Studying the micromechanism of water injection to suppress coal and gas protrusion

The sudden ejection of coal and gas within a short period of time from inside the coal wall to the mining work space during the underground mining process of coal mines is referred to as the phenomenon of coal and gas protrusion.^1–3 The tunnel will be filled with a large amount of gases along with the accumulation of a large amount of coal dust after protrusion, thus resulting in the suffocation of the personnel.⁴ Moreover, in addition to damaging the shaft facilities, ventilation system, power supply, communication, monitoring, and other systems, it can even cause gas and coal dust explosion accidents, which is one of the most serious disasters in coal mines.^5,6 In recent years, in order to reduce gas protrusion, many researchers have put efforts to enhance the coal seam seepage and improve the gas extraction efficiency.^7,8 Studies and experimental investigations have shown that significant changes in the mechanical properties of coal take place along with the pressure distribution at the tunnel front via water injection to wet the coal body. Wetting of the coal body obviously reduces its permeability and the amount of gas gushing out from the coal drops significantly with water playing an obvious obstructive role to the movement of gas.^9,10 Coal is an important source of fossil energy with abundant reserves. Although the world is rich in coal reserves, about half of the world’s coal reserves are accounted for by LRC, such as lignite and sub bituminous coal.¹¹ Therefore, studying the adsorption mechanism of gas and water in low-rank coal can provide a theoretical basis for the basic research on the prevention and control of coal and gas protrusion and can also provide some guidance to improve the efficiency of gas extraction and promote coal bed methane mining.

The adsorption behavior of CH₄ and H₂O molecules in coal is very complex, and both physical tests and molecular simulations have been the focus of current research on coal adsorption behavior. The physical tests concentrate mainly on the effect of external temperature, pressure, and water content on gas adsorption performance. By considering the influence of temperature through the dynamic testing device of coal seam gas adsorption–desorption deformation, Zhang et al. established a model and concluded that the ability of coal to adsorb CH₄ will be inhibited by increased temperature, and increasing temperature results in the decrease of both adsorption and desorption constants.¹² Liu et al. experimentally investigated the quantitative relationship between diffusion flux and temperature for gas-bearing coal particles of different coal ranks, and the results showed that increasing temperature induces large desorption of adsorbed gas.¹³ Zhang et al. conducted experiments on the simultaneous adsorption and swelling deformation of coal during gas adsorption in the presence of conditions having varying water content and obtained that water plays an inhibitory role in the adsorption expansion deformation of coal. With increasing water content, first, the saturated adsorption amount decreased, which was followed by an increase.¹⁴ By using coal samples from Australia and China, Day et al. experimentally observed lower rank coals to be affected more by moisture compared to the higher rank coals, the heat of adsorption is decreased by increasing water content, and the amount of methane adsorbed by coal is affected by the presence of water.¹⁵ However, an experimental study on the effect of liquid water on methane adsorption from coal conducted by Zhang et al. found that for low-rank coals, water had a greater effect on the adsorption capacity of and reduced adsorption of methane but for coals with a high degree of metamorphism, water was found to have a lesser effect on the adsorption capacity, and the presence of liquid water in water-injected coal samples was found to increase methane adsorption.¹⁶ However, mechanistic investigation for the adsorption of CH₄ and H₂O on the surface of low-rank coal by experimental means is difficult. In molecular simulations, the researchers construct molecular models for the coal surface to elucidate the differences in adsorption mechanisms and adsorption properties of CH₄ molecules as well as H₂O molecules based on the molecular structure of coal from a microscopic perspective. The main factors that determine the adsorption properties of coal molecules are the pore structure, degree of metamorphosis, defects, and surface functional groups. Zhou et al. employed density functional theory to compare the adsorption energy of CH₄ and H₂O molecules on coal surfaces having different degrees of metamorphism and concluded that irrespective of order, the adsorption energy of H₂O molecules on coal surfaces was greater than that of CH₄ molecules.¹⁷ Wang et al. simulated the local surface of coal using modified graphite and employed DFT theory to study the influence of defects on the hydrophilicity of coal molecules. The results showed that the hydrophilicity of the local surface of coal increased with defects, and the order of defects in the improvement for hydrophilicity was double vacancy defects > single vacancy defects > Stone–Wales defects.¹⁸ Xiang et al. employed grand canonical ensemble Monte Carlo (GCMC) and molecular dynamics (MD) methods to study the adsorption behavior of the Yanzhou coal model and concluded that all the isothermal adsorption curves of single-component CH₄, CO₂, and H₂O agreed well with the Langmuir model, and the order of relative magnitudes of adsorption was CH₄ < CO₂ < H₂O, with high temperatures being unfavorable for adsorption.¹⁹ Zhao et al. employed the DFT simulation method to investigate the interaction mechanism between the molecules of H₂O, CO₂, CH₄, and various OFGs on the coal surface and obtained that for different small molecules, the order of adsorption stability with OFG was H₂O > CO₂ > CH₄. Compared with other OFG, –COOH was found to have stronger interaction with small molecules.²⁰ Wang et al. observed the strength of adsorption of OFGs on the coal surface on H₂O molecules to follow the order of –COOH > –OH > –CHO > –OCH₃, which was obtained by employing DFT for investigating the interaction of OFGs on the coal surface with H₂O molecules.²¹ 

There are various reports in the literature on the simulations and calculations for the adsorption of H₂O and CH₄ molecules on the surface of LRC molecules, but the analysis of the adsorption of small molecules at the atomic and electronic levels is still relatively rare.^22–24 To investigate the adsorption behaviors of CH₄ and H₂O molecules with initial LRC molecules and coal molecules grafted with different OFGs, the electrostatic potentials and frontier orbitals of different molecular models were analyzed based on DFT, and the interactions of CH₄ and H₂O molecules with different LRC models were compared to explore the adsorption mechanism and provide a theoretical basis for the preventing and controlling of coal and gas protrusion.

The model having CH₃ on a six-ring aromatic cluster was selected as the initial LRC surface during quantum chemical calculations for comprehensive analysis of the effect of OFGs in LRC on the adsorption of CH₄ and H₂O molecules. This initial surface containing only carbon and hydrogen atoms is defined as an unfunctionalized C–LRC structure. After that, four functionalized structures were formed by modifying the C–LRC model with four OFGs, such as OH–LRC, COOH–LRC, C=O–LRC, and OCH₃–LRC.²⁵ The models of five LRC surfaces are shown in Fig. 1.

Density functional theory can be used to simulate and calculate molecular properties and adsorption energies by studying the electronic structure of multi electron systems. Geometry optimization was carried out with fine control by employing Dmol³ as the module with Material Studio being the simulation software. A number of 500 cycles were used to ensure the convergence of geometric optimization. In the calculation of electronic structure, electron exchange interaction was calculated by the Perdew–Burke–Ernzerhof (PBE)^26,27 functional form of generalized gradient approximation (GGA),²⁸ while the Grimme method of PBE generalized function was used for the dispersion correction of DFT in order to reduce the drawback of GGA generalized function, which cannot accurately describe the hydrogen bonds and van der Waals forces.²⁹ DFT semi-core pseudopods and DNP basis groups were, respectively, used to describe the nuclear and valence electrons,³⁰ without limiting electron spin. The SCF convergence control and orbit cutoff accuracy were set to fine, the maximum SCF period was 500, and the smearing value was 0.005 Ha.³¹ The convergence criteria of displacement, force, and energy were 0.005 Å, 0.002 Ha/Å, and 1.0 × 10⁻⁵ Ha, respectively.

Adsorption energy is used to express the adsorption stability of CH₄ and H₂O molecules on different LRC surfaces, and the value is negative due to the exothermic nature of the reaction. The larger the absolute value, the stronger the adsorption and vice versa. The formula for calculating the adsorption energy is as follows:

where E_ads is the adsorption energy of CH₄ and H₂O molecules on different LRC surfaces (kJ/mol) E_A/B is the total energy of the stabilized system after the adsorption of CH₄ or H₂O molecules on different LRC surfaces (kJ/mol), E_A is the energy of different LRC before adsorption (kJ/mol), and E_B is the energy of CH₄ or H₂O molecules before adsorption.

The electrostatic potential is a qualitative indicator of the positive and negative charges of the atoms in different molecules. The projections of van der Waals surface electrostatic potential for CH₄ molecules, H₂O molecules, and different LRC models are shown in Fig. 2. The blue area in the figure is the negative electrostatic potential, i.e., the charge with negative electrical properties is presented by the blue area of the figure with darker the color, the smaller the value of electrostatic potential, implying more sufficient electrons; and the red area in the figure is positive electrostatic potential, the charge with positive electrical properties is presented by red area of the figure with darker the color, the greater the value of electrostatic potential, implying relatively lack of electrons. For a clear view of the projection of electrostatic potential, 0.017 was taken as the value of different model isosurface surfaces, and then, the maximum and minimum values of the electrostatic potential for each model were marked in the figure. As can be seen from Fig. 2, in the C–LRC model, negative electrostatic potential implying less negative charge is exhibited on the benzene ring structure, while the positive electrostatic potential is exhibited by the hydrogen atoms at the edges. The minima for electrostatic potential were generated near the lone pair of electrons of the oxygen atom in each OFG, with all of them being smaller than the negative electrostatic potential of the benzene ring structure in the C–LRC model. In addition, the electrostatic potential maxima were observed on the hydrogen atoms in each functional group, with all of them being larger than the positive electrostatic potential of hydrogen atoms in the C–LRC model. Except for the regions near the hydrogen atoms, which exhibit a positive electrostatic potential, the CH₄ molecule shows a negative electrostatic potential in all other regions. The oxygen atom in the H₂O molecule exhibits a negative electrostatic potential, while the hydrogen atom exhibits a positive electrostatic potential, and the positive and negative electrostatic potentials have large polarization points. It can be predicted that the hydrogen atom down and close to the benzene ring structure of the C–LRC model and the oxygen atom in the OFGs are responsible for the more stable adsorption of CH₄ molecules due to electrostatic attraction. The hydrogen atoms in the H₂O molecule tend to interact with the benzene ring structure of the C–LRC model and the oxygen atoms in the OFGs, while the oxygen atoms tend to interact with the hydrogen atoms in the OFGs. In addition, the value of the electrostatic potential of a hydrogen atom in the H₂O molecule is much larger than that of the hydrogen atom in the CH₄ molecule, while the value of the negative electrostatic potential of an oxygen atom in the H₂O molecule is much smaller than that of carbon atom in the CH₄ molecule. This implies stronger electrostatic attraction between H₂O molecules and different LRC model surfaces, i.e., more stable adsorption of H₂O molecules on the LRC model compared to CH₄ molecules.

According to the frontier orbital theory, the higher the value of the HOMO orbital, the easier it is for the molecule to contribute electrons; and the lower the value of the LUMO orbital, the easier it is for the molecule to accept electrons.³² The frontier orbital energies of different LRC models and molecules of CH₄ and H₂O are presented in Table I. As can be seen from Table I, the LRC models containing the strongly polar OFGs, such as –COOH and –OH, have lower values of the LUMO orbitals, thus indicating that the polar OFGs easily gain electrons and interact easily with polar H₂O molecules, which also indicate weaker interactions with non-polar CH₄ molecules. The LRC models containing –C=O and –OCH₃ with OFGs having weak polarity show large LUMO orbital values, indicating weak electron obtaining ability of –C=O and –OCH₃.

The “easy transition principle” in the frontier orbital indicates that the reaction activity is related to the energy gap between the highest occupied molecular orbital and the lowest unoccupied molecular orbital. The smaller the absolute value of energy difference ΔE between the HOMO orbital of one molecule and the LUMO orbital of the other, the more favorable will be the interaction between the two.³³ The calculated frontier orbital energy differences between different LRC models and CH₄ and H₂O molecules are presented in Table II. As can be seen from Table II, for CH₄ molecules, ΔE₁ < ΔE₂, except for the more polar OFGs, indicating that the HOMO orbitals of different LRC models are prone to interact with the LUMO orbitals of CH₄ molecules. For the H₂O molecule, ΔE₂ < ΔE₁, for all the OFGs, indicating that the LUMO orbitals of different LRC models are prone to interact with the HOMO orbitals of the H₂O molecule. Comparative analysis of ΔE₂ shows that in comparison to the model of unfunctionalized LRC molecule, ΔE₂ between the LUMO orbital of the OFG model and the HOMO orbital of the H₂O molecule is smaller, with the smallest ΔE₂ observed for the strongly polar LRC model. This indicates that the H₂O molecule is easily adsorbed on the strongly polar LRC model, due to the ease of interaction of the H₂O molecule with the strongly polar functional groups via dipole interaction and formation of strong hydrogen bonds, with the COOH–LRC model forming two hydrogen bonds. By comparing the ΔE of CH₄ and H₂O molecules, the energy gaps between the frontier orbitals of different LRC models and H₂O molecules can be seen to be smaller than those between the LRC models and CH₄ molecules, indicating that the strength of adsorption of H₂O molecules in different LRC models is more compared to the CH₄ molecules.

As shown in Fig. 3(a), three adsorption sites were considered on the surface of the C–LRC model, namely, above the C atom of the benzene ring (top), on the C–C bond of the benzene ring (bridge), and in the center of the benzene ring (center). The fourth adsorption site was obtained by placing the CH₄/H₂O molecules in the vicinity of the OFGs. The adsorption of CH₄ and H₂O molecules in different LRC models was described in two and three adsorption directions, respectively, as shown in Fig. 4. In the CH₄ molecule, three hydrogen atoms point to the vacuum direction, i.e., up adsorption direction, and three hydrogen atoms point to the model surface, i.e., down adsorption direction; in the H₂O molecule, two hydrogen atoms point to the vacuum direction, i.e., up adsorption direction, and two hydrogen atoms point to the model surface, i.e., down adsorption direction, and the H₂O molecule was parallel to the model surface, i.e., parallel adsorption direction. When placing CH₄/H₂O molecules, the center of placement was taken for both molecules, and the C and O atoms were taken as the center of placement for CH₄ and H₂O molecules, respectively. The initial distances of the placement centers of CH₄/H₂O molecules adsorbed on the surface of different LRC models were all 3 Å, as shown in Fig. 3(b).

Density functional theory calculations were performed for different adsorption conformations of CH₄ molecules and H₂O molecules on different LRC surfaces to investigate the adsorption of CH₄ molecules and H₂O molecules on the original LRC surface and specific OFG sites. The optimized conformations of CH₄ and H₂O molecules with the lowest energy on different LRC are shown in Figs. 5 and 6, respectively, with the respective corresponding initial conformations being shown in Figs. 4 and 7, and Table III presents the adsorption parameters of the optimal conformations. From Table III, it can be seen that the down adsorption mode is the most stable adsorption configuration of CH₄ and H₂O molecules on different LRC surfaces except for C–LRC and OCH₃–LRC surfaces, indicating the more stable structure of the down configuration with obvious advantages, while the BD adsorption configuration composed of CH₄ and H₂O molecules on C–LRC surfaces with Bridge as the adsorption site is the most stable, which is consistent with the predicted results of electrostatic potential. From Figs. 4 and 5 and Table III, a significantly larger absolute value of adsorption energy of H₂O molecules is observed compared to that of CH₄ molecules, regardless of the presence or absence of OFGs or the nature of the functionalized structure. Together with a significantly smaller adsorption equilibrium distance of H₂O molecules compared to that of CH₄ molecules indicate a relatively stronger force between the H₂O molecules and different LRC model surfaces. The formation of hydrogen bonds between the H₂O molecule and each OFG is the primary reason behind this. The adsorption energy calculation results are consistent with the electrostatic potential and frontier orbital analysis.

Among the oxygen-containing functionalized structures, the trend for the absolute value of adsorption energy for the CH₄ molecule is OCH₃–LRC structure (−9.643 kJ/mol) > C=O–LRC structure (−8.625 kJ/mol) > OH–LRC structure (−7.241 kJ/mol) > COOH–LRC structure (−6.194 kJ/mol), but they are all lower than the unfunctionalized C–LRC structure (−10.749 kJ/mol). Thus, the presence of OFGs reduces the adsorption properties of CH₄ molecules on the surface of LRC, while the degree of reduction varies for functional groups with different polarities. This is due to less electron transfer taking place during the interaction of very stable CH₄ molecule with an ortho-tetrahedral structure with OFGs. The order of adsorption capacity of CH₄ molecules with different LRC model surfaces is C–LRC > OCH₃–LRC > C=O–LRC > OH–LRC > COOH–LRC, which is the order of hydrophobicity of functional groups and is consistent with the order of the absolute magnitude of the adsorption energy of CH₄ molecules at each OFGs calculated by Xiang and Lei³⁴ It shows that hydrophilic functional groups are not favorable for the adsorption of CH₄ molecules, and hydrophobic functional groups have stronger adsorption capability for the adsorption of CH₄ molecules.

For H₂O molecules, the order of adsorption strength to different LRC surfaces is COOH–LRC > OH–LRC > C=O–LRC > OCH₃–LRC > C–LRC. This is also the order of polarity of functional groups and is consistent with the order of absolute magnitude of adsorption energy of H₂O molecules at each OFGs calculated by Cheng et al.³⁵ It shows that the presence of OFGs on the surface of LRC enhances the adsorption of H₂O molecules. The absolute values of adsorption energies of H₂O molecules with OFGs are all greater than those of the unfunctionalized model surfaces (−32.572 kJ/mol) due to the formation of 2, 1, 1, 1, hydrogen bonds between the H₂O molecules and the COOH–LRC, OH–LRC, C=O–LRC, and OCH₃–LRC surfaces, respectively. The magnitude of the absolute value of adsorption energy corroborates the equilibrium distance of the H₂O molecule adsorbed on the OFG.

The Mulliken atomic charges of CH₄ and H₂O molecules after being adsorbed on the surfaces of different LRC models were calculated for illustrating the adsorption behavior of the two molecules. Since the CH₄ and H₂O are neutral molecules, before interaction, the charge of individual molecules is 0 e. Thus, after adsorption on the LRC model, the charge of CH₄ and H₂O molecules is the charge transferred during interaction. The Mulliken charges transferred between different LRC model surfaces and CH₄ or H₂O molecules are presented in Tables IV and V, respectively. Electron losses and electron gains are represented by positive and negative values, respectively.

As can be seen from Table IV, the charge transfers are all less than 0.01 e (−0.005e, −0.006e, −0.005e, −0.002e, and −0.002e, respectively) for the adsorption of CH₄ molecules on different LRC models, while the adsorption equilibrium distances are all greater than 3 Å, reaching the covalent bond length (3–5 Å). This shows that there is no hydrogen bonding in the adsorption configuration, and physical adsorption is responsible for the adsorption of CH₄ molecules on different LRC models with van der Waals forces being responsible for the interactions. This is due to the special orthotetrahedral structure of the CH₄ molecule, where the attraction of electropositive hydrogen atoms to the oxygen atoms in the OFGs is almost canceled out by the repulsion caused by electronegative carbon atoms, thus reducing the interaction with the models. As can be seen from Table V, larger charge transfers of 0.032e and 0.034e are observed for the interaction of the oxygen atom in the H₂O molecule with the hydrogen atom in the OFG, indicating a stronger hydrogen bond. At this time, the value of the LUMO orbital is lower corresponding to the strongly polar OFG, resulting in easier acceptance of electrons by the OFG, and thus, the H₂O molecule also loses electrons, which implies that the charge analysis is consistent with the frontier orbital analysis. In contrast, smaller charge transfers of −0.016 and −0.012 e are observed when the hydrogen atoms in the H₂O molecule interact with the oxygen atoms in the OFG, respectively, indicating weak hydrogen bonds. This is because of the more nucleophilic nature of the oxygen atom in the H₂O molecule compared to that in the OFG, which is consistent with the van der Waals force electrostatic potential projection in Fig. 2 and with the frontier orbital analysis. The charge transfer and hydrogen bond lengths between H₂O molecules and various OFGs follow the order of COOH–LRC > OH–LRC > C=O–LRC > OCH₃–LRC, and it can be concluded that H₂O molecules prefer to interact with hydrogen atoms attached to oxygen atoms in OFGs, i.e., the configuration of O–H bonds in OFGs as hydrogen bond donors and oxygen atoms in H₂O molecules as hydrogen bond acceptors forms the strongest hydrogen bonds. For the adsorption of the H₂O molecule in the C–LRC model, the adsorption equilibrium distance of 3.213 Å is within the range of van der Waals force, indicating that no hydrogen bonds are formed by the H₂O molecule on the surface of the C–LRC model, and during the interaction, the charge transfer is −0.017 e, which is greater than the charge transfer when H₂O molecule adsorbs on the surface of C=O–LRC and OCH₃–LRC models. This is because the adsorption of H₂O molecules on different surfaces is also influenced by the van der Waals forces between the H₂O molecule and the benzene ring as well as by the spatial site resistance effect of the OFGs.

In combination with the calculated adsorption energy and charge analysis of CH₄ and H₂O molecules on different LRC models, it can be concluded that the greater the absolute value of the adsorption energy of different small molecules in the LRC model, the more obvious the charge transfer between the two molecules. The adsorption stability in each model structure shows the trend H₂O > CH₄.

The interaction mechanism of CH₄ and H₂O molecules with different low-rank coal surfaces was analyzed at the atomic and electronic levels by numerical simulation methods, and the following conclusions were drawn.

1. For different LRC models, the order of magnitude for the minimum values of the electrostatic potential on the surface was C=O–LRC < COOH–LRC < OH–LRC < OCH₃–LRC; for the maximum values of electrostatic potential the order was: OH–LRC > COOH–LRC > C=O–LRC > OCH₃–LRC.

2. The HOMO and LUMO orbitals of different LRC models were prone to interact with the LUMO orbitals of CH₄ molecules and the HOMO orbitals of H₂O molecules, respectively, and when adsorption takes place in the presence of strongly polar OFGs, H₂O molecules were the more likely to form hydrogen bonds.

3. For CH₄ molecules, the presence of OFGs on the surface of the LRC model reduced the adsorption properties, and the order of strength for the five structures was C–LRC > OCH₃–LRC > C=O–LRC > OH–LRC > COOH–LRC. For H₂O molecules, the presence of OFGs on the surface of the LRC model enhanced the adsorption properties, and the order of strength for the five structures was COOH–LRC > OH–LRC > C=O–LRC > OCH₃–LRC > C–LRC.

4. For each OFGs, the adsorption of H₂O molecules was more stable compared to the CH₄ molecules. It showed that wetting the surface of LRC via water injection can eliminate or reduce the risk of coal seam outbursts.

This work was supported by the National Key R&D Program of China (Grant No. 2021YFC3001300). The authors would like to thank all the reviewers who participated in the review as well as MJEditor (www.mjeditor.com) for providing English editing services during the preparation of this manuscript.

The authors have no conflicts to disclose.

Jiayun Lun: Provided ideas for the paper; Software simulation; Check the paper. Haoliang Han: Software simulation; Data integration. Xinliang Fang: Writing. Junling Ding: Revision; Language touch-ups. Nan Jia: Check the format of the paper.

Jiayun Lun: Conceptualization (equal); Funding acquisition (equal); Software (equal). Haoliang Han: Data curation (equal); Funding acquisition (equal); Software (equal). Xinliang Fang: Writing – original draft (equal). Junling Ding: Writing – review & editing (equal). Nan Jia: Supervision (equal).

The data that support the findings of this study are available within the article.