than that of CO

_{2}, which makes the interaction force between CH

_{4}molecules in the micropores stronger, resulting in a greater degree of diffusion obstruction.

#### 3.3. Influence of Moisture Content on Diffusion Performance

_{2}and CH

_{4}when the adsorption temperature is 298.15 K; the adsorption pressure is 5 MPa; and the water content is 0%, 1%, 2%, 3% and 5%. Through linear fitting of the mean azimuth shift curve, the diffusion coefficients of CO

_{2}and CH

_{4}under different water content conditions were obtained, as shown in Table 3. The simulation results show that with an increase in water content in the coal molecular model, the diffusion coefficients of the two gas molecules CO

_{2}and CH

_{4}decrease significantly, indicating that water is not conducive to the diffusion of gas in the coal seam. This is because the increase in water content not only occupies the pore space and blocks the diffusion channel of gas in the coal, but also the coal matrix will expand and deform after absorbing water. The effective channel is narrowed and the collision chance between the gas and the hole wall increases, so diffusion is blocked. In addition, water will form ice-like clusters when adsorbed at the adsorption sites on the coal surface [22,24], which can make the micropores clogged.

_{2}and CH

_{4}when the temperature is 298.15 K; the pressure is 5 MPa; and the water content is 1%, 2% and 4%. It can be found from the simulation results that when the water content is 1%, 3% and 5%, the maximum equipotential values of CO

_{2}are 1.074, 1.766 and 2.196, and the maximum equipotential values of CH

_{4}are 1.574, 2.374 and 3.089, respectively. The equipotential values of CO

_{2}and CH

_{4}gradually increase with an increase in water content. The reason is that an increase in water content in coal makes the H bond between water molecules stronger, which promotes the interaction force between water molecules and the induction force on CO

_{2}and CH

_{4}molecules. As a result, the potential energy of the system increases with an increase in water content, resulting in the obstruction of gas diffusion. Under the same water condition, the equipotential value of CH

_{4}is higher than that of CO

_{2}because of the hydration of CH

_{4}by H

_{2}O [25].

## 4. Conclusions

_{2}and CH

_{4}gas using a macromolecular structure model of non-cohesive coal in Chicheng Coal Mine, and investigates the influence of different temperatures, pressures and water contents on the diffusion performance of CO

_{2}and CH

_{4}gas adsorbed by coal and the microscopic mechanism. The main conclusions are as follows:

- (1)
- In the dry-mode macromolecular model, the diffusion coefficients of CO
_{2}and CH_{4}gradually increase with an increase in temperature, and a high temperature is conducive to gas diffusion. Under the same conditions, the diffusion coefficient of CH_{4}is lower than that of CO_{2}, and the diffusion activation energy of CO_{2}is 4.57 kJ·mol^{−1}, while that of CH_{4}is 3.56 kJ·mol^{−1}. - (2)
- In the dry-mode macromolecular model, with an increase in pressure, the diffusion coefficients of CO
_{2}and CH_{4}gradually decrease, and the equipotential values of CO_{2}and CH_{4}gradually increase, and a high pressure is not conducive to the diffusion of gas in the coal macromolecular model. - (3)
- In the water-containing coal macromolecular model, with an increase in water content, the diffusion coefficients of CO
_{2}and CH_{4}significantly decrease, and the equipotential values of CO_{2}and CH_{4}gradually increase, and water is not conducive to the diffusion of gas in the coal macromolecular model.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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Gas Type | Diffusivity at Different Pressures /×10^{−9} m^{2}·s^{−1} | ||||
---|---|---|---|---|---|

1 MPa | 3 MPa | 5 MPa | 7 MPa | 9 MPa | |

CO_{2} | 1.04 | 0.96 | 0.89 | 0.85 | 0.83 |

CH_{4} | 0.77 | 0.75 | 0.71 | 0.67 | 0.62 |

Gas Type | Diffusivity at Different Pressures /×10^{−9} m^{2}·s^{−1} | ||||
---|---|---|---|---|---|

1 MPa | 3 MPa | 5 MPa | 7 MPa | 9 MPa | |

CO_{2} | 1.04 | 0.96 | 0.89 | 0.85 | 0.83 |

CH_{4} | 0.77 | 0.75 | 0.71 | 0.67 | 0.62 |

Gas Type | Diffusion Coefficient under Different Water Content /×10^{−9} m^{2}·s^{−1} | ||||
---|---|---|---|---|---|

0% | 1% | 2% | 3% | 5% | |

CO_{2} | 0.89 | 0.76 | 0.66 | 0.55 | 0.40 |

CH_{4} | 0.71 | 0.63 | 0.54 | 0.46 | 0.33 |

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**MDPI and ACS Style**

Yan, J.; Jia, B.; Liu, B.; Zhang, J.
Molecular Simulation of Coal Molecular Diffusion Properties in Chicheng Coal Mine. *Molecules* **2023**, *28*, 6933.
https://doi.org/10.3390/molecules28196933

**AMA Style**

Yan J, Jia B, Liu B, Zhang J.
Molecular Simulation of Coal Molecular Diffusion Properties in Chicheng Coal Mine. *Molecules*. 2023; 28(19):6933.
https://doi.org/10.3390/molecules28196933

**Chicago/Turabian Style**

Yan, Jingxue, Baoshan Jia, Baogang Liu, and Jinyi Zhang.
2023. "Molecular Simulation of Coal Molecular Diffusion Properties in Chicheng Coal Mine" *Molecules* 28, no. 19: 6933.
https://doi.org/10.3390/molecules28196933