Gas adsorption and desorption and displacement has a significant effect on coal deformation and permeability evolution during the primary recovery of coalbed methane (CBM) and enhanced coalbed methane recovery (ECBM). The objectives are to (1) quantify the coal deformation and permeability change caused by methane (CH4) displacement with carbon dioxide (CO2) and (2) model the transportation of CH4 and CO2 in deformed coalbed. In this study, the gas adsorption and desorption and displacement, coal deformation, and permeability evolution during CBM and ECBM recovery were described by an internally consistent adsorption-strain-permeability model, of which the simplified local density (SLD) adsorption theory, a theoretical strain model, and a matchstick-based permeability model were rigorous coupled. The coupled model was then verified with all of the CH4 and CO2 measured gas adsorption and desorption and coal strain data published in the past 60 years. Next, sensitivity analysis was further conducted on the coupled model to highlight and calibrate its performance. Finally, the coupled model was integrated into the Transport of Unsaturated Groundwater and Heat Simulator (TOUGH2) to simulate the ECBM process. The results show that the coupled model can simultaneously describe gas adsorption and desorption and displacement, coal deformation, and permeability evolution during ECBM recovery with only six parameters, including slit width, solid solid interaction potential energy parameter, surface areas of CH4 and CO2, adsorption expansion modulus, and initial porosity. The coupled model can predict both CH4 and CO2 adsorption and the induced coal deformation fairly accurately at a pressure up to 20 MPa, and the average relative errors are within 9.76% and 9.14%, respectively. The results also suggest that the adsorption capacity of CO2 is 2-5 times as large as that of CH4, and the volumetric strain induced by CO2 adsorption is 2-8 times as large as that caused by CH4 adsorption. While the stronger adsorption capacity of CO2 on coal offers an option for CO2-ECBM, matrix swelling due to CH4 displacement with CO2 may narrow down or even close the cleat, significantly reducing the permeability and thus impacting the injection efficiency. Last but not least, the original TOUGH2 simulator predicts similar results with several other CBM simulators. However, it is impossible that 90% of CH4 can be displaced within 90 days. Considering the coal deformation and permeability change due to CH4 displacement with CO2, the modified TOUGH2 simulator shows that only 24% of CH4 is displaced in the first 90 days, and it takes about 1800 days to displace 90% or more. Advances in the understanding of CH4 displacement by CO2 and their transportation mechanisms in coal seams suggests that the success of CO2-ECBM depends on the optimal management of matrix swelling.