## 4 Results  
### Effect of Injected CO\({}_{2}\) Pressure on CO\({}_{2}\)-Ecbm  
According to [25; 26], hydraulic-mechanical-thermal coupled model of CO\({}_{2}\)-ECBM can effectively reveal the influence of CO\({}_{2}\) storage on CH\({}_{4}\) production. Therefore, we investigate the distribution rule of CO\({}_{2}\) and CH\({}_{4}\) molar concentrations in CBM over a period of 30 years to study the effect of CO\({}_{2}\) injection pressure on CO\({}_{2}\)-ECBM at constant temperature and variable pressure. The injected CO\({}_{2}\) pressures are 4, 6, and 8 MPa, and the initial temperature of the coal seam is 273 K. Figure 3 shows the migration relationship of CH\({}_{4}\) and CO\({}_{2}\) molar concentration with time under injected CO\({}_{2}\) of variable pressure. Figure 2: Numerical model of CO\({}_{2}\) displacement of coalbed methane: (**a**) geological model of enhancing CBM recovery by injecting CO\({}_{2}\) with heat injection; (**b**) numerical simulation model for CO\({}_{2}\)-ECBM; and (**c**) initial porosity of CO\({}_{2}\)-ECBM. Figure 3: _Cont._  
Figure 3: Distribution of CH\({}_{4}\) molar concentration and CO\({}_{2}\) molar concentration under different injection CO\({}_{2}\) pressures: (**a**) distribution of CH\({}_{4}\) molar concentration at 4 MPa injection pressure; (**b**) distribution of CO\({}_{2}\) molar concentration at 4 MPa injection pressure; (**c**) distribution of CH\({}_{4}\) molar concentration at 6 MPa injection pressure; (**d**) distribution of CO\({}_{2}\) molar concentration at 6 MPa injection pressure; (**e**) distribution of CH\({}_{4}\) molar concentration at 8 MPa injection pressure; and (**f**) distribution of CO\({}_{2}\) molar concentration at 8 MPa injection pressure. Figure 3 shows the migration of CH\({}_{4}\) and CO\({}_{2}\) molar concentration with time under different injected CO\({}_{2}\) pressures. Figure 3a,c,e shows CH\({}_{4}\) molar concentration when the injection pressure is 4, 6, and 8 MPa, respectively. It can be seen that the CO\({}_{2}\) injection pressure significantly affects the displacement and migration rate of CH\({}_{4}\). Moreover, higher CO\({}_{2}\) injection pressures are associated with faster CH\({}_{4}\) migration rates and lower molar concentrations. Figure 3b-f shows the molar concentration of CO\({}_{2}\) when the injection pressure is 4, 6, and 8 MPa, respectively. Increasing the injection pressure and time leads to an increase in influence radius and molar CO\({}_{2}\) concentration in the coal seam. After 30 years of production, when the injection pressure is 4 and 6 MPa, the influence radius of CO\({}_{2}\) is 32 and 55 m, respectively. CO\({}_{2}\) reaches the producing well 17 years after production at an injection pressure of 8 MPa. The results are basically consistent with [25; 26]. Figure 4 shows the variation of CH\({}_{4}\) molar concentration per unit volume of the diagonal with time. The CH\({}_{4}\) molar concentration increases from the injection well to the displacement front and reaches the maximum value at the latter. The same results can be obtained from the displacement front to the production well because the displacement front is the area with the greatest gas pressure caused by migration. At a certain point along the diagonal of the model, longer displacement times are associated with low CH\({}_{4}\) molar concentrations, and higher injection pressures are associated with faster CH\({}_{4}\) migration and lower molar concentration. After the injected CO\({}_{2}\) pressure reaches 8 MPa for 30 years, the maximum molar concentration of CH\({}_{4}\) in the coal seam is \(1.42\times 10^{3}\) (mol/m\({}^{3}\)), and the production rate is 92%. Figure 5 shows the variation of CO\({}_{2}\) molar concentration per unit volume of the diagonal with time. Shorter distances from the injection well are associated with greater amounts of CO\({}_{2}\). There is no CO\({}_{2}\) from the displacement front to the production well.