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Parameter prediction of factors influencing methane adsorption for coal macromolecules under different water molecular morphologies
*Corresponding author: E-mail address: zhangyilongck@163.com (Y. Zhang)
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Received: ,
Accepted: ,
Abstract
Gas (methane) is a major hazard in coal mines, coexisting with coal seams and often adsorbed within them. The presence of moisture and pre-adsorption forms significantly affects methane adsorption. To optimize and predict key influencing factors, this study used molecular simulation and orthogonal analysis to construct cluster water coal macromolecular models (CY-CW-CMM) and random water coal macromolecular models (CY-RW-CMM) for Chiyu Mine (CY) coal. The intrinsic relationship between the two models and their absolute methane adsorption behaviors were analyzed under varying water content, temperature, and pressure. Fourier transform infrared (FTIR) spectroscopy experiments further verified the functional group changes before methane adsorption. Results showed that as water molecules increased, the maximum electrostatic potential energy of CY-RW-CMM was slightly lower than CY-CW-CMM due to dispersed water molecules occupying high-energy adsorption sites, reducing adsorption space. After methane adsorption, CY-RW-CMM exhibited weaker capacity due to the “roughness” of water molecules in pore structures and strong fusion effects with coal macromolecules. The optimal conditions for methane adsorption were determined as 1% water molecular content, 10 MPa pressure, and 283.15 K temperature, with water content being the dominant factor in both models. FTIR tests showed soaked coal had more oxygen-containing functional groups, including OH-OH hydrogen bonding, -CH2 asymmetric stretching, and increased C=O and benzene ring tertiary substituents, all of which reduced methane adsorption capacity. This study provides valuable insights into improving gas extraction efficiency and understanding coal adsorption mechanisms.
Keywords
Different water molecular morphologies
Methane adsorption
Molecular simulation
Orthogonal analysis method
Parameter prediction for influence factors

1. Introduction
As an important part of traditional fossil fuels, coal plays a pivotal role in global primary energy consumption, and its efficient utilization and clean transformation are crucial for global energy security and sustainable development [1]. Similarly, methane is one of the major hazards in coal mines, and coal is a natural adsorbent [2]. Once methane is adsorbed, the coal body undergoes strong expansion and deformation, causing different degrees of changes in the coal strength, porous media pore structure medium and stress state [3]. However, there are many factors affecting methane adsorption. Water is a major factor; it exists in various forms (adsorbed water, random water, and capillary water) within coal seams, preferentially occupying most of the pore structure and adsorption space, forming a pre-adsorption process, whose the methane adsorption capacities, adsorption rate are closely connection with their own coal properties and coexisting with the methane and competing for adsorption [4].
In recent years, the study of methane adsorption characteristics for coal under the influence of moisture has been the focus of many scholars for a long time [5]. When water penetrates coal seams, the adsorption competition between pre-adsorbed water and methane limited further methane adsorption on the coal matrix, while the unadsorbed water can only maintain the drop in methane adsorption capacity by dipping into the hydrophobic pore structure [6]. Domestic and foreign scholars have conducted a lot of laboratory experiments and molecular simulations in this field [7]. To illustrate the experimental aspect, Wang et al. [8] found that the effect of moisture content on methane adsorption was closely related to the physical properties of coal itself; Chen et al. [9] had all verified that methane adsorption capacities on the coal surface or inside the pore rose with the increasing pressure, on the contrary, the absolute methane adsorption under the same pressure gradually decreased with the growth of temperature and moisture content; Numerous experiments had shown that regardless of the coal rank, the saturation adsorption capacity of dry samples was inevitably greater than that of equilibrium water until the “critical moisture content” was reached, and then the methane desorption rate increased [10]. However, Zhang et al. [11] found that the adsorption of CH4 and CO2 decreases with the increase in moisture content. At a moisture content of 5%, water clusters will form on the coal matrix surface, and at 10%, they will significantly block the nanopores, thereby hindering diffusion.
For the same reasons, with the rapid development of molecular simulation technology, some relevant scholars have also made significant progress in studying the influence law of methane adsorption for coal macromolecules under the influence of water molecules [12], By the ways of certain examples, Ni et al. [13] demonstrated that water molecules were difficult to displace by adsorbed methane molecules, illustrating the relatively high free energy barriers; Feng et al. [14] elucidated the effect of humidity on the adsorption desorption capacity for shale by clarifying that CH4 desorption was impeded regardless of the water molecular contents; Li et al. [15] concluded that water showed stronger affinity than methane for all functional groups, and that increasing water content led to only a gradual reduction in methane adsorption in the remaining pore space, indicating that pore filling was not the dominant cause of competitive adsorption; Chen et al. [16] demonstrated that at the same equilibrium pressure, methane adsorption rate decreased with increasing water molecular content, but the methane adsorption capacity gradually enhanced with increasing adsorption equilibrium pressure. Zhang et al. [17] simulated the occupancy of water in pores larger than 5 Å within the Wiser coal matrix, emphasizing the dominant role of polar functional groups in water adsorption. Existing molecular simulation studies on water-coal-methane interactions mostly focus on a single form of water molecule, without comparing the different impacts of various water forms that actually exist in coal seams. This lack of comparative analysis of different water forms prevents the elucidation of the intrinsic relationship between water distribution and adsorption inhibition strength.
Methods for determining the prediction of a parameter of interest in the field of coal mining are usually orthogonal analysis method and response surface method, with the former being the most commonly used [18]. Wang et al. [19] combined the orthogonal design method with multiple regression analysis, and applied the polar deviation and ANOVA to screen the influencing factors, and determined that the depth of coal seam burial was the dominant factor of methane outflow; Yang et al. [20] determined the contribution rate of each factor by regression-based Shapley value decomposition method, established the regression equation and decomposed the validation. The results showed that the thickness of the coal seam was the decisive factor and the natural factors had a high contribution rate to the amount of methane outflow; Aji et al. [21] thoroughly investigated the effects of TOC and pore size distribution (PSD) of shale samples on the methane adsorption capacity by means of experimental measurements and a variety of statistical analyses, comparing the applicability of different adsorption isotherm models to the adsorption behavior of shale, and found that the Toth model fitted the best; Li et al. [22] conducted orthogonal tests and various tests on coal samples from high gas prone spontaneous combustion coal mines, and the results showed that methane desorption decreased by increasing temperature and increased by increasing pressure, the pore volume and specific surface area varied with temperature and pressure, and change of the characteristic temperature point of desorbed coal samples reflected the enhancement of their spontaneous combustion activity. While most of the above methods can be mentioned as mostly probed at the macroscopic level, studies at the molecular level are limited.
According to the statements of the foregoing, although scholars have achieved breakthrough progress in studying methane adsorption in coal seams (coal macromolecules) under the influence of moisture (water molecules), the research has been overly focused on the basic exploration of a single water form and single-factor analysis. There is a lack of consideration for three aspects: how different water molecule forms regulate methane adsorption at the molecular scale, the quantitative difference analysis of adsorption mechanisms caused by different water molecule distributions, and analogical studies on multi-variable factors and their parameter prediction. Based on these facts, this study mainly adopts molecular simulation methods, taking coal macromolecules from Chiyu Coal Mine (CY) of China Jindi Group Co., Ltd. as the research object. It constructs a cluster water-coal macromolecular model and a random water-coal macromolecular model to clarify the internal connection between the two models and the laws of methane adsorption. Subsequently, orthogonal analysis experiments are used to determine the optimal parameters and main factors of water molecular content, pressure, and temperature. The study aims to verify the effective laws of functional group changes during the methane adsorption process (before molecular simulation) through laboratory experiments of Fourier transform infrared spectroscopy (FTIR), laying the foundation for subsequent laboratory experiments and on-site application of methane adsorption. The research results provide a scientific basis for guiding the macro-scale gas (methane) extraction efficiency.
2. Materials and Methods
2.1. Model construction and internal connection
In this manuscript, the coal samples from the 2# coal seam of the Chiyu coal mine were selected as the object. The following procedure was employed initially: grinding→drying→acid washing→agitation→filtering→inspection→re-drying, etc. The contained structures (carbon spectrum, functional groups and heteroatoms, etc.) were determined through relevant experiments [23], the molecular formula and molecular weight constructed by reusing Chemdraw Software were C286H206O5N4S4 and 3902, respectively, wherein the calculated C, H, O, N, and S with elemental percentages of 87.95%, 5.28%, 2.05%, 1.44%, and 3.28%. The proportions of H/C, O/C, N/C, and S/C were 0.72, 0.017, 0.014, and 0.014, respectively. Given that coal macromolecules exhibit an”approximate” polymeric state structure, the model was constructed and optimized in Materials Studio (MS) through a series of steps, including energy minimization and multiple annealing cycles, to obtain a structure with the lowest possible non-periodic energy (Figure 1a). Subsequently, 12 coal macromolecules were incorporated to form a periodic cell. By applying successive NPT and NVT ensembles combined with several annealing optimizations, the system converged to a coal molecular density of 1.2 g∙cm-3, which falls within the actual density range of coal [24]. The final cell dimensions were a=b=c=40.18 Å. At this stage, the relative atomic coordinates, bond angles, molecular conformations, and pore distributions of the coal macromolecular chains were completely stabilized, thereby establishing a “benchmark invariant structure” for subsequent water molecular insertion.

- (a) optimization and annealing of coal macromolecular model. (b) CY-CW-CMM. (c) CY-RW-CMM. Construction process of coal macromolecular models under different water molecular morphologies.
Under the premise of maintaining an identical unit cell size, two models were established: the Chiyu cluster water–coal macromolecular model (CY-CW-CMM) and the Chiyu random water–coal macromolecular model (CY-RW-CMM). In the CY-CW-CMM, water molecules form stable hydrogen-bonded clusters that anchor near the polar functional groups (hydroxyl and carboxyl groups) of coal macromolecules. This model reflects the multilayer aggregation adsorption mechanism of moisture in coal: water molecules are first adsorbed at the polar sites of coal via electrostatic interactions, and subsequently aggregate into ordered clusters through intermolecular hydrogen bonding, without altering the structural integrity of coal macromolecules. Even after energy minimization, the water molecules remain in a stable “clustered state” (Figure 1b). According to Eq. (1), prior to methane adsorption, increasing water content leads to a simultaneous increase in both the maximum negative van der Waals energy and the maximum negative electrostatic potential energy of the system, with the latter exceeding the former (Table 1). This indicates that intense intermolecular collisions occur among water molecules, accompanied by the aggregation of hydrogen and hydroxide ions. Due to spatial constraints, water molecules form multimolecular aggregates, a fraction of which react with certain coal macromolecular sites. These aggregates and reaction products occupy the pore space within coal macromolecules, thereby reducing the available adsorption volume to 0.16-0.18 cm3∙g-1, as determined by Connolly N₂ and He probe analyses.
| Model | Water molecular content (%) | Van de waals energy (kcal∙mol-1) | Electrostatic potential energy (kcal∙mol-1) |
|---|---|---|---|
| CY-CW-CMM | 1 | -920.205 | -94.19 |
| 2 | -852.832 | -458.77 | |
| 3 | -784.816 | -855.54 | |
| 4 | -730.215 | -1217.91 | |
| 5 | -617.89 | -1627.08 | |
| CY-RW-CMM | 1 | -982.958 | -48.18 |
| 2 | -980.859 | -353.82 | |
| 3 | -955.226 | -690.7 | |
| 4 | -921.554 | -1081.02 | |
| 5 | -888.913 | -1442.41 |
In contrast, in CY-RW-CMM, water molecules are randomly distributed, without a fixed aggregated structure. They freely diffuse to fill the free space in coal pores and enable coal-water molecules to form an organic whole and optimize. After optimization, they are in a dispersed state and fully integrate into the pore structure (Figure 1c). With the increase in water molecule content, the maximum negative van der Waals energy and maximum negative electrostatic potential energy also increase. However, the maximum electrostatic potential energy of CY-RW-CMM is lower than that of CY-CW-CMM, while the maximum negative van der Waals energy shows the opposite trend (Table 1). This suggests that ions decomposed from water molecules may undergo vigorous reactions with certain functional groups in coal macromolecules, occupying high-energy adsorption sites and the entire pore structure, which leads to an even smaller adsorption space (with a value of 0.15 cm3∙g-1-0.17 cm3∙g-1 as calculated using the Connelly N₂ probe and He probe). Therefore, when considering the fugacity state of water molecules, a single water molecule may be anchored around hydroxyl or carboxyl groups, which does not necessarily reflect the trend of water molecule state changes. If multiple water molecules can aggregate with each other and do not completely flow into the pore structures of other coal macromolecules, when intense collisions occur, the water molecules will diffuse into other pore structures; this indicates that the two models represent different occurrence states of water molecules in coal. The water molecular energy after interaction was calculated according to Eq. (1)
Where: Ewater - Water molecular energy after interaction; Ecoal-water- Energy from mixing coal and water molecules; Ecoal - coal molecular energy.
2.2. Simulation method and adsorption process
To simulate and analyze the methane adsorption law of the two types of models. Using the giant canonical monte carlo (GCMC) method and considering methane is as an incompressible gas, the interactions of coal macromolecules with the two types of water molecule models were represented through the L-J (12-6) potential function, and then the interatomic distance parameter () and energy parameter () were taken arithmetically and geometrically averaged Eqs. (2-4), respectively [25].
where: - distance between atoms i and j; - truncation radius of the L-J potential function (12-6), 15.5 Å; and and - depth and radius of the potential well of L-J (12-6); and and - methane molecular diameter and intermolecular distance; and - interaction energies between molecules i and j of methane.
The adsorption process was chosen to use the fix pressure setting in the Sorption module to select the range of force field and number of steps, in which the force field and charge were chosen to be COMPASS II and Use Current, respectively, the electrostatic potential energy and van der Waals energy were chosen to be Ewald and Atom Based, and the number of equilibrium steps and production steps were both 4 × 108, and the range of pressures was set to be 0.001 MPa-10 MPa (interval 2 MPa), and the conversion relationship between pressure and fugacity was considered [26]; the temperature range was set at 283.15 K-303.15 K (interval: 5 K), and each pressure and temperature were simulated five times, and the average value was taken as the final absolute adsorption simulation result (Eq. 5), which provided a guarantee for determining the three main parameters of water molecular content, temperature and pressure.
Where: : absolute adsorption capacity (mmol·g⁻1); n: number of methane adsorbed for the corresponding pressure; M: relative molecular weight of individual coal molecules (g·mol⁻1); N: Number of coal molecules added
3. Results and Discussion
3.1. Methane absolute adsorption capacities by coal macromolecules under water molecular morphologies
Whether for the CY-CW-CMM model or the CY-RW-CMM model, at the same temperature, methane adsorption capacity basically reached a steady state once a specific pressure was attained as pressure increased. When the water molecule content was identical, the methane adsorption capacity decreased with rising temperature. With an increase in water molecular content, the absolute methane adsorption capacity consistently exhibited a decreasing trend. These observations demonstrate that the presence of water molecules and elevated temperature exert a significant inhibitory effect on methane adsorption by coal macromolecules, while pressure plays a promotional role in enhancing methane adsorption capacity. These results are consistent with the findings reported in previous studies [27,28]. Meanwhile, under high-pressure and low-temperature conditions, the driving force for methane adsorption is strong enough to allow methane to access the limited remaining space not occupied by water molecules. In contrast, under low-pressure and high-temperature conditions, the competitive advantage of water molecules is overwhelming, and the increased thermal motion of methane further impedes its adsorption (Figures 2a-l).

- (a) CW,2MPa. (b) RW,2MPa. (c) CW,4MPa. (d) RW,4MPa. (e) CW,6MPa. (f) RW,6MPa. (g) CW,8MPa. (h) RW,8MPa. (i) CW,10MPa. (j) RW,10MPa. (Absolute methane adsorption capacity is shown in Figure a-j.) (k) Methane adsorption under different conditions in CW. (l) Methane adsorption under different conditions in RW. (m) Pore structure distribution in the CW. (n) Pore structure distribution in the RW and attached the modified version next to the original image.

- (a) CW,2MPa. (b) RW,2MPa. (c) CW,4MPa. (d) RW,4MPa. (e) CW,6MPa. (f) RW,6MPa. (g) CW,8MPa. (h) RW,8MPa. (i) CW,10MPa. (j) RW,10MPa. (Absolute methane adsorption capacity is shown in Figure a-j.) (k) Methane adsorption under different conditions in CW. (l) Methane adsorption under different conditions in RW. (m) Pore structure distribution in the CW. (n) Pore structure distribution in the RW and attached the modified version next to the original image.

- (a) CW,2MPa. (b) RW,2MPa. (c) CW,4MPa. (d) RW,4MPa. (e) CW,6MPa. (f) RW,6MPa. (g) CW,8MPa. (h) RW,8MPa. (i) CW,10MPa. (j) RW,10MPa. (Absolute methane adsorption capacity is shown in Figure a-j.) (k) Methane adsorption under different conditions in CW. (l) Methane adsorption under different conditions in RW. (m) Pore structure distribution in the CW. (n) Pore structure distribution in the RW and attached the modified version next to the original image.
The difference was that when water molecular contents were increased from 1% to 5%, absolute adsorption capacity decreased in both models, with the decline in absolute adsorption capacity being more pronounced in CY-RW-CMM than in CY-CW-CMM. The two main reasons were as follows:
(1) with the addition of water molecules, the free pore structure of the CY-CW-CMM model basically remained unchanged, indicating that the larger the range of pore size structure, the corresponding peaks were close to 0. In the skeleton macroporous structure after immersion, the corresponding peaks then decreased, proving to be favorable for methane adsorption. In the small pore structure of the skeleton, water molecules were completely active in these ranges, and if water molecules competed with each other, the transport effect was greatly limited. The immersed water molecules caused the specific surface areas of coal macromolecules to be reduced, absolute adsorption capacities to be decreased, and corresponding peak values to be relatively increased (Figure 2m). Similarly, in CY-RW-CMM, with the increase of water molecules, the range of free pore structure was gradually smaller, then the resulting skeleton large and small pore structure were shifted to smaller region, and peaks corresponding to the range of the skeleton large pore structure were relatively lower, on the contrary, the peak corresponding to the range of small pore in the skeleton increased, indicating that the accumulation for a large number of water molecules produced certain “rough structure” or existed in closed form, which caused transport interference and reached an inaccessible state, then specific surface areas were weaker and occupied larger proportion of the pore structure, resulting in lower absolute adsorption capacity capacities and further enhancement of the peak (Figure 2n).
(2) Adding the same number of water molecules to the two types of models, the ratios of H/C and O/C increased significantly, and oxygen atoms of water molecules with strong electronegativity and hydrogen atoms reacted with coal macromolecules, so that not only occupied the pore structure, but also changed the aromaticity, which led to reduction in absolute methane adsorption capacities of and weakened the polar interactions and affinities between the methane and coal macromolecules. Both of them, for H/C, a higher ratio means that coal macromolecular structures were richer in hydrogen-rich groups. In CY-CW-CMM, hydrogen-rich groups may form interactions with water molecules, such as hydrogen bonding. Due to the intervention of water molecules, some of the active sites that can interact with methane molecules were occupied, resulting in a decrease in absolute methane adsorption capacities; in CY-RW-CMM, the interaction between water and coal macromolecules was wider, and a large amount of random water molecules formed “water film,” which further impeded the methane diffusion to the pore interior and adsorption, and the reduction of absolute methane adsorption capacities was even more significant compared with those in CY-CW-CMM. Meanwhile, for O/C, the larger proportion indicated that coal macromolecules contained more oxygen-containing functional groups (carboxyl and hydroxyl groups). In CY-CW-CMM, water molecules preferentially combined with oxygen-containing functional groups to form local water-functional group complexes, which changed the distribution of electron clouds and the spatial environment around the functional groups, thus weakening the adsorption between methane and functional groups and decreasing the absolute methane adsorption capacities. When in CY-RW-CMM, the water molecules not only combined with the oxygen-containing functional groups, but also filled into the pore structure, which greatly compressed the methane adsorption space, and changed the polarity and surface energy of the whole pore system due to the presence of water, which were not conducive to the non-polar methane adsorption, resulting in a significant decrease in absolute methane adsorption. This process analysis provided an important reference for which specific functional group had an effect on methane adsorption.
3.2. Parameter prediction of factors influencing methane adsorption for two types of models
3.2.1. Orthogonal experimental design and prediction model construction
Orthogonal test method is carried out in multivariate optimization tests, based on mathematical statistics and orthogonality principles, to select typical training models from a huge amount of test data. The data in the orthogonal table are used to scientifically arrange to compare multiple variables simultaneously, so as to obtain the best test results with the smallest number of tests, which is usually combined with polar analysis and ANOVA to clarify the effectiveness of the results of orthogonal tests [29]. According to the above simulation results of the absolute methane adsorption capacities, the method was used to identify the water molecular content, temperature, and pressure as the main influencing factors of the simulation results, and each influencing factor did not interfere with the others. The regression analysis equation (Eq. 6) was used to effectively predict the influence of the main factors on the absolute methane adsorption capacities.
where: - absolute methane adsorption capacities; - the intercept term; - the regression coefficient, which represents the effect of each independent variable on the dependent variable; - water molecular content; - pressure; - temperature; and - the error term, which represents the random variation not explained by the two types of models.
Water molecular contents (), pressures (), and temperatures () were used as the three factors in the orthogonal design of absolute methane adsorption capacities, and five levels were set for each factor. The orthogonal level design with 5 levels and 3 factors was used with 25 sets of test scenarios (L25 (53)). By constructing the matrix, a total of 25 test scenarios were randomly selected to predict and analyze the main impact parameters of the regression for each of the two types of models (Table 2).
| No. | Parameters(j) | CY-CW-CMM | ||
|---|---|---|---|---|
| Water molecular content (%) | Pressure (MPa) | Temperature (K) | Absolute methane adsorption capacity (mmol∙g-1) | |
| 1 | 1 | 2 | 283.15 | 1.39 |
| 2 | 1 | 4 | 288.15 | 1.58 |
| 3 | 1 | 6 | 293.15 | 1.66 |
| 4 | 1 | 8 | 298.15 | 1.69 |
| 5 | 1 | 10 | 303.15 | 1.69 |
| 6 | 2 | 2 | 288.15 | 1.21 |
| 7 | 2 | 4 | 293.15 | 1.36 |
| 8 | 2 | 6 | 298.15 | 1.42 |
| 9 | 2 | 8 | 303.15 | 1.45 |
| 10 | 2 | 10 | 283.15 | 1.65 |
| 11 | 3 | 2 | 293.15 | 1.05 |
| 12 | 3 | 4 | 298.15 | 1.15 |
| 13 | 3 | 6 | 303.15 | 1.22 |
| 14 | 3 | 8 | 283.15 | 1.48 |
| 15 | 3 | 10 | 288.15 | 1.43 |
| 16 | 4 | 2 | 298.15 | 0.94 |
| 17 | 4 | 4 | 303.15 | 1.06 |
| 18 | 4 | 6 | 283.15 | 1.36 |
| 19 | 4 | 8 | 288.15 | 1.34 |
| 20 | 4 | 10 | 293.15 | 1.34 |
| 21 | 5 | 2 | 303.15 | 0.85 |
| 22 | 5 | 4 | 283.15 | 1.11 |
| 23 | 5 | 6 | 288.15 | 1.17 |
| 24 | 5 | 8 | 293.15 | 1.18 |
| 25 | 5 | 10 | 298.15 | 1.15 |
| No. | Parameters(j) | CY-RW-CMM | ||
| Water molecular content (%) | Pressure (MPa) | Temperature (K) | Absolute methane adsorption capacity (mmol∙g-1) | |
| 1 | 1 | 2 | 283.15 | 1.34 |
| 2 | 1 | 4 | 288.15 | 1.32 |
| 3 | 1 | 6 | 293.15 | 1.39 |
| 4 | 1 | 8 | 298.15 | 1.38 |
| 5 | 1 | 10 | 303.15 | 1.35 |
| 6 | 2 | 2 | 288.15 | 1.05 |
| 7 | 2 | 4 | 293.15 | 1.15 |
| 8 | 2 | 6 | 298.15 | 1.22 |
| 9 | 2 | 8 | 303.15 | 1.20 |
| 10 | 2 | 10 | 283.15 | 1.41 |
| 11 | 3 | 2 | 293.15 | 0.81 |
| 12 | 3 | 4 | 298.15 | 0.91 |
| 13 | 3 | 6 | 303.15 | 0.90 |
| 14 | 3 | 8 | 283.15 | 1.10 |
| 15 | 3 | 10 | 288.15 | 1.11 |
| 16 | 4 | 2 | 298.15 | 0.58 |
| 17 | 4 | 4 | 303.15 | 0.60 |
| 18 | 4 | 6 | 283.15 | 0.83 |
| 19 | 4 | 8 | 288.15 | 0.85 |
| 20 | 4 | 10 | 293.15 | 0.82 |
| 21 | 5 | 2 | 303.15 | 0.46 |
| 22 | 5 | 4 | 283.15 | 0.70 |
| 23 | 5 | 6 | 288.15 | 0.73 |
| 24 | 5 | 8 | 293.15 | 0.73 |
| 25 | 5 | 10 | 298.15 | 0.72 |
3.2.2. Analysis of parameter prediction for main influencing factors on methane adsorption
3.2.2.1. Extreme variance analysis
Based on the above theory of orthogonal tests, the method of extreme variance analysis (EVA) (also known as visual analysis) is used to reveal the effects of each type of factor on the results of the two types of models in orthogonal tests. That is to say, the results corresponding to the same level of each factor are averaged, and then the minimum average value is subtracted from the maximum average value of each level to obtain the extreme deviation values. These values can reflect the influence of different levels of a given factor on the index of interest; the larger the values, indicate that the degree of influence (weight) of the factor on the test results were more significant [30]. The formula for their calculations is as follows (Eqs. 7-8):
Where: - the extreme deviation in the column; - the arithmetic mean of the test results corresponding to the factor at the level of the orthogonal table; - the sum of the test indicators corresponding to the level of the factor of the orthogonal table; - the number of occurrences of a factor level in the orthogonal table.
After completing the analysis of the orthogonal tests for the two types of models, Table 3 presented the interactions of three-level parameters (including water molecular contents, pressures, and temperatures). As to select specific levels of the three variables, the variables for each parameter were shown in Figure 3, among which in Figure 3(a), it was found that the absolute methane adsorption capacities of both types of models induced by the water molecular content were linearly negatively correlated, and the larger the slopes of the linear negative correlation were, the smaller the absolute methane adsorption capacities were, then the larger the linear fits were and the more precise they were, which mean that under the conditions of same water molecular content, CY-RW-CMM reduced the absolute methane adsorption capacities more than CY-CW-CMM, and the inhibition effect was the most obvious; The pressure-induced absolute methane adsorption capacities for both models were found to be positively correlated and consistent with the Langmuir type I curve (Eq. 9) in Figure 3(b), and there fits were compatible with the patterns of previous studies in both experimental and simulation results [31]. The difference was found that from the two types of models and Eq. 9 that when the multiplications of ab were smaller and the values of c were larger, then the absolute methane adsorption capacities were even larger, suggesting that more methane was adsorbed by the CY-CW-CMM than by the CY-RW-CMM over a certain range of pressures, whereas the fitting degrees were both the same (R2=0.995); Linear negative correlations were found in Figure 3(c) for the absolute methane adsorption capacities of both models caused by temperature, and the larger the slopes of the linear negative correlation and the higher the degrees of fit, the smaller the absolute methane adsorption capacities, indicating that CY-RW-CMM similarly reduced more absolute adsorption capacity capacities than CY-CW-CMM under the same temperature conditions, and the thermal movement of methane was intensified, leading to decrease in the attraction between them and the adsorbent surface. However, the magnitude of the negative correlation slope corresponding to temperature was not as significant as the magnitude of the negative correlation slope corresponding to water molecular content, proving that water molecular content had the greatest effect on the absolute methane adsorption capacity.
| CY-CW-CMM | Water molecular content | Pressure | Temperature | CY-RW-CMM | Water molecular content | Pressure | Temperature |
|---|---|---|---|---|---|---|---|
| K1 | 8.00 | 5.43 | 7 | K1 | 6.76 | 4.24 | 5.37 |
| K2 | 7.10 | 6.25 | 6.72 | K2 | 6.03 | 4.67 | 5.06 |
| K3 | 6.33 | 6.83 | 6.58 | K3 | 4.82 | 5.06 | 4.88 |
| K4 | 6.04 | 7.14 | 6.35 | K4 | 3.68 | 5.25 | 4.8 |
| K5 | 5.45 | 7.26 | 6.27 | K5 | 3.33 | 5.4 | 4.51 |
| k1 | 1.60 | 1.09 | 1.4 | k1 | 1.35 | 0.85 | 1.07 |
| k2 | 1.42 | 1.25 | 1.34 | k2 | 1.21 | 0.93 | 1.01 |
| k3 | 1.27 | 1.37 | 1.32 | k3 | 0.96 | 1.01 | 0.98 |
| k4 | 1.21 | 1.43 | 1.27 | k4 | 0.74 | 1.05 | 0.96 |
| k5 | 1.09 | 1.45 | 1.25 | k5 | 0.67 | 1.08 | 0.9 |
| Rj | 0.51 | 0.36 | 0.15 | Rj | 0.69 | 0.23 | 0.17 |
Note: Ki and ki are the sum and mean of absolute methane adsorption capacity at level i, respectively; Rj is the range. All K1-K5, k1-k5 and R values are in mmolg-1.

- (a) Water molecular content. (b) Pressure. (c) Temperature. (d) Extreme variance analysis. Variation in absolute methane adsorption capacities due to three influential parameters and extreme variance analysis.
To effectively determine whether the results were reasonable or not, based on the above Eq. 9 and the results of calculating the extreme deviation () in the above table (Table 4), the analysis of the factors influencing the absolute methane adsorption of the two types of models were obtained from the strongest to the weakest order of the water molecular content, pressure and temperature (Figure 3d). From the results of the extreme difference values of the two types of models, it can be seen that the extreme difference values of CY-RW-CMM under the conditions of water molecular content and temperature were larger than those of CY-CW-CMM, which indicates that the inhibition of methane adsorption by the former was obvious. However, for pressure, the higher the CY-CW-CMM extreme difference value than that of CY-RW-CMM, the larger the adsorbed methane adsorption, which verified the validity of the above results. Similarly, the larger the absolute value of the results of the extreme differences in the water molecular content corresponding to the three factors in the two types of models, the more the water molecular content influences and inhibits the absolute methane adsorption capacity. To more intuitively analysis the effect of each factor on absolute methane adsorption capacities for coal macromolecules, according to the results of the extreme variance analysis in the above table (Table 4) to do the analysis of the effect of each factor on the change of absolute methane adsorption capacities of the analysis of the graph (Figures 3a-c), respectively, the optimal combination of the level of the three factors was determined to be the water molecular content of 1%, the pressure of 10 MPa and the temperature at 283.15 K.
| Model | dfj | P | ||||
|---|---|---|---|---|---|---|
| CY-CW-CMM | Water molecular content | 0.781 | 4 | 0.195 | 198 | <0.01 |
| Pressure | 0.451 | 4 | 0.113 | 114 | <0.01 | |
| Temperature | 0.069 | 4 | 0.017 | 17 | <0.01 | |
| CY-RW-CMM | Water molecular content | 1.736 | 4 | 0.434 | 674 | <0.01 |
| Pressure | 0.177 | 4 | 0.044 | 68 | <0.01 | |
| Temperature | 0.081 | 4 | 0.02 | 31 | <0.01 |
Note: Statistical significance was assessed at α = 0.05. P < 0.05 indicates statistical significance (all effects shown are significant; P < 0.01 as reported in the table).
3.2.2.2. Analysis of variance
The results of the extreme variance analysis described above were limited to distinguishing data fluctuations that occur as a result of the effects of the level of each variable, and did not allow for the determination of the real error, the evaluation of the differences between the means, or the parametric dominance. To overcome their limitations, the results of the experiment were subjected to ANOVA in order to perform error analysis more accurately, as well as to make a judgment on the significance of the factors. This approach (ANOVA) involved consulting the table to derive the critical value , given the significance level . The value of each factor was then calculated and compared with the critical value. If > and the greater the difference between the two, the greater the influence of the factor on the indicator and the higher the significance [32]. The sum () and the variance () of squared differences of each parameter were calculated as follows (Eqs. 10-11). The freedom degree of each parameter was .
Based on ANOVA and the fitted equations (Eq. 6) for absolute methane adsorption capacities under the three parameters, Figure 4 and Table 4 observed that the P-values of water molecular content, pressure, and temperature were less than 0.05 in both types of models, which were proved to be the key factors affecting the absolute methane adsorption capacities. The F test critical value table determined F0.05 (4, 4) = 6.3882. For CY-CW-CMM corresponding to water molecular content, pressure and temperature, the magnitudes of F-value relationship were 198>114>17>6.3882, among the three significant influencing factors, the water molecular content was the significant influencing factor; The F-value magnitude relationships of CY-RW-CM corresponding to water molecular content, pressure and temperature were 674>68>31>6.3882, which also proved that the water molecular content was a principal influencing factor for the absolute methane adsorption capacity. In addition, by comparing the sum of squares of water molecular content, pressure, and temperature with their errors in the two types of models, it can be concluded that the dominant factor affecting the absolute methane adsorption capacities was the water molecular content.

- (a) CY-CW-CMM. (b) CY-RW-CMM. Regression standardized prediction.
3.3. Experimental changes in functional groups before methane adsorption
3.3.1. Fourier transform infrared indoor experiment
Based on the aforementioned prediction of 1% moisture content and the identified key controlling factors, fresh coal samples were prepared as follows. First, a raw coal block was crushed using a crusher and sieved to obtain particles with a size of 100 mesh. A 5 g portion was placed into the first sealed bag as the original coal sample. Another 5 g portion was then taken, and distilled water was dropped onto its surface until the total weight reached 5.05 g. This sample was transferred to a beaker and subsequently dried in an oven at 60°C for 24 h; it was designated as the water-sprayed coal sample (corresponding to the molecular model CY-CW-CMM). Finally, a portion of coal exceeding 5 g was soaked in a beaker of pure water for 7 days, followed by vacuum filtration and natural air-drying in a fume hood at room temperature for 72 h. After drying, the sample was stored in the third sealed bag and designated as the water-soaked coal sample (corresponding to the molecular model CY-RW-CMM) (Figure 5).

- Three modes of coal sample handling.
FT-IR tests were carried out on the three coal samples, and the overall trends of the transmittance curves were basically the same (the spectral features were basically in the range of wave numbers from 400 cm-1 to 4000 cm-1), which were mainly divided into four regions (Figure 6), including hydroxyl groups (3600 cm-1∼3000 cm-1), aliphatic hydrocarbons (3000 cm-1∼2800 cm-1), oxygen-containing functional groups (1800 cm-1∼1000 cm-1) and aromatic hydrocarbons (900 cm-1∼700 cm-1).

- Results of FT-IR test for three coal samples.
3.3.2. Distribution characteristics of major functional groups
3.3.2.1. Hydroxyl groups (3600 cm-1∼3000 cm-1)
The hydroxyl groups in the three coal samples (raw coal, water-sprayed coal, and water-soaked coal) primarily exist in the forms of OH–π hydrogen bonds, OH–OH hydrogen bonds, cyclic hydrogen bonds, and OH–N hydrogen bonds (Figures 7a-c). Among these, OH–OH hydrogen bonds constitute the largest proportion: 51.28% in raw coal, 57.48% in water-sprayed coal, and 61.09% in water-soaked coal, with the highest value observed in the latter. This increase can be attributed to the fact that, when water molecules reach suitable distances and spatial orientations, they readily form self-associated hydrogen bonds with hydroxyl groups in coal. These OH–OH hydrogen bonds occupy adsorption sites that would otherwise be available for methane, thereby reducing methane adsorption capacity. In contrast, OH–π hydrogen bonds, which facilitate the interaction between methane and the aromatic ring structures of coal through van der Waals forces and thus enhance adsorption, are most abundant in raw coal (24.03%), but decrease in the water-treated samples (16.78% in water-sprayed coal and 15.45% in water-soaked coal), further weakening methane adsorption. Hydrogen bonds with cyclic structures (≈22%) and OH–N hydrogen bonds (the least abundant type) exhibit no significant differences among the three samples, and thus exert relatively minor effects on adsorption (Figure 7d).

- (a) Raw coal. (b)Water-sprayed coal. (c) Water-soaked coal. (d) Percentage of –OH bonding types (%). FT-IR fitting spectra of hydroxyl structures.
3.3.2.2. Aliphatic hydrocarbons (3000 cm-1∼2800 cm-1)
Coal contains methyl (-CH₃), methylene (-CH₂), and methine (-CH) groups, which exhibit characteristic peaks corresponding to asymmetric/symmetric stretching vibrations (Figures 8a-c). The key change is that the proportion of -CH₂ asymmetric stretching vibrations in water-soaked coal increases significantly: 31.38% (raw coal) →34.90% (water-sprayed coal)→47.48% (water-soaked coal) Figure 8(d). This indicates that water treatment may promote the formation of short-chain alkanes in coal; these short-chain alkanes fill the pore structure of coal and compress the methane adsorption space.

- (a) Raw coal. (b) Water-sprayed coal. (c) Water-soaked coal. (d) Percentage of aliphatic C–H structures (%). Fourier fitting spectra of aliphatic hydrocarbon structures.
In contrast, the symmetric stretching vibration of -CH in water-soaked coal decreases to the lowest value (12.96%). This may be attributed to the enhanced hydrophilicity of coal; water molecules occupy the surface of the coal matrix, which weakens the methane adsorption capacity.
3.3.2.3. Oxygen-containing functional groups (1800 cm-1∼1000 cm−1)
Oxygen-containing functional groups in coal are primarily composed of phenols, alcohols, ethers, and esters (Figures 9a-c), with the most significant variations observed in two categories: (1) conjugated C=O, whose proportion increases markedly after water treatment, reaching 38.21% in water-soaked coal compared with 28.11% in raw coal; and (2) phenolic/ether C–O, which reaches its maximum proportion in water-sprayed coal (25.82%), representing an increase of 9.24% relative to raw coal (16.58%) (Figure 9d).

- (a) Raw coal. (b) Water-sprayed coal. (c) Water-soaked coal. (d) Percentage of oxygen-containing structures (%). Fourier fitting spectra of oxygen-containing functional group structures.
Overall, the proportion of polar oxygen-containing functional groups follows the order: water-soaked coal (80.25%) > water-sprayed coal (73.78%) > raw coal (66.51%). These polar groups may alter the electron cloud distribution within coal macromolecules, thereby weakening the non-polar interactions between methane (a non-polar molecule) and coal [33]. Moreover, the increased aromatic C=O stretching vibrations observed in water-soaked coal (23%) may occupy high-energy adsorption sites, which further reduces methane adsorption capacity.
3.3.2.4. Aromatic structure (900 cm-1 to 700 cm-1)
Aromatic structures in coal primarily consist of pentasubstituted benzene rings (864–865 cm⁻1), tetrasubstituted benzene rings (833–836 cm⁻1), trisubstituted benzene rings (785–807 cm⁻1), and disubstituted benzene rings (747–748 cm⁻1) (Figure 10). Among these, the most pronounced variation is observed in the proportion of trisubstituted benzene rings, which increases progressively from 34.25% in raw coal to 36.04% in water-sprayed coal and 37.41% in water-soaked coal. This trend suggests that higher degrees of substitution may alter the electron cloud density of aromatic rings, thereby weakening the van der Waals interactions between methane molecules and the aromatic structures. Consequently, raw coal, with its relatively lower degree of ring substitution, exhibits a stronger methane adsorption capacity compared with the water-treated samples.

- (a) Raw coal. (b) Water-sprayed coal. (c) Water-soaked coal. (d) Percentage of aromatic structures (%). Fourier fitting spectra of aromatic structures.
In addition, the proportion of tetrasubstituted benzene rings increases in water-soaked coal (10.93%) relative to raw coal (8.21%), while the proportions of pentasubstituted and disubstituted benzene rings remain essentially unchanged. These findings indicate that water-induced variations in substituent groups within the aromatic structures contribute to the overall reduction in methane adsorption capacity in the water-sprayed and water-soaked coal samples.
4. Conclusions
Construction of two models and before methane adsorption can be found that with the increase of water molecular contents, average negative van der Waals energy and electrostatic potential energy increased significantly, but CY-RW-CMM model of the maximum electrostatic potential energy slightly less than CY-CW-CMM model, and maximum negative van der Waals on the contrary, the former was strong collision due to the water molecules, occupying the entire coal macromolecular pore structure and adsorption space position, the latter was according to the water molecular position dispersion, occupied the whole coal macromolecular high adsorption site and produced the smaller adsorption space.
Both CY-CW-CMM and CY-RW-CMM exhibit a significant decrease in absolute methane adsorption capacity at higher water molecule content and temperature, yet an increase in adsorption capacity at higher pressure. The adsorption capacity of CY-RW-CMM is notably lower, primarily because random water molecules in this model form “rough structures” and “water films” in coal (via hydrogen bonds/functional group interactions with coal), which fill the pores. For CY coal, clustered water (CY-CW-CMM) retains free pores; random water (CY-RW-CMM) is dispersed and occupies high-energy sites. At the same water molecule content, the random water model has a lower adsorption capacity, indicating that the morphology of water exerts a stronger influence on adsorption than water molecular content.
The negative slopes corresponding to the effect of water molecular content were significantly larger than those corresponding to the effect of temperature (KCY-RW-CMM > KCY-CW-CMM), which illustrated a more obvious inhibitory effect of the water molecular content on the absolute adsorption capacity of CY-RW-CMM; the optimal combination of the three level factors was determined to be the water molecular content of 1%, the pressure of 10 MPa and the temperature at 283.15 K, and the dominant factor affecting the absolute methane adsorption capacities were both the water molecular content for two types of models.
Three coal sample groups tested via infrared spectroscopy showed significant changes in reactive groups after water treatment. Compared with raw and water-sprayed coal, water-soaked coal had more polar oxygen-containing functional groups (the most abundant oxygen component), indicating stronger methane adsorption inhibition when coal absorbs sufficient water. Occupancy ratio results confirmed that OH-OH hydrogen bonding (self-bonding), -CH₂ asymmetric stretching vibration, and increased C=O/benzene ring tertiary substitutions are the main functional groups reducing methane adsorption capacity.
Acknowledgment
This study was supported by the Project of Education Department of Guizhou Province (KY[2019]164), Natural Science Foundation of the Education Department of Liaoning Province (LNKQZ20222334), National Natural Science Foundation of China (52274204, 52104195), China Association for Science and Technology “Young Talent Promotion Project” (2022QNRC001).
CRediT authorship contribution statement
Yilong Zhang: Conceptualization, Funding acquisition, Supervision, Writing - review & editing. XinPu Ding and Yang Xu: Conceptualization, Methodology, Investigation, Data curation, Formal analysis, Visualization, Writing - original draft. Jingyi Liu, Zhenyang Liu, Zhibin Yang and Gang Bai: Investigation, Writing - review & editing.
Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Data availability
The data and materials used to support the findings of this study are available from the corresponding author upon request.
Declaration of generative AI and AI-assisted technologies in the writing process
The authors confirm that there was no use of artificial intelligence (AI)-assisted technology for assisting in the writing or editing of the manuscript and no images were manipulated using AI.
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