## 1 Introduction  
Coal and gas outburst is one of the common disasters in the mining process, which severely affects the production system and restricts the safe and efficient production of coal mines [1; 2; 3; 4; 5; 6; 7; 8; 9]. Since the first coal and gas outburst occurred in France in 1834 [10], many coal and gas outburst accidents have been reported around the world [11; 12; 13], of which about 50% occurred in China [14; 15]. There are various factors affecting coal and gas outbursts, among which the pore structure of the coal body, the strength of the coal body, and the adsorption characteristics of the coal body significantly affect coal and gas outbursts [16; 17; 18; 19; 20]. As coal has a double pore structure, it is generally believed that the gas in coal has three states, namely free, adsorbed, and absorbed states. The adsorbed gas accounts for a large ratio, which is about 80% to 90% of the total. The form of physical adsorption is distributed on the surface of coal body fractures, micropores, and molecular particles. Because of the existence of adsorbed gas, the physical and mechanical properties of the coal body become very complicated, which not only changes the mechanical properties of the gas-containing coal but also causes changes in the ground stress field and the gas pressure field in the coal seam. Therefore, it is of particular significance to have an in-depth understanding of the adsorption characteristics of coal. A large number of laboratory studies have been carried out by scientists in China and overseas on the adsorption characteristics of coal [21; 22; 23; 24; 25; 26]. The pore structure of coal [27; 28], the adsorption characteristics of gas [29], the pore volume, and specific surface area of coal determine the adsorption performance of coal to some extent. At the same time, the water content, the microscopic composition of the coal, the temperature, and pressure have a great influence on the adsorption characteristics of the coal. [PERSON] and [PERSON] [30] studied the effect of coal water content and composition on the adsorption characteristics of methane-carbon dioxide mixed gas and found that water could enhance the ability of the coal matrix to adsorb gas. The composition and the molecular structure of coal affect the adsorption capacity of coal to gas, whereas the microscopic composition of coal affects the diffusion rate of adsorbed gas [31]. Current studies have shown that gas adsorption capacity decreased with increasing temperature [32] and was positively correlated with pressure over a particular pressure range [33]. To further elucidate the adsorption characteristics of the coal body, the kinetics of gas adsorption in the coal body have been studied extensively, which theoretically described the adsorption characteristics of the coal body [34; 35; 36]. The French chemist [PERSON] proposed a one-component gas adsorption model, which is also known as the Langmuir model [37]. Due to the simplicity and clear physical meaning of each parameter of this model, the corresponding equation of this model has been widely used to describe the adsorption kinetics of gas on the surface of coal [38]. Given that coal bed gas contains multiple gas ingredients, some researchers have proposed the multi-component adsorption equation. The widely used multi-component adsorption model includes the extended-Langmuir equation and the ideal adsorbed solution theory. Since the gas outburst from the coal seam of the mine is predominated with CO\({}_{2}\) and CH\({}_{4}\), the gases used in the laboratory simulation are mainly CO\({}_{2}\) and N\({}_{2}\). It is critical to understand the adsorption characteristics of different gases. Therefore, to understand the adsorption characteristics of CO\({}_{2}\), CH\({}_{4}\), and N\({}_{2}\), the adsorption properties of coal to different gases have been intensively studied in China and overseas [39; 40; 41; 42]. For example, experiments by [PERSON], [PERSON] et al.