## 4 Results and Discussions
### Effect of CO\({}_{2}\) Injection on Coalled Methane Production
#### 4.1.4 Variation of Reservoir Permeability  
The scientific connotation of the effectiveness of CO\({}_{2}\)-ECBM mainly includes the CO\({}_{2}\) storage mechanism and storage capacity, and the increase rate of CH\({}_{4}\) yield, which are also the basic theoretical and technical problems faced by CO\({}_{2}\)-ECBM. The effectiveness  
Figure 11: 300 days, 500 days, 1000 days, 1500 days (**a**) Distribution cloud diagram of adsorbed \(CH_{4}\) in \(CBM\) (**b**) adsorption cloud diagram of adsorbed \(CH_{4}\) in \(CO_{2}\)-\(ECBM\) (**c**) adsorption cloud diagram of adsorbed \(CO_{2}\) in \(CO_{2}\)-\(ECBM\).  
of CO\({}_{2}\)-ECBM also becomes the premise and foundation of the safety and economy of CO\({}_{2}\)-ECBM. The injectivity of CO\({}_{2}\) can be characterized by injection pressure, injection rate, cumulative injection volume and other parameters, which are mainly related to the permeability of the coal seam and its dynamic changes. Therefore, it is necessary to study the permeability evolution of the reservoir. With the injection of CO\({}_{2}\), the permeability of coal seams will decrease, which often affects the injectivity of CO\({}_{2}\)[46].  
The evolution of permeability in the CO\({}_{2}\)-ECBM process is a very complex phenomenon, which is determined by the stress effect and the adsorption swelling effect. On the one hand, effective stress increases and permeability decreases because of cleat compression [47]. On the other hand, the matrix expands, the seepage channel is compressed, and the permeability will decrease, along with CO2 adsorption, as CH\({}_{4}\) desorption occurs, matrix shrinkage, seepage channel opens, permeability will increase [46].  
During direct exploitation (Figure 12a), the reservoir permeability increases with time, and the closer to the production well is, the higher the permeability will be. This is because with the production, the pressure near the production well decreases, CH\({}_{4}\) desorbs, the matrix shrinks, then the permeability increases. In addition, the increase of effective stress leads to the decrease of permeability. However, the increase of permeability caused by matrix shrinkage deformation dominates. Therefore, the permeability increases compared with the initial permeability.  
In the case of CO\({}_{2}\) injection (Figure 12b), for the area near injection well, the decrease of effective stress will lead to the increase of permeability near the gas injection well, while the matrix expansion caused by competitive adsorption will lead to the decrease of permeability. At this time, the expansion deformation caused by the competitive adsorption of CO\({}_{2}\) and CH\({}_{4}\) dominates, and the permeability near the gas injection well decreases rapidly.  
For the area near the production well, when the production time is short, the injected CO\({}_{2}\) does not affect the production well. At this time, the stress effect reduces the permeability, and the matrix shrinkage effect caused by CH\({}_{4}\) desorption leads to the increase of permeability, but the matrix shrinkage effect caused by CH\({}_{4}\) desorption dominates. Therefore, the permeability of the production well is larger than the initial permeability.