## 1 Introduction  
CH\({}_{4}\) is a high-quality, efficient energy source and is also the second-largest greenhouse gas after carbon dioxide [1, 2]. CH\({}_{4}\) emissions account for about 18% of the global emissions of greenhouse gases, and their development and utilization are of great significance for clean energy and carbon emission reduction [3]. CH\({}_{4}\) is mainly stored in coal seams in adsorbed and free states, of which more than 80-90% is stored in adsorbed states. Research on the adsorption capacity of coal for methane is an important basis for the calculation and exploitation of coalbed methane reserves [4].  
In recent years, numerous scholars have carried out a lot of research on the characterization of CH\({}_{4}\) adsorption by coal. [PERSON] et al. quantitatively characterized the methane adsorption characteristics using microporous filling and monolayer adsorption theory and clarified the mechanism of methane adsorption in adsorption pores [5]. [PERSON] et al. investigated the effect of water on the adsorption characteristics of coal and found a linear relationship between the CH\({}_{4}\) adsorption content of coal and the water content [6]. [PERSON] et al. studied the adsorption characteristics of gas after the addition of low-temperature liquid nitrogen, utilizing a low-temperature liquid nitrogen adsorption instrument, and concluded that the temperature decreases the content of oxygen-containing functional groups [7]. [PERSON] studied the adsorption of methane by coal through molecular simulation and concluded that the porosity, temperature, water, and ash content of coal affected the adsorption of methane by coal [8]. [PERSON] et al. investigated the effect of water on the desorption/adsorption of CBM and found that the effect of water on adsorption in coal reservoirs is limited by the pore structure and that the mode of coal-water interaction in micropores is the core of CBM adsorption [9]. [PERSON] et al. concluded that the adsorption amount of the coal body is inversely proportional to the water content by conducting coal rock adsorption experiments [10]. [PERSON] et al. investigated the change in the adsorption energy of coal bodies under different temperature and pressure conditions and concluded that the physical properties and internal chemical structure of coal bodies would affect the change in gas adsorption energy [11]. [PERSON] et al. investigated the adsorption of CH\({}_{4}\) by nanopores using molecular simulation and concluded that the change in CH\({}_{4}\) adsorption was related to temperature, pressure, and burial depth, and was consistent with the reasons for the change in adsorption amount and adsorption heat [12]. [PERSON] et al. investigated the relationship between the pore structure of the coal body and the adsorption of the gas at different temperatures. Researchers used low-temperature nitrogen adsorption and isothermal adsorption experiments to study the free energy of adsorption and entropy of adsorption of coal samples, concluding that both decreased gradually with an increase in temperature [13]. [PERSON] et al. found that initial free gas pressure affects the heat of adsorption of the coal body, and the larger the initial gas pressure is, the smaller the heat of adsorption is [14].  
The existing studies mainly focus on the CH\({}_{4}\) adsorption characteristics under the influence of single factors of temperature and water content, and there are a lack of studies on the influence of the coupling of the two. Therefore, in this paper, we use a coal sample from the Ping coal mine (PM) as the research object and utilize molecular simulation methods to study the effects of different temperatures, water contents, and the coupling of the two on the CH\({}_{4}\) adsorption characteristics.